http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2581971/Genetics. 2008 Nov; 180(3): 1725–1742.

doi:  10.1534/genetics.108.091942

PMCID: PMC2581971

Dominance, Overdominance and Epistasis Condition the Heterosis in Two Heterotic Rice HybridsLanzhi Li,* Kaiyang Lu,† Zhaoming Chen,* Tongmin Mu,† Zhongli Hu,*†,1 and Xinqi Li‡

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Abstract

HETEROSIS, a term to describe the superiority of heterozygous genotypes over their corresponding parental genotypes (S HULL   1908 ), has been under investigation for ∼100 years, but no consensus exists about the genetic basis underlying this very important phenomenon. Two contending hypotheses, the dominance hypothesis and the overdominance hypothesis, were proposed to explain this phenomenon about one century ago. The dominance hypothesis attributes heterosis to canceling of deleterious or inferior recessive alleles contributed by one parent, by beneficial or superior dominant alleles contributed by the other parent in the heterozygous genotypes at different loci (D AVENPORT   1908 ; B RUCE   1910 ; J ONES   1917 ). The overdominance hypothesis attributes heterosis to the superior fitness of heterozygous genotypes over homozygous genotypes at a single locus (E AST   1908 ; S HULL   1908 ).

Molecular markers and their linkage maps have greatly facilitated the identification of individual loci conditioning heterosis and the estimation of gene action of underlying loci. Quantitative trait locus (QTL) mapping studies aiming at understanding the genetic basis of heterosis have been conducted in rice and other crops (X IAO   et al . 1995 ; L I   et al . 1997 , 2001; Y U   et al . 1997 ;L UO   et al . 2001 ; H UA   et al . 2002 , 2003; S EMEL   et al . 2006 ; F RASCAROLI   et al . 2007 ;M ELCHINGER   et al . 2007a ,b). Evidence from such studies suggests that heterosis may be attributable to dominance (X IAO   et al . 1995 ; C OCKERHAM   and Z ENG   1996 ), overdominance (S TUBER   et al . 1992; L I   et al . 2001 ; L UO   et al . 2001 ), pseudo-overdominance due to tightly linked loci with beneficial or superior dominant alleles in repulsion phase (C ROW   2000 ;L IPPMAN   and Z AMIR   2007 ), or epistasis (S CHNELL   and C OCKERHAM   1992 ; L I   et al . 2001 ;L UO   et al . 2001 ).

Heterosis is the base of the great success in hybrid rice. Currently, hybrid rice accounts for ∼55% of the total planting acreage of paddy rice in China and the annual increased rice production resulting from planting hybrid rice amounts to ∼20 million metric tones, which can provide a main staple food for >70 million people (L U   et al . 2002 ). Hybrid rice varieties have a yield advantage of ∼10–20% over the best conventional inbred varieties using similar cultivation conditions (L U   e t al . 2002 ). Besides the large planting in China, hybrid rice varieties are also widely planted in >20 countries around the world.

Previous studies indicated the genetic basis of heterosis in rice is very complicated and various, depending on study materials and analysis approaches (X IAO   et al . 1995 ; Y U   et al . 1997 ; L I et al . 2001; H UA   et al . 2002 , 2003). The objective of this study was to identify the main-effect QTL and digenic epistatic loci underlying heterosis of nine important agronomic and economic traits of rice and estimate the gene action of each QTL and interaction using a triple-testcross cross (TTC) design to shed light on the understanding of the genetic basis of heterosis in two diverse and highly heterotic rice hybrids.

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MATERIALS AND METHODSPopulations:

Two highly heterotic rice hybrids, one intersubspecific between 9024 (indica) and LH422 (japonica) and one intrasubspecific between Zhenshan97 (indica) and Minghui63 (indica), were employed in this study. From the F1 of the intersubspecific hybrid (designated as IJ hybrid hereafter), 194 F7 lines were developed by single-seed descent. From the F1 of the intrasubspecific hybrid (designated as II hybrid hereafter), 222 F12 lines were developed through 11 consecutive selfing generations. Each of these F7 and F12 lines was derived from a different F2 plant. No positive or negative selection was performed during each of the selfing generations. A single plant from each of these 194 F7 lines and 222 F12 lines was chosen randomly and backcrossed to each of its two respective parents to produce backcross progeny and selfed to generate F8 or F13 lines.

Phenotypic variation:

For the IJ hybrid, two backcross populations having 194 lines each, 194 F8 recombinant inbred lines (RILs), along with the two parental lines and their F1, were arranged in a field in a randomized complete block design with two replications for phenotypic evaluation in the summer season of 1992 at the China National Hybrid Rice Research and Development Center, Changsha, Hunan, China. Twenty-seven plants (three rows × 9 plants per row) were planted at a density of 300,000 plants per hectare in each of 1170 plots. The middle 5 plants in the central row of each plot were used for phenotypic trait evaluation and data collection.

For the II hybrid, the two backcross populations with 222 lines each, the corresponding 222 F13 RILs, along with two parental lines and their F1, were laid out in a field in a randomized complete block design with two replications for phenotypic evaluation in the summer season of 2006 at the experimental farm of the Huazhong Agricultural University, Wuhan, Hubei, China. Twenty-one-day-old seedlings were transplanted into three-row plots with each plot consisting of a single row of a RIL and two rows of backcross (BC) hybrids. There were seven plants in each row, with 16.7 cm between plants within each row and 26.7 cm between rows. The middle five plants in each row were used for phenotypic trait evaluation and data collection.

Nine quantitative traits of agronomic and economic importance evaluated were heading date (HD) (in days), plant height (PH) (in centimeters), tillers per plant (TP), panicle length (PL) (in centimeters), filled grains per panicle (FGPP), percentage of seed set (SS), grain density (GD) (in grain numbers per centimeter of panicle length), 1000-grain weight (KGW) (in grams), and grain yield (YD) (in tons/hectare). Means over replications, for each trait, for the RIL and each of two backcross populations, were used for QTL and other analyses.

Analysis of field data and of heterosis:

For each hybrid, data of recombinant inbred (RI) and BC populations were analyzed separately. SAS PROC GLM (SAS I NSTITUTE   1996 ) was used to test the differences among RILs and the corresponding BC hybrids. Heterosis was evaluated in BC populations by midparental heterosis (Hmp). Hmp = F1 − (RIL + recurrent parent)/2. F1's are mean trait values of individual BC hybrids while RIL is the corresponding RIL parent for each of the BC hybrids, and recurrent parent is 9024 or LH422 in the IJ hybrid and Zhenshan 97 or Minghui 63 in the II hybrid. To distinguish one from another, the RIL is designated as RILij in the IJ hybrid and as RILii in the II hybrid.

Following K EARSEY   et al . (2003)  and F RASCAROLI   et al . (2007) , the crosses of the n RILs to the two recurrent parents are referred as “L1i” and “L2i” (i = 1 ∼ n), respectively. The two independent sets of data by summation (L1i + L2i) and by subtraction (L2i − L1i) of the two BC populations' values hereafter are referred to as the “SUM” data set and the “DIFF” data set, respectively. Variation within the SUM data set is due to additive effects and variation within the DIFF data set is due to dominance effects when combined over two BC populations.

In this study, for the IJ hybrid, L1i and L2i represent the n = 194 RILs to 9024 and LH422, respectively; while for the II hybrid, L1i and L2i represent the n = 222 RILs to Zhenshan97 and Minghui63, respectively. To distinguish one from another, the two data sets SUM and DIFF in the IJ hybrid are referred as SUMij and DIFFij and those in the II hybrid as SUMii and DIFFii.

NCIII and TTC analysis:

ANOVA was used to test for additive (L1i + L2i) and dominance (L2i − L1i) variation by following the standard North Carolina design III (NCIII) and for epistatic variation (L1i + L2i − P) by following the extended TTC design as described byK EARSEY   and J INKS   (1968) , with P indicated as the RI population in this study. Additive (VA) and dominance (VD) components of genetic variance were estimated and used to calculate the average degree of dominance [as √(2VD/VA)], which is a weighted mean of the level of dominance over all segregating loci (K EARSEY   and P OONI   1996 ).

Genetic linkage maps:

For the IJ hybrid, a subset of 141 polymorphic RFLP markers was selected from the rice high-density molecular map (C AUSSE   et al . 1994 ) to construct the linkage map of the RI population by X IAO   et al . (1995) . For the II hybrid, a linkage map was constructed by X ING   et al . (2002) , which consisted of 221 marker loci and covered a total of 1796 cM.

QTL mapping and detection of dominance degree of main-effect QTL and epistatic-effect QTL:QTL mapping:

QTL analysis was performed separately for the RI, the midparental heterosis (Hmp) of two backcross populations, and two independent data sets SUM and DIFF in the IJhybrid and the II hybrid. In the absence of epistasis, the analysis of RIL and SUM data sets identifies QTL with an additive effect (a), whereas the analysis of Hmp and DIFF data sets detects QTL with a dominance effect (d) (F RASCAROLI   et al . 2007 ).

Analysis of main-effect QTL (M-QTL) was conducted in each mapping population by composite-interval mapping, using WinQTLcart (Z ENG   1994 ). A LOD score of 2.0 was selected as the threshold for the presence of a main-effect QTL based on the total map distance and the average distance between markers. QTL detected in different populations or for different traits were considered as common if their estimated map position was within a 20-cM distance (G ROH   et al . 1998 ), which is a common approach in comparative mapping. Following F RASCAROLI   et al . (2007) , in the absence of epistasis, the expectation of genetic effects in RIL, SUM, Hmp, and DIFF data was a, a, d/2, and d.

Analysis of digenic interaction was conducted in each mapping population by the mixed linear approach and by the use of the computer software QTLMAPPER ver. 1.0 (W ANG   et al . 1999 ). The analysis was first conducted without considering epistasis to confirm the QTL detected with the method previously described and then with epistasis considered in the model. A threshold of LOD ≥ 3.0 (P < 0.001) was used for declaring the presence of a putative pair of epistatic QTL.

Genetic analysis methods for estimating QTL dominance degree:

North Carolina design III (NCIII) was put forward by C OMSTOCK   and R OBINSON   (1952) . In a NCIII design, male progeny from generation 2 (F2, which were treated as a base population) of two inbred strains are backcrossed to their grandmothers (marked as L1 and L2), and their progeny are arranged in a completely randomized block design (C OMSTOCK   and R OBINSON   1952 ). In 1968, an NCIII design was developed by Kearsey and Jinks. In their theory, the F3, F4, … , Fn, double haploid (DH), and RIL also can be treated as base populations. Following Kearsey, the base population was crossed to the two parents (P1 and P2) indicated as L1 and L2. With the data of L1 + L2 and L1 − L2, the genetic parameters of QTL such as additive effect, dominant effect, and the degree of dominance could be estimated.

On the basis of the correlation analysis of detected M-QTL and digenic interaction proposed by H U   et al . (1995 , 2002), regression and variance analysis of two data L1 + L2 and L1 − L2when the base population was the DH population could be deduced as follows (Tables 1 and and2 2 ).

TABLE 1

Genetic expectation of regression coefficients of L1+ L2 and L1 − L2 when the base population was the DH population

TABLE 2

Genetic expectation of variance components of L1 +L2 and L1 − L2 when the base population was the DH population

On the basis of the methodology proposed, we developed a software QTLIII (not published yet), which is suitable for analyzing the additive effect, dominant effect, and dominance degree of

QTL (including one-factor, two-factor, and three-factor ANOVA, see Tables 1 and and2). 2 ). In this study, it was used to estimate dominance degree of main-effect and epistatic-effect QTL.

The degree of dominance of a M-QTL was estimated as |d/a|. For this purpose, for all QTL declared as significant within any data set, dominant and additive effects were estimated in SUM and DIFF data sets by QTLIII with ANOVA analysis. These estimates were used to calculate |d/a| and classify the QTL as additive (A) (|d/a| < 0.2), partial dominance (PD) (0.2 ≤ |d/a| < 0.8), dominance (D) (0.8 ≤ |d/a| < 1.2), and overdominance (OD) (|d/a| ≥ 1.2) according to S TUBER   et al . (1987) .

Genetic expectations of the parameters estimated in the epistatic models differ on the basis of genetic composition of data sets analyzed. For the SUM data set, the estimated interaction is expected to be predominantly additive × additive (aa), whereas for the DIFF data set it is expected to be predominantly dominance × dominance (dd). In this study, |dd/aa|, defined as epistasis dominance degree (EDD), was estimated by the software QTLIII with ANOVA analysis. These estimates were used to calculate |dd/aa| to classify the epistatic QTL as A (|dd/aa| < 0.2), PD (0.2 ≤ |dd/aa| < 0.8), D (0.8 ≤ |dd/aa| < 1.2), and OD (|dd/aa| ≥ 1.2).

Relationship between genomewide or chromosomewide molecular marker heterozygosity and phenotypic trait performance and heterosis:

GGT (V AN   1999 ) was used to calculate genome ratios (percentage of total genome originated from one parental genome) for each line in the RI population, initially for the whole genome and then for each chromosome. Relationship between molecular marker heterozygosity and phenotypic performance was tested by regressing phenotypic performance on whole-genome heterozygosity in two backcross populations in both IJ and II hybrids. Meanwhile, to elucidate the relationship between observed heterosis and heterozygosity, (i) the Hmp and DIFF values were respectively regressed against heterozygosity across the whole genome using linear regression (when the DIFF data set was used as a dependent variable, genome heterozygosity of each backcross population was the independent variable), and (ii) the Hmp values were regressed against heterozygosity on individual chromosomes by multiple regression.

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RESULTSF1 heterosis:

In the IJ hybrid, LH422 showed significant higher mean trait values than 9024 (Table 3). All nine traits except heading date in F1 had a higher value than both parents. For midparental heterosis, yield showed the strongest significant heterosis (25.58%), followed by 1000-grain weight (15.82%), plant height (15.34%), panicle length (9.42%), tillers per plant (8.00%), seed set (4.06%), and heading date (1.74%). However, the F1 hybrid had a lower trait value for filled

grains per panicle and grain density than the parental lines, with negative heterosis of 2.08 and 10.17%, respectively.

TABLE 3

Mean values of nine important agronomic traits of P1, P2, F1, RIL, and their two backcross populations in two rice elite hybrids

In the II hybrid, the parent Minghui63 had a significantly higher phenotypic value than Zhenshan97 for all nine traits investigated (Table 3). The F1 hybrid had 91 days to heading, similar to Minghui63, which took more days to heading than Zhenshan97. The values of the other traits were significantly higher in F1 than in both parents. The midparental heterosis of the F1 plants was strongest for yield (83.09%), followed by filled grains per panicle (29.13%), plant height (21.94%), heading date (17.46%), seed set (16.68%), grain density (13.86%), panicle length (13.42%), tillers per plant (11.09%), and 1000-grain weight (8.21%).

Heterosis in RI and BC populations:

RIL and parental inbred mean values (Table 3) were not significantly different for any trait in both IJ and II hybrids.

Significant heterosis for yield was observed in II hybrid BC populations, but not in IJ hybrid BC populations. Most of the other traits did not show significant heterosis in BC populations of both IJ and II hybrids.

For the IJ hybrid, the mean values of the 9024BC and LH422BC populations were 80.96 and 81.21 for heading date, 107.28 and 110.83 for plant height, 10.38 and 9.55 for tillers per plant, 24.60 and 25.27 for panicle length, 83.20 and 98.28 for filled grains per panicle, 60.66 and 62.75 for seed set, 5.60 and 6.25 for grain density, 26.31 and 24.45 for 1000-grain weight, and 6.14 and 6.18 for yield. The heterosis was 24.45 (29.5%) and 3.12 (7.0%) for heading date, 6.45 (6.4%) and 5.10 (4.6%) for plant height, −0.30 (−2.8%) and 0.28 (3.0%) for tillers per plant, 1.65 (7.2%) and 1.36 (5.5%) for panicle length, −5.90 (−6.6%) and −1.56 (−1.8%) for filled grains per panicle, −7.39 (−10.9%) and 4.62 (6.9%) for seed set, 0.62 (12.5%) and 0.97 (20.8%) for grain density, 2.19 (9.1%) and 1.58 (5.9%) for 1000-grain weight, and −0.16 (−2.5%) and 0.14 (2.3%) for yield, in the 9024BC and LH422BC populations, respectively.

For the II hybrid, the mean values of the Zhenshan97BC and Minghui63BC populations were 75.44 and 85.44 for heading date, 113.11 and 113.50 for plant height, 11.99 and 12.00 for tillers per plant, 23.32 and 24.81 for panicle length, 121.81 and 126.15 for filled grains per panicle, 79.42 and 81.29 for seed set, 5.22 and 5.09 for grain density, 26.26 and 26.74 for 1000-grain weight, and 6.73 and 7.56 for yield. The heterosis values were −11.53 (−15.9%) and −1.53 (−1.8%) for heading date, 1.72 (1.7%) and 2.11 (1.9%) for plant height, 0.59 (1.1%) and 0.59 (0.9%) for tillers per plant, −0.75 (−3.5%) and 0.74 (3.1%) for panicle length, 4.7 (4.5%) and 9.04 (7.7%) for filled grains per panicle, 4.89 (10.7%) and 8.75 (13.6%) for seed set, 0.34 (7.1%) and 0.21 (4.3%) for grain density, −1.64 (−0.64%) and −0.16 (−0.6%) for 1000-grain weight, and 1.82 (36.9%) and 1.04 (15.9%) for yield in the Zhenshan97BC and Minghui63BC populations, respectively.

NCIII and TTC analysis:

TTC analysis allows us to test nonallelic interactions. Significant additive × additive ([aa]) epistasis was detected for all traits in both IJ and II hybrids (Table 4). The epistasis due to additive × dominance or dominance × dominance ([ad] and [dd]) was significant for all traits in the IJ hybrid and all the traits except tillers per plant in the II hybrid.

TABLE 4

NCIII and TTC analyses of the two rice hybrids

In this study, NCIII analysis led to the estimates of VA (additive variance) and VD (dominance variance), which were always highly significant (P < 0.005) in both hybrids, except for the VDof tillers per plant in the II hybrid, which was significant at P < 0.05 (Table 4).

M-QTL:

QTL detected in RIL, SUM, two Hmp, and DIFF data sets in IJ and II hybrids are shown in Tables 5 and and6, 6 , respectively. In total, 76 and 41 QTL were revealed in five data sets of IJ and II hybrids, respectively. Most of these QTL explained <10% of variation individually. Five QTL (6.76%) in the IJ hybrid and 4 (9.76%) in the II hybrid accounted for >20% of phenotypic variation individually.

TABLE 5

Main-effect QTL resolved in the IJ hybrid

TABLE 6

Main-effect QTL resolved in the II hybrid

HD:

In the IJ hybrid, 10 QTL were detected. Three showed an additive effect, 4 a partial-to-complete dominant effect, and 3 an overdominant effect. Six of the 9 QTL showing a dominant effect identified in Hmp and DIFFij were negative, with alleles from 9024 increasing the trait value. In the II hybrid, 8 QTL were found. Three exhibited an additive effect and 5 a partial-to-complete dominant effect. Four of the 5 QTL displaying a dominant effect revealed in Hmp and DIFFii were positive, with alleles from Minghui63 increasing the trait value.

PH:

In the IJ hybrid, 12 QTL were found. Six were classified as additive, 3 as partial-to-complete dominance, and 4 as overdominance. In the II hybrid, 4 QTL were detected. Three were found to be additive and 1 in Zhenshan97Hmp to be overdominant. No QTL was identified in SUMii.

TP:

In the IJ hybrid, four QTL were identified with two showing an additive effect, one an overdominant effect, and one a partial dominant effect. No QTL was found in the LH422Hmp and DIFFij data sets. In the II hybrid, five QTL were detected with two exhibiting an additive effect, one a dominant effect, and two an overdominant effect.

PL:

In the IJ hybrid, 11 QTL were found with 5 classified as an additive effect, 4 as an overdominant effect, and 2 as a partial-to-complete dominant effect. In the II hybrid, 2 QTL in RIL and 1 QTL in SUMii were detected, displaying an additive effect and with alleles from Minghui63 increasing the trait value.

FGPP:

In the IJ hybrid, six QTL were found with three behaving like an additive effect, two like a partial-dominant effect, and one like an overdominant effect. In the II hybrid, two QTL were detected with one appearing to be an overdominant effect and one a partial-dominant effect. No QTL was revealed in Hmp and DIFFii.

SS:

In the IJ hybrid, 10 QTL were found with 4 displaying an additive effect, 4 a partial-dominant effect, and 2 an overdominant effect. In the II hybrid, only 1 QTL was detected in DIFFii data, showing overdominant effect, and the alleles from Zhenshan97 increased the trait value.

GD:

In the IJ hybrid, seven QTL were identified with two exhibiting an additive effect, two a partial-to-complete dominant effect, and three an overdominant effect. No QTL was detected in 9024Hmp. In the II hybrid, four QTL were revealed with two showing an additive effect, one a partial-dominant effect, and one an overdominant effect. No QTL was found in Minghui63Hmp and DIFFii data sets.

KGW:

In the IJ hybrid, 10 QTL were revealed with 5 displaying an additive effect, 3 a partial-dominant effect, and 2 an overdominant effect. No QTL was found in 9024Hmp. In the IIhybrid, 8 QTL were detected with 2 showing an additive effect, 3 a partial-to-complete dominant effect, and 3 an overdominant effect.

YD:

In the IJ hybrid, six QTL were identified with two exhibiting an additive effect, three a dominant effect, and one an overdominant effect. No QTL was found in SUMij and LH422Hmp. In the II hybrid, six QTL were detected with one showing an additive effect and five an overdominant effect. No QTL was found in Zhenshan97Hmp and SUMii data sets.

Digenic interaction:

Table 7 shows the digenic interactions detected in DIFFij data in the IJhybrid. A total of 46 digenic interactions were found in DIFFij data. No significant interaction was found for yield.

The variation explained by individual interaction ranges from 2.0 to 10.1%. The proportion of total variation explained by all digenic interaction was ∼30% in most traits. The highest value of total variation was observed for panicle length in the DIFFij data set (45.1%), which mainly reflected the dominance × dominance digenic interactions.

TABLE 7

Digenic interactions in the DIFFij data set in the IJhybrid

Table 8 shows the digenic interaction identified in DIFFii data in the II hybrid. In total, 81 digenic interactions were revealed. Each interaction generally showed modest R2 < 10% for all significant interactions except one interaction with 18.1%. However, in the IJ hybrid, the total variation explained by all digenic interactions was >40% for most of the traits. The highest value of total R2 was observed for SS in the DIFFii data set (52.7%).

TABLE 8

Digenic interactions in the DIFFii data set in the IIhybrid

Table 9 summarizes the digenic interaction detected in RIL, SUM, Hmp, and DIFF data sets of IJ and II hybrids. Most of the detected interactions involved QTL without a significant main effect and each interaction showed a modest R2 < 10% for all traits. However, it should be noted that an interaction occurred between two significant M-QTL in Minghui63Hmp for 1000-grain weight, which explained 43.4% of phenotypic variation (data not shown here).

TABLE 9

Summaries of digenic interaction in five data sets of the two hybrids

In the IJ hybrid, the number of digenic interactions detected for each trait varies from none to 10 in the RILij population with an average of 3.22, and the variance explained (R2) by each pair was up to 39.1% with an average of 16.4%. The number of digenic interactions detected in the SUMij data set varies from two to 7 with an average 3.44, and the R2 of each pair varies from 10.9 to 44.7% with an average of 21.8%. For digenic interaction of dominance × dominance, on average, 1.11, 1.11, and 2.00 QTL pairs with an additive effect were detected in 9024Hmp, LH422Hmp, and DIFFij and had a contribution rate of 6.0, 6.4, and 12.2%, respectively; 2.11, 2.44, and 2.22 QTL pairs with partial-to-complete dominance were detected in 9024Hmp, LH422Hmp, and DIFFij and had a contribution rate of 14.7, 15.2, and 13.3%, respectively; and 1.67, 1.33, and 0.89 QTL pairs with overdominance were detected in 9024Hmp, LH422Hmp, and DIFFij and had a contribution rate of 10.6, 8.4, and 4.5%, respectively.

For the II hybrid, the number of digenic interactions identified for each trait varies from none to 12 in the RILii population with an average of 8.11 and had a contribution rate (R2) up to 87.0%, with an average of 47.9%. The number of digenic interactions detected in the SUMii data set varies from none to 14 with an average of 7.44, and each pair had an R2 up to 59.4% with an average of 40.4%. For digenic interaction of dominance × dominance, on average, 1.44, 0.11, and 1.22 QTL pairs with additive effect were detected in Zhenshan97Hmp, Minghui63Hmp, and DIFFii and had a contribution rate of 7.0, 0.7, and 7.4%, respectively; 5.44, 1.56, and 2.44 QTL pairs with partial-to-complete dominance were detected in Zhensha97Hmp, Minghui63Hmp, and DIFFii and had a contribution rate of 27.7, 13.8, and 11.8%, respectively; and 2.44, 0.89, and 5.33 QTL pairs with overdominance were detected in Zhenshan97Hmp, Minghui63Hmp, and DIFFii and had a contribution rate of 12.2, 5.3, and 25.3%, respectively.

Relationship between trait performance and genomewide or chromosomewide marker heterozygosity:

The correlation coefficients (Table 10) between level of genomewide heterozygosity and performance per se of the two backcross populations were not significant for most of the traits in both IJ and II hybrids (except plant height in 9024BC and 1000-grain weight in Minghui63BC). The analysis of the relationship between level of heterozygosity and level of heterosis (as evaluated in Hmp and DIFF) showed that correlation coefficients, for several traits, were slightly higher than those previously shown, but still not significant for most traits. The significant correlation coefficients were found for plant height, heading date, and 1000-grain weight in the IJ hybrid and for tillers per plant in the II hybrid.

TABLE 10

Correlation coefficients between genomewide molecular marker heterozygosity and phenotypic values

In this study, the Hmp value was regressed against heterozygosity on individual chromosomes using multiple linear regression (Table 11). The hybrid performance was also poorly associated with marker heterozygosity in most chromosomes. There were 8, 6, 8, and 5 significant regressions between trait value and marker heterozygosity in individual chromosomes resolved in 9024Hmp, LH422Hmp, Zhenshan97Hmp, and Minghui63Hmp, respectively. Nineteen of these 27 (70.3%) significant regressions were associated with one or two M-QTL and/or digenic interaction. In the IJ hybrid, the F-test value was significant for panicle length and grain density in 9024Hmp and for plant height and heading date in LH422Hmp. While in the IIhybrid, the F-test value was significant for plant height in Zhenshan97Hmp and for yield in Minghui63Hmp. The coefficients (r2) for most traits were <0.10 in both IJ and II hybrids.

TABLE 11

Significant regression coefficients of midparent values of backcross populations on individual chromosome marker heterozygosity for the indicated traits

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DISCUSSIONChoice of the experimental design and statistical methods:

NCIII and TTC designs are most suitable for studies of heterosis in the presence of epistasis because they

provide estimates of augmented dominance effects (K USTERER   et al . 2007a ,b). Meanwhile, compared

with the F2 or the F3 population, RILs as parents for producing testcross progenies offer few advantages.

First, the effects of linkage are reduced because linkage disequilibrium between tightly linked loci is

almost half of that in the F2 population. Second, use of homozygous parents (RIL) maximizes the genetic

variance among testcross progenies and leads to an increased power in F-tests and reduced standard errors

of variance component and dominance effect estimates since RILs are homozygous at almost all of the

genetic loci while F2 plants have 50% heterozygous loci. Third, RILs are immoral and testcross progeny

can be repeatedly generated and tested as needed.

Up to now, several studies have been conducted to try to understand the genetic basis of heterosis in rice

(X IAO   et al . 1995 ; L I   et al . 2001 ; L UO   et al . 2001 ; H UA   et al . 2002 , 2003). However, the causes

underlying this important phenomenon have remained unclear and none of these studies quantified the

gene action of QTL. In this study, with two derived data sets (SUM and DIFF) and the software

developed by us, we resolved the dominance degree for all of the M-QTL and digenic interactions. The

statistical method employed in this study is much more precise and informative to understand the causes

of heterosis in rice since it classifies underlying QTL into A, PD, D, and OD on the basis of degree of

dominance.

It should be noted that the A, PD, D, and OD referred to in this study are different from the additive

effect, dominant effect, and overdominant effect in a traditional dominant–additive model. In fact, as well

as in hybrid F1, since each locus is in heterozygosis, only gene action of dominance, dominance ×

dominance, dominance × dominance × dominance, etc., existed in Hmp and DIFF. Therefore, in this

study, A, PD, D, and OD were treated only as a scale for quantifying the degree of dominance (d) or

dominance × dominance (dd) effect.

Heterosis for the traits studied:

In the two hybrids investigated here, grain yield showed the strongest heterosis among the nine traits

studied (25.58% in the IJ hybrid and 83.09% in the IIhybrid), consistent with the findings of previous

studies conducted on rice (L I   et al . 2001 ; L UO et al . 2001 ) as well as other cereal crops (T OLLENAAR   et al .

2004; H OECKER   et al . 2006 ). Heterosis for the other traits was <20% in the IJ hybrid and <30% in

the II hybrid. Negative heterosis for filled grains per panicle and grain density was observed in

the IJ hybrid. These results confirm that heterosis of yield components was much less than grain yield

itself (L I   et al . 2001 ).

For the IJ hybrid, the Hmp of some backcross lines was stronger than that of F1, while some other

backcross lines expressed an Hmp in the opposite direction. This result is in harmony with the study

conducted by M EI   et al . (2005)  in which an indica/japonica hybrid was also used. It can be concluded

that heterosis was generally related to the average level of heterozygosity in a hybrid population but

poorly correlated with heterozygosity at the individual level (Z HANG   et al . 1995 ; Y U   et al . 1997 ). This

conclusion also can be confirmed by the fact that the correlation between marker heterozygosity and trait

expression is negligible.

For the II hybrid, the heterosis in BC populations was much lower than that in F1. This may be due to the

fact that the two intraspecific parents are more genetically similar than the two interspecific parents

of IJ hybrids. The reduction in the proportion of heterozygous loci in the BCF1 population probably

caused the reduced average level of heterosis in the BCF1compared to the hybrid between two parents.

NCIII and TTC analysis:

For the traits showing highly significant epistasis, VA and VD estimates are to some extent biased

(K EARSEY   and P OONI   1996 ) and so are the average degree of dominance estimates. In the IJ hybrid,

highly significant [aa], [ad], and [dd] epistasis was observed for all the traits studied. In the II hybrid, the

average degree of dominance for most traits was <1.00, except for plant height (1.18) and grain yield

(1.20), suggesting an important contribution of overdominance to the heterosis of these two traits. For

epistasis conducted by TTC analysis, [aa] was highly significant (P ≤ 0.005) for all traits, and [ad] and

[dd] for most of traits, except for yield and grain density (significant at P ≤ 0.01), panicle length

(significant atP ≤ 0.05), and tillers per plant (not significant). Therefore, epistasis appeared to be of more

importance than intralocus interaction in affecting heterosis in these two elite hybrids. A similar

conclusion was drawn in Arabidopsis by K USTERER   et al . (2007a)  in which a TTC family derived from

the Arabidopsis C24 × Col-0 was analyzed, and it was found that epistasis across environments was more

important for most traits. However, in the TTC design with recombinant inbred lines of the maize B73 ×

H99 (F RASCAROLI   et al . 2007 ), the epistasis was found not significant for most traits.

Genetic basis of heterosis in two highly heterotic hybrids of rice:

Our analyses allowed the identification of several QTL for each of the traits investigated. Most individual

QTL explained modest variation (<10%), and only four QTL in the IJ hybrid and five QTL in

the II hybrid contributed >20% variation individually (Tables 5 and and6), 6 ), confirming that the

heterosis is a polygenic phenomenon (H ALLAUER   and M IRANDA   1981 ; K USTERER   et al . 2007a ).

The proportion of QTL with an additive or a dominant effect is different between the two hybrids. Among

the 74 main-effect QTL detected in the IJ hybrid, 24 (32%) showed a gene action of partial-to-complete

dominance, 20 (26%) showed overdominance, and 32 (42%) showed an additive effect; while among the

41 main-effect QTL identified in the II hybrid, 12 (29%) exhibited partial-to-complete dominance, 16

(39%) showed overdominance, and 13 (32%) showed an additive effect. These results indicate that

dominance and overdominance played an important role in conditioning the heterosis in these two

hybrids. Also, the results from the dominance degree (|d/a|) of main-effect QTL estimated by QTLIII with

regression analysis and by WinQTLcart (Z ENG   1994 ) show that, although the dominance degrees were

not exactly consistent with each other by the three approaches (ANOVA, regression analysis,

WinQTLcart), the proportions of QTL detected with dominance and with overdominance were >25%

each.

The importance of dominance and overdominance conditioning the heterosis of these two hybrids seems

different. In the IJ hybrid, the proportion of QTL showing a gene action of overdominance is less than

that with partial-to-complete dominance. This result was also found in the study conducted by X IAO   et al .

(1995) using the same materials, but a different analysis method. However, in the II hybrid, the

proportion of QTL exhibiting a gene action of overdominance is more than the proportion of those having

a gene action of partial-to-complete dominance. This result is in harmony with other studies, especially

the work conducted on the F2:3 families derived from the cross between Zhenshan97 and Minghui63

byY U   et al . (1997) . However, although a relatively higher portion of QTL demonstrated overdominance

in the II hybrid, QTL exhibiting high levels of overdominant effects are not necessarily indicative of true

overdominance, but rather can be the result of dominant alleles linked in repulsion (pseudo-

overdominance).

Compared to M-QTL detected in these two hybrids, only two QTL for heading date were found in a

similar genomic region bordered by the same molecular markers. This may be due to the fact that very

few markers were common across these two linkage maps. On chromosome 1, one QTL was detected

between RG811 and RG173 in the IJ hybrid, showing an additive effect. One QTL between RM243 and

RG173 was detected in the II hybrid, displaying a partial-dominant effect. On chromosome 8, one QTL

between RG333 and RZ562 in the IJ hybrid and one between C1121 and RG333 in the II hybrid

exhibited an additive effect, thus suggesting that, even in the same or a similar genomic region bordered

by the same molecular markers in different hybrids, the gene action of QTL could be different due to

interaction of different alleles at the QTL. It should be noted that, for the two hybrids that were planted in

different environments, the type of gene action may be influenced by environmental effect.

Various levels of negative dominance were observed at some QTL for each trait, indicating that

heterozygosity was not necessarily always favorable for the expression of the trait even in highly heterotic

hybrids. For both hybrids studied here, dominant effects of the detected QTL were always bidirectional,

resulting in the cancellation of positive and negative dominant effects contributed by different QTL

controlling the trait, which explains the poor relationship observed between marker heterozygosity and

trait expression. A good consistency was also found in other studies of rice (Y U   et al . 1997 ; M EI   et al .

2005), but in contrast with the study (F RASCAROLI   et al . 2007 ) in maize.

There were a large number of digenic interactions found to have effects on the traits of the two hybrids

studied here. Two pronounced features were notably found for the epistasis in this study. First, although

individual interaction had a modest R2 (phenotypic variation), <10% in most cases (data not shown) for

each trait of the two hybrids, the total variation explained by all the significant digenic interactions for the

trait was much greater than that by all the M-QTL affecting the same trait for most traits.

Similar to a large number of empirical studies in other selfing and outcrossing plant species

(A LLARD   1988 ; L I   et al . 2001 ; M EI   et al . 2005 ), most epistasis occurred between complementary loci

with no detectable main effects. In many fewer cases, epistasis occurred between a M-QTL and a

complementary locus and in only seven cases in the IJ hybrid and two in the II hybrid between M-QTL.

By using the same population of IJ hybrids reported here, X IAO   et al . (1995)  was unable to detect

epistasis due to the unavailability of appropriate mapping methodology (L I   et al . 2001 ).

It should be noted that the two digenic interactions in the II hybrid occurred between M-QTL accounting

for a large variation for 1000-grain weight detected in Minghui63Hmp and for panicle length detected in

Zhenshan97BC, explaining 43.4 and 23.8% of the variation, respectively (data not shown). When a M-

QTL is involved in the epistatic interaction, the effect of the single-locus QTL is mostly dependent on the

genotypes of the other locus and can sometimes be negated by the genotypes of a second locus. Thus an

attempt to utilize the QTL in the breeding programs needs to consider such epistatic effects, especially the

interaction occurring between two significant M-QTL and having a high phenotypic variation.

Another feature of digenic interaction in this study is that both partial-to-complete dominance and

overdominance played an important role in conditioning heterosis. Shown in Table 9 is the relative

importance of additive and nonadditive gene action of digenic interaction summarized by comparing the

genetic effects detected in the SUM and DIFF data sets by QTL with ANOVA analysis.

For the additive × additive digenic interactions, there were an average of 3.22 and 3.44 pairs detected in

the RILij and SUMij data sets for each trait in the IJ hybrid, contributing 16.4 and 21.8% phenotypic

variation, respectively; while in the II hybrid, an average of 8.11 and 7.44 pairs were detected in the RILii

and SUMii data sets for each trait, explaining 47.9 and 40.4% of the phenotypic variation, respectively.

There were a total of 135 and 188 dominance × dominance digenic interactions detected in Hmp and

DIFF in the IJ and II hybrids, respectively. The proportion of digenic interactions displaying partial-to-

complete dominance was a little more than that showing overdominance in both hybrids. There were 62

(45.2%) and 85 (45.2%) digenic interactions that behaved like partial-to-complete dominance, 36 (26.7%)

and 78 (41.5%) digenic interactions that exhibited overdominance, and 37 (28.1%) and 25 (13.3%)

digenic interactions that displayed an additive effect, in IJ and II hybrids, respectively.

The poor relationship between total genomewide molecular marker heterozygosity and phenotypic trait

performance was observed for almost all the traits in this study (Table 10). This result is different from

the study of maize performed by F RASCAROLI   et al . (2007)  in which they found that there was a high

relationship between marker heterozygosity level and performance per se and heterosis (as evaluated in

Hmp and DIFF) for most traits. To further investigate the relationship between observed heterosis and

heterozygosity, Hmp value was regressed against heterozygosity on individual chromosomes, using

multiple linear regression. As shown in Table 11, the hybrid performance was also poorly associated with

marker heterozygosity in most chromosomes, although it was relatively more significant than that with

whole-genome heterozygosity. Nineteen of the 27 (70.4%) significant regressions by individual

chromosomes were associated with one or two M-QTL and/or digenic interaction, indicating that marker

heterozygosity in individual chromosomes in QTL regions was important for phenotypic variation. This

finding is consistent with S YED   and C HEN 's (2005) result of the relationship between heterozygosity and

heterosis in Arabidopsis. Therefore, the hybrid vigor is poorly related to heterozygosity of the whole

genome and on individual chromosomes in rice, which further confirms that the genetic basis or

mechanism of heterosis of rice is different from that of maize.

Our results indicate that heterosis in rice is very complex, reflected by the large number of loci involved,

their wide genomic distribution, and complex epistatic relationships, and that the nonallelic interactions

(epistasis) play a relatively more important role than allelic interactions (M-QTL) in conditioning the

heterosis of these two highly heterotic hybrids, implicating that marker-assisted selection in heterosis

breeding to significantly enhance the heterosis of desirable traits may be very challenging.

So far almost all of the documented studies on revealing the genetic basis of heterosis are limited to

classical quantitative genetics and QTL mapping using molecular markers. The advancements in

functional genomics have created a novel avenue to study the genetic basis of heterosis at the gene-

expression level. DNA microarrays can quantify expression of tens of thousands of genes on a single

DNA chip (S CHENA   et al . 1998 ). The timing, level, and relationship of the transcription of two different

alleles of the same gene in the hybrids can be compared with that of their corresponding parental lines by

using microarrays (S TUPAR   and S PRINGER   2006 ; S WANSON -W AGNER   et al . 2006 ). Functional genomics

approaches to elucidating the genetic basis of heterosis would turn the study of this very important and

still controversial issue into a new chapter in its history. Evidence from functional expression studies of

genes underlying heterosis would elevate our understanding of the genetic basis of heterosis to a new

level.

Go to:

Acknowledgments

We gratefully acknowledge the expert technical assistance of Qifa Zhang on trial design and analysis and

the skillful assistance of Yingguo Zhu in field trials. We thank Jinhua Xiao and Yunchun Song for

valuable suggestions for improving the manuscript. This work was financially supported by the 973

Program (no. 2006CB101707), the 863 Program (no. 2003AA207160), the National Natural Science

Foundation of China (no. 30270760), and the Key Grant Project of the Chinese Ministry of Education

(no. 307018).

Go to:

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Heterotic string theoryFrom Wikipedia, the free encyclopedia

This article is about string theory. For heterosis in biology, see Heterosis.

String theory

Fundamental objects

String

Brane

D-brane

Perturbative theory

Bosonic

Superstring

Type I

Type II (IIA / IIB)

Heterotic (SO(32) · E8×E8)

Non-perturbative results

S-duality

T-duality

M-theory

AdS/CFT correspondence

Phenomenology

Phenomenology

Cosmology

Landscape

Mathematics

Mirror symmetry

Monstrous moonshine

Related concepts

Conformal field theory

Holographic principle

Kaluza–Klein theory

o Quantum gravity

o Supergravity

Supersymmetry

Theory of everything

Twistor string theory

Theorists

Arkani-Hamed

Banks

Dijkgraaf

Duff

Fischler

Gates

Gliozzi

Green

Greene

Gross

Gubser

Harvey

Hořava

Kaku

Klebanov

Kontsevich

Maldacena

Mandelstam

Martinec

Minwalla

Moore

Motl

Nekrasov

Neveu

Olive

Polchinski

Polyakov

Randall

Ramond

Rohm

Scherk

Schwarz

Seiberg

Sen

Shenker

S ơ n

Strominger

Sundrum

Susskind

't Hooft

Townsend

Vafa

Veneziano

E. Verlinde

H. Verlinde

Witten

Yau

Zaslow

History

Glossary

V

T

E

In string theory, a heterotic string is a closed string (or loop) which is a hybrid ('heterotic') of a superstring and a bosonic string. There are two kinds of heterotic string, the heterotic SO(32) and the heterotic E8 × E8, abbreviated toHO and HE. Heterotic string theory was first developed in 1985 by David Gross, Jeffrey Harvey, Emil Martinec, and Ryan Rohm (the so-called "Princeton String Quartet"[1]), in one of the key papers that fueled the first superstring revolution.

In string theory, the left-moving and the right-moving excitations are completely decoupled,[2] and it is possible to construct a string theory whose left-moving (counter-clockwise) excitations are treated as a bosonic string propagating inD = 26 dimensions, while the right-moving (clock-wise) excitations are treated as a superstring in D = 10 dimensions.

The mismatched 16 dimensions must be compactified on an even, self-dual lattice (a discrete subgroup of a linear space). There are two possible even self-dual lattices in 16 dimensions, and it leads to two types of the heterotic string. They differ by the gauge group in 10 dimensions. One gauge group isSO(32) (the HO string) while the other is E8  ×   E 8 (the HE string).[3]

These two gauge groups also turned out to be the only two anomaly-free gauge groups that can be coupled to the N = 1 supergravity in 10 dimensions other than U(1)496 and E8 × U(1)248, which is suspected to lie in theswampland.

Every heterotic string must be a closed string, not an open string; it is not possible to define any boundary conditions that would relate the left-moving and the right-moving excitations because they have a different character.

A heterotic string is embedded in the membrane that creates harmonics on the string which translate into mass and energy through mechanisms discussed above.[clarification needed]

String duality[edit]

String duality is a class of symmetries in physics that link different string theories. In the 1990s, it was realized that the strong coupling limit of the HO theory is type I string theory — a theory that also contains open strings; this relation is called S-duality. The HO and HE theories are also related by T-duality.

Because the various superstring theories were shown to be related by dualities, it was proposed that that each type of string was a different aspect of a single underlying theory called M-theory.

References[edit]

1. ̂  Dennis Overbye, "String theory, at 20, explains it all (or not)". NY Times, 2004-12-072. ̂  String Theory and M-Theory by Becker, Becker and Schwarz (2006), p. 2533. ̂  Joseph Polchinski (1998). String Theory: Volume 2, p. 45.

HeterosisFrom Wikipedia, the free encyclopedia

Not to be confused with Heterozygosity, or with Heterotic string theory.

See also: Heterozygote advantage

"Heterotic" redirects here. For the musical group Heterotic, see Mike Paradinas.

A mixed-breed dog

Heterosis, hybrid vigor, or outbreeding enhancement, is the improved or increased function of any biological quality in a hybrid offspring. The adjective derived from heterosis is heterotic.

An offspring exhibits heterosis if its traits are enhanced as a result of mixing the genetic contributions of its parents. These effects can be due to Mendelian or non-Mendelian inheritance.

Contents

  [hide] 

1   Definitions 2   Dominance versus overdominance 3   Genetic basis 4   Historical retrospective 5   Notes 6   Controversy 7   Genetic and epigenetic bases of heterosis

o 7.1   MHC in animals

8   In plants o 8.1   Corn (maize)

o 8.2   Rice ( Oryza sativa )

9   Hybrid livestock o 9.1   Poultry

10   Heterosis in dogs 11   Humans 12   See also 13   References 14   Further reading

Definitions[edit]

In proposing the term heterosis to replace the older term heterozygosis, G.H. Shull aimed to avoid limiting the term to the effects that can be explained by heterozygosity in Mendelian inheritance. [1]

The physiological vigor of an organism as manifested in its rapidity of growth, its height and general robustness, is positively correlated with the degree of dissimilarity in the gametes by whose union the organism was formed … The more numerous the differences between the uniting gametes — at least within certain limits — the greater on the whole is the amount of stimulation … These differences need not be Mendelian in their inheritance … To avoid the implication that all the genotypic differences which stimulate cell-division, growth and other physiological activities of an organism are Mendelian in their inheritance and also to gain brevity of expression I suggest … that the word 'heterosis' be adopted.

Heterosis is often discussed as the opposite of inbreeding depression although differences in these two concepts can be seen in evolutionary considerations such as the role of genetic variation or the effects of genetic drift in small populations on these concepts. Inbreeding depression occurs when related parents have children with traits that negatively influence theirfitness largely due to homozygosity. In such instances, outcrossing should result in heterosis.

Not all outcrosses result in heterosis. For example, when a hybrid inherits traits from its parents that are not fully compatible, fitness can be reduced. This is a form of outbreeding depression.

Dominance versus overdominance[edit]

Dominance versus overdominance is a scientific controversy in the field of genetics that has persisted for more than a century.[2] These two alternative hypotheses were first stated in 1908.

Genetic basis[edit]

When a population is small or inbred, it tends to lose genetic diversity. Inbreeding depression is the loss of fitness due to loss of genetic diversity. Inbred strains tend to be homozygous for recessive alleles that are mildly harmful (or produce a trait that is undesirable from the standpoint of the breeder). Heterosis or hybrid vigor, on the other hand, is the tendency of outbred strains to exceed both inbred parents in fitness.

Selective breeding of plants and animals, including hybridization, began long before there was an understanding of underlying scientific principles. In the early 20th century, after Mendel's laws came to be understood and accepted, geneticists undertook to explain the superior vigor of many plant hybrids. Two competing hypotheses, which are not mutually exclusive, were developed:[3]

Genetic basis of heterosis. Dominance hypothesis. Scenario A. Fewer genes are under-expressed in the homozygous

individual. Gene expression in the offspring is equal to the expression of the fittest parent. Overdominance

hypothesis.Scenario B. Over-expression of certain genes in the heterozygous offspring. (The size of the circle depicts the

expression level of gene A)

Dominance hypothesis. The dominance hypothesis attributes the superiority of hybrids to the suppression of undesirable recessive alleles from one parent by dominant alleles from the other. It attributes the poor performance of inbred strains to loss of genetic diversity, with the strains becoming purely homozygous at many loci. The dominance hypothesis was first expressed in 1908 by the geneticist Charles Davenport.[4]

Overdominance hypothesis. Certain combinations of alleles that can be obtained by crossing two inbred strains are advantageous in the heterozygote. The overdominance hypothesis attributes the heterozygote advantage to the survival of many alleles that are recessive and harmful in homozygotes. It attributes the poor performance of inbred strains to a high percentage of these harmful recessives. The overdominance hypothesis was developed independently by Edward M. East (1908)[5] and George Shull(1908).[6]

Dominance and overdominance have different consequences for thegene expression profile of the individuals. If over-dominance is the main cause for the fitness advantages of heterosis, then there should be an over-expression of certain genes in the heterozygous offspring compared to the homozygous parents. On the other hand, if dominance is the cause, fewer genes should be under-expressed in the heterozygous offspring compared to the parents. Furthermore, for any given gene, the expression should be comparable to the one observed in the fitter of the two parents.

Historical retrospective[edit]

Population geneticist James Crow, who in his younger days believed that overdominance was a major contributor to hybrid vigor undertook a retrospective review of the developing science.[7] According to Crow, the demonstration of several cases of heterozygote advantage in Drosophila and other organisms first caused great enthusiasm for the overdominance theory among scientists studying plant hybridization. But overdominance implies that yields on an inbred strain should decrease as inbred strains are selected for the performance of their hybrid crosses, as the proportion of harmful recessives in the inbred population rises. Over the years, experimentation in plant genetics has proven that the reverse occurs, that yields increase in both the inbred strains and the hybrids, suggesting that dominance alone may be adequate to explain the superior yield of hybrids. Only a few conclusive cases of overdominance have been reported in all of genetics. Since the 1980s, as experimental evidence has mounted, the dominance theory has made a comeback.

Crow writes, "The current view ... is that the dominance hypothesis is the major explanation of inbreeding decline and the high yield of hybrids. There is little statistical evidence for contributions from overdominance and epistasis. But whether the best hybrids are getting an extra boost from overdominance or favorable epistatic contributions remains an open question."[7]

Notes[edit]

1. Jump up ̂  George Harrison Shull (1948). "What Is "Heterosis"?". Genetics 33 (5): 439–446. PMC 1209417. PMID 17247290.

2. Jump up ̂  Birchler, J.A.; Auger, D.L.; Riddle, N.C. (2003). In search of the molecular basis of heterosis. The Plant Cell. 15: 2236–2239.

3. Jump up ̂  Crow, James F. (1948). "Alternative Hypotheses of Hybrid Vigor". Genetics 33 (5): 477–487.4. Jump up ̂  Davenport CB (1908). "Degeneration, albinism and inbreeding". Science 28 (718):

455. doi:10.1126/science.28.718.454-b.PMID 17771943.5. Jump up ̂  East EM (1908). "Inbreeding in corn". Reports of the Connecticut Agricultural Experiments

Station for 1907: 419–428.6. Jump up ̂  Shull GH (1908). "The composition of a field of maize". Reports of the American Breeders

Association: 296–301.7. ^ Jump up to: a  b Crow, James F. (1998). "90 Years Ago: The Beginning of Hybrid Maize". Genetics 148 (3):

923–928. PMC 1460037.PMID 9539413.

Controversy[edit]

The term heterosis often causes confusion and even controversy, particularly in selective breeding of domestic animals, because it is sometimes (incorrectly) claimed that all crossbred plants and animals are "genetically superior" to their parents, due to heterosis[citation needed]. However, there are two problems with this claim:

First, according to an article published in the journal Genome Biology, "genetic superiority" is an ill-defined term and not generally accepted terminology within the scientific field of genetics. [1] A related term fitness is well defined, but it can rarely be directly measured. Instead, scientists use objective, measurable quantities, such as the number of seeds a plant produces, the germination rate of a seed, or the percentage of organisms that survive to reproductive age.[2] From this perspective, crossbred plants and animals exhibiting heterosis may have "superior" traits, but this does not necessarily equate to any evidence of outright "genetic superiority". Use of the term "superiority" is commonplace for example in crop breeding, where it is well understood to mean a better-yielding, more robust plant for agriculture. Such a plant may yield better on a farm, but would likely struggle to survive in the wild, making this use open to misinterpretation. In human genetics any question of "genetic superiority" is even more

problematic due to the historical and political implications of any such claim. Some may even go as far as to describe it as a questionable value judgement in the realm of politics, not science. [1]

Second, not all hybrids exhibit heterosis (see outbreeding depression).

An example of the ambiguous value judgements imposed on hybrids and hybrid vigor is the mule. While mules are almost always infertile, they are valued for a combination of hardiness and temperament that is different from either of their horse or donkey parents. While these qualities may make them "superior" for particular uses by humans, the infertility issue implies that these animals would most likely become extinct without the intervention of humans through animal husbandry, making them "inferior" in terms of natural selection.

Genetic and epigenetic bases of heterosis[edit]

Main articles: Dominance versus overdominance, Histone H3 and microRNA

Since the early 1900s (as discussed in the article Dominance versus overdominance) two competing genetic hypotheses, not necessarily mutually exclusive, have been developed to explain hybrid vigor. More recently, an epigenetic component of hybrid vigor has also been established. [3][4]

The genetic dominance hypothesis attributes the superiority of hybrids to the masking of expression of undesirable (deleterious) recessive alleles from one parent by dominant (usually wild-type) alleles from the other (see Complementation (genetics)). It attributes the poor performance of inbred strains to the expression of homozygous deleterious recessive alleles. The genetic overdominance hypothesis states that some combinations of alleles (which can be obtained by crossing two inbred strains) are especially advantageous when paired in a heterozygous individual. This hypothesis is commonly invoked to explain the persistence of some alleles (most famously the Sickle cell trait allele) that are harmful in homozygotes. In normal circumstances, such harmful alleles would be removed from a population through the process of natural selection. Like the dominance hypothesis, it attributes the poor performance of inbred strains to expression of such harmful recessive alleles. In any case, outcross matings provide the benefit of masking deleterious recessive alleles in progeny. This benefit has been proposed to be a major factor in the maintenance of sexual reproduction among eukaryotes, as summarized in the article Evolution of sexual reproduction.

An epigenetic contribution to heterosis has been established in plants,[4] and it has also been reported in animals.[5] MicroRNAs  (miRNAs), discovered in 1993, are a class of non-coding small RNAs which repress the translation of messenger RNAs (mRNAs) or cause degradation of mRNAs.[6] In hybrid plants, most miRNAs have non-additive expression (it might be higher or lower than the levels in the parents).[4] This suggests that the small RNAs are involved in the growth, vigor and adaptation of hybrids.[4]

It was also shown[3] that hybrid vigor in an allopolyploid hybrid of two Arabidopsis species was due to epigenetic control in the upstream regions of two genes, which caused major downstream alteration in chlorophyll and starch accumulation. The mechanism involves acetylation and/or methylation of specific amino acids in histone H3, a protein closely associated with DNA, which can either activate or repress associated genes.

MHC in animals[edit]

One example of where particular genes may be important in vertebrate animals for heterosis is the major histocompatibility complex. Vertebrates inherit several copies of both MHC class I and MHC class II from each parent, which are used inantigen presentation as part of the adaptive immune system. Each different copy of the genes is able to bind and present a different set of potential peptides to T-lymphocytes. These genes are highly polymorphic throughout populations, but will be more similar in smaller, more closely related populations. Breeding between more genetically distant individuals will decrease the chance of inheriting two alleles which are the same

or similar, allowing a more diverse range of peptides to be presented. This therefore gives a decreased chance that any particular pathogen will not be recognised, and means that more antigenic proteins on any pathogen are likely to be recognised, giving a greater range of T-cell activation and therefore a greater response. This will also mean that the immunity acquired to the pathogen will be against a greater range of antigens, meaning that the pathogen must mutate more before immunity is lost. Thus hybrids will be less likely to be succumb to pathogenic disease and will be more capable of fighting off infection.

In plants[edit]

Crosses between inbreds from different heterotic groups result in vigorous F1 hybrids with significantly more heterosis than F1 hybrids from inbreds within the same heterotic group or pattern. Heterotic groups are created by plant breeders to classify inbred lines, and can be progressively improved by reciprocal recurrent selection.

Heterosis is used to increase yields, uniformity, and vigor. Hybrid breeding methods are used in maize, sorghum, rice, sugar beet, onion, spinach, sunflowers, broccoli and to create a more psychoactive cannabis.

Corn (maize)[edit]

Nearly all field corn (maize) grown in most developed nations exhibits heterosis. Modern corn hybrids substantially outyield conventional cultivars and respond better to fertilizer.

Corn heterosis was famously demonstrated in the early 20th century by George H. Shull and Edward M. East after hybrid corn was invented by Dr. William James Beal of Michigan State University based on work begun in 1879 at the urging ofCharles Darwin. Dr. Beal's work led to the first published account of a field experiment demonstrating hybrid vigor in corn, byEugene Davenport and Perry Holden, 1881. These various pioneers of botany and related fields showed that crosses of inbred lines made from a Southern dent and a Northern flint, respectively, showed substantial heterosis and outyielded conventional cultivars of that era. However, at that time such hybrids could not be economically made on a large scale for use by farmers. Donald F. Jones at the Connecticut Agricultural Experiment Station, New Haven invented the first practical method of producing a high-yielding hybrid maize in 1914-1917. Jones' method produced a double-cross hybrid, which requires two crossing steps working from four distinct original inbred lines. Later work by corn breeders produced inbred lines with sufficient vigor for practical production of a commercial hybrid in a single step, the single-cross hybrids. Single-cross hybrids are made from just two original parent inbreds. They are generally more vigorous and also more uniform than the earlier double-cross hybrids. The process of creating these hybrids often involves detasseling.

Temperate maize hybrids are derived from two main heterotic groups: Iowa Stiff Stalk Synthetic, often referred to as BSSS,[clarification needed] and non stiff stalk.[citation needed]

Rice (Oryza sativa)[edit]

Rice production has seen enormous rise in China due to heavy uses of hybrid rice. In China, efforts have generated a super hybrid rice strain (LYP9) with a production capability of ~15 tons per hectare. In India also, several varieties have shown high vigor, including RH-10 and Suruchi 5401.

Hybrid livestock[edit]

The concept of heterosis is also applied in the production of commercial livestock. In cattle, hybrids between Black Angusand Hereford produce a hybrid known as a "Black Baldy". In swine, "blue butts" are produced by the cross of Hampshire and Yorkshire. Other, more exotic hybrids such as "beefalo" are also used for specialty markets.

Poultry[edit]

Within poultry, sex-linked genes have been used to create hybrids in which males and females can be sorted at one day old by color. Specific genes used for this are genes for barring and wing feather growth. Crosses of this sort create what are sold as Black Sex-links, Red Sex-links, and various other crosses that are known by trade names.

Commercial broilers are produced by crossing different strains of White Rocks and White Cornish, the Cornish providing a large frame and the Rocks providing the fast rate of gain. The hybrid vigor produced allows the production of uniform birds with a marketable carcass at 6–9 weeks of age.

Likewise, hybrids between different strains of White Leghorn are used to produce laying flocks that provide the majority of white eggs for sale in the United States.

Heterosis in dogs[edit]

John Scott and John Fuller performed a detailed study of purebred cocker spaniels, purebred basenjis, and hybrids between them.[7] They found that hybrids ran faster than either parent, perhaps due to heterosis. Other characteristics, such as basal heart rate, did not show any heterosis -- the dog's basal heart rate was close to the average of its parents -- perhaps due to the additive effects of multiple genes.[8]

Sometimes people working on a dog breeding program find no useful heterosis.[9]

Humans[edit]

See also: Exogamy

Human beings are all extremely genetically similar to one another, but less similar, than for instance dogs.[10][11][12] Michael Mingroni has proposed heterosis, in the form of hybrid vigor associated with historical reductions of the levels of inbreeding, as an explanation of the Flynn effect, the steady rise in IQ test scores around the world during the twentieth century. However, James R. Flynn has pointed out that even if everyone mated with a sibling in 1900, subsequent increases in heterosis would not be a sufficient explanation of the observed IQ gains.[13]

See also[edit]

F1 hybrid Genetic admixture Heterozygote advantage

References[edit]

1. ^ Jump up to: a  b Risch N, Burchard E, Ziv E, Tang H (July 2002)."Categorization of humans in biomedical research: genes, race and disease". Genome Biol. 3 (7): comment2007.doi:10.1186/gb-2002-3-7-comment2007. PMC 139378.PMID 12184798.

2. Jump up ̂  Weller SG, Sakai AK, Thai DA, Tom J, Rankin AE (November 2005). "Inbreeding depression and heterosis in populations of Schiedea viscosa, a highly selfing species". J. Evol. Biol. 18 (6): 1434–44.doi:10.1111/j.1420-9101.2005.00965.x.PMID 16313456.

3. ^ Jump up to: a  b Ni Z, Kim ED, Ha M et al. (January 2009). "Altered circadian rhythms regulate growth vigour in hybrids and allopolyploids". Nature 457 (7227): 327–31.doi:10.1038/nature07523. PMC 2679702.PMID 19029881.

4. ^ Jump up to: a  b c d Baranwal VK, Mikkilineni V, Zehr UB, Tyagi AK, Kapoor S (November 2012). "Heterosis: emerging ideas about hybrid vigour". J. Exp. Bot. 63 (18): 6309–14.doi:10.1093/jxb/ers291. PMID 23095992.

5. Jump up ̂  Han Z, Mtango NR, Patel BG, Sapienza C, Latham KE (October 2008). "Hybrid vigor and transgenerational epigenetic effects on early mouse embryo phenotype".Biol. Reprod. 79 (4): 638–48.doi:10.1095/biolreprod.108.069096. PMC 2844494.PMID 18562704.

6. Jump up ̂  Zhou Y, Ferguson J, Chang JT, Kluger Y (2007). "Inter- and intra-combinatorial regulation by transcription factors and microRNAs". BMC Genomics 8: 396.doi:10.1186/1471-2164-8-396. PMC 2206040.PMID 17971223.

7. Jump up ̂  Tyrone C. Spady; Elaine A. Ostrander. "Canine Behavioral Genetics: Pointing Out the Phenotypes and Herding up the Genes". 2008. doi:10.1016/j.ajhg.2007.12.001

8. Jump up ̂  John Paul Scott and John L. Fuller. "Genetics and the Social Behavior of the Dog". 1965. p. 307 and p. 313.

9. Jump up ̂  Per Jensen. "The Behavioural Biology of Dogs". 2007. p. 179.10. Jump up ̂  Hawks, John (2013). "Significance of Neandertal and Denisovan Genomes in Human

Evolution". Annual Review of Anthropology (Annual Reviews) 42: 433–449, 438.doi:10.1146/annurev-anthro-092412-155548. ISBN 978-0-8243-1942-7. ISSN 0084-6570. Retrieved 4 January 2014.The shared evolutionary history of living humans has resulted in a high relatedness among all living people, as indicated for example by the very low fixation index (FST) among living human populations.

11. Jump up ̂  Barbujani, Guido; Colonna, Vincenza (15 September 2011). "Chapter 6: Genetic Basis of Human Biodiversity: An Update". In Zachos, Frank E.; Habel, Jan Christian.Biodiversity Hotspots: Distribution and Protection of Conservation Priority Areas. Springer. pp. 97–119.doi:10.1007/978-3-642-20992-5_6. ISBN 978-3-642-20992-5. Retrieved 23 November 2013. The massive efforts to study the human genome in detail have produced extraordinary amounts of genetic data. Although we still fail to understand the molecular bases of most complex traits, including many common diseases, we now have a clearer idea of the degree of genetic resemblance between humans and other primate species. We also know that humans are genetically very close to each other, indeed more than any other primates, that most of our genetic diversity is accounted for by individual differences within populations, and that only a small fraction of the species’ genetic variance falls between populations and geographic groups thereof.

12. Jump up ̂  Ramachandran, Sohini; Tang, Hua; Gutenkunst, Ryan N.; Bustamante, Carlos D. (2010). "Chapter 20: Genetics and Genomics of Human Population Structure". In Speicher, Michael R.; Antonarakis, Stylianos E.; Motulsky, Arno G.Vogel and Motulsky's Human Genetics: Problems and Approaches (PDF). Heidelberg: Springer Scientific. pp. 589–615. doi:10.1007/978-3-540-37654-5. ISBN 978-3-540-37653-8. Retrieved 29 October 2013. Lay summary(4 September 2010). Most studies of human population genetics begin by citing a seminal 1972 paper by Richard Lewontin bearing the title of this subsection [29]. Given the central role this work has played in our field, we will begin by discussing it briefly and return to its conclusions throughout the chapter. ... A key conclusion of the paper is that 85.4% of the total genetic variation observed occurred within each group. That is, he reported that the vast majority of genetic differences are found within populations rather than between them. ... His finding has been reproduced in study after study up through the present: two random individuals from any one group (which could be a continent or even a local population) are almost as different as any two random individuals from the entire world

13. Jump up ̂  Mackintosh, N.J. (2011). IQ and Human Intelligence. Oxford, UK: Oxford University Press, p. 291.

Heterosis, hybrid vigor, or outbreeding enhancement, is the improved or increased function of any

biological quality in a hybrid offspring. The adjective derived from heterosis is heterotic.

An offspring exhibits heterosis if its traits are enhanced as a result of mixing the genetic contributions of its

parents. These effects can be due to Mendelian or non-Mendelian inheritance.

…. How heterosis works:

An epigenetic contribution to heterosis has been established in plants,[4] and it has also been reported in

animals.[5] MicroRNAs  (miRNAs), discovered in 1993, are a class of non-coding small RNAs which repress the

translation of messenger RNAs (mRNAs) or cause degradation of mRNAs.[6] In hybrid plants, most miRNAs

have non-additive expression (it might be higher or lower than the levels in the parents).[4] This suggests that

the small RNAs are involved in the growth, vigor and adaptation of hybrids.[4]

It was also shown[3] that hybrid vigor in an allopolyploid hybrid of two Arabidopsis species was due to epigenetic

control in the upstream regions of two genes, which caused major downstream alteration in chlorophyll and

starch accumulation. The mechanism involves acetylation and/or methylation of specific amino acids in histone

H3, a protein closely associated with DNA, which can either activate or repress associated genes.

http://link.springer.com/article/10.1007%2FBF00303911#page-1

Theoretical and Applied Genetics

22. XI. 1982, Volume 63, Issue 4, pp 373-380

Heterosis breeding in rice (Oryza sativaL.)

S. S. Virmani,  R. C. Aquino,  G. S. Khush

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Summary

Studies conducted at the International Rice Research Institute (IRRI) during 1980 and 1981 have shown up to 73% heterosis, 59% heterobeltiosis and 34% standard heterosis for yield in rice. The latter was estimated in comparison to commercial varieties: IR36 and IR42 (yield 4–5 t/ha in wet season trials and 7–8 t/ha in dry season trials). Generally speaking, absolute yield was lower and extent of standard heterosis was higher in wet season than in dry season with some exception. Yields up to 5.9 t/ha (22% standard heterosis) in the wet season and 10.4 t/ha (34% standard heterosis) in the dry season were obtained. Most of the hybrids performed better in some season while some performed

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better in both seasons. Hybrids showed better lodging resistance although they were 5–10 cm taller. F1 hybrids had significant positive correlations with the parental traits viz., yield (r = 0.446), tillering (r = 0.746), height (r = 0.810) and flowering (r = 0.843). Selection of parents among elite breeding lines on the basis of their per se yield performance, diverse origin and resistance to insects and diseases should give heterotic combination. Yield advantage of hybrids was due primarily to increase in number of spikelets per unit area even though tiller number was reduced. Grain weight was either the same or slightly higher. High yielding hybrids also showed significant heterosis and heterobeltiosis for total dry matter and harvest index. For commercial utilization of heterosis in rice, effective male sterility and fertility restoration systems are available and up to 45% natural outcrossing on male sterile lines has been observed. Consequently, F1 rice hybrid have been successfully developed and used in China. Prospects of developing hybrid rice varieties elsewhere appear bright especially in countries that have organized seed production, certification and distribution programs and where hybrid seed can be produced at a reasonable cost.

Communicated by H. F. Linskens

1. Akbar, M.; Yabuno, T. (1975): Breeding for saline resistant varieties of rice. III. Response of F1 hybrids to salinity in reciprocal crosses between Jhona 349 and Magnolia. Jpn. J. Breed. 25, 215–220

2. Anonymous (1977): Rice breeding in China. Int. Rice Res. Newsletter 2, 27–283. Athwal, D.S.; Virmani, S.S. (1972): Cytoplasmic male sterility and hybrid breeding in rice. In: Rice

breeding, pp. 615–620. Laguna, Philippines: Int. Rice Res. Inst. (Los Banos), Annu. Rep.4. Carnahan, H.L.; Erickson, J.R.; Tseng, S.T.; Rutger, J.N. (1972): Outlook for hybrid rice in USA. In: Rice

breeding, pp. 603–607. Laguna, Philippines: Int. Rice Res. Inst. (Los Banos), Annu. Rep.5. Craigmiles, J.P.; Stansel, J.W.; Flinchum, W.T. (1968): Feasibility of hybrid rice. Crop Sci. 8, 720–7226. Erickson, J.R. (1969): Cytoplasmic male sterility in rice (Oryza sativa L.). Agron, Abstr. 67. Fonseca, S.; Patterson, F.L. (1968): Hybrid vigor in a seven-parent diallel cross in common winter

wheat (Triticum aestivum L.). Crop Sci. 8, 85–888. Int. Rice Res. Inst. (Los Banos) (1980): Annu. Rep. 1979; Laguna, Philippines, pp. 1579. Jones, J.W. (1926): Hybrid vigour in rice. J. Am. Soc. Agron. 18, 423–42810. Khaleque, M.A.; Jorder, O.I.; Enus, A.M. (1977): Heterosis and combining ability in a diallel cross of rice.

Bangladesh J. Agric. Sci. 4, 137–14511. Kumar, I.; Saini, S.S. (1980): Estimates of genetic effects for various quantitative characters in rice

(Oryza sativa L.). Genet. Agrar. 34, 35–4812. Lin, S.C.; Yuan, L.P. (1980): Hybrid rice breeding in China. In: Innovative approaches to rice breeding,

pp. 35–51. Laguna, Philippines: Int. Rice Res. Inst. (Los Banos), Annu. Rep.13. Matzinger, D.F.; Mann, T.J.; Cockerham, C.C. (1962): Diallel cross in Nicotiana tabacum. Crop Sci. 2,

383–38614. McDonald, D.J.; Gilmore, E.C.; Stansel, J.W. (1971): Heterosis for rate of gross photosynthesis in rice.

Agron. Abstr. 11–1215. Parmar, K.S. (1974): Studies of problems in producing hybrid rice and mutational rectification of some

undesirable traits of three popular tall varieties of rice (Oryza sativa L.). Ph.D. Thesis, p. 233. Vallabh Vidyanagar, Gujrat (India): The Sardar Patel University

16. Shinjyo, C.; Omura, T. (1966): Cytoplasmic male sterility and fertility restoration in rice (Oryza sativa L.). Sci. Bull. Coll. Agric. Univ., Ryukyus 22, 1–57

17. Stansel, J.W.; Craigmiles, J.P. (1966): Hybrid rice: problems and potentials. Rice J. 69, 14–1518. Swaminathan, M.S.; Siddiq, E.A.; Sharma, S.D. (1972): Outlook for hybrid rice in India. In: Rice

breeding, pp. 609–613. Laguna, Philippines: Int. Rice Res. Inst. (Los Banos) Annu. Rep.19. Virmani, S.S.; Chaudhary, R.C.; Khush, G.S. (1981): Current outlook on hybrid rice. Oryza 18, 67–8420. Virmani, S.S.; Khush, G.S.; Bacalangco, E.H.; Yang, R.C. (1980): Natural outcrossing on cytoplasmic

male sterile lines of rice under tropical conditions. Int. Rice Res. Newslett. 5, 5–621. Watanabe, Y. (1971): Establishment of cytoplasmic and genetic male sterile lines by means of indica-

japonica cross. Oryza 8, 9–16

22. Yuan, Long-Ping (1966): A preliminary report on the male sterility in rice. Sci. Bull. 4, 32–3423. Yuan, Long-Ping (1972): An introduction to the breeding of male sterile lines in rice. Proc. 2nd

Workshop on Genetics, Hainan, Guangdong, March 1972 (in Chinese)

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Genomic analysis of hybrid rice varieties reveals numerous superior alleles that contribute to heterosis

Xuehui Huang, Shihua Yang, Junyi Gong, Yan Zhao, Qi Feng, Hao Gong, Wenjun Li, Qilin Zhan, Benyi Cheng, Junhui Xia, Neng Chen, Zhongna Hao, Kunyan Liu, Chuanrang Zhu, Tao Huang, Qiang Zhao, Lei Zhang, Danlin Fan, Congcong Zhou, Yiqi Lu et al. Affiliations Contributions Corresponding author

Nature Communications

6,

Article number:

6258

doi:10.1038/ncomms7258

Received

04 August 2014

Accepted

09 January 2015

Published

05 February 2015

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Abstract Abstract• Introduction • Results • Discussion • Methods • Additional information • References • Acknowledgements • Author information • Supplementary information

Exploitation of heterosis is one of the most important applications of genetics in agriculture. However, the genetic mechanisms of heterosis are only partly understood, and a global view of heterosis from a representative number of hybrid combinations is lacking. Here we develop an integrated genomic approach to construct a genome map for 1,495 elite hybrid rice varieties and

their inbred parental lines. We investigate 38 agronomic traits and identify 130 associated loci. In-depth analyses of the effects of heterozygous genotypes reveal that there are only a few loci with strong overdominance effects in hybrids, but a strong correlation is observed between the yield and the number of superior alleles. While most parental inbred lines have only a small number of superior alleles, high-yielding hybrid varieties have several. We conclude that the accumulation of numerous rare superior alleles with positive dominance is an important contributor to the heterotic phenomena.

http://artsci.wustl.edu/~anthro/articles/heterosis%20myth.htm

Heterosis?Do Hybrids Make A Difference?

Jean-Pierre Berlan and Richard C Lewontin, "Operation Terminator"

    In 1907 Hugo de Vries, the most influential biologist of his day who "rediscovered" Mendel's laws (4), was the only one to realise that in an applied science like agricultural genetics, economics took precedence over science: what is profitable affects, or even determines, what is "scientifically true" (5).      He investigated replacing the technique of improving cereals by isolation, which dated back to the early 19th century and was based on the fact that the plants go on to breed true - and therefore bring no profits to the investor - by the continuous selection method. According to this method, justified by the best science of the time, Darwinism, varieties "deteriorate" in the farmer's field. This method cannot improve the plants, as was demonstrated empirically by Nilsson at the Svalöf Institute in Sweden in 1892 and confirmed by the earliest work inspired by Mendel at the beginning of this century. Thus, even then, a technique that was profitable but incapable of bringing the slightest progress replaced one that was useful to society but generated no profits...     Ignorant of the history of their own discipline and of the work of de Vries in particular (6), the 20th century's agricultural geneticists repeated the same scenario. At the end of the 1930s they triumphed with "hybrid" maize, which was extravagantly fêted (7). The technique of hybridisation, which has become the model for agronomic research the world over, is now used in around 20 food species and a dozen others are likely to follow. Poultry of every kind and a large number of pigs are also "hybrids". On the strength of a sham theoretical explanation of hybrid vigour, heterosis-superdominance (8), geneticists have tried since the mid-1930s to get the hybrid

technique generally accepted following their success with maize in the United States. "Hybrids increase yield", they say. This puts the theory of heterosis in a nutshell: having different genes - "hybridity" - is beneficial per se.      In reality, what distinguishes this varietal type from all the others is the reduction in yield in the next generation - that is, in plain terms, sterility. As a result, the farmer is obliged to buy his "seed" in every year. But varietal progress can only come from improving populations by selection, the very thing that this quest for hybrids prevents. Apparently unaware of what they are doing, the agricultural geneticists have dialectically overturned reality: they state they are using a biological phenomenon, heterosis, to increase yield, while actually using inbreeding to create sterility.

see also:

Berlan, J. P. and R. Lewontin (1986). "The Political Economy of Hybrid Corn." Monthly Review 38(July-August): 35-47. Berlan, J.-P. and R. Lewontin (1986). "Breeders' Rights and Patenting Life Forms." Nature 322(28 August): 785-788.

 

Coors, J. G. (1999). "Selection Methodology and Heterosis." In Genetics and the Exploitation of Heterosis in Crops, ed. by J. G. Coors and S. Pandey, pp. 225-245. Madison WI: ASA-CSSA-SSSA. (the data suggest "the unsettling conclusion" that OPV breeding has been more effective in increasing yield than hybrid breeding; also see Cleveland 2001, "The case of yield stability"))

GRAIN, "Hybrid rice in Asia: An unfolding threat" March 2000

Heterosis as a myth

Scientists have yet to explain how heterosis works and some, such as Jean-Pierre Berlan, of the Institut National de la Recherche Agronomique in France, believe that it is actually a myth. Berlan maintains that while rice may demonstrate some hybrid vigor , "The real phenomenon is inbreeding depression." 61Hybrids appear to produce high yields because they out-yield the parental lines they were crossed from by a significant margin. However, Berlan argues that yields from the parental lines are depressed by the many backcrosses that breeders must make for them to be stable. Thus, hybridisation does not necessarily produce "improved varieties"; it only improves upon the parental lines.

While the scientific theory of heterosis remains unexplained, the economic impact does not. The costs of hybrid rice seeds are very high: up to 15 times higher than seeds from elite inbred varieties. 62   The major problem is that seed yields are very low, making seed production costly. Farmers who buy these expensive seeds season after season face the added burden of low market prices for their harvest. The selling price for hybrid rice is significantly lower than the price of regular rice in both India and China, two countries with the most experience.

Some farmers call hybridisation "the scam of the century." 63   Why? If you compare the trajectory taken by two contrasting crops in a country like France – wheat, which is self-pollinated like rice, and corn, which cross-pollinates and can easily be hybridized – the picture is shocking. Wheat and corn were both grown from local populations until hybrid corn took off 40 years ago. In those 40 years, the public research sector continued to work on improving non-hybrid wheat, while the private sector took control of corn breeding, which became entirely devoted to hybrids. The result for the farmer is clear. Wheat yields between the early 1960s and the late 1990s were multiplied by 2.2 whereas the corn yields barely doubled. At the end of the four decades, wheat seed prices were three times the cost of the grain whereas corn seed prices were 30 times the cost of the grain. For hybrids, then, the yield increase has been lower but the price increase has been spectacular. This is why farmers feel short-changed by hybrization: the science is "not explained and unexplainable" , 64   the yield increases have not matched those of the inbred crops and yet the seed prices have shot through the roof. Research to improve the performance of open-pollinated corn varieties – which the private sector is not interested in, since farmers can save the seed – might have provided much more sustainable options than hybrids. Will the same happen in rice?

61 . Personal communication, 26 January 2000. 62 . S.S. Virmani, "Hybrid Rice", op. cit. , p. 403. 63 . Jacques Laigneau, "La guerre des semences fermières", Coordination Rurale, Auch, décembre 1999. 64 . Ibid.

http://www.hindawi.com/journals/isrn/2012/682824/

ISRN BotanyVolume 2012 (2012), Article ID 682824, 12 pageshttp://dx.doi.org/10.5402/2012/682824Review Article

Heterosis: Many Genes, Many Mechanisms—End the Search for an Undiscovered Unifying Theory

Shawn Kaeppler

Department of Agronomy, University of Wisconsin, 1575 Linden Drive, Madison, WI 53706, USA

Received 24 September 2012; Accepted 11 October 2012

Academic Editors: H.-J. Huang, K.-B. Lim, and S. Schornack

Copyright © 2012 Shawn Kaeppler. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Heterosis is the increase in vigor that is observed in progenies of matings of diverse individuals from different species, isolated populations, or selected strains within species or populations. Heterosis has been of immense economic value in agriculture and has important implications regarding the fitness and fecundity of individuals in natural populations. Genetic models based on complementation of deleterious alleles, especially in the context of linkage and epistasis, are consistent with many observed manifestations of heterosis. The search for the genes and alleles that underlie heterosis, as well as for broader allele-independent, genomewide mechanisms, has encompassed many species and systems. Common themes across these studies indicate that sequence diversity is necessary but not sufficient to produce heterotic phenotypes, and that the molecular pathways that produce heterosis involve chromatin modification, transcriptional control, translation and protein processing, and interactions between and within developmental and biochemical pathways. Taken together, there are many and diverse molecular mechanisms that translate DNA into phenotype, and it is the combination of all these mechanisms across many genes that produce heterosis in complex traits.

1. Introduction

Heterosis has been observed and, in some cases, harnessed in many diverse systems. Examples of interspecies crosses of mammals that produce heterotic phenotypes include the mule resulting from a cross between a male donkey and a female horse, and the liger resulting from a cross between a lion and a tiger. In both cases, these interspecific hybrids are larger and, by some measures, more vigorous than the parents. However, many interspecific hybrids suffer from reduced longevity and reductions in fertility. Heterosis in humans has been proposed, sometimes controversially, to affect multiple phenotypes including attractiveness [1], IQ [2, 3], and height [4–6]. In agricultural settings, there are numerous examples in which heterosis has been harnessed to create more productive and more uniform products including livestock [7–11] and crop plants (reviewed in [12–19]). Heterosis can also be captured and fixed through the process of polyploidization which is common in the plant kingdom (reviewed in [13, 14, 20]). In this case, hybrids formed by sexual combination of unreduced gametes or by hybridization followed by chromosome doubling are often fertile and have often been classified as a new species. Polyploid individuals show a general trend toward an increase in size, and the capture of heterotic genetic effects can further enhance their fitness and productivity.

The impressive phenotypic manifestations of heterotic hybrids coupled with the economic importance of hybrid strains have led to extensive research to understand its basis. This research has followed evolving knowledge of genome composition and genetic and biochemical mechanisms and is enabled by technical advances that facilitate new measurements of phenotypes and molecular processes.

2. How Is Heterosis Defined?

Historical accounts of the development of the modern concept of heterosis are provided in several excellent articles [15, 21–23]. Documentation of the importance of inbreeding and performance included descriptions by early agriculturists who noted the deleterious effects of inbreeding in both plants and animals and took measures to minimize this effect. Collins [24] documents activities of primitive tribes to mitigate inbreeding and maximize heterosis by placing seeds of multiple strains within each hill of maize that they planted. Darwin [25] experimentally evaluated the detrimental effect of mating among relatives supporting the idea that genetic diversity is related to hybrid vigor. Research on maize was important in developing some of the early ideas of heterosis [26–29] and has continued as an important experimental organism to the present. Shull’s [30] article “The composition of a field of maize” is widely regarded as it provided seminal foundational ideas for inbreeding and hybridization in crop plants and was important in nucleating research in the recent era.

The fundamental concept of heterosis, as envisioned by Shull, is that deleterious alleles persist in large random-mating populations. Inbreeding due to drift, population isolation, or consanguineous mating by plan or by chance reduces vigor of individuals or populations due to increasing homozygosity of deleterious alleles. Vigor is restored by crossing among divergent types as recessive deleterious alleles are complemented in the hybrid state. This fundamental idea is consistent with many examples of heterosis across species.

Heterosis is quantified on an individual or population basis as the difference in the performance of the hybrid relative to the average of the inbred parents (termed the mid-parent value). For quantitative genetic analysis, the deviation of the hybrid relative to the mid-parent is the relevant value. In a practical context, high-parent heterosis, which measures the superiority of the hybrid relative to the best parent, is the important metric.

The conceptual opposite of heterosis is inbreeding depression [31]. This is the loss of vigor following related matings. Heterosis is often viewed as maximizing heterozygosity and, in contrast, inbreeding depression is due to reduction in heterozygosity. Inbreeding depression is measured as the reduction in performance in proportion to reduction in heterozygosity. Inbreeding depression is important in many settings including agriculture such as in maintenance of heirloom varieties, conservation biology, and human health. In any circumstance in which matings occur in small populations and/or assortative mating occurs, there is an increased risk of reduction in vigor and homozygosity of deleterious alleles in genotypic contexts that are otherwise rare in populations.It is important to emphasize that measures of heterosis are phenotype-dependent. For example, interspecific mammalian hybrids may display increased size, vigor, and other desirable fitness traits, but have are often highly sterile and therefore have reduced fecundity. Flint-Garcia et al. [32] measured 17 traits among 267 maize hybrids and found that the amount of heterosis in any hybrid relative to its parents was trait-dependent and that hybrids could not be simply classified as heterotic or nonheterotic. From a research standpoint, this indicates that the search for mechanisms of heterosis must be conducted within the biological context of specific traits; in a practical context, it motivates research to better predict heterotic hybrids that will provide maximum productivity for specific traits of interest.

3. A Case for the Dominance Hypothesis: Early 1900s to Present

According to quantitative genetic theory, heterosis can result from dominance, overdominance, or epistasis. Overdominance is an intra-allelic interaction in which the presence of multiple alleles leads to greater performance than homozygosity for either allelic state. If overdominance is the predominant basis of heterosis, then populations and breeding strategies that maximize heterozygosity will result in the best performance. On the

other hand, if dominance or epistasis is the primary mechanism of heterosis, natural or breeding populations, and therefore individuals, will become fixed for favorable alleles and perform equally to any hybrid. This issue was addressed from the early to mid-1900s by analysis of variance components (summarized in Hallauer et al. [33]).Variance decomposition studies in hybrid maize populations using mating designs such as the North Carolina Design III resulted in significant estimates of overdominant gene action (summarized in [33]). However, Moll et al. [34] and Gardner and Lonnquist [35] realized that variance estimates could be confounded by linkage. Specifically, if positive and negative alleles were in repulsion phase linkage and the gene action of each locus was partial to complete dominance, the alleles at the two loci would frequently segregate together resulting in estimates of overdominance. In the Moll et al. [34] and Gardner and Lonnquist [35] studies, the average degree of dominance was estimated in the first generation of intermating from a population cross and then after intermating incrementally for multiple generations. The result of these studies was that the estimate of the average degree of dominance decreased, consistent with partial dominance—not overdominance—of most loci contributing to heterosis coupled with repulsion phase linkage.The importance of dominance versus overdominance was further supported by recurrent selection studies in which populations were evaluated in crosses with each other, or with an inbred tester. Research by Russell et al. [36] in maize supported dominance versus overdominance as the primary basis of heterosis. One component of their study was the comparison of response to selection of populations selected based on performance of a cross with an inbred tester versus a population tester. If overdominance is the primary mechanism of heterosis, then the inbred tester would improve the population more than the population tester because in an inbred, alleles are fixed whereas in a population, they are intermediate in frequency. The result of this component of the study was that the inbred and population tester improved performance of the population similarly, consistent with the importance of dominance relative to overdominance. A second component of the Russell et al. [36] study was the analysis of selection in two populations based on performance of the population cross. If overdominance was the primary basis of heterosis, the populations would diverge due to selection and increase homozygosity of alternative alleles within the populations to maximize heterozygosity and performance of the population cross. The result would be increasing performance of the population cross and decreasing performance of the populations per se. Alternatively, if dominance (or epistasis) were the primary mechanism of heterosis, the frequency of the favorable allele would increase in each population, and therefore also in the population cross, resulting in increasing performance of the populations and populations cross. The result of their study found increasing performance in all populations, supporting the importance of dominance versus overdominance. Note also that the level of linkage

disequilibrium in these materials was likely quite low, minimizing confounding effects of pseudooverdominance.Quantitative trait locus (QTL) mapping studies in maize are also consistent with dominance versus overdominance as the prevalent type of gene action underlying heterosis for productivity. Initial QTL studies indicated many QTL with overdominant gene action in populations derived from heterotic maize hybrids for traits such as yield and plant height [37, 38]. However, subsequent genetic dissection of an QTL with estimated overdominant gene action showed that the original QTL could be separated into two, linked QTLs in repulsion phase with dominant gene action [39, 40] conducted a QTL mapping study using 3 recombinant inbred populations using a North Carolina Design III approach. The results of this study were consistent with previous studies in maize. Overdominant gene action was estimated for QTL controlling grain yield, but those QTL were found in centromeric regions with high linkage disequilibrium (LD) and were interpreted as pseudooverdominance. Consistent with many other studies, the degree of heterosis was trait-dependent, with greatest heterosis for yield. Therefore, recent QTL mapping studies in maize are also generally consistent with a prevalence of dominance underlying heterotic traits including yield and yield components and growth traits such as plant height.Xiao et al. [41] evaluated heterosis for ten traits per se using a testcross evaluation of a recombinant inbred line population derived from an interspecific indica × japonica cross in rice. The authors concluded that dominance was the primary basis of heterosis in this cross based on evidence from QTL, the absence of significant digenic epistatic interactions, and the relatively low relationship between marker heterozygosity and performance for most traits. Furthermore, two inbred lines from the population exceeded the performance of the hybrid, consistent with the proposition that, under the dominance hypothesis, it is possible to produce a homozygous individual that contains all the favorable alleles that produced the observed hybrid performance.

Despite a preponderance of evidence for the role of dominance in heterosis for yield in plants, especially in the context of linkage resulting in pseudooverdominance, there are observations that are inconsistent with the dominance hypothesis. One important observation is that, in some hybrids, the performance of the hybrid is greater than the sum of the parents. Given complete dominance, the maximum performance of the hybrid would be equal to the sum of the parents. Furthermore, as described below, well-documented examples of overdominance exist, and there is growing evidence for the role of epistasis using new experimental and statistical approaches.

4. Overdominance: Rationale and Examples

Overdominance is conceptually consistent with the idea that genetic dissimilarity per se stimulates vigor and, in a practical context, the optimum genetic state is heterozygosity versus homozygosity for favorable alleles. Overdominance provides an explanation for examples in which hybrid performance is greater than the sum of the parents, an incongruity with the dominance hypothesis.

Estimates of overdominant gene action have now generally been attributed to pseudooverdominance as described above. However, intriguing examples of overdominance have been reported. A biochemical example of overdominance provided by Schwartz and Laughner [42] was intellectually important in fueling the ongoing debate regarding the basis of heterosis. This study involved the activity of the enzyme adh1, which functions as a heterodimer. An allele of the enzyme with high activity was combined with an allele that had heat tolerance. The activity of the resulting biallelic enzyme was superior to that of either monoallelic form under specific stress conditions. This result provides a conceptual basis to consider molecular mechanisms by which intra-allelic interactions would provide increased performance and stress tolerance.Krieger et al. [43] reported a single-gene model for overdominance based on developmental timing. In this study, heterozygosity for a functional allele and a loss-of-function allele at the single flower truss (SFT) locus in tomato results in overdominant fruit yield. This gene is homologous to Arabidopsis Flowering Locus T(FT) which is involved in the production of the flowering hormone florigen. Overdominant gene action for yield, in this example, is a result of shifting the developmental program so that an increased number of flowering inflorescences can form in the heterozygote relative to the wild-type homozygote which ends inflorescence production earlier and the mutant homozygote that produces limited inflorescences and more vegetative growth. In contrast to the specific example of an intra-allelic interaction in the case of adh1heterosis, the SFT result is based on dosage-dependent molecular expression (possibly additive) that results in a balance of gene product that is manifested in an overdominant phenotype. The SFT result is also compelling as there are likely multiple examples of intra- and inter-specific hybrids in which loss-of-function or allelic absence due to presence/absence variation (PAV) are combined in hybrids with a functional allele. Finally, this example highlights the potential productivity outcomes of fine-tuning developmental programs.Semel et al. [44] evaluated gene action for 35 traits in tomato using an introgression line population in which each line of the cultivated tomato (Solanum lycopersicum) parent contained a small contribution from the genome of the wild species Solanum pennellii. The introgression lines were crossed to a cultivated line to produce hybrids. Most of the reproductive traits related to seed and fruit yield exhibited overdominance, while

nonreproductive traits related primarily to morphological characteristics did not. Based on the fact that some traits exhibited overdominance while others did not, the authors argued that this study supported true overdominance as opposed to pseudooverdominance. Additional research is required to assess whether this interpretation is correct.

These examples and others not included here provide evidence that overdominance can play a role in heterosis. However, the majority of the studies to date, based on response to selection, genetic variance partitioning, and QTL mapping are consistent with a lesser role for overdominance than dominance.

5. Epistasis: Emerging Evidence for the Role of Epistasis in Heterosis

The role of epistasis in heterosis remains elusive, although recent experiments provide increasing evidence for its importance. Estimates of epistatic variance in early studies of heterosis were limited by experiment size and computational capacity. Recent studies utilizing molecular markers and modern, computationally intensive statistical approaches, have increased ability to detect epistatic interactions.

Generation means analysis provided some of the first compelling evidence for the role of epistasis in hybrid performance. A recent example provided by Wolf and Hallauer [45] used a means-based analysis to support of role of epistasis in heterosis. The triple testcross analysis compares the relative performance of segregating progeny when testcrossed to both parents and to the F1 hybrid. Deviation in performance of the F1 testcross from the average of the parental testcrosses is consistent with epistatic gene action. Using this approach, the authors detected epistasis for multiple traits including yield, yield components, and timing of development among progeny of the heterotic hybrid B73 × Mo17.Recent studies in maize, rice, and Arabidopsis based on QTL mapping report epistasis for various traits. Kusterer et al. [46] used a triple-testcross design in the context of QTL analysis in Arabidopsis to characterize the importance of epistasis for biomass traits. This research was complemented by a related study of near isogenic lines [47, 48]. Recent QTL mapping studies support the role of epistasis in rice [49–51]. The type of epistasis varies in these studies, from primarily additive × additive epistasis to dominant epistatic interactions, at least in part due to experimental materials and approach. Yu et al. [49] evaluated inbred F2-derived F3 families from the intraspecific cross Zhenshan97 × Minghui63 and reported a predominance of additive × additive interactions underlying performance for grain yield. In contrast, Li et al. [50] evaluated backcross (BC) and testcross hybrids from progeny of an interspecific japonica × indica hybrid and reported overdominant epistatic interactions. Hua et al. [51] evaluated an “immortalized F2” population based on intermating recombinant-inbred lines and reported the important role in dominant × dominant epistatic interactions. Interpreting and summarizing

trends across these studies, (1) interspecific populations whose parents have been genetically separated for a greater period of time exhibit more segregation and a greater degree of epistatic gene action, (2) experimental designs which utilize individuals with more heterozygosity (testcross or intermated RIL) detect higher levels of dominance, and (3) interpretation of overdominance remains confounded with pseudooverdominance in most studies.It is logical to consider the potential relevance in the context of metabolic and physiological pathways. One physiological pathway that has been studied specifically in the context of heterosis is gibberellic acid (GA) metabolism and signaling. Production of GA involves a multistep pathway, and transduction of the GA signal involves a complex signaling network. Therefore, this metabolic and signaling pathway provides ample opportunity for the expression of epistatic gene action. In maize, inbreds contain less endogenous GA and precursors than corresponding hybrids [52]. Application of exogenous GA stimulates growth of inbreds more than hybrids [53, 54], consistent with the hypothesis that the reduced efficiency of inbreds to produce GA results in reduced biomass accumulation. A recent study in rice provides similar support for the role of GA in heterosis for biomass accumulation [55]. This study provided metabolic and transcriptome evidence to support the importance of GA synthesis and signaling in heterosis during rice seedling development.The role of epistasis in heterotic and nonheterotic trait performance remains intriguing and perplexing. Conceptually, it is clear that many and diverse complex pathways interact to produce phenotypes in individuals supporting the likelihood that genetic epistasis should be detected. However, genetic epistasis requires not only interacting molecular pathways, but also allelic variation within interacting pathways of sufficient magnitude to provide a significant statistical interaction. Large QTL mapping studies find little evidence for epistatic interactions for specific developmental, architectural, and biochemical traits [56–58] although, as described previously, heterosis is greater for highly complex traits such as grain yield, traits for which quantitative genetic studies more often support the role of epistasis. In cases in which qualitative mutations have been introgressed into multiple genetic backgrounds, there is compelling evidence that expression is highly background-dependent. Therefore, it is logical by extension that genes of smaller effect should interact in the same way. However, the effect of individual genes/QTL must be of sufficient magnitude for interactions to be detectable within the constraints of specific experimental designs and population sizes. Understanding of the role of epistasis in heterosis and expression of other traits will continue to improve as molecular tools and statistical approaches advance. Current evidence suggests that there is much more to be learned about epistatic gene interactions underlying heterosis.It is important to recognize that estimates of gene action are based on a logical framework of genes, alleles, and allelic effects (e.g., Falconer and

Mackay [59]), and interpretations are only relevant in the context of that framework. In the next section, I will discuss molecular mechanisms that are consistent with that framework. However, mechanisms of phenotypic variation due to locus-independent, genomewide mechanisms have been proposed and will be summarized later in this paper. Note that phenotypic variation due to these mechanisms will still be partitioned within the context of gene-specific models in variance component studies due to restrictions in the model, but may actually result from a more general mechanism.

6. Molecular Evidence Consistent with Quantitative Genetic Models

The concept of heterosis has evolved parallel to discoveries on the molecular basis of mutation, the control of transcription and translation, and the discovery of heritable chromatin-based allelic states. Quantitative genetic models underlying current breeding and variance partitioning models are based on heritable allelic variation that provides consistent effects within defined genetic and environmental contexts. An early and still prevalent model of alternative allelic states is the presence of every gene in all individuals of a species with an array of sequence variants that could confer minor to extreme functional consequences including intermediate-to-complete loss-of-function alleles. This concept is consistent with extensive single-nucleotide polymorphism (SNP), indel, and transposon variation found within and near genes when comparing individual genomes within species [60–65]. The discovery that plant genomes contain a large proportion of repetitive transposons raises the possibility for transposons to influence the expression of nearby genes including altering expression levels, producing ectopic gene expression, and producing allelic variation by introducing footprints following insertion and excision [66]. Recently, the growing realization of the importance of presence-absence variation (PAV) and copy number variation (CNV) supports the concept of pangenomes within species in which all individuals within a species may not contain a copy of all the genes found across the species [67–70]. Finally, heritable epialleles [71] provide a sequence-independent mechanism to produce altered expression levels that might be able to more rapidly revert to support rapid direct or natural evolutionary change.

All of these allele-generating mechanisms—SNPs, transposons, PAVs, and epialleles—are consistent with the hypothesis that locus-specific intra-allelic interactions with some degree of dominance are responsible for heterosis. For example, SNPs can reduce function by altering the activity or productivity of enzymes or by reducing the efficiency of transcription factor binding. Loss-of-function could result from SNPs producing nonsense alleles or altering splice junctions, or loss of transcript due to absence of a sequence or by epigenetic silencing. Alleles with reduced or complete loss of function can be accumulated in random-mating highly heterozygous populations of individuals. Upon inbreeding, homozygosity of deleterious alleles would

result in loss of vigor (inbreeding depression) that would be restored by mating of genetically unrelated individuals.

Novel alleles occur in the context of chromosomal locations, and recent studies that define the nonlinearity of recombination event frequency across the chromosome [72] are consistent with observations of pseudooverdominance. Accumulation of mutations in centromeric regions with limited recombination results in quantitative genetic estimates of overdominance in variance analysis and QTL studies due to the high degree of persistent linkage disequilibrium in these regions. The potential of regions with limited recombination to harbor deleterious alleles that rarely have the opportunity to recombine is the basis of the concept of heterotic patterns used by plant breeders, is consistent with heterosis observed in genetically isolated natural and artificial populations, and provides a basis of the value of polyploidy to fix heterotic gene interactions by combining divergent but related genomes.Heterotic patterns used by plant breeders [73] provide a useful conceptual model to discuss heterosis in isolated populations. Breeders have purposefully separated breeding lines into distinct groups (parental pools) and limited intermating between pools as a way to maximize the performance of hybrids between parents selected from the groups. Consider, for example, the possibility that a species with 10 chromosomes has a pair of loci on each of the 10 chromosomes 1 centimorgan apart in repulsion phase with dominant gene action. It would be relatively straightforward based on phenotype or genotype to develop two breeding pools that would be fixed for the complementing allelic pairs at each of those 10 positions producing full performance of the hybrids between the pools. However, gametes containing recombination events in each of the intervals would be required to produce an individual out of the founder population with favorable alleles at all 20 loci (10 pairs). In a single generation, this combination would occur at a frequency of  in 10 trillion individuals, more than 5 times the number of corn plants grown in the United States in any year. In reality, the situation is much more complex with multiple loci in repulsion phase in genomic regions of high and persistent LD making it logical to capture the performance potential of linkage blocks as opposed to trying to identify exceptionally rare recombinant types that resolve repulsion-phase linkages. This concept can be applied to geographically or genetically isolated populations. Inbreeding due to drift would lead to divergence of genomic blocks in high LD regions resulting in reduced overall performance. After many generations of separation, heterosis would be observed upon crossing the populations to each other due to complementation.

While the dominance hypothesis has been described by some as the “old view” of heterosis, it is consistent with the majority and diversity of results observed across species including predictable heritability for performance when populations are subjected to selection, estimates of gene action in controlled experiments, and recent information on the molecular basis of

allelism. Nevertheless, it is possible that quantitative genetic models conceived in the early 1900s do not adequately capture all of the molecular mechanisms understood today, and there are at least anecdotal accounts of specific hybrids that perform beyond expectation based on classical quantitative genetic models. These observations continue to spur research into molecular mechanisms, perhaps genomewide and locus-independent, that are needed to explain at least some component of heterosis.

7. Genomic Analysis of Heterosis

Phenotype is the result of the interpretation of genetic information through the processes of transcription, translation, and metabolism and development. Genomic studies have, therefore, assessed the transcriptome, proteome, metabolome, and related control mechanisms in inbreds and hybrids as an approach to evaluate the relationship between observed phenotypes and underlying molecular pathways. The simplest interpretation would be a direct relationship between molecular expression and observed phenotype, such that additive amounts of transcript would produce an intermediate phenotype. It is important to note that the connection between molecular measures and final phenotype will likely not be that clear, as in the tomato example of overdominance cited above [43] in which the intermediate transcriptional expression at the SFTlocus resulted in overdominance for yield.Transcriptome studies measure the relative total amount of transcript per locus, or can measure the relative contribution of each allele in hybrids. Both types of information are useful and complementary, but it is important to recognize that they are different measures of transcription and that neither provides information on transcript of an individual gene per cell. Genome-wide studies of the transcriptome in inbred versus hybrid parents reveal that a majority of genes are expressed in an additive manner [74–76], and a smaller proportion of genes show nonadditive expression of which a very small percent show expression outside the parental values (transcriptional overdominance or epistasis). Non-additive gene action could result from genetic and epigenetic intra-allelic interactions including paramutation, or from interallelic interactions (epistasis). One example of an epistatic interaction resulting in expression beyond parental values would be the complementation of alleles in a heterodimeric transcription factor that would result in transcriptional activation of a pathway in a hybrid that is not transcriptionally active in either parent due to absence of one component. It is notable that this type of epistatic interaction is rarely observed in genomewide transcriptome studies.Overall transcription at a locus is a combined contribution from each parent. It is possible that an additive value of expression could result from a linear contribution of each parental allele in the hybrid relative to its expression in the inbred (cis control) or could be due to the heterozygote of a distant controlling factor modulating the level of expression (trans control). Stupar

and Springer [74] evaluated the allelic contribution to expression in the hybrid across multiple loci and found that the majority of loci were controlled in cis. This is generally consistent with observations by Guo et al. [77] who studied genomewide allele-specific expression in maize hybrids and found primarily intermediate contributions from both parents with some loci exhibiting maternal or paternal bias. In a related study, Guo et al. [78] reported that paternally biased expression was higher under the stress of high plant density and higher in an old hybrid versus a new hybrid indicating a potentially important environmental component to observed expression values.Additive transcript levels of genes could result in non-additive phenotypic performance in several ways. First, presence of a single favorable allele may be sufficient to provide protein function equivalent to the high-parent level even if both are expressed and the favorable allele is present in only one-half the amount. Second, additive expression levels could be observed in the hybrid in cases of a presence-absence allelic contrast in the parent with one parent having no expression and the other expressing a functional product. The hybrid may have only half the expression of the parent containing the gene, but that amount of expression could be sufficient to complement the deficiency due to the absence of the gene in the other parent. Therefore, the observed results are consistent with quantitative genetic observations based on phenotype. It is notable that the hybrid is generally a predictable combination of the inbred parents and that it does not exhibit genomewide luxuriant transcription levels which are not predictable by parental expression levels as suggested by some models [79].Various studies have measured small RNA levels in inbreds and hybrids, some of which present a strong suggestion for the role of small RNAs in heterosis [80, 81]. A recent study in maize using Illumina sequencing and qPCR confirmation revealed that, as with gene transcription, small RNA levels are generally additive in the hybrid with amounts predictable based on the inbred [82]. It is possible that, as with genic transcription factors, additive interactions among different small RNAs could result in non-additive expression of the loci that they control, although this type of expression is a minority. An interesting finding in the Barber et al. [82] study was the observation that hybrid maize plants relative to their inbred parents, all containing the mop1 mutation (a protein which is necessary for most 24nt small RNA production), were equally or more heterotic than nonmutant hybrids. This result indicates that this specific class of small RNAs is not required for heterotic phenotypic expression in maize hybrids.Proteomic analysis is another approach that has been used to characterize molecular components of heterosis. Proteomic analysis of seedling roots of maize [83–86] and rice [87] indicates that non-additive expression of proteins in hybrids versus inbreds is more frequent than non-additive transcriptional variation. Dahal et al. [88] compared two heterotic maize hybrids to a non-heterotic hybrid. They found that proteins enriched in stress response and protein and carbon metabolism were differentially expressed in

heterotic hybrids. Their results indicated that the degree of heterosis was correlated with the frequency of protein isoforms and/or modifications.

In summary, extensive genomic studies provide insights but no direct answers regarding the basis of heterosis. All modes of gene action—additivity, dominance, overdominance, and epistasis—are observed at the molecular level, but the interpretation of those molecular effects to final phenotype remains complex and largely undefined. Overall, the results are consistent with the importance of specific allelic variants in the manifestation of heterosis and with the predictable inheritance of molecular phenotypes. However, some mechanisms have been proposed that are independent of allelic effects and rather are genomewide responses to genomic diversity. These potential mechanisms will be discussed in the following section.

8. Genomewide Models to Explain Heterosis

Heterotic expression of phenotypes is, in many instances, correlated with genetic distance [89–93]. While this is generally true, the relationship is clearest in the comparison of hybrids with similar adaptation, and which have been selected for productivity (summarized by Melchinger [94]). An example would be the collection of public and private, off-PVP maize inbreds released in the US that have been selected for performance in generally similar contexts. Within this group, there would be an expectation of a strong correlation between genetic diversity and performance based on the breeding method by which the lines were developed. As the genetic distance becomes greater, and complexities of adaptation are introduced, the relationship between performance and genetic diversity is lost. Therefore, genetic diversity per se is not the sole basis for heterosis. By extension, other mechanisms that generate diversity such as mutagenesis would not be expected to produce heterosis commensurate with the degree of divergence. Nevertheless, it has been postulated that the genome has mechanisms to sense diversity and the response to diversity can be translated into heterotic performance. Genomewide mechanisms are those considered to be gene/allele-independent. Note that, based on this definition, genomewide mechanisms would also be considered to be trait-independent producing heterosis for all traits to a similar degree. In general, heterosis across hybrids is not general but rather is trait-specific (summarized in Kaeppler [95]).One genomewide mechanism that has been proposed as a basis of heterosis is changes in DNA methylation, or more broadly, chromatin state. Heritable epigenetic variation is a common attribute of plant genomes, likely more frequent than sequence variation (Becker and Weigel [96]). The possibility of directed, or at least more frequent, changes in DNA methylation in hybrids relative to their inbred progenitors is consistent with the potential stimulation of growth based on diversity per se. It is also commensurate with allele- and locus-specific observations of paramutation [97–99] in which the allelic interaction results in a heritable change in expression state, an

observation inconsistent with the tenets of quantitative genetic theory. Recent studies of genomewide methylation analysis by sequencing inbreds and hybrids suggest that repeatable methylation changes upon hybridization, likely directed by small RNAs, may be somewhat common [100, 101], but more research is needed to understand the impact of these changes on gene expression and phenotype.Sequence-based analysis of DNA methylation provides more detail than previous studies based on total proportion of 5-methyl cytosine in the genome, but studies based on proportion of methylated cytosines provide some intriguing hints about environmental influences on methylation changes, and potential differences among species. Tsfartis et al. [102] reported reduced levels of DNA methylation in hybrid relative to inbred maize plants and found the reductions to be related to stress (planting density). Furthermore, alterations in methylation were found to be heritable. Recently, Vergeer et al. [103] reported that inbreeding in Scabiosa is correlated with increased genomewide DNA methylation and methylation is reduced in hybrids. Furthermore, they report that application of a demethylating agent, 5-azacytidine, to inbreds restored productivity to the hybrid level. While 5-azacytidine has genomewide effects, it is not clear if the observed stimulation of vigor is a locus-specific effect, perhaps related with flowering. This result is in contrast to Shen et al. [101] who reported increases in DNA methylation in hybrids relative to inbred progenitors and reduced vigor in hybrids treated with a chemical that reduced methylation. Generally, in species exhibiting inbreeding depression, little evidence exists that neither DNA methylation or chromatin mutants, nor chemical treatments to reduce DNA methylation or alter histone modification, will stimulate vigor. In most cases, vigor would be expected to be reduced in these mutants and by these treatments.Goff [104] proposed a model accounting from multigenic heterosis based on gains in energy efficiency due to protein processing in hybrids relative to inbreds. The model proposes that allelic choice available in hybrids but not inbreds provides hybrids the opportunity to detect and express preferentially the favorable allele. By minimizing expression of alleles that will require energy-intensive protein recycling, hybrids realize a synergistic growth benefit that begins to be realized during early growth with benefits accumulating throughout the life-cycle of the plant. This idea is consistent with the idea that diversity per se is not the basis of heterosis, but maximizing “quality” alleles in hybrids contributes to performance regardless of the function of those genes. It is in contrast to the observation that manifestation of heterosis is trait-dependent. Genomewide models of heterosis predict that vigor for all heterotic traits would benefit similarly.

9. Polyploidy, Aneuploidy, and Heterosis

Polyploidy provides a mechanism to capture heterotic gene combinations. In addition, the phenotypic consequences of gene copy number in polyploids

and aneuploids, even those containing single alleles at all loci, may offer hints about mechanisms underlying heterosis [13, 20, 105].

Allopolyploids are formed by the union of distinct genomes in a single nucleus. The process of allopolyploidization can result from hybridization followed by somatic chromosome doubling or, more frequently, fertilization of unreduced gametes. Allelic complementation at common loci in the homoeologous genomes is fixed upon polyploidization, thereby fixing heterotic potential contributed by the component species. This mechanism of capturing heterotic performance through the process of polyploidization is consistent with the dominance/overdominance/epistatic models described above. Furthermore, polyploids have additional opportunity for epistatic interactions due to potential segregation of interacting loci contributed by the component genomes as well as independent segregation of allelic variants at homoeologous loci.

An interesting observation in autopolyploids of progressive heterosis [106]. Progressive heterosis is the increase in performance of individuals as the probability of allelic diversity increases. Specifically, the level of performance is greater when more than two alleles at a locus are possible than when only two alleles can be present. The observation of progressive heterosis has alternatively been interpreted as consistent with pseudooverdominance due to repulsion phase linkage of dominant alleles [107] and as an argument against simple complementation and for higher-order intra-allelic interactions [12]. Across diploid species, the bulk of current evidence supports complementation (dominance) versus intra-allelic interactions (overdominance).An intriguing phenotypic consequence of polyploidy and aneuploidy is the difference in performance due to the number of genomic complements, or to variation in doses of whole chromosomes or portions of chromosomes, and these consequences may have implications for heterosis [12, 108, 109]. These differences in performance can occur independent of any allelic diversity. Haploids in plants are generally lacking vigor, and doubled haploids (dihaploids) are as vigorous as sexually derived individuals of the same ploidy while being completely homozygous. In cases, where polyploid series have been produced, individuals of higher ploidy are often more vigorous than lower ploidy progenitors, although fertility is often compromised. Therefore, increased performance for traits such as forage yield is possible in the absence of allelic diversity simply by increasing DNA content per cell. On the other hand, altering the dosage of chromosomes or chromosome segments in aneuploids often reduces vigor and performance. In aneuploids, under- and over-representation of chromosome segments similarly results in reduced vigor. Therefore, pathways clearly exist across organisms to sense gene dosage [109], and the phenotypic consequences of polyploidy and aneuploidy are similar to differential performance of inbreds and hybrids. In the context of the dramatic presence/absence and copy number variation observed in many species, it is interesting to consider the possibility that

dosage sensing is an allele-independent mechanism underlying heterosis. For example, consider that through segregation of PAV/CNV alleles, inbreds accumulate a specific level of average dosage imbalance across the genome due to segregation and result in reduction in vigor. Hybrids formed between crosses of inbred lines would have average gene copy number across the genome that would be less deviant than either inbred parent restoring vigor. From a breeding standpoint, if dosage imbalance is important in performance, selection based on performance would tend to minimize CNV in genomes, at least at loci subject to a dosage response.

10. Summary and Integration

It is clear that much remains to be learned about genome composition and the role of transcription, translation, and posttranslational mechanisms in interpreting genes into phenotype. While it is certain that future discoveries will explain more about the process of heterosis, it is my opinion that a new and undiscovered molecular mechanism is not needed to ultimately explain heterosis. Heterosis is greatest for highly complex traits composed of multiple component phenotypes. An accumulation of the effects of a large number of genes with small effects and some level of dominance, taken in the context of recombination across the genome, is sufficient to explain heterosis and is consistent with directed and natural evolution. Mechanistically, the undiscovered territory is the multiplicity of specific mechanisms by which the cumulative influence of a large number of allelic variants is manifested.

Discussions of heterosis are often confused by inconsistent separation of absolute measurement of performance (yield, productivity, etc.) versus true measures of heterosis which is the deviation of the performance of a hybrid individual or population from its parental progenitor. Performance of many traits has been shown to be inherited in an expected and repeatable manner, indicating that performance in the hybrid state cannot be the result of mechanisms that are not manifested through selection and inbreeding. Quantitative genetic models based on dominance and epistasis explain heterosis, observed phenotypic variation and are consistent with observations of reduced heterosis (deviation of hybrid performance from mean of inbreds) as the performance of hybrids is improved. Recent genomic studies which show that large regions of the genome have limited recombination, providing a mechanism for the accumulation of deleterious mutations that can only be resolved and purged in rare recombinant gametes. The increasing number of ways that deleterious alleles can be produced including SNPs, transposon insertions and signatures, PAV, and epiallelic variation provides new ways to account for formation of deleterious alleles. The bulk of available data are highly consistent with the dominance (complementation) hypothesis as the primary basis of heterosis. Furthermore, heterosis is of greatest magnitude in highly complex traits such

as grain yield which is affected by many interacting developmental, metabolic, and environment response pathways supporting that a large number of genes, likely each with small effects, are cumulatively responsible in the context of interacting (epistatic) pathways to explain performance and heterosis. Diverse molecular mechanisms that interpret DNA sequence into phenotype will be involved, and research to characterize pathways and fundamental molecular mechanisms will be important to understand heterosis in the context of diverse phenotypes, each independently displaying heterosis in specific genetic contexts.

There is no missing, gene-independent, unifying mechanism to explain heterosis—heterosis is the result of the diversity of genes, pathways, and processes known and yet to be discovered. Specific examples may highlight one mechanism or process in the context of a specific trait and genetic context, but those examples are just examples and do not overshadow the fact that extant natural variation is the resulting accumulation of the results of millennia of mutation and natural and artificial selection manifested in the organisms that we measure today. To say that there is no missing unifying mechanism is not meant to diminish the importance of fundamental research. Rather it is meant to highlight the importance of diverse fundamental experiments to ultimately understand biologically and economically important phenomena such as heterosis and to suggest that the final answer to the basis of heterosis will be the accumulation of results of many and diverse studies and not a singular, unifying, novel discovery.

Acknowledgments

The authors acknowledges support from the DOE Great Lakes Bioenergy Research Center (DOE BER Office of Science DE-FC02-07ER64494) and the National Institute of Food and Agriculture, United States Department of Agriculture Project WIS01330.

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