genetic-statistical analysis of growth in selected and unselected mouse lines

Experimental Animal Science

Genetic-statistical analysis of growth in selected and unselected mouse lines*

ULLA RENNE 1 , MARTINA LANGHAMMER 1, ERIKA WYTRWAT 1,

GERHARD DIETL 1 and LUTZ B~NGER 2

1 Research Institute for Biology of Farm Animals, Dummerstorf, Germany 2 Institute of Cell, Animal and Population Biology, University of Edinburgh,

Edinburgh, UK

Summary

The growth of males sampled from two mouse lines long-term selected for over 86 generations on body weight (DUG) or on protein amount (DUGP) was analysed from birth till 120 days of age and compared to the growth of an unselected control line (DUKs). Animals from the selected lines are already approximately 40 to 50% heavier at birth than the controls. This divergence increases to about 210 to 240% at the 120 day of age. With birth weights of 2.2 and 2.4 g and weights of 78 and 89 g at the 120 day these selection lines are the heaviest known mouse lines.

The fit of three modified non-linear growth functions (GOMPERTZ function, LOGISTIC function, RICHARDS function) was compared and the effect of three different data inputs elucidated. The modification was undertaken to use parameters having a direct biological meaning, for example: A: theoretical final body weight, B: maximum weight gain, C: age at maximum weight gain, D (only RICHARDS function): determines the position of the inflection point in relation to the final weight. All three models fit the observed data very well (r 2 = 0.94%0.998), with a slight advantage for the RICHARDS function. There were no substantial effects of the data input (averages, single values, fitting a curve for every animal with subsequent averaging the parameters).

The high growth of the selected mice is connected with very substantial changes in the final weight and in the maximum weight gain, whereas the changes of the age at the point of inflection were, although partially significant, relatively small and dependent on the model used.

Key words: Mice, long-term selection, body weight, growth function

*All procedures have been performed in accordance with German animal welfare legislation.

J. Exp. Anita. Sci. 2003; 42:218-232 Urban & Fischer Verlag http://www.urbanfischer.de/j ournals/jeansc 0939-8600/03/42/04-218 $15.00/0

Genetic-statistical analysis of growth in selected and unselected mouse lines 219

Introduction

Body weight is easy to measure in small mammals, e.g. mice and rats, and is usually obtained in many experiments at one or a few age points. How often and at which ages body weight is recorded is determined by the specific objectives of such experiments. But what if one wants to compare weights from the own experiment with those published by other authors or if one would like to map his weight data, gathered possibly on one sex of a certain mouse line, into the general landscape of mouse weights? For this it would be advantageous to have weights in every experiment at very many age points or at certain "standard" ages (e.g. at birth, weaning, at mating etc.). Such standards however are not

defined and weaning and mating ages vary widely between experiments. To improve this situation POILEY (1972) published growth tables (ages from 1 to over

100 days) of 38 widely used mouse lines to give growth references for many mouse lines. However, if the growth of animals over age could be described by a growth curve only 3 or 4 parameters would be needed per mouse, experimental group, sex, line etc. to describe their growth over a wide range of ages with sufficient accuracy. The change of growth caused by experimental factors or e.g. by growth selection could then be described by the change of the parameters of the growth curve, which can be tested with statistical standard methods.

Many different so-called growth functions have been used to relate the body weight to the age of the animals (e.g. TAYLOR, 1965; BAKKER, 1974; EISEN, 1976; GmLE et al. 1994-

1996). The RICHARDS function (RICHARDS, 1959) can be considered as the classical base equation for the description of the growth of animals and it is in general very flexible. This function, modified forms of it, and similar growth models were widely employed

and their principal usefulness seems indisputable (e.g. BA~Z~R, 1974; EISEN, 1976). With their help, large amounts of body weight data can be condensed to 3 or 4 parameters, which are usually sufficient to describe the development in body weight over age with high accuracy and allow interpolation, and to a certain extent some extrapolations.

The objectives of this study are: (1) to describe the growth of the two heaviest known mouse selection lines in order to allow these data to be used as a reference line for other studies, (2) to elucidate growth changes caused by growth selection, (3) to compare the fitting ability of three different growth functions, and (4) to investigate the effects of different forms of data inputs on the estimated parameters.

Materials and methods

A selection experiment was implemented 1975 in the Dummerstorf mouse lab, comprising two selection lines, selected on body weight (DU6) or protein amount (DU6P) at 42 days of age, and an nnselected control line (DUKs). This experiment has been described earlier in detail (BONGER et al., 1998) and will therefore here only be summarised (Tab. 1). The selection lines were derived from an outbred base population developed in 1969/70 by a systematic cross of 4 inbred and 4 outbred strains (SCH~LER, 1985). Selection was maintained for 106 generations and is still ongoing. The selection response in male body weight at 42 days till generation 106 is shown in Figure 1.

220 U. RENNE et al.

Table 1: Experimental design.

DUKs DU6 DU6P

generations 9 to 106 0 to 106 0 to 106

selection trait at random body weight at day 42 protein amount at day 42 of two test males of two test males (BW42) (PA 42)

selection procedure full sib groups for the sum of 2 test males per litter

litter size standardisation to 8/9 at birth

pairs/generation 80 80 80

Ne in generation 0 160 160 160

successful pairs (%) 95.13 69.47 80.16

proportion selected (%) 45.79 52.13 58.18

i (= SD/sdp) 0.09_+0.14 0.73_+0.17 0.65_+0.19

SD (g) 0.43 _+ 0.66 5.36 _+ 1.66 0.48 _+ 0.14

SD - selection differential (averaged over generations); sdp - phenotypic standard deviation; i - selection intensity

I - - D U K s f v - - D U 6 f v - - D U 6 P f v 1

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2e I I I I I I I I I I I I I I I I I I I I I 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105

g e n e r a t i o n

Fig. 1. Selection response in body weight 42 of the mouse lines DUKs, DU6 and DU6P over the generations. Means for 29 to 79 mate mice per data point (generation and line) are shown, fv: fitted function values using the EXPONENTIAL function (see below); ov: observed values. DUKs: unselected control, DU6: selection for high body weigt at 42 d, DU6P: selection for high protein amount in the carcass at 42d. For statistic description of the selection response in body weight a modified exponential model y = A - (A - C) exp [- B x / (A - C)] was used described by B~OER und HERRENDORFER, 1994. Parameter A (selection limit), B (maximum selection response) and C (initial value) were 92.6 g, 0.56 g/gen, 31.8 g in DU6 and 59.4 g, 0.60 g/gen and 30.1 g in DU6P, respectively.


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Male animals (n -- 18 to 19 per line) from generation 86 were randomly sampled from different litters from lines DUKs, DU6 and DU6P and weighed individually on Sartorius animal preci- sion scales (LC 620 S-0D2) from birth up to day 120 of life (ages: 0, 5, 10, 15, 21, 25, 30, 35, 42, 60, 80, 120 days). All experimental animals were reared together with the whole litter in PVC cages with a 255 cm 2 floor space till weaning (21 d). At weaning sexes were separated and the experimental animals were kept with their male full sibs in the same cage till 120 d. Mice were housed in a semi-barrier system under conventional conditions in a windowless mouse lab. Air was exchanged 12 times per hour and coarsely filtered (but no bacteria filter). The room temperature was between 22.4 and 22.7 °C, humidi- ty between 50 and 60% and a 12L :12D light cycle was applied. All in-going materials and objects were sterilised or disinfected and staff had to take a shower and disinfected hands and arms. Fixed formula food for laboratory mice (Altromin ® 1314: protein 22.5%, fat 5%, raw fibre 4.5%, ash 6.5%, germ reduced by heat during the production process, Altromin GmbH, Lage, Ger- many) was supplied ad libitum and fresh tap water was provided. Once per year the mice were checked for specific pathogens. These assays have been car- fled out by GIM Wildenbmch based on the recommendations of the Gesell- schaft f~r Versuchstierkunde - Society for Laboratory Animal Science (GV- SOLAS) and of the Federation of Euro- pean Laboratory Animal Science Asso- ciations (FELASA) (NICKLAS et al., 2002).

Three growth curves were fitted to the data describing the growth processes in the various mouse lines: the GOM- PE~TZ (GoMPERTZ, 1832; LAIRD et al., 1965; GmLE et al., 1994-96), the LOG~S- TIC (NELDER, 1961; MONTEIRO and FAL-

CONER, 1966) and the RICHARDS func-

tion (RICHARDS, 1959). To use parame-

222 U. RENNE et al.

ters, which are immediately biologically interpretable and to minimise least squares directly, modified forms of all three models have been employed, which were presented earlier (Br3NGER et al., 1982; Bi~NGER and SCHON~LDER, 1984), apart from the modified P, XCHARDS function (SCHON- FELDER, personal communication). The functions and some of their important characteristics are presented in Table 2. The definitions for the parameters used are as follows: A - theoretical final body weight (g) B - maximum weight gain (g/d) C - age at the maximum weight gain (d) D - (in PdCHAP, DS model only) position of point of inflection (PoI) in relation to A

The body weight at age C is = A/(D+I) lm. Additionally the effects of different data inputs on the estimated parameters were elucidated: • input 1: Weights per line were averaged for every age point and growth curves were fitted to

these 12 means per line. • input 2: Fitting of the growth curves to all individual body weights data (18 to 19 data points per

line and age) • input 3: Fitting of the growth curves for each individual mouse data set separately and averaging

the parameters per line. Statistical analysis was carried out using the SAS program package. The estimation of the

parameters of the growth functions was undertaken using the NLIN procedure of the SAS System for Windows Release 6.08 (SAS Institute Inc., Cary, NC 27513, USA). The means were pairwise tested using t- or Welch-test.

Results

To allow the use of the observed data for fitting additional growth models, the means

and standard deviations of body weight at all 12 ages and for all 3 lines are given in Table 3

together with the results of pairwise comparisons.

The mean 42 d weights calculated for all animals from the 3 lines in generation 86

(Fig. 1; DUKs: 27.5 g, DU6:62 .2 g, DU6P: 52.9 g) allow the conclusion that the sampled

animals (Tab. 3) are representative for these lines in generation 86.

Both selection lines are significantly heavier than the control line (DUKs) at birth and

this difference increases with age. The protein selected mice (DU6P) are even heavier

than those from the body weight selected line (DU6) at birth, but are outgrown by DU6

from 15 days onwards. Animals from the selected lines are about 40 to 50% heavier at

birth than the controls, and this divergence increases to 240 and 212% at 120 day of age.

The results of fitting growth curves to the observed weights are shown in Table 4 and 5

and a graphical illustration of the fit of the observed data for all three lines by the GOM-

PE~TZ (GM), the LOGISTIC (LM) and the RICHARDS model (RM) is given in Figures 2, 3

and 4, respectively.

In general all three models fit the growth of the control and selected lines quite well, as

the coefficient of determination varies between 0.949 and 0.998 only (Tab. 5). The RM

reaches the best fit, regardless of the form of the data inpu t and of the mouse line, which

is expected as this model has one parameter more than the other two models. Whereas the

body weight at inflection (BWI) is fixed in both three-parameter-models (LM: BWI =

Genetic-statistical analysis of growth in selected and unselected mouse lines

Table 3. Means (X) and standard deviations (s) for body weight (g) at different ages (t).

223

age DUKs DU6 DU6P day

n R s n R s n ~ s

0 18 1.59 c 0.14 19 2.198 0.16 18 2.38 a 0.28 5 18 3.42 b 0.57 19 5.51 a 0.93 18 5.70 a 0.70

10 18 5.66 b 0.79 19 9.73 a 0.77 18 9.22 a 0.98 15 18 7.31 ° 1.14 19 12.67 a 1.21 18 11.42 b 1.65 21 18 11.01 ° 1.92 19 21.57 a 1.94 18 19.69 b 2.37 25 18 15.25 c 2.41 19 32.16 a 2.62 18 28.338 2.63 30 18 20.68 ° 2.67 19 43.23 a 4.01 18 39.048 3.18 35 18 25.18 ~ 2.29 19 53.07 a 3.30 18 46.66 b 3.35 42 18 28.26 ° 1.86 19 62.21 a 2.83 18 53.39 b 3.53 60 18 32.17 c 2.16 19 77.04 a 4.04 18 62.188 4.00 80 18 34.10 ° 2.10 19 86.28 a 6.62 18 70.13 b 5.69

120 18 37.34 ° 4.07 19 88.71 a 7.57 18 78.31 b 9.66

Means sharing a common character in their superscript are not significantly different (P > 0.05).

A/2, GM: BWI = A/2.718 (e)) the denominator is determined by the parameter D in the

RICHARDS model (Tab. 2), which has to be estimated and thus enables the RM to be more

flexible. Concluding from the residual sums of squares the second best model is the LM

for the control line and the GM for the selection lines (Tab. 5). The better fit of the GM

function for lines DU6 and DU6P presumably reflects a change of the growth curves

caused by the selection on growth. This means the highest weight gain per day (-- point of

inflection, PoI) in unselected mice seems to be when about half of the final weight is

reached, as the PoI for the GOMP~RTZ and LOgiSTIC growth curve is fixed in relation to the

final body weight (A). The PoI of the RICHARDS function is not f ixed but has to be esti-

mated and can have different positions because it is a function of D. The denominators

(Tab. 2) in the GM and LM are 2.718 and 2.0, respectively, which means the BWI are

fixed at 37% and 50% of A. The denominator for the RM can be calculated from parame-

ter D (Tab. 2) and is, as expected, in the control line close to 2 (varies between 2.07 and

2.17), whereas it varies between 2.40 and 2.43 in DU6P and between 2.39 and 2.76 in

DU6, which is close to Euler 's number e, the denominator in the GM (Tab. 2).

Regardless of the model and the data input there is a very clear change in the growth

curve of the selected mice. Whereas the final weight (parameter A) for the control is esti-

mated between 34.9 and 36.3 g (over models and data inputs) the corresponding values

for lines DU6 and DU6P were 85.9 to 89.4 g and 72.0 to 76.5 g and are significantly

higher, by about 250 and 206%.

The maximum weight gain (parameter B) is estimated as 0.80 to 0.89 g per day in the

control. Animals from lines DU6 and DU6P gain 1.96 to 2.13 and 1.56 to 1.74 g per day,

respectively, which is a similar relative change as for the final weight.

224 U. RENNE et al.

Table 4. Growth curve parameters for body weight development.

Model Data input Para- DUKs DU6 DU6P

meter

mean s mean s mean s

GOMPERTZ Dam input 1 A 36.34 ° 0.96 89,04 a 1.47 75.42 b 2.17

B 0.83 c 0.06 1,96 a 0.08 1.57 b 0.11

C 21.59 ° 0.87 25.13 a 0.54 24.23 b 0.97

Data input 2 A 36.34 ° 0.41 89,04 a 0.71 75.42 b 0.86

B 0.83 ° 0.02 1,96 a 0.04 1.57 b 0.04

C 21.59 ° 0.37 25,13 a 0.26 24.23 b 0.38

Data input 3 A 36.39 c 3.08 89.44 a 5.86 75.80 b 8.44

B 0.84 c 0.07 1.97 a 0.21 1.58 b 0.11

C 21.75 b 1.99 25.31 a 1.41 24.39 a 1.99

LOGISTIC Data input 1 A 35.08 c 0.73 85.92 a 1.58 72.05 u 2.23

B 0.91 ° 0.06 2.12 a 0.12 1.74 ̀o 0.16

C 27.31 c 0.80 30.98 a 0.74 29.95 b 1.25

Data input 2 A 35,08 ° 0.34 85.92 a 0.63 72.05 b 0.76

B 0.91 c 0.02 2.12 a 0.05 1.74 b 0.06

C 27.31 c 0.37 30.98 a 0.29 29.95 b 0.42

Data input 3 A 35.12 c 2.76 86.24 a 5.25 72.38 b 7.42

B 0.92 ° 0.08 2.13 a 0.19 1.74 b 0.13

C 27.38 b 2.03 31.17 a 1.75 30.13 a 2.31

RICHARDS Data input 1 A 35.23 ° 0.84 87.99 ~ 1.53 75.55 b 2.72

B 0.84 c 0.06 1,99 ~ 0.09 1.56 b 0.12

C 26.08 ab 2.52 27.14 a 1.70 23.99 b 3.66

D 0.63 a 0.44 0.26 b 0.23 -0.03 c 0.37

Data input 2 A 35.39 c 0.88 87.99 a 0.76 75.55 u 1.02

B 0.88 c 0.07 1.99 a 0.04 1.56 b 0.05

C 25.89 b 2.60 27.14 ~ 0.84 23.99 c 1.37

D 0.67 a 0.48 0.26 b 0.11 -0.03 ° 0.14

Data input 3 A 35.72 c 3.61 88.89 a 6.78 76.45 b 10.37

B 0.91 ~ 0.12 2 .0P 0.26 1.59 b 0.13

C 25.47 ~b 4.31 26.95 ~ 2.38 24.00 b 2.54

D 0.83 b 0.85 0.30 ~ 0.46 0.06 a 0.40

Parameter estimates sharing a common character in their superscript are not significantly different (P > 0.05).

C o n s i d e r i n g the e s t i m a t e d age at the P o I it b e c o m e s c lear tha t the r e su l t s d e p e n d v e r y

m u c h o n the m o d e l (Tab . 4). F r o m the G M and L M o n e w o u l d c o n c l u d e tha t se lec ted ani-

m a l s are 2 to 3 d a y s o lde r at th is po in t . T h e r e su l t s o f the C e s t ima t e f r o m the R M s h o w a

d i f f e r en t p ic ture . I n d e p e n d e n t f r o m data input the con t r o l a n i m a l s are a b o u t 25.5 to 26 d

Genetic-statistical analysis of growth in selected and unselected mouse lines

Table 5. Residual sums of squares (RRS) and coefficients of determination (r2).

225

Model Data input DUKs DU6 DU6P

RRS r 2 RRS r 2 RRS r ~

GOMPERTZ Data input 1 15.61 0.991 32.25 0.997 66.83 0.991 Data input 2 1186.4 0.964 3600.4 0.983 4472.9 0.969

LOGISTIC Data input 1 12.47 0.993 52.44 0.995 104.4 0.986 Data input 2 1727.0 0.950 3984.1 0.981 5148.4 0.964

RICHARDS Data input 1 11.96 0.993 26.64 0.998 66.79 0.991 Data input 2 1129.9 0.966 3493.9 0.984 4472.1 0.969

1 O0 -

90

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70

50

o 40

30

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10

• DUKsov - - D U K s fv

,i. DU6 ov - - D U 6 fv

• DU6Pov ~ D U G P f v ~ •

[ ]

• l i

0 . . . . . . . . . . . . . . . . . l l l l l l I 0 10 20 30 40 50 60 70 80 90 1 O0 110 120

age (d)

Fig. 2. Development of body weight in lines DUKs, DUG and DUGP: GOMPERTZ function has been applied (data input 1). DUKs: unselected control, DU6: selection for high body weight at 42 d, DU6P: selection for high protein amount in the carcass at 42 d. fv - fitted function values; ov - observed values.

old. The males from line DU6 are about 0.5 to 1 d older, however the difference is mostly

non-significant. Males from line DU6P are on average about 2 days younger (about 24 d),

but again the difference is significant in one case only. The parameters A and B are

changed by selection in a very substantial way whereas the changes in the age at the point

of inflection are very small and mostly non-significant. As growth at this time (from

weaning till about 42 days) is almost linear, this parameter is hard to estimate.

226 U. RENNE et al.

100

90

8O

70

60

~ 50

N 4O

3O

20

10

i • DUKs ov ~ D U K s fv • DU6 ov ~ D U 6 fv • [] DU6P o v ~ D U 6 P ~

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, l : : ', ', 1 ', ', ', ', ', ', ', : ', ', 0 10 20 30 40 50 60 70 80

age (d)

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90 100 110 120

Fig, 3. Development of body weight in lines DUKs, DU6 and DU6P: LOGISTIC function has been applied. For further details see legend to Fig. 2.

100 1 T • DUKsov ~ D U K s f v

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6o • {

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10

0 0 10 20 30 40 50 60 70 80 90 ~ 00 110 120

age (d)

Fig. 4. Development of body weight in lines DUKs, DU6 and DU6P: RICHARDS function has been applied. For fitrther details see legend to Fig. 2.


2.0

1.8

1.6

1.4

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~ 1.0

o ~ O.8

0.6

0.4

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0.0 0 10 20 30 40 50 60 70 80 90 100 110 120

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Fig. 5. Description of growth rate as a function of the age in lines DUKs, DU6 and DU6P: PdCHAm)S function has been applied. For further details see legend to Fig. 2.

As differences in the age at the maximum weight gain between the lines are relatively small and only partially significant, the ages at the maximum of the curves for the growth rate (Fig. 5) therefore vary little compared with the maximum weight gain (amplitude of

the curves). The data input has in general no substantial effect on the parameter estimates (Tab. 4),

especially data input 1 and 2 produce very similar results, which means there is no difference if values per line and age will be averaged before fitting the growth curves or not. In both cases SAS provides approximate standard deviations. The advantage of data input 3, i.e. fitting a growth curve for each animal and averaging the parameter estimates over all individuals of a line, seems to provide better estimates for the standard deviation. This input allows the use of conventional statistical tests between line means like t- or WELCH-test.

Discussion

The lines DU6 and DU6P represent the longest growth selection experiments in mice with recently 106 completed generations and this experiment yielded the biggest selection response compared to all known growth selection experiments in mice, probably due to the length of the experiment, the population size used and the heterogeneity of the base population (BOHGER et al., 2001a). In DU6 the body weight at 42 d (selection age) was increased from initial 29.8 to 69.5 g (generation 106) and in DU6P from 30.1 to 55.30 g (Fig. 1).

228 U. RENNE et al.

2.6,

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• DU6P ov

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0.04 0.01 1.39 1.52

r z 0.965 0,901

! ! ! = ! . : ; : ; : .- : • . _. : • : : . ; ; ; : ;

10 20 30 40 50 60 70 80 90 100 t10 120 130

a g e (d}

Fig. 6. Development of the ratio between selection lines (SL: DU6 and DU6P) and control line body weight fitted by the exponential model, described in legend of Figure 1.

Growth of mice from the selection lines DU6 and DU6P:

This paper focuses on the description of the body weight from birth to 120 d of age in male mice of these two lines (Tables 2 and 3, Figs. 2, 3 and 4), which can be used as a ref-

erence to put mouse weights obtained in other experiments or of wild mice into a per- spective. The growth curves allow interpolation and to a certain degree also an extrapola- tion, although they usually underestimate weights in very old animals, which mostly have a small but more or less linear increase, probably due to fat aggregation, which the mod-

els do not account very well for (B/JNGER and SCH6NFELDER, 1984). DU6 and DU6P mice were with 2.2 and 2.4 g, respectively from birth onwards signifi-

cantly heavier than the control, which agrees with findings of GONEREN et al. (1996), who already report a growth difference in utero (from day 10 after fertilisation) between foe- tuses of a high and low body weight line. It is interesting to note that the selection on pro-

tein amount (DU6P) resulted in significantly higher birth weights than the selection on body weight (DU6), although DU6 animals reach substantial higher mature weights (Tab. 3). At 120 days the DUKs, DU6 and DU6P have multiplied their birth weight by a factor of 24, 41 and 33 and they reach average mature weights of 37, 89 and 78 g, respectively. The ratio of the selection line values to the control is increasing from 1.39 (DU6) and 1.52 (DU6P) at birth to 2.47 and 2.09 at 120 d (Fig. 6) reflecting that the body weights of the selection lines diverge with increasing age from those of the control line until they asymptotically approach final ratios of about 2.5 and 2.1, respectively.


A recent review on body weight limits in laboratory mice (BONGER et al., 2001a) focused on the growth of various world wide existing growth lines with special considera- tion of growth limits and described the development of some of those lines in detail, i. e. the LG/J strain (originated from GOODALE, 1938, 1941), the lines developed by BAKKER (1974) in the Netherlands, the Edinburgh growth lines (SHARP et al., 1984; BONGER and HILL, 1999) and the DU6. The DU6 line has been proven to be the heaviest mouse line and is for example with an approximate mature weight of 86 g ca. 1.7 fold heavier than the commercially available 'high growth' inbred line LG/J (Jackson Laboratories), which is derived from GOODALE'S line (for detailed discussion see BONGER et al., 2001a,b). This review excluded mice with very extreme fatness as ob/ob and db/db mice, which are homozygous for two recessive mutations, creating either deficiencies in leptin production or reception. Such mice sometimes can reach almost similar weights as the DU6 and DU6P, but mostly at a higher age and they contain almost 50% fat (B~)N6ER et al., 2002). The DU6 and DU6P are mouse lines, which tend to have an increased fatness, when compared with their unselected control DUKs at a higher age. But even at 120 days their fat content on average were only about 20 and 18%, respectively, (DUKs: 11%; BONGER et al., 1998).

G r o w t h c h a n g e s c a u s e d b y g r o w t h se lec t ion :

Although selection has changed the body weights and parameters A and B in both lines in a dramatic way, the principal shape of the growth curve is not altered, the change is

t , 0 '

0.9 ,

0 . 8 ,

0 , 7 ,

0 . 6 ,

0 , 5 ,

0.4,

0.3,

0 .2-

0 .1- d

0 . 0 i ; , ; -" ; -" -" -" -" " " ; ; ; ; ; ; , ] ] I I I I

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Fig. 7. Development of the ratio between the body weight at every age point and the mature weight (parameter A) using the function values of the RM with data input 1 (Tab. 4).

230 U. RENNE et al.

rather 'proportional'. Essentially, one needs to multiply parameter A by about 2.5 and 2.1 (DU6, DU6P) and parameter B by 2.36 and 1.85, respectively (Tab. 4; example RM, data input 1) and keeping C more or less constant to transform the growth curve of a control mouse into one of the selection lines.

Results reported here in principle agree very well with a growth description of mice of the same lines from 0 to 120 days of age, which was given in generation 32 (BON~ER, 1987), also using a GOMPERTZ function. As there were 54 generations of intense selection between this earlier study and the recent experiment, the comparison to those values opens an additional opportunity to elucidate the effects of selection on the growth curve parameters. The weight at birth was significantly increased as well and the estimated mature weights (A) were: 41.4 g (DUKs), 77.3 g (DU6) and 67.8 g (DU6P), which are obviously lower in both selection lines than in the recent study (36.3, 89.0, 75.4 g; Tab. 4). This is expected as there was further substantial selection response from generation 32 till 86 (Fig. 1). Therefore the estimates for the maximum weight gain in lines DU6 (B = 1.45 g/d) and DU6P (B -- 1.30 g/d) in generation 32 were also lower than in this study, whereas the estimates for the DUKs agreed well (Bgen 32 = 0.84 g/d Bge n 86 = 0.83 g/d; Tab. 4). The age at which animals reach a maximum weight gain did not change substantially from gen 32 till now despite the high selection response (DUKs: 21.8 d vs. 21.9 d; DU6: 26.2 d vs. 25.1 d; DU6P: 24.6 d vs.24.2 d, with the first value from gen 32 and the second from gen 86). This within line comparison 'gen 32 vs. 86' confirms the results from the comparison of the selection lines with the control in one generation (here 86), with strong changes in the estimated final body weights (2.5 and 2.1 fold) and the maximum body weights gains (2.4 and 1.8 fold), whereas changes in the age at the maximum gain are relatively small (Tab. 4).

Another noticeable change in the body weight development by selection is in the ratio of body weights at earlier ages in relation to the final weight, indicating the degree of maturity. A plot of this ratio over age shows, that the control is maturing faster than both selection lines, with differences from about 3 to 8% (Fig. 7).

F i t t i ng ab i l i ty o f t h ree d i f f e r e n t g r o w t h fu n c t i o n s :

All three models used here, proved to be very good in fitting the observed data, although the RM was generally slightly superior, due to the use of a forth parameter. Comparing the other two models, which using three parameters, the LM fitted the data of the control better, whereas the GM was slightly superior for the selection lines, probably reflecting a small change of the point of inflection (parameter C) in relation to the mature weight (A) by selection. TIMON and EISEN (1969) compared the LM and RM to describe the growth curve of mice selected on postweaning gain and reported also only slight differences in the fitting ability of both models. In a similar approach EISEN et al. (1969) compared the LM, GM and the BERTALANFFY model for the description of mice selected divergently on 42 d body weight, where he found a slightly better fit of the LM for the high selected mice and the controls, whereas all three models fitted very well the growth of the small mice.


It is interesting to note, that the fit of growth curves also depends very much on the age

span involved e.g. the LM underestimated the mature body weights at 120 d more than

the other models (Fig. 2-4)

However, if it will be possible to include body composition measurements on living

animals into a future experiment and to extend the time period much over 120 d it may be

feasible to dissect further differences in growth trajectories. For example, from about 60 d

onwards there are line differences (Fig. 2.4), which could be fitted simply by linear

regression, but probably reflecting only differences in fat aggregation.

Effects of different forms of 'data inputs' on the estimated parameters:

There were no substantial effects of the 'data input' on the parameter estimates (Tab.

4), especially data input 1 and 2 produced very similar results. This indicates that the

parameter estimates are only slightly affected if the values per line and age will be aver-

aged before fitting or if all data points were used in the fitting procedure. In both cases

SAS provides approximate standard deviations. However, there is a clear advantage of

data input 3, i.e. fitting a growth curve for each individual and averaging afterwards the

obtained parameter estimates over all animals per line. This approach seems to provide

more realistic estimates for the variance of the parameters and allows the use of conven-

tional statistical tests for the comparison of line specific parameter estimates like the t- or

WELCH-test.

Acknowledgements The work of LB was partially funded by a Grant from Cotswold International. We thank

William G. Hill, Hermann H. Swalve, Charlotte Bruley and D. Halligan for comments and sugges- tions on the manuscript, Sabine Hinrichs and Heidemarie Bittner for technical assistance.

References

BAKKER, H. 1974. Effect of selection for relative growth rate and body weight of mice on rate, composition and efficiency of growth. Mededelingen-Landbouwhogeschool-Wageningen 74: 1-94.

BONGER, L. 1987. Direct and correlated effects of long-term selection for different growth traits in laboratory mice. Genetische Probleme in der Tierzucht, FzT Dummerstorf-Rostock Heft 13: 1-90.

BfJNGER, L., J. FORSTING, K. L. McDONALD, S. HORVAT, J. DUNCAN, S. HOCHSCHEID, W. G. HILL, and J. R. SPEAKMAN 2002. Long-term divergent selection in mice indicates regulation system for body fatness that is independent of leptin production and reception. FASEB J 10.1096/fj.02- 0111fje.

BONGER, L. and W. G. HILL 1999. Inbred lines derived from long-term divergent selection on fat content and body weight. Mammalian Genome 10, 645-648.

BONGER, L., A. LAIDLAW, G. BULF1ELD, E. J. EISEN, J. F. MEDRANO, G. E. BRADFORD, F. PIRCHNER, U. RENNE, W. SCnLOTE, and W. G. HILL. 200lb. Inbred lines of mice derived from long-term growth selected lines: unique resources for mapping growth genes. Mammalian Genome 12: 678-686.

232 U. RENNE et al.

BONGER, L., U. RENNE, G. DIETL, and S. KUHLA. 1998. Long-term selection for protein amount over 70 generations in mice. Genetical Research 72: 93-109.

BONGER, L., U. RENNE, and R. C. BuIs. 2001a. Body weight limits in mice - Long-term selection and single genes. Encyclopedia of Genetics (Reeve, E. C. R., ed), 337-360, Fitzroy Dearborn Publishers, London, Chicago.

B•NGER, L. and E. SCHONFELDER. 1984. Lifetime performance of growth selected lab mice females - growth curve. Probleme der angewandten Statistik 11:185-199.

B~NGER, L., E. SCttONFELDER, and L. SCULLER. 1982. Evaluation of stress tolerance in laboratory mice - ontogenesis of endurance fitness. Zoologische Jahrbticher-Abteilung Allgemeine Zoolo- gie und Physiologie der Tiere 86: 141-147.

EISEN, E. J. 1976. Results of growth curve analyses in mice and rats. Journal of Animal Science 42: 1008-1023.

EISEN, E. J., B. J. LANG, and J. E. LEGATES. 1969. Comparison, of growth functions within and between lines of mice selected for large and small body weight. Theoretical and Applied Ge- netics 39: 251-260.

NICKLAS, W., P. BANEUX, R. BOOT, T. DECELLE, A. A. DEENY, M. FUMANELLI, and B. ILLGEN- WILCKE. 2002. Recommendations for the health monitoring of rodent and rabbit colonies in breeding and experimental units. Laboratory Animals 36: 20-42.

GILLE, U., F. V. SALOMON, O. RIECK, A. GERICKE, and B. LUDWIG. 1994-96. Growth in rats (Rattus- norvegicus berkenhout). 1. Growth of body-mass - a comparison of different models. Journal of Experimental Animal Science 37:190-199.

GOODALE, H. D. 1938. A study of the inheritance of body weight in the albino mouse by selection. J. Hered. 29: 101-112.

GOODALE, H. D. 1941. Progress report on the possibilities in progeny test breeding. Science 94: 442-443.

GOMPERTZ, B. 1832. On the Nature of the Function Expressive of the Law of Human Mortality, and on a New Mode of Determining the Value of Life Contingencies. Philos. Trans. R. Soc. Lond. B. Biol. Sci. 123: 513-585.

GONEREN, G., L. BiNGER, I. M. HASTINGS, and W. G. HILL. 1996. Prenatal growth in lines of mice selected for body weight. Journal of Animal Breeding and Genetics 113: 535-543.

LAIRD, A. K., S. A. TYLER, and A. D. BARTON. 1965. Dynamics of normal growth. Growth 29: 233-248.

MONTEIRO, L. S. and D. S. FALCONER. 1966. Compensatory growth and sexual maturity in mice. Animal Production 8: 174-192.

NELDER, J. A. 1961. The fitting of a generalization of the logistic curve. Biometrica 17:89-110. POILEY, S. M. 1972. Growth tables for 66 strains and stocks of laboratory animals. Laboratory Ani-

mal Science 22: 759-779. RICHARDS, F. J. 1959. A flexible growth function for empirical use. J. exp. Botany 10: 290-300. NCHI3NFELDER, E. personal communication. SCHOLER, L. 1985. The mice outbred strain Fzt: DU and its application in animal breeding research.

Archives of Animal Breeding 28: 357-363. SHARP, G. L., W. G. HILL, and A. ROBERTSON. 1984. Effects of selection on growth, body composi-

tion and food intake in mice. 1. Responses in selected traits. Genetical Research 43, 75-92. TAYLOR, S. C. S. 1965. A relation between mature weight and time taken to mature in mammals.

Animal Production 7: 203-220. TIMON, V .M. and E. J. EISEN. 1969. Comparison of growth curves of mice selected and unselected

for postweaning gain. Theor. Appl. Genetics 39:345-351.

Corresponding author: ULLA RENNE, Department of Genetics and Biometry, Research Institute for the Biology of Farm Animals, Wilhelm-Stahl-Allee 2, 18196 Dummerstorf, Germany Tel.: ++49-38208-68920; Fax: ++49-38208-68602; e-mail address: [email protected]

genetic-statistical analysis of growth in selected and unselected mouse lines

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