66, 233-249 relationship between abundance and body size

Journal of Animal A critical assessment of the form of the interspecific Ecology 1997,

66, 233-249 relationship between abundance and body size in animals TIM M. BLACKBURN* and KEVIN J. GASTONt

*NERC Centre for Population Biology, Imperial College at Silwood Park, Ascot, Berkshire SL5 7PY, UK; and tDepartment of Animal and Plant Sciences, University of Sheffield, Sheffield SIO 2TN, UK

Summary

1. Despite a wealth of studies for a wide variety of animal assemblages, the form of the interspecific relationship between abundance and body size is still contentious. At

least three different patterns have been suggested, which can broadly be characterized as negative and linear, negative but non-linear, and polygonal. At least eight different mechanisms have been suggested whereby the linear (or non-linear) and polygonal patterns can be reconciled. 2. We collated data from the literature on over 500 interspecific plots of the abundance-body size relationship with two aims. First, to examine the extent to which published studies support the different forms proposed for the relationship; and secondly, to test whether any of the mechanisms that have been suggested to reconcile linear and polygonal patterns actually do so. 3. The data revealed that abundance-body size relationships commonly assume both linear negative and polygonal forms. Around 25% of all plots of the relationship show a positive regression slope. 4. Of the eight mechanisms that have been suggested to reconcile linear and polygonal

patterns, we were able to test five. Of these, only the measure of density used by a study explains none of the observed variation in abundance-body size relationships. Variation in the regression slope between studies is only explained by the type of data

used (compilations vs. samples) and the scale of study (local vs. regional): compilation studies at regional scales show more linear negative relationships, while sample studies

performed at local scales show more polygonal patterns. General linear modelling indicates that study scale is the most important factor influencing when different relationships are likely to arise. 5. Our results show that different patterns tend to arise at different scales of study, but

say nothing about whether the patterns are real or artefactual. Polygonal relationships potentially contain an artefactual component, resulting from sampling methodology inadequate to elucidate the abundances of the less common species in any given assemblage. However, the presence of a sampling artefact does not indicate the shape of the underlying relationship from which a sample is taken, or indeed whether samples would exhibit any other shape were artefacts excluded. 6. Linear and polygonal patterns are not necessarily mutually exclusive, but may both indicate the 'true' abundance-body size relationship at different spatial scales. We conclude by suggesting that much more attention be paid to the effect of spatial scale on this relationship, especially given that scale of measurement can have subtle but severe consequences.

Key-words: abundance, allometry, animals, body size, macroecology.

Journal of Animal Ecology (1997), 66, 233-249

^~ ~~Introduction , .the interactions that determine the distribution and Introduction ? 1997 British abundance of organisms (Krebs 1972; after Andre- Ecological Society Ecology has been defined as the scientific study of wartha 1961). Therefore a considerable body of bio-

233

This content downloaded from 38.66.77.2 on Thu, 06 Jul 2017 12:50:29 UTCAll use subject to http://about.jstor.org/terms

logical literature has been devoted to documenting patterns of distribution and abundance, and to identi- fying the mechanisms that generate those patterns (see

reviews in Krebs 1972; Begon, Harper & Townsend 1990; Gaston 1994; Brown 1995), as an early step on the road to understanding how the great diversity of life is structured. A good proportion of this literature has focused on the identification of characteristics of

organisms that are associated with the abundance and distribution they attain, in the hope that association

may to some degree reflect causation. In animal ecol-

ogy, one association that has received particular atten-

tion, at least since it was given prominence by Elton (1927), is the interspecific relationship between body size and abundance in animals.

The relationship between abundance and body size has been one of the most extensively studied interspecific patterns in ecology (see reviews in Cotgreave 1993; Blackburn & Lawton 1994). In excess of 50 papers have dealt with the subject, and the relationship has been documented for species from most major environments and taxa. Unfortunately, this has not led to a consensus over the nature of the under-

lying patterns, let alone the mechanisms which generate them. These two issues are tightly bound, because the mechanism favoured will depend on the relationship it is required to explain.

Logically, a small-bodied species has the capacity to be more abundant than one of large size. The upper

limit on possible abundance is set by the number of individuals that can physically be packed into a given

area (or volume for species living in three dimensions;

e.g. Nee, Harvey & Cotgreave 1992). In practice, this maximum density is never (or perhaps seldom) achieved because resource requirements cannot be satisfied under such extremes of packing. Never- theless, since resource requirements scale positively with body size (Peters 1983; Calder 1984; Reiss 1989), the maximum density attainable by species should scale negatively with size.

There are also reasons to believe that the minimum

density a species can sustain scales negatively with body size (Lawton 1989, 1990). At the limit, no sexual

species can exist when so widely dispersed that finding a mate and reproducing are unlikely events within the

lifetime of an individual. In most taxa, large-bodied species are more vagile and longer-lived than small- bodied (Lindstedt & Calder 1981; Calder 1984; Read & Harvey 1989; Sether 1989), so they should be able to persist at lower densities. Populations of large- bodied species may also fluctuate less, so that large- bodied species have lower minimum viable population sizes (Pimm 1991; Lawton 1994). In combination with the expectation that maximum densities scale negatively with body size, the general relationship between body size and density should therefore also be negative. A number of studies support this prediction, when both body size and density are logarithmically transformed (Damuth 1981, 1987; Peters & Raelson

1984; Marquet, Navarette & Castilla 1990; Nee et al. 1991; Peters & Wassenberg 1993; Strayer 1994; Ebenman et al. 1995; Fig. la). In other words, density (D) scales with body size (M) as D = cMY, where c is a constant and y is negative.

Many other studies have found relationships that are not simply negative and linear. For example, Brown & Maurer (1987) calculated the abundances of land birds, using data from the North American Breeding Bird Survey. Plotted against body mass, they

produce a complex 'polygonal' relationship (Fig. lb). Maximum abundance peaks at intermediate, not the smallest, body masses, while minimum abundance is constant across all masses. Similar relationships have been shown in a wide variety of taxa (e.g. Morse, Stork

& Lawton 1988; Gaston 1988; Basset & Kitching 1991; Novotny 1992; Blackburn et al. 1993a; Cotgreave, Middleton & Hill 1993; Blackburn & Lawton 1994; Cambefort 1994; Nilsson, Elmberg & Sjoberg 1994). While the precise details differ between studies, poly-

gonal relationships are typically characterized by the absence of a marked increase in the minimum abun-

dance of small-bodied species, and by a low correlation between abundance and size. Frequently,

E

0

0

a,

10 -(a) 104 -

103 - 4

102 -

101 -

100 -

10-2 -

10?

h 100 I0 -W

0

U)

? 10 U)

0 0

Z=l

u, r_

9.

0

,*

0

S

101 102 103 101 101 106 101

:?.?

0

@0 0 0

0* f,m

i. .*; ?0 *es 1 10 100 1000

Body mass (g)

0

0

S

10000

Fig. 1. The relationship between body mass (g) and (a) density (numbers per km2, n = 467) for a selection of mammals of the world (from Damuth 1987), and (b) density (individuals per BBS route, n = 380) for North American land birds (Brown & Maurer 1987).

234

Animal

abundance-body size relationships

? 1997 British

Ecological Society Journal of Animal Ecology, 66, 233-249


peak abundance is at intermediate body sizes, and sometimes the overall relationship is actually positive.

Recently, evidence has been presented for a third pattern in abundance-body size relationships that combines some features of the previous two (Damuth 1993; Marquet, Navarette & Castilla 1995; Silva & Downing 1995). This is derived from work on mammalian primary consumers and suggests that the relationship is essentially negative, but non-linear; density generally increases as body mass decreases, but peak abundance is attained between 0-1 and 1 kg, not by species of minimum mass (this feature is actu-

ally shown by Fig. la). Although the slope of the over-

all relationship is -0-75, slopes plotted within taxa tend to be shallower for those with species generally

smaller than 1 kg, and steeper for taxa with species generally heavier than 1 kg. Species near 1 kg attain higher densities than expected from a -0 75 relationship, altering the slope within the taxa to which they

belong (Damuth 1993). Silva & Downing (1995) show similar effects for mammalian herbivores, insectivores

and carnivores. In addition, they find that the lowest

density is not attained by the largest species; LOWESS regression indicates that the slope levels out at large sizes. The reason is unclear, although Silva & Down- ing suggest a number of possibilities, including that large mammals may make more efficient use of resources, or that very low density populations may simply not be viable.

Reconciling the different relationships

In sum, despite strong theoretical reasons for expect-

ing a negative abundance-body size relationship, the evidence for such a pattern seems ambiguous. Eight mechanisms have been proposed to explain why different relationships have been obtained, and in par-

ticular to reconcile why linear and polygonal patterns

may both be found. Different patterns have been hypothesized to result: 1. From comparisons across different kinds of data (Lawton 1989). In general, simple linear negative relationships are obtained for data compiled from a wide variety of literature sources. These sources are often single- or few-species studies from a range of geographic areas, and densities may have been estimated using a wide variety of methodologies. Con- versely, polygonal relationships are generally recovered when single areas are sampled to give abundance estimates for all the species in a given taxon

that are present, usually using a single or consistent method.

2. From samples at different spatial scales (Lawton 1989, 1990). Polygonal relationships tend to arise from

studies performed at local or restricted sites (e.g. Morse et al. 1988), whereas linear negative relationships tend to arise as the geographic coverage or geographic spread of data increases. 3. From differences in the density measures used

(Damuth 1987, 1991; Lawton 1989). Linear negative relationships are typically characterized as arising from plots of ecological densities, and polygonal relationships from crude densities. Ecological density is generally defined as the density of a species in suit-

able habitat, and crude density as the density of a species in a sample from a given area (e.g. Damuth 1981, 1987; Gregory & Blackburn 1995; Silva & Downing 1995). 4. Because of differences in the ranges of variation represented by the species included in the plots (Law-

ton 1989). Linear negative relationships are typically obtained from plots spanning several orders of magnitude of body sizes or abundances, whereas the ranges spanned by species in polygonal relationships are typically, although not always, less. Polygonal relationships are therefore often suggested to be simply

segments of an overall linear negative relationship, which would be recovered if the range of body sizes in the polygonal relationship was increased. 5. Because polygonal relationships are random samples from an underlying abundance-body size relationship (Blackburn, Harvey & Pagel 1990; Blackburn, Lawton & Pimm 1993b; Currie 1993). Blackburn et al. (1990) showed that a polygonal relationship between abundance and body size could arise as a result of random sampling of individuals from an underlying distribution where there was no relationship between abundance and body size (see also Blackburn et al. 1993b). Currie (1993) gave visual, although not statistical, evidence that a polygonal relationship could be generated by random samples from a linear negative relationship, within the same restricted range of body sizes. 6. Because of differences in how taxa utilize space (Juanes 1986). In some cases, a polygonal relationship

may be recovered if species in a taxon utilize the environment in three spatial dimensions. Since densities are generally measured in terms of areas (at least

in the terrestrial environment), the linear negative relationship between density and body size may break

down if species are actually utilizing different volumes

of space. That birds are perceived generally to show weaker abundance-body size relationships than mammals has been argued to result from this effect (Juanes

1986; Cotgreave & Harvey 1992). 7. Depending on the taxonomic composition of the assemblage (Nee et al. 1991; Silva & Downing 1995). Abundance-body mass relationships are often positive within taxa at low taxonomic levels (e.g. tribes or genera) (Nee et al. 1991; Blackburn et al. 1994). Further, analyses of mammalian assemblages show non-linear relationships, so that large-bodied species have densities that are higher than expected, and small-bodied species have densities that are lower (Damuth 1993; Silva & Downing 1995). Analyses of closely related species, or mammal assemblages composed entirely of small-bodied or large-bodied species, might then be expected to show a non-significant, or

235

T.M. Blackburn &

K.J. Gaston

? 1997 British

Ecological Society Journal of Animal

Ecology, 66, 233-249


even positive, relationship, even if completely sampled, because that is the underlying global relationship for that range of body sizes. 8. Because of the effect of migrant species (Damuth 1987; Cotgreave 1994b). The abundances of migrant species may be influenced by factors outside the area in which they are censused. Assemblages with high proportions of migrant species (principally bird assemblages) may therefore show weaker abundance- body size relationships.

All eight mechanisms are plausible, albeit some more than others. However, no systematic evaluation of the alternatives has been undertaken, although the

body of published studies is now more than adequate to test at least some of them. Many of the mechanisms

assert that a polygonal relationship arises as a cor- ruption of a negative linear relationship between abundance and body size. However, there has been no quantitative assessment of the form of the relationship

found in the studies so far published. In the remainder

of this paper, we examine the extent to which published literature supports the hypothesis of a negative

relationship between abundance and body size, and test whether the mechanisms that have been suggested

to reconcile different patterns actually do so. We have

limited consideration to the relationship between abundance and body size across species; the question of what mediates phylogenetic patterns in the form of

the relationship within taxa (e.g. Nee et al. 1991, 1992;

Cotgreave & Harvey 1992, 1994; Blackburn et al. 1994; Cotgreave & Stockley 1994; Cotgreave 1994a,b, 1995) is an interesting, but separate, issue.

Methods

A review of the ecological literature yielded information on over 500 different plots of the abundance-

body size relationship, including over 300 for which quantitative data on its form (e.g. regression slope, coefficient of determination, sample size) were available (data from Damuth 1981, 1987, 1993; Peters & Wassenberg 1983; Juanes 1986; Robinson & Redford 1986; Strayer & Likens 1986; Brown & Maurer 1986, 1987; Gaston 1988; Macpherson 1989; Owen & Gil- bert 1989; Marquet et al. 1990; Basset & Kitching 1991; Maurer, Ford & Rapoport 1991; Nee et al. 1991; Cotgreave & Harvey 1992; Griffiths 1992; Novotn'y 1992; Cotgreave et al. 1993; Currie & Fritz 1993; Blackburn et al. 1993a, 1994; Blackburn & Lawton 1994; Cambefort 1994; Cotgreave & Stockley 1994; Nilsson et al. 1994; Thiollay 1994; Cotgreave 1994a, 1995; Ebenman et al. 1995; Gregory & Blackburn 1995; Silva & Downing 1995; Greenwood et al. 1996). The relationships compiled included assemblages spanning a wide variety of taxa, trophic groups, geographic regions and habitats (Table 1), and from three to 856 species (mean = 69). Some of the data sources were previous compilations, and others included sum- maries of the form of the relationship for a large

number of local assemblages without formally pre- senting the results for each one (e.g. Juanes 1986; Cotgreave & Harvey 1992; Cotgreave et al. 1993; Cotgreave & Stockley 1994). An exhaustive review of the literature would probably turn up many more studies.

We categorized each estimate of the abundance- body size relationship in an assemblage as either inde-

pendent or dependent. The question of what con- stitutes an independent estimate is difficult to answer

unambiguously. For example, Damuth (1987) pro- duced a plot of the abundance-body size relationship using data from 667 species from taxa spanning vir- tually the entire range of the Kingdom Animalia. One

could argue that since any other relationship must involve data that are a subset of the Animalia, all others are a subset of this one. More problematically, many of the relationships plotted by Brown & Maurer

(1986) for local bird assemblages use abundance estimates for subsets of the species in the abundance- body size plot for North American landbirds (Brown & Maurer 1987). We defined a relationship as independent if there was no reason to believe it was based

principally on a subset of the actual data used for any other abundance-body size relationship in the literature. Under this definition, both examples above are actually independent; although the same species in the same geographic areas may appear in more than one relationship, it is unlikely that any of the relationships defined as independent are dependent on the form of any other. Examples of relationships that

we defined as dependent on data from a more general plot include the 'constructed communities' presented by Damuth (1981), the dietary subsets of the Neo- tropical forest mammal relationship in Robinson & Redford (1986), and the dung beetle plots from sub- sites of the South African game reserve faunas presented by Blackburn et al. (1993a). Independent and dependent plots were considered separately in our analyses.

For each abundance-body size relationship, we also recorded the following information.

DATA TYPE

Relationships were separated on the basis of whether they used data compiled from a wide variety of litera-

ture sources (compilation studies), or from samples of single areas (usually using a single or consistent method) giving abundance estimates for all the species in a given taxon or assemblage that inhabit the area (sample studies).

SPATIAL SCALE

We separated relationships on the basis of whether they were plotted at local or regional scales. In general,

a relationship was considered to be plotted at the regional scale if it encompassed the fauna of a geo-

236

Animal


? 1997 British


Ecology, 66, 233-249


237

T.M. Blackburn &

K.J. Gaston

Table 1. A summary of the characteristics of the 330 assemblages for which quantitative data on abundance-body size relationships were available. This tabulation includes dependent and independent estimates. Note that not all assemblages can be classified to one of the categories in each set (e.g. many include primary and secondary consumers), so that not all sums equal 330

Environment n Region n Taxon n Trophic level n

Terrestrial 253 Tropical 100 Invertebrate 64 Scavenger 25 Aquatic 36 Temperate 155 Vertebrate 259 Primary consumer 77

Both 7 Secondary consumer 37 North America 68 Omnivore 6 South America 39 Insect 41

Europe 35 Fish 22 Africa 71 Bird 78 Asia 16 Mammal 157

Australia 3

political unit (e.g. Ivory Coast, Sweden, 'Basque coun- try') or was a compilation of data for taxa across several regions (e.g. figure 1 in Damuth 1981). It was considered to be at the local scale if it encompassed the fauna of a restricted site or habitat (e.g. Richmond

Park in England, tropical grassland in Uganda), even if the data were compiled from wider sources (e.g. table 1 in Damuth 1981). Few studies raised the com- plications of intermediate scales.

DENSITY MEASURE

Relationships were separated on the basis of whether they used crude or ecological densities. Assigning a density measure to one or other category can be difficult. Although they are frequently considered as if distinct dichotomous states, crude and ecological densities are better thought of as two ends of a spectrum that can be calculated for any given species, because 'suitable habitat' is not readily defined. We assumed that densities were crude if measured in a

given area for all species (e.g. Morse et al. 1988), and ecological if measured on a species-by-species basis (e.g. Damuth 1981), unless the opinions of the authors were otherwise.

BODY SIZE RANGE

We recorded the range of body masses across which an

abundance-body size relationship was plotted, using only those where body mass was the size measure, or

where length could be converted to mass using a length-mass regression (e.g. Blackburn et al. 1993a). This variable could not be normalized by trans- formations, and so was analysed non-parametrically.

DIMENSIONALITY OF ASSEMBLAGE

Relationships were categorized depending on whether the taxa use the environment in two or three dimen-

sions. The latter category includes bird, tree canopy and pelagic aquatic assemblages; the former category consists mainly of assemblages of non-volant

mammals, but includes several benthic fish, dung beetle

and flightless bird assemblages. Relationships plotted with subsets of species that could be assigned to both categories (e.g. plots including non-volant mammals and bats) were excluded from analysis of this variable.

Simple linear negative relationships between abun-

dance and body size differ from polygonal relationships in the amount of variance in abundance that is

explained by body size, and in the magnitude of the regression slope. To test whether each of the above mechanisms explains the difference between linear and

polygonal relationships, we asked whether there were consistent differences in the slopes and coefficients of

determination (r2-values) of relationships depending on how they were classified. For example, if linear and

polygonal relationships result from different density measures, we would expect relationships plotted with crude densities to have lower coefficients of deter-

mination and higher (i.e. less steeply negative) slope values than relationships plotted with ecological densities. Only regression slopes calculated using the method of ordinary least squares (OLS, or model I) were used for the purposes of comparison. Coefficients

of determination were square root transformed for analysis (note that the square root of r2 does not equal r, but does equal Ir ), to conform better with the

assumptions of OLS regression analysis. Ideally, we would have tested the relationship between body size and the residuals from abundance-body size regression; residuals from polygonal and linear relationships should show different patterns. However, data were available for too few of the abun-

dance-body size plots to make this a practical option.

Results

Qualitative information on the sign of the model I regression slope was available for 534 of the abundance-body size relationships. Four-hundred and three relationships had negative slopes, 129 had positive slopes and two slopes were exactly zero (as reported); therefore, 25% of these studies did not show negative relationships. Quantitative information

? 1997 British



on the model I regression slope was available of these relationships. The frequency histogra

291 slopes for which body size was measured showed a pronounced peak between -0 5 ar with a mean slope value of -0 51 (Fig. 2a). per cent of these quantitative slopes were pc

just the subset of 119 independent relations] considered, this rose to 23%.

Quantitative information on the coefficient

mination was available for 326 studies. Body s

often explained little of the variance in ab (mean + SE = 0-33 + 0-017; Fig. 2b); the so true if the sample was restricted to independ

mates (mean + SE = 0 18 + 0 019). The m: of the coefficient was negatively correlated size of the assemblage (Spearman rank cor rho = -0-18, n = 326, P = 0-0012), but this ship disappeared when analysis was restricted

pendent estimates (rho = 0-02, n = 133, P = sum, despite sound theoretical reasons for e a negative abundance-body size relationshi plethora of studies, the ability of body size t(

80 - (a)

0

a

U-

LL

I

60 -

40 -

2u - _

-45 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0-5 0

OLS regression slope

60

40

20

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Coefficient of determination

? 1997 British


Ecology, 66, 233-249

Fig. 2. (a) The frequency distribution of model I : slopes from 291 plots of abundance against body m zontal axis labels indicate the lowest slope valu histogram bar; for example, the first bar includes st regression slopes from -4-25 to -4-01. (b) The distribution of coefficients of determination from 3:

abundance against body mass. Horizontal axis labe the lowest coefficient value in each histogram bz case; for example, the first bar includes stu coefficients from 0 to 0-049.

for 303 population densities is generally weak, as has been Lm of the noted several times before with smaller data sets

as mass (Blackburn et al. 1993a; Blackburn & Lawton 1994; id - 10, Blackburn, Lawton & Gregory 1996). Thirteen Despite qualitatively similar distributions of )sitive; if regression slope signs, dependent and independent hips was relationships showed quantitative differences. Slopes

from independent estimates of the abundance-body of deter- size relationship were significantly shallower than size most those based on data subsets (Table 2). Body mass undance also explained different amounts of the variance in tme was abundance when dependent and independent esti- lent estimates were used (Table 2). Further consideration of agnitude the different abundance-body size relationships is with the based on independent estimates, except where indi- -relation, cated otherwise. relation- Abundance-body size relationships based on com- l to inde- pilation data had significantly higher coefficients of 0-84). In determination, and more steeply negative slopes, than xpecting relationships based on sample data (Table 3). In fact, p, and a the difference between independent and dependent o predict data in estimates of the slope and coefficient of deter-

mination of the abundance-body mass relationship (Table 2) disappeared once the data type used was taken into account (Fig. 3). This was principally because most (90%) independent estimates were from sample data, and most (63%) dependent estimates used data subsets from wider compilations. Regression slopes were significantly more steeply negative and coefficients of determination were significantly higher in studies performed at regional scales (Table 4). This was not a consequence of local studies predominantly using sample data; both scale of study and data type explained significant amounts

Mi of the variation in both regression slope and coefficient of determination (Fig. 4).

Studies using crude and ecological densities showed no significant differences in either regression slopes or

coefficients of determination of the relationships they

reported (Table 5). The apparent relation of abundance-body size pattern to density measure seems more likely to arise because the density measure is itself related to differences in scale and data type. This

was impossible to test using data type, because there was only one study that we considered to be a compilation using crude densities. However, when study scale was included in the analysis, studies using ecological densities showed significantly higher

UI coefficients of determination than those using crude 0.9

densities, but no significant difference in slope (Fig. 5).

The hypothesis that different patterns arise because regression lass. Hori- of differences in the ranges of variation represented ie in each by the species received equivocal support. This udieswith hypothesis suggests that observed polygonal abun- frequency dance-body size relationships are segments of an 26 plots of underlying linear negative relationship. A small seg- is indicate Is ind ach ment of a broader relationship is, on average, expected dies with to have the same regression slope as the relationship

from which it is a segment, but a lower coefficient of

238

Animal


.2n AI


239

T.M. Blackburn &

K.J. Gaston

Table 2. OLS slope and rl (/ transform of r2) values from estimates of the abundance-body size relationship defined as either independent or dependent (see Methods), together with the results (F, P) of an ANOVA testing for differences in the distributions of the respective statistics. Only relationships plotted using body mass data are included in this analysis

Estimate Mean (+ SE) n F P

Slope Independent -0-335 + 0-0449 119 20-34 <0-0001 Dependent -0-634 + 0-0479 139

Irl

Independent 0-367 + 0-0214 122 33-99 <0-0001 Dependent 0-567 + 0-0254 154

Table 3. OLS slope and Ir (r/ transform of r2) values from estimates of the abundance-body size relationship using data either from single samples or from literature compilations (see Methods), together with the results (F, P) of an ANOVA testing for differences in the distributions of the respective statistics

Estimate Mean (? SE) n F P

Slope

Sample -0-291 + 0-047 107 9-26 0-0029 Compilation -0-729 + 0-094 12

Irl

Sample 0-334 + 0-020 109 23-67 <0-0001 Compilation 0-644 + 0-088 13

determination (Draper & Smith 1981). Why this is so is best illustrated by imagining successively smaller pieces snipped out of the relationship in Fig. la; the regression slope remains the same, but as the error variance in abundance approaches the variance in body mass, the rectangle of points more and more closely approximates a blob. Increases in the range of body sizes across which relationships are plotted should be accompanied by a smooth increase in the associated coefficient of determination but no change

in the regression slope (Currie 1993). There was indeed a general tendency for the

coefficient of determination to increase with the range

of body masses across which an abundance-body mass relationship was calculated (Spearman rank correlation, rho = 0-3, n = 77, P = 0-009; Fig. 6a), as predicted. However, this was not the smooth increase

expected from theory (Currie 1993), as shown more clearly if body size range was divided into a number of discrete classes (Fig. 6b). Further, regression slopes tended to decrease as the range of body masses increased (rho = -0 31, n = 74, P = 0 008), contrary to prediction; again this decrease was not smooth (Fig. 6c).

In some cases, a polygonal relationship has been hypothesized to result if species utilize the environment in three spatial dimensions. We examined two separate questions in relation to this mechanism. Do taxa that generally use the environment in two dimen-

sions show quantitatively different abundance-body size relationships from those that use it in three? Do

birds and mammals show quantitatively different abundance-body size relationships?

We found some evidence that the dimensionality explanation does indeed contribute to variation in the

abundance-body size relationship. Assemblages using a two-dimensional environment had higher coefficients of determination than assemblages using three, but their regression slopes were not more steeply

negative (Table 6). The same pattern was obtained in the comparison of birds and mammals; the distributions of OLS slopes estimated for birds and mam-

mals were not significantly different, but mammal assemblages showed significantly higher coefficients of determination (Table 6). However, the similarity between the effects of dimensionality and taxon is not surprising, because most assemblages using the environment in three dimensions consist of birds, and

most assemblages using the environment in two dimensions consist of mammals.

There was no difference in the regression slopes of the abundance-body mass relationship between those assemblages or taxa considered to use the environment in two or in three dimensions, but body mass was a better predictor of abundance in the former subset. The obvious explanation for similar slopes but different coefficients of determination is that bird

assemblages and assemblages using a three-dimensional environment consist of species covering a smaller

range of body masses. In fact, bird assemblages cover a larger range of body masses than mammal assemblages (Mann-Whitney U-test, z = 4-64, n =65,

? 1997 British


Ecology, 66, 233-249


Sample

-0-2 -

a,

0.

0

C,

-4

0

C

a

a

T

.

-0.4 -

-0-6 -

-0.8 -

-1

I

I

T

I

T I i r

I I

Compilation

T

0

-

0-8 c 0.8 0

a

E

0.6 " 0 a

04 ~

C

0

a, 0?4

c m

I D I D

Independent/dependent

Fig. 3. Mean (?SE) OLS regression slope (circles) and coefficient of determination (diamonds) for independent (I) and dependent (D) relationships in studies performed on sample or compilation data. There is a significant effect of the

data type on both slope (two-factor ANOVA, F1,254 = 14-2, P = 0-0002) and coefficient (F1,272 = 85-3, P < 0-0001), but dependency significantly affects neither (slope, F,254 =- 1-0, P = 0-32; coefficient, F,272 = 0.5, P = 0.5), and there is no significant interaction (slope, Fi,254 = 11, P = 03; coefficient, F,,272 = 17, P= 0-2). Dependency does not explain variance in either the slope or coefficient of determination in addition to that explained by data type. Statistics were calculated using /-transformed coefficient of determination.

P < 0-0001), and assemblages using space in three dimensions span a larger range of masses than those using space in two dimensions (Mann-Whitney U- test, z = 4-22, n = 74, P < 0-0001). Moreover, the difference in coefficients was not just a consequence of

differences in scale or the use of compilation compared

with sampling data in the different assemblage types; mammals and assemblages using a two-dimensional environment showed consistently higher coefficients when these factors were controlled for statistically (Table 7).

The results of our analyses examining the factors that have been suggested to affect the regression slope

and coefficient of determination of the relationship between abundance and body size are summarized in Table 8. Regression slopes were only affected by study

scale and data type, and these both explained independent amounts of the variation in slope when analysed together (Fig. 4). Coefficients of determination were affected by all the factors tested except density

-0.2 -

-0-3 -

a -0.4 0

-j -0.5 0

i -0.6

Sample

T

1

Compilation

i

;i

i T

1L

-0.7 -

II

T

I I

c

0

0.8 =(a

a

a

0.6 4 0

a

0.4 '2

r- 0

0.2 ar a

0- t

Local Regional Local Regional

Scale of study

Fig. 4. Mean (?SE) OLS regression slope (circles) and coefficient of determination (diamonds) for relationships in studies performed at local and regional scales, using either sample or compilation data. Both the scale of study and the type of data used have significant effects on both the slope (scale, F,267= 62, P = 0013; data type, F, 267= 79, P = 0-005) and the coefficient (scale, F,285 = 8.3, P = 0.0043; data type, FI,285 = 149-3, P < 0-0001). There is also a significant interaction between the effects of scale and data type on both the slope and the coefficient (slope, F,267 = 7-9, P = 0-005; coefficient, F,285 = 18-1, P < 0-0001). The analysis was performed on both independent and dependent estimates of the relationship, because there were no independent estimates at local scales using compilation data. Statistics were calculated using >/-transformed coefficient of determination.

measure. However, all these results are potentially affected by multicollinearity, as many of the variables

we tested will be closely related (e.g. the dimensionality of an assemblage and the taxon of which it

is composed). We used general linear modelling to examine whether these relationships are independent, or the result of correlation between the different

factors. Body size range was logl0 transformed to reduce its skewness. This approach showed that only study scale explains significant amounts of the variation in the slope and coefficient of determination of abundance-body mass relationships when all the factors listed in Table 8 are considered together (Table 9). From these maximal models, a stepwise backwards elimination procedure was used to produce minimal adequate models (Crawley 1993). For regression slope, this model contained only study scale

? 1997 British


Ecology, 66, 233-249

Table 4. OLS slope and r (V transform of r2) values from estimates of the abundance-body size relationship using data either from local or regional studies (see Methods), together with the results (F, P) of an ANOVA testing for differences in the distributions of the respective statistics

Estimate Mean (? SE) n F P

Slope Local -0-245 + 0-050 96 16-36 <0.0001

Regional -0-692 + 0-058 21

Irl

Local 0-330 + 0-021 98 8-87 0-0035

Regional 0-485 + 0-055 22

240

Animal


.

c


241

T.M. Blackburn &

K.J. Gaston

Table 5. OLS slope and Irl (J/ transform of r2) values from estimates of the abundance-body size relationship using either crude or ecological densities (see Methods), together with the results (F, P) of an ANOVA testing for differences in the distributions of the respective statistics


Slope Crude -0-515 + 0-073 19 1-46 0-23

Ecological -0-352 + 0-073 58

Irl Crude 0-342 + 0-037 20 2-40 0-13

Ecological 0-443 + 0-035 60

(F1,115 = 16-36, P < 0-0001), but dimensionali entered the equivalent model for the coeffic determination (study scale, F,,114 = 5-12, P = dimensionality, F1,14 = 8.19, P = 0-005).

Discussion

Eight factors have been suggested to cause, tribute to, the variation observed in the form

of interspecific abundance-body size relationsl animals. Our compilation of data from pu plots enabled us to test directly five of these considered in isolation, each factor we tested some degree affect the abundance-body size re

ship, with the exception of the measure of employed. However, the significance of most apparently results because they are related to va

in the spatial scale of study. For example, sti small scales tend to cover small ranges of bo and use sample data. Spatial scale is the only v

consistently correlated with variation in the dance-body size relationship.

The failure of the measure of density to in

0

4) 0

C,

.1

0 0

0

cu m

-0.25 -

-0.5 -

-0-75

? 1997 British


-1

I

i

T I

I

C E C E

Density measure

Fig. 5. Mean (?SE) OLS regression slope (circl coefficient of determination (diamonds) for inde relationships in studies performed at local and scales, using either crude (C) or ecological (E) d Scale of study has significant effects on both the slop

F1,7 = 8-6, P = 00045) and the coefficient (F1, P = 0-032), but density measure only has a significa on the latter (slope, F,,7 = 007, P = 08; co( F 74 = 69, P = 0-01). Statistics were calculate( /-transformed coefficient of determination.

ity also abundance-body size relationships is not surprising. :ient of As observed in the Methods, crude and ecological = 0-026; densities are actually just the two extremes of a con-

tinuum of densities that can be determined for a given

number of individuals, depending on the area used for the calculation. Therefore, there will often be inter-

gradation of these measures, and in many cases the or con- distinction may be difficult or arbitrary. For example, of plots both Damuth (1981) and Silva & Downing (1995) hips for claim that their density measures are ecological. How- lblished ever, many of their estimates, particularly for large . When mammals, come from censuses of nature or game i did to reserves, performed across very large areas. One such elation- source was Green (1979), who sampled large mammal density populations in Upper Volta throughout a national factors park of area 1000 km2. Whether the densities reported iriation for, say, hippopotamus, Hippopotamus amphibius L. adies at and warthog Phacochoerus aethiopicus (Pallas) are )dy size truly ecological, or even comparable, given the likely variable differences in how these species use the park area is abun- unknown, and probably not determinable from the

original source. The problem of comparability per- lfluence vades the interspecific analysis of densities (Gaston

1994; Blackburn & Gaston 1996, 1997; Smallwood & Schonewald 1996). Since the difference between crude

and ecological densities is not absolute, but one of 0.6 degree, it is unlikely that absolutely different abun- ? :dance-body size patterns would result from attempts

0. to classify studies as using either crude or ecological O densities.

Currie (1993) makes two points in respect of density

measures. First, they will only affect the slope of the 0.2 o

c abundance-body size relationship if there is an inter- aaction between body size and the density measure

0 used. If the 'crudeness' of the density measure used is random with respect to size, the slope estimate will be unbiased, although increased variance in the density

pendent measure (e.g. mixing of crude and ecological densities) regional will lead to increased variance around the regression lensities. line. Currie gives the example that if the densities of >e (scale, small-bodied species tend to be seasonal minima, but 74= 4'8, those of large-bodied species seasonal maxima, then .nt effect nt effect . the regression slope would tend to be over-estimated efficient,

d using (i.e. less negative than in reality). A more insidious, and realistic, possibility is that small- and large-bodied


242

Animal


(a) 1-0 1 0

E 0

a 0.8 er_

c 0.6 0

a

E 0.4 a)

0 0.2

5) a

0

0 0

C 0

a

E C

0

a, 0

c

0

U

a

0.75 -

0.5 -

0.25 -

0

0

-0.25 -

0.

c

4) -0.5 -

-0.75 -

-1

? 1997 British


Ecology, 66, 233-249

S S0 S~~~

* 0 0

.' 0

* % .0 * S . ?~ * D0o *0

0 -? . L0:0

0 :*

1 10

Body mass range (orders of magnitud

(b)

3 3 31

T

13

-T

J.

28

0-1 1-2 2-4 4-8

Size range (orders of magnitude)

-(c)

31

T 26

T

3 l

-T 12

1

I I i I

0-1 1-2 2-4 4-8

Size range (orders of magnitude)

Fig. 6. (a) The relationship between the x/-t coefficient of determination reported by a stu( range of body masses (orders of magnitude) spai species for which data were used. (b) The same i as above, but with the body mass range divided i classes. (c) The relationship between the OLS slope reported by a study and the range of b spanned by the species, with the body mass rang magnitude) divided into discrete classes. In (b) a indicate standard errors, and numbers by eac] sample sizes. A study was included in size range its size range was >0 and < 1, and so on.

species differ in respect to where along t ecological density continuum they tend te within definitions of 'crude' and ecological extent the precise use of crude and ecologice

is random with respect to body size is a and one that has not generally been addrei literature. Nevertheless, the lack of effect

measure on regression slope suggests that t

a strong size bias in the use of densities at the crude

* and ecological ends of the density spectrum. The lack of effect of density measure on the

coefficient of determination could also be argued to indicate that there is no mixing of density measures in

different studies (plots stated to use ecological densities really do so, and likewise those stated to use crude densities). An alternative interpretation is that the measures are always mixed to some degree, so that

a statement about the density measure used in any particular interspecific study is largely meaningless. We favour the latter interpretation. Since densities for

any single species fall on a continuum, we find it unlikely in the extreme that the densities in any given

~i ~ study will represent a similar quantity for all species, 2 as the above example from Green (1979) illustrates.

The second point Currie (1993) makes is that if crude and ecological density show an approximately constant difference, then the slopes of the respective

relationships plotted using them should be parallel, although of differing elevation. All else being equal, crude and ecological densities should therefore reveal the same patterns. He presents abundance-body size relationships from Damuth (1981), calculated using

8-16 ecological densities, and Peters & Wassenberg (1983), using crude densities for the same taxa, to show that the slopes are in fact very similar using both measures.

His conclusion is that there is no evidence that density

measure systematically biases the slope. However, how crude Peters & Wassenberg's data are is open to debate. They seem to us to lie more towards the

2 ecological end of the density spectrum. If, as is likely, both studies combine densities from a variety of points

?? ~ along the continuum, then it is hardly surprising that they show no significant differences. Perhaps more than anything, they serve to highlight how difficult it

8-16 is to make such distinctions. The likely reason that different density measures

ransformed have been considered to affect the abundance-body dy and the size relationship obtained is that there is an interaction nned by the between density measures and other factors. In par- relationship nto discrete ticular, density estimates from single-species studies regression are compiled into estimates of regional relationships, ody masses and are most often claimed to be ecological, whereas e (orders of relationships at local scales use density estimates from nd (c), bars sample studies that are usually defined as crude. Study h point are class 0-1consistent effects on the regression slope

and coefficient of determination of abundance-body size relationships, with more steeply negative slopes and higher coefficients at regional scales (Tables 8 and 9).

the crude-

o lie, even '. To what

al densities

key issue, ssed in the

of density here is not

Two of the factors suggested to affect the form of the abundance-body size relationship - the body size range and dimensionality of an assemblage - explain variation in the strength of the relationship, but do not help with understanding the variation in its slope. As predicted by Currie (1993), the coefficient of deter-

mination increases with the range of body sizes over which relationships are plotted. However, this pattern

1


243

T.M. Blackburn &

K.J. Gaston

Table 6. OLS slope and I r (1/ transform of r2) values from estimates of the abundance-body size relationship for (a) assemblages considered to use the environment in two or three dimensions (Dimensionality), and (b) bird and mammal assemblages (Taxon), together with the results (F, P) of ANOVAS testing for differences in the distributions of the statistics


(a) Dimensionality Slope Two-dimensional -0-286 + 0-078 56 0-49 0-49 Three-dimensional -0-350 + 0.050 59

Irl Two-dimensional 0-407 + 0-032 56 7-37 0-0076

Three-dimensional 0-299 + 0-024 62

(b) Taxon Slope Birds -0-370 + 0-056 51 1-14 0-29

Mammals -0-264 + 0-082 52

Irl Birds 0-299 + 0-024 54 6-63 0-012

Mammals 0-403 + 0-033 52

is not simple; rather, the increase is only exhibited over large body size ranges. Further, the regression slope changes quite markedly with body size range (Fig. 6). These patterns suggest that body size range alone cannot cause the difference between polygonal and linear relationships. It is across small body size ranges in particular that the predictions of this mech-

anism are most clearly violated, implying that poly-

gonal relationships (which generally have small size ranges) are not simply segments of linear patterns. This is another mechanism that seems unlikely to act in isolation, but could exacerbate the differences caused by other mechanisms; relationships plotted across a small range of body sizes tend to use sample data, and to be local in scale. Assemblages of species that use the environment in

three dimensions have regression slopes that do not differ from those of assemblages that use the environment in two dimensions, but show more variation around those regression slopes. In one sense, dimensionality is simply another way in which error can be introduced into density estimates (Blackburn & Gaston 1997), and the algebraic points raised by Currie

? 1997 British


(1993) for the effect of density measure (see above) equally apply here. However, the multivariate analysis

suggests that the effect of dimensionality may be quite

general, and serves to emphasize the difficulty of com-

paring the densities of species that use the environment in different ways. The results presented here imply that, for a given body size, species that use the environment in three dimensions can exhibit a wider

range of densities than those that use it in two dimen-

sions, at all scales of study. Nevertheless, it seems less

likely that this is a true biological effect than that it is

the result of problems in assigning an accurate denominator for calculating density in species that perceive a three-dimensional environment. The effec-

tive size of 1 km2 of forest for a deer and a woodpecker,

for example, will clearly differ enormously, yet the density of both may be calculated with the same denominator.

Sample and compilation data give rise to abundance-body size relationships that differ in both slope

and coefficient of determination (Table 8). However, showing that sample and compilation studies reveal different relationships is only part of the problem. It

Table 7. 1 rI (w/ transform of r2) values from estimates of the abundance-body size relationship in mammal and bird assemblages, and in assemblages considered to use the environment in two or three dimensions, using different data types and measured at different spatial scales (see Methods). Sample sizes are given in parentheses. Only relationships plotted using body mass data are included in the analyses. Each pair of numbers is significantly (P < 0-005) different when compared using two-factor ANOVA within data type and within study scale (e.g. coefficients of determination are higher for mammals than for birds in both regional and local studies)

Data type Study scale

Sample data Compilation data Local studies Regional studies

Birds 0-286 (48) 0-402 (6) 0-272 (41) 0-384 (13) Mammals 0-371 (48) 0-790 (4) 0-369 (46) 0-620 (5)

Two-dimensional 0-373 (52) 0-840 (4) 0-371 (49) 0-621 (6) Three-dimensional 0-298 (57) 0-308 (5) 0-289 (49) 0-339 (13)


244

Animal


Table 8. A summary of the results of analyses examining the factors that have been suggested to affect the regression slope and coefficient of determination of the relationship between abundance and body size. See Methods for definitions of the various factors; + indicates that both factors were analysed simultaneously using two-factor ANOVA

Factor Regression slope Coefficient of determination

Data type More negative in compilation than in Higher in compilation than in sample sample data data

Study scale More negative at regional than at local Higher at regional than at local scales scales

Data type + study scale As for each factor separately As for each factor separately Density measure No effect No effect Density measure + study scale No effect Higher at regional scales and using

ecological densities Body size variation Does not support the prediction that slope Some support for the prediction that the

should stay constant across different size coefficient should increase with size range ranges

Dimensionality No effect Higher for assemblages using a 2, rather than 3, dimensional environment

Mammal vs. bird assemblages No effect Higher in mammal than in bird assemblages

remains to be proven that either has logical precedence, and therefore reveals the 'true' pattern. Compilation data, for example, may significantly underestimate the number of rare species in faunas. They come primarily from single-species studies, which are likely to be studies of abundant species (e.g.

Kunin & Gaston 1993) conducted in areas where the species is common (Lawton 1989, 1990; Blackburn & Lawton 1994). As such, they are more likely to be representative of the maximum than the mean density

attained by species, and of the abundances of common species.

Sample data, in contrast, are usually claimed to avoid this problem by including good numbers of rare

species in the sample. However, this statement hides a pitfall. Species may be rare in sample data for three

reasons. First, they are genuinely rare. Secondly, they

? 1997 British


may be transient in the assemblage; individuals of transient or 'tourist' species have no intimate or last- ing association with the assemblage in which they have

been, by chance, found (Gaston et al. 1993). Thirdly, they are rare in the sample because the sample is inadequate to reveal their true level of abundance. This is equivalent to the veiling problem in species- abundance distributions (Preston 1948; Nee et al. 1991). The usual frequency distribution of species abundances means that any veiling will tend to inflate

the number of apparently rare species, while many truly rare species may not appear in the sample at all.

Therefore, although sample data often include many species at low abundance, this may actually tell us very little about the abundance of truly rare species in

relation to body size. In those studies using sample data where rare species are certainly included and

Table 9. Results of general linear models testing for relationships between the statistic in the first row and the factor in the first column, when all factors are considered simultaneously in the model. These maximal models explained 17-4% of the variation in regression slope and 20-3% of the variation in coefficient of determination. SS = sum of squares; d.f. = degrees of freedom; F= F-ratio; taxon = bird or mammal assemblage; dimensionality = whether the assemblage utilizes two or three spatial dimensions; study scale = either local or regional study; data type = either sample or compilation; density measure = crude or ecological; body size variation = log10 body mass range in the study. Coefficient of determination was square root transformed for analysis. Only independent estimates (see Methods) were included in these analyses (Note that the degrees of freedom for the minimal adequate models reported in the text are higher than those here because not all of the independent variables were available for all assemblages. The minimal adequate models only show slight qualitative differences to those reported if restricted to the same subset of assemblages as these maximal models)

Regression slope Coefficient of determination

Factor SS squares d.f. F P SS squares d.f. F P

Taxon 0-020 1 0075 0-786 0-023 1 0-528 0-470

Dimensionality 0-074 1 0-271 0-605 0-121 1 2-760 0-102 Study scale 1-108 1 4-043 0-049 0-176 1 4-018 0-050 Data type 0-325 1 1-188 0-281 0-009 1 0-214 0-645 Density measure 0-303 1 1-107 0-298 0-019 1 0-432 0-514 Body size variation 0-009 1 0-034 0-854 0-010 1 0-224 0-638

Error 14-796 54 2-502 57


with good density estimates, the observed relationship

appears to be intermediate in strength between linear

and polygonal forms (e.g. Nee et al. 1991; Gregory & Blackburn 1995).

Arguments about veiling have been cleverly used by Nee et al. (1992) to suggest that the true abundance-body size relationship would probably still be approximately linear negative if species of all abundances are included in compilation studies. They assume that the underlying species-abundance distribution for any given taxonomic assemblage is well approximated by the canonical lognormal (Preston 1962; that is, the standard deviation of abundances in

the distribution is about 4, measured on the log2 scale).

The abundances of those species plotted in compilation studies can then be treated as if they were a veiled sample from this distribution. This allows an estimate of the probable minimum abundance for species not included in the compilation (those beyond the veil line). From this argument, the predicted mini-

mum abundances of small organisms (e.g. nematodes) are still vastly greater than the maximum density of large organisms (e.g. mammals). Across a large range of taxa and body sizes, at least, a linear negative abun-

dance-body size relationship should survive the addition of rare species.

Nee et al.'s argument is particularly attractive because we would not expect the radical departure from lognormality in species-abundance distributions

that would be necessary to falsify it. Nevertheless, the

exact pattern will depend on whether there is any systematic relationship between the variance of the abundance distribution and the mean body size of a taxon. Any such systematic relationship is perhaps unlikely to have a significant effect across the largest

range of sizes (e.g. nematodes to mammals), but may be more relevant at within-taxon scales. It is at the

scale of the individual taxon that the exact relationship

between abundance and body size becomes contentious; few doubt that bacteria can live at higher densities than elephants. Whether variance in abundance is likely to be the same across species of small or large mammals, however, is unclear.

An important question is how minimum viable den-

sity scales with body size across species within a taxon

(Lawton 1990; Blackburn et al. 1993b). If it had the same exponent as mean or maximum density, that would be strong evidence that the general abundance- body size relationship was linear negative. Evidence that it does indeed scale in this way has been provided by Silva & Downing (1994), who studied the densities of mammal species or populations recognized by IUCN - The World Conservation Union as being reduced to levels low enough to make their continued survival of serious concern. They reasoned that where assessment of the extinction risks faced by such popu-

lations indicated that they suffered from low densities,

then the population concerned actually existed close to its minimum viable level. Density data from 143

such populations scaled with body mass to the power of -0-68, not significantly different from -0-75. Larger-bodied species can sustain lower minimum densities.

Silva & Downing's (1994) analysis explicitly focuses on rare and endangered populations of species. As they point out, estimates of density from such populations are only surrogates for true estimates of mini-

mum viable density. Surrogates are needed because the extensive studies required to obtain true estimates

make such data too scarce for the type of analysis necessary to elucidate their allometry. However, using

data on endangered populations introduces a logical problem to the analyses. It is difficult to claim that these densities represent minimum viable values when

the populations from which they are obtained are in serious danger of extinction; in other words, when the

populations are quite likely not to be viable. This is especially true given that Silva & Downing explicitly used species that suffered from low densities. Whether the bias that this introduces will be constant across all

body sizes depends on how the perception of rarity scales with size (Gaston & Blackburn 1995).

A similar argument to that for data type can be raised for the precedence of patterns revealed by studies

at different spatial scales. Study scale is the most con-

sistent predictor of variation in abundance-body size relationships (Tables 8 and 9), but it is difficult to argue that either scale has logical primacy. Polygonal local relationships could conceivably sum to give more

linear negative regional patterns. Alternatively, negative regional relationships could certainly give rise to polygonal patterns at local scales. Spatial patterns in species abundances clearly indicate that even common species in a taxon can be rare at many sites within their range when there is no question of a sampling artefact, and that this is true for species of all body sizes (Taylor, Woiwod & Perry 1978; Gaston 1994; Mehlman 1994; Brown, Mehlman & Stevens 1995). The simple presence of variation in abundance-body size relationships does not necessarily lead to the con-

clusion that some studies are showing an 'incorrect' pattern.

The data we compiled did not allow tests of the influence of three of the mechanisms suggested to produce different patterns in plots of abundance against body size. The first of these suggests that different patterns arise because of the presence of migrants in some assemblages, because abundances of

these species may be influenced by factors outside the area in which they are censused (Damuth 1987; Cotgreave 1994b). A general effect of migrants seems unlikely, because they will be a minor component of most assemblages. However, one exception may be bird assemblages. These have significantly weaker abundance-range size relationships than mammals (Tables 6 and 7). Clearly, there may be several reasons for this difference (e.g. dimensionality), but the effect

of migrants may contribute to the pattern. One way

245

T.M. Blackburn & K.J. Gaston

? 1997 British


Ecology, 66, 233-249


to test for this effect would be to compare abundance-

body size relationships in assemblages with different proportions of migrant birds. Nevertheless, an unequivocal test will be complicated, because the proportion of migrants in bird assemblages varies with latitude (Newton & Dale 1996), along with many other factors that may influence assemblage structure.

The second mechanism that we could not test is

that different patterns arise because polygonal relationships are essentially random samples from an underlying abundance-body size relationship; this underlying relationship may or may not be assumed to be linear negative. For example, Blackburn et al. (1990) showed that a polygonal relationship between abundance and body size could arise as a result of random sampling of individuals from an underlying distribution where there was no relationship between abundance and body size. Alternatively, Currie (1993)

gave visual, although not statistical, evidence that a polygonal relationship could be generated by random samples from a linear negative relationship, within the

same restricted range of body sizes. Either way, this argument implies that the polygonal relationship is of

essentially artefactual origin.

The case for an artefactual component, at least, to the polygonal abundance-body size relationship is strong. The lower limit to abundance in many of these

studies is the same across all body sizes, and cor- responds to that of a species represented in the sample

by a single individual, suggesting that it is set by the

limitations of the sampling technique (Blackburn et al. 1990; Currie 1993). It is an explanation that fits well with the tendency for polygonal patterns to arise

from local samples, and linear relationships from regional compilations. Given the area encompassed by regional studies, it is unlikely that many density

estimates from them will be based on the presence of only one animal. Likewise, compilation data often come from single- or few-species studies; it is unlikely

that many single-species studies would produce a density estimate based on a single individual. An artefactual component to polygonal relationships can also explain their failure to fit the size range mechanism; they may have a restricted size range, but their shape is more than a consequence of this compression.

The random sampling mechanism does, however, leave unanswered two key questions. First, what is the

underlying relationship between abundance and body size? Random sampling models do not have to pos- tulate an underlying linear negative relationship to recover a polygonal relationship (Blackburn et al. 1990). Also, it is not clear at what level of sampling the true species-abundance distribution would be unveiled; any relationship different from simple linear

negative could be argued to arise from inadequate sampling in the absence of an objective test. Since the question of the occurrence of rare species in compilation studies is unresolved, and the applicability of Nee et al.'s (1992) veiling argument within taxa is

unclear, it cannot be assumed that increased sampling

will necessarily recover a linear negative relationship.

The second question is whether local abundance- body size relationships are entirely a consequence of sampling artefacts: to what extent would the strength

and shape of the relationship differ given more com-

prehensive local sampling? The tendency for species to be rare at many sites within their range (see above),

and the apparently genuine effect of study scale, means

that polygonal relationships at local sites might reasonably be expected in the absence of any sampling

artefacts. Another example of a feature of polygonal abundance-body size relationships that has been suggested to be artefactual in origin (Blackburn et al. 1990) is the tendency for maximal abundance to peak

at intermediate body sizes (e.g. Brown & Maurer 1987;

Morse et al. 1988; Gaston 1988). However, the recog- nition of an analogous decrease in maximum density at the smallest sizes in compilation studies (Damuth 1993; Silva & Downing 1995; Fig. la), and a potential mechanism for the decline (Brown & Maurer 1987; Brown 1995) suggests that it may be real. That the decline can result from a sampling artefact does not mean that it does.

In fact, there is little to suggest that the strength of

the abundance-body size relationship in local assemblages would be markedly altered by more com- prehensive sampling. Both Carrascal & Telleria (1991) and Gregory & Blackburn (1995) show that relationships strengthen as the density measure used changes from the crude to the ecological end of the spectrum,

but in neither case does body mass explain more than 30% of the variation in density (cf. 74% in Damuth's

(1981) mammal data). As has frequently been pointed out (Currie 1993; Cotgreave 1993; Blackburn & Law- ton 1994; Silva & Downing 1995), even strong negative abundance-body size relationships usually show densities spanning up to four orders of magnitude at any given body size (e.g. Damuth 1981, 1987). At local scales, this is likely to translate into blob-like relationships, so that body size is not a good predictor

of a species' abundance in local assemblages even if all sampling artefacts could be circumvented.

The third mechanism that we could not test is that

different relationships are expected depending on the

taxonomic composition of the assemblage (Silva & Downing 1995). This suggestion stems from recent analyses implying that the mammalian abundance- body size relationship is non-linear, so that large- bodied species have densities that are higher than expected, and small-bodied species have densities that are lower (Damuth 1993; Silva & Downing 1995). An assemblage composed entirely of small-bodied species might then be expected to show a non-significant, or even positive, relationship, even if completely sampled, because that is the underlying global relationship for that range of body sizes.

While evidence for a non-linear abundance-body size relationship has been presented for a number of

246

Animal


? 1997 British



247 mammalian trophic groups, the generality of such T.M. Blackburn & patterns is as yet unknown. Presumably, this mech- K.J. Gaston anism for generating non-significant abundance-body

size relationships would only work within taxa; other-

wise, a linear negative global relationship would be unlikely. It could potentially explain within-taxon variation in the exponent of the interspecific relation-

ship. However, other mechanisms are probably more likely to produce the markedly different patterns typi-

fied as polygonal and linear negative relationships. This mechanism also ignores the large body of literature that systematically examines the abundance- body size relationship at all taxonomic levels (Nee et al. 1991; Cotgreave & Harvey 1992, 1994; Blackburn et al. 1994; Cotgreave & Stockley 1994; Cotgreave 1994a,b, 1995; Gregory 1995), and which suggests that

the arguments about taxonomic composition raised in relation to the shape of interspecific relationships are simplistic.

Perhaps the most significant problem for the taxo-

nomic composition hypothesis arises from the effect on density values of the area over which density is censused. There are two components to any animal density, number of animals and census area, and vari-

ation in either can affect the observed density of a species. Broadly negative interspecific relationships between density and body size can arise because small-

bodied species tend to be censused across smaller areas

than large-bodied species (Smallwood & Schonewald 1996; Blackburn & Gaston 1996, 1997). Given this mechanism, it is straightforward to imagine a simple extension that could give rise to a flattening of the linear negative relationship for mammals (e.g. Silva & Downing 1995) at both the smallest and largest body sizes. Census area may not scale perfectly with body size. If shrews and mice, for example, were censused

over the same sized areas (because minimum sensible census areas are reached before minimum body sizes), then the observed flattening would be expected in consequence. A similar argument applies to censuses of the largest mammals: numbers of warthogs and hippopotamuses, for example, are counted over the same area of game reserve.

The tendency to measure small mammal populations at the scale of trapping grids, and large mammal populations at the scale of nature reserves, suggests the possibility that there may be systematic differences in the relative use made of census areas by

animals of different body sizes (Blackburn & Gaston 1996). The clear implication is that different kinds of densities are being measured for large and small animals, and that the interpretation of patterns of abundance from such interspecific comparisons will be confounded by uncertainty as to what is actually being compared. This adds weight to suggestions that

? 1997 British the strong negative relationship recovered from com- Ecological Society pilation studies may in part be an artefact of the data Journal of Animal used. It also causes the sobering reflection that despite Ecology, 66, 233-249 the mass of data collected and analyses performed,

we are still some considerable distance from a good understanding of what is the shape of the abundance- body size relationship in animals. Given that relation-

ships between abundance and body size depend on the scale of study, and that the allometric scaling of census area can have undesirable consequences for the form of the relationship observed, we suggest that in future much more attention is paid to the effect of spatial scale.

Acknowledgements

We thank John Lawton, Marina Silva and an anony- mous referee for comments on this work, which was

supported by NERC grant GST/03/1211, and the core

grant to the NERC Centre for Population Biology. K.J.G. is a Royal Society University Research Fellow.

References

Andrewartha, H.G. (1961) Introduction to the Study of Ani- mal Populations. University of Chicago Press, Chicago.

Basset, Y. & Kitching, R.L. (1991) Species number, species abundance and body length of arboreal arthropods associated with an Australian rainforest tree. Ecological Ento- mology, 16, 391-402.

Begon, M., Harper, J.L. & Townsend, C.R. (1990) Ecology. Individuals, Populations and Communities. Blackwell Scien- tific Publications, Oxford.

Blackburn, T.M. & Gaston, K.J. (1996) Abundance-body size relationships: the area you census tells you more. Oikos, 75, 303-309.

Blackburn, T.M. & Gaston, K.J. (1997) Who is rare? Artefacts and complexities in rarity determination. The Biology of Rarity (eds W. E. Kunin & K. J. Gaston), pp. 48-60. Chapman & Hall, London.

Blackburn, T.M. & Lawton, J.H. (1994) Population abundance and body size in animal assemblages. Philosophical Transactions of the Royal Society, B, 343, 33-39.

Blackburn, T.M., Brown, V.K., Doube, B.M., Greenwood, J.J.D., Lawton, J.H. & Stork, N.E. (1993a) The relationship between body size and abundance in natural animal assemblages. Journal of Animal Ecology, 62, 519-528.

Blackburn, T.M., Gates, S., Lawton, J.H. & Greenwood, J.J.D. (1994) Relations between body size, abundance and taxonomy of birds wintering in Britain and Ireland. Philo- sophical Transactions of the Royal Society, B, 343, 135- 144.

Blackburn, T.M., Harvey, P.H. & Pagel, M.D. (1990) Species number, population density and body size in natural communities. Journal of Animal Ecology, 59, 335-346.

Blackburn, T.M., Lawton, J.H. & Gregory, R.D. (1996) Relationships between abundances and life histories of British birds. Journal of Animal Ecology, 65, 52-62.

Blackburn, T.M., Lawton, J.H. & Pimm, S.L. (1993b) Non- metabolic explanations for the relationship between body size and animal abundance. Journal of Animal Ecology, 62, 694-702.

Brown, J.H. (1995) Macroecology. University of Chicago Press, Chicago.

Brown, J.H. & Maurer, B.A. (1986) Body size, ecological dominance and Cope's Rule. Nature, 324, 248-250.

Brown, J.H. & Maurer, B.A. (1987) Evolution of species assemblages: effects of energetic constraints and species dynamics on the diversification of the American avifauna. American Naturalist, 130, 1-17.


Brown, J.H., Mehlman, D.W. & Stevens, G.C. (1995) Spatial variation in abundance. Ecology, 76, 2028-2043.

Calder, W.A. (1984) Size, Function and Life History. Harvard University Press, Cambridge, Massachusetts.

Cambefort, Y. (1994) Body size, abundance and geographical distribution of Afrotropical dung beetles (Coleoptera: Scarabaeidae). Acta Oecologica, 15, 165-179.

Carrascal, L.M. & Telleria, J.L. (1991) Bird size and density: a regional approach. American Naturalist, 138, 777-784.

Cotgreave, P. (1993) The relationship between body size and population abundance in animals. Trends in Ecology and Evolution, 8, 244-248.

Cotgreave, P. (1994a) The relation between body size and abundance in a bird community: the effects of phylogeny and competition. Proceedings of the Royal Society, B, 256, 147-149.

Cotgreave, P. (1994b) Migration, body-size and abundance in bird communities. Ibis, 136, 493-496.

Cotgreave, P. (1995) Population density, body mass and niche overlap in Australian birds. Functional Ecology, 9, 285-289.

Cotgreave, P. & Harvey, P.H. (1992) Relationships between body size, abundance and phylogeny in bird communities. Functional Ecology, 6, 248-256.

Cotgreave, P. & Harvey, P.H. (1994) Phylogeny and the relationship between body size and abundance in bird communities. Functional Ecology, 8, 219-228.

Cotgreave, P. & Stockley, P. (1994) Body size, insectivory and abundance in assemblages of small mammals. Oikos, 71, 89-96.

Cotgreave, P., Middleton, D.A.J. & Hill, M.J. (1993) The relationship between body size and population size in bro- meliad tank faunas. Biological Journal of the Linnean Society, 42, 367-380.

Crawley, M.J. (1993) GLIMfor Ecologists. Blackwell Scien- tific Publications, Oxford.

Currie, D.J. (1993) What shape is the relationship between body size and population density? Oikos, 66, 353-358.

Currie, D.J. & Fritz, J.T. (1993) Global patterns of animal abundance and species energy use. Oikos, 67, 56-68.

Damuth, J. (1981) Population density and body size in mammals. Nature, 290, 699-700.

Damuth, J. (1987) Interspecific allometry of population density in mammals and other animals: the independence of body mass and population energy use. Biological Journal of the Linnean Society, 31, 193-246.

Damuth, J. (1991) Of size and abundance. Nature, 351, 268- 269.

Damuth, J. (1993) Cope's rule, the island rule and the scaling of mammalian population density. Nature, 365, 748-750.

Draper, N.R. & Smith, H. (1981) Applied Regression Analy- sis, 2nd edn. Wiley, New York.

Ebenman, B., Hedenstr6m, A., Wennergren, U., Ekstam, B., Landin, J. & Tyrberg, T. (1995) The relationship between population density and body size: the role of extinction and mobility. Oikos, 73, 225-230.

Elton, C. (1927) Animal Ecology. Sidgwick & Jackson, Lon- don.

Gaston, K.J. (1988) Patterns in the local and regional dynamics of moth populations. Oikos, 53, 49-57.

Gaston, K.J. (1994) Rarity. Chapman & Hall, London. Gaston, K.J. & Blackburn, T.M. (1995) Birds, body size and

the threat of extinction. Philosophical Transactions of the Royal Society, B, 347, 205-212.

Gaston, K.J., Blackburn, T.M., Hammond, P.M. & Stork, N.E. (1993) Relationships between abundance and body size - where do tourists fit? Ecological Entomology, 18, 310-314.

Green, A.A. (1979) Density estimate of the larger mammals of Arli National Park, Upper Volta. Mammalia, 43, 59- 70.

Greenwood, J.J.D., Gregory, R.D., Harris, S., Morris, P.A. & Yalden, D.W. (1996) Relationships between abundance, body size and species number in British birds and mammals. Philosophical Transactions of the Royal Society, B, 351, 265-278.

Gregory, R.D. (1995) Phylogeny and relations among abundance, geographical range and body size of British breeding birds. Philosophical Transactions of the Royal Society, B, 349, 345-351.

Gregory, R.D. & Blackburn, T.M. (1995) Abundance and body size in British birds: reconciling regional and ecological densities. Oikos, 72, 151-154.

Griffiths, D. (1992) Size, abundance, and energy use in communities. Journal of Animal Ecology, 61, 307-315.

Juanes, F. (1986) Population density and body size in birds. American Naturalist, 128, 921-929.

Krebs, C. (1972) Ecology. The Experimental Analysis of Dis- tribution and Abundance. Harper & Row, New York.

Kunin, W.E. & Gaston, K.J. (1993) The biology of rarity: patterns, causes and consequences. Trends in Ecology and Evolution, 8, 298-301.

Lawton, J.H. (1989) What is the relationship between population density and body size in animals? Oikos, 55, 429- 434.

Lawton, J.H. (1990) Species richness and population dynamics of animal assemblages. Patterns in body-size: abundance space. Philosophical Transactions of the Royal Society, B, 330, 283-291.

Lawton, J.H. (1994) Population dynamic principles. Philo- sophical Transactions of the Royal Society, B, 344, 61-68.

Linstedt, S.L. & Calder, W.A. (1981) Body size, physiological time, and longevity of homeothermic animals. Quarterly Review of Biology, 56, 1-31.

Macpherson, E. (1989) Influence of geographical distribution, body size and diet on population density of benthic fishes off Namibia (South West Africa). Marine Ecology Progress Series, 50, 295-299.

Marquet, P.A., Navarette, S.A. & Castilla, J.C. (1990) Scal- ing population density to body size in rocky intertidal communities. Science, 250, 1125-1127.

Marquet, P.A., Navarette, S.A. & Castilla, J.C. (1995) Body size, population density, and the energetic equivalence rule. Journal of Animal Ecology, 64, 325-332.

Maurer, B.A., Ford, H.A. & Rapoport, E.H. (1991) Extinc- tion rate, body size, and avifaunal diversity. Acta XX Congressus Internationalis Ornithologici, 826-834.

Mehlman, D.W. (1994) Rarity in North American passerine birds. Conservation Biology, 8, 1141-1145.

Morse, D.R., Stork, N.E. & Lawton, J.H. (1988) Species number, species abundance and body length relationships of arboreal beetles in Bornean lowland rain forest trees.

Ecological Entomology, 13, 25-37. Nee, S., Harvey, P.H. & Cotgreave, P. (1992) Population

persistence and the natural relationships between body size and abundance. Conservation of Biodiversity for Sus- tainable Development (eds O.T. Sandlund, K. Hindar & A.H.D. Brown), pp. 124-136. Scandinavian University Press, Oslo.

Nee, S., Read, A.F., Greenwood, J.J.D. & Harvey, P.H. (1991) The relationship between abundance and body size in British birds. Nature, 351, 312-313.

Newton, I. & Dale, L. (1996) Relationships between migration and latitude among west European birds. Jour- nal of Animal Ecology, 65, 137-146.

Nilsson, A.N., Elmberg, J. & Sjoberg, K. (1994) Abundance and species richness patterns of predaceous diving beetles (Coleoptera, Dytiscidae) in Swedish lakes. Journal of Bio- geography, 21, 197-206.

Novotny, V. (1992) Community structure of Auchenor- ryncha (Homoptera) in montane rain forest in Vietnam. Journal of Tropical Ecology, 8, 169-179.

248

Animal


? 1997 British



Owen, J. & Gilbert, F.S. (1989) On the abundance of hover- flies (Syrphidae). Oikos, 55, 183-193.

Peters, R.H. (1983) The Ecological Implications of Body Size. Cambridge University Press, Cambridge.

Peters, R.H. & Raelson, J.V. (1984) Relations between individual size and mammalian population density. American Naturalist, 124, 498-517.

Peters, R.H. & Wassenberg, K. (1983) The effect of body size on animal abundance. Oecologia, 60, 89-96.

Pimm, S.L. (1991) The Balance of Nature? Ecological Issues in the Conservation of Species and Communities. University of Chicago Press, Chicago.

Preston, F.W. (1948) The commonness, and rarity, of species. Ecology, 29, 254-283.

Preston, F.W. (1962) The canonical distribution of commonness and rarity. Ecology, 43, 185-215, 410-432.

Read, A.F. & Harvey, P.H. (1989) Life history differences among the eutherian radiations. Journal of Zoology, London, 219, 329-353.

Reiss, M.J. (1989) The Allometry of Growth and Repro- duction. Cambridge University Press, Cambridge.

Robinson, J.G. & Redford, K.H. (1986) Body size, diet, and population density of Neotropic forest mammals. Ameri- can Naturalist, 128, 665-680.

Saether, B.-E. (1989) Survival rates in relation to body weight in European birds. Ornis Scandinavica, 20, 13-21.

Silva, M. & Downing, J.A. (1994) Allometric scaling of minimal mammal densities. Conservation Biology, 8, 732-743.

Silva, M. & Downing, J.A. (1995) The allometric scaling of density and body mass: a nonlinear relationship for terrestrial mammals. American Naturalist, 145, 704-727.

Smallwood, K.S. & Schonewald, C. (1996) Scaling population density and spatial pattern for terrestrial mammalian carnivores. Oecologia, 105, 329-335.

Strayer, D.L. (1994) Body size and abundance of benthic animals in Mirror Lake, New Hampshire. Freshwater Biology, 32, 83-90.

Strayer, D. & Likens, G.E. (1986) An energy budget for the zoobenthos of Mirror Lake, New Hampshire. Ecology, 67, 303-313.

Taylor, L.R., Woiwod, I.P. & Perry, J.N. (1978) The density dependence of spatial behaviour and the rarity of random- ness. Journal of Animal Ecology, 47, 383-406.

Thiollay, J.-M. (1994) Structure, density and rarity in an Amazonian rainforest bird community. Journal of Tropical Ecology, 10, 449-481.

Received 25 March 1996; revision received 25 July 1996

? 1997 British


Ecology, 66, 233-249

249

T.M. Blackburn &

K.J. Gaston


66, 233-249 relationship between abundance and body size

Documents