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VtyuUsOIKOS 75: 303-309. Copenhagen 1996

Abundance-body size relationships: the area you census tellsyou more

Tim M. Blackburn and Kevin J. Gaston

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Blackburn, T. M. and Gaston, K. J. 1996. Abundance-body size relationships: thearea you census tells you more. - Oikos 75: 303-309.

The interspecific relationship between abundance and body size in animals is oftenclaimed to be strongly negative, with species abundance limited by energetic requirements. This view has been criticized for a number of reasons, but is still widelyaccepted. Here, we provide evidence of further fundamental difficulties with thisrelationship as derived from compendium studies. We suggest that there is a potentialartcfactual component to these relationships resulting from variation in the areasover which the densities of species of different body size are censused, and differencesin the ways species use these areas. While the interspecific relationship between bodysize and abundance is still likely to be negative after accounting for the artefactualcomponent, the slope of the relationship is unlikely to support energetic equivalencearguments.

T. M. Blackburn, NERC Centre for Population Biology, Imperial College at SilwoodPark, Ascot, Berkshire, U.K. SL5 7PY. - K. J. Gusiun, Dept of Entomology. NaturalHistory Museum. Cromwell Rd. London, U.K. SW7 5BD (present address: Dept ofBiology, Imperial College at Silwood Park, Ascot, Berkshire, U.K. SL5 7P Y).

Considerable attention has been focused on the interspecific relationship between abundance and body size(Damuth 1981, 1987, 1993, Peters 1983, Peters andWasscnberg 1983, Peters and Raelson 1984, Juanes1986, Brown and Maurer 1987, Marquet et al. 1990,Cotgreave and Harvey 1991, 1992, 1994, Nee et al.1991, Blackburn et al. 1993a, b. Cotgreave 1993, 1994,Currie 1993, Blackburn and Lawton 1994). Initial studies revealed a strong, negative interaction, with bodymass generally explaining 60-70% of the variation inanimal abundance (with both variables log-transformed; Damuth 1981, 1987, Peters 1983, Peters andWassenberg 1983, Peters and Raelson 1984). Further,the slope of this relationship typically approximated to-0.75 within trophic groups (e.g. mammalian herbivores), using ordinary least squares regression. Sincebody mass scales with metabolic rate to the 0.75 power(Kleiber 1962), the -0.75 exponent between size and

/Accepted 5 July 1995Copyright © OIKOS 1996ISSN 0030-1299Printed in Ireland all rights reserved

abundance was taken as evidence that a species' abundance is limited by its energetic requirements, and thatequal amounts of energy are available to each species ina community: the so-called 'energetic equivalence rule'(Damuth 1981. 1987, 1991, Nee et al. 1991).

The view that a species' abundance is determined byits body size has been criticised (Brown and Maurer1986, 1987, Lawton 1989, 1991, Blackburn et al. 1993a,b, Blackburn and Lawton 1994). The principal difficultyis that the data used to establish the -0.75 relationshipbetween abundance and body size are not derived fromsamples of whole communities, but tend to be compen-dia front the literature. They maytheretore"undercsti-matc thcTnumber of rare species, and small-bodied rarespecies in particular (Brown and Maurer 1987, Morseet al. 1988, Lawton 1989, 1991). Subsequent studiessampling whole assemblages of taxonomically similaranimals have revealed polygonal relationships between

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densities; our own statistical treatment (see above)highlights the problem, but does not solve it. Evenaside from the problem of co-linearity, controlling forarea essentially assumes that intraspecific density-arearelationships have similar trajectories, and that biologically comparable densities can be generated by standardising study area (the same problem occurs in wholeassemblage studies where all densities are estimatedusing a common study area). The first assumptionseems likely to be erroneous; intraspecific density-arearelations certainly differ markedly (Fig. 4). The secondassumption seems equally dubious. A common measureof ecological density is unlikely to equate to measurement of density over the same sized area: elephants anddik-diks, for example, will certainly make different useof a standardised study area. The veiling of densityestimates in whole assemblage studies is another consequence of a fixed sample area. That species density

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Fig. 4. The relationship between log,,, density and log,,, censusarea in a) Peromyscus maniculatus (Rodcnlia). slope = —0.818.r2 = 0.766. p < 0.0005, n — 11; b) Aepyccms mulampus (Artio-dactyla), slope = -0.021. r2 = 0.001, p> 0.9. « = 9 (excludingthe obvious outlier, slope = -0.44, r2 = 0.458, />< 0.065,n = 8); and c) Loxodonta africana (Proboscidea),slope = —0.155. r2 = 0.287, p <0.06, n = 13. Each point is themean density (km-2) and mean area (km2) in one study.

musl be correlated lo some extent with the area overwhich density is measured, because the latter is used inthe calculation of the former, is irrelevant to thesearguments. The problem of which density of Peromyscus maniculatus to compare with which density ofLoxodonta africana remains.

This said, it is noteworthy that when controlling forthe size of study area, the resulting body size: abundance relationship (Fig. 3) seems broadly intermediatein form between relationships documented in compendium studies (Damuth 1981, 1987, 1993, Peters andWassenberg 1983, Peters and Raelson 1984) and relationships documented in whole assemblage studies(Brown and Maurer 1987, Gaston 1988, Morse et al.1988, Blackburn et al. 1993a), with characteristicsof both patterns (see also Gregory and Blackburn1995). For example, the low correlation is similar tothat seen in assemblage studies, but the lack of veiling

_ (IWft) OIKOS 75:2 |l-%) 307

at low abundances is characteristic of compendiumstudies.

ConclusionThere is a growing list of criticisms of studies describinga strong negative relationship between body size andecological density based on compendium data, andattributing that relationship to energetic equivalence(see reviews in Cotgreave 1993, Blackburn and Lawton1994), including problems of undersampling rare species, likely inequalities in energy distribution betweenspecies (Lawton 1989, 1991), and combining exponentsexcluding error terms (see e.g. Sugihara 1989, Blackburn and Gaston 1994. Medel et al. 1995). Problemsarising from the confounding effect of census area cannow be added to this list. It seems reasonable toconclude that a strong interspecific relationship betweenthe body size of a species and the area over which itsdensity is measured results from a combination ofbiolocical and non-biological factors. This results indifferences in the kinds of densities calculated for species of different body sizes, and contributes to a strongnegative relationship between the density and body sizeof species. While the density size relationship is stilllikely to be negative after accounting for area effects,the suggestion that this relationship provides evidencefor energetic equivalence seems unlikely.

Acknowledgements We thank Bob Molt for helpful discussion Peter Coigreave, David Currie. Jeremy Greenwood andJohn Lawlon for comments on earlier versions oT thismanuscript, and the staff of the library at the Natural HistoryMuseum. London, for their co-operation wiih l.terah.rcsearches. T.M.B. was supporled by NhRC grant GR3/8029.

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