Nordic Society Oikos
Relationships between Body Size and Population Density of Animals: The Problem of the Scaling of Study Area in Relation to Body Size Author(s): Christopher N. Johnson Reviewed work(s): Source: Oikos, Vol. 85, No. 3 (Jun., 1999), pp. 565-569 Published by: Blackwell Publishing on behalf of Nordic Society Oikos Stable URL: http://www.jstor.org/stable/3546706 . Accessed: 06/11/2011 22:10 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]
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Relationshipsbetween body size and population density of animals: the problem of the scaling of study area in relation to body size ChristopherN. Johnson, Dept of Zoology and Tropical Ecology, James Cook Univ., Townsville, Qld 4811, Australia (christopher.johnson(@jcu.edu.au).
Body size and population density have generally been found to be negatively related among animal species (Damuth 1981, 1987, Peters 1983). This relationship has attracted a great deal of interest because it suggests that some mechanism linked to body size controls much of the variation among species in abundance. Early studies suggested that this mechanism was limitation of population density by energy availability, which produces a negative relationship between body size and population density because large-bodied species require more energy per individual than small species. Support for this idea came from the finding that the slope of the decline of population density with body mass is often approximately -0.75. Because this value cancels the 0.75 scaling of individual metabolic rate with body mass, it follows that species of different body size are held to approximately the same rates of energy use at the population level (the 'energy equivalence rule'). This interpretation has been criticized on several grounds (Lawton 1989, Cotgreave 1993). The most recent criticism has been the suggestion that the magnitude of the decline in abundance with body mass has been systematically overestimated because investigators tend to estimate population densities of large-bodied species over areas that are too large (Blackburn and Gaston 1996, Smallwood et al. 1996). Large areas contain a greater variety of habitats than small areas. Therefore, as study area increases, so too does the proportion of sampled habitats that may be suboptimal for the species being surveyed. If densities are calculated without reference to the distribution of animals among habitats within the study area, surveys over large areas will tend to return lower estimates of density than surveys over small areas. Study area might increase with body size for reasons unrelated to variation OIKOS 85:3 (1999)
between species in true abundance. Smallwood et al. (1996) suggest that investigators might choose large areas to survey large-bodied species on the (untested) assumption that their population densities will be lower. Study area might also vary with body size because of differences in techniques used to estimate abundances of small and large species. For example, small mammal populations are typically sampled by trapping which, because it is labour-intensive, is restricted to small areas. In contrast, large mammals can often be counted by visual surveys which are more easily extended over large areas. If study area varies systematically with body size for reasons of the convenience or biases of investigators, then biologically meaningless relationships between body size and measured population density could be produced. Blackburn and Gaston (1996) and Smallwood et al. (1996) tested for a confounding effect of study area on the relationship between body mass and density in mammalian herbivores and mammalian carnivores respectively. They re-examined data sets in which there were strong relationships between body mass and measured population density (r2 = 0.70 and r2 = 0.46) with slopes consistent with energy equivalence (- 0.74 and - 0.76). However, in both data sets study area also increased with body mass and was a better predictor of population density than was body mass. When the effects of study area on population density were removed by multiple regression, the negative relationship between body mass and population density remained significant for mammalian herbivores but was very weak (r2 = 0.07) and the magnitude of its slope (-0.27) was much less than requiredto produce energetic equivalence. In mammalian carnivores, no relationship between body mass and density remained after the 565
relationshipbetween study area and population density was removed. This paper responds to Blackburn and Gaston (1996) and Smallwoodet al. (1996) in two ways: first, I give an alternativeinterpretationof their results in which the relationship of population density with study area is viewed as artefactualand the relationship with size is real. And second, I briefly consider the problem of how census area should be scaled with body mass to revealbiologicallymeaningfulrelationshipsbetweenbody mass and populationdensity.
the relationshipbetween density and body size. Census area would emergeas a better predictorof population density than body mass, and when analysedby multipleregressionbody mass would lose significance. It is importantto note that, for this to happen, it is not necessary for the matching of study area with population density to be perfectly consistent across differentspecies. It remainstrue, however,that when there is a degree of adjustmentof study area by investigatorsto the true densitiesof their study populations, then study area will emerge as a predictorof populationdensity;and, to the extent that this adjustment is more precise than the effect of body size on population density, study area will tend to displace body size as a predictorof population density. The The area-density relationship as artefact results given by Blackburnand Gaston (1996) and The results of the analyses of Blackburnand Gaston Smallwood et al. (1996) are as consistent with this (1996) and Smallwood et al. (1996) would also be interpretationas they are with their preferredexplaproducedif body mass was indeed a primarycause of nation, in which variation in census area actually variation among species in population density, but if causes variationin measureddensity. field workerstended to adjust study area to the density of the populations being surveyed. Most biologists beginninga survey of an animal populationwill have some idea in mind of the minimumnumberof How should census area scale with body size? animals that must be counted for the survey to be meaningful;this should be especially true when the As Blackburnand Gaston (1996) argue, we have no objectiveof the surveyis to begin a study of ecology objective basis to decide how much of the spatial or population dynamics,but would apply if only to variation in a species' abundanceshould be included allow a reasonablyprecise estimationof density. The in a standard measure of its population density. investigatorwill thereforewant to be reasonablycer- Therefore, we have no criterion for identifying the tain that the area chosen for study is large enough most appropriatesurvey area for any species. But, if that a worthwhilesample can be obtained. However, the densitiesof large and small speciesare to be comconstraintson resourcesand time will tend to work pared, it is necessarythat the areas over which they against study areas that are needlessly large. As a are studied be roughly equivalentin relation to the result, study areas should tend to be varied upwards spatial scale over which density varies within species. for low-densitypopulations,and downwardsfor high- There are two reasons to believe that this scale should generallyincrease with body size. (1) Smalldensitypopulations. The adjustmentof study area to populationdensity bodied species respond to environmentalvariation at might be achieved in two main ways. First, some finer spatial scales than large species, because they form of preliminarysamplingmight be undertakento generallyhave narrowerrequirementsfor shelter,food decide on the area needed to return an acceptably resourcesand microclimates(Lawton 1989). This will large sample of animals. This preliminarysampling result, at any given scale, in small species being more could take the form of an explicitly designed pilot patchily distributedthan large species - a large area survey or, perhaps more often, might consist of un- containing what is essentially homogeneous habitat structuredpreliminarywork designed to provide the for elephantswill incorporatefine-scaleheterogeneity investigatorwith a feeling for the rate of encounters representingmany distincthabitat types from the perwith animalsthat is likely to be achievedin a formal spectiveof mice. (2) In mammalsespecially,the range survey. Second, furtheradjustmentof the scale of the of individual movement is much greater for large study might be made in responseto early results - a than for small species - an individualelephantranges low rate of capturesor sightingswill be compensated throughan area many times that requiredby a whole by increasingthe size of the trappinggrid or by ex- population of mice. Therefore,the spatial scale over which comparablegradients in abundance are protendingtransects,for example. The effect of such direct matchingof study area to duced must be much greater for elephants than for populationdensity will be to producecorrelationsnot mice. Both these mechanismsmake it generallynecessary only betweencensus area and the variationin population density due to body size, but also between cen- that study area should increase with body size to sus area and the residualvariationof density around compensatefor the change in the scale of habitat use 566
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Table 1. Summaryof regressionsamongbody mass (g), populationdensity(ha- ), censusarea (ha) and home-rangearea (ha) in 36 speciesof Australianmammals(see Fig. 1). All F ratios are significantat p< 0.0001. Dependentvariable
Density Density Study area Home-range Study area
Body mass Study area Body mass Body mass home-range
-0.54 (0.09) -0.66 (0.09) 0.66 (0.10) 0.61 (0.10) 0.89 (0.11)
5.58 (0.32) 5.07 (0.18) -0.29 (0.36) -0.97 (0.33) 0.99 (0.140)
0.46 0.59 0.51 0.52 0.67
32.75 55.06 38.51 39.00 68.54
with body size. Whether the way in which investigators have actually scaled study area with body size has been appropriate is a more difficult question to answer, but I suggest that a useful test might be to compare the scaling of study area with body size to the scaling of home-range area with body size. This is because the mean home range of individuals in a population is a measure that reflects the scale at which individual animals use their environment and, as argued above, home-range size is one factor that will directly influence the spatial scale over which variation in population density will be significant. If study areas increase with body size at approximately the same rate that homerange area increases with body size, this would suggest that the scaling of study area might be biologically appropriate. Smallwood et al. (1996) found that the increase with study area with body size among carnivorous mammals had a slope of 0.92. This is close to the increase of home-range size with body size in carnivores. The most extensive evaluation of home-range allometry in the Carnivora revealed a slope 0.91 for the relationship (Gittleman and Harvey 1982, calculated from data in their Table 1); this is less than the value found by Harestad and Bunnell (1979) of 1.37 for North American carnivores, but close to the value of 1.03 produced by Lindstedt et al. (1986) in their re-analysis of Harestad and Bunnell's data to remove a bias due to methods used to estimate home ranges. Blackburn and Gaston (1996) do not provide a value for the scaling of census area with mass for herbivorous mammals, but inspection of their Fig. 1 suggests that it is slightly above 1.0. Studies of home-range allometry in herbivorous mammals have revealed slopes of 1.00 (North American species, Harestad and Bunnell 1979), 1.26 (Primates, Harvey and Pagel 1991) and 1.12-1.33 (rodents, varying diet types, Mace and Harvey 1983). The data given above suggest that the areas over which mammals are typically surveyed increase with body size in roughly the same proportion that the scale of movement of individual mammals increases with body size. However these comparisons are very loose, because the samples of species used to calculate the allometries of census area and home-range size differ from one another. Below, I overcome this problem by comparing the allometries of census area and homeOIKOS 85:3 (1999)
range size in a single sample of Australian mammals, including only species for which both variables have been measured.
5 m (0
4 4-, .A
on 'j0) _.
Log mass (gm)
5 m (U
4 U) -o
Log census area (ha) Fig. 1. Relationships between (a) body mass and density and (b) census area and density among Australian herbivorous marsupials and rodents. Lines were fitted by least-squares regression; see Table 1 for summary statistics. Sources of data are not given in this paper, but are available on request.
Size, area and abundance in Australian herbivorousmammals I compiled data on home-range area (of females in ha), population density (ha-') and census area (ha) for the 36 species of Australian herbivorous marsupials and rodents for which the full complement of data was available, and tested these for association with female body mass (g). Where several estimates were available for the same species, I took mean values after log-transformation. I followed Blackburn and Gaston (1996) and Smallwood et al. (1996) in defining census area as the actual area directly surveyed rather than the size of the area over which the density of records of individuals was extrapolated. To allow direct comparison with previous studies I used ordinary least-squares regression and did not control for phylogeny. Results of regression analyses are summarized in Table 1. There were significant negative regressions of density on mass and density on study area (Fig. 1), and significant positive regressions of home-range area on mass and study area on mass. The slope of the relationship between population density and body mass was significantly less steep than -0.75. The best predictor of population density was study area, which accounted for 59% of the variation in population density (body mass accounted for only 47%). When both body mass and study area were entered in a multiple regression analysis to predict population density, study area remained significant (F= 15.41, p< 0.001) while body mass did not (F= 3.61, p = 0.07). The slopes of the regressions of study area and home-range area on body mass were very similar (0.66 and 0.61, respectively, no significant difference). Study area and home-range area were closely related (r2= 0.67) with a regression slope below but not significantly different from one. Fig. 2 shows that study area tended to be about ten times larger than home-range area, regardless of body size. Body mass explained none of the residual variation in study area (F,34 = 2.06, p= 0.16) around the relationship between home-range area and study area, whereas home-range area did explain a significant proportion (Fl 34 =6.94, p = 0.01) of the residual variation in study area around the relationship between body mass and study area.
Conclusion For mammals, study area generally increases with body size in parallel with the increase of home-range area with body size, and home-range area is a better predictor of study area than is body size. Because home-range area is a reflection of the spatial scales over which different species use their environments, this analysis suggests that study area remains approximately constant relative to the scale of habitat use for species of
0 0 0
J 01 u
Log home range (ha) Fig. 2. Relationship between census area and home-range area among Australian herbivorous marsupials and rodents. The
dotted line representsequivalenceof census area and homerange area, the solid line is the line fitted by least-squares regression;see Table 1 for summarystatistics. different sizes. This should provide some confidence that, at least for mammals, observed relationships between abundance and body size are biologically meaningful, and are not simply artefacts of investigator-bias in the choice of study areas. If anything, large mammals tend to be censused over areas that are slightly smaller relative to home-range size than are small mammals, so that the only systematic bias might be an overestimation of population densities of large species. It remains true that study area is a better predictor of population density than is body mass. However, this could plausibly be due to a process in which investigators vary the sizes of their study areas in relation to the densities of populations under study, rather than to an artefactual effect of census area on measured density. Acknowledgements - I thank Julian Caley and Phil Munday for comments.
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