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© 2001 Blackwell Science Ltd. http://www.blackwell-science.com/geb

469

RESEARCH ARTICLE

Global Ecology & Biogeography

(2001)

10

, 469–485

Blackwell Science, Ltd

Effects of body mass, climate, geography, and census area on population density of terrestrial mammals

MARINA SILVA

1

, MICHAEL BRIMACOMBE

2

and JOHN A. DOWNING

3

1

Department of Biology, University of Prince Edward Island, 550 University Avenue, Charlottetown, Prince Edward Island, Canada C1A 4P3, Canada. E-mail: [email protected]

2

Department of Preventive Medicine and Community Health, New Jersey School of Medicine and East Orange VA Hospital, 88 Ross Street, East Orange NJ 07018, USA. E-mail: [email protected]

3

Department of Animal Ecology,

124 Science II, Iowa State University, Ames, Iowa 50011–3221, U.S.A. E-mail: [email protected]

ABSTRACT

Aim

The aim of this study was to investigate theeffects of climate, geography, census area and thedistribution of body mass on the mass : densityrelationship in terrestrial mammal populations.

Location

The areas covered include most majorterrestrial biomes including the tropics, savannas,and temperate forests.

Method

Data on population density and bodymass from 827 populations belonging to 330 dif-ferent terrestrial mammal species were derivedfrom a review of the literature.

Results

LOWESS and polynomial regression ana-lysis indicated that the overall mass : density rela-tionship on log-log scales was not linear and thatthe slope of this relationship behaves differently acrossthe range of body mass. Body mass explainedbetween 37 and 67% of the variability in popula-tion density depending upon the dietary categoryor the biome group. We also developed two multi-variate models that can explain up to 65% of the

variability in population density in terrestrialmammals. We also tested for a confounding effectof census area on the mass : density relationshipon log-log scales in terrestrial mammals.

Conclusions

Our findings support previousstudies suggesting that body mass is a major pre-dictor of the variance in population density interrestrial mammals. We suggest that the non-linearity of the mass : density relationship mayresult from the fact that the overall distributionof body mass is a mixture of distributions acrossdietary groups and biomes. In contrast to bodymass, our results indicate that climatic and geo-graphical factors have a minor effect on populationdensity. Although census area was closely corre-lated with body mass, body mass was generally abetter predictor of population density than wascensus area.

Key words

Body mass distribution, census area,climate, latitude, macroecology, mass density rela-tionship, precipitation, temperature, terrestrialmammals.

INTRODUCTION

During the past two decades, a number of studieshave examined the relationship between body mass

(M) and population density (D) across a widevariety of habitats and in various animal groups(e.g. Damuth, 1981, 1987; Blackburn

et al.

, 1990,1993; Blackburn

et al.

, 1993; Currie, 1993; Silva& Downing, 1995; Blackburn & Gaston, 1997;Silva

et al.

, 1997). However, despite the largenumber of studies, no consensus has yet beenreached regarding various issues associated withthe mass : density (M : D) relationship.

1

Corresponding author: Marina Silva, Department of Bio-logy, University of Prince Edward Island, 550 UniversityAvenue, Charlottetown, Prince Edward Island, Canada C1A4P3. E-mail: [email protected]

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Several authors (Damuth, 1981, 1987; Peters &Wassenberg, 1983; Peters & Raelson, 1984; Robinson& Redford, 1986; Macpherson, 1989; Marquet

et al.

, 1990) have found the slope of the M : Drelationship on log-log scales to be approxi-mately –0.75. This was taken as evidence thatprocesses associated with energy use are import-ant in generating M : D relationships (Damuth,1981). Total energy used by a population can beestimated by multiplying D by average individualmetabolic rate (e.g. Damuth, 1981, 1987; Brown& Maurer, 1986; Silva & Downing, 1995). Theallometric relationship between M and metabolicrate (R) typically has an exponent of 0.75 on log-log scales, suggesting that if the exponent of theM : D relationship is approximately –0.75, thenthe total energy used (E) by a population would beindependent of M (or E

=

R

×

D

=

M

0.75

×

M

–0.75

=

M

0

) (Damuth, 1981, 1987). This conclusion is nowknown as the energetic equivalence rule (Damuth,1981). However, other studies have provided evid-ence suggesting that mammalian species do notalways conform to this rule (e.g. Peters & Raelson,1984; Marquet

et al.

, 1995; Silva & Downing, 1995).For instance, Silva & Downing (1995) found anon-linear relationship between log D and log Mwhere the slope value varies across the range ofM covered by terrestrial mammals, implying thata single slope value may be inappropriate. How-ever, Griffiths (1998) pointed out the possibilitythat Silva & Downing’s (1995) trend may partiallybe an artefact of the smoothing procedure.

Another issue that is intensively debated isthe necessity of standardizing D or M by actualcensus area (Blackburn & Gaston, 1996a, 1999a,b;Smallwood

et al.

, 1996; Johnson, 1999). The censusarea mechanism suggests that small-bodied spe-cies are generally censused across smaller areasthan large-bodied size species. Consequently, M : Drelationships may result partially from differencesin survey area among studies from which densityestimates are gathered (Blackburn & Gaston,1996a, 1999a, 1999b; Smallwood

et al.

, 1996). Whenexamining the M : D relationship in mammaliancarnivores, Smallwood

et al

. (1996) found astrong relationship (

r

2

=

0.46) between M and Dwith an exponent of –0.76. However, the effect ofM on D became insignificant after the effect ofcensus area on D was removed from the ana-lysis. Similarly, Blackburn & Gaston (1996a) founda strong M : D relationship (

r

2

=

0.70) with an

exponent of –0.74 in mammalian herbivores, butonly a weak relationship between M and D(

r

2

=

0.07) with a shallower exponent (–0.27) afterthe effects of census area on D were consideredin the analysis. Johnson (1999) argued that asolution to solve this problem may be to adjustthe study area to the density of the populationbeing surveyed. However, he also pointed outthat this may also produce correlations betweencensus area and the residual variation of densityaround the M : D relationship.

It is also possible that much of the disagree-ment between previous studies regarding theslope value may be associated with differences inbody sizes of community members and/or under-lying M distributions across trophic levels, spatialscale or biomes (e.g. Brown & Nicoletto, 1991;Loder

et al.

, 1997; Griffiths, 1998; Marquet &Cofré, 1999). Griffiths (1998) pointed out thatoverall M : D relationships may result from amixture of component relations with exponentsthat differ from the overall exponent as distribu-tions of M are rarely uniform. Furthermore, thedistributions of body masses of terrestrial mam-mals can also vary depending upon the spatialscale of the study. Brown & Nicoletto (1991)found that the distribution for the entire NorthAmerican continent was highly modal and right-skewed, those for local habitats were uniform,and those for the biomes were intermediatebetween the one for the continent and those forthe local habitats. Marquet & Cofré (1999)showed that, in general, these patterns also holdfor the body size distribution of terrestrial mam-mals in South America. In addition, it has alsobeen suggested that M : D relationships can varydepending on body sizes of community membersand the range of sizes (Currie, 1993; Silva &Downing, 1995). This suggests that M : D relation-ships may be quite different for mammals belong-ing to different trophic groups, found in differentbiomes, or showing different M distributions.

Although controversy surrounds various issuesassociated with the M : D relationship, moststudies agree that there is a considerable amountof variability in D left unexplained by variationsin M. In terrestrial mammals, D varies between3 and 4 orders of magnitude at any given M andgenerally accounts for about 40–70% of thelogarithm of this variance (e.g. Damuth, 1981, 1987;Peters & Raelson, 1984; Robinson & Redford,


Patterns of population density

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1986; Silva & Downing, 1995). This suggests thata large amount of the variability in mammaliandensity may be related to variations betweenpopulations resulting from the influence of otherfactors. In addition to M, other biotic factorshave also been found to account for some of thevariability in mammalian densities (Clutton-Brock& Harvey, 1977; Peters & Raelson, 1984; Robinson& Redford, 1986; Damuth, 1987, 1993; Silva &Downing, 1995). In virtually all of these studies,trophic level has been reported to be the mostimportant factor beyond M affecting mammalianabundance (e.g. Robinson & Redford, 1986; Silva& Downing, 1995; Silva

et al.

, 1997). It has alsobeen suggested that phylogenetic relatednessbetween the species may also influence popula-tion density and the M : D relationship (e.g.Harvey & Pagel, 1991; Nee

et al.

, 1991; Cotgreave& Harvey, 1992, 1994). However, the considera-tion of phylogenetic relatedness between speciesin macroecological studies is still a controversialissue. For British birds, Nee

et al

. (1991) showedthat although across species the relationship betweenM and D was negative, no significant relationshipbetween these two variables occurred when thetaxonomic groups were examined separately.However, it has been argued that phylogeneticmethods favour explanations based on phylogenyat the expense of explanations based on ecology(Westoby

et al.

, 1995a, 1995b, 1995c). Phylogeneticrelationships provide information on whathappened millions of years ago while populationabundance is controlled by events that happen ona much shorter time scale (Cotgreave, 1995).Ricklefs & Starck (1996) also argued that phylo-genetic methods tend to result in weak correlationsand broad confidence limits around parameterestimates obtained in macroecological studies.

In contrast to M or trophic level, the influenceof local environmental conditions such as energyavailability or climate on the relationship betweenM and D has received little attention even thoughfield studies have shown their effect on averagepopulation abundance to be important (e.g.Caughley, 1964; Churchill, 1991; Roberts & Dunbar,1991). An explanation may be that most priorstudies have investigated the M : D relationshipat the species level rather than population level,thus local environmental conditions could notbe examined. Another reason is that measuresof energy availability (e.g. productivity, food

production) are rare in the mammalian literatureand even rarer when coupled with detailed studiesof mammalian abundance. However, several studieshave shown that primary productivity and habitatvegetation are strongly correlated with climaticfactors such as precipitation and temperature (e.g.Rosenzweig, 1968; Phillipson, 1975; Whittaker,1975; Coe

et al.

, 1976; Fritz & Duncan, 1994).This suggests that climatic factors can be used assurrogates for energy availability to mammalsand may account for some of the variability inD. Currie & Fritz (1993) investigated the effect ofvarious climatic factors on D in 135 mammalianpopulations and found this to be negligible afteraccounting for M. They also found that D declineswith increasing evapotranspiration, suggesting thathabitats of low primary productivity may supportgreater mammal densities than those of highproductivity. However, theoretical arguments sug-gest that available energy may limit the carryingcapacity of habitats (e.g. Hutchinson, 1959; Brown,1981), suggesting the possibility that in energy-rich habitats mammalian populations would reachhigher densities. Support for this hypothesis comesfrom studies that have reported differences indensities at the species level between temperateand tropical mammals of similar M (Peters &Raelson, 1984; Damuth, 1987).

Geographic descriptors such as latitude, longit-ude or altitude often combine both geographicaland climatological information regarding environ-mental conditions surrounding animal popula-tions. Although the effects of both longitude andaltitude on D have rarely been investigated inmacroecological studies, several studies have pro-vided some controversial information regardingthe effects of latitude on mammalian abund-ance. On one hand, some studies have shownthat mammalian diversity is high at low latitudes(e.g. Baker, 1967; Fleming, 1973; Wilson, 1974;Rapoport, 1982; Stevens, 1989), suggesting thatniche space may be small for populations inhab-iting the tropics. On the other hand, the com-bined effect on population density of high levelsof both primary productivity and species divers-ity may result in no latitudinal variations in D(Blackburn & Gaston, 1996b,c; Johnson, 1998). Ifniche space is limited in the tropics, one possibletrend for the effect of latitude on D is that mammalpopulations inhabiting the tropics maintain lowerdensities than those occurring at higher latitudes


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where competition for niche space may be lessimportant. Recently, Johnson (1998) examined dis-tribution and abundance in Australian mammalsand found a significantly positive correlationbetween D and latitude. In addition, Cotgreave& Stockley (1994) found that communities ofinsectivores near the equator show less stronglynegative relationships between population abund-ance and M than those occurring at high latitudes,suggesting that the strength of the correlationbetween M and D may also be subject to latitudinalvariations. Support for the idea of no latitudinalvariations in D comes from Currie & Fritz (1993),who found that latitude had a minor effect on Dafter accounting for variations in M, suggestingthat latitudinal variations in animal abundance areweak. In the light of these studies, it is presentlynot clear whether latitude has an effect on D.

The goal of this study is to examine the generalrelationship between M and D at the populationlevel in terrestrial nonvolant mammalian spe-cies. We will investigate the effects of climate andgeography on mammalian population density asreflected in dietary categories and terrestrialbiomes. In particular, we predict that differencesin M : D relationships would reflect differences inM distributions between trophic categories andterrestrial biomes. We will also test for a confound-ing effect of census area on the M : D relationshipin terrestrial nonvolant mammalian species.

METHODS

Data

Data on D (individuals/km

2

) and M (kg) wereobtained from a database derived from a system-atic review of the literature described in detailelsewhere (Silva & Downing, 1995). Based ontheir food habits, populations were classified intothree dietary categories: herbivores, insectivoresand carnivores. Information on food habits wasobtained from individual population studies orfrom related works (Eisenberg, 1981; Nowak,1991). Census area estimates (A; km

2

) were alsoobtained from individual population studies. Theentire dataset and reference list used in this studyare available on request from M. Silva.

Global biomes (taïga, desert, savanna, grass-land, tropical dry forest, temperate dry forest,tropical rain forest and temperate rain forest)

of studied populations were determined usingWhittaker’s (1975) protocol. This classification isbased on zones of temperature and precipitation.For example, taïga and desert are differentiatedon the basis of temperature while grassland andtemperate dry forest are primarily differentiatedon the basis of precipitation. Average annualtemperature (

°

C) and total annual precipitation(mm) data were taken directly from populationstudies when published or from a world climaticdatabase (Wernstedt, 1972). Geographic informa-tion such as latitude (

°

), longitude (

°

) and altitude(m) of study sites were obtained from populationstudies, or were estimated from geographical sitedescriptors. As a major purpose of this study wasthe investigation of the effects of both climateand geography, we excluded from our datasetpopulations for which we could not ascertain geo-graphical location (latitude and longitude) and atleast one climatic variable.

Analysis

D, M and A values were transformed logarithmic-ally to reduce heteroscedasticity (Gujarati, 1978).The data were analysed using various graphicaland statistical procedures. Graphical analysesincluded non-parametric techniques such askernel density-based histograms (Wand & Jones,1995) and locally weighted sequential smoothing(LOWESS; Cleveland, 1979). LOWESS is a non-parametric local least squares graphical proce-dure that was developed to be a robust meansof finding patterns in refractory data (Cleveland& McGill, 1985). In this study, LOWESS is usedto help determine the unbiased form of therelationship between M and D both overall andacross biomes and trophic groups. Polynomialregression analysis was used to assess the statist-ical significance of non-linearities detected byLOWESS. M distributions were examined forlog-normality using the Wilk–Shapiro test, theKolmogorov–Smirnov test and the chi-square test(Sokal & Rohlf, 1981; Zar, 1996).

Multivariate cluster analysis employing a centroid-based selection procedure was used to examinecorrelations and clusters between variables. Thecentroid approach is a common measure of nearnessthat uses distances based on Pearson correlationvalues to group the variables by degree of similar-ity (Johnson & Wichern, 1992). Clusters apparent



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in the Pearson correlation matrix itself will forthe most part be apparent in the dendogram plotwhich reflects a broad multiple-correlation setting.In addition, multiple regression models were alsodeveloped to examine the relationship between Dand explanatory variables. Since census area valueswere available for approximately 46% of the studiescomprising the database, we present the results ofthese analyses separately.

It is important to underline that phylogeneticmethods focus on the variation found amongspecies rather than among populations. However,for a given species both body mass and popu-lation density can vary depending on variousfactors including climatic conditions and foodavailability. In particular, population density of agiven species can vary by more than three ordersof magnitude across its range of distribution.For example, the impala (

Aepyceros melampus

)average population densities vary from 0.02/km

2

inKafue National Park (Dowsett, 1966) to 49.7/km

2

in Akagera National Park (Montfort, 1972). Sinceone of the main objectives of this study was toinvestigate the effects of climatic conditions andgeographical location, the use of data on mam-malian populations rather than species averageswas fundamental. In this study, therefore, we havenot attempted to use any phylogenetic methodbecause accurate information to reconstruct phylo-genetic relatedness among populations withinmammalian species does not yet exist.

RESULTS

The collected data were for 827 distinct populationsbelonging to 330 different terrestrial mammalspecies covering the range of M from 0.0026 to3000 kg. The database included species from 16different mammalian orders (Wilson & Reeder,1992) and eight different terrestrial biomes. D variedfrom 0.004 to 12 500 ind/km

2

and followed anoverall log-normal distribution (Wilk–Shapiro;Kolmogorov–Smirnov;

χ

2

,

P

> 0.05).

Effects of body mass

Overall, the distribution of M did not differsignificantly from a log-normal distribution (Wilk–Shapiro, Kolmogorov–Smirnov,

χ

2

,

P

> 0.05) (Fig. 1).However, when populations were separated onthe basis of dietary categories, the shape of M

distributions differed significantly from eachother as well as from the log-normal distribution(Fig. 1). For herbivores, the M distribution dif-fered significantly from the log-normal distribu-tion (Wilk–Shapiro and

χ

2

,

P

< 0.01). Moreover,Kernel density plots showed some evidence thatthe M distribution of herbivores may be bimodalwith one mode at about 0.01–0.1 kg and anotherat 10–100 kg (Fig. 2). For insectivores, the ana-lyses were inconclusive. While the Wilk–Shapirotest supported the log-normal distribution (

P

> 0.05),the chi-square test indicated that the M distribu-tion of insectivores differed significantly from thelog-normal distribution (

P

< 0.05). Our analysesalso indicated that the M distribution of carnivoreswas not statistically distinguishable from the log-normal distribution (Wilk–Shapiro and

χ

2

,

P

>0.05). M distributions for biomes for which thesample size was sufficiently large (

n

=

30) were alsoexamined. With the exception of the temperaterain forest, none of these distributions were log-normal (Fig. 3). Although some of these differ-ences may reflect differences in sample size, theymay also reflect differences in species composition.

Log M was a useful predictor of Log D interrestrial mammals, explaining about 59% of thevariability in Log D when all mammals werepooled together (Table 1). However, LOWESSand polynomial regression analysis indicated thatthe overall Log M : Log D relationship is non-linear,suggesting that the slope of this relationshipbehaves differently across the range of M-values(Fig. 4, Table 1). With the exception of insect-ivores, the coefficient of Log M (Table 1) differedsignificantly from –1 (95% confidence intervals)for all mammals and across dietary groups.LOWESS and polynomial regression analyses alsoshowed significantly non-linear relationships forboth herbivores and insectivores, suggesting thatboth the slope and the correlation value of theLog M : Log D relationship varies among dietarygroups. For instance, the correlation betweenLog M and Log D appeared to be stronger in carni-vores than in any other dietary group. Analysisof the Log M : Log D relationship across biomes(

n

=

30) also resulted in various non-linear rela-tionships and different correlation values (seeLOWESS lines in Fig. 5). Log M alone explainedbetween 37 and 62% of the variability in Log Dacross biomes. Furthermore, the slopes of theserelationships were all significantly different from


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–1 (95% confidence limits of the slopes; Fig. 5).However, no significant differences in slope valuewere found between tropical and temperate biomes(test for homogeneity of slopes;

P

> 0.05).

Effects of climate and geography

Log D was significantly correlated with variousexplanatory variables (Table 2). Log M was alsostrongly correlated with most of the otherexplanatory variables, with the exceptions ofprecipitation and altitude. Cluster analysis showedthat Log D is more strongly correlated with bothlatitude and altitude than it is with Log M,although underlying latent variables may berelevant here (Fig. 6a). In fact, it takes the inclu-sion of diet in the analysis to bring Log M andLog D closer together (Fig. 6b).

Using multiple regression, we developed twomodels that fit the overall data (Table 3).

Although the effect of Log M was included inboth models, the Log M : Log D relationship waslinear in Model I, while in Model II the variableLog M was non-linearly related to Log D.Besides M, only the effects of diet and biomewere found to be significant in Model I. Whilethe non-linear component was statistically signi-ficant, Model II explained only approximately 1%more of the variation in Log D than Model I(Table 3), and approximately 3% more than themodel including exclusively Log M (see Table 1).

Effects of census area

Census area values (A) were available for 377populations (approximately 46%) comprising thedatabase. The distribution of log A values followedan overall log-normal distribution (Wilk–Shapiroand

χ

2

,

P

> 0.05). Lack of inclusion of censusvalues seems a random but pervasive phenomenon

Fig. 1 Frequency distributions of log10 transformed body masses (kg) for all mammals (n = 827), herbivores(n = 675), insectivores (n = 91), and carnivores (n = 61).



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across the studies included in the database, sug-gesting that no undue selection bias was inducedby incorporating census values. Log M explainedbetween 52% and 62% of the variation in Log D(Table 4). Although LOWESS indicated somenon-linearities (Fig. 7), the polynomial regressionanalysis did not detect any significant (

P

> 0.05)curvilinearity in the Log M : Log D relationshipeither for all mammals or across dietary groups.Therefore, it is difficult to affirm that the non-linearities in the Log M : Log D relationships maybe a consequence of census area for this particulardataset. Our analyses also showed that the resid-uals of the Log M : Log D relationships were stillsignificantly correlated with log A (except forinsectivores) even though the correlations wereweak (Table 4). The relationship between log Aand Log D were also statistically significant, butlog A was generally a weaker predictor of Log Dthan was Log M. Furthermore, the residuals of

the log A : Log D relationships were significantlycorrelated with Log M, although the slope wassignificantly shallower than –0.75 both for allmammals and herbivores, but not for insectivoresand carnivores (95% confidence intervals). Thebest multivariate model including census area andother explanatory variables (Log D

=

−

0.008

−

0.608 Log M

−

0.160 log A

+

0.003 Longitude

+

1.715

×

10

–4

Altitude + 0.144 Biome

+

0.036Temperature

−

0.367 Diet;

n

=

275;

r

2

=

0.66; all

P

-values < 0.02) explained approximately 13% moreof the overall variation in Log D than the modelincluding exclusively Log M (see Table 5).

DISCUSSION

Our findings showed that Log M alone can predictbetween 37% and 67% of the variability in Log Ddepending upon the dietary category or biomegroup. Although other factors not examined in

Fig. 2 Kernel density distributions of log10 transformed body mass (kg) for all mammals (n = 827), herbivores(n = 675), insectivores (n = 91), and carnivores (n = 61).


476 M. Silva et al.

© 2001 Blackwell Science Ltd, Global Ecology & Biogeography, 10, 469–485

this study may also explain a high proportion ofthe variance in mammalian population density,our findings support previous studies suggestingthat M is a major predictor of the variance in D

in terrestrial mammals (e.g. Peters & Raelson,1984; Damuth, 1987; Currie & Fritz, 1993). Thismay suggest that the size of a mammal’s bodyputs a more determining limit on mammalian

Fig. 3 Frequency distributions of log10 transformed body masses (kg) of terrestrial mammals occurring invarious biomes. Biomes included are only those for which n = 30. DW is the Kolmogorov–Smirnov statisticand ‘p’ is the probability associated with DW.


Patterns of population density 477


population abundance than any other environ-mental factor examined in this study.

This study also provides evidence supportingthe idea that the slope of the Log M : Log D

relationship varies across the range of M (Brown& Maurer, 1989; Silva & Downing, 1995),suggesting that the Log M : Log D relationshipis not linear. Although we did not examine E in

Table 1 Relationship between the logarithm of population density (Log D; ind/km2) and the logarithm ofbody mass (Log M; kg) in mammals of various dietary categories. Models were developed using polynomialregression analysis. Only coefficients significantly different (P < 0.05) from zero are shown. r2 is the coefficientof determination of the models and n is the sample size

Group Model

All mammals Log D = 1.36 − 0.83(Log M) − 0.05(Log M2) + 0.04(Log M3)SE(Log M) = 0.039 r2 = 0.5868 n = 827

Herbivores Log D = 1.43 − 0.68(Log M)SE(Log M) = 0.021 r2 = 0.6113 n = 675

Insectivores Log D = 0.90 − 0.89(Log M) − 0.14 log (M2)SE(Log M) = 0.116 r2 = 0.4971 n = 91

Carnivores Log D = 1.41 − 1.83(Log M) − 0.34(Log M2) + 0.28(Log M3)SE(Log M) = 0.297 r2 = 0.6742 n = 61

Fig. 4 Relationship between the log10 of body mass (Log M) and the log10 of population density (Log D) forall mammals (n = 827), herbivores (n = 675), insectivores (n = 91), and carnivores (n = 61). The curves representLOWESS fits (tension 0.5) to the data.


478 M. Silva et al.


this study, the systematic changes observed in theslopes of the Log M : Log D relationships can beseen as evidence that small and large mammalsdiffer in terms of energy used. Silva & Downing

(1995) suggested various explanations for the sig-nificant differences in energy use within terrestrialmammals including that population densities ofvery small mammals may be limited by the

Fig. 5 Relationship between the log10 of body mass (Log M) and the log10 of population density (Log D) forterrestrial mammals occurring in various terrestrial biomes. Biomes included are only those for which n = 30.The straight lines are simple log-log linear fits while the dotted curves represent LOWESS fits (tension 0.5) tothe data. SE(Log M) are the standard errors of the slope value of the Log M : Log D relationship for each biome.




energetic costs associated with living near to theultimate body size constraints imposed by theenergetics of homeothermy. At the other end ofthe body size spectrum, it is possible that largemammals may make more efficient use of resourcesor, perhaps, that populations of extremely largemammals that have persisted at extremely lowdensities may simply have been driven to extinc-tion. Support for the non-linearity of the Log M :Log D relationship found in this study alsocomes from empirical and theoretical analysisthat have reported allometric scaling of variousecological traits (e.g. continental populationextinction of species) that are not monotonicallyrelated to M (Pimm, 1992; Marquet et al., 1995;Marquet & Taper, 1998).

Our analyses also showed that the non-linearityof the Log M : Log D relationship may resultfrom the fact that the overall distribution of Mis a mixture of distributions across dietary groupsand biomes. Differences in Log M : Log D relation-ships were often associated with differences in Mdistributions. Given the large overall sample size,and especially because of the large number ofherbivores, our findings suggest that the non-linearity of Log M : Log D relationships may be morethan an artefact of the smoothing (LOWESS)procedure. Differences in M distribution mayaffect the slope value of Log M : Log D relation-ships because it has been shown previously thatbody sizes of community members as well as therange of sizes can affect M : D relationships(Currie, 1993; Silva & Downing, 1995). Theseresults also provide support for Griffiths’s (1998)

Table 2 Results of the Pearson correlation analyses among continuous explanatory variables for all mammals(n = 827). The variable ‘Lat’ is absolute latitude (°), ‘Long’ is absolute longitude (°); ‘Alt’ is altitude (m),‘Log M’ is the logarithm of body mass (kg), ‘P’ is total annual precipitation (mm), and ‘T’ is average annualtemperature (°C)

Lat Long Alt Log M Log D P T

Lat —Long 0.18** —Alt −0.12** 0.08* —Log M −0.54** −0.24** NS —Log D 0.36** 0.22** NS −0.76** —P −0.38** NS −0.41** NS NS —T −0.70** NS −0.34** 0.37** −0.27** 0.48** —

*P < 0.05; ** P < 0.01; NS indicates P > 0.05.

Fig. 6 Cluster analysis using the correlation andsimilarity matrices between variables. Analysisincludes (top panel) all variables excluding biomeand diet, and (bottom panel) all variables includingbiome and diet. Variables are the log10 of body mass(Log M), log10 of population density (Log D), diet,absolute value of latitude (Ab Lat), absolute value oflongitude (Ab Long), altitude (ALT), precipitation(P), temperature (T) and biome.


480 M. Silva et al.


idea that some of the disagreement between pre-vious studies may result from differences amongM distributions (e.g. Damuth, 1981, 1987; Peters& Raelson, 1984; Robinson & Redford, 1986; Silva& Downing, 1995). Although in most macro-ecological studies the range of body mass of non-volant terrestrial mammals is covered adequately,the datasets generally differed in terms of bothspecies composition and the fraction of the world’s

terrestrial mammals that are included. Many ofthese studies are based on compiled data fromdifferent communities and therefore may besubject to large sampling and selection biases. Inaddition, studies of mammalian communities areoften limited to taxonomically related species(e.g. Chew & Chew, 1970; Freese et al., 1982;Brown, 1984) or may reflect the interests of theinvestigator (e.g. Bourlière, 1961; Peres, 1990)

Table 3 Models describing the statistical effect of body mass (Log M; kg), climate and geography onpopulation density (Log D; ind/km2) in terrestrial mammals. Models were developed using Stepwise multipleregression. Only coefficients significantly different (P < 0.05) from zero are shown. Latitude (Lat) is absolutelatitude (°) and (P) is total annual precipitation (mm). n is the sample size and r2 is the multiple coefficientof determination

Model

ILog D = 1.15 − 0.668 Log M − 0.42 Diet + 0.061 Biomen = 666 R2 = 0.61 P < 0.001

IILog D = 1.33 − 0.802 Log M − 0.055 Log M2 + 0.039 Log M3 − 0.402 Diet + 0.004 Lat + 4 × 10−5 Pn = 666 R2 = 0.62 P < 0.0011

1 All coefficients are significant at P < 0.001 except Log M2 (P = 0.018), Lat (P = 0.026), and P (P = 0.021).

Table 4 Ordinary least squares regressions (OLS) of Log M (kg) on Log D (ind/km2) and log A (km2) onLog D for populations for which census area values were available (n = 377). We also present the results ofOLS for the relationship between the residuals of Log M : Log D relationships (relationship 1) and log A, aswell as the relationship between the residuals of log A : Log D (relationship 2) and Log M for all mammalsand across dietary groups

Group Log M : Log D log A : Log D

a b ± SE r2 P a b ± SE r2 P

All mammals (n = 377) 1.271 –0.685 ± 0.034 0.52 0.00001 1.450 –0.575 ± 0.037 0.39 0.00001Herbivores (n = 313) 1.420 –0.713 ± 0.036 0.55 0.00001 1.458 –0.561 ± 0.039 0.40 0.00001Insectivores (n = 27) 0.735 –0.836 ± 0.153 0.55 0.00001 1.700 –0.459 ± 0.186 0.20 0.0210Carnivores (n = 37) 1.060 –1.309 ± 0.175 0.62 0.00001 1.332 –0.883 ± 0.177 0.42 0.00001

Residuals of Log M : Log D and log A Residuals of Log A : Log D and Log M

a b ± SE r2 P a b ± SE r2 P

All mammals (n = 377) 0.186 –0.113 ± 0.033 0.03 0.0006 0.310 –0.276 ± 0.036 0.14 0.00001Herbivores (n = 313) 0.171 –0.097 ± 0.033 0.03 0.0037 0.375 –0.282 ± 0.039 0.14 0.00001Insectivores (n = 27) 0.097 –0.129 ± 0.138 0.03 0.3560 –0.462 –0.621 ± 0.161 0.37 0.0007Carnivores (n = 37) 0.457 –0.343 ± 0.163 0.16 0.0132 0.532 –0.768 ± 0.172 0.36 0.0001

a, Intercept; b, slope; SE, standard error of the slope; r2, coefficient of determination; P, probability that the correlation could occur by chance alone; n, sample size.




Fig. 7 Relationship between the log10 of body mass (Log M) and the log10 of population density (Log D) forterrestrial mammal populations for which census area values were available (n = 377). The curves representLOWESS fits (tension 0.5) to the data.

Table 5 Models describing the statistical effect of Log M (kg), census area, climate and geography on Log D(km2) in terrestrial mammal populations for which census area values were available (n = 377). Models weredeveloped using Stepwise multiple regression. Only coefficients significantly different (P < 0.05) from zero areshown. Latitude (Lat) is absolute latitude (°) and precipitation (P) is total annual precipitation (mm). n isthe sample size and r2 is the multiple coefficient of determination

Group Model

All Mammals Log D = −0.608 Log M − 0.160 log A + 0.003 Long + 1.715 × 10−4 Alt + 0.144 Biome − 0.367 Diet + 0.036Tr2 = 0.66 n = 275

Herbivores Log D = 0.638 − 0.186 log A − 0.601 Log M + 0.006 Long + 2.596 × 10−4 Pr2 = 0.66 n = 227

Insectivores Log D = 1.004 − 0.037 Lat − 0.525 log A − 0.935 Log Mr2 = 0.78 n = 22

Carnivores Log D = −0.781 − 0.834 Log M + 0.265 Biome + 8.198 × 10−4 Altr2 = 0.74 n = 26


482 M. Silva et al.


and not the species that are really present in thestudy area. This finding may also explain whyslope values can vary when individual mammaliancommunities are analysed separately (for examplesee Table 3 in Silva & Downing, 1995). Mamma-lian communities generally differ in species com-position, thus we can expect that they would alsodiffer in M distribution. Although this does notnecessarily mean that they would differ in Log M :Log D relationships, our findings suggest thatcommunities may show differences in M : D rela-tionships depending on the trophic groups andbody sizes of community members, the M dis-tribution, as well as the terrestrial biome wherethey occur.

In contrast to M, climatic and geographicalfactors have a negligible effect on D, suggestingthat environmental conditions may be poor pre-dictors of abundance in mammalian populations.Similar results were found by Currie & Fritz(1993) who also investigated the joint effects ofclimate and geography on mammalian popula-tion density and energy use. Since many ecolo-gical variables and processes are scale-dependent,with patterns and processes at one scale notapplying to other scales, it is possible thatalthough field studies have shown that variablessuch as altitude and climatic conditions affectpopulation density (e.g. Caughley, 1964; Churchill,1991), this cannot be extrapolated to a largerspatial scale. Another explanation may be thatsince M is significantly correlated with most ofthe geographical and climatic factors examinedhere, some of the variability in D explained by Mmay result from climatic and/or geographical dif-ferences among habitats occupied by populations.Currie & Fritz (1993) also reported significantcorrelations between M and some of the explan-atory variables examined in their study.

The significant positive relationship between Dand latitude reported in our analyses indicatesthat D increases with increasing latitude. Thisresult concurs with Johnson’s (1998) findings onthe effects of latitude on the abundance ofAustralian mammals. As Johnson (1998) suggested,the simplest explanation for this trend is thatsince at low latitudes species diversity is high andniche space is possibly restricted, the spatialdensity of mammal populations in tropical areasmay be limited by the interaction between thesetwo factors. It is also possible that higher climatic

stability in the tropics may allow mammal popula-tions to sustain themselves at minimal densitiesthat are lower than minimal densities sustainablein temperate climates (Silva & Downing, 1994).Our findings also showed a negative relationshipbetween Log M and latitude, as reported by Currie& Fritz (1993). This may reflect the fact that trop-ical studies in our dataset focused on large-bodiedspecies (Blackburn & Gaston, 1999a). It is interest-ing to mention, however, that the mean Log Mdid not differ significantly between the biomesfor which n ≥ 30; the only exception was thesavanna biome for which the mean Log M wassignificantly greater than that of other biomes( and Tukey’s multiple comparison test;P > 0.05). It is also possible that our findings reflectthe current patterns of geographical distributionof mammalian species. A substantial fraction ofthe large mammalian fauna of various regions ofthe world including northern Eurasia, NorthAmerica and southern South America have dis-appeared since humans started to expand theirgeographical range (e.g. Brown, 1995; Brown &Lomolino, 1998). Not only is the global speciesdiversity in mammals the highest at low latitudes,partially explaining why more species are foundat these latitudes including large-bodied ones,but it is also where large-bodied mammals arecurrently the most abundant and diverse.

Considerable attention has recently beenfocused on the effects of census area on theM : D relationship (e.g. Blackburn & Gaston,1996a, 1999a, 1999b; Johnson, 1999). It was feltthat undue bias had not been induced by thisrestriction as the inclusion of census area inreported studies seemed a random phenomena.Although the models incorporating census areagave a much improved overall fit of the M : Drelationship, especially for secondary consumerssuch as insectivores and carnivores, our findingsdo not confirm previous studies (e.g. Blackburn& Gaston, 1996a; Smallwood et al., 1996) sug-gesting that census area is a better predictor ofthe density of a mammalian species than is itsbody size. It is difficult to explain why our resultswould differ from these studies, but one possibil-ity is that our study is based on population abund-ances rather than species averages. The closecorrelation of census area and body mass valuesboth overall and across all dietary levels raises aserious difficulty in the interpretation that can




be offered for such results. Type of species andtherefore expected body mass are often predeter-mined aspects of abundance studies reflectinginvestigator interest (Johnson, 1999). This wouldseem to imply that census area would often be apredetermined component and most probably acomponent expected to be highly correlated withbody mass. This was observed in this database,obscuring the use of census area as a clearly inter-pretable element of species-abundance models.Here, the inclusion of both density and censusarea as distinct variables in the regression ana-lysis explaining body mass leads to this difficulty.

Previous studies on the patterns of variation inpopulation density have been dominated by theeffects of M and to a lesser extent diet, becausethese two variables explain a large portion of thevariation in density of mammals both at the popu-lation and the species level. Our findings showthat variables such as temperature, precipitation,and latitude only have a minor and often non-significant effect on D. On the other hand, it seemsclear that an issue which needs more careful con-sideration is the relationship between the distribu-tion of M and the slope value of the Log M :Log D relationship. Although other factors notyet examined may explain the differences in slopevalues between or within studies, a rigorous ana-lysis of the implications that M distributions mayhave on allometric studies appears to be needed.

ACKNOWLEDGMENTS

We thank Peter Cotgreave for reading and com-menting on an earlier version of this manuscript.We are also grateful to Mark V. Lomolino andtwo anonymous reviewers for their comments andsuggestions on the manuscript. This research wassupported by operating grants to J.A. Downingand M. Silva from the Natural Science and Engin-eering Research Council of Canada (NSERC).

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BIOSKETCHES

Marina Silva is an Assistant Professor in the Department of Biology at University of Prince Edward Island. Her research interests include macroecology and conservation biology. Her work focuses on the study of the implications of spatial scale and habitat fragmentation on the patterns of abundance and diversity of mammal and amphibian populations.

Michael Brimacombe is an Associate Professor in the Department of Preventive Medicine, New Jersey Medical School, University of Medicine and Dentistry of New Jersey. He is a medical biostatistician with interests in modelling of clinical, biological and environmental data.

John A. Downing is a Professor in the Department of Animal Ecology at Iowa State University. His research interests include biogeochemistry, marine ecology, sustainable agriculture, allometry and predictive ecology.


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