Size-Abundance Relationships in an Amazonian Bird Community

18 Pages·2013·0.67 MB·English

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Faculty Publications in the Biological Sciences Papers in the Biological Sciences
2-2003
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IImmpplliiccaattiioonnss ffoorr tthhee EEnneerrggeettiicc EEqquuiivvaalleennccee RRuullee
Sabrina E. Russo
University of Nebraska - Lincoln, [email protected]
Scott K. Robinson
University of Illinois at Urbana-Champaign
John Terborgh
Duke University, [email protected]
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Russo, Sabrina E.; Robinson, Scott K.; and Terborgh, John, "Size-Abundance Relationships in an
Amazonian Bird Community: Implications for the Energetic Equivalence Rule" (2003). Faculty Publications
in the Biological Sciences. 253.
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Russo, Robinson & Terborgh in the American Naturalist (February 2003) 161(2). Copyright 2003, University of Chicago. Used by permission.
vol. 161, no. 2 the american naturalist february 2003
Size-Abundance Relationships in an Amazonian
Bird Community: Implications for the
Energetic Equivalence Rule
Sabrina E. Russo,1,* Scott K. Robinson,1 and John Terborgh2
1.DepartmentofAnimalBiology,UniversityofIllinois,Urbana, Therelationshipbetweenbodysizeandpopulationdensity
Illinois61801; has been extensively examined because it has broad im-
2.CenterforTropicalConservation,DukeUniversity,P.O.Box plicationsforthestructureofandenergyflowinecological
90381,Durham,NorthCarolina27708-0381
communities (Damuth 1981, 1987; Brown and Maurer
1987;Pageletal.1991;IlliusandGordon1992;Taperand
SubmittedMay10,2001;AcceptedAugust27,2002;
Marquet1996),geographicrangesize(BrownandMaurer
ElectronicallypublishedFebruary5,2003
1987;GastonandBlackburn1996),patternsofbiodiversity
and evolution (Brown and Maurer 1986, 1987; Damuth
1993;Siemannetal.1996),andthegeneralityandpotential
theoretical underpinnings of allometric scaling laws
abstract: We studied size-abundance relationships in a species-
(Morse et al. 1985; Dobson and Headrick 1995; West et
rich Amazonian bird community and found that the slope of the
al.1997;Enquistetal.1998;RitchieandOlff1999;Enquist
logarithmicrelationshipbetweenpopulationdensityandbodymass
(bp(cid:1)0.22)issignificantlyshallowerthanexpectedunderDamuth’s andNiklas2001,2002).Damuth(1981,1987)investigated
thelogarithmicrelationshipbetweenbodymassandpop-
energeticequivalencerule(EER),whichstatesthatpopulationenergy
use(PEU)isindependentofspeciesbodymass.Weusedestimates ulation density for mammals spanning several orders of
ofavianfieldmetabolicratestoexaminethelogarithmicrelationship magnitude in size, and he found a slope of (cid:1)0.75. The
between PEU and body mass and its variation among ecological negativeslopehasbeensuggestedtoreflectmetabolicpro-
guilds. The relationship for all species had a significantly positive cesses;thatis,largeranimalsshouldhavelowerpopulation
slope (bp0.46), indicating that PEU of larger species was greater densitiesbecausetheyusemoreenergypercapitaperunit
than that of smaller species. Analyses of guilds revealedsignificant
time (Peters 1983). Because the logarithmic relationship
variation. The slopes of the frugivore-omnivore, insectivore, and
between mammals’ resting metabolic rate and body mass
granivore guilds were all significantly positive, with that of the
has an estimated slope of 0.75 (Peters 1983), Damuth
frugivore-omnivore guild being the steepest. In contrast, PEU did
(1981, 1987) proposed the energetic equivalence rule
notvarysignificantlywithspeciesbodymassamongraptors.These
(EER). This rule states that the energy used by a species’
results were confirmed in analyses using both species values and
phylogeneticallyindependentcontrasts,andtheresultsdonotsup- local population (population energy use [PEU]) is inde-
porttheEERinthiscommunity.Thespatialdistributionofresources pendentofitsbodymass.Energeticconstraintsmaythere-
andmechanismsofinterferencecompetitionwithinguildsmayex- fore influence the structure of ecological communities
plain why most patterns differed from the predictions of theEER. (Damuth 1981, 1987), such as by placing an upper limit
Other sources of variation, including the effects of scale, are also on the population densities of large species.
discussed.
IftheEERisamoregeneralruleofcommunitystructure
(Damuth 1981, 1987), then it may be expected to apply
Keywords:energeticequivalencerule,Neotropics,aviancommunity
at the community scale, as well as at regional or global
structure,bodymass,populationdensity,phylogeneticallyindepen-
scales. In such a case, the absolute value of the slope of
dentcontrasts.
thesize-abundancerelationshipshouldnotbesignificantly
different from the slope of the logarithmic relationship
between body mass and field metabolic rate (FMR) for a
given assemblage of species. Scrutiny of the size-
* E-mail:[email protected].
Am.Nat.2003.Vol.161,pp.267–283.(cid:1)2003byTheUniversityofChicago. abundance relationship in animals, however, shows vari-
0003-0147/2003/16102-010172$15.00.Allrightsreserved. ationacrosstaxonomic,spatial,andgeographicscales,but
268 The American Naturalist
Table 1: Chronological summary from the literature of ordinary least squares regression statistics of the logarithmic
relationshipbetweenbody massand populationdensityfor birds
Region Guilda Slope 95% CIb R2 nc Probability Reference
North America All guilds (cid:1).19 ((cid:1).47, .09) .03 60 1.05 Petersand Wassenberg1983
North America Herbivores .21 ((cid:1).21, .63) .05 22 1.05 Petersand Wassenberg1983
North America Carnivores (cid:1).52 ((cid:1).89, (cid:1).16) .18 38 !.05 Petersand Wassenberg1983
North America All guilds (cid:1).30 NGd NGd 197 NGd Brown and Maurer 1986
North America All guilds (cid:1).49 ((cid:1).57, (cid:1).40) .18 564 .0001 Juanes 1986
North America Herbivores (cid:1).02 ((cid:1).20, .16) .001 56 .81 Juanes 1986
North America Omnivores (cid:1).23 ((cid:1).60, (cid:1).14) .03 47 .22 Juanes 1986
North America Insectivores (cid:1).31 ((cid:1).40, (cid:1).22) .09 442 .001 Juanes 1986
North America Raptors (cid:1)2.22 ((cid:1)3.18, (cid:1)1.26) .58 19 .001 Juanes 1986
North America All guilds (cid:1).09 ((cid:1).15, (cid:1).02) .02 380 !.05 Brown and Maurer 1987
Great Britain All guilds (cid:1).75 ((cid:1)1.06, (cid:1).44) .14 147 .0001 Nee et al. 1991
Sweden All guilds (cid:1).77 ((cid:1)1.00, (cid:1).54) .18 206 .0001 Nee et al. 1991
Global All guilds (cid:1).60 NGd .15 437 .0001 Cotgreaveand Harvey 1992
Great Britain All guildse (cid:1).57 NGd .08 175 .0002 Blackburn et al. 1994
Ireland All guildse (cid:1).74 NGd .11 149 .0002 Blackburn et al. 1994
Panama All guilds (cid:1).25 NGd .05 25 .30 Brawn et al. 1995
Australia All guilds (cid:1).82 ((cid:1).97, (cid:1).66) .35 200 .001 Cotgreave1995
Australia Nonpasserines (cid:1)1.03 ((cid:1)1.52, (cid:1).97) .27 57 .0001 Cotgreave1995
Australia Passerines (cid:1).42 ((cid:1).36, (cid:1).17) .11 143 .0001 Cotgreave1995
Great Britain All guilds (cid:1).57 NGd NGd 156 .0001 Gregory 1995
Great Britain Nonpasserines (cid:1).31 NGd NGd 79 .04 Gregory 1995
Great Britain Passerines (cid:1).23 NGd NGd 77 .15 Gregory 1995
Great Britain All guilds (cid:1).79 ((cid:1)1.12, (cid:1).45) .13 144 .001 Greenwood et al. 1996
Great Britain All guildse (cid:1)1.43 ((cid:1)2.21, (cid:1).64) .21 51 .001 Greenwood et al. 1996
a Allstudiesareofresidentbreedingbirds,exceptwhereotherwisenoted.
b The 95% confidence interval(95%CI)for eachslope isgiven.Whenthe95%CIwasnotreported,itwascalculatedfromthereported
standarderroroftheregressionslopeandsamplesize.
c Thesamplesize(n)isthenumberofspecies.
d NGmeans“notgiven.”
e Studywasofwinteringmigrants.
the mechanisms underlying the relationship and its vari- usewithrespecttobodysizeamongspeciesinaviancom-
ation remain obscure (Cotgreave 1993; Blackburn and munities,thentheslopeofthesize-abundancerelationship
Gaston 1997; Marquet 2000). Patterns in size-abundance for birds should be in the range of (cid:1)0.645 to (cid:1)0.717.
relationships in plants tend to be more consistent across Among birds in temperate communities, some size-
multiple scales (Enquist et al. 1998, 1999; Enquist and abundance relationships fit these expectations (table 1).
Niklas 2002). Although many analyses of size-abundance Many slope estimates for birds, however, are shallower
relationships in animals use global- or regional-scaledata than(cid:1)0.681,andsomearenotsignificantlydifferentfrom
setscompiledfromtheliterature,manyworkershavesug- 0 (table 1). Birds in a Panamanian lowland forest have a
gested that smaller-scale analyses, such as at the level of shallowslope((cid:1)0.25)thatissignificantlydifferentneither
completecommunities,maybemorelikelytorevealmech- from(cid:1)0.681norfrom0(Brawnetal.1995).Furthermore,
anisms responsible for patterns in size-abundance rela- some studies have found the shape of the scatterplot de-
tionships (Blackburn et al. 1990, 1993a). Patterns at scribingtherelationshipintemperatebirdstoreachapeak
smaller scales of analysis, however, tend to be more var- at intermediate body masses (Brown and Maurer 1987),
iableandtoshowlessstatisticallysignificantrelationships rather than being linear and negative (Damuth 1981,
than ones at larger scales (Currie 1993; Blackburn and 1987);thisindicatesthatthemostabundantavianspecies
Gaston1997),particularlyinbirds(PetersandWassenberg are of intermediate size.
1983). Explanations for variation in the size-abundance rela-
A recent estimate of the slope of the logarithmic rela- tionship are related to energetics, scale of analysis, eco-
tionship between body mass and FMR for birds is 0.681 logical factors, and evolutionary history (Lawton 1989;
(95% confidence interval [CI]p0.645 to 0.717; Nagy et Blackburn et al. 1993b; Cotgreave 1993; Blackburn and
al. 1999). If there is an equitable distribution of resource Gaston 1997). This article focuses on ecological factors
Energetic Equivalence Rule in Amazonian Birds 269
andevolutionaryhistory,interpretingtheireffectsinlight tendtoformguildsinwhichinterspecificcompetitionmay
of potential effects of scale. The ecological attributes of be intense. Within such groups, large body size maypro-
habitatstructureandspeciesmembershipinanecological vide benefits in interspecific competitive interactions, es-
guild may affect size-abundance relationships. Habitats peciallyifaccesstoresourcesisdeterminedbyinterference
varyinresourceavailabilityandvegetationstructureboth competition. The effects of interspecific competition on
temporally and spatially (Bell et al. 1991). If such vari- resource access may adversely affect the abundance of
ability affects avian species composition or population smaller species, which would explain slopes greater than
densities in different habitats, then variation in the slope or equal to 0 found in these groups. In contrast,analyses
of the size-abundance relationship among habitats may of wintering British, Irish, and resident Australian birds
result.Size-abundancerelationshipsalsomaydifferamong did not find any statistically significant tendency in the
ecological guilds of birds (Peters and Wassenberg 1983; probability of obtaining a positive or a negative slope re-
Juanes1986).Amongtemperatebirds,insectivoreandcar- lated to taxon rank (Blackburn et al. 1994; Cotgreave
nivore guilds tend to have negative slopes, whereas her- 1995). Nonetheless, in data from an Arizona experiment
bivore and omnivore guilds tend to have slopes not sig- thatmanipulatedlevelsofcompetitionamongbirds,tribes
nificantly different from 0, although this pattern is not that demonstrated strong interspecific competition were
consistent among studies (table 1). Nonetheless, having those in which the largest species were most abundant
slopes not different from 0 in some guilds suggests that (Cotgreave 1994).
larger species may be more abundant than would be ex- TheAmazonianbirdassemblageexaminedinourstudy
pected under the EER. hasseveralcharacteristicsthatallowauniquecontribution
Ifvariationinpopulationdensityisconstrainedbybody toourunderstandingoftherelationshipbetweensizeand
size via, for example, ecological orenergeticmechanisms, abundanceandtherelationship’simplicationsforpatterns
then these traits should exhibit correlation across phylo- ofPEUamongspecies.First,toourknowledge,theseanal-
genetic history. Most examinations of thesize-abundance yses are the first exploration of thiskindforalocal,sym-
relationship have used statisticalanalysisofspeciesvalues patricassemblageoftropicalbirds.Whethertemperateand
without incorporating either phylogenetic or taxonomic tropical birds differ in size-abundance relationships has
information, but more recent analyses have incorporated been largely unexamined. This empirical gap may be im-
these sources of variation(Neeetal.1991;Cotgreaveand portant, given the potential for differences in metabolic
Harvey1992,1994;Blackburnetal.1994;Cotgreave1994, ratesbetweentemperateandtropicaltaxa(VleckandVleck
1995; Gregory 1995). Comparative studies should incor- 1979; Hails 1983). Second, these data are from complete
porate phylogeny because trait values tend to be more studiesoftheaviancommunitiesinthreelocalrainforest
similar among closely related species (Felsenstein 1985; habitats, censused using the same methods and often by
Grafen 1989; Harvey and Pagel 1991). Although popula- the same observers (Terborgh et al. 1990; Robinson and
tion density is often an ecologically labile trait, closely Terborgh 1997; S. K. Robinson and J. Terborgh, unpub-
related species may share other traits that constrain pop- lished data). Potential biases introduced from data com-
ulation densities to be similar, and this has been shown piledfromliteraturesourcesusingdiversemethodsingeo-
tobethecaseforsomeavianlife-historytraits(Blackburn graphically distant communities are thereby reduced
et al. 1996). Consequently, species values may not be in- (Lawton 1989). In addition, examining whether the size-
dependent of one another, which violates a fundamental abundancerelationshipmightconstraincommunitystruc-
assumption of most statistical tests. Nonindependence turemaybemostappropriatelydoneusingadatasetfrom
amongdatapointscanresultininflatedteststatisticsand a complete community study rather than data compiled
inappropriate conclusions concerning the nature of the fromtheliterature(Blackburnetal.1990;Pageletal.1991;
relationship between the traits in question (Martins and CotgreaveandHarvey1992).Third,thisavianassemblage
Garland 1991; Harvey and Rambaut 1998; Garland and isveryspeciesrich,withmorethan400residentlandbirds,
Ives 2000). providing a large data set with which to examine sources
Ithasprovendifficulttodifferentiatebetweentheeffects ofvariationinthesize-abundancerelationship.Finally,the
of evolutionary history and those of ecological similarity studysiteispristineandhasexperiencedlittleornohuman
within guilds on the size-abundance relationship. In an developmentorexploitation,sothatavianpopulationden-
analysis of British birds, the slopes of size-abundance re- sities should not be influenced by contemporary human
lationships in higher taxonomic ranks were negative, impacts.
whereas those in lower ranks were more likely to be pos- We addressed three questions. Does the slope of the
itive (Nee et al. 1991). The authors suggested that phy- logarithmic relationship between body mass and popu-
logeneticallydistinctgroups,thatis,thosewithalongtime lationdensitydiffersignificantlyfromtheslopeof(cid:1)0.681
sincedivergencefromtheirmostrecentcommonancestor, expectedundertheEER?Doestheslopeofthelogarithmic
270 The American Naturalist
relationship between body mass and PEU differ signifi- is above the level of the floodplain and is dominated by
cantlyfromtheslopeof0expectedundertheEER?Finally, very old, yet very heterogeneous forests.
do the slopes of the logarithmic relationships between Populationdensities(numberofindividualsper100ha)
body mass and abundance and between body mass and were estimated based on a combination of spot-mapping
PEU vary among habitats or ecological guilds? (Kendeigh 1944), mist-netting, transect, and breeding
We tested for differences in the size-abundance rela- group census methods. Census methods are described in
tionship attributable to habitat using avian population detailinTerborghetal.(1990)andRobinsonandTerborgh
densitiesinthreehabitatsofincreasingstructuralandflo- (1997)andarebrieflysummarizedhere.Censusplotareas
ristic complexity: late successional forest, mature flood- ineachhabitatwerelatesuccessionalforest,60ha;mature
plainforest,andterrafirme(upland)forest.Wetestedfor floodplainforest,97ha;andterrafirmeforest,70ha.Each
differencesinthesize-abundancerelationshipamongfour plot was censused systematically for at least one season.
trophicguilds:frugivore-omnivore,granivore,insectivore, Spot-mapping records were supplemented by mist-net
and raptor. We analyzed species trait values without in- captures,whichhelpedtodetectnonvocalspeciesandalso
corporatingphylogeneticinformation,andweusedaphy- to provide color-bandedindividualstohelpdelineateter-
logenetic hypothesis to calculate independent contrasts ritories of understory species. All records of each species
(Felsenstein 1985; Harvey and Pagel 1991). wereplottedonmaps,andterritorialboundarieswerees-
timated and then used to obtain estimates of population
density. For nonterritorial species, we estimated popula-
Study Area and Methods
tion density bycounting males atleks(manakinsandco-
Estimates of avian population densities were compiled tingas)orbyrecordingthemaximumnumberofindivid-
from published and unpublished studies of avian com- ualsobservedatfruitingtrees.Territorysizeestimateswere
munity structure in floodplain and upland habitats in based on an average of 15–30 registrations per pair. The
Manu´ National Park, Madre de Dios, southeastern Peru, variety of census methods used and the use of spot map-
within 5 km of the Cocha Cashu Biological Station ping minimized any potential bias in population density
(11(cid:2)54(cid:1)S, 71(cid:2)18(cid:1)W, elevation approximately 400 m; Ter- estimates that might result from using only song census
borgh et al. 1990; Robinson and Terborgh 1997; S. K. methods (see Calder 2000). Species for which our census
Robinson and J. Terborgh, unpublished data). The area methodswouldhaveproducedabiasedpopulationdensity
liesneartheclimaticboundarybetweenTropicalandSub- estimate (Apodidae, Trochilidae, Chloroceryle inda, Chlo-
tropical Moist Forest in the Holdridgesystem(Holdridge roceryle aenea, Piculus leucolaemus, Piculus chrysochloros,
1967). Cacicus cela, Psarocolius oseryi, Psarocolius decumanus,
All census plots, except the one in terra firme, were Psarocolius angustifrons, and Psarocolius yuracares) were
withinthewhitewaterManu´ River’s6-km-widefloodplain, excluded from the data set. Although swifts (Apodidae)
whichcontainsacomplexmosaicofsuccessionalandma- andhummingbirds(Trochilidae)aresomeofthesmallest
ture forest stands that resulted from the meandering and speciesinthiscommunity,theavailableestimatesofpop-
floodingdynamicsoftheriver(TerborghandPetren1991). ulation densities for these species span a range from rare
The botanical characteristics and structure of the flood- to abundant (Terborgh et al. 1990); this makes any bias
plainanduplandhabitatshavebeendescribedindetailin resulting from their exclusion from the analysis unlikely.
previous publications (Foster 1990; Terborgh and Petren Migratory species also were excluded (Chordeiles minor,
1991; Robinson andTerborgh1997).Briefly,astheManu´ Chordeiles rupestris, Coccyzus americanus, Coccyzus mela-
River meanders across its floodplain, it creates sand coryphus, Contopus borealis, Contopus virens, Vireo oliva-
beaches along the point bar that are colonized by early ceous). Body masses (in grams) were field measurements
successionalvegetation.Theearlystagesofthisfloodplain from birds measured at the four census plots or from
succession have species-poor bird communities and few museum specimens collected elsewhere in southeastern
coexistingsyntopiccongeners.Latersuccessionalstagesin Peru or Bolivia (Louisiana State University Museum of
the floodplain consist of “transitional” forest, as the veg- Natural History, Field Museum of Natural History).
etation structure becomes more complex and the plant Population energy use (kJ per species per day per 100
andbirdcommunitiesmorediverse,andsomeoftheearly ha) was calculated as the product of individualmetabolic
successional species are lost. Mature floodplain forest, rate (kJ per individual per day) and population density
probablyatleastseveralhundredyearsold(Terborghand (Taper and Marquet 1996). Ideally, calculation of PEUin
Petren 1991), is floristically diverse and has a complex this study should use species- or genus-specific estimates
verticalstructure.Ofthefourhabitatsinthisstudy,mature of FMR for tropical birds. Unfortunately, such data are
floodplain forest contains the greatest numbers of bird not available. Feeding guild may be an important source
species and coexisting congeners. Upland, or terra firme, ofinterspecificvariationinmetabolicrate(McNab1988),
Energetic Equivalence Rule in Amazonian Birds 271
although analyses using methods that incorporate phy- variation in the slope (interaction terms) and in the least
logenetic information have failed to find differences squares means (main effects) attributable to habitat and
among guilds (Bennet and Harvey 1987). Interspecific guild. Leastsquares means reflectthevariationinaverage
studies of metabolic rate have also shown that tropical avian population density. In the full model with all main
bird species, particularly frugivores, may have reduced effects and interactions, neitherthe maineffectofhabitat
metabolic rates, relative to birds from higher latitudes nor the interactions between habitat and body mass and
(Weathers 1979, 1997; Bartholomew et al. 1983; Hails between habitat and guild explained asignificantamount
1983). However, substantialwithin-familyvariationexists of the variation in population density (table 2). These
in whether tropical species’ metabolic rates are higher or results indicate that average mean avian population den-
lowerthanwouldbepredictedbasedontemperatespecies sity,theslopeofthesize-abundancerelationship,andpop-
(Vleck and Vleck 1979; Schleucher 1999; McNab 2001). ulation densities of species in each guild, respectively,did
We therefore consider the available literature to be inad- not vary significantly among habitats. These terms were
equate to provide detailed taxon- or guild-specific esti- thereforepooledintoerrorforallsubsequentanalyses.In
matesofFMRforuseinthisstudy.Althoughearlystudies all subsequent analyses, we used a logarithmic transfor-
indicated that metabolic rates differed between passerine mation of either mean population density for species oc-
andnonpasserinebirds(LasiewskiandDawson1967;Ben- curring in more than one habitat or the observed popu-
net and Harvey 1987), a recent analysis that incorporates lation density for species occurringin onlyonehabitatas
phylogenetic information found no differences in meta- the dependent variable in size-abundance analyses and
bolicratebetweenpasserinesandnonpasserines(Reynolds PEUcalculations.Eachspecies,therefore,wasrepresented
and Lee 1996). For these reasons, we elected to calculate by only one point in the data set, which allowed results
PEUusingtheallometricrelationshipforFMRforallbirds basedonspeciesvaluestobecompareddirectlywiththose
presented in Nagy (1999). Some studies suggest that fru- based on phylogenetically independent contrasts.
givorousspeciesmayhavelowermetabolicratesthanspe- We also tested whether the relationships of population
ciesofotherfeedingguilds(McNab1986,1988,2001).To density and PEU to body mass, using species values and
accountforthispotentialsourceofvariation,wealsocon- phylogenetically independent contrasts, would best be
ductedPEUanalyseswithanindividualmetabolicratethat modeled using a single error variance for all guilds or
was reduced by 75% (McNab 2001) for all species in the separateerrorvariancesforeachguild.Unequalvariances
frugivore-omnivore guild. Neither the slope nor the sig- among guilds would affect the comparisons of slopes
nificance of the overall relationship or of each guild was among guilds. In all cases, comparisons of the scores of
significantly affected by this adjustment. theAkaikeInformationCriterionforthetwomodelsusing
The four guilds were broadly defined, given that most themixedprocedureinSASindicatedthatthemodelusing
species’dietsarenotknownindetail(Remsenetal.1993). a single variance for all guilds was the best model(Burn-
Ingeneral,dietsofspeciesconsideredfrugivore-omnivores hamandAnderson1998).Wethereforeusedthestandard
contain mostly fruit, supplemented by insects, nectar, output of the mixed procedure for comparisonsofslopes
small vertebrates, or seeds. Granivores, insectivores, and among guilds, and we adjusted for multiple comparisons
raptors consume primarilyseeds,insects,andvertebrates, using Tukey’s HSD method (Zar 1996) with an
respectively, although species in these guilds may supple- experiment-wise error rate of P!0.05.
ment their diets to an unknown and presumably small The choice of an appropriate regression model to use
extent with other food items. inallometricanalysesisacomplicatedissue(Rayner1985;
McArdle 1988). In our study, as in most allometric anal-
yses, the independent variable (body mass) cannot be as-
Statistical Analysis
Using the mixed procedure in SAS (SAS Institute 2000),
Table 2: Mixed model statistics for the relationshipbetween
we modeled the relationship between body mass, popu-
body mass and population density for birds in three Neo-
lation density, habitat (late successional, mature flood-
tropical rain forest habitatsand four ecologicalguilds
plain, and terra firme forests), and ecological guild
Fixed effect df F value Probability
(frugivore-omnivore, granivore, insectivore, and raptor)
using species trait values. For all analyses, body massand Log(body mass) 1,293 11.19 .0009
population density were logarithmically transformed.Be- Guild 3,265 3.00 .0312
causemanyspeciesoccurredinmorethanonehabitatand Habitat 2,339 .07 .9315
thereforewererepresentedmorethanonceinthedataset, Guild # habitat 6,355 .56 .7616
Log(body mass)# guild 3,265 3.39 .0185
random effects were included in the model by treating
Log(body mass)# habitat 2,334 .54 .5831
species as nested within guild. We tested for significant
272 The American Naturalist
sumed to be measured without error, which is an as- tropicalbirdspecies,suchaphylogenyisnotavailable.We
sumption of ordinary least squares (OLS) regression.The thereforeconstructedaphylogenythatincludedallspecies
general structuralrelation(GSR)maybeemployedtoac- represented in our data set, based on phylogenetic hy-
count for the error variances in the dependent and in- potheses forthese taxapublishedintheliteraturecitedin
dependentvariablesifthesequantitiesareknown(Rayner theappendix.WeusedthephylogenetichypothesisofSib-
1985). As is often the case in analyses of size-abundance ley and Ahlquist (1990) to represent the backbone of the
relationships,ourdatadonotcontaininformationonthe tree (lower nodes) because their phylogeny achieves the
errorvarianceinpopulationdensity,makingitimpossible most complete taxon sampling atlowertaxonomiclevels.
to use the GSR. In such cases, some workers have advo- For higher taxonomic levels, we used clade-specific,pub-
cated use of reduced major axis (RMA) regression (e.g., lished phylogenetic hypotheses (appendix) for taxa not
Griffiths1998),althoughothersdiscourageitsuse(Harvey represented in Sibley and Ahlquist (1990) or when taxon
and Pagel 1991). samplingofacladewasmorecompletethanthatinSibley
The fact that the predictor variable is subject to error and Ahlquist (1990). Taxa for which no information on
isnottheonlycriterionforselectingRMAregression.The phylogeneticrelationshipswasavailablewereplacedinthe
RMA method assumes that the ratio between the error tree assuming sister taxon relationships according to the
variances in the dependent and independent variables is taxonomy of Sibley and Monroe (1990).
equal to that of the variances in these variables (Rayner Because the final phylogenetic tree was a composite
1985; McArdle 1988). This assumption, however, is un- from multiple sources, branch lengths could not be esti-
likelytobetrueforourpopulationdensityandbodymass mated. We therefore tested whether appropriately stan-
data. This is because the error variance in body mass is a dardized contrasts could be obtained by using uniform
very small proportion of the variance in body mass, branch lengths or by using branch lengths assigned with
whereas the error variance in population density is likely the assumption that the ages of taxa are proportional to
tobearelativelymuchgreaterproportionofthevariance the number of species they contain (Grafen’s branch
inpopulationdensity.TheslopeestimateprovidedbyOLS lengths; Grafen 1989; Purvis and Rambaut 1995). We ex-
regression has little or no bias when the error variance is aminedthecorrelationbetweentheabsolutevaluesofthe
substantiallysmallerthanthevarianceoftheindependent standardized contrasts and their standard deviations to
variable(Madansky1959;DraperandSmith1998).When ensurethatbranchlengthswereappropriatelyscaled(Gar-
the independent variable is subject to error, the slope es- land et al. 1992; Diaz-Uriarte and Garland 1996). Using
timated by OLS regression should be multiplied by the Grafen’s branchlengthsresultedinsubstantiallymoreas-
term [1(cid:2)(j2/j2)], where j2 is the error variance and j2 sumptionviolations.Usinguniformbranchlengths,inall
u X u X
is the variance in the independent variable (Madansky but five of 15 cases, there was no statistically significant
1959; Draper and Smith 1998). Using measurements of relationshipbetweenthesevariables.Comparativeanalyses
body masses of multiple individuals of each species to using the method of phylogenetically independent con-
calculate j2, we used this equation to estimate that error trasts should use appropriately standardized contrasts
u
in body mass measurement results in a 0.5% shallower (Garland et al. 1992); however, limitations to options for
slopethanwouldbeestimatedifbodymassweremeasured standardizing contrasts arise when branch lengthscannot
withouterror.Thissmalldegreeofbiasisunlikelytoaffect beestimatedfromthephylogeny,asisthecasehere.Sim-
our conclusions. We therefore used OLS regression in all ulationshaveshownthatphylogeneticallybasedstatistical
analyses because the assumptions of this model better fit methods generally perform better than nonphylogenetic
ourdatathandothoseofRMAregression.Asanadditional ones, even under deviations from the Brownian motion
verification of the validity of OLS regression, an orthog- model,whichoccurswhencontrastsarenotproperlystan-
onalquantileregressionmethodwasusedtocalculatethe dardized (Diaz-Uriarte and Garland 1996). Therefore, all
slope of the relationship between population density and contrasts were calculated using uniform branch lengths
body mass. This method yields estimates that converge because this method allowed standardization of mostbut
strongly to the true values of parameters when there is not all contrast variables. Regressions involving contrasts
error in the predictor variable (He and Liang 2000). that did not appear to be standardized properly are in-
Phylogeneticallyindependentcontrasts,asimplemented dicated in tables 3 and 4. For the five cases with a statis-
in the computer program CAIC (Purvis and Rambaut tically significant correlation between the absolute values
1995),wereusedtoexaminetherelationshipbetweenbody ofthestandardizedcontrastsandtheirstandarddeviations,
massandpopulationdensityandbetweenbodymassand the Pearson correlation coefficients were relatively low
PEU for all species combined and for species in each of ((cid:1)0.18 to (cid:1)0.35), and inspection of the scatterplot did
the four ecological guilds individually. Although an ideal not reveal a strong relationship. Nonetheless, for regres-
comparativetestwoulduseacompletephylogenyofNeo- sions involving potentially improperly standardized con-
Energetic Equivalence Rule in Amazonian Birds 273
Table3:Ordinaryleastsquaresregressionstatisticsfortherelationshipbetweenpopulationdensityandbodymass
based on nonphylogenetic(species)and phylogenetic(contrasts)analysesof all data and data grouped by guild
Probability Correlation Probability
n Slope (SE) 95% CI (slope p 0) coefficient (slope p (cid:1).681)
Nonphylogenetic:
All data (R2 p .08) 272 (cid:1).22 (.04) ((cid:1).31, (cid:1).13) .0001 (cid:1).29a .0005
Ecologicalguild:
Frugivore-omnivore 69 .03 (.09)A ((cid:1).14, .21) .7098 .05 .0005
Granivore 24 (cid:1).30 (.15)A,B ((cid:1).62, .02) .0514 (cid:1).38 .025
Insectivore 160 (cid:1).32 (.08)B ((cid:1).49, (cid:1).16) .0001 (cid:1).30a .0005
Raptor 19 (cid:1).58 (.26)A,B ((cid:1)1.13, (cid:1).04) .0200 (cid:1).46a 1.05
Phylogenetic:
All data (R2 p .02) 204 (cid:1).18 (.09) ((cid:1).36, (cid:1).02) .047 (cid:1).14a .0005
Ecologicalguild:
Frugivore-omnivore 55 (cid:1).07 (.16)A ((cid:1).38, .24) .657b (cid:1).06 .025
Granivore 15 (cid:1).45 (.21)A ((cid:1).91, .01) .054 (cid:1).49 1.05
Insectivore 115 (cid:1).22 (.14)A ((cid:1).51, .06) .126b (cid:1).14 .025
Raptor 18 (cid:1).31 (.21)A ((cid:1).76, .14) .166 (cid:1).33 1.05
Note:Thestandarderror(SE)and95%confidenceinterval(95%CI)ofeachslopearegiven.Differencesinslopesamongguildsare
indicatednexttotheparameterestimateforeachguild,basedonplannedcomparisonsusingTukey’sHSDmethodwithanexperiment-
wiseerrorrateofP!.05.
a StatisticallysignificantPearson’scorrelationcoefficient.Forphylogeneticanalyses,thesecorrelationswereforcedthroughtheorigin.
b Regressionsinvolvingindependentcontraststhatcouldnotbeappropriatelystandardized.Theserelationshipsalsowereexamined
usingsigntests.Thesigntestwasconsistentwiththeregressionforthefrugivore-omnivoreguildbutsuggestedastatisticallysignificant
negativerelationshipfortheinsectivoreguild.
trasts,wealsoperformedsignteststoevaluatethevalidity significant, but body mass explained only a small pro-
of these regressions (tables 3, 4). portion of the variation in population density (Fp
Whethertheshapeofthescatterplotoftherelationship 24.52, dfp1,270, P!.0001, R2p0.08; fig. 1A). The
between population density and body mass is influenced slope of the regression was significantly greater than
by evolutionary constraints was investigated using two (cid:1)0.681(one-tailed;tp11.525,dfp270,P!.0005;table
methodstoestimatetheupperboundslope(UBS):quan- 3).Theslopeestimateusingorthogonalquantileregression
tile regression on species values (Scharf et al. 1998; Cade was (cid:1)0.27 (95% CI: (cid:1)0.36, (cid:1)0.18). These confidence
et al. 1999; Buchinsky 2001) and a method developed by intervals include the OLS slope estimate of (cid:1)0.22. The
Blackburn etal. (1992).Ifconstraintsontheshapeofthe estimate of the UBS using the 90% quantile was not sig-
scatterplotwereconsistentwiththeEER,thentheUBSof nificantly different from 0 (bp(cid:1)0.07; 95% CI: (cid:1)0.23,
the scatterplot would be expected to approach (cid:1)0.681. 0.08),andtheestimatethatusedthemethodofBlackburn
The UBS was estimated using quantile regression on the etal.(1992)was(cid:1)0.18(Pp.017;95%CI:(cid:1)0.04,(cid:1)0.32).
90% quantile of population density (Scharf et al. 1998). Average population densities differed among guilds (least
Using the method of Blackburn et al. (1992), the body squares means; Fp3.49, dfp3,264, Pp.0163), with
mass data were divided into 17 size classes, with no size
granivoreshavingasignificantlyhigheraveragepopulation
class having fewer than three species (data points). The density than insectivores (Pp.0489).
species with the highest population density in each size
Variationintheslopeofthesize-abundancerelationship
class was selected, for a total of 17 points in the UBS attributable to guild was significant (Fp3.91, dfp
regression analysis. 3,264, Pp.0093; fig. 2). Only slopes for insectivore and
Student’st-test(SokalandRohlf1995)wasusedtotest
raptor guilds were significantly different from0 (table3).
whether slopes were different from a slope of (cid:1)0.681 ex-
The slopes of all guilds except raptors were significantly
pectedundertheEER.Throughoutthisarticle,significance shallower than (cid:1)0.681 (table 3). The slope of the
is assessed at the P!.05 level.
frugivore-omnivoreguilddifferedsignificantlyfromthose
of insectivores (Pp.0036) and raptors (Pp.0262), but
Results
nootheramong-guildcomparisonsweresignificantlydif-
Nonphylogenetic Regression (Species Analysis)
ferent (table 3). Only the difference between frugivore-
Based on species values, the overall negative relationship omnivoreandinsectivoreguildsremainedstatisticallysig-
betweenbodymassandpopulationdensitywasstatistically nificant (experiment-wise P!.05) after adjusting for
274 The American Naturalist
Table4:Ordinaryleastsquaresregressionstatisticsfortherelationshipbetweenpopulation
energy use and body mass based on nonphylogenetic (species) and phylogenetic(con-
trasts)analysesof all data and data grouped by guild
Probability Correlation
n Slope (SE) 95% CI (slope p 0) coefficient
Nonphylogenetic:
All data (R2 p .29) 272 .46 (0.08) (.33, .55) .0005 .54a
Ecologicalguild:
Frugivore-omnivore 69 .71 (.09)A (.54, .89) .0005 .70a
Granivore 24 .38 (.15)A,B (.06, .70) .0137 .46a
Insectivore 160 .36 (.08)B (.19, .52) .0005 .33a
Raptor 19 .10 (.26)A,B ((cid:1).45, .65) .7054 .09
Phylogenetic:
All data (R2 p .12) 204 .49 (.09) (.26, .62) .0001b .34a
Ecologicalguild:
Frugivore-omnivore 55 .56 (.16)A (.24, .88) .0009b .44a
Granivore 15 .23 (.21)A ((cid:1).22, .70) .2922 .28
Insectivore 115 .46 (.14)A (.18, .74) .0018b .28a
Raptor 18 .37 (.21)A ((cid:1).08, .82) .0996 .39
Note:Thestandarderror(SE)and95%confidenceinterval(95%CI)ofeachslopearegiven.Differences
in slopes among guilds are indicatednext to the parameter estimateforeachguild,basedonplanned
comparisonsusingTukey’sHSDmethodwithanexperiment-wiseerrorrateofP!.05.
a StatisticallysignificantPearson’scorrelationcoefficients;forphylogeneticanalyses,thesecorrelations
wereforcedthroughtheorigin.
b Regressions involving independent contrasts that could not be appropriately standardized. These
relationshipsalsowereexaminedusingsigntests.Thesigntestwasconsistentwiththeregressionforall
casesexceptthefrugivore-omnivoreguild,whichsuggestedamarginallynonsignificant(Pp.052)positive
relationship.
multiple comparisons. Although the difference between nificant(Fp3.98,dfp1,203,Pp.047,R2p0.02;fig.
the slopes for the frugivore-omnivore and raptor guilds 1B), butagain, body mass explainedlittleofthevariation
wasnotstatisticallysignificantafteradjustingformultiple in population density. The negative slope also was signif-
comparisons (frugivore-omnivore vs. raptor guilds: tp icantly different from 0 (one-tailed; tp(cid:1)1.994, dfp
2.24, critical qp2.57), the magnitude of the difference 202, Pp.047; table 3) and was significantly shallower
between the slope estimatessuggeststhatthedifferenceis than (cid:1)0.681 (one-tailed; tp5.57, dfp202, P!.0005;
biologicallysignificant.However,thetestmayhavelacked table3).Slopesofguildsdidnotdiffersignificantly(table
powertodetectadifferenceduetothehighstandarderror 3).Noneoftheslopesforguildsdifferedsignificantlyfrom
oftheslopeestimateandthelowsamplesizefortheraptor 0, althoughtheslopesforfrugivore-omnivoresandinsec-
guild. tivores both differed significantly from (cid:1)0.681 (table 3).
The relationship between PEUandbodymassalsowas Based on independent contrasts, the relationship be-
statisticallysignificant(Fp108.69,dfp1,270,P!.001, tween PEU and body mass was statistically significant
R2p0.29;fig.3A),withaslopesignificantlygreaterthan (Fp28.33, dfp1,203, P!.0001, R2p0.12; fig. 3B),
0 (one-tailed; tp10.43, dfp270, P!.0001; table 4). with a slope significantly greater than 0 (one-tailed; tp
Variation attributable to guild was significant (Fp3.91, 5.322, dfp202, P!.001; table 4). Slopes of guilds did
dfp3,264, Pp.0093). Only the slope for the raptor notdiffer significantly(table 4).Theslopesfortheraptor
guild was not different from 0; slopes for all other guilds andgranivore guilds werenotdifferentfrom0;slopesfor
were significantly positive (table 4). Differences among all other guilds were significantly positive (table 4).
guildsintheslopeofthebodysize–PEUrelationshippar-
alleledthoseforthesize-abundancerelationship(table4).
Discussion
Sources of Variation
Independent Contrasts Analyses
Nonphylogenetic (species) and phylogenetic (contrasts)
The regression of phylogenetically independent contrasts analysesofthesize-abundancerelationshipforAmazonian
of population density and body mass was statisticallysig- birds in this communitygavesimilarresults.Bothregres-
Energetic Equivalence Rule in Amazonian Birds 275
senstein 1985; Harvey and Pagel 1991). Nonetheless, the
low coefficients of determination indicate that many
unaccounted-for sources of variation affect the size-
abundancerelationshipforAmazonianbirdsinthiscom-
munity.Ouranalysisisconsistentwithseveralstudiesthat
conclude that the relationship between body mass and
population density can be highly variable (e.g., Pagel et
al.1991;Blackburnetal.1993b;Brawnetal.1995;Black-
burn and Gaston 1997). Rather than simple regressions,
analyses investigating the sources of variation in the re-
lationship, such as the ecologicalandphylogeneticattrib-
utes addressed in this study, may be more informative.
The resource availability in and vegetation structureof
successional habitats are often temporally and spatially
more variable than those in mature forest understory
(Frankie et al. 1974; Croat 1975; Stiles 1975; Opler et al.
1980). If such variability affects avian taxonomic com-
position or population densities of earlysuccessionalver-
sus mature forests, differences in the slope of the size-
abundance relationship among habitats may result. Our
findingofnodifferenceinslopesamongthethreehabitats,
based on nonphylogenetic analyses (see “Study Area and
Methods”; table 2), contrasts with previous studies that
found that the slope of the size-abundance relationship
for birds had a significantly negative correlation with a
foliage volume index (Teller´ıa and Carrasca´l 1994).
Based on nonphylogenetic analyses, guilds differed in
the slope of the size-abundance relationship (tables 2, 3).
Theslopesofallguildsexceptforraptorsweresignificantly
different from the (cid:1)0.681 slope expected under the EER
(table 3). Relative to the raptor guild, the slopes for the
other three guilds were much shallower, suggesting that
larger species in frugivore-omnivore, granivore, and in-
sectivore guilds are more abundant than would be pre-
dicted based on energetics. These results would not be
expectediftheEERwereasignificantfactoraffectingpop-
ulation densities in these guilds. The significantinfluence
of guild on the size-abundance relationship is also con-
sistent with findings that foraging guild is a significant
Figure 1: A, Scatterplot of species values of populationdensityversus
body mass. Ordinary least squaresregressionlineand95%confidence source of variation in demographic traits of Panamanian
intervalsoftheslopearedepicted.Lettersrepresentguilddesignationof forest birds (Brawn et al. 1995).
each point:f,frugivore-omnivore;g,granivore;i,insectivore;r,raptor. Phylogenetic analyses indicated no statistically signifi-
B, Scatterplot of phylogenetically independent contrasts of population
cant differences among guilds in the slope of the size-
densityversusbodymass.Ordinaryleastsquaresregressionlineand95%
abundancerelationship(table3).Onepossibleexplanation
confidenceintervalsoftheslopearedepicted.Notedifferenceinscales.
forthisresultisthatevolutionaryrelationshipsandfeeding
guild may be correlated to an extent that varies among
sions were statistically significant, with similarslopesthat guilds. For example, all raptor species are represented in
were significantly shallower than the slope of (cid:1)0.681, twoclades,andthemajorityofinsectivoresarerepresented
which would be the slope expected if the EER applied in in three clades. Thus, controlling for the effects of phy-
this bird community (table 3). That the size-abundance logeny may remove from the analysis some variation at-
relationship retained statistical significance after account- tributabletofeedingguild.Somesimilarities,however,ex-
ing for phylogeny suggests that these two traits are likely isted between the two analyses. In the phylogenetic
tohaveundergonesomeformofcorrelatedevolution(Fel- analysis, slopes of the frugivore-omnivoreandinsectivore