Null Models Chapter 4

8/13/2019 Null Models Chapter 4

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NICHE OVERLAP

NICHE OV ERLAP AND LIMITING SIMILARITYHistorically, analyses of niche overlap were based on the theory of limitingsimilarity M acArthur and Levins 1967). This model predicts the coexistenceof species and the overlap in their utilization of resources along a single,ordered resource dimension. T he overlap of species 2 on species 1 in resourceuse is calculated as

where U I R ) nd U 2 R ) re the util ization functions for species 1 and 2,respectively. Overlaps calculated this way have been equated with thecom petition coefficients of the Lotka-Volterra equation s Levin s 1968). Inother words, the am ount of o verlap in resource ut i lizat ion is assum ed to beproportional to the intensity of com petition betw een two species Sc ho ene r1974b).

Community change in the limiting similarity model comes about throughrepeated colonization and extinction of species with different util izationcurves. If adjacent species are too close together, one of the pair w ll goextinct, depending on th e overlap and the carrying capacity of the environ ment,as dictated by the Lotka-Volterra equations Schoen er 1986a). On the otherhand, if two species are widely separated on the resource axis, a third speciescan be sandw iched between them. A fter repeated c olonizations and extinctions,an equilibrium will be established, with a maximum number of coexistingspecies separated by a critical minim um spacing Figure 4.1).

The prediction of a limit to similarity is sensitive to a number of assump-tions, including: 1) the norm ality of the resource utilization curves Rou gh-garden 1974); 2) the measu remen t of overlap by Equation 4.1 Abram s 1975);3) the linearity of the zero isoclines assumed by the Lotka-Volterra model


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esource trnens~on

Figure 4 1 Resource utilization and limiting similarity in the MacArthur and Levins(1967) model. The m odel predicts a limit d lw) o the similarity of competing species.This theory motivated a vast amount of ecological research into patterns of niche over-lap, but relatively few studies have compared overlap patterns to an appropriate nullmodel. From Schoener (l9 86 a) , with permission.

(Schoener 1976a); (4) the presence or absen ce of environm ental stochasticity(M ay and M acA rthur 1972; Turelli 1978a,b).

NICHE OVERL P NDEVOLUTION RY DISPL CEM ENT

Limiting similarity m odels predict a reduction in niche overlap of comp etitorsthrough ecological assortment of colonization and extinction. A second se t ofmodels also predicts a reduction in niche overlap through genetic change incom peting populations that cause s evolutionary shifts in niche position and/orniche width (Bulmer 1974). These models were inspired by the pattern ofcharacter displacement in allopatric versus sym patric populations (B rown andW ilson 1956) and by H utchinson s (1959 ) suggestion that com peting speciesmight differ in body size by a co nstant ratio (see Chapter 6). These mo dels aresensitive to the amo unt of within- and between -phen otype variance (Taper andCas e 1992 ), whether or not resources are completely utilized (Milligan 1985 ),and the symm etry of resource use between species (Slatkin 1980). Dep endingon the underlying assumptions, some of these models predict a substantialdisplacement of compe titors (Gotelli and Boss ert 1991; Taper and Case 1992);others predict little displacement, or even convergence of utilization pheno-types (Slatkin 1980; Ab ram s 1986).


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Niche Overlap 6 7

TESTING NICHE OVE RL P P TTERNSThe central prediction of both ecological and evolutionary models of displace-ment is that species should overlap less in resource use than they would in theabsence of competition (Schoener 1974a). How has this body of ecologicaltheory been treated in em pirical analyses? First, empiricists hav e largely aban -doned the idea of discovering a magic nu mber for limiting similarity or bodysize differences (see Chapter 6). Instead, the qualitative prediction that com-petition should lead to reduced ove rlap has been investigated. Early an alysesfocused on the descr iption and quantif ication of resource use (Schoener1986a). If one had faith in the underlying theory of limiting similarity andcharacter displacement, then utilization differences between species wouldreflect resource partitioning.

But this approach now seems naive. Even in the absence of competition,different species will utilize resources in different ways (Sa le 1974). Th e meredemonstration of utilization differences is no longer accepted as sufficientevid ence for comp etition (Connell 1980). Null models ha ve been used to askwhat niche overlap patterns would be expected in the absence of competition(Silvertown 1983). If com petition influences resource utilization at the com m u-nity level, niche overlap in nature should be significantly less than in anid e a li ~ e d ompetition-free community (Schoener 1974a).

Few studies of niche overlap are based on the direct measurement of re-source utilization curves along an ordered niche axis, as diagrammed in Fig-ure 4.1. Stud ies of dietary and habitat n iches usually rely on discrete, unorderedresource states, and studies of characte r displacement rely on m easurements ofbody size or morphology, which are assumed to reflect resource utilization.Schluter and G rant's (1984) study of Ga lip ag os finches is a notable exception,and their finding that utilization and availability cu rves are asymm etrical andpolymodal contradicts one of the important underlying assumptions of nichetheory (see Chapter 6 .

Although null models can be used to establish whether observed nicheove rlap is mo re or less than ex pec ted by cha nce , it is still difficult to inferthe mec hanism s responsible fo r such patterns. For exam ple, most null mod -els d o not distinguish between ecologica l niche shifts and evo lutionarycha racter displa cem ent (Case an d Side11 1983). Interpreting pa tterns of highniche overlap can be equally problematic. High niche overlap may ref lectintense com petition fo r shared resources or, alternatively, a surp lus of re-sources and the absenc e of com petit ion (Glasser and Price 1988 ) . Bothscenarios have been revealed in experimental f ield studies of competit ion(Schoener 1983) .


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Interestingly, null mod el studies of niche overlap hav e not addressed thesealternatives, and interpretations have been remarkab ly con sistent: those auth orswh o detected unusually low o verlap have conclud ed that comp etition has beenan important force, either currently or in the past (e.g., Pianka et al. 1979),whereas those who found unusually large niche overlap have concluded thatcompetition is not currently im portant (e.g., Tokeshi 198 6; Griffiths 1987). Forany particular pair of species, the finding that niche overlap is statisticallylow er than exp ected is difficult to evaluate. Phylogenetic an d historical effectsmay result in different utilization patterns for this pair that have nothing to d owith competitive interactions. However, it is more difficult to explain stronglow-o verlap patterns for an assem blage of several coexisting species.he Utilization atrix

Construction of a utilization matrix is the starting point for a null modelanalysis of niche overlap. An investigator first defines a set of resource states,and then measures the utilization of these resources by each species in theassemblage. For example, if the states are microhabitats, then the number ofindividual occurrences of each species in the different microhabitats is re-corded. Likewise, if dietary categ ories are of interest, the num ber or volum e ofprey items in ea ch category is measured.

Utilization data often summarize extensive collecting efforts and naturalhistory observations on undisturbed comm unities. Pianka s (1986) long-termstudies are noteworthy in this regard. Twelve person-years of field work inAustralia, North America, and South Africa yielded collections representingover 9 0 species and 15,000 individuals of desert lizards, with detailed observ a-tions on their microhabitat utilization and stomach contents. Table 4 1 illus-

Table 4 1Frequency of microhabitat utilization by five species of North Am erican lizards

MicrohabitatSpecies Open Grass Bush Tree OtherCnemidophorus t igris 0.475 0.025 0.424 0.025 0.051Uta stanshuriana 0.279 0.046 0.473 0.046 0.156Phr ynosomaplatyrhinos 0.950 0.000 0.050 0.000 0.000Crotaphytus wislizeni 0.613 0.007 0.321 0.007 0.052Adapted and s implified from A ppendix C of Pianka 1986).


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Niche Overlap 6 9

trates a utilization matrix with a small subset of Pianka's (198 6) data. Speciesand resource states are represented by rows and columns, respectively. Theentries in the matrix p represent the fraction of total utilization by species i ofresource state j The matrix summarizes resource utilization along a singleresource axis, which may be either ordered o r unordered.

verlap ndicesHow can overlap between species be quantified with a utilization matrix?Many different indices have been proposed to measure the overlap betweenindividual species pairs, and to quantify the overall niche breadth or degre eof specialization of each species. Becau se these indices w ere first derived fromthe theory of limiting similarity, they emphasize painvise comparisons ofoverlap along ordered resource axes, although the calculations work equallywell with unordered resource states. For a pair of species, the overlap inresource use of species 2 on species 1 can be measured in terms of thefreque ncy of utilization p)of n different resource states. So me com monly usedindices include

where p is the frequency of utilization of resource state i by species x. Thisfamiliar index by MacArthur and Levins (1967) is the discrete version ofEquation 4 1 Early studies equated this overlap with the Lotka-Volterra com-petition coefficient (Levins 1968), althou gh this equivalen ce cannot be readilyjustified (Lawlor 1980a). Equation 4 2 is asymmetrical, in that the overlap ofspecies 2 on species doe s not equal the overlap of species on species 2.Pianka (1973) proposed a modified symmetrical index:

In this index, the denom inator has been norm alized, but the stability prop er-ties are the same as those of Equation 4.2 (May 1975b). Th e Czekanowski


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Index (Feinsinger et al 1981) has also been used as a simple measure of thearea of intersection of two utilization histograms:

Finally, Colwell and Futuyma (197 1 proposed an information theory indexthat quantifies the uncertainty in a utilization matrix. Sim ilar equ ations hav ebeen use d to quantify the nich e breadth of a spec ies, that is, the exten t to whicha species is specialized o r generalized in its utilization of resou rces (F einsin geret al. 1981).

As in the study of species diversity, there is a large, unsatisfying literature,mostly from the 1970s, that explores different algebraic measures of nicheove rlap (e.g., Colw ell and Futuym a 1971; Pielou 1972b; Hurlbert 1978; Petra-itis 1979). Niche overlap indices are invariably correlated with one another,sam ple-size dependent (Han ski 1978), and only tenuously linked to theories ofcompetition (L awlor 1980a). In the abse nce of an appropriate null model, it isimpossible to evaluate or compare these indices, either among species oramong comm unities. For example, under some circumstances, average over-lap, as measured by Equation 4.4 can actually increase following speciesdeletion from a com mu nity (Thomson an d Rusterholz 1982). Even w ith anappropriate null model, different indices can generate different results. In astudy of niche shifts in Greater Antillean nolis comm unities, observed over-laps were usually less than ex pec ted, but the null hypothesis was rejected m oreoften using Equation 4.2 than Equation 4.3 (Haefner 1988a).Weighted versus Unw eighted IndicesTh e most important assu mption implicit in the use of overlap indic es is that allresource states are equally available to all species. If resource states are notequally abundant, observed overlaps in utilization may not accurately reflectsimilarity in resource use. In particular, if some resource states are extremelycom mon and others are extremely rare, species may appear very sim ilar in theirresource utilization (Lawlor 1980a).

How can resourc e indices be m odified to accoun t for resource availability?Colwell and Futuyma (1971) suggested expansion of the resource utilizationmatrix in proportion to the total utilization of each category. The resourcecategories in the expanded m atrix are assumed to be equiprobable and thus toprovide a better measure of species electivities. The Colwell and Futuyma(1971) technique has been applied to associations of drosophilid flies on


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Niche Overlap 71

different plant types (Sabath and Jones 1973) and anuran larvae in tropicalponds (Heyer 1974). However, the Colwell and Futuyma (1971) expansion issomewhat arbitrary and sample-size dependent (Hanski 1978) and still requirescomparison with an appropriate null model (e.g., Sale 1974; Inger and Colwell

977).Schoener (1974b) and Lawlor (1980a) both suggested modifications of ex-

isting indices to account for the electivity, the relative ability (or preference)of a consumer to catch and consume a particular prey type. In the simplest case,consumers will use resources in the proportions in which they are available inthe environment (Holling Type I functional response). Thus

where Rj is the relative density of resource and b is the electivity of species ifor resource j Thus, the utilization p,) of resource state j can be high eitherbecause the electivity for that resource is large, or because the resource is verycommon. Lawlor (1980a) argued that electivities are more relevant to theoriesof limiting similarity than direct utilizations, in part because electivities are abetter measure of a consumer's phenotype. Incorporating resource availabilitymay have a major effect on measures of overlap. Table 4.2 illustrates samplecalculations for some of Pianka's (1986) data on microhabitat utilization byNorth American lizards. Calculated overlaps vary, depending on the availabil-ity of different resource states.

In theory, independent resource measurements could be incorporated withmeasures of utilization to estimate electivities, but in practice these data arerarely available. In addition, it may be impossible to realistically compare thedensities of different resource categories. Consequently, the relative consump-

Table 4 2Pairwise niche overl ap of North A meric an lizards.

Cnemidophorus Uta Phrynosoma Crotaphyrustigris stansburiana platyrhinos wislizeni

Cnemidophorus tigris 0.934 0.776 0.969Uta stansburiana 0.806 0.528 0.831Phrynosorna platyrhino s 0.967 0.636 0.906Crotaphy tus wislizeni 0.991 0.75 0.986Each entry is the overlap in utilization, calculated with Equation 4.3. Above the diagonal: overlap calculatedassuming resource states are equally available. Below the diagonal: overlap calculated assuming that 95%of tlae available microhabitats are bushes. Based on the utilization data in Table 4.1.


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7 2 Chapter 4

tion of different prey items may serv e as the mo st relevant bioassay ofavailability (Colwell and Futuyma 1971; but see Han ski 1978). If spec ies areusing resources randomly, then the summed resource use across species willreflect the relative availability of different resource states. Lawlor (1980a)advocated this approach for estimating electivities, and the Colw ell and Futu-ym a (1971) matrix e xpan sion produced a similar weighting.

If resou rce states are not equally ab und ant, observ ed utilizations will tend tooverestimate th e am ount of eco logical overlap. Electivities b ased o n m arginalresource totals remove som e of this bias, and ma y b e a m ore reliable measureof ecological overlap. For ex amp le, only tw o of 1 0 mean utilization overlap sfor Pianka's (1967) North American lizard communities differed from nullmodel expec tations, whereas all 10 mean electivities differed significantly(Lawlor 1980b). For G reater Antillean nolis com mun ities, significant resultswere somewhat more common when comparing electivities versus utilizationoverlaps (Haefner 1988a). Some critics object to the use of marginal con-straints in null model simulations (C ase 1 983a), on the groun ds that thesemarginals may themselves be influenced by competition (Colwell and Winkler1984). Analyses of niche overlap can be greatly affected by the meth ods usedto estimate electivities (Law lor 1980a; Haefner 1988 a), but m arginal con-straints do not autom atically bias the test towards ac cep ting the null hypothesis.

We see two potential problems with electivity calculations. The first is thatthe electivities that are estimated from summ ed resource use will be influencednot only by the relative availability of different resource states, but also byoverall productivity (Haefner 1988a). Second, Equation 4.5 may adequatelydescribe the utilization of different microhabitats, but more complex functionsmay be necessary to characterize prey utilization, which can be affected bysearch im ages, handling times, and satiation levels.

Moreover, electivities m ay give large, counterintuitive weight to trace co m-ponents in pooled diets (Winemiller and Pianka 1990 ). This will be especiallytrue when electivities are estimated without reference to an appropriate sam-pling model (Ricklefs an d Lau 1980). On the other hand , observed utilizationsare biased towards the finding of large overlap when certain resou rce states arevery common. To overcome these problems, Winemiller and Pianka 1 990)proposed a hybrid ind ex, the geom etric mea n of utilization an d electivity:

ll 4.6)They suggested that g should reduce the positive correlation of p with

resource ava ilability and the negative correlation of a,,with resource availabil-ity without entirely eliminating available resources from the analysis. How-ever, electivity and utilization measure two different things, and it may not be


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Niche Overlup 73

wise to combine them in an aggregate index. One advantage of using observedutilizations p,,) to test niche ove rlap is that the tests will be conservative withrespect to competition hypotheses. Because unequal resource availability willlead to large overlap, we can be sure that the reduction in overlap is strongwhen the null hypothesis is rejected. At least in comparison to idealizedcommunities of known structure, results were quite similar for pi i and g jWinemiller and Pianka 1990).

ultidimensional Niche etrics

Once an appropriate utilization measure and resource weighting have beenselected, there is still the problem that the niche of a species is rarely repre-sented along a single resource axis. Most authors have appreciated the multidi-mensional nature of the niche and have measured utilization along severalresource axes. M ost of these are sub divisions of the major niche axes of time,space, and food Schoener 1974a). Multivariate approaches can be useful forreducing the number of correlated variables to a handful of independent re-source axes Green 1971). But even if individual utilization curves ar e properlyevaluated , com parisons in multidimensional niche space are problematic. Sp e-cifically, the overlap am ong spec ies in multidim ensional sp ace could be higheror lower than overlap along individual niche dim ensions Figure 4.2).

RISOI IRCE X I S R E S O U RC E X I S R E S O U R C E X I S h

Figure 4.2. Multidimensional niche overlap is not always reflected in overlap along in-dividual dimensions. In the left-hand plot, niche overlap of species A and B along tworesource axes is independent, and the product accurately reflects total overlap. In themiddle and right-hand plots, resource use is not independent, and the total overlap can-not be readily predicted from utilization of individual resources. From E. R . Pianka,R . B . Huey, and L. R . Lawlor. Niche segregation in desert lizards. In Anulysis of Ecological Systems. D. J Horn, R . D. Mitchell, and G. R . Stairs eds). Copyright 1979by the Ohio State University Press. Reprinted by permission. All rights reserved.


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74 Chapter

The re are two extrem e cases. First, suppose that uniform re sourc e utilizationfor a species is entirely indep ende nt along tw o orthogonal resource axes (x andy . Utilization of this rectangular niche space can be estimated as the simpleproduct of overlap (xy). At the other extreme, utilization a long tw o niche axesmay be entirely correlated, so that knowing the utilization along one axisallows you to predict the other. In this case, the arithmetic average of the twoaxes ((x y / 2 is the best estimate of multidimensional utilization. Thissummation overlap represents a maximum upper bound for overlap in a

multidimensional niche space (May 1975b). Between these extremes, there isno way to predict from the unidimensional overlaps whether true overlap islarge or small. The geometric mean overlap 6)ay serve as a usefulapproximation of multidimensional overlap (Case 1983a), because it will al-ways lie abov e the arithmetic mean and below the product mean .

ggregate Statistics for Pairwise OverlapsEven in proper m ultidimensional form , the overlaps calculated fo r eac h speciespair do not convey a fill1 picture of niche overlap at the community level.Several different statistics have been proposed for su mm arizing overlap for anentire assemblage. One obvious measure is the mean or median of all [iainvise overlaps. The median may be preferable, because it will reflect t enonnormal distribution of painvise overlaps. However, the expected medianoverlap quickly converges on the mean as species number increases (Case1983a .

M ean or median ov erlap is a useful sum mary statistic for niche analyses,but, as a single number, i t hides a good deal of pattern at the communitylevel (Pianka 1980 . Inger and Colwell (1977) recomm ended a m ore subtlemeasure. For each of the n species, order the remaining n 1 neighbors onthe basis of their overlap . If a single util ization meas ure is used, the order-ing is based on the pairwise overlaps. If multiple niche axes are retained, then 1 neighbors can be rank ed acco rding to Euclidian distances. These order-i n g ~re then ave raged to give the mean overlap of the first, secon d, n 1neighbo rs in niche space. By definition, overlap is highest w ith the closestneighbor, then drops off as more dissimilar neighbors ar e compared (Fig-ure 4.3 . The plot of average overlap versus ranked neighbor distance canthen be compared to the predictions of null models. Com parisons w ith a l lneighbors in niche space are of interest , because the h ypothesis of diffusecompetition predicts that util ization will be affected by many competingspecies (MacArthur 1972; Pianka 1974).


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Niche Overlap 7

Figure 4 3 Nearest-neighbor plots inniche space for three assemblages of r Eve rg reenamphibians and reptiles in Thailand. Dec iduousEach point represents the average griculturalniche overlap of each species with itsnth nearest neighbor. These curvescan be compared with the predictionsof null models and are more sensitiveindicators of community structurethan a simple median or mean of pair-wise niche overlap. From Inger andColwell 1977), with permission.

1 3 5 7 9 1 1 1 3Nearness order ( n )

Stil l another approach is to com pute the m ean overlap for each species pairand compare i t to the expected overlap for that pair in a null community.Particular pairs of sp ecies ma y e xhibit nonrandom patterns of ove rlap that maynot be apparent from the mean or median overlap of all possible pairs. How-ever, assessing the statistical significanc e of m any non indepe nden t pairs m aybe problem atic (see Chapter 7). Haefner (1988a) comp ared all three m easureswith the same data set. He detected significant overlap more frequently withnearest neighbor and individual pairwise overlaps than with the mean overlapfor an entire assemblage.

NULL MODEL FOR THE HUTCHINSONI N NICHEHow would niche overlap patterns appear in the complete absence of co mpeti-tion? If we co uld answ er this question , we w ould have a reference for com par-ison with observed patterns of overlap. Innis and H aefner (198 0) addressed thequestion with a detailed simulation of the Hutchinsonian niche that excludedcompetitive processes. Th e Innis and Haefne r (1980) model began with randomplacement of rectangular niches of species in a two-dimensional niche space(Figure 4.4). Popu lations of each species were u niformly distributed through-out the niche spac e and w ere chang ed by tw o processes: (1) a rando m, uniformdeviate was added at each t ime step, which cou ld either increase or decreasepopulation size; (2) pop ulations were reduc ed in size through perfect p reda-


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t Figure 4.4. null model ofniche overlap. Seven hypo-thetical species are randomlyplaced in niche space, andniche overlap is calculatedfrom the area of overlap.Niches change in size from sto-chastic growth and reductionfrom randomly occurring pred-ators. From Innis and Haefner1980), with permission.

tors. A predato r niche was superimposed on the populations, and all individu-als within that niche were remov ed. Niches of populations that declined to zerowere removed from the simulation.

At each t ime step, the model generated the average niche size , averageoverlap between n iches, species diversity , number of niches, average popu-lat ion size , and average number of neighbors. The model predicted that inthe absence of compet i t ion , n iche over lap would range f rom 25 to 100% fora community of special ists or general ists , respect ively. The lower boundcompared favorably wi th some es t imates of minimal ove r lap f rom m amm al(Brown 1975) and l iza rd (Pianka 1974) comm uni t ies . The m odel a lso pro-vided a basel ine for comparisons with Pianka 's (1972) niche overlaphypothesis: i f competi t ion w ere impo rtant , the num ber of species in acommunity would be negat ively correla ted with average niche overlap.However, i f the niche breadth of colonizing species was variable , ra therthan constant , the Innis and H aefner (1980) mod el a lso predicted a negat ivecorrela t ion, even in the absenc e of com peti t ion.

The Innis and Haefner 1980) model is an important f i rst s tep towardunderstanding n iche dyn am ics in the absence of comp eti t ion. How ever, it isa complex mod el , and much of the output is cast in terms of dimension lessparam eters that are diff icul t to interpret . M ost empirical null mod el studieshave o pted for a sim pler approach through the random izat ion of ut i lizationor species occurrence matrices. We outl ine these me thods in the fol lowingsect ions.


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icheOverlap

S MPLING ERROR IN NICHE INDICESTwo basic approaches have been used in null models of niche overlap:1 ) random ization of util izat ion functions fo r dietary or activi ty data, and

(2) randomization of species occurrences. Both approaches assume thatuti l izat ion frequencies have been est imated accurately, which is probablytrue if many individuals or dietary i tems have been sampled. But at smallsample sizes, estimates of utilization frequency may be biased and giveinaccurate est imates of niche overlap. In the extreme case, i f only oneindividual of a species is sam pled, it will app ear to be a specialist onwhatever microhabitat i t happens to be found in. Thes e sam e problems arisein the s tudy of diversity indices (Chap ter 2) and relat ive abundan ce patterns(Chapter 3).

Ricklefs and La u 1980) used Mo nte C arlo s imulations to explore bias inseveral com mo n niche overlap indices. Estimates of overlap were system at-ically biased do wnw ard w hen sam ple s ize was small and when exp ectedoverlap was high. Even with samples as large as 25 or 50, bias in someindices was substantial (Figure 4.5). To date, most null mod el analyses ofniche overlap ha ve not incorpo rated this sampling variabili ty. R andom izingthe raw utilization data (counts of individuals or dietary items) rather thanthe utilization frequencies would control for this source of bias.

value and the number of individuals 4 10sampled. Th e coefficient of com mu -

8nity S,,) is equivalent to OI2 n Equa-tion 4.4. From R icklefs and Lau 006dI 980), with permission.

0.04

Figure 4.5. Bias in niche overlap indi-ces as a function of the true overlao

Asymptotic coefficientof communi ty S, , )

number ofobserv t~onr

5


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R NDOMIZ TION OF SPECIES OCCURRENCES

Imagine a source pool of species, each with its own utilization function, thatcolo nizes a small island. If competition lim its niche overl ap, then the particularcombination of species that coexist on the island should have lower overlapthan a randomly assembled set of species from the same source pool. Asimulation of this scena rio treats the utilization functio ns for each species orpopulation) as constants and randomizes the combination of species that co-occur. This analysis will be sensitive to the composition of the source poolfauna an d w hether species are sampled equiprobably.

Case 1983a) used this approach in a study of niche overlap of 18 species oflizards on 37 islands in the Sea of Cortez. Utilization along four niche axestime of day, microhabitat, food size, and food type) was summarized as the

product, su mm ation, and geom etric mea n of ove rlap between ea ch species pair.Using realistic criteria, Case 1983 a) delineated a source pool of 18 mainlandspecies that could potentially colonize each island. Observed island com mun i-ties we re a subset of these 18 spec ies, and island species richness rang ed from1 to 13. For ea ch island with i species, Case 1983a) enum erated all the uniquecombinations I:) of exactly i species as null co mm unities. For 30 of the 37islands, the observed ov erlap was less than the median overlap for null comm u-nities of the same size Figure 4.6 . Th is result suggests that species com bina-

~ ~ ~ ~ l l l l l l l l2 3 4 5 6 9 1 12 13 14 I5 16 7 18

Specles NumberFigure 4.6. Niche overlap of insular lizard communities in the Sea of Cortez. Thesolid line is the median overlap for all possible combinations of a given number ofspecies, assuming species colonize islands equiprobably. Most observed island assem-blages fell below this expectation, suggesting that niche overlap was less than wouldbe expected with random colonization. From Case 1983a), with permission.


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Niche verlap 7 9

tions that coexisted o n islands had lowe r niche overlap than wou ld be exp ectedin the absence of comp etition.

An alternative to the competition hypothesis is that low overlap reflectednonra ndom patterns of resource availability o n islands. If the sa me nonove rlap-ping sets of resources were presen t on several islands, the same comb inationsof low-overlap spec ies would tend to be found . For most island size class es, animprobably small number of species combinations was represented (Case1983a), suggesting that the same low-overlap configurations tended to recur.Th is result argues against the competition hypothesis and in favor of the idea ofnonra ndom resource distributions.

Both of the preceding tests assumed that species colonized islands equi-probably. Case (1983a) relaxed this assum ption with a simulation in which theprobability of placement of each species in a random community was propor-tional to the number of island occurrences (Connor and Simberloff 1979).Com pared to this model, only 23 of the 37 islands fell below the med ian, whichis marginally nonsignificant (0.05 p 0. lo ), but still indicative of low nicheoverlap . Thu s, differential dispersal ability of species may have contributed tothe pattern of reduced niche overlap of insular lizards in the Gulf of Cortez.However, it is difficult to know whether the low overlap is a cause or aconseq uence of differential suc cess of species o n islands.

Schoener (1988a) also examined niche overlap of island lizard speciessampled from a larger source pool. He analyzed utilization of seven micro-habitat categories on satellite islands of the Greater Antilles, and found thatcoexisting species usually differed in the structural habitats they occupied. Ontwo-species islands, each species occupied a different structural category. Co-existence in the same habitat w as only found o nce on three-species islands, andnever on four-species islands.

How likely w ere these patterns to have arisen by c hanc e? Schoener (1988a)compared these habitat occupancy patterns to a null model based on fourdifferent source po ol definitions: ( 1 ) all species from the appropriate main-land (one of the fou r Grea ter An tilles source islands); (2) the subset ofmainland species whose structural-habitat categories were found on smallislands; (3) only species prese nt on two -, three-, or four-species islands (i.e., thearchipelag o metho d of using only spe cies present on the islands); and 4) thosespecies found on islands with equa l or lesser species richness.

For each source pool, Scho ener (1988a) assum ed that all microh abitats wereequally available a nd used a binomial exp ansion to calculate the tail probabilityof observing a given number of co-occurring species. About 15% of the testswere significant at the 0.05 level, and significant results were consistentlyobtained only for sou rce pool (2), which Schoener (1988a) considered to be the


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most realistic of the four. Among the island sets, four-species islands andsatellite islands of Cub a frequently sh owe d nonrandom p atterns.

The se studies by Schoener (1988a) and Case (1983a) suggest that com -paring overlap values of observed com munities with those of null com mu -nities draw n from a larger source pool is an effective meth od fo r evaluatingniche overlap. However, the results will be sensitive to sample size, meth-ods used fo r designating source pools , and assumptions about the coloniza-tion potential of species.

RANDOMIZATION OF UTILIZATION MATRICESAlthough comparisons of niche overlap in real communities with overlap innull comm unities derived from an appropriate source are worthwhile, no suchexternal reference is available in many cases. Instead, the obse rved utiliza-

tion matrix must be used to estimate overlap values in the absence of com-petition. The randomization algorithms (RAs) described below assume thatinterspecific variation in resource utilization provides information about ex-pected niche overlap in the absence of competition. Lawlor (1980b) developedfour algorithms that are listed in increasing order according to the amount oforiginal utilization data retained in the null com mu nity:

1 RA1 For each species, utilization of each dietary catego ry is re-placed by a rand om uniform num ber [0,1]. After random ization,entries in the matrix are scaled s o that the row sums for eachspecies sum to 1 O

2. RA2 . Resource utilization is again replaced by a rando m uniformnum ber [0,1], but only for those resource states in which utiliza-tion is greater than zero. Those resource states that we re not usedin nature by a species are left in the zero state. As in R A1 , rowsum s are rescaled after randomization.

3 RA 3. Resource utilization fo r eac h species is not replaced by arandom number. Instead, the observed utilizations are randomlyreassigned to different resource categorie s ( scrambled zeros ;W inemiller and Pianka 1990). Becau se the rows of the utilizationmatrix are sim ply reshuffled (Inger and Colwell 1977), R A 3 ef-fectively retains observed niche b readths for each species (Sale1974).

4. RA 4. Only the nonzero resource state s in each row a re reshuffled( conserved zeros ; Winemiller and Pianka 1990). As in RA 2,


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iche verlap 1

the placement of the zeros is retained. Of the four algorithms,RA4 produces synthetic communities in which utilizations aremost similar to the original communities.

The four randomization algorithms differ in whether utilizations are re-shuffled or replaced by a random number, and in whether the zeros in thematrix are retained or not (Table 4.3 . Both decisions have implications for thestructure of the null community, and affect the power of the test.

By replacing the observed utilizations with a uniform random variate (RAl),we assume that utilization of any resource state is possible and equiprobable. Atthe other extreme, reshuffling of nonzero utilizations (RA4) assumes that onlypermutations of nonzero utilizations are permissible. All these algorithms arereasonable methods for constructing random communities, although we still donot have a clear expectation of how utilization spectra should look in commu-nities that are unstructured by competition (Bradley and Bradley 1985).

This problem is highlighted in the treatment of the zero states. Assumingthat sampling effort has been sufficient to ensure that the zeros are not due toinadequate censusing of individuals or dietary items, there are two principalinterpretations of a zero in a utilization matrix. The first is that the observedutilization values are determined primarily by competition. In this case, compe-tition is so severe that some species are completely denied the use of certainresources by the presence of competitors. R l is consistent with this interpre-tation, because it allows a species in the null community to use a resource thatit does not exploit in nature.

The other interpretation of zeros in the utilization matrix is that species arenot able to use all resource states in a community because of constraints relatedto behavior, morphology, physiology, or phylogeny. These restrictions have

able 4.3F o u r n u ll mo d e l r an d o mi za t io n a l g o ri t hm s R A )

Ze r o s t a te s Ze r o s t a te sr an d o mi zed r e t a i n ed

O b s e r v ed u t il iz a ti o ns d r aw n f r o m a u n i f or m R A R A 2distr ibutionObserve d u t il iza t ions r esh uf f l ed RA3 R A 4Th e algorithms dif fer in whether unused resource states zeros) are retained or randomized andin whether observed utilizations are reshuffled or replaced with a value drawn random ly from auniform distribution. Adapted from Pianka 1986 ).


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nothing to do with present or past comp etition , and should not be obscu red in anull mode l test. Following this logic, RA2 and RA4 ensure that species whichdo not use certain resource states in nature never do so in a null communityeither. RA3 is a compromise. It retains the same number of zero states in thesimulation, but doe s not constrain those zero s to their original placem ent.

PERFORM NCE OF R NDOMIZ TION LGORITHM SWhat patterns result from these different simulations? R I destroys all struc-ture in the matrix and usually results in null communities that exhibit a highmean and sm all variance in overlap. Figure 4.7 com pares pairwise overlaps inmicrohabitat use of ground beetles collected in pitfall traps with simulatedoverlaps based on RA1 Kobayashi 199 1 . Observed overlaps were m uch m orevariable than those predicted by RA1, and followed a nearly uniform distribu-tion, com pared to a peaked distribution of overlap values fo r the null com mu-

40 Figure 4.7. Observed and ex-pected niche overlap of groundbeetles collected from pitfall traps20 in Towada-Hachimantai NationalPark, Japan. Each histogramshows the distribution of speciespairs with niche overlap calcu-lated according to methods in Col-well and Futuyma 1971). The- 2> dashed line is the expected value

Z generated by R A 1. R A createsW null assemblages with a high

mean and low variance in niche[LL overlap. From S. Kobayashi.1991 Interspecific relations in

I \40 I forest floor coleopteran assem-\ blages: niche overlap and guild

structure. esearches on Popula20 tion Ecology 33:345-360 Figure

2 page 352.00 .2 4 6 8 1.0

NICHE OVERL P


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I .o0.8 b Puudo. Scrarnbl.d)

0.6F,G

0.4

0.2

0.0 0 2 4 6 8 10.o0.8- u u d oCa..rr*d)m- -- - Pu ud o. Osr.mbl.d)A zi

B J G 6 Oq600 0.4-2Q)h 0.2.

Rank of Neighbor In Niche SpaceFigure 4.9. Benchmark performance of RA3 and RA4 compared to idealized commu-nities. The three graphs correspond to patterns of high, medium, and low niche over-lap of species organized into two internal guilds of five species each A-E, F-J). Foreach assemblage, the observed average overlap is plotted as a function of the nth near-est neighbor. This curve drops off sharply beyond four nearest neighbors, which is theboundary for the internal guilds. Note that RA4 [Pseudo Conserved)] closely mimicsthe observed overlap patterns, whereas RA3 [Pseudo Scrambled)] produces a distinc-tive nearest-neighbor curve that reveals internal guild structure n the high- and me-dium-overlap trials. From Winemiller and Pianka 1990), with permission.


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Niche Overlap 85

remaining six resources. Species in trial 12 had medium overlap for a coregroup of 40 shared resources and 60 nonoverlapping resources. All simulationswere compared to observed comm unities using Inger and Colwell s (1977) nearest-neighbor distance. Statistical significance was assessed by the percentage of ran-domized mean overlaps that exceeded mean observed overlap.

The se benchmark tests revealed that RA 3 w as superior to RA 4 in detectingnonrandom ove rlap. For exam ple, in trials (1)-(3) (two equal-sized guilds), thenull hypothesis was never rejected fo r RA4 but was significant for RA 3 underconditions of low and medium overlap. RA3 always generated a decreasingcurve of average nearest-neighbor distances that did not change much as afunction of resource ove rlap (Figure 4.9). In trials (1)-(6), R A 3 accuratelyrevealed the internal guild structure of the assemblages: overlap in RA3 cor-rectly fell below the observed curve for the first fou r (or seven) nearest neig h-bors, which were in the sam e guild, and above the observed curve for the moredistant neighbors, which w ere in different guilds. Whe n n o guild structure waspresent, simulated overlaps did not differ significantly from observed values.Thu s, differences between observed overlaps and null comm unities c an dependon internal guild structure as well as average overlap. For these reasons,nearest-neighbor plots may be superior to mean or average overlap values(Haefner 1988a). Finally, for shared resou rce scenarios, significant guild struc-ture for RA3 was detected only when observed overlap was high. RA3, theoriginal matrix shuffling used by Sa le (1974) and by Inger and Colwell (1977),may be the best existing algorithm to use in resource overlap null models.

V RI NCE IN NICHE OV ERL P

Simulations can be used to study the variance as well as the mean of resourceoverlap. With RA3, variance in randomized communities generally decreasedas neighbor distance increased (Winemiller and Pianka 1990 . In contrast,observed variances in amphibian (Inger and Colwell 197 7), lizard (Pianka1986), and fish (Winem iller and Pian ka 1990) comm unities exhibited a sharppeak at an intermediate neighbor distance (Figure 4.10). Both Inger and Col-well (1977) and Pian ka (1986) interpreted this peak as evidenc e for the exis-tence of internal guild structure. At low nearest-neighbor distances, variance inoverlap is small, because all the species belong to the same guild. As nearest-neighbor distance increases, variance in overlap increases a s som e neighborsare sampled from other guilds. Finally, variance decreases at large neighbordistances because distant neighbors belong to different guilds. Null modelcomparisons with hypothetical communities that exhibit internal guild struc-


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Radaanda. Auotralla. I 6 Ylcrohabltalabawad

a Puudo. Scnmblad Zaro)

Rodaanda. Auatralla, 19 Prayb..Wadu d o Ssnmblad Zaro)

Radaando, Aualralla, 2 1 P r yt O b m a d

b Puudo. Scnmblad Zero buwaduudo. Scrambld Zero)

Rank of eighbor in iche SpaceFigure 4.10. Comparisons of standard deviations of dietary and microhabitat nicheoverlap of Australian lizards with the predictions of RA3. Most assemblages exhibiteda peak in variance at intermediate neighbor distance that was not present in the ran-domized communities. From Winemiller and Pianka (1990),with permission.

ture confirm this interpretation of the variance peak (Eric R. Pianka, personalcommunication). Whether cogent alternative explanations for the variancepeak can be constructed remains to be seen.

Bradley and Bradley (1985) argued that nonrandom overlap patterns asrevealed by RAI-RA4 need not imply competitive interactions. They pointedout that RA1-RA4 not only eliminate relationships among consumers, but alsoobscure the tendency for consumers to specialize on related types of resources.In RA1-RA4 the transition from one resource state to another is equiprobable( random environment model), whereas in nature, species will tend to forageon similar resources ( structured environment model). Bradley and Bradley


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iche verlap 8

Randomized RandomGrasshopper EnvironmentData Model

o ActualGrasshopper

DataC

Randomized lHerptileData

nm nrStructuredEnvironmentModelG

Random lEnvironmentModel

Actual l Structured lHerptileData EnvironmentModelFigure 4.11. Alternative randomizations of niche overlap data. A and B show observed andrandomized (RA I) niche overlap data of Joem and Lawlor (198 1; see Figure 4.8). C and Dshow the standard deviation of niche overlap for the nth nearest neighbor from Inger andColwell (1977; see Figure 4.3). E H show two alternative null models that use Markovtransitions to specify consumers that move randomly between different resource states( random environment model ) or that preferentially choose similar resources ( struc-tured environment model ). Note the similarity of the observed data to the structured envi-ronment model. From Bradley and Bradley 1985), with permission.

1985) used a Markovian model to s imula te a consumer ' s t rans i t ion be tweenre sou rce s t a t e s unde r t he se t w o scena r i o s . T he r andom env i ronm en t m ode lmatched the predict ions of Lawlor ' s 1980b) RA3 fo r pa i nv ise ove r l aps andvar i ances of over l ap . In cont ras t , t he s t ruc tured envi ronme nt m odel p rov ided agoo d match wi th the observed da ta , i nc lud ing the var i ance peak a t i n t e rmedia tene ighbor d i s t ances (F igure 4 .11).


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One could argue that Bradley and Bradley's (1985) model is too restrictiveto test patterns of evolutionary divergence, because species would have moreopportunity to specialize o n different resources in the face of persistent com pe-tition. In any case, their results suggest that competitive interactions andinternal guild structure are not the only possible explanations for nonrandompatterns of niche ove rlap.

R NDOM IZ TION OF RESOURCE UTILIZ TION PE KS

Rather than analyze niche overlap per se, some authors have examined thespacing of utilization peaks on a single resource dimension. If species arecompeting for this resource, utilization peaks should be evenly spaced. Therationale and statistical analyses re identical to studies of flow ering phenologyof competing plants (Chapter 5) and body sizes of competing consumers(Chapter 6).

The null model in this case is MacArthur's (1957, 1960) broken stick-anumber line is broken into random segments, and the length of each segmentrepresents the spacing of resource peaks between two adjacent species (seeChapter 3). De Vita (1979) used the broken-stick m odel to comp are mea suresof resource utilization peaks within assemblages of tropical hummingbirds(Snow and Snow 1972), herbivorous stem-boring insects (R athcke 1976), andtropical intertidal snails (Kohn 1959). For each assemblage, De Vita (1979)compared segment lengths of individual species pairs with those predicted bythe broken-stick model. The obse rved points all fell within tw o standard devia-tions of the predicted values, and De Vita (1979) concluded that the nullhypothesis cou ld not be rejected.

Three criticisms apply to De Vita's 1979) analysis. First, the distancesbetween resource peaks are not independent points, so they should not becompared simultaneously to the null predictions (Pielou 198 1). Second, D eVita (1979) did not provide an explicit test for evaluating the fit of the nullmodel. Th e fact that all the points fell within tw o standard deviation s was not avalid test (Shelly and Christensen 1982). Finally, distances measured for theterminal specie s are arbitrary and not equiv alent to distances between adja-

cent spec ies (De Vita 1979; Cole 1981).Bush and H olm es (1983 ) offered a biological system a nd a new analysis that

addressed all three criticisms. The spacing of helminth parasites along thesmall intestine of Lesser Scaup duck s (Aythya affinis) is well suited for tests ofniche displacement. The vertebrate intestine is a complex linear gradient forparasites with biologically defined end points, the position of individuals


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Niche Overlap 89

NUM ER OF SPECIESFigure 4.12. Variation of niche distances between adjacent helminth species co-occur-ring in the small intestine of lesser scaup (Aythya afii nis).The solid line is the pre-dicted value from the broken-stick model. Each point represents an independentassemblage. The results suggest that the spacing of the median individual of each para-site species is more regular than expected. From Bush, A O., and J C. Holmes. 1983.Niche separation and the broken stick model: use with multiple assemblages.Ameri-can Naturalist 122:849-859. Copyright 1983 by The University of Chicago. Re-printed by permission of the publisher.

within the gradient can be determined accurately, and many replicate commu-nities can be sampled.

Bush and Holmes (1983) measured location as the placement of themedian individual of a species. They summarized community dispersion pat-terns as a single number, the variance of segment lengths. This is the sameapproach used by Poole and Rathcke (1979) in their analyses of phenologicaloverlap (Chapter 5). Whereas Poole and Rathcke (1979) derived the expectedvariance analytically, Bush and Holmes (1983) estimated it with a simulation ofthe broken stick. The observed variance was less than expected for mostassemblages (Figure 4.12), suggesting that the spatial occurrence of species


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able4 4Summar y of null model studies of resource utilization

Overlap MultidimensionalCitation Taxon Samples measurement Resources niche Randomization Overla p

Schoener West Indian Anolis1988) lizards 37)

Griffiths Smooth and palmate1987) newts Triturus)

2)Case 1983 Sea of Cortezlizards 18

Pianka et a1 Kalahari lacertid1979) lizards 7)

Australian Ctenotus7)

Australian geckos9)

Australian Varanus5)

24 island communities,compared to sourcepools fromGreater Antilleanislands

Funnel-trap samplesfrom a single pondin mid-Wales

37 island communities

Long-term censuses,diet analysis 10sites




Number of co-occurringspecies in eachmicrohabitat

Eq. 4.4

Eq. 4.3

Eq. 4.3

Eq. 4.3

Eq. 4.3

Eq. 4.3

Structuralmicrohabitat 8)

Pond locationmicrohabitat 7)

Time of year 22)Food type 24)Food size 1 8)Microhabitat I6Time of day-

temperature 24)Microhabitat 15)Time of day 24)Prey volume 1 9)Microhabitat 15)Time of day 24)Prey volume 1 9)Microhabitat 15)Time of day 24)Prey volume 19)Microhabitat 15)Time of day 24)Prey volume 19)

No Binomial exact tests,assuming equi-probable speciesplacement andequivalent resourceavailability

Product, average , RA3individual

Geometric mean Utilization fixed;Species sampledequiprobably orweighted by occur-rence) from archi-pelago source pool

Multiplicative RA2Summation meansMultiplicative RA2Summation meansMultiplicative RA2Summation meansMultiplicative RA2Summation means

E, but only forappropriate sourcepools with habitatspecialistseliminated.

Microhabitat: >ETime: >E

Microhabitat: =EFood:Time: = EMicrohabitat: =Food: ETime: EMicrohabitat: EFood: ETime: >EMicrohabitat: EFood: =ETime: = E


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Kalahari skinks (4) Long-term censuse s,diet analysis 10sites

Kalahari geckos (6) Long-term censuses,diet analysis 1 0sites

Australian Long-term censuses,Amphibolurus (7) diet analysis 10sites

North American Long-term censuse s,saurofauna (9j diet analysis 10sitesKalahari saurofauna Long-term censuse s,

17) diet analysis 1 0sitesAustralian Long-term censuses,

saurofauna (40) diet analysis 10sites

Tokeshi Chironomids of Replicated vegetation(1986) River Tud, eastern samples. Gut

England (9) conten ts ofchironomids

Sale (1974) MacArthur s (1958) Foraging time inwarblers of New differentEngland (4) microh abitats

Eq. 4.3 Microhabitat (15)Time of day (24)Prey volume (19)Eq. 4.3 Microhabitat (IS )Time of day (24)

Prey volume (19)Eq. 4.3 Microhabitat (1 5)Time of day (24)

Prey volume (19)Eq. 4.3 Microhabitat (IS)Time of day (24)Prey volume (19)Eq. 4.3 Microhabitat (IS )

Time of day (24)Prey volume (19)Eq. 4.3 Microhabitat (15)

Time of day (24)Prey volume (19)T i e : geometric Time of year (365 )mean proportion Diet (3)

of the overlappingarea under tworesourceutilization curves[0,1] D iet: Eq. 4.4

Eq. 4.4 Foraging zone ( I 6)

MultiplicativeSummation meansMultiplicativeSummation meansMultiplicativeSummation meansMultiplicativeSummation meansMultiplicativeSummation meansMultiplicativeSummation meansNo Time: (a) resourcepeaks placed

randomly; (b)resource peakslimited tononwinter monthsDiet: RA

RA3

Microhabitat:Food:Time: =Microhabitat:Food: =Time: >Microhabitat:Food:Time: >Microhabitat:Food:Time: =Microhabitat:Food:Time: >Microhabitat:Food:Time: =Time: >Diet: > or =

(in different months)

(Table continues on nextpage )


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Table 4 4Summary of null model studies of resource utilization Continued)

Overlap MultidimensionalCitation Taxon Samples measurement Resourc es niche Randomization Overlap

Sale (1974)

Kobayashi(1991)

Field (1992)

Haefner(1988a)

Inger andColwell(1977)

Ueckert and Han- Stomach contentssen s (1972)grasshoppers ofColorado (14)

Forest-floor coleopt- Pitfall trapserans of Toweda-HachimantaiNational Park,Japan (18)

Spider-hunting Water/pitfall trapspompilid waspsat a Brecklandheath (24)

Greater Antillean First-sightingnolis lizard observations

communities ofSchoener andSchoener(1971a,b) (9)

He~petofauna f Quadrat, transectbmadleaf ever- censusesgreen forest, decid-uous dipterocarpforest, and agri-cultural land inThailand (1 05)

Eq. 4.4

Colwell-Futuymaindex

Eq. 4.3

Eq. 4.2, Eq. 4.3

Colwell-Futuymaindex, withweighting forresourceavailability

Dietary category(20)

Habitat 6)Bait types (5)

Microhabitat (7)Time of year (9)

Perch diameterPerch height

Microhabitat (26)

Individual Habitat: EBait type: EHabitat x Bait type:

O E

No RAl, weighted by Microhabitat: Eestimated areas of Time of year: Emicrohabitats andabundance of species

Product Random selection of Mixed. Eq .2 givesSummation individuals and less significantIndividual placement in sites; overlapthan Eq 4.3.overlaps weighted Use of mean,by Lawlor s median, or geometric(1980b) electivities mean gives weak rto account for no support for nicheunequal resource shifts. ank ordersavailability give better support.

Principal RA3 var) E for closestcomponents of neighborsniche axes


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Joem andLawlor1981)MacNallyand

Doolan1986)Winemillerand

Pianka1990)

Grasshoppers of 3 First sightings and gutarid grassland content analysescommunities nwestem Texas 35)

Cicadas of eastem First sightingsAustralia 9)

Freshwater fish Gut content analysesassemblages ofCano Maraca,Venezuela wetseason) 59)Freshwater fish Gut content analysesassemblages ofCano Volcan,Venezuela wetseason) 19)

Freshwater fish Gut content analysesassemblages ofCano Agua Fria,Venezuela wetseason) 50)

Freshwater fish Gut content analysesassemblages ofQuebadra,Venezuela wetseason) 23)

Average groupcentroiddistances inmultivariateniche space

Eq 4.3 withstandardizedelectivitycoefficients




Plant resource 56) No Inger-ColwellMicrohabitat 27) comparison ofneighbors.var) >

Habitat I 6) Yes, factor All possible n-species =Morphology 10) analysis combinations wereBehavior 15) reducing to 3 compared for aniche axes particular guildPrey 94) No

Prey 68)

Prey 82)

Prey 67)

Taxon: number in parentheses is number of species compared. Resources: number in parentheses is number of resource states. Overlap: = observed overlap, = expectedoverlap based on the null model. Inequalities indicate statistically significant pattems p 0.05). var) = observed variances of overlap: otherwise. pattems refer to median ormean of pairwise niche overlaps.


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was significantly regular. Note that a regular spacing does not preclude highoverlap, because the analysis considers only the distribution of utilizationpeaks (Cole 1981).

SUMM ARY OF FINDINGS

Table 4 4 describes som e of the studies that have used null m odels to exam ineresource overlap. It is difficult to summ arize the findings, because the method svary widely from one study to the next. However, nearly all of these studiesdetected some nonrandomness in niche overlap, although not always in anegative direction. M ost studies included m ore than on e resource axis, summ a-rized as a me an o r aggregate overlap. Few studies explored the use of electivit-ies versus utilizations, even thou gh this may greatly affect the results. Finally,most studies randomized utilizations directly, even though these indices aresample-size dependent. In 1977, Inger and Colwell noted there is no suchthing as a standard protocol for commu nity analysis. Th e same thing can besaid with respect to overla p studies today. How ever, we now hav e a num ber ofnull mo dels that can be used to assess the m ean, v ariance, and nearest-neighbordistance of niche over lap in the absenc e of species interactions.

RECOMMENDATIONS

Several decisions need to be m ade in a null model an alysis of niche overlap.Electivity measures are theoretically desirable, but utilization measures areusually more practical for analysis. Niche overlap analyses should ideally bebased on 50 or m ore observations of use of food item s or other resources byeach species. If not, the indices may be biased, and the simulation proceduresof Ricklefs and Lau (1 980) should be followed. Th e choice of an overlap indexis somewhat arbitrary; w e suggest Pianka's (197 3) index as sym metric measureof overlap between two species. To summarize overlap for an entire assem-blage, we recomm end using the median overlap and Inger and C olwell's (1977)nearest-neighbor plots of the mean and variance of overlap. If the source poolfor an assemb lage can be estimated independently, we recom men d the proce-dures of C ase (1983a) and Scho ener (1988a) for determ ining whether ov erlapis unusually low fo r the particular combination of coexisting species. If there isno independent source pool, the observed utilization data will have to berandomized. Lawlor's (l98 0b ) R A and RA 2 seem to be the most desirable forthis purpose.

Null Models Chapter 4

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