null models chapter 8

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SPECIES AREA RELATIONSHIPS

SPECIES AREA REL.ATIONSHIPS

In Chapter 7, we pointed out that a major difficulty in assessing co-occur-rence patterns was variation in site quality. If some sites are more favorablethan others for all species, patterns of species aggregation will emerge thatdo not reflect interspecific interactions (Pielou and Pielou 1968). Variationin site quality is often manifest in total species richness, which should becontrolled for in null models of species co-occurrence (Connor and Sim-berloff 1970).

But why is species richness greater in some sites than in others? This questionis an important one that has been studied independently of factors that deter-mine co-occurrence. Area is the most basic correlate of species richness. Largeareas support more species than small areas, although the relationship is rarelylinear. For oceanic archipelagoes, species number roughly doubles for everytenfold increase in island area (Darlington 1957). The species-area relationshipis most obvious when the sites are true islands (Figure 8.1). For example,mammalian species richness is well correlated with area in archipelagoes ofoceanic, land-bridge, coastal, and river islands (Wright 198 Lomolino 1984).

Species richness also correlates with the area of most insular patches ofhabitat. Familiar examples include mammals of forested mountaintops (Brown1971), decapod crustaceans of pocilloporid coral heads (Abele 1976), andinsects of thistleheads (Brown and Kodric-Brown 1977). Areas need noteven be insular. Species number is related to area for vascular plants ofdifferent-sized quadrats (Connor and McCoy 1979), lumbricid earthworms oEuropean sites (Judas 198X), and parasitic fungi of British trees, where areawas defined as the geographic range of the host plant species (Strong and Levin1975). Species-area relationships hold for tropical and temperate archipelagoes(Schoener 1976b) and for fossil and extant assemblages of entire continents(Flessa 1975).


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SUND ISL NDS

Figure 8.1. Species-area relationship for land and water birds of the Sunda Islands.Numbers indicate different islands (1 Christmas Island, 23 =New Guinea). Note thelogarithmic transformation of both axes. Data such as these were used to support theequilibrium model, although other models may account for the species-area relation-ship as well. From MacArthur and Wilson (1963), with permission.

1000

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I

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One of ecolog y's few genu ine laws (Scho ener 1976 b), the species-arearelationship has been described and interpreted for over 120 years (McGuin-ness 1984a), but there is little agreement on its cause. Some authors haveviewed it as a dynamic balance between immigration and emigration (Mac-Arthu r and Wilson 1963, 1 967) that ma y ultimately reflect energetic constraintson comm unity development (Wright 1983 . Bec ause of their insularity, naturereserves hav e been liken ed to islands, and species-area curv es have fo rmed thebasis for conservation strategy (Wilson and Willis 1975). Others have sug-gested that the species-area relationship embodies little more than a passivesampling effect and may have no biological significance (Conno r and M cCoy1979). A null model that treats islands as targets and individuals as passivepropagules incorporates minimal biological forces, but may account for thespecies-area relationsh ip (Arrhenius 1921; Co leman 1981 ; Colem an et al.1982). In this chapter, we review four hypotheses that have been put forth toexplain the species-area relationship, d iscuss other patterns that are predictedby these mechanisms, and describe the use of null models in understandingspecies-area curv es.

10 100 1000 10.000 100.000R E I N S Q U R E M I L E S


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Species-Area Relation ships 209

WHAT MECHANISMS ACCOUNTFOR SPECIES-AREA CURVES?In spite of the generality of the species-area relationship, it is likely to resultfrom a variety of forces that reflect the sampling properties of islands, habitatvariability, population processes, and the underlying species abundance distri-bution (Figure 8.2). To date, four distinct mechanisms have been proposed toaccount for the species-area relationship. These mechanisms are not mutuallyexclusive, but they do emphasize different processes that can cause a correla-tion between species richness and area:

1 The disturbance hypothesis Disturbances that reduce species di-versity are more common on small islands than on large islands(McGuinness 1984a).

2. The habitat diversity hypothesis Large areas contain more habi-tats and hence more species (Williams 1943).

3 The passive sampling hypothesis Large areas function as tar-gets that sample more individuals, and hence more species(Arrhenius 1921; Coleman 1981; Coleman et al. 1982).4 The equ ilibrium hypothesis Large areas support larger popula-tion sizes of all resident species than do small islands. Conse-quently, the probability of stochastic extinction is reduced onlarge islands (Munroe 1948; Preston 1962; MacArthur and Wil-son 1963, 1967).

IFlgure 8.2. Mechanisms controlling the rela- SL R Elionship between area and species number. l t r a d t t~ o n a l ~ n d e p e n d e n t v a r i a b le )Several mechanisms may contribute to the ap-

l~arently traightforward correlation between S Ero log ica l spaceand A . From Haila 1983) , with permission. Amo u n t h e te r o g e n e i t yo f e c o / o g ~ c a l r e s o u r c e s

tNum ber o f i n d ~ v ~ d u a l sSpe r tes -abun dance d ts t rt bu t lonS P E C I E S N U M B E Rt r a d ~ t ~ o n a l ependen t va rcable )


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able8 1Predicted patterns for hypotheses that explain the species-area relationship

Habitat PassiveEquilibrium diversity sampling DisturbancePattern hypothesis hypothesis hypothesis hypothesisSubstantial turnover Yes Yes or no No Yes (small

islands)S A correlation for equal- Yes No No No

sized quadratsFit with passive sampling Yes or no Yes or no Yes Yes or nomodelFit with habitat-unit model No Yes No No

These h ypotheses ha ve no t received equ al a t tent ion in the l i terature. T hedis turbance hypothesis , for example, was offered as an explanat ion forspecies-area relat ionships on ly in the 1980s (McG uinness 1984a ) . Andal though the passive sampling hypothesis was f i rs t int roduced more than7 0 years ago (Arrhenius 1921) , it has only recent ly been em ploy ed as a nul lmodel for the sp ecies-area relat ionship. Th e equi l ibr ium hy pothesis , aspopular ized by MacArthur and Wilson (1967) , dominated the l i terature inthe 1960s and 1970s, and w as of ten accepted without adequate proof (Wil-l iamson 1989 ) . Gi lber t (1980) reviewed the uncr it ical acceptance of thetheory dur ing this per iod, and B oecklen and Simberloff (1986) discussed i tspremature appl icat ion to the design of nature reserves , through faunalcollapse and relaxation mo dels.

The essent ial problem was that many authors viewed the species-arearelat ionship as suff icient evidence for the equi l ibr ium theory, wi thout acr i t ical evaluat ion of the al ternat ives . Al though the four hypotheses al lpredict a species-area relationship, each ha s a di f ferent set of assum ptionsand a unique set of addi t ional predict ions (Table 8.1) . In the fol lowingsect ions, we review the assu mptions, predict ions, and cr i t ical tes ts of eachhypothesis . Next , we explain how nul l models have been used to examinetwo par t icular sp ecies-area patterns: 1) the s lope of the species-area regres-s ion, which has been interpreted as a measure of isolat ion, and (2) theconstancy of species number S) through t ime, which has been taken as anindicator of equil ibrium status.


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Species Area Relationships 21 1

THE DISTURB NCE HYPOTHESIS

If small islands are disproportionately subject to chronic disturbances thatremove species, then a species-area relationship will result (McGuinness1984a). This hypothesis assumes that small islands are more vulnerable todisturbance, and that species richness increases as disturbance frequency de-creases. Like the MacArthur and Wilson (1967) model, the disturbance hypoth-esis predicts that turnover on small islands should be substantial. However, theMacArthur and Wilson (1967) model predicts continuous turnover, whereas thedisturbance model predicts synchronous extinctions. A more fundamental dif-ference is that the MacArthur and Wilson (1967) model envisions all commu-nities as being in an ecological equilibrium, whereas the disturbance hypothesisdescribes small-island communities in a state of disequilibrium.

Evidence for the disturbance hypothesis comes from sessile marine commu-nities, where fouling panel:; (Osman 1977) or intertidal boulders (McGuinness1984b) function as islands. Wave action and predation often control diversity inthese space-limited systems (Sousa 1984), although the perturbations may notalways lead to a species-area relationship. For example, in intertidal boulderfields of California, species richness was greatest on intermediate-sized boul-ders. Small boulders had low species richness because they were chronicallydisturbed by wave action. But large boulders also had low species richnessbecause they were rarely overturned and became dominated by a few species ofcompetitively superior algae (Sousa 1979). Thus, even if disturbance frequencyis correlated with island area, it may not always lead to a species-area relation-ship. Biotic "disturbances" may also lead to species-area relationships. In forestbird assemblages, for example, species-area slopes were steeper for guilds thatwere susceptible to nest predation (Martin 1988), suggesting that this distur-bance may be more important in small forest patches. The increased perime-terlarea ratio ensures that any "edge effects" will be relatively more severe onsmall islands.

TH E H BIT T DIVERSITY HYPO THESIS

The habitat diversity hypothesis assumes that species diversity is controlled bythe availability of different habitat types. This model predicts that habitatdiversity increases with area, and that species richness increases with habitatdiversity. Area per se has a minor effect on species richness, and instead servesas a surrogate variable for underlying habitat diversity (Williams 1943).


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212 Chapter

1 2 4 1 2 4 1 2 4Area krn2)

Figure 8.3. Relationship between area and habitat diversity. The x axis is the plot areafor regions of England and Wales, and they axis is the number of geological types re-corded in those areas. The box-and-whisker plots illustrate the extremes (verticallines), quartiles (box ends), and medians (horizontal lines) for multiple observations.The sloping line connects the medians with the total number of geological types ob-served for the entire area. Note the logarithmic transformation of both axes. The close rela-tionship between area and habitat diversity may e responsible for many species-arearelationships. From Williamson (1981),with permission of Oxford University Press.

The habitat diversity hypothesis implies that habitat specialization is impor-tant. This explana tion fits the naturalist s perspective that man y species can bereliably located by paying close attention to their habitat affinities. If uniquehabitat types are foun d only on large islands o r areas, then species richness willinevitably increase w ith area. In the W est Indian av ifauna, for examp le, single-island endem ics such as the Zapata Wren of Cu ba (Ferm inia cerv erai) and theElfin Woods Warbler of Puerto Rico (Dendroica angelae) are habitat special-ists wh ose ex clusive occurren ce on large islands contributes to the species-arearelationship.

Sev eral studies have confirm ed the basic relationship be tween habitat diver-sity and species richness, in both terrestrial (e.g., MacArthur and MacArthur1961) and marine (e.g., Abele 1974) communities. Much less common arestudies of the direct relationsh ip between habitat diversity an d area itself. Fo rexample the number of geological formations in the Lake District of Englandwas well-correlated with plot area, and the slope of the relationship variedbetween 0.20 and 0.35 on a log-log scale (Figure 8.3; W illiamson 1981). Many


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species-area relationships may reflect this underlying pattern of habitat varia-tion and area (Scheuring 1991).

On the other hand, many species are not strict habitat specialists, and spe-cies-area relationships are found in very hom ogeneous habitats, such as man -grove or partina islands (W ilson and Simberloff 1969; Rey 1981). But even inapparently homogeneous habitats, the perimeterlarea ratio will change withisland size. and this edge effect may represent an important elem ent ofhabitat diversity (Schoener and Schoener 1981; Janzen 1983). How ever, with-out an experimental manipulation, it may be impossible to distinguish thecontributions of area and perimeter to species richness (Blouin and Connor1985).

ultiple Regression odelsHow has the habitat diversity hypothesis usually been tested? Historically,habitat and area effects were partitioned with multiple regression analyses(Hamilton et al. 1 963; Sinipson 1 974; Con nor and Simberloff 1978). If habitatdiversity is important, it should make a statistical contribution to speciesrichness abo ve and beyond the variation explained by area . Although the test isconceptually valid, the tight correlation between area and habitat diversitycompromises the statistical analysis. Consequently, the biological interpreta-tion of multiple regressions is problematic, and it has been difficult to teaseapart the contributions of area and habitat diversity to specie s richnes s (Conn orand Simberloff 1978).

For example, bird species richness in isolated woodlots was well correlatedwith area and vegetation structure (Blake and K arr 1987 ), but in a multipleregression ana lysis, only the area effect was statistically significant. How ever,species richness of interior forest birds was correlated with both area andhabitat diversity, whereas richness of edg e species was influenced by only areaand perimeter. Moreover, habitat diversity was correlated with the abund ancesof particular specie s, suggesting that habitat diversity influenced specie s occu r-rence and hence total spec ies richness.

M ultiple regression an alyses can be v ery sensitive to statistical outliers. Forplants of the British Isles, number of soil types contributed significantly tospecies richness (Johnson and Simberloff 1974 ), but only if the islan d of GreatBritain was exc luded from the analysis (M cCoy and Conn or 1976). Thus, themeasured effects of habitat diversity on species richness may hinge on whichgroup s of spec ies and which g roups of islands are consid ered.

None of these whole-island tests is very satisfying . By empha sizing thehabitat diversity of an entire island, multiple regression analyses neglect the


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Figure 8.4. Effects of habitat diversity on within-island distributions of species. Eachcircle is an island, and the divisions within the circle represent different habitat types.The letters represent individuals of different species. In A), the species-area relation-ship arises because each species is a specialist on a single habitat type. In B), habitatdiversity does not contribute to the species-area relationship because individuals of thedifferent species occur randomly with respect to habitat type within an island.

spatial patterns of species occurre nce wit in islands. If the habitat diversityhypothesis is correct, species will be distributed nonrandomly with respect todifferent habitats within a single island. n contrast, species may occur ran-dom ly within habitats if any of the other three hypo theses is correc t Fig-ure 8.4 .he Habitat Unit Model

This suggests a promising avenue for testing the habitat diversity hypothesis.First, map the habitats of each island, and then record the occurrence of eachspecies within those habitats. If the habitat diversity hypothesis is correct, therelative areas of different habitats should be a better predictor of speciesrichness than total island area.


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Species Area Relationships 215

Densities d l onmain land

Habitat A

Habitat

Habitot

Habitat D

Islandtota l are a =a,+ a e + a o

Figure 8.5. Construction of a prevalence function. The density (d ) of species in differ-ent habitats on the mainland and the relative area (a ) of those habitats on the islandgenerate the expected density of each species on an island. From Haila et al. 1983),with permission.

Buckley (1982) took exactly this approach in a study of plant speciesrichness of the Lowe ndal Island s of W estern Australia. Fo r each of 22 islands,Buckley (1982) recorded the distribution of vascular plants in three habitattypes: white sand, limestone, and red sand. He next categorized the plantspecies acco rding to the habitat types in which they occurred. T here were threegroup s of habitat specialists that occu rred in only on e habitat, three group s ofspecies that occu rred in exactly tw o of the habitats, and on e group of ubiquitousspecies that accurred in all three habitats. For a se t of n habitats in an arch ipel-ago, there will be 2 such group ings or habitat units.

For each habitat unit, Bu ckley (19 82) then con structed a species-area curv e,using the combined area of the component habitats of each island. Summingthe predicted values across all the habitat units gave the expected number ofspecies for an island. This expectation was com pared t o the predictions fro m asimple species-area regression that ignored habitats. For 7 of the 22 islands,the predictions of the habitat unit model were superior to those of the simpleregression. It is importa nt to note that B uckle y's (1982 ) result was not a trivialconsequence of extreme habitat specialization, because most of the speciesoccurred in two or m ore habitats.

Haila and Jarvinen (1 983) took this approach on e step further and mea surednot only the occu rrence , but also the abund anc e, of individual species. Sim ilar


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Figure 8 6 Prevalence functions for 8 species of insectivorous birds of the land Is-lands of Finland. Five island size-classes are represented on the x axis. They axisgives the logarithm of the prevalence function that is the ratio of the observed to theexpected island density. Symbols indicate data from different yearly censuses. For ex-pectations greater than breeding pairs the vertical solid line indicates the range andthe vertical open bar indicates the standard deviation. Note that for some species theexpected density on small islands is effectively zero. From Haila et al. 1983), withpermission.


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to Diamon d s (1975) incidence function (see Cha pter 7) , the prevalencefunction is the ratio of observed to expected density of a given species onislands of different size (Figure 8.5) . For bird species of the h i n d Islandsof Finland, Haila et al . (1983) constructed the prevalence function byestimating mainland densities of species in different habitats (Figure 8.6).This model accurately predicted species richness, and the authors con-cluded that a sampling metaphor was appropriate to explain avian speciesoccurrence in this archipelago. Note that the mo del of H aila et al . (1983) isactually a hybrid of the habitat diversity hypothesis and the passive sam-pling hypothesis, explained later in this chapter.

In sum, the habitat unit model and the prevalence function are useful toolsfor evaluating the role of habitat diversity in producing species-area correla-tions. Because they emphasize the occurrence of species within particularhabitats on islands, they a re more pow erful tests of the habitat diversity hypo th-esis than conventional regression analyses.

TH E EQUI[LI RIUM HYPOTHESISPopularized by MacArthur and Wilson (1963, 1967) and independentlydeveloped by Munroe (1948; see Brown and Lom olino 1989), the equilib-rium theory envisions island spec ies richness as a balance b etwee n rates ofcolonization from a mainland source pool of P species and island extinc-tions of established populations. The theory has two sets of assumptions,one concerning the demography of island populations and the other con-cerning com munity-level rates of im migration and extinction. The theory isusually presented in terms of the rate assumptions, but ultimately these arederived from processes at the population level. The population-level as-sumptions are as follows:

1 . Th e species-abundance distribution of the mainland source poolis a canonical log norma l (see Ch apter 3). This assum ption is notabsolutely necessary for the mode l, but it does generate quan tita-tive predictions about the form and slop e of the spec ies-arearelationship.

2. The summ ed abundance of all species is proportional to island area.3 Th e probability of popula tion extinction is inversely proportional

to island population size.4 Th e probability of colonization is inversely proportional to island

isolation or distance from th e source pool.


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The comm unity-level assumptions are:1 Th e imm igration rate (num ber of new speciesttime) decreases

with increasing species number on the island and decreases withincreasing isolation of the island.

2. Th e extinction rate (numb er of species disappearingltime) in-creases with increasing species number on the island and de-creases with increasing island size.

Finally, the predictions that arise from the equ ilibrium model are:1. There should be substantial turnover in species composition

through time.2. The species-area curve should be best fit by a power function

S CA ), where S is species richness, A is island area , and C andare fitted constants.

3 Th e slope of the curve on a log-log plot (z) should approx imate0.26 for isolated archipelagoes, and should be shallow er with de -creasing isolation.4. Species numb er on an island should be relatively constan tthrough time, although som e variability in S is expected becauseextinctions and recolonizations are stochastic (D iamond andMay 1977).

5. In a comparison of equal-sized quad rats, species density shouldbe higher on the mainland or on large islands than on sm allislands.

TESTS OF THE ASSUMPTIONSIn the following sections, we review the evidence supporting the importantassumptions and predictions of the equilibrium theory. Some, but not all, ofthese patterns have been tested with null models.o Extinction and Immigration Rates Vary with Species Number

Graphs of extinction and immigration rates as a function of spe cies num ber arethe most famous summary of the MacArthur and Wilson 1967) model. Theprecise shape of these curves depends on species interactions and imm igrationdyna mics. If species extinctions are indepe nden t (a noninteractive com mu nity)


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Species-Area Relationships 2 19

umber of species on island umber of spec ies on islandFigure 8.7. Concave and linear immigration I) and extinction E)curves. The originalMacArthur and Wilson 1 963) model presented concave immigration and extinctioncurves, whereas a Markovian model generates linear curves.

and species immigrations are equiprobable, the curves are strictly linear. Incontrast, an interactive or heterogeneous assemblage will give concave im-migration and extinction curve s (MacA rthur 1972 ), which is how the theorywas originally presented (Figure 8.7). This distinction is important for nullmodel tests of species constancy, which we describe later in this chapter,How ever, for a qualitative test of the M acArthur and W ilson (1967 ) mo del, it issufficient to show that the immigration rate falls and the extinction rate riseswith increasing island species richness.

In spite of the obvious im portance of the immigration and extinction curvesto the equilibrium theory, long-term sampling data are necessary to constructthem, and there are few examples from the literature. Strong and Rey (1982)dem onstrated a significant increase in extinction rate and a significant decreasein immigration rate for insect recolonization of fumigated Spartina islands(Rey 1981). Williamson (1981) assembled three other examples from long-term census data in insular assemblages. Fo r an established bird com mu nity inEastern W ood, Williamson 198 1) plotted extinction an d immigration rates as afunction of species num ber for 26 yearly censuses. Im migration rates declinedsignificantly with S but extinction rates did not increase significantly (Fig-ure 8.8). For birds of Skokholm Island, only the extinction rate was sig-nificantly correlated with island species richness. The correlation for theimm igration cur ve was nonsignificant and h ad a positive, not a negative, slope.

Williamson s (1981) final exam ple w as plant coloniza tion data for the volca-nic island of Surtsey. In this study, the highest immigration rates occurred notat the start of colonization, but after some initial pioneer species becameestablished, perhaps indicating successional chan ges in the hospitability of theisland. In all of these exam ples, the variance abo ut the cu rves w as substantial,


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pec~es reedingFigure 8.8. Immigration and extinction curves for breeding birds of Eastern Wood.The immigration curve decreases significantly with increasing S, as predicted by theMacArthur and Wilson 1967)model, but the increase in the extinction rate is not sig-nificant. Compare with Figure 8.7. From Williamson 1981),with permission of Ox-ford University Press.

suggesting that species number had only a very mino r effect on local immigra-tion and extinction rates.Do Population Sizes Vary with Island AreaIn spite of the critical imp ortance of population size and stochastic extinctio n tothe MacArthur an d Wilson 1 967) theory, relatively few studies have exam inedhow total population size of an individual species changes as a function ofisland area Haila and Jarvinen 1981). O ne problem is that MacA rthur andWilson 1967 ) were not entirely explicit about what the predicted patternswere. As developed by Scho ener 1976b), there are tw o possibilities. T he firstis that the faun a is noninteractive and pop ulation size is proportional to area. Inthe second model, competition is proportional to species number, so thataverage population size is a function of both island area and species richness.Whether or not the fa un a is interactive, it would seem that a basic prediction ofthe MacA rthur and Wilson 1967 ) model is that equilibrium population sizesincrease with island area Preston 1962 ).


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density co mpe nsation (MacA rthur et al. 1972; Wright 1980), habitat shifts(Ricklefs and Cox 1978; Crow ell 1 983), and ecolo gical release from predatorsand competitors (Toft and Schoener 1983) suggests that island area is notalways the overriding factor that determ ines insular population size.

TESTS OF THE PREDICTIONSIs There Substantial Turnover in Species CompositionTurnover is one of the most salient features of MacArthur and Wilson (1967)equilibrium communities. It distinguishes the MacArthur and Wilson (1967)model from other scenarios of insular community assembly, including co-evolutionary models of species interaction (see Chapters 6 and 7) and non-interactive colonization models with little or no turnover (Case and Cody1987). Unfortunately, turnove r in island popu lations may be difficu lt to estab -lish. M easure s of turnover are affected by the thoroughness of sam pling effortat different times (Lynch and Johnson 1974), the length of the census interval(Diamond an d M ay 1977), sampling error (Nilsson and N ilsson 1983), theestablishment of a species equilibrium (McC oy 1982 ), the occurrenc e of habi-tat change between censuses (D.L. Lack 1976), and the use of relative versusabsolute turnover rates (Schoener 1988b).

Mo re importantly, the measu rem ent of turnov er depends critically on how aninvestig ator defines colonization , extinc tion, and residency status. If vagrant ornonresident spec ies are included in the calculations , estim ates of turnover canbe greatly inflated. For example, Simberloff and Wilson (1969) initially esti-mated turnover rates of insect species colonizing mangrove islands at 0.67species per island per day. Simberloff (1976a) reanalyzed the data and elimi-nated probable transients and widely dispersing species. The revised turnoverestim ate was only 1.5 specie s per island per year Similarly, W hitcom b et al.(1977 ) computed turnov er rates for forest birds of 15-25% ov er 30 years. Butif edg e species and wide-ranging raptors were exclu ded, the turnover was closeto (McCoy 1982). W illiamson (1989) concluded that the M acArthur andWilson (1967) model is thus "true, but trivial." In other words, many commu-nities do display substantial turnover, but this inevitably occurs among tran-sient, peripheral sp ecies that may not be typical residents of the comm unity.

However, not all "transient" turnover is biologically uninteresting. It isimportant to distinguish between turnover of populations and turnover ofindividuals through movement among sites. In som e cases, com mu nity assem -bly occurs through individual movement. For example, breeding birds of


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Species-Area Relationships 223

con iferous forest seasonally co lonize habitat fragme nts and establish breedingterritories Ha ila e t al. 19 93), so that turnov er do es not reflect true populationextinction. Haila e t al. 199 3) suggested that seasonal move me nt of indiv idu-als is likely to be very important in the structure of many boreal animalcommunities.Is the Species Area Curve Best Fit y a Power Function?Th e log normal d istribution prov ided a theoretical justification for using thepow er function in species-area studies Preston 1962 ). Bu t if the speciesabundance distr ibution is not log normal, other transformations may bemore appropriate. For example, if a log ser ies descr ibes abundances, anexpo nential sem i- log) transformation will l inear ize the species-area rela-t ionship Fisher e t al . 1943; W ill iams 1943, 1947b). McGu inness 1984 a)reviewed the exten sive history of efforts by plant ec ologists to infer thecorrect functional form of the species-area relationship. For anima l ecolo-gists , the power func tion quickly bec ame synon ym ous with the log normaldistr ibution Preston 1960, 1962 ) and the equilibr ium model M acArthu rand Wilson 19 67). However , Colem an et al . 1982) warned that inferringthe species abundance distr ibution from the species-area transformationrequires that the same distribution hold for all islands in an archipelago,which is a tenuous assum ption.

W hat is the empirical ev idence that the power fun ction or the exponentialprovides the best f i t to species-area data? Conno r and McCoy 1979 ) f i tregression m odels to a heteroge neou s collection of 100 species-area cu rvesfrom the literature. Using logarithmic and untransformed data, they chosethe best-f i t t ing model as the one that l inear ized the curve and minimized2least-squares deviations high . In some cases, more than one model f i tthe data equally well ( r2 values differed by less than 5 ) . These criteriawere somew hat arbitrary Sugih ara 1981 ) , but without repeated measure-ments of species r ichness o n is lands of identical s ize, there seem s to be n ooth er reasonable way to assess the fit of a regression mo del Co nno r et al.1983).

Although the power function log-log mo del) f i t three-quarters of the datasets, it was the best-f i tt ing m odel in o nly 4 3 of 119 cases. T he expo nentialmodel did not fare any better , and in many cases, the untransformed datagave the best f i t . Unless the assumptions of the MacArthur and Wilson1967) model can be confirmed independently, there seems to be l i t t le

biological significance to the transformation that best linearizes a species-area curve.


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224 hapter8

What Is the Observed Value of z and W hat Is Its Significance?Although the log-log transformation may have little biological significance,there is a long tradition of interpreting the slope of this regression in the contextof equilibrium theory. The impetus came from Preston (1962), who derived aslope of 0.26 for an archipelago of isolates sampled from a log normaldistribution. He felt that sampling errors and other factors would lead to slopevalues in the range of 0.17 to 0.33, whereas MacArthur and Wilson (1967)accepted a range of 0.20 to 0.35. May (1975a) derived slopes in the range of0.15 to 0.39 for a variety of log normal distributions, and Schoener (1976b)predicted slopes between 0 and 0.5 for an equilibrium model with speciesinteractions.

Within the equilibrium framework, species-area slopes were thought toreflect the degree of isolation of an archipelago. In the original MacArthur andWilson (1967) model, isolation affected only the immigration curve, so thatdistant islands had lower species richness and distant archipelagoes had steeperslopes. Lomolino (1984) confirmed this pattern for mammals in island archi-pelagoes: the slope of the species-area relationship was correlated with therelative isolation of an archipelago (Figure 8.10).However, isolation may affect the extinction rate as well (Brown and Kod-ric-Brown 1977), making it unclear what slope ought to be expected. Schoener(197613) thought that distant archipelagoes would e colonized primarily via a

o l : : : : : : :1 00 2 0 0 3 0 0 4I S O L A T I O N

Figure 8.10. Effects of isolation (average distance to the nearest mainland or large is-land) on the slope of the species-area regression. Each symbol represents a different ar-chipelago. As the original MacArthur and Wilson (1967) model predicted, slopes weresteeper for more isolated archipelagoes. From Lomolino, M. V 1984. Mammalian is-land biogeography: effects of area, isolation and vagility. Oecologia 61:376-382, Fig-ure 2. Copyright @ 1984 by Springer-VerlagGmbH Co KG


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stepping stone effect from other occupied islands, rather than from a distantsource pool. In addition, the pool of species for a distant archipelago may besmaller than for a close archipelago. In Schoener's (1976b) models, theseeffects generated shallower slopes for distant archipelagoes, a pattern that holdsfor some avian species-area data. These extensions of the MacArthur andWilson (1967) model suggest that a wide range of slopes are possible forequilibrium communities.

Slopes of species-area curves have also been used to compare taxa within anarchipelago. 4 shallow species-area slope for a taxonomic group has often beeninterpreted as an indicator of good colonization potential (Terborgh 1973a;Faaborg 1979): because successful colonizers can reach many islands in anarchipelago, the increase in species richness due to area is much weaker thanfor a group of poor dispersers.

But before species-area slopes can be interpreted in the context of equilib-rium theory, other forces that affect must be considered. First, there are anumber of statistical decisions that affect the slope of the species-area curve(Loehle 1990b). For example, the estimate of the slope will depend on whetherthe power function or the linear log-log model is fit. The two models are notequivalent; they treat the error term differently and may give different slopeestimates (Wright 1981). The slope of the curve may also be affected by therange of island sizes considered. If the range of areas sampled is too narrow, thearea effect may not be statistically significant (Dunn and Loehle 1988). Slopesalso tend to be much steeper for archipelagoes of small islands than largeislands (Martin 1981). Finally, slope estimates may be sensitive to the particu-lar islands included in the sample. For example, the estimated species-areaslope for butterflies of woodland lots (Shreeve and Mason 1980) is 0.28 n = 22lots), but ranges from 0.23 to 0.35, following the deletion of a single islandfrom the sample (Boecklen and Gotelli 1984). This sort of statistical variationsuggests that differences in slope will have to be substantial to reflect anybiological meaning.

For these reasons, comparisons of slope among different taxonomic groupsare problematic. For Neotropical birds, species-area slopes varied markedlyamong different families (Terborgh 1973a; Faaborg 1979). However, most ofthis variation in slope could be attributed to variation in species richness withinfamilies (Gotelli and Abele 1982). Regardless of dispersal potential, familieswith very few species will have shallow species-area slopes (Figure 8.11). Theestimated slope in a regression is also proportional to the correlation coeffi-cient. Grafen (1984) showed similar effects of species richness on the compar-ison of alues among guilds of insects associated with British trees (Kennedyand Southwood 1984).


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Figure 8.11. Effects of speciesrichness on the slope of thespecies-area regression. Eachpoint is a different family ofWest Indian land birds. FromGotelli and Abele 1982),with permission.

F MILY S I Z E

In addition to these important statistical considerations, slopes of species-area curves will be influenced by biological forces that are not explicitlyconsid ered in the equilibrium model. Fo r exam ple, habitat diversity will affectthe slope as different species sets are added with new habitat types on largeislands (Williams 1943). From published studies of forest plots in the easternUnited States, Boecklen (1986) quantified habitat diversity with a principalcomponents analysis of vegetation measures, and then randomly combinedplots of differing size and habitat diversity. Species-area curves for breedingbirds were steeper for archipelagoes with strong habitat heterogeneity.

Incidence functions and minimal area requirements of particular species canalso generate a range of slope values that span the interval suggested by theequilibrium hypothesis (Abbott 1983). Disturbance (McG uinness 1984a) and pre-dation (M artin 1988) may also change the slope of the curve. Finally, species-areacurves may change during the course of colonization (Schoener and Schoener1981), although for vascular plants on lake islands in Sweden, the slope did notchange during a century of primary succession (Rydin and Bo rgegh d 1988).

Given all these factors, it is not surprising that Con nor and M cCo y's (1979)literature survey yielded a wide range of slope values, of which only 55 fellwithin the liberal range suggested by MacArthur and Wilson (Abbott 1983).Connor and McCoy (1979) suggested that any tendency for slope values tocluster between 0.2 and 0.4 was an artifact. They argued that the pattern wasgenerated by the small variance in sp ecies num ber relative to variance in islandarea, and by the fact that sm all or nonsignificant correlation coefficients wouldbe underrepresented in the literature. Because the estimated slope in a regres-sion is the product of the correlation coefficient and the ratio of variances of yto x it follow s that slopes in this range are often expected by chan ce.


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Predictedbserved

Figure 8.12. Distribution of 100 species-area slopes. Although most observed valuesfall between 0 .20 and 0.30 , this pattern is predicted by the observed variances in areaand species richness and by the observed distribution of correlation coefficients. Re-printed by pennission of the publisher from Connor,E F., E D. McCoy, and B. J.Cosby. 1983. Model discrimination and expected slope values in species-areastudies. American Naturalist 122:789-796. Copyright 1983 by The University ofChicago.

Sugihara 1981) argued that this analysis was incorrect and that observedslopes were significantly clustered in a narrow range. However, a reanalysisusing observed variances and marginal distributions of r confirm ed that therewa s no tendency for slopes to cluster Figure 8.12). For carefully selectedarchipelag oes, it may be possible to interpret relative values of z Martin 1981).But the most sensible view is that slopes of species-area curves are simplyfitted constan ts, with little or no biological significance Con nor and M cCo y1979; Gilbert 1980; Abbo tt 1983).

Less attention has been given to the intercep t of the species-area relations hipGould 1979), although the statistical problems will be similar to those of slope

analyses. Nevertheless, if the slopes of two species-area curves are identical,the intercept represents the expected species richness after controlling fordifferences in area. For examp le, Abe le 1976) com pared species richness ofdecap od crustaceans inhabiting coral heads in co nstant and fluctuating environ-ments. Although there was a significant species-area relationship, the intercept


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228 hapter

was higher for coral heads in the fluctuating environment, indicating greaterlocal species richness. Note that a comparison of intercepts statistically re-moves th e effect of area from the com parison of specie s richness.

The initial appeal of the equilibrium theory motivated much research inbiogeography (Brown 1981 ), bu t the interpretation of species-area slopes hasbeen a largely unproductive avenue. There are some com mu nities that seem tofit the MacArthur and Wilson (1967) model (e.g., Rey 1981), but the criticaltests co m e from observations of turnover and popula tion extinction s on islands,not from statistical cu rve fitting. Like the H utchinsonian size ratio of 1.3 (seeChapter 6), the z value of 0.26 is anoth er of ecolo gy's magic numbers that hasnot withstood detailed scrutiny.Is Species Number Constant Through TimeAlthough the MacArthur and Wilson (1967) model describes a steady-statebalance between immigration and extinction, it does not predict a strict con-stancy in S through time, because immigration and extinction curves reflectunderlying probabilities of discrete events (Diamond and Gilpin 1980). Theintersection of the immigration and extinction curves yields the expectedspecies num ber w ith an associated variance.

But how mu ch variability is acceptable? In other words, how mu ch changeis expected in species number at equilibrium for the MacArthur and Wilson(1967) model? Keough and Butler (1983) noted that many ad hoc limits havebeen invoked in the literature; authors have claimed a species equilibrium fortemporal coefficients of variation (CV) between 5 and 75%. Using literaturedata and com puter simulations of different sam pling distribution s, Keough andButler (1983) suggested a rough empirical limit of approximately 10%. Co m-parison w ith any cutpoint is dependent on sam ple size, and Keough and Bu tler(1983) provided statistical tests for deciding wh ether the CV is greater o r lessthan som e hypothesized value. Applying the 10% rule to their ow n da ta onmarine epifaun a of mollusc shells, they rejected the null hypothesis-temporalfluctuations in S were too large to be considered in equilibrium. Much of thevariability in S was due to chance colonization of she lls by colonial asc idians,which were superior space competitors. Predation by monocanthid fishes re-moved these asc idians and greatly reduced the variability.

Even with such an empirical guide, documentation of equilibrium is tricky.Species number on real or virtual islands is always bounded between 0 and Pthe species pool size, so the fact that a mean and a variance can be calculatedfor a series of censu s data need not imply an underlying equ ilibrium (Bo ecklenand Nocedal 1991). Instead, an explicit null model for temporal change in


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species richness should be used. If a real comm unity is in equ ilibrium, temporalfluctuations in S should be substantially smaller than predicted by the nullmodel.

Simber loff 1983~)sed a Markov mo del of species colonization and extinc-tion to contrast with the M acArthur and W ilson 1967 ) equilibrium model. Foreach species k in the source pool, the Markov model assumes a constantprobability of successfu l imm igration during a given time period ik) and aconstant probability of e xtinction ek). Th e correspo nding probabilities of notimmigrating and not going extinct are 1 k) and 1 ek ), espectively. Theseprobabilities need not be equ ivalent for all species. If sp ecies immig rations andextinctions are independent of o ne another, an equilibrium will be reached at

This noninteractive Markov model has been derived many times, for bothisland biogeography m odels Bossert 1968; Simberloff 1 969; Gilpin and Dia-mond 1981) and analogo us single-species metap opulation models Gotelli1991). The M arkov m odel generates linear imm igration and extinction curves,in contrast to the concav e curves of the M acArthur and W ilson 1967 ) model.Both models predict an equilibrium determined by the balance between im-migration and extinction, and both models predict that species number willdec line if it is abo ve that equilibr ium .

However, the forces leading to this decline are somewhat different for thetwo m odels. In the Markov mo del, species richness declines above equilibrium ,because it is imp robable that such a large num ber of species will persist hroughtime. Extinctions will outnumber colonizations and S will decline. Demo-graphic factors are not invoked in these extinctions. In the MacArthur andWilson 1967:) mode l, an increase in S implies a decline in the popu lation sizeof each comp onent species, because of an assumed limit on summ ed popu lationdensities. With smaller population sizes, the probability of extinction increasesand species number declines. In the MacA rthur and Wilson 1967) mo del, theimmigration and extinction curves are more divergent than in the Markovmo del, so that species num ber w ill return mo re rapidly if it is displaced eitherabove or below equilibrium. The steeper the curves and the greater theirconcavity, the faster the return to equilibrium Figure 8.13; Diamond andGilpin 1980).

Thu s, in a regulated Mac Arthu r and Wilson 1967 ) equilibrium, variance orchange in S should be smaller than under the null hypothesis of the Markovmodel. Simberloff 1 9 8 3 ~ ) it the Markov model to bird census data from


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E ZB 2 F: 2 1 sa C BSPE IES

Figure 8.13. Effects of immigration 0 and extinction E) curves on frequency distribu-tion of species number S ) at equilibrium. The steeper and more concave the immigra-tion and extinction curves, the less variability in S at equilibrium. Reprinted bypermission of the publisher from Diamond, J. M., and M. E. Gilpin. 1980. Turnovernoise: contribution to variance in species number and prediction from immigrationand extinction curves. American Naturalist 115 :884 889 . Copyright O 1980 by TheUniversity of Chicago.

Skokholm Island and the Fam e Islands, and the forested plot of Eastern Wood(Figure 8.14). Because independent estimates of extinction and immigrationprobabilit ies were not available, Simberloff (1983~)stimated them from thesequential censu s data. Using the M arkov transition probabilities, Simberloff( 1 9 8 3 ~ ) enerated a null distribution by simulating each species trajectory,starting with the island composition observ ed in the initial census.

The null hypothesis was never rejected in the direction of the regulatedequilibrium, and observed m easures of variance in S were usually in the wrongtail of the distribution. Fo r the S kokh olm data, the variance w as significantlygreater than even that predicted by the M arkov mod el. Th is result is consisten twith W illiamson s 1981) finding that the immigration curve for these datashowed a nonsignificant increase w ith species richness. With the imm igrationand extinction curves both increasing with S fluctuations in species num ber


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/ Eastern Wood

1 2 3ear

Figure 8.14. Species trajectories for birds of Skokholm Island and Fame Islands andEastern Wood. Vertical lines indicate years in which more than one census was con-ducted. These trajectories could not usually be distinguished from those generated bya noninteractive Markovian model (see Figure 8.7). Reprinted with permission fromSimberloff,D. 1983. When is an island community in equilibrium? Science 220: 1275-1277. CopyrighiO 1983American Association for the Advancement of Science.

will be especially large. Simberloff ( 1 9 8 3 ~ )onclud ed there was little evidencefro m these analyses to suppo rt a mod el of regulated species equilibrium.

S i m b e r l o f f ~ 1 9 8 3 ~ ) nalysis was predicated on the id ea that the observedsequence of presences and absences provided a reasonable empirical estimateof extinction and immigration probabilities. Boecklen and Nocedal (1991)explored this problem with seven s pecies trajectories draw n from the literature.They assumed that the estimated transition probabilities were true and simu-lated 3 new presen ce-absen ce ma trices for each s et of trajectories. Transitionprobabilities were again estimated from each new matrix, and 10 00 additionalspecies trajectories were generated. Finally, the 3 estimates of cumulativeprobabilities w ere com pared to the probability value estima ted from th e origi-nal presence-absence matrix. If estimates of transition probabilities from theoriginal matrix were valid, they should hav e been eq uivalent to those that weresecondarily estimated from the new prese nce-abs ence matrices.

However, the original and derived probability estimates usually did notagree. Som etimes the observed probability values were too co nservative, andsometimes they were overly liberal; results varied unpredictably among datasets. This analysis also showed that coefficients of variation, even if testedstatistically by the Keough and Butler (1983) method, were unreliable indica-tors of equilibrium status. Boecklen and Nocedal (1991) concluded that al-


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232 hapter 8

though the Markov model was probably valid for testing equilibrium status,transition probabilities should not be estimated from the sam e data set to be tested.

reanalysis using m aximum likelihood estimates (Clark nd Rosenzweig 1994)would be informative, because the transition probabilities estimated by Simberloff( 1 9 8 3 ~ )nd by Boecklen and Nocedal(1991) may be biased in some cases.Does Species Richness Increase in Equal Sized Quadrats?An important prediction from Preston 's (1962) work has been relatively neglec tedin the species-area literature: in an equilibrium community, not only will totalspecies richness be greater on the mainland than on islands, but so will speciesrichness in equal sizedquadrats. This is because the m ainland supports many rarespecies from the tail of the log normal d istribution that would not occur on islands.A similar logic can be applied to a comparison of large and small islands. If theMacArthur and Wilson (1967) model is correct, there should be a significantcorrelation between S and island area for equal-sized quadrats sampled wit inislands.

Westman (1983) first tested this hypothesis in xeric shrublands of the Cali-fornia Channel Islands. Although there was a significant overall species-arearelationship, the number of plant species per quadrat showed no relationshipwith island area. Kelly et al. (1989) found only a weak positive correlationbetween island area and local richness of plants for islands in Lak e Mana pouri,New Zealand. Island ar ea accounted for no more than 17% of the variance inspecies numb er in equal-sized quad rats, whereas area accounted for 92% of thevariation in whole-island species richness (Quinn et al. 1987).

For anim al com mu nities, Steven s (1986 ) exam ined the species-area relation-ship for wood-boring insects and their host plants by sam pling insect comm u-nities at different sites within the geographic range of the host. Althoughspecies richness of insects was co rrelated with the size of the g eograph ic rangeof the host species (the me asurem ent of area ), richness within sites did notshow a significant host-area effect. All these studies point to the fact thatspecies were not uniformly distributed within an island. The results suggestthat total island area (or host geographic range size) did not ha ve a direct effecton local population size and hence on total species richness.

THE PASSIVE SAMPLING HYPOTHESISBiological processes such as local extinction, chronic disturbance , and habitatspecialization have provided competing ex planations for the species-area rela-


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tionship. But the correlation could also arise as purely a sampling phenomenon.The passive sampling hypothesis (Connor and McCoy 1979) envisions individ-uals as darts and islands as targets of different area. Continuing thisanalogy, different colors of darts represent the different species, and the dartsare tossed randomly at the array of targets. It follows that large islands willaccumulate more darts, and hence more species, than will small islands.

Arrhenius 1921) introduced this model and found good agreement betweenobserved and predicted species richness for plants in quadrats of different size.However, the passive sampling hypothesis was largely ignored in the species-area literature until Coleman (1981; Coleman et al. 1982) developed the theorymathematically.The passive sampling hypothesis has only two assumptions:

1. 'The probability that an individual or a species occurs on an islandis proportional to island area.

2. Islands sample individuals randomly and independently. In otherwords, inter- or intraspecific forces do not modify the probabilityof individual occurrence.

Given these assumptions, the passive sampling hypothesis predicts the ex-pected species richness for an island as

E ( s . ) = C ~ - --= k,

where a is the area of the jth island, T is the summed area of all islands, and n,is the abunclance of species i summed over all islands. The term inside thesummation sign is the probability that species i occurs on the island, given n,dart tosses at the target. When summed across all species, this gives theexpected species number.

Coleman (1981) also derived the variance of species richness and the ex-pected slope of the species-area curve, which could be compared to valuesderived from equilibrium theory or other hypotheses. However, Coleman's(1981) slope test may not always discriminate among different hypotheses(McGuinness 1984a). Because the expected slope is ultimately determined bythe species abundance distribution, a range of curves is possible. The extremesare a linear species-area relationship for an inequitable species abundancedistribution and a steep, monotonic curve for a perfectly equitable assemblage(Figure 8.15). Exponential or power function curves may lie between these twoextremes (McGuinness 1984a). These curves are identical in shape to those


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Species Area Relationships 235Io 10 area m

Figure 8.16. Observed and expected plant species richness legumes, milkweeds, andgoldenrods) for prairie remnants. The solid line is the expected value based on a passivesampling model adapted for presence-absence data. Reprinted from Simberloff,D., and N.Gotelli. 1984. Effects of insularisation on plant species richness in the prairie-forest eco-tone. Biological Conservation 29:27-46, p. 35. Copyright O 1984, with kind permissionfrom Elsevier Science Ltd, The Boulevard, Langford Lane, Kidlington OX5 GB, UK.

One disadvantage of the passive sampling hypothesis is that it requiresmeasurements of island population sizes. Because these data are difficult toobtain, there hav e been relatively few tests of the passive sa mp ling hypothesis.If abundance data are not available, an analogous test can e conducted withpresence-absence data. Observed species occurrences are reshuffled random lyamong islands, with probabilities of occurrence proportional to island areas.Simberloff and Gotelli 1984) used this me thod to predict plant species richnessin prairie and forest remnants. The observed and expected species richnessshowed reasonable agreement, although richness was somewhat higher thanexpected for very small patches and lower than expected for large patchesFigure 8.16).

When data are avai lable on the dis t r ibut ion of individuals , the passivesampl ing hypothesi s has proven useful as a base l ine for exam ining species-area curves. The hypothesis adequately explained over half of the species-area curves for sessi le organisms of rocky inter t idal boulders in Austral iaM cGuinness 1984b) . For breeding bi rds on i s lands in a Pennsylvania

reservoir , the passive sam pling hypothe sis provided a bet ter f i t to species-area data than did a po we r or expo nent ial funct ion Figure 8.17). t a largerspat ial scale, passive sampling character ized most species-area relat ion-ships for vascular p lants of the Appalachian Mounta ins and provided amethod for es t ima t ing the num ber of rare species to be foun d in a regionM iller and W ieger t 1989 ) .


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Figure 8.1 7. Fit of the exponential func-.:. tion, power function, and passive sam -

pling model to species-area data. The xaxis is the logarithm of island area, ex-pressed as a proportion of the total areaof the archipelago. Th ey axis is the log-arithm of island species number. Eachpoint is the observed number of breed-ing bird species on forest islands inPymatuning Lake for censu s data intwo consecutive years. The straight line

q 10 is the power function, th dashed curveI is the exponential function, and thesolid curve is the expectation from the

In other communit ies , however , the pass ive sampling model overes t imatesspecies r ichness . For example , Gote l l i e t a l. 1987) tes ted the m ode l for anamp hipod-m ollusc assem blage that colonized ar ti f ic ia l subst ra tes in the Gu lf ofMe xico. Obse rved sp ecies r ichness w as less than expected, and the devia t ionsbecam e m ore severe as co lon iza tion p roceeded , pe rhaps du e to c rowding in aspace-l imited habitat . Fo r natural roc k islands, Ryti 1984) a l so found tha t thespecies r ichness of perennia l p lants was less than predic ted by the pass ive

f passive sampling model. Exponential2 r and power functions were fit by stan-

rn 1979 dard linear regression. Note the supe-.... rior fit of the passive sampling modelto observed data. From Coleman et al.1982), with permission.


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tion probabilities may be problematic Boe cklen and Nocedal 1991; Clark andRosenzweig 1994). Critical tests of the M acArthur and Wilson 1967) equilib-rium mod el include evidence of population turn over Simberloff 1976a), mea-surement of imm igration and extinction rates a s a function of species richnessW illiamson 1981 ; Strong and Rey 1982 ,and do cum entation of a species-arearelationship within equal-s ized qua drats Kelly et al. 1989). Further studies ofthe species-area slope or the best-fitting transformation will not allow forcritical tests. Instead, researchers should concentrate on unique predictionsassociated with hypotheses for the species-area relationship Table 8.1).

null models chapter 8

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