Proc. Nat. Acad. Sci. USA Vol. 71, No. 5, pp. 21412145, May 1974 Niche Overlap ad Diffuse Competitio (desert lizards/resource partitioig/commuity structure/species diversity) ERIC R. PIANKA Departmet of Zoology, Uiversity of Texas at Austi, Austi, Texas 78712 Commuicated by Edward 0. Wilso, March 11, 1974 ABSTRACT Curret theory predicts a distict upper limit o the permissible degree of iche overlap; moreover, theory suggests that maximal tolerable overlap should be relatively isesitive to evirometal variability. Data preseted here demostrate that, withi the lizard subset of atural desert commuities, iche overlap decreases both with icreasig evirometal variability ad with icreasig umbers of lizard species. The latter two factors are themselves positively correlated. A partial correlatio aalysis is iterpreted as idicatig that the extet of tolerable iche overlap does ot ecessarily decrease due to evirometal variability, but rather that overlap is probably more closely related to the umber of potetial iterspecific competitors i a commuity, or what has bee termed "diffuse competitio." This result leds support to the "iche overlap hypothesis," which asserts that maximal tolerable overlap should vary iversely with the itesity of competitio. Moreover, this empirical discovery idicates that iche overlap theory could be profitably expaded to icorporate the umber of competig species. Although the average amout of overlap betwee pairs of species decreases with the itesity of diffuse competitio, the overall degree of competitive ihibitio tolerated by idividuals comprisig a average species could evertheless remai relatively costat, provided that extesive iche overlap with a few competitors is roughly equivalet to lower average overlap with a greater umber of competitors. NICHE OVERLAP THEORY The ways i which species withi ecological commuities partitio available resources amog themselves is a major determiat of the diversity of coexistig species. All else beig equal, a commuity with more resource sharig, or greater iche overlap, will clearly support more species tha oe with less iche overlap. I attempts to uderstad competitio ad determiats of species diversity, populatio biologists have reasoed that coexistig species must differ i their ecological requiremets by at least some miimal amout to avoid competitive exclusio. Such thikig has led to the related cocepts of "character displacemet" (1), "limitig similarity" (2), "species packig" (3, 4), ad "maximum tolerable iche overlap," which is simply the otio that there must be a upper limit o the permissible degree of iche overlap (58). May ad MacArthur (5) recetly developed a elegat aalytic model of iche overlap as a fuctio of evirometal variability. Their theory predicts a upper limit o the degree of tolerable overlap; moreover, the derivatio suggests that maximal permissible overlap should be relatively isesitive to both umber of species ad evirometal variability. The MayMacArthur iche overlap model assumes a equilibrium 2141 commuity i a fully saturated eviromet with all resources beig used fully; as such, variatio i the itesity of competitio is ot modelled (see also ext paragraph). The model assumes a oedimesioal resource spectrum, but May (7) recetly idicated that the argumet ca be expaded without qualitative chage to a multidimesioal iche space. I developmet of this theory, May ad Mac Arthur express the iverse of iche overlap as a ratio of the distace betwee the ceters of two "ultilizatio curves" (iche separatio) over the stadard deviatio i utilizatio (iche breadth), with the latter assumed to be costat ad idetical for all species. Their model thus somewhat cofouds iche overlap ad iche breadth. Estimates of overlap i resource utilizatio have ofte bee equated with the "competitio coefficiets" or "alphas" of the much overworked LotkaVolterra competitio equatios: i NiE dn1 in [ jnq'~ 1 1 dt Ki where i ad j subscript each of the differet species, Ni is the abudace of the ith species, ri is its maximal itrisic rate of icrease per capita, Ki is the "carryig capacity" of species i, ad aij represets the per capita competitive ihibitio of species j o the populatio growth rate of species i. Alphas are extremely difficult to estimate directly except by populatio removal experimets, ad ecologists have ofte equated estimates of overlap with competitio coefficiets (9). However, temptig though it may be, equatig overlap with competitio is a extremely dubious ad misleadig procedure (10, 11). Clearly iche overlap, i itself, eed ot ecessitate competitio; i fact, there may ofte be a iverse relatioship betwee overlap ad competitio. If resources are ot i short supply, two orgaisms ca share them without detrimet to oe aother. Thus, extesive iche overlap may actually be correlated with reduced competitio. Similarly, disjuct iches may ofte idicate avoidace of competitio i situatios where it could potetially be severe. Such reasoig led me to propose that maximal tolerable iche overlap should be lower i itesely competitive situatios tha i eviromets with lower demad/supply ratios; I termed this the "iche overlap hypothesis" (8). Diffuse competitio MacArthur (4) coied the term "diffuse competitio" to describe the total competitive effects of a umber of iterspecific competitors. To illustrate the cocept, cosider Eq.
2142 Zoology: Piaka 1. At equilibrium, all dni/dt must equal zero; that is Ni* = Ki E aijnj [2] ji'i where Ni* is the equilibrium abudace of species i. Eq. 2 must be true for all i at equilibrium. Note that the term, E aji Nj, icreases with the umber of competig species, joi, ad that the equilibrium abudace of species i, No*, decreases as oe sums over a greater umber of competitors. Further, ote that a little bit of competitive ihibitio by a lot of other species (diffuse competitio) ca be equivalet to strog competitive ihibitio by fewer competig species. DESERT LIZARD COMMUNITIES A series of 28 study areas at similar latitudes o three cotiets support from 4 to 40 sympatric species of desert lizards (1214). Estimated species desities ad lizard species diversities for these sites have bee give elsewhere (14). My assistats ad I recorded data o microhabitat, time of activity, ad stomach cotets of over 15,000 lizards of some 91 species o these desert study areas, which I use for the followig aalysis of iche overlap. Results preseted rather briefly here are documeted more fully elsewhere (14). Evirometal variability I deserts, water is a master limitig factor, ad logterm mea aual precipitatio is very strogly correlated with average aual productivity, Moreover, stadard deviatio i aual precipitatio ca be cosidered a idicator of evirometal variability sice yeartoyear variatio i aual precipitatio should geerate temporal variability i food availability. I estimated both the logterm mea ad stadard deviatio i aual precipitatio from earby weather statios for most study areas. Both precipitatio statistics are sigificatly correlated with lizard species desities ad diversities (rs > 0.41, Ps < 0.05 to 0.001). Niche dimesioality Although some pairs of sympatric competitors avoid competitio primarily through differeces i the use of a sigle resource gradiet or iche dimesio, it is far more prevalet for coexistig species to differ i their use of two or more iche dimesios simultaeously. Pairs with high overlap alog oe dimesio ofte overlap relatively little alog aother, reducig overall effective iche overlap [see figure 6.7, page 198 i Piaka (11) ad/or figure 1 i May (16)1. Like most aimals, desert lizards subdivide resources i three major ways: they differ i what they eat, where they forage, ad whe they are active. Ecological differeces i each of these three iche dimesios should reduce competitio ad thus facilitate coexistece of a variety of species. It is difficult or impossible to evaluate the degree of iterdepedece of these three iche dimesios for most lizard species because the aimals move ad are active over a period of time. However, the degree to which foods eate deped upo microhabitat ca be assessed i some relatively sedetary subterraea skiks (15); i these lizards, diet ad microhabitat appear to be largely idepedet. Clear iteractios amog iche dimesios are apparet i other cases (13, 14). The vast majority of iterspecific pairs of sympatric lizard species have substatial iche separatio alog oe or more of Proc. Nat. Acad. Sci. USA 71 (1974) these three iche dimesios (trophic, spatial, ad/or temporal), makig it uecessary to subdivide the three basic dimesios ay further to aalyze resource partitioig i these lizard commuities. Niche dimesioality has aother importat aspect: the umber of potetial eighbors i iche space icreases more or less geometrically with the umber of iche dimesios actually subdivided (4, 14). Hece a greater umber of effective iche dimesios provides a greater potetial for diffuse competitio. Niche overlap Overlap has bee quatified i umerous ways (2, 9, 10, 13). The particular overlap idex used is somewhat arbitrary sice similar qualitative results are obtaied with a wide variety of idices. Here I use the followig modificatio (13) of the equatio first proposed by MacArthur ad Levis (2) ad Levis (12) for estimatig competitio coefficiets, or alphas, from field data o resource utilizatio: where pij ad pf jk kj Ipj2 Pik2 represet the proportios of the ith resource used by the jth ad kth species. May (16) discusses a mathematical ratioale for the coveiece of this symmetric measure over the origial asymmetric form. I do ot cosider values obtaied from this equatio "competitio coefficiets," but rather merely measures of iche overlap (see above ad refs. 10 ad 11 for further discussio of the distictio betwee overlap ad competitio). Thus calculated, the average extet of overlap alog various dimesios differs amog the three cotietal desertlizard systems (Table 1). For example, overlap i microhabitat is high i North America where may lizards frequet the ope spaces betwee plats, whereas dietary overlap is high i the Kalahari desert of souther Africa where termites domiate the diets of may species of lizards (13). Overlap is relatively low alog all three iche dimesios i the most diverse lizard commuities of Australia (13, 14). Estimatig overall iche overlap alog three dimesios is difficult ad ca be quite treacherous (16). Ideally, a proper multidimesioal aalysis of resource utilizatio ad iche separatio alog more tha a sigle iche dimesio should proceed through estimatio of the simultaeous proportioal utilizatio of all resources alog each separate iche dimesio. Thus, oe would like to work with the proportio of prey type i captured i microhabitat j by species k, or the true multidimesioal pijks. However, i practice it is extremely difficult or eve impossible to obtai such multidimesioal utilizatio data, because aimals usually itegrate over both space ad time (stomachs cotai prey captured over a period of time ad i a variety of microhabitats). Some progress toward uderstadig overall iche overlap alog several dimesios ca, however, be made usig oly the proportioal utilizatios alog each of the compoet iche dimesios, as follows (forgreater detail, see ref. 16). Provided that iche dimesios are truly idepedet (orthogoal), with for example ay give prey item beig equally likely to be captured i ay microhabitat, overall
Proc. Nat. Acad. Sci. USA 71 (1974) Niche Overlap ad Diffuse Competitio 2143 0.7 0.6 w 0.5 0 :r0.4 0.3 0.2 * North America Kalahari A Australia 0 A r=0.69 P< 0.001 * A 'IE A* A A 0.7 _ L 0.6 North America U Kala haria ~~Australia 0 11~~~~~~~~~ C5 r=r0.73 w 0.5_ *U A P < 0.001 > 0.5 w 0.4_ Em z < 0.3 A AA ~AAA 2 ~ ~~~~0 ~ 0 2 ~~~~ *.0 0.2 _ 0.1 ~ *0 S,. 5 10 15 20 5TANDARD DEVIATION IN ANNUAL PRECIPITATION FIG. 1. Average overall summatio iche overlap plotted agaist the stadard deviatio i aual precipitatio. Cotiets coded by shape, as idicated. Although oe of the correlatios withi cotietal desert systems is sigificat, the correlatio coefficiet for all areas is highly sigificat statistically. However, whe the umber of lizard species o various areas is held costat by partial correlatio, this correlatio disappears. Compare with Fig. 2. multidimesioal utilizatio is simply the product of the separate uidimesioal utilizatios (16); that is, Pijk = Pik X Pjke I this case, overlaps alog compoet iche dimesios ca simply be multiplied to estimate overall multi 1 L Il 5 10 15 20 25 30 35 ESTIMATED NUMBER OF UZARD SPECIES 40 FIG. 2. Average overall summatio iche overlap plotted agaist the estimated umber of lizard species. Cotiets coded by shape, as idicated. Similar iverse correlatios exist with overall multiplicative overlap values ad with three differet estimates of maximal tolerable iche overlap (see text). dimesioal iche overlap (16). However, should iche dimesios be etirely depedet upo oe aother (with for example, each prey type occurrig i oly a particular microhabitat), there is actually oly a sigle resource dimesio. Uder such complete depedecy, true "multidimesioal" overlap is best estimated by the arithmetic mea of the overlaps alog compoet dimesios; such "summatio over TABLE 1. Estimates of the umber of lizard species ad average iche overlap values for 28 desert study areas o three cotiets Estimates of average overall iche overlap Average icheoverlap Multiplicative S Largest teth Summatio species Food Microhabitat Time (All) (Nozero) (All) (Multiplicative) (Summatio) No. of lizard North America 4 0.49 0.80 0.58 0.20.0.20 0.63 0.41 0.76 5 0.75 0.78 0.53 0.33 0.36 0.69 0.73 0.90 5 0.52 0.92 0.49 0.25 0.36 0.64 0.71 0.90 6 0.55 0.55 0.47 0.22 0.37 0.52 0.61 0.86 6 0.34 0.55 0.20 0.12 0.27 0.43 0.57 0.75 7 0.39 0.42 0.31 0.11 0.39 0.37 0.52 0.82 8 0.56 0.31 0.32 0.10 0.24 0.40 0.37 0.74 9 0.28 0.52 0.58 0.11 0.23 0.46 0.50 0.82 9 0.38 0.32 0.39 0.06 0.18 0.36 0.37 0.70 10 0.37 0.33 0.50 0.08 0.25 0.40 0.20 0.76 Kalahari 11 0.92 0.35 0.28 0.18 0.41 0.52 0.69 0.89 13 0.36 0.39 0.30 0.08 0.26 0.35 0.50 0.80 13 0.56 0.47 0.34 0.13 0.36 0.46 0.61 0.85 14 0.56 0.21 0.15 0.04 0.27 0.31 0.19 0.61 15 0.45 0.23 0.21 0.04 0.22 0.30 0.31 0.70 15 0.56 0.25 0.24 0.06 0.23 0.35 0.44 0.76 16 0.72 0.22 0.23 0.09 0.35 0.39 0.64 0.80 16 0.44 0.22 0.24 0.05 0.22 0.30 0.34 0.73 16 0.71 0.28 0.26 0.11 0.36 0.42 0.69 0.88 18 0.51 0.26 0.27 0.07 0.24 0.35 0.44 0.77 Australia 18 0.23 0.16 0.18 0.01 0.14 0.19 0.08 0.59 20 0.18 0.36 0.13 0.01 0.02 0.22 0.10 0.54 28 0.25 0.32 0.16 0.03 0.21 0.24 0.23 0.65 29 0.27 0.30 0.27 0.04 0.23 0.28 0.29 0.69 30 0.23 0.24 0.19 0.02 0.19 0.22 0.14 0.59 30 0.37 0.24 0.27 0.03 0.18 0.28 0.26 0.66 31 0.19 0.28 0.18 0.02 0.16 0.22 0.14 0.60 40 0.23 0.25 0.22 0.02 0.15 0.24 0.19 0.61
2144 Zoology: Piaka 10 r a 0.86 9 _ P40.001 I 87 AdA AA @ i6 ^AAL A AAAA 0O_ 4 0 %0 5 10 15 20 25 30 35 ESTIMATED NUMBER OF LIZARD SPECIES 40 FIG. 3. Average total iche overlap (summatio) plotted agaist the estimated umber of lizard species, to show that total iche overlap icreases with lizard species desity eve though overlap betwee average pairs of species decreases (compare with Fig. 2). Cotiets coded by shape as i previous figures. laps" costitute upper bouds o the true multidimesioal overlap (16). Sice real iche dimesios are presumably seldom, if ever, either perfectly idepedet or perfectly depedet, either the multiplicatio or the summatio techique is etirely satisfactory. Summatio overlaps geerally overestimate true iche overlap, whereas multiplicative overall overlaps ofte uderestimate true multidimesioal iche overlap (16). I a attempt to overcome these very cosiderable difficulties, I computed estimates of overall overlap by both multiplicatio ad summatio of the overlaps alog the three compoet iche dimesios (Table 1). Whe overlaps alog the three dimesios are multiplied, the vast majority of iterspecific pairs overlap very little or ot at all (13, 14). The possible umber of such ooverlappig pairs icreases markedly with the size of overall iche space, which is greater i more diverse saurofauas (13, 14). Overlap betwee those pairs with some overlap is of greatest iterest as it should reflect limitig similarity ad/or maximal tolerable overlap. Average overlap values for each iche dimesio i the various desert systems are listed i Table 1, alog with meas of all multiplicative overlaps ad all summatio overlaps (recall that the latter represet upper bouds o the true multidimesioal overlap). Meas of all ozero multiplicative overlap pairs ad the averages of the largest teth of all multiplicative ad summatio overlaps are also give, as these are more likely to reflect maximal tolerable overlap. All five methods of estimatig overall overlap produce strogly correlated values (rs = 0.67 to 0.97, Ps < 0.01 to 0.001). Estimates of overall iche overlap are strogly correlated with both the stadard deviatio i precipitatio (Fig. 1) ad with the umber of lizard species (Fig. 2). At first glace, Fig. 1 seems somewhat at odds with May ad MacArthur's predictio that maximal overlap should be isesitive to evirometal variability. However, the overlap values used here are ot etirely appropriate for testig the MayMacArthur theory, sice this model is expressed i terms of the ratio of iche separatio over iche breadth, effectively the iverse of iche overlap scaled by iche breadth. To approximate coditios of their model more closely, I estimated iche separatio as oe mius overlap for all iterspecific pairs i each cotietal desertlizard system, ad expressed these values as ratios of separatio over stadardized iche breadths (Table TABLE 2. Proc. Nat. Acad. Sci. USA 71 (1974) Meas ad 96% cofidece limits o ratios of iche separatio over iche breadth Niche dimesio North America Kalahari Australia Food 3.73(2.874.59) 2.51(2.212.81) 5.18(5.05.36) Microhabitat 5.79(4.836.74) 4.23(3.854.61) 4.60(4.484.72) Time 2.78(2.03.56) 5.08(4.485.68) 5.11(4.935.29) Overall 0.50(0.380.62) 1. 54(1.161.92) 1.03(1.01.06) 2). Such a aalysis modified results preseted i Figs. 1 ad 2 oly slightly. Distict differeces amog the three cotiets are still apparet. Moreover, a areabyarea aalysis also shows that iche separatio over iche breadth ratios ted to icrease with lizard species desity. Clearly iche separatio over iche breadth ratios are ot costat betwee the three desert systems. I used partial correlatio aalysis i a attempt to iterpret factors ifluecig iche overlap. Whe the effects of lizard species desity are held costat by partial correlatio, average overall summatio overlap ad mea ozero multiplicative overlap do ot remai sigificatly correlated with the stadard deviatio i precipitatio. However, the iverse correlatios betwee lizard species desity ad both measures of overall iche overlap remai sigificat at the 0.01 level whe stadard deviatio i precipitatio is held costat by partial correlatio. These results suggest that, as predicted, the extet of tolerable iche overlap is ot ecessarily a fuctio of the degree of evirometal variability, but rather that maximal overlap is more closely related to the umber of competig species ad the itesity of diffuse competitio. Evidetly, stroger diffuse competitio requires greater average iche separatio amog coexistig lizard species. Low overlap with lots of competitors may be similar to high overlap with fewer iterspecific competitors. Rather tha remaiig costat, iche overlap seems to be adjusted to the umber of competig species, perhaps resultig i a relatively costat level of iterspecific competitive ihibitio for a average species eve i commuities that differ widely i diversity. A first hypothesis might be that total overlap with sympatric species remais costat; Fig. 3 shows that total overlap actually icreases with lizard species desity, eve though the average amout of overlap betwee pairs decreases. I coclusio, empirical results preseted here support the iche overlap hypothesis, which predicts that maximal tolerable iche overlap should decrease with icreasig itesity of competitio. Moreover, these data idicate that iche overlap theory eeds to be modified to icorporate more fully the pheomeo of diffuse competitio. 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