W 1 i I W W W I l W ! WW ! ) fifiéWWW A WWIWWWWI 31293 01074 5312 ‘ LIBRARY Michigan Sun University . This is to certify that the thesis entitled ON THE EVALUATION OF RESOURCE USE AND COMMUNITY STRUCTURE presented by Larry Bryant Crowder has been accepted towards fulfillment of the requirements for Ph . D. degree in Zoology WWW William E. Cooper Major professor Date February 24, 1978 0-7639 ON THE EVALUATION OF RESOURCE USE AND COMMUNITY STRUCTURE By Larry Bryant Crowder A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Zoology 1978 ABSTRACT ON THE EVALUATION OF RESOURCE USE AND COMMUNITY STRUCTURE By Larry Bryant Crowder The resource use patterns of individual species and the partition- ing of resources among the species in a community are important considerations in community ecology. Most recent resource partitioning studies have employed niche theory in the quantification of overlaps in resource use among two or more species. A potential problem in the use of these point estimates for niche overlaps is that there is no statistical assurance of their reliability. The measurement of niche overlap is less popular than in the past; assumptions of the models are implicated as well as problems interpreting the calculated overlap values. Our inability to accurately measure overlaps has undoubtedly aggravated interpretation problems and could explain in part the increasing abandonment of niche overlaps. In this thesis, I develop an interval estimate of niche overlap which allows the estimation of sample sizes necessary to accurately measure niche overlap. Samples of up to 105 per species are necessary to measure niche overlap accurately to the second digit right of the decimal. Confidence intervals are calculated for a case study on limiting similarity. Manipulative experimentation provides an appealing alternative to simple observation and overlap estimation based on both logical and statistical grounds. Patterns of resource partitioning have seemed so similar in certain communities, that it has prompted many authors to ask if there Larry Bryant Crowder is an organized pattern in the way communities are assembled. Of course, the only way to uncover presumed consistencies is to examine communities comparatively. Community comparisons are often made between communities with entirely different species assemblages which exist under similar conditions. If it can be shown that structuring forces exist which are powerful enough to force historically and phylogenetically distinct communities to converge in structure, we may be well on our way to establishing any "assembly rules" for community structure which may exist. A neutral model analysis of convergence in resource use patterns provides an alternative hypothesis for two extant hypotheses on convergence. For a case study on lizard community convergence, the model reveals that one of these convergence hypotheses is logically faulty and the data cannot support the other hypothesis. Interval estimation and neutral modeling are powerful tools which can be applied to a wide class of problems in ecology. Both approaches can aid in experimental design by providing for rigorous testing of alternative hypotheses. ACKNOWLEDGMENTS I thank first William E. Cooper, my major professor, who provided an exciting and stimulating environment for the pursuit of this and other work. I also thank my committee members, Donald L. Beaver, Earl E. Werner and Erik D. Goodman for their suggestions and advice throughout my graduate career. Richard Hill, Jack King, Philip Crowley and Hal Caswell provided valuable insights at various junctures. I gratefully acknowledge financial support from NSF-RANN Grant GI-ZO to Herman E. Koenig and William E. Cooper, from EPA R803859010 to Erik D. Goodman and from the Department of Zoology. I am also grateful for the opportunity to collaborate with William E. Cooper on NSF-DEB 77-04818. My wife Judy provided encouragement, support and much love throughout this study; for this I am forever grateful. This thesis is dedicated to the loving memory of Earl M. Crowder and Billie V. Morris. ii TABLE OF CONTENTS LIST OF TABLES . . . . . . . . . . . . . . LIST OF FIGURES. . . . . . . . . . . . . . . . INTRODUCTION . . . . . . . . . . . . . . . . . Resource use and community structure. Convergence of community structure. The evaluation of hypotheses. . . . . SAMPLE SIZE AND CONFIDENCE INTERVAL ESTIMATES FOR NICHE OVERLAP, a. . . . . . . . . . . . . Niche overlap: measurement and interpretation. . Relation of a to the subdivision of a single resource axis. . . . . . . . . . Sample size and confidence intervals for a(d) A confidence interval estimate for o(d/w) Alternatives. . . . . . . . . . . . . ECOLOGICAL CONVERGENCE OF COMMUNITY STRUCTURE: MODEL ANALYSIS. . . . . . . . . . . . . . Convergence and community structure . A neutral model for resource use . . . Within-continent comparisons . . . Between-continent comparisons . . . . . . Discussion . . . . . . . . . . . . . . . iii A PAGE vi 10 13 21 26 26 29 31 37 42 iv TABLE OF CONTENTS-~Continued PAGE DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Interval estimation of ecological parameters. . . . . . . . 44 Neutral models as null hypotheses . . . . . . . . . . . . . 45 Recommendations for the evaluation of resource use, community structure and convergence. . . . . . . . . . 47 LIST OF REFERENCES . . . . . . . . . . . . . . . . . . . . . . . 50 TABLE LIST OF TABLES PAGE Point estimate and 3_95% confidence interval for d/w based on adjacent species pairs from Terborgh's antbird data. . . 24 Community matrix for Terborgh's antbirds. Cells contain point estimate for a(d/w) bounded by the 3_95% confidence interval for a . . . . . . . . . . . . . . . . . . . . . . 24 LIST OF FIGURES FIGURE PAGE 1. Resource use curves of two species along a resource axis a. d is the distance between means u and u , and o is the standard deviation common to both curves. . . . . . . . . . . 12 Confidence intervals for various values of d/o vs. sample size from each species. Solid circles represent 95% confidence intervals for a(d) and hollow circles represent 3_9S% confidence for a(d/w) . . . . . . . . . . . . . . . . . 15 Sample sizes required to distinguish particular a values from values which are larger . . . . . . . . . . . . . . . . 17 Sample size required to distinguish particular a values from values which are smaller . . . . . . . . . . . . . . . . 19 Foraging height relationships among the antbirds of genus (Myrmotherula. Thickened bars indicate one standard deviation and narrow bars show the entire range of observations. The number of observations for each species is given over the appropriate bar. (After MacArthur 1972, provided by J. Terborgh). . . . . . . . . . . . . . . . . . . 23 Between and within continent comparisons of resource use in California and Chile. Region maps include estimated frequencies of the four microhabitat types. . . . . . . . . . 28 Within-continent comparisons. Chapparral species pairs. The mean and 2 SD from 10 runs of the neutral models are given for the comparison of each Chapparral species with its "analogue” and with the five montane species from the same continent. Species pairs and numbers of observations for each run are given with California species on the left of each pair. Pairs (after Fuentes 1976): A - Cnemidophorus tigris (216) & Callopistes maculatus (17); B - Uta stansburiana (486) & Liolaemus lemniscatus (79); C - Sceloporus orcutti (111) & Liolaemus monticola (37); D - Sceloporus occidentalis (183) & Liolaemus fuscus (18); E - Sceloporus occidentalis (99) & Liolaemus tenuis (l4) . . . . . . . . . . . . . . . . . . . . 33 Within-continent comparisons. Montane species pairs. Comparisons similar to Figure 7. Pairs (after Fuentes 1976): A - Gerrhonotus multicarinatus (2) & Urostrophus troquatus (1); B - Eumeces skiltonianus (16) & Liolaemus schroderi (23); vi vii LIST OF FIGURES-~Continued 8. 10. (continued) C - Uta stanburiana (104) & Liolaemus nigroviridus (46); D -Sceloporus graciosus (64) & Liolaemus nigroviridus (61); Sceloporus occidentalis (44) & Liolaemus tenuis (22) . . . . . . . . . . . . . . . . 36 Between-continent comparisons. Chapparral species pairs. Mean and 2 SD are given from the neutral model for similarity of species pairs. Triangles are data from Fuentes (1976). Species pairs are those given in Figure 7. . . . . . . . . . 39 Between-continent comparisons. Montane species pairs. Mean ans 2 SD are given from the neutral model for similarity of species pairs. Triangles are data from Fuentes (1976). Species pairs are those given in Figure 8. . . . . . . . . . 41 INTRODUCTION Resource use and community structure How organisms find, obtain and use resources has been a major question since man first examined the natural world around him. Naturalists have provided autecological information on diet, habitat and the use of resources for many species. Early studies often examined the habits of single species and how they are constrained by physical factors. Morphological variates were often related to the types of foods eaten or habitats occupied. Grinnell (1904,1917) was among the first of these naturalists to extend the study of single species to the problems of species interactions and resource partition- ing. He is credited with originating the niche concept as well as anticipating the competitive exclusion principle (Whittaker and Levin 1975). The study of species interactions (e.g., competition) places a high priority on understanding resource use patterns within communities of organisms. Physical factors such as temperature or humidity may constrain a species' dynamics, but they are not resources over which two species can compete. Ecologists have employed the naturalist's approach to morphological variates, habitat use and foraging patterns in order to establish how various species interact in the exploitation of resources. While much of modern ecology is based on competition as the major mechanism in the partitioning of limited resources, other mechanisms clearly influence resource use. Species interactions such as predation, parasitism and various symbiotic or coevolutionary interactions may have profound effects on resource use patterns. Another often overlooked effect on resource use patterns in communities is that of resource availability--an animal cannot 2§g_a resource which cannot be found or obtained. That a species co-occurs with a resource which seems to be obtainable is not evidence for the species use of that resource. Animals traveling through a particular habitat may not actually use any resources there (Schroder and Rosenzweig 1975). Similarly, prey behavior may prevent a predator from eating co-occuring prey of acceptable types and sizes (Charnov, Orians and Hyatt 1976). In assessing resource use, ecologists commonly examine guts or observe animals regularly occupying certain habitats. The concurrent monitoring of resource availability would allow comparisons of use to availability as well as guaranteeing that when competition is claimed, resources are indeed limiting. Presumably, increased understanding of the differences in morphology and resource use among closely related species would aid our understanding of species diversity within whole communities. The examination of species interactions and resource partitioning has become a basis for much of community ecology. As Schoener (1974a) has pointed out, since Hutchinson (1959) first asked "Why are there so many kinds of animals?" resource partitioning studies have grown exponentially at a rate four times that of typical scientific works. Most recent resource use studies have been couched in terms of the niche hypervolume concept of Hutchinson (1957). The way in which niche space is subdivided by the species in a community may be referred to as community structure. Patterns of resource subdivision have seemed so similar in certain communities, that it has prompted many authors to ask if there is structural consistency to these patterns. Diamond (1975) went so far as to propose that there exist "assembly rules" for community structure-— that there is an organized pattern in the way communities are assembled. Presumably, all one needs do is examine many communities, uncover consistencies in resource use patterns, and suggest hypothetical assembly rules which are then subjected to test. Of course, the only way to uncover presumed consistencies in resource use patterns is to examine communities comparatively. This may be done by comparing communities composed of the same species at different points in space or time and see if, under similar conditions, resources are partitioned in similar ways. Community comparisons are also employed with entirely different species assemblages which exist under similar conditions. The question becomes "whether very similar physical environments, acting on phylo- genetically dissimilar organisms in different parts of the world, will produce structurally and functionally similar systems" (Di Castri and Mooney 1973). If it can be shown that structuring forces exist which are powerful enough to force historically and phylogenetically distinct communities to converge in structure, we may be well on our way to uncovering any "assembly rules" which may exist. Convergence of community structure The question is do community properties converge? In particular, does community structure converge? Ecologists have recently begun to examine the possibility that community structure may converge under a given set of environmental conditions (Cody l968,l974,1975, Recher 1969, Pianka 1973,1975, Karr and James 1975, Sage 1973, Fuentes 1976). In its simplest form, convergence may occur in numbers of species in communities in similar environments. Recher (1969) showed that the number of species in Australian bird communities exactly parallels that in American bird communities in comparable habitats. However, many avian niches appear to be fundamentally different on the two continents (Pianka 1974). Cody (1968,1974) has reviewed similar patterns of species diversity for grassland and forest bird communities, but parallels are not exact. Similarity in resource partitioning was noted in grassland birds by Cody (1968). Data on vertical and horizontal habitat distribution, morphology and foraging behavior of grassland bird communities from Chile and North America implicated some ecological equivalents, but there was no isomorphic mapping of species analogues. Recently (Cody 1974), the approach was extended to a more complex pair of bird communities in shrubby and woodland areas of California and Chile. Some species matching was possible, but no recent attempts by Cody to apply this analysis has shown greater similarities than in the grassland bird communities. Pianka (1973,1975) has compared desert lizard communities from North America, Africa and Australia and has concluded that differences more than outweigh similarities in community structure. Fuentes (1976) employed a relative criterion for convergence of community structure. His hypothesis of convergence states that community structure should be more similar with respect to habitat, food and time of activity in lizards in similar habitat sites between continents than in nearby communities on the same altitudinal transect. The relative similarity approach was justified on the basis of allowing for possible historical or phylogenetic constraints which are likely to prevent close convergence. If the hypothesis can be confirmed, the selective effects of environmental similarity can be taken to be more important than taxonomic or historical constraints. The evaluation of hypotheses Given the complex and multiple hypotheses relating resource use patterns and community structure, there is a distinct need to apply careful scientific method. During the early stages of the development of a theory or paradigm (Kuhn 1970) scientists seem to favor attempts to verify or confirm that natural patterns fit (in one way or the other) the predictions of the theory (Kuhn 1970). Popper (1963), however, argues that a theory can be considered "corroborated" only if it has withstood repeated and severe tests of its predictions. This "falsifi- cationist" approach to science considers that theories can only be accepted after stringent testing. In reality, this tack is seldom taken unless the investigators are already aware of some limitations in the theory (Kuhn 1970). That science best proceeds by the elimination of competing hypotheses has been argued thoroughly elsewhere (Popper 1959,1963, Platt 1964). Platt (1964) summarized a method he refers to as strong inference. The method requires 1) Devising alternative hypotheses, 2) Devising one or more "crucial experiments," with alternative possible outsomes, each of which will, as nearly as possible, exclude one or more of the hypotheses, 3) Carrying out the experiment so as to get a clean result, 4) Iterating the procedure. In this work, I interpret some recent work in resource use patterns and community structure in relation to Platt's method. In addition to creating alternative hypotheses and devising the "crucial" experiment, Platt emphasizes that experiments must be designed and carried out so as to get a clean result. Thus, experimental results must eliminate or support alternative hypotheses in a statistically significant way. Resource use studies have commonly included a measure of overlap in the use of resources by two or more species. In its simplest form, niche overlap is calculated on a single niche dimension such as food size or vertical habitat. Numerous hypotheses relating resource use patterns and community structure have employed point estimates of niche overlap, but none have developed an interval estimate for niche overlap. As I show (in chapter 2) for a particular measure of niche overlap, interval estimation can aid considerably in the design of a "crucial" experiment and the production of a clean result by allowing estimation of proper sample sizes for the resolution of alternative hypotheses. I employ an example from the theory of limiting similarity as a case study to demonstrate the approach. Of course, the generation of alternative hypotheses is also a non- trivial task. A classic alternative hypothesis is the null hypothesis-- for which, in complex situations, a neutral model (Caswell 1976) is an appropriate substitute. Neutral models have provided many insights for biologists from population genetics (Kimura and Ohta 1971) to paleo— biology (Raup et a1 1973). Caswell (1976,1977) provides a summary of some extant biological neutral models. In chapter 3, I develop a neutral model for resource use which provides an alternative hypothesis for two extant hypotheses on community convergence. Finally, I discuss the value of interval estimation and neutral modeling in experimental design. Interval estimates of ecological indices are necessary to determine the validity of a particular hypothesis test and to estimate adequate sample sizes. Neutral models provide alternative hypotheses as well as providing a measure of severity for hypothesis testing. As Caswell (1977) has noted, if a particular pattern is generated by both the theory and a neutral model, then the tests of the theory based on that pattern have absolutely no severity or power. Interval estimation and neutral models are general- ized tools; this thesis demonstrates their applicability to some current theory in community ecology and underscores their usefulness to ecologists. SAMPLE SIZE AND CONFIDENCE INTERVAL ESTIMATES FOR NICHE OVERLAP, a. Niche overlap; measurement and interpretation Recently, ecological theory and field work have paid increasing attention to the measurement and interpretation of niche overlaps (a) in an effort to understand the processes which have produced them. Estimates of niche overlap have been calculated in several ways and are often referred to as competition coefficients (aij) even though overlap does not necessarily imply competition (Colwell and Futuyma 1971). Niche overlap measures on single resource axes have been combined in numerous ways to estimate the overlap in resource use for n dimensions. Cody (1974) has calculated n dimensional overlaps by taking the product of single axis overlaps (product a) and by taking a simple average (summation a). But May (1975) has argued that, in general, there is no substitute for directly measuring the species' full multidimensional overlaps. Niche overlap estimates for all pairwise interactions in a community have been combined into a matrix of coefficients: the community matrix. Stability properties of this matrix have been explored thoroughly (Levins 1968, May 1973a, VanderMeer 1970), as have the relationships between overall competition coefficients and the underlying models of resource use (MacArthur 1969,1970,1972). Limiting similarity and community invasibility have also been examined in terms of niche overlap estimates (MacArthur and Levins 1967, MacArthur 1969, 1971,1972, May and MacArthur 1972, May 1973b, Roughgarden 1974, Abrams 1975). All of these arguments are dependent for their resolution on reliable estimates for a. This chapter examines the overlap estimate of MacArthur (1972), which assumes normal resource use curves. This assumption allows the use of parametric statistics to estimate a confidence interval for d. Then the range of reliability for overlap estimates over different sample sizes is explored with and without restrictive assumptions about equality of variances. Sample sizes are estimated for hypothesis testing and confidence intervals are calculated for a case study on limiting similarity. Interval estimates of niche overlaps are necessary to provide valid test of hypotheses involving overlaps. Relation of a to the subdivisions of a single resource axis MacArthur and Levins' (1967) original estimate of niche overlap assumes a community of m species competing for an array of resources which may be subdivided into n categories. If the utilization function pia (i = 1,2...,m; a = 1,2,...,n) is assumed to measure the relative utilization of the ath resource by the ith species, the two species interaction coefficient is / pm (1) Since the utilization functions pia are difficult to measure directly, resources are often subdivided into discrete categories and the percentage of time (or diet) spent in each category by the animal describes the utilization function. Weighting terms may be added for resource turnover rates and other effects (MacArthur 1972). Schoener (1974b) has thoroughly discussed the difficulties with estimating a in 10 the field. But no matter how difficult it is to estimate a's from field data or how difficult estimates may be to interpret, an investi- gator who chooses to calculate a must know how reliable his estimates are. MacArthur (1972) has derived an expression for a as a function of the distance between two utilization means u and uz, which assumes 1 normally distributed utilization functions (Figure 1). For equal variances (012 = 022 r 02), MacArthur (1972) has shown that 2 2 -d /4o (2) o(d) = e When the variances are assumed homogeneous but unknown, both d and 0 must be estimated from the data. In this case, a is a function of the ratio of d to w (the o estimator). 2 a(d/w) = e_l/4(d/w) (3) Sample size and confidence intervals for a(d) If the variances of the resource use curves are assumed equal, the confidence interval for a is simply functionally related to the confidence interval for d. Confidence intervals for d may be estimated using t statistics (Sokal and Rolhf 1969). A confidence interval for the difference of two means (d = u - ul) from normal populations with 2 common variance (wz) of unknown value may be estimated from a t- distribution (Sokal and Rohlf 1969). For (1-y) 100% confidence with sample sizes of n1 and n2 the estimator is (Y-Y)it S 1 2 (4) ll .w0>H§U SUOQ OH COEEOU COHUNH>M~u pumpcmum ecu ma 0 mam .N H mem moudomou m wcoam mmfiooam o3u mo mm>uzo mm: mousomom : mum a memos cow3umn moamumfiw mcu mg m .m .H mudwwm 12 G mumnommm N: 13 where S is the pooled standard deviation 2 2 (n1 - l)S1 + (n2 - 1)S2 n1 + n2 - 2 (5) For simplicity, I assume 0 = 02 = o = l and estimate 95% confidence 1 intervals for a(d) for various combinations of d/o (Figure 2). Even at sample sizes of 1000 from each species, the confidence intervals are reasonably large, especially in the midrange of a values where the slope of the functional relationship between d/o and a is the greatest. Sample sizes for hypothesis tests of differences from a particular overlap value are given in Figures 3 and 4. Samples for each species of up to 100,000 are required to distinguish a's to the second digit to the right of the decimal. Of course, necessary sample size is dependent on the proximity of the two species on the resource axis. Intermediate a's (1 §_d/w : 2) will require the largest sample sizes. Since MacArthur's (1972) a estimate allows the use of parametric statistics, it also likely provides the minimum sample sizes for other a measures which may require non-parametric confidence intervals. A confidence interval estimate for a(d/w) If the assumption of normal resource utilization functions is acceptable, it is possible to generate a confidence interval estimate for a(d/w). This requires the construction of a confidence region for the joint estimation of d and w. Derivations of precise joint confidence regions of this kind are difficult at best (Mood and Graybill 1963, Kendall and Stuart 1963). However, the confidence region may be estimated by using the individual confidence estimates for d and w, l4 .A3\vvd How mocmmwmaoo Nmm.M ucmmouaou moHouHo 3oHHo: mam Auvv MOM mam>uouafi moaowwmcoo Nma ucmmmuawp mmHoHHo vwaom .wmwooam Loam Eouw muwm oHaEmm .m> o\w mo mmDHm> msofium> How mHm>Hmucfi moamvwwcoo .N muswwm 15 d/O‘ ~ (I0) . (2 0) (4.0) IOOO BQQ§QQ¢nNfiO d/o '(5) . (LS) - (3 0) IOOO ,’A Q QOtQ'fiouqqmm_o 83 O'IVA VIM-IV SAMPLE SIZE 16 Figure 3. Sample sizes required to distinguish particular a values from values which are larger. l7 ALPHA VALUES J2..O.4.5.6.7.89. 0001.0.vo ”LN—m uniz.91>.24 1.00 M. axillaris .48>.15>.02 .76>.26>.02 1.00 M. haematonota .48>.02>.00 .05>.00>.00 .65>.33>.09 1.00 Table 2. Community matrix for Terborgh's antbirds. Cells contain point estimate for o(d/w) bounded by the 395% confidence interval for a. 25 estimated accurately. In view of the large samples necessary to properly distinguish some current ecological hypotheses (e.g., limiting similarity), it may be necessary to consider alternative experimental systems where large sample sizes are possible. For example, if samples of 10,000 are needed, we cannot consider most vertebrates. Yet there are some questions as to whether some current theories even apply to invertebrates (Wilson 1975, Wiens 1977, May 1975). Given that necessary sample sizes are not available to measure overlaps with sufficient precision, what alternatives are available? Based on problems with theoretical assumptions alone, there are appealing alternatives to measuring overlaps. For example, perturbation experiments (c.f. Schroder and Rosenzweig 1975, Werner and Hall 1976, 1977) are thought to provide much better evidence for competition than simple overlap measures. Even if overlaps are measured, manipulation may lead to large shifts in overlap values (Schroder and Rosenzweig 1975, Werner and Hall 1976,1977) such that these differences may be detectable at reasonable sample sizes. Without manipulation, we stand little chance of measuring or interpreting niche overlaps accurately. It is clear that until we know more than we do now, competitive overlaps will have to be examined the hard way--with manipulative experiments (Grant 1972,1975, DeBendictis 1974, Schroder and Rosenzweig 1975, Werner and Hall 1976). In this way, the mechanisms underlying the overlaps can be examined rather than the overlaps themselves. Manipulative experiments are preferable because they allow the consider- ation (and/or elimination) of several alternative hypotheses which may explain the observed overlap equally well. ECOLOGICAL CONVERGENCE OF COMMUNITY STRUCTURE: A NEUTRAL MODEL ANALYSIS Convergence of community structure Ecologists have recently begun to examine the possibility that community structures on different continents may converge under similar long term environmental conditions (Cody, l968,l974,1975, Recher 1969, DiCastri and Mboney 1973, Sage 1973, Pianka 1973, Karr and James 1975). Since historical and phylogenetic differences between continents may prevent the evolution of identical community structures, Fuentes (1976) proposed a relative measure for convergence of community structures that depends on within-continent comparisons as well as the usual between-continent comparisons (Figure 6). His hypothesis was stated as follows: "Physiognomically similar sites in the two continents should have lizard community structures that are more similar to each other than to the structure of lizard communities in nearby areas on the same [altitudinal-vegetational] transect." Fuentes examined the convergence of lizard communities from California and Chile by considering the numbers of species, habitat and food use, time of activity, and foraging behavior. Resource use patterns of each species were expressed as a multidimensional vector. The angle between the resource use vectors of two species varies between 1° and 90° as the species vary from identical resource use patterns to completely independent patterns. The major supporting evidence claimed for the species analogue assignments was derived from microhabitat use data (Fuentes 1976). Fuentes also asserted that the general pattern of habitat, food and time use "strongly supports the convergence hypothesis." 26 27 Figure 6. Between and within continent comparisons of resource use in California and Chile. Region maps include estimated frequencies of the four microhabitat types. 28 CALIFORNIA A WITHIN CONTINENT BETWEEN BETWEEN CONTINENT CONTINENT CHILE WITHIN CONTINENT V CHAPPARRAL MONTANE BUSHES TREES ROCKS Duns. OPEN GROUND 29 Fuentes, however, failed to consider an important alternative hypothesis: that convergence patterns in resource use are simply due to similarities in the proportions of available resources on "similar" sites. This "null hypothesis," presented here in the form of a neutral model is as follows: convergence patterns in microhabitat use presented by Fuentes (1976) as support for his hypothesis are not significantly different from what might be expected by chance alone. A neutral model for resource use A neutral model of an observed phenomenon is one in which the effects of proposed causal mechanisms are completely removed. Moreover, neutral models must be stated relative to a particular hypothesis and are only neutral to mechanisms eliminated explicitly. The model for resource use presented here simply assumes that animals select resources randomly in an environment in which different resources are not equally frequent. The model eliminates all other effects and is therefore neutral to these influences. For further discussion on the neutral model approach see Caswell (1976,1977). The model does not explain or attempt to account for species differences within a habitat on a continent. It deals solely with comparisons of similar habitats between-continents (e.g., chapparral vs. chapparral) and of different habitats within-continents (e.g., chapparral vs. montane), which Fuentes' hypothesis employs explicitly. Micro— habitat use is explored because, according to Fuentes, such data provide strong support for his hypothesis. In the model, resource availability for each resource category is calculated as a proportion of the total resources available. For example, in chapparral lizards, microhabitat availability for each 3O microhabitat category (open ground, ground under bushes, rocks, and trees) is based solely on the proportion of these microhabitats in the chapparral environment. Consequently, since the model assumes random resource selection, the proportions of resources actually used are closely correlated with the proportions of resources available. Since Fuentes did not give estimates of resource availability from his study sites, the model uses data estimated from the literature. Mooney and Parsons (1973) presented data on vegetation types in MOnroe Canyon, California, a region that covers 355 ha and includes altitudes in the range of Fuentes' chapparral site. They estimate that 74.6% of the watershed is covered by bushes, 11.9% is sage and barren areas (relatively open) and 13.5% is covered by trees. No data are available for percent cover of rocks. Assuming that Fuentes' microhabitat cate— gories are independent of each other, the model divides the sage and barren area equally into rocks and open ground. In Australian montane communities trees dominate with an understory of sclerophyllous shrubs (Sprecht 1973). The projective cover for trees is 30-70%. The model assumes that trees account for 50% of the cover in Fuentes' montane system. Since no data are available on the distribution of rocks and open ground microhabitat, the model assumes them to be the same as in the chapparral 6% each. The remaining 38% is assigned to "ground under bushes." Obviously, this analysis would benefit from having frequency data on the microhabitats for Fuentes' study sites (see Figure 6). The process of random microhabitat selection by the lizards in the model is similar to placing random points on a line segment which has been subdivided into microhabitat categories according to the proportion 31 of each category in the environment. For example, in the chapparral environment, a line segment between 0 and 1 would be subdivided into four microhabitat categories: open ground (0.00 §_x <0.06) ground under bushes (0.06 j_x fiw mum can some you maowum>ummno mo muonsoa paw mufima mowomam .ucoSAuaoo 05mm msu aoum mofiomam ocmucoe m>Hm ocu cufia mam :mowoamam: muw nuw3 mmwomam Hmuumaamno some mo coma Inmano map How cm>ww mum Howoa Hmuunm: osu mo mean OH Scum am N new name one .muwma mowomam Housmammzu .msomwumasoo unocfiuaoolcfisuwz .m ouswwm 33 mm 2n. mmamdm 44mm 44mm 44mmouwfic mnsmmHOAA w Away momOHomuw msuoaoamom I a ”Aocv mspapfi>ouwfia msawmaoaq a A¢OHV mamfiusnnmum mu: I o ”Ava «Hocoounom mnsmmaofiq a Away macmwcouafixm moumszm I m “Adv msumsuuou manaouumoub w ANV maumafiumowuaae msuococuuou I < ”Aonma mouamsm umummv mufimm .H ounwfim ou umHfiEHm maomfiumnsou .muwmm mmfiomam mcmucoz .mcowwumaaou unocwucou dwcufiz .w madman 36 m~= wz<._.zoz i1.... +. +. an .0 V0 0V Vo— .mm mz<._.zoz 0. cm on .0d .om on .2. .0m .00 (8333930) EWONV lVlIQVHOHDIN 37 different continents tend to converge under similar long term environ- mental conditions? Are species analogues from Fuentes' between-continent comparisons significantly more alike than would be expected by chance? Between-continent comparisons In general, Fuentes' chapparral species analogues are no more alike in their microhabitat use than would be expected by chance (Figure 9). Species analogues are those assigned by Fuentes (Note that a similar study of chapparral lizard community structures in Chile and California not cited by Fuentes reported a different species assemblage and assigned different species analogues [Sage 1973]). All microhabitat angles recalculated from Fuentes (1976) (with minor errors in Fuentes' angle calculations corrected) fail to differ significantly from those expected from the neutral model with the exception of one species pair (B), which is significantly (p < .001) less similar in microhabitat use than would be expected by chance alone. Significance was assigned by checking the probability that the angle from Fuentes could have come from the distribution given by ten runs of the neutral model. All neutral model distributions did not differ from Normal (Kolmogorov-Smirnov goodness of fit p > .2). Similarly, Fuentes' montane species analogues are not strikingly similar in their use of microhabitats (Figure 10). Two of the five species paris (C,E) are less alike than would be expected by chance (p < .05). All other angles are indistinguishable from those expected from the neutral model. Thus, when Fuentes' data yield microhabitat use angles which Figure 9. Between-Continent Mean and 2 SD are of species pairs. Species pairs are 38 Comparisons. Chapparral Species Pairs. given from the neutral model for similarity Triangles are data from Fuentes (1976). those given in Figure 7. 39 2 Amummome m402< ._.<._._m