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GEB188.fm Page 39 Thursday, March 16, 2000 10:34 AM Global Ecology & Biogeography (2000) 9, 39 – 58 I S L A N D B I OGE OG R AP HY S P E C I A L I S S U E A species-based theory of insular zoogeography Blackwell Science, Ltd MARK V. LOMOLINO Oklahoma Biological Survey, Oklahoma Natural Heritage Inventory and Department of Zoology, University of Oklahoma, Norman, OK 73019, U.S.A. E-mail: [email protected] ABSTRACT 1 I present an alternative to the equilibrium theory of island biogeography, one which is based on the premise that many of the more general patterns in insular community structure result from, not despite, nonrandom variation among species. 2 For the sake of simplicity, the model is limited to patterns and processes operating over scales of ecological space and time: evolution is not included in the current version of the model. 3 The model assumes, as did MacArthur and Wilson’s model, that insular community structure is dynamic in ecological time, but the model does not assume a balance, or equilibrium, of immigration and extinction. INTRODUCTION The great diversity of patterns we study in biogeography all derive from three fundamental forces: immigration, extinction and evolution. Therefore, our ability to understand patterns in insular community structure will rest upon our understanding how these processes vary with characteristics of the species and islands in question. The tripartite model of island biogeography (see Lomolino, 2000; see also Heaney, 1986, 2000) represents a very general conceptualization of these interrelationships, explaining how the relative importance of immigration, extinction and evolution should vary with island area and isolation, and with differences in resource requirements and immigration abilities among species groups. My purpose in this paper is to present a more focused, species-based model that can serve as a useful tool for understand- 4 The model presented here is hierarchical, phenomenological (it requires little parameterization beyond that which is directly derived from distributional data), graphical, and it includes potential feedback processes (including interspecific interactions). 5 The model offers an alternative explanation for a variety of patterns ranging from distributions of individual species, species–area and species– isolation relationships, to patterns of assembly of insular communities. The model also generates some new predictions and identifies some potentially important areas for future studies. Key words Area, assembly, equilibrium theory, extinction, immigration, insular distribution function, island biogeography, isolation. ing a diversity of patterns within ecological space and time. The model presented here thus operates within a subset of the tripartite space, reducing it to a two-dimensional model where speciation is assumed to be too infrequent to have a significant influence on insular community structure. Speciation will, of course, set the pool of species that can colonize a given island, but the species pool is assumed to be constant across the archipelago. Even within ecological time, however, this assumption may be challenged. For example, focal archipelagoes may lie within transition zones between two or more prospective species pools (e.g. montane forest mammals of the American South-west [Lomolino et al., 1989; Lomolino & Davis, 1997;] and many insular biotas of Wallacea). My hope is that other researchers will take up the challenge of expanding this two-dimensional model or will offer alternative models that include © 2000 Blackwell Science Ltd. http://www.blackwell-science.com/geb 39 GEB188.fm Page 40 Thursday, March 16, 2000 10:34 AM 40 M. V. Lomolino the influence of speciation and other events occurring over evolutionary and geological time scales (see Heaney, 2000; Ward & Thornton, 2000). Despite this limitation, the model presented here can explain a diversity of patterns in insular community structure ranging from distributions of particular species within an archipelago to differences in patterns of species richness and composition across archipelagoes and among faunal groups. Let me first summarize some of the salient features of this model (see also Lomolino, 1986). 1 The model is species-based. Not only do islands vary in fundamental characteristics such as isolation and area, but species also differ with respect to their abilities to immigrate to and to survive on islands. To the degree to which such interspecific variation is nonrandom, it will result in regular patterns in insular community structure. Again, many of the common patterns in biogeography may result from, not despite, nonrandom variation among species (see Diamond, 1975). 2 The model assumes that insular community structure is dynamic in ecological time. Immigration and extinction of focal species is assumed to be recurrent, but the model does not assume a balance, or equilibrium, of these processes. 3 The model is primarily phenomenological. It requires very little parameterization beyond that which can be directly derived from distribution patterns of the focal species. 4 The model is hierarchical. It addresses the factors that may influence distribution patterns at scales ranging from single species and particular islands to complexes of different faunal groups and archipelagoes. 5 The model includes potential feedback among system components. One factor that becomes important at the scale of entire communities is interspecific interaction. The community level version of this model explicitly considers interspecific interactions and the potential for covariation of immigration abilities, resource requirements and ecological dominance (i.e. the ability of one species to outcompete or prey upon another). 6 The model is graphical and, at least in terms of the examples presented here, restricted to zoogeographic patterns. These features reflect my limitations and not any ultimate constraints of the model. I hope that others, more proficient with mathematical modelling and with more knowledge regarding biogeography of insular plants will choose to fill in these gaps. Indeed, metapopulation biologists such as Hanski and colleagues (e.g. see Hanski & Gilpin, 1997) have made great progress modelling the dynamics of populations occupying patchy habitats. Unlike the model presented here, metapopulation models are largely stochastic and equilibrial. The deterministic, graphical model presented here, and metapopulation models may be viewed as alternative, but complementary approaches, both derived from the dynamic theory of island biogeography championed by MacArthur & Wilson (1967). In the following sections I develop the model in a hierarchical fashion, starting with a singlespecies, one-archipelago version of the model. I then expand the model to predict how the distribution of a focal species should vary with differences among archipelagoes: namely differences in immigration filters and regional productivity (i.e. area-specific carrying capacity of insular environments). Finally, I model differences in insular distributions of suites of species to explore patterns in assembly of communities within as well as among archipelagoes. A FOCAL SPECIES MODEL The fundamental component of the hierarchical model is the insular distribution function, which describes how populations of a particular focal species should be distributed across the two geographical dimensions of island area and isolation (Fig. 1; see Lomolino, 1986). The insular distribution function can be represented by a line, or curve, separating islands inhabited by a focal species from those where the species is absent. The salient features of the insular distribution function can be derived with a very conservative set of assumptions. 1 The immigration rate of the focal species (number of individuals of this species reaching the island per unit time) decreases with increased isolation. Therefore, the time between immigrations (Ti) should increase with isolation. (Note that immigration rate as defined here is conceptually different from that of the equilibrium model. Because there is no reason to believe that the number of individuals reaching an island per © 2000 Blackwell Science Ltd, Global Ecology & Biogeography, 9, 39 – 58 GEB188.fm Page 41 Thursday, March 16, 2000 10:34 AM A species-based theory of insular zoogeography 41 Fig. 1 The general form of the insular distribution function for a focal species (dark symbols indicate presence, open symbols indicate absence of the focal species). The insular distribution function delineates those combinations of area and isolation for which expected persistence time equals time between immigrations. The focal species is expected to occur on islands that fall above the insular distribution function. Fig. 2 Frequency distribution and cumulative frequency distribution of immigration abilities (distances, units arbitrary) for individuals of a hypothetical focal species. Because immigration abilities are expected to exhibit a strong central tendency (likely a lognormal or log-skewed distribution), the cumulative number of individuals whose immigration abilities extend beyond a target island should decrease (and Ti should increase) as a sigmoidal function of island isolation. unit time will vary with species richness, the current model does not predict an equilibrium of immigration and extinction). 2 The persistence time (T p), which equals the expected time to extinction of a newly established population of the focal species, should increase with island area. 3 Populations of the focal species should occur on those islands where Tp > Ti, i.e. where additional immigrants reach an island before a resident population is expected to go extinct. 4 Immigration abilities of the focal species should exhibit a strong central tendency. The frequency distribution of this trait should be unimodal and likely to take the form of a lognormal or log-skewed function, with most individuals clustering about the modal immigration ability or distance (Fig. 2). Given that the above assumptions hold true for most species, we can derive the form of the insular distribution function and explain some common patterns as well as some apparent anomalies in island biogeography. First, because Ti increases with isolation, Tp (and therefore island area) also must increase with isolation to maintain populations of the focal species. Thus, the insular distribution function should have a positive slope: i.e. critical minimum areas to maintain populations of the focal species should increase with island isolation. Second, given that Assumption 4 is valid, then the cumulative number of individuals capable of immigrating to an island should decrease as a negative sigmoidal function of island isolation (dashed line in Fig. 2). Accordingly, critical minimum areas (and insular distribution functions) should vary as positive sigmoidal functions of isolation (Fig. 1). The predicted nonlinear form of the insular distribution function has important implications with respect to scale dependence of biogeographic patterns, which I discuss in a subsequent section. The precise form of the insular distribution function will depend on a variety of species’ and system characteristics that affect Ti and Tp. Yet all insular distribution functions have two readily interpretable components: • an intercept, which is a direct measure of resource levels required to maintain populations of the focal species on the less-isolated islands, and; • a generalized slope, which is an inverse measure of immigration abilities of the species. © 2000 Blackwell Science Ltd, Global Ecology & Biogeography, 9, 39 – 58 GEB188.fm Page 42 Thursday, March 16, 2000 10:34 AM 42 M. V. Lomolino Fig. 3 The predicted effects of interspecific differences in resource requirements on insular distribution functions (size of circles depicts relative size of the islands). Regional differences in primary productivity (or carrying capacity per area of island) should have equivalent effects on insular distribution functions; i.e. intercepts of insular distribution functions should be higher for larger, more specialized and more energy intensive species, or for the same species occurring in archipelagoes with relatively low primary productivity. Therefore, intercepts of insular distribution functions should increase as we consider larger, more specialized, or otherwise more resourceintensive species (Fig. 3). The slope of the insular distribution function, which describes how rapidly critical minimum areas should increase with isolation, should be higher for less vagile species (Fig. 4). The actual intercepts and slopes of insular distribution functions can be estimated using empirical data on species distributions and logistic regression, linear or nonlinear regression, or discriminant analysis (see Lomolino, 1986; Lomolino et al., 1989). Differences in insular distribution functions among archipelagoes Abilities of species to immigrate to and maintain populations on islands are influenced by a combination of species and system characteristics. While islands vary substantially in their physical characteristics, archipelagoes are typically assumed by biogeographers to be internally homogeneous Fig. 4 The predicted effects of interspecific differences in vagility (active immigration abilities) on insular distribution functions. Regional differences in impedances of immigration barriers should have equivalent effects on insular distribution functions; i.e. slopes of insular distribution functions should be higher for less vagile species, or for the same species occurring in archipelagoes with more formidable barriers. with respect to other factors affecting immigration and extinctions. That is, immigration filters, climate, primary productivity and other regional scale factors are assumed to be invariant across islands. When making comparisons among archipelagoes, however, this assumption becomes more tenuous and may mask some interesting, large scale patterns. In fact, archipelagoes are likely to differ with respect to two principal features that bear directly on insular distribution functions: the nature of immigration filters (i.e. the characteristics of intervening seascapes or landscapes that impede immigration), and the level of primary productivity, habitat characteristics and other factors that influence carrying capacities of insular environments. The effects of both of these regional scale factors on differences in insular distribution functions for a given species among archipelagoes are equivalent to those associated with differences among species. That is, their effects can be modelled as changes in the slope and intercept of the insular distribution function (Figs 3 and 4). For a given focal species, the intercept of its insular distribution function should be higher © 2000 Blackwell Science Ltd, Global Ecology & Biogeography, 9, 39 – 58 GEB188.fm Page 43 Thursday, March 16, 2000 10:34 AM A species-based theory of insular zoogeography 43 Fig. 5 Effects of different sampling regimes on apparent patterns of distribution of a hypothetical species (darkened symbols depict presence, open symbols depict absence). Depending on the region sampled, the same species may appear to exhibit a variety of distribution patterns with respect to island area and isolation (see text). in archipelagoes with relatively low primary productivity and the slope should be steeper in archipelagoes with more formidable barriers to immigration. Again, both immigration abilities and abilities to maintain insular populations are relative measures that may only have meaning in the context of specific archipelagoes and environmental conditions. Scale-dependence of insular distribution functions If insular distribution functions were linear, then patterns of insular distributions would be scale independent. For each incremental increase in isolation, critical minimum areas would increase a constant amount regardless of the actual range in isolation considered. However, insular distribution functions should not be linear, but sigmoidal. Depending on the portion of the geographical template surveyed, different researchers may make some apparently contradictory inferences about the factors limiting distributions of the same species. For example, researchers surveying islands in regions a or c of Fig. 5 would conclude that the insular distribution of this species is primarily limited by island area, but would estimate very different critical areas (i.e. much smaller in a than in c). On the other hand, researchers surveying islands in region b of Fig. 5 would conclude that area is relatively unimportant and that the insular distribution of this species is most strongly influenced by island isolation. These apparent contradictions are clarified, however, when we sample a much broader range of islands ( d in Fig. 5) to reveal that the three patterns are components of a more general pattern, the insular distribution function. Some examples of insular distribution functions The empirical insular distribution functions illustrated in Fig. 6 exhibit the predicted form of this function, i.e. critical minimum areas © 2000 Blackwell Science Ltd, Global Ecology & Biogeography, 9, 39 – 58 GEB188.fm Page 44 Thursday, March 16, 2000 10:34 AM 44 M. V. Lomolino Fig. 6 Empirical distribution patterns of four species of terrestrial vertebrates inhabiting islands. a) masked shrew in the Great Lakes archipelagoes, U.S.A., Lomolino (1993); b – d) birds of the guild Parus in the Danish archipelago, data from Wiggins & Moller (1997); e) the endangered Ouachita Mountain river shiner Lythrurus snelsoni Robison, among isolated pools of eastern Oklahoma, U.S.A., data from Taylor (1997); darkened symbols depict presence, open symbols depict absence. to maintain insular populations of these species increase with isolation. I have also analysed insular distribution functions for a large number of other species (mostly mammals and birds) from a variety of archipelagoes of true or habitat islands (Lomolino, 1986, 1988; Lomolino et al., 1989; Lomolino & Davis, 1997, 1988). Not surprisingly, insular distribution functions vary markedly among species and archipelagoes, but much of the variation appears consistent with the model’s predictions. For example, insular distribution functions should have a slope © 2000 Blackwell Science Ltd, Global Ecology & Biogeography, 9, 39 – 58 GEB188.fm Page 45 Thursday, March 16, 2000 10:34 AM A species-based theory of insular zoogeography near zero for relaxation faunas (Fig. 7a–c), corresponding to the biogeographic space circumscribed by c in Fig. 5 (relaxation faunas are those experiencing gradual species loss due to increased isolation following habitat change; see Brown, 1971, 1978; Diamond, 1972; Heaney, 1986). In contrast, insular distribution functions of nonvolant mammals of the less-isolated islands of the Great Lakes Region (Fig. 7d), where immigration events occur on an annual basis, are quite different. In this case, the slopes of insular distribution functions vary in a manner consistent with the relative immigration abilities of the species. Studies of cross-ice movements of these species (Lomolino, 1988, 1989, 1993) indicate that, consistent with bioenergetic considerations, winter immigration rates increase with body size. Accordingly, the slopes of insular distribution functions are steepest for shrews and meadow voles (corresponding to region b of Fig. 5), intermediate for tree squirrels and rabbits (regions a and b), and not significantly different from zero for deer, red fox and racoons (region a). The insular distribution function for eastern chipmunks also has a slope of zero, but for just the opposite reason. Chipmunks are not just small, but they are the only hibernators in this species group, and thus are very limited in their abilities to travel across ice to colonize islands in this region (much like relaxation faunas; see above references). To date, I have made only a limited number of comparisons of insular distribution functions among archipelagoes, but the results again appear consistent with the predicted shifts in insular distribution functions illustrated in Fig. 4. For example, in comparison with montane forest islands of the Great Basin, those found further south in the American Southwest (in Arizona, New Mexico, and southern Utah and Colorado) are separated by more mesic, and therefore, less formidable barriers to immigration by boreal forest mammals. Comparisons between these archipelagoes reveal that, consistent with the model, populations of nonvolant mammals can maintain populations on much smaller and geographically more isolated islands in the American South-west (Lomolino et al., 1989; Lomolino & Davis, 1997). Hazel grouse (Bonasa bonasia) inhabiting fragmented 45 coniferous forests in Sweden exhibit the same interarchipelago pattern (Aberg et al., 1995). In contrast to landscapes where the intervening habitat is second growth forests, in landscapes dominated by more isolating, agricultural fields, populations of this coniferous forest bird are restricted to much larger and less isolated islands (Fig. 7e). ASSEMBLY OF INSULAR COMMUNITIES Many of the most general patterns in assembly of insular communities may result from nonrandom variation in insular distribution functions among species. In order to expand the focal species model to account for patterns in insular community structure, I make the following assumptions. 1 Just as individuals of a focal species are expected to exhibit strong central tendencies in traits closely related to fitness (here, immigration abilities and resource requirements), groups of closely related species (e.g. assemblages of passerine birds, of bats, or of nonvolant mammals) should also exhibit strong central tendencies in these traits. 2 Immigration abilities and resource requirements (and therefore the slopes and intercepts of insular distribution functions) should covary among species. 3 Insular distributions of a group of species may be strongly influenced by interspecific interactions, many of which may be highly asymmetrical (e.g. predation, amensalism, parasitism, and asymmetrical competition). Given the above assumptions, we can explain the general form of species–area and species– isolation relationships, species checkerboards (sensu Diamond, 1975), and other patterns of codistributions of species including community nestedness (i.e. the tendency for species lists on relatively depauperate islands to form proper subsets of those on richer, larger or less-isolated islands; see Patterson & Atmar, 1986; Lomolino, 1996; Wright et al., 1998). Patterns in species richness Let us first consider the general forms of the species–area and species–isolation relationships, © 2000 Blackwell Science Ltd, Global Ecology & Biogeography, 9, 39 – 58 GEB188.fm Page 46 Thursday, March 16, 2000 10:34 AM M. V. Lomolino Fig. 7 46 © 2000 Blackwell Science Ltd, Global Ecology & Biogeography, 9, 39 – 58 GEB188.fm Page 47 Thursday, March 16, 2000 10:34 AM A species-based theory of insular zoogeography 47 Fig. 7 a–d) Insular distribution patterns of nonvolant mammals on isolated archipelagoes. a) relaxation fauna of montane forest islands of the Great Basin, North America, data from Brown (1978); b) relaxation fauna of the islands of Bass Straits, Australia, data from Hope (1973); c) a hypothetical relaxation fauna; and d) a nearshore archipelago of the Great Lakes region (after Lomolino, 1986). Species occur on islands that fall above or to the left of the lines. Although distributions of the species illustrated in a and b appear to be uninfluenced by isolation, this may be an artefact of the sampling regime. That is, isolation effects may have been detected if less-isolated islands were included in these studies (depicted by dashed line in c; darkened symbols depict presence, open symbols depict absence); e) Effects of differences in immigration filters on insular distribution functions of Hazel grouse (Bonasa bonasia) in fragmented forests in Sweden (Aberg et al., 1995). As predicted by the model shown in Fig. 4, the slope of the insular distribution function for this species increased where forests were surrounded by less hospitable habitats (agricultural fields [triangles] vs. second growth, managed forest [circles]; presence and absence is indicated by filled and unfilled symbols, respectively). which follow directly from Assumption 1, above. Because most ecologically significant traits are correlated with body size (see Peters, 1983; Calder, 1984; Brown, 1995), I expect that the frequency distribution of resource requirements and immigration abilities among species will take a similar form. That is, these frequency distributions should take the form of log-normal or log-skewed functions, with most species clustering about relatively low, modal levels of resource requirements and relatively low immigration abilities (Fig. 8a). Cumulative frequency distributions of these functions should thus take the form of positive sigmoidal curves (dashed line in Fig. 8a). We can now derive the form of the species– area relationship. As lifetime energy budgets, home range, territory size, and other measurements of area requirements are directly related to resource requirements, we can substitute ‘area’ for resource requirements. As area increases along the abscissa of Fig. 8a, an increasing number of species should be able to find adequate resources to maintain populations on the target islands (i.e. Tp will exceed Ti for more and more species). Thus, species richness of the focal group should increase as a positive sigmoidal function of island area (Fig. 8-b). The predicted form of the species– area relationship is similar to those of models commonly used to investigate this pattern (e.g. the power and semi-log models), with one key distinction. Only the sigmoidal model predicts what MacArthur & Wilson (1967; pp. 30–33) termed the ‘small island effect’ — the tendency for species richness of some insular biotas to remain relatively low and apparently independent of area for the smallest islands (small island effects are reported by Wiens, 1962; Niering, © 2000 Blackwell Science Ltd, Global Ecology & Biogeography, 9, 39 – 58 GEB188.fm Page 48 Thursday, March 16, 2000 10:34 AM 48 M. V. Lomolino Fig. 8 a) Frequency distribution (shaded) and cumulative frequency distributions (dashed lines) of resource requirements (in units of area) and immigration abilities (in units of distance) of a group of species. Because these traits are expected to show strong central tendencies within a species group, cumulative frequency distributions of these traits should take the form of positive sigmoidal functions; b) and c) Given the patterns illustrated in a, the species–area and species–isolation relationships should also be sigmoidal functions. 1963; Whitehead & Jones, 1969; Woodroffe, 1986; Dunn & Loehle, 1988). For reasons similar to those discussed above, the species–isolation relationship should also take the form of a sigmoidal function (Fig. 8c). This relationship, however, is one of attenuation, not accumulation: as isolation increases, fewer species are likely to immigrate to an island frequently enough to maintain insular populations (i.e. Ti will exceed Tp for more and more of these species). The rate of decline in species richness (dashed line in Fig. 8c) should, in fact, be inversely related to the cumulative frequency distribution of immigration abilities. Therefore, as isolation increases, richness should decline, very gradually at first until isolation exceeds immigration abilities of the least vagile species, more rapidly as isolation approaches the modal immigration abilities of the species group, and then asymptotically approach zero beyond this point. Again, sigmoidal curves imply scale dependence, in this case scale-dependent variation in community parameters (species richness and species composition of insular communities). For example, the effects of area or isolation on species richness will be difficult to detect (slopes of species–area and species–isolation curves near zero) if biogeographic surveys are limited to the very small or very large islands, or to those too close or too distant to the mainland to detect the effects of isolation. Also, just as insular distribution functions of focal species should shift with differences among species groups and archipelagoes, species–area and species–isolation curves should shift in a similar manner. For example, species–area curves should shift toward the right (i.e. toward larger island size; Fig. 9a) for groups of species with relatively high resource and area requirements (e.g. for groups of endotherms vs. ectotherms, or for relatively © 2000 Blackwell Science Ltd, Global Ecology & Biogeography, 9, 39 – 58 GEB188.fm Page 49 Thursday, March 16, 2000 10:34 AM A species-based theory of insular zoogeography 49 large vs. small animals). I expect equivalent shifts in species–area curves among archipelagoes differing in primary productivity and area-specific carrying capacity (i.e. right-ward shifts for archipelagoes with relatively low carrying capacity). In a similar fashion, species– isolation curves should shift to the right (i.e. toward more isolated islands) for groups of species with relatively high vagilities (e.g. birds or bats vs. nonvolant mammals) or, equivalently, for archipelagoes surrounded by less formidable immigration filters (Fig. 9b,c). Patterns in species composition Fig. 9 Predicted and observed effects of differences among species and among archipelagoes on species– area and species–isolation relationships. a) Species– area curves should shift toward the right (larger islands required to support the same number of species) for faunal groups with relatively high resource requirements (e.g. groups comprised of relatively large vs. small animals), or for the same species group occurring in archipelagoes with relatively low primary productivity (low area-specific carrying capacities). b) Species–isolation curves should shift toward the right (toward more isolated islands) for groups of species with relatively high immigration abilities (birds and bats vs. nonvolant mammals), or for the same group of species in archipelagoes surrounded by less formidable barriers. c) Species–isolation relationships of non-volant mammals on archipelagoes in the Great Lakes Region, U.S.A., appear consistent with the predicted pattern illustrated in b. Species richness (measured as residuals about species–area curves for each archipelago) declines more slowly in lacustrine archipelagoes (Lakes Huron and Michigan) where currents are relatively weak and the ice is more stable (after Lomolino, 1994). While the species–area and species–isolation relationships are island biogeography’s most common and first recognized patterns, many of the field’s most intriguing questions concern patterns in species composition. To the degree to which these patterns are predictable, they reflect nonrandom variation in insular distribution functions among species or among archipelagoes. I have already predicted that, rather than being uniformly or randomly distributed among species, resource requirements and immigration abilities should exhibit a strong central tendency (Assumption 1 above, Fig. 8). In addition, because most biological traits are correlated with body size, it is likely that resource requirements and immigration abilities (i.e. the intercepts and slopes of the insular distribution function) will covary with body size and therefore with each other (Assumption 2). For example, immigration abilities and resource requirements of non-volant mammals appear to show positive covariation: larger species tend to be better immigrators, but also require larger islands to maintain their populations (Lomolino, 1988, 1989). Yet for other groups of species, immigration abilities and resource requirements may be inversely correlated. For example, small size in microsnails and other small invertebrates may confer both superior immigration abilities (primarily by aerial dispersal) and lower resource requirements (see Vagvolgyi, 1975). These alternative forms of covariation have important implications with respect to assembly patterns of insular communities (Fig. 10). Where immigration abilities are inversely correlated with resource requirements (better immigrators © 2000 Blackwell Science Ltd, Global Ecology & Biogeography, 9, 39 – 58 GEB188.fm Page 50 Thursday, March 16, 2000 10:34 AM 50 M. V. Lomolino Fig. 10 Effects of two alternative patterns of covariation of resource requirements and immigration abilities on assembly and nestedness of insular communities. Solid lines depict insular distribution functions for three hypothetical species (A, B, C) in two archipelagoes. a) Where better immigrators require smaller islands to maintain their populations, assembly sequences should be constant (i.e. first species A, then B, and then C) and nestedness should be relatively high, regardless of the biogeographic space surveyed. b) Where better immigrators require more resources (larger islands) to maintain their populations, assembly of insular communities should be complex and nestedness should be relatively low, especially when biogeographic surveys include a broad range in island area and isolation. c) Expected patterns of nestedness for the two hypothetical archipelagoes illustrated in a and b. can maintain populations on smaller islands), patterns of community assembly should be very regular indeed. Regardless of the ranges of isolation and area surveyed, nestedness of insular communities should be very high, with species accumulating in the same sequence across all portions of the archipelago (in the hypothetical case of Fig. 10a, always species A first, then B, then C). On the other hand, where better immigrators require larger islands to maintain insular populations, even this relatively simple model predicts a complex pattern of assembly. In the hypothetical case illustrated in Fig. 10b, almost all possible combinations of species are predicted to inhabit islands depending on their isolation and area. Species accumulation sequences should be C first, then B, then A on the less-isolated islands, B, then A, then C on the islands of intermediate isolation, but A, then B, then C on the most isolated islands (note that community nestedness is inversely related to how often insular distribution functions intersect). Therefore, under this scenario, nestedness of insular communities should be relatively low (Fig. 10c), unless biogeographic surveys are conducted within just a limited range of isolation or area. Unfortunately, logistics often dictate that our surveys be limited in just this manner (typically including islands that vary less than an order of magnitude in isolation © 2000 Blackwell Science Ltd, Global Ecology & Biogeography, 9, 39 – 58 GEB188.fm Page 51 Thursday, March 16, 2000 10:34 AM A species-based theory of insular zoogeography from the mainland). This may contribute to the fact that reported levels of community nestedness are typically quite high. Yet, given appropriately designed biogeographic surveys, species accumulation sequences should vary substantially, albeit in a predictable manner, among islands and archipelagoes. The influence of interspecific interactions When Jared Diamond first wrote about assembly rules, it was in his seminal chapter, dedicated to Robert MacArthur. Diamond accepted one of MacArthur’s great challenges, to understand ‘the existence of alternative stable communities’ (Diamond, 1975; p. 345). While the hierarchical model developed above contributes toward this goal, it still needs an additional layer of complexity; namely feedback among the model’s components. The community level model of Fig. 10 describes the potential, or fundamental ranges of insular populations. Their realized ranges, however, may be strongly influenced by interspecific interactions (Fox & Fox, 2000). The nature of these feedback effects can be quite complex, including simple and diffuse, direct and indirect interactions among many species. We can, however, simplify the task of modelling the effects of interspecific interactions by reducing the problem to a ‘community’ of just two species that engage in some type of negative, asymmetrical interaction. That is, where their fundamental ranges overlap, one species will always exclude the other and therefore reduce its realized range. It is again important to consider potential covariation among species traits. Just as immigration abilities and resource requirements may covary among species, ecological dominance (the ability of populations of one species to exclude those of another) may covary with one of these traits. For example, among terrestrial vertebrates, predators tend to be larger than their prey and, thus, may also require larger islands to maintain insular populations. Whatever the pattern of covariation in a particular species group, it has strong implications with respect to realized ranges of the focal species. In the two hypothetical cases illustrated in Fig. 11, ecological dominants are predicted to exclude the other species where their fundamental insular distribution functions overlap, 51 except on the very large islands where the second species is likely to find ecological refugia. This species should also find refugia on islands lacking the ecological dominant. This condition would be met on small islands if ecological dominants have high resource requirements, or on the more isolated islands if ecological dominants are relatively poor immigrators. Distribution patterns of some freshwater fish in Oklahoma (Fig. 12a), and of small mammals inhabiting archipelagoes of the Great Lakes Region, U.S.A. (Fig. 12b), appear consistent with the interactive version of this model. Returning to Diamond’s (1975) paper, one of the most striking patterns he examined was species checkerboards, where members of the same guild often exhibit exclusive distributions. The interactive version of the hierarchical model can provide a useful spatial context for this pattern and may also help identify potential differences in immigration abilities, resource requirements and ecological dominance among species. Without plotting species distributions across the bivariate plot of area and isolation it would be difficult to distinguish between two fundamentally different types of checkerboards. In the first case, the component species may be distributed as true spatial checkerboards, i.e. uniformly distributed across the biogeographic space illustrated in Fig. 13a. This is what we would expect if the species were equivalent with respect to immigration abilities and resource requirements (i.e. if their fundamental insular distribution functions were identical). Alternatively and perhaps in most cases, however, immigration abilities and resource requirements will differ among species and the ‘checkerboard’ will thus have a strong spatial bias (Fig. 12a,b). Codistributions of species within Diamond’s fruit pigeon, cuckoo-dove and gleaning flycatcher guilds appear consistent with this alternative, biogeographically biased form of checker-boarding (Fig. 13a,b,c). In fact, the pattern of exclusive distributions of some guild members (specifically Ptilinopus solomenensis, Macropygia mackinlayi, and Pachycephala melanura) on smaller islands is difficult to explain without invoking the potential importance of negative interspecific interactions; in this case, competition (see Diamond, 1975). In comparison to other guild members, these species may be competitively inferior but, because of © 2000 Blackwell Science Ltd, Global Ecology & Biogeography, 9, 39 – 58 GEB188.fm Page 52 Thursday, March 16, 2000 10:34 AM 52 M. V. Lomolino Fig. 11 Effects of interspecific interactions on realized insular distribution functions of two hypothetical species. Solid lines indicate the insular distribution functions of two species: these delimit the fundamental range of each species (i.e. the ranges in isolation and area where each species is expected to occur in the absence of ecological exclusion). a) Here the better immigrator, species B, suffers ecological exclusion where the fundamental ranges of the two overlap. Species B, however, should persist in ecological refugia afforded by relatively large islands, and on isolated islands lacking the less vagile, species A. b) Here, the better immigrator, species B, excludes the second species where their fundamental ranges overlap. Species A, however, should persist in ecological refugia afforded by relatively large islands, and on smaller islands that lack species B. © 2000 Blackwell Science Ltd, Global Ecology & Biogeography, 9, 39 – 58 GEB188.fm Page 53 Thursday, March 16, 2000 10:34 AM A species-based theory of insular zoogeography 53 Fig. 12 Empirical patterns of insular distributions reflecting the likely influence of interspecific interactions. a) Distributions of two species of freshwater fish among pools of the Red River in Oklahoma (data from Taylor, 1997). Small mouth bass (Micropterus dolomieu Lacapede) appear to dominate in interspecific interactions with the creek chub (Semotilus atromaculatus Mitchell), but the bass appears more limited in dispersal abilities. As a result, the distributions of these species is nearly exclusive, with populations of small mouth bass being restricted to the less-isolated pools, while all but one population of the creek chub are restricted to the most-isolated pools. The one exception is the occurrence of both species on a relatively large, less-isolated pool (i.e. one large and near enough to maintain populations of creek chubs despite the effects of competition and possible predation from small mouth bass). b) Insular distribution patterns of two species of nonvolant mammals on islands of Lake Huron and Lake Michigan (S = shrews [Blarina brevicauda Say and Sorex cinereus Kerr], D = deermice [Peromyscus maniculatus Wagner]). Because shrews tend to be relatively poor immigrators, their populations are generally restricted to the less-isolated islands. By preying on insular deermice (especially juveniles), shrews may be able to exclude populations of these rodents from relatively small, less-isolated islands (see Lomolino, 1984 for a similar pattern with insular voles and shrews). On the other hand, the ecologically subordinant but more vagile deermice may find refugia on the more isolated or larger islands. © 2000 Blackwell Science Ltd, Global Ecology & Biogeography, 9, 39 – 58 GEB188.fm Page 54 Thursday, March 16, 2000 10:34 AM 54 M. V. Lomolino Fig. 13 a) A biogeographic checker-board distribution of two hypothetical species. In this case, both species are uniformly distributed across the bivariate, biogeographic space (i.e. their distributions are independent of isolation and area), but they never occupy the same island. This pattern would be expected where competition is intense, but species are essentially equivalent with respect to immigration abilities and resource requirements. b–d) In contrast to the above, hypothetical pattern, analysis of insular distribution patterns for three of Diamond’s (1975) avian guilds reveals that exclusive distributions are often achieved by species segregating their realized distributions over different ranges of isolation and area (data from D.R. Perault and M.V. Lomolino, unpublished report 1996; see also Fig. 12). Regression analysis was used to estimate linear insular distribution functions of these species (see Lomolino, 1986). Insular distributions were significantly (P < 0.05) associated with island area and isolation for Ptilinopus rivoli, P. solomenensis, Macropygia nigrirostris, and Pachcephala pectoralis. Insular distributions were significantly associated with area (but not with isolation) for P. melanura, and marginally (P < 0.09) associated with area for M. mackinlayi. © 2000 Blackwell Science Ltd, Global Ecology & Biogeography, 9, 39 – 58 GEB188.fm Page 55 Thursday, March 16, 2000 10:34 AM A species-based theory of insular zoogeography 55 Fig. 13 continued. their relatively low resource requirements and/ or superior immigration abilities, they are able to maintain populations on relatively small or isolated islands. CONCLUSION The hierarchical, species-based model remains fundamentally simple in that its thesis is that most patterns of insular community structure result from non-random variation in immigration and extinction. It assumes that insular populations of a focal species should be more likely to occur on islands where they immigrate more frequently than they go extinct, and that immigrations and extinctions are strongly influenced by island isolation and island area, respectively. To explain some very general patterns in © 2000 Blackwell Science Ltd, Global Ecology & Biogeography, 9, 39 – 58 GEB188.fm Page 56 Thursday, March 16, 2000 10:34 AM 56 M. V. Lomolino the assembly of insular communities, the model makes the additional assumptions that immigration abilities and resource requirements vary in a non-random manner among species, and that these traits may covary. The community level version of this model also assumes that insular distributions can be strongly influenced by interspecific interactions. Thus, the model is based on a very conservative set of assumptions. Yet this simple model can account for a variety of island biogeography’s most general patterns, makes additional predictions, and identifies some key topics for future studies. Perhaps the most interesting and potentially insightful topic for research concerns patterns of covariation of immigration abilities and resource requirements among species. Potential covariation in system characteristics, such as in the nature of immigration filters and regional variation in productivity, also seems to be a fertile subject for future research. Do islands found in areas with relatively high productivity (e.g. lower latitudes or lower elevations) also tend to be surrounded by my more isolating immigration filters? Or, to paraphrase Janzen (1967), we may ask whether mountain passes (immigration filters) really are ‘higher’, or more isolating in the tropics? A fundamental limitation of the speciesbased model is that it is limited to ecological time scales. The assumption that speciation is relatively unimportant should be challenged more frequently, especially at large spatial scales (e.g. when comparing patterns among archipelagoes). Speciation events will of course be rare in ecological time, but the legacies of such events should be considered alternative, or complementary explanations for extant patterns. For example, the current model assumes that speciation determines the species pool capable of colonizing the focal islands. While this seems unquestionable, the implicit assumption here is that each archipelago is served by just one species pool. Yet we know this is unlikely for many archipelagoes, such as those situated along a transition zone, or those subject to relatively frequent, intra-archipelago speciation. In the latter case, restriction of a species to what appear to be the more isolated islands, rather than reflecting ecological exclusion by less vagile predators or competitors, may simply indicate that the focal species is derived from a different species pool. Again, the degree to which such historical legacies need to be considered will vary with the spatial scale of the study, as well as with the propensity of the biotic group in question to speciate on islands (see McCall et al., 1996). The graphical and largely deterministic model presented here and the mathematical models of metapopulation biologists are both products of the scientific revolution canonized by MacArthur & Wilson’s (1967) theory (Harrison, 1991). Their theory replaced the static view of isolated communities with one based on the premise that insular community structure resulted from recurrent, rather than unique, immigrations and extinctions (see Dexter, 1978; Brown & Lomolino, 1998). These two approaches to modelling dynamic, isolated communities differ in some important respects: the model presented here is deterministic, while metapopulation approaches are primarily stochastic and equilibrial. The heuristic value of such models, however, is difficult to deny. Various metapopulation models now include spatially explicit approaches, multispecies models, and alternative (stochastic) explanations for patterns in species richness and species incidence (e.g. see Ebenhard, 1991; Hanski, 1992, 1994, 1997; Hanski et al., 1996; Wahlberg et al., 1996; Hanski & Gilpin, 1997; Hanski & Gyllenberg, 1997; Moilanen et al., 1998; Morrison, 1998). Therefore, despite the differences in these alternative approaches, they may both be viewed as valuable and complementary approaches derived from the same paradigm of dynamic island biogeography (i.e. MacArthur and Wilson’s model). In conclusion, the hierarchical, species-based model presented here appears to have high heuristic potential for understanding and, by extension, for conserving biological diversity of many isolated communities. The degree to which this potential is realized will strongly depend on our ability to conduct biogeographic surveys and other research focusing on the factors that most strongly influence the fundamental biogeographic processes — immigration, extinction and evolution. ACKNOWLEDGMENTS James H. Brown, Rob Channell, I. Hanski, Lawrence Heaney, Michael Kaspari, Michael Moulton, David Perault, Gregory A. Smith and © 2000 Blackwell Science Ltd, Global Ecology & Biogeography, 9, 39 – 58 GEB188.fm Page 57 Thursday, March 16, 2000 10:34 AM A species-based theory of insular zoogeography Chris Taylor provided valuable comments on the manuscript. 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