5 Competition and Coexistence of Mobile Animals

Ecological Studies Vol 161, page proofs as of Juli 29, 2002 5 Competition and Coexistence of Mobile Animals M. Ritchie 5.1 Introduction Competitive interactions among species lie at the foundation of our understanding of the structure and diversity of ecological communities. For the past century, various theoretical, laboratory and field studies have sought to understand how species that compete can coexist. Almost two decades ago, two influential reviews (Connell 1983; Schoener 1983) demonstrated that, at least in published studies, interspecific competition appears to be frequent. Just as importantly, these reviews found little evidence for competitive exclusion, that is, when one species completely eliminates another species when they occur together. In these reviews, competitive exclusion appeared especially rare for mobile animal species, as opposed to sedentary species such as inter-tidal organisms and vascular plants. Since 1983, competition theory has focused on identifying mechanisms to explain this “unexpected” prevalence of coexistence. In this chapter, I show that mobile animal species are highly likely to coexist because of their ability to move and make choices. These choices result in resource or habitat partitioning that allow exclusive use of resources, so that the structure of communities can be predicted largely in the absence of detailed knowledge of competitive dynamics. Because mobile animals move, their lives have an important feature: choice. Mobile animals can sample many aspects of their environment and thus have the ability to go to certain places and avoid others or to select certain patches or types of resources and ignore others. These choices may be constrained by particular physiological and morphological characteristics of the animals, so that differences among species in these characteristics can dictate differences in their choices. However, many of these choices are phenotypically or behaviorally plastic, or “adaptive” (Abrams 1988), and this plasticity allows individuals of a species to compensate in part to competition from other species. The possibility of choice also suggests that heterogeneity in distributions of resources and habitat plays a large role in competitive coexistence, because greater heterogeneity implies more available choices. Scale is a central factor F. Kröner, Heidelberg Ecological Studies, Vol. 161 U. Sommer, B. Worm (Eds.) Competition and Coexistence © Springer-Verlag Berlin Heidelberg 2003 Ecological Studies Vol 161, page proofs as of Juli 29, 2002 110 M. Ritchie affecting the importance of heterogeneity to choice, because the scale at which animals perceive the environment may influence the amount and heterogeneity of resources they detect (Ritchie 1998). If organisms perceive the environment at a large scale of resolution, they detect resources as being in a few large clusters, or as coarse-grained. If they perceive the environment at a small scale of resolution, they detect many fine-grained details and lots of very small clusters of resources. This idea dates back to “fitness sets” (Levins 1962), whereby animals that perceive the environment as fine-grained have many more available choices than animals that perceive it as coarse-grained. However, the importance of scale in affecting an organism’s grain, choices and perceived heterogeneity, and thus competitive coexistence, still is not widely appreciated or explored. Choice and scale differences among species yield the potential for coexistence, but the details of how they generate it are not agreed upon. Classical niche theory (MacArthur 1958; Levins 1968) assumed that differences among two species in the use of a spectrum of resource types, such as prey size or physical habitats, simply reduced the per capita competitive effects of the two species on each other. This translated into smaller competition coefficients in the classical Lotka-Volterra competition models. This made coexistence more likely, but certainly not assured. Schoener (1976), however, suggested that such differences in resource or habitat use among species allow exclusive resources. That is, each species has exclusive use of some resources that cannot be used by other species, in addition to the resources the two species share. If so, then the fundamental nature and outcome of competition is changed, and coexistence and equilibrium population densities become a function of the amount of a species’ exclusive resources relative to the amount of shared resources and the exclusive resources of other species. This idea has been largely ignored by ecologists, but has been found in several cases (Belovsky 1984, 1986; Chase 1996; Schmitz et al. 1997). If competition commonly occurs for shared and exclusive resources, then this provides a major new tool for a general understanding of competition. Competitive outcomes, and thus coexistence, are dictated by constraints on the amount of exclusive and shared resources for two species, and not by the detailed population dynamics of competition for shared resources. In this chapter, I review examples of the major mechanisms of competition among mobile animals and how these mechanisms contribute to competitive coexistence. These examples suggest that competition can and does occur among mobile animals, that coexistence is very likely, and that competition for shared and exclusive resources may be a major mechanism of coexistence. Furthermore, recent work suggests that a general understanding of competition via coexistence through exclusive resources will allow ecologists to address an old, but unresolved set of questions. These questions relate to understanding competition among multiple species, not just pairs of similar species, and how competition, together with predation, colonization, and local F. Kröner, Heidelberg Ecological Studies Vol 161, page proofs as of Juli 29, 2002 Competition and Coexistence of Mobile Animals 111 extinction contribute to community structure and diversity.A critical component of this understanding lies in linking choice with heterogeneity and grain, or the scale at which species respond to the environment. The most recent work suggests that this linkage generates exclusive resources and contributes significantly to coexistence among species. 5.2 Competition Among Mobile Animals Extensive field experimental studies (Connell 1983; Schoener 1983; Sih et al. 1985) suggest that, among species pairs of mobile animals that seem likely to compete, competition can be detected in 60–80 % of studies. Competition occurs in a variety of taxa, including terrestrial and aquatic insects (Belovsky 1986; Evans 1995; Wissinger et al. 1996), salamanders (Hairston 1981, 1986; Wilbur 1997; Brodman 1999), lizards (Losos and Spiller 1999; Petren and Case 1996, 1998), birds (Wiens 1992; Loeb and Hooper 1997) small (Heske et al. 1994; Rosenzweig and Abramsky 1997; Fasola and Canova 2000; Morris et al. 2000) and large mammals (Edwards et al. 1996), and fish (Werner and Hall 1979). Competition resulted in competitive exclusion of a species in very few cases. Generally, each species differs in some critical way that allows it to avoid competitive exclusion, even when competition is asymmetric, i.e., one species is strongly numerically dominant to the other. Among sedentary organisms, such as terrestrial plants and rocky intertidal organisms, species also differ considerably, but one species very often competitively excludes others. Why is coexistence much more prevalent among mobile animals? Although species excluded in previous competition may no longer be present in existing communities, and thus experiments are biased against detecting competitive exclusion, competition among existing mobile animal species appears much more likely to result in coexistence than is competition among sedentary organisms (Connell 1983; Schoener 1983). The early theory of competition (Lotka 1925; Volterra 1926; Gause 1934) readily showed that species could coexist if they each could not reach densities that would exclude the other. The common interpretation is that coexistence results when intraspecific competition limits a species’ density more strongly than interspecific competition. In Lotka-Volterra competition, the per capita effect of one species on another is constant, so coexistence is possible only if species’ effects on each other are weaker than their effects on themselves. Much later, Tilman (1982) showed that constant per capita competitive effects result when species use all available resources only at different rates. If species are limited by a single resource, such as silicon, nitrogen, or a food species (Chaps. 3, 4, Rothhaupt 1988), then the species that can persist on the lowest availability of that resource will competitively exclude the other. If species compete for two or more resources, coexistence becomes possible, but F. Kröner, Heidelberg Ecological Studies Vol 161, page proofs as of Juli 29, 2002 112 M. Ritchie only under a relatively narrow range of supply rates for the two types or resources. These models assume that resources are “well-mixed” in the environment and that both species use all available resources, only at different rates. Two decades of research of diets of mobile animals show that, for any given pair of species, each species uses some resources (prey types, seed sizes, plant parts, etc.) that the other cannot. Until the mid-1970s, the common interpretation was that competition coefficients were constant but low if species showed low overlap in resource use (MacArthur 1958; Levins 1968; Vandermeer 1972). However, Schoener (1976) noticed that, if some resources used by each species did not overlap, then species would not both use all available resources, only at different rates. Instead, some resources would be exclusively available to each species. In a series of mechanistic competition models, he showed that sufficiently abundant exclusive resources for each species could support at least a nominal density of each species regardless of the intensity of competition for shared resources, and thus virtually guarantee coexistence. Why do exclusive resources for each species lead to coexistence whereas constant per capita competitive effects yield it only under certain conditions? Simple isocline diagrams of competitive interactions illustrate this (Fig. 5.1). Classic Lotka-Volterra competition, in which per capita competitive effects are constant, yields linear isoclines (Fig. 5.1A), or combinations of the two species’ densities that lead to zero population growth for the two species. Coexistence occurs only under a restricted range of conditions, i.e., species’ carrying capacities and per capita competitive effects – which begged the question why coexistence was observed so often in the field (Hutchinson 1959). In laboratory experiments with fruit flies, Ayala et al. (1973) found that per capita competitive effects of one fruit fly species were weaker when the other species was at low density. These density-dependent, and thus not constant, per capita effects yield non-linear isoclines (Fig. 5.1B). Such effects allow coexistence to occur under a wider range of conditions, but competitive exclusion is still a likely possibility. If each species has some exclusive resources in addition to shared resources, then these exclusive resources can potentially maintain a certain density of each species that is unaffected by competition from other species, K'. Thus, interspecific competition cannot reduce a species’ density below K'. This minimum density ‘bends” the competitive isoclines for each species, so that they asymptote at the species’ density at K'. In this case, coexistence of the pair of species occurs under all carrying capacities greater than K' (Fig. 5.1C), and competitive exclusion is impossible as long as exclusive resources are sufficiently abundant that K' can be a viable population. There is circumstantial evidence for exclusive resources among animal species pairs in field data. First, literally hundreds of studies show that pairs of species do not overlap completely in diet, so that diet items used only by one species may constitute an exclusive resource. However, these “snapshots” of F. Kröner, Heidelberg Ecological Studies Vol 161, page proofs as of Juli 29, 2002 Competition and Coexistence of Mobile Animals 113 (B) Density-Dependent Competition Coefficients (A) Constant Competition Coefficients N2 N2 dN1/dt =0 dN1/dt =0 K2 K2 dN2/dt =0 K1 dN2/dt =0 K1 N1 N1 (C) Competition with Exclusive Resources N2 dN1/dt =0 K2 dN2/dt =0 K’2 K’1 K1 N1 Fig. 5.1A–C. Hypothetical diagrams of zero net growth isoclines for two competing species, with their respective equilibrium points. Isoclines represent combinations of the numbers of the two species (N1, N2) that lead to either zero population growth of species 1 (dN1/dt=0) or of species 2 (dN2/dt=0). A Isoclines reflect classic Lotka-Volterra competition in which species use the same resources but at different rates. B Isoclines reflect density-dependent competition in which the competitive effects of species 1 on species 2 weaken as species 2 becomes rarer, and vice versa, as observed in experiments with fruit flies (Ayala et al. 1973). C isoclines reflect exclusive resources for each species, following Schoener (1976). In this case, N1' and N2' individuals of species 1 and 2, respectively, can persist only on their exclusive resource diet overlap can be misleading, i.e., species may converge in diet toward the more productive resource type as competition intensifies (Abrams 1990; Ritchie and Tilman 1993) and diet overlap may change with species’ densities. Likewise, diets may diverge under more intense competition in other situations (Abrams 1990; Ritchie and Tilman 1993), implying that more resources are exclusively used and available under intense competition. Better evidence for exclusive resources comes from field experiments with herbivores. Among herbivores, species of different size may choose resource items of different size and quality because of a trade-off between greater F. Kröner, Heidelberg Ecological Studies Vol 161, page proofs as of Juli 29, 2002 114 M. Ritchie retention and digestion of low quality food in the digestive tract vs. higher metabolic rate, and thus resource requirements, for larger animals (Van Soest 1985; Belovsky 1986, 1997). Different-sized herbivore species therefore may partition plant parts (twigs, leaves, or parts of leaves) by their relative size and quality (protein, soluble carbohydrate, and secondary chemical content) in a way that generates unique sets of plant parts that are exclusively available to each species (Fig. 5.2A). Are there good examples of this trade-off generating the predicted exclusive resources and competitive coexistence? Moose (Alces alces) and snowshoe hare (Lepus canadensis) in the boreal forest on Isle Royale, Michigan, USA, use exclusive sets of woody twigs during winter (Belovsky 1984) (Fig. 5.2B). Moose require large twigs, but these can be of low quality (protein content). Hares used smaller twigs than moose, but these were of higher quality than those required by moose. Furthermore, moose have access to twigs growing higher aboveground than hares can reach, which provides them with additional exclusive resources. Belovsky empirically derived competitive isoclines for each species (Fig. 5.2C) that strongly resemble those expected from theory (Fig. 5.1C) and fit the curve shape expected from Schoener’s (1976) model of competition for shared and exclusive resources better than the line expected from a Lotka-Volterra model. The snowshoe hare isocline is generated from islands with hare but no moose and islands with moose at lower than expected densities because of their difficulty in colonizing islands. The moose isocline is generated from islands with moose but no hare, and sites on the main island with different densities of hare. The expected equilibrium densities from the fitted curves matches closely the average twig utilization of moose and hare on the main island, and these densities closely correspond with the densities that are apparently supported by their respective exclusive resources. Similar trade-offs and competitive dynamics were found for two competing grasshopper species in Montana grassland (Belovsky 1986) with experimental manipulation of densities in field cages (Fig. 5.2D). The isocline for each species (target) was determined by placing the same number of the target species in the cage initially and maintaining the other species’ density at different levels in different replicates and allowing populations inside cages to decline to a constant density over the next 45 days. The amount of available exclusive and shared resources was not measured, but the larger of the two grasshopper species, the migratory grasshopper Melanoplus sanguinipes (0.45 g), used larger leaves of lower dry-matter digestibility than the smaller species, the red-legged grasshopper M. femurrubrum (0.25 g). The red-legged grasshopper used smaller leaves of higher dry-matter digestibility than those used by the migratory grasshoppers. Similar exclusive resources and asymptotic isoclines also were found in another study of competition in grasshoppers between a grass-feeding specialist and mixed feeder on both grasses and forbs (Chase 1996). These few experiments are intriguing, but new experiF. Kröner, Heidelberg Ecological Studies Vol 161, page proofs as of Juli 29, 2002 Competition and Coexistence of Mobile Animals 115 (B) Moose and Snowshoe Hare (A) Theory Shared Q*S Q*L Exclusive to Large B*S B*L % Mineral + Protein Quality Exclusive to Small 20 15 10 5 Exclusive to Moose 0 0 Bite Size 1 Moose 8 6 4 2 0 0 5 10 15 20 3 4 5 6 7 (D) Grasshopper Isoclines #Migratory Grasshoppers # Twigs Removed by Hare Hare 10 2 Twig Diameter (mm) (C) Moose and Snowshoe Hare Isoclines 12 Shared Exclusive to Hare 25 # Twigs Removed by Moose Red-Legged Isocline 6 Migratory Isocline 5 4 3 2 1 0 0 1 2 3 4 5 6 # Red-Legged Grasshoppers Fig. 5.2A–D. Examples of the application of competition for exclusive resources to generalist herbivores. A Hypothetical diagram (redrawn from Belovsky 1986, 1997) of minimum plant quality (QS*, QL*) and bite sizes (BS*, BL*) for small (S) and large (L) herbivores. Bite size (B*) is the minimum acceptable item size accepted by an herbivore species. Trade-offs in these minimum thresholds lead to exclusive resources for each species. B Observed minimum acceptable twig quality (mineral + protein content) and twig bite size (diameter, mm) for moose and snowshoe hare relative to maximum twig quality and size in the environment at Isle Royale National Park, Michigan, USA (redrawn from Belovsky 1984). Note the much larger exclusive resource for moose and the decline in maximum quality of shared twigs with increasing twig size (twigs decline in quality as they get thicker and more woody). C Empirically derived competitive isoclines for moose and snowshoe hare (Belovsky 1984), assuming that the density of twigs eaten by snowshoe hare (45° cut) and moose (shredded cut) are proportional to population density. D Experimentally determined isoclines and expected equilibrium point for two competing grasshopper species in replicate field cages in Montana grassland (redrawn from Belovsky 1986) F. Kröner, Heidelberg Ecological Studies Vol 161, page proofs as of Juli 29, 2002 116 M. Ritchie mental tests with other taxa and trophic positions are needed to explore the generality of competition for exclusive resources. The average twig utilization levels for both moose and hare and the observed densities of the two grasshopper species are near the values predicted from each species’ calculated exclusive resource. This occurs because intense competition for shared resources quickly reduces each species’ population densities to their respective K’. Thus, densities approach those that can be supported by only exclusive resources, despite the fact that the pairs of species are competing for some shared resources. Habitat segregation is another important mechanism of avoiding competition that can generate exclusive resources and robust conditions for species coexistence. Habitat selection is often density-dependent (Fretwell 1972; Morris et al. 2000), so that, when a species is at sufficiently high densities, individuals may be forced to use a less-preferred habitat and face competition from another species. Theoretically, such habitat shifts generate non-linear competitive isoclines with a perpendicular intersection, implying weak competition near equilibrium (Fig. 5.3). As shown with Rosenzweig’s (1981) “isoleg” model, the “flattening” of isoclines, even over just a range of competitor densities, can make species coexistence likely. The isolegs reveal densities at which each species find it profitable to occupy their less preferred habitat The isoclines are flattened, or perpendicular, when two species, N1 and N2, are at densities in the region between the isolegs. The species are able to use only their different preferred habitats and avoid competition. At a high density of species 1, N1>>N2 (below the isolegs), species 1 will also use shrubland in addition to grassland and therefore compete with species 2, yielding linear isoclines. Likewise, when species 2 is very abundant N2>>N1 (above the isolegs), it will use grassland habitat, compete with species 1 and yield linear isoclines. Exclusive habitat use among species can arise from trade-offs in their risk of predation, food patch size and quality, or different abiotic conditions among different habitats. The best examples of this come from granivorous rodent communities in the Middle East (Brown et al. 1994; Rosenzweig and Abramsky 1997; Garb et al. 2000) and southwestern United States (Brown et al. 1979; Heske et al. 1994). Although most experiments and other studies of competition have not searched specifically for exclusive resources, the prevalence of coexistence, and differentiation among species in size, diet, habitat selection, and predation risk constitute a strong fingerprint of exclusive resources. More importantly, exclusive resources imply that trade-offs in species traits do more than just allow them to use resources at different rates. Instead, trade-offs generate access to resources and spaces that make coexistence a probable, rather than unusual, outcome of competition. If so, the detailed dynamics and full set of parameters governing competition may be largely irrelevant to understanding competitive outcomes. Perhaps the most important thing to know about two competing species is what determines their respective sets of exclusive F. Kröner, Heidelberg Ecological Studies Vol 161, page proofs as of Juli 29, 2002 Competition and Coexistence of Mobile Animals 117 Competition with Habitat Segregation Sp. 2 Uses Grass&Shrubs Species 2 Species 1 N2 dN2/dt = 0 Habitat Preferences Sp. 2 Uses Shrubs Sp. 1 Uses Grass Isolegs K2 Sp. 1 Uses Shrubs&Grass dN1/dt = 0 Grassland Shrubland K1 N1 Fig. 5.3. Hypothetical example of Rosenzweig’s isoleg model for two small mammal species (densities N1, N2) with density-dependent habitat selection. In this case, species 1 prefers grassland, while species 2 prefers shrubland. At density combinations, given by the two increasing dashed lines (isolegs), where a species’ own density is low enough and/or competitor density is high enough, a species will select completely for its preferred habitat. When both species do this (the region between the isolegs), the isoclines for each species (dN1/dt=0, dN2/dt=0) flatten, so that each species is effectively using exclusive resources and coexistence is assured resources. Rather than measuring per capita competitive effects, measuring the abundance of exclusive resources and how they are converted into population size K' may be more useful. Such measurements would require identifying the important morphological and physiological traits of species that determine exclusive resources. Ecologists ultimately wish to understand coexistence in whole communities, that is, among multiple species.While specific species pairs warrant more detailed study of their competitive dynamics, a general understanding of coexistence will probably come from relating competitive outcomes to traits of multiple species. Resources that are exclusive when a pair of species competes might not be exclusive when multiple species compete. Consequently, there is an increased need to understand competition in terms of exclusive resources, and the multi-species trade-offs that generate them (Grime 1979; Tilman 1990). If there are general patterns in the form of those trade-offs, then coexistence models that ignore the detailed dynamics of species and focus on the constraints on species’ exclusive resources may provide a powerful tool for understanding how competitive interactions structure communities and limit species diversity. F. Kröner, Heidelberg Ecological Studies Vol 161, page proofs as of Juli 29, 2002 118 M. Ritchie 5.3 Heterogeneity, Trade-Offs and Competition Trade-offs between food quantity and quality, food abundance and predation risk, or food and abiotic conditions may generally constrain competitive interactions among mobile animals, just as trade-offs in resource use and colonization ability may define plant competition (Tilman 1994; Chaps. 2, 3, 7). Why would the trade-offs be different for mobile vs sedentary animals? What factors constrain these trade-offs? To answer these questions, we must return again to issues of choice and scale. For animals to have choices in food and habitat, and for species to differ in their choices, there must be heterogeneity in food types (size, nutrition, ease of handling etc.) and habitat (patch size, resource density). Heterogeneity in food size, patch size, or habitat patch size is especially critical if competing species share a common resource type. One species cannot choose large food patches or safe habitats if there is no variation in food patch size or habitat safety. Such heterogeneity must exist in either space or time. Heterogeneity in space is particularly important for mobile animals, since they encounter potentially many food patches and habitat types in their movements, if such things vary across space. Traditional competition models, such as Lotka-Volterra, assume, either explicitly or implicitly, that resources are uniformly or randomly distributed. In this case, resource density is not scale-dependent. There is thus no variation in resource density, food patch size, or habitat among which different species can choose. Consequently, competition is determined by the different rates at which species consume resources, leading to the classic resourcebased models of Tilman (1976, 1982) and Huisman et al. (1999) (see Chaps. 2, 3). If resources, food, or habitats are heterogeneous, then even species competing for a single limiting resource have the opportunity, through choices, to select different-sized clusters of resources or habitat. The importance of heterogeneity and size in influencing coexistence is illustrated nicely in a field experiment with generalist grasshoppers in a Minnesota old-field prairie (Ritchie and Tilman 1992). This experiment showed how the outcome of competition changed in association with heterogeneity in plant food quality. For June (early) grass-feeding grasshopper species, the smaller (0.5 g) speckle-winged grasshopper Arphia conspersa and the larger (1 g) red-winged grasshopper Pardalophora apiculata competed strongly when placed at high density in field cages. The speckle-winged grasshopper competitively excluded the red-winged (5.4A), as predicted by their ability to reduce grass biomass to a lower level than the red-winged grasshopper (Fig. 5.4B). In this case, the diets of the two species contained about 80 % of the grass Poa pratensis whether alone or in competition. These results are highly consistent with the competitive exclusion of red-winged by speckle-winged grasshoppers expected if both species reduced a completely shared single resource but at different rates. F. Kröner, Heidelberg Ecological Studies Vol 161, page proofs as of Juli 29, 2002 Competition and Coexistence of Mobile Animals 119 (A) Early Season (C) Late Season CV[N] = 0.16 CV[N] = 0.51 Speckle-winged Red-winged 25 12 10 2 15 #/m 2 20 #/m Red-Legged Two-Striped 14 10 8 6 4 5 2 0 0 Alone (B) Early Grass Biomass 35 60 Biomass (g/m2) Biomass (g/m2) 40 Alone Together 30 25 20 15 10 5 Fig. 5 0 SpeckleWinged Redwinged Together Empty Together (D) Late Forb Biomass 50 40 30 20 10 0 RedLegged TwoStriped Together Empty Fig. 5.4A–D. Examples of competition among grasshopper species in June (early) and August late in 0.36 m2 field cages (Ritchie and Tilman 1992). A Competitive exclusion of the red-winged grasshopper by the speckle-winged grasshopper (mean ± SE densities after 30 days in cages). B Mean (±) biomass of grasses (mainly Poa pratensis and Schizachyrium scoparium) with different combinations of grasshopper species and without grasshoppers, showing the reduction in grass biomass by grasshoppers and the greater reduction in grass biomass by the speckle-winged grasshopper. C Competitive coexistence of the red-legged and two-striped grasshoppers, based on mean (±SE) densities after 30 days in cages. D Effects of grasshoppers on forb biomass (mean + SE), showing about equal reduction of forb biomass by both species In contrast, in August (late), the smaller (0.3 g) forb-feeding red-legged grasshopper Melanoplus femurrubrum competed with but coexisted with the larger (0.85 g) two-striped grasshopper M. bivittatus (Fig. 5.4C). This occurred despite the fact that both species dramatically reduced forb biomass by 75 %, and the red-legged grasshopper reduced it to a slightly lower level than the two-striped grasshopper (Fig. 5.4D). Interestingly, the coefficient of variation (C.V.) among different forb species in tissue N, a nutrient commonly limiting to herbivores, was much higher in August than the C.V. of N in grasses in June. In addition, both species consumed 75 % of their diet as forbs when alone, but in competition, individual red-legged grasshoppers increased the proportion of forbs in their diet to 95 %, while two-striped grasshoppers decreased the proportion of forbs and increased the proportion of grasses F. Kröner, Heidelberg Ecological Studies Vol 161, page proofs as of Juli 29, 2002 120 M. Ritchie diet to 50 %. These results are consistent with a hypothesis that the late-season grasshopper species were able to partition a heterogeneous distribution of N among grasses and forbs. Furthermore, the larger species selected resource with lower N content (grasses) in response to competition, while the smaller species selected the resource with higher N content (forbs) more strongly. It was not determined in the study whether these diet shifts led to the use of exclusive resources. However, these results, coupled with previous results (Belovsky 1986, 1997; Chase 1996) for grasshoppers, provide circumstantial evidence for the role of heterogeneity in generating exclusive resources and competitive coexistence. More detailed experimental tests need to be performed in other systems and taxa to determine the generality of these results and the role of exclusive resources in competition. 5.4 Scale and Heterogeneity Heterogeneity is scale-dependent, but ecologists seldom recognize this (Wiens 1995). One species, which detects variation at a very small scale of resolution or “grain”, finds many choices. Another species, which detects variation at a very large scale, may find the environment to be very homogeneous because the species averages across the detailed variation detected by the smaller-scaled species (Fig. 5.5). For example, humans might find a stretch of beach sand to be very homogeneous because their scale of detection averages across literally billions of sand grains.A sand flea, on the other hand, may find tremendous variation in the density of algae from one clump of sand grains to another, and thus find the beach to be very heterogeneous. Size is a critical species characteristic that may influence the scale of resolution with which animals perceive the environment, as seen in the size difference between a human and a sand flea. It thus seems likely that body size, which is often different among coexisting species, influences how much heterogeneity is detected and therefore what choices are available to a species. Thinking explicitly about heterogeneity and size opens the door for incorporating size into predictions about competitive outcomes. Coupling organism scale with heterogeneity means that consumer choices of different resource cluster size, as constrained by size or morphology, reflect different scales of resolution. Larger-scaled species may only select resource clusters that exceed a certain density, so that small resource clusters are effectively ignored (Fig. 5.5). This is a restatement of optimal foraging theory from a resource distribution and scale perspective (Ritchie 1998). For non-randomly moving foragers attempting to maximize their encounter with resources, smaller-scaled species should experience a higher average resource density per patch (volume sampled) and greater numbers of acceptable resource patches. Larger species encounter fewer acceptable patches, which F. Kröner, Heidelberg Ecological Studies Vol 161, page proofs as of Juli 29, 2002 Competition and Coexistence of Mobile Animals 121 D = 1.64 Grain = 5 160 Patches Density = 0.18 Grain = 20 74 Patches Density = 0.12 Grain = 40 25 Patches Density = 0.08 Fig. 5.5. Hypothetical landscapes (fractal dimension D=1.64) illustrating the reduction in perceived resource density and increase in average resource patch size with increasing scale of perception, or “grain,” of foraging animals (bold circles). Smaller-grained species detect all small resource patches and perceive large patches as conglomerates of small patches. They thus perceive a high density (fraction of landscape occupied) of resources but a low average resource patch size. Larger-grained species ignore the isolated small patches (colored gray when ignored), thus perceiving a lower overall density of resources but a greater average patch size of resources. Note how the density of resources within the spatial unit of resolution (circles, radius=grain) centered on resource-occupied space, decreases as the size of the spatial unit increases. Thus, any given “patch,” though larger on average, will decline in resource concentration as a forager’s grain size increases. (Ritchie 1998) contain absolutely more resources per patch (volume sampled), but the resources occur at a lower density per unit volume sampled. If large and small species search the same number of patches per unit time, then the larger species also samples a greater total volume per unit time. These mathematical outcomes predict that species measure different quantities of a single resource by virtue of their different scales, and may thus differ in the rate of consumption of resources. Clearly, however, trade-offs in number, resource density and size of resource patches encountered or accepted, as well as search rate, suggest that differences in foraging scale among species provide some potential for coexistence. Recently, Wilson et al. (1999) has found that two marine snail species (Tegula sp.) have different foraging strategies: (1) “diggers,” with a small scale of resolution, reduce resource densities within patches to a lower level (smaller minimum resource cluster size, and (2) “grazers,” with a larger foraging scale, leave patches with a higher remaining resource density but have a higher search rate, i.e., sample more patches per unit time, than diggers. These alternative strategies, which trade-off patch size selectivity with mobility and search rate, contribute to the species’ coexistence in the field. Consequently, size differences among species and non-uniform or non-random (heterogeF. Kröner, Heidelberg Ecological Studies Vol 161, page proofs as of Juli 29, 2002 122 M. Ritchie neous) distributions of resources and habitat allow species to differ in their choices in ways that contribute to competitive coexistence. Other traits besides size, per se, may determine a species’ grain or scale of perception, such as activity range, and sensory system. For example, a terrestrial herbivorous snail is unlikely to perceive the environment at the same scale of resolution as a more mobile grasshopper even though they are of similar body length and potentially consume the same food. Likewise, snakes, which rely on olfactory perception to hunt small mammal prey, may perceive the environment at a much smaller scale of resolution than raptors, which fly and use vision to hunt similar prey (Capizzi and Luiseli 1996). Although the idea of differences in grain size among species is not new (Hutchinson and MacArthur 1959; Levins 1962), few data have been collected to test it. Recent studies suggest that species behaviorally alter their scale of resolution, or minimum food density within a patch, in response to resource density and distribution (Morgan et al. 1997; Ritchie 1998; Kotler and Brown 1999) in a manner predicted by optimal foraging theory. For example, Morgan et al. (1997) measured “giving up densities”, or GUDs, the density of seeds within a feeding patch at which a forager will “give up” and move to another patch, for fox squirrels (Sciurus niger). They found that squirrels applied a single GUD, or minimum food patch size, when food patch density varied in a fine-grained manner (among feeding trays), as predicted by classical optimal foraging theory (Charnov 1976).When food density varied at a large spatial scale (all trays among different forest patches), squirrels varied their GUD according to the food density at each site, with squirrels at the high food density site giving up on patches at higher food densities than those at low food density sites. Therefore, species may differ morphologically, physiologically, and behaviorally in ways that lead to differences in their grain or scale of perception and that potentially allow competitive coexistence. The issue of scale and heterogeneity becomes even more important when one considers that many resource, food, and habitat distributions in nature are approximately fractal. Fractal objects include the familiar Koch snowflakes and Cantor sets of popular books (Mandelbrot 1982; Barnsley 1988) that repeat a particular geometric shape at ever-larger spatial scales, such that it is impossible to determine what scale an image is being observed. Distributions are also fractal if they are statistically self-similar, that is, have the same statistical pattern of distribution across a range of scales of observation. In ecology, the resource distributions that affect competitive interactions occur are typically evaluated across at least two to three orders of magnitude in scale of observation. The measured quantities of fractal distributions are scale-dependent: more of the quantity is detected when measured with a finer scale of resolution (grain) (Fig. 5.6; Milne 1992; Milne et al. 1992; Ritchie 1998). Some recent work (Palmer 1992; Milne et al. 1992; Brown 1995; Ritchie 1998; Ritchie and Olff 1999) suggests that fractal geometry may provide a new F. Kröner, Heidelberg Ecological Studies Vol 161, page proofs as of Juli 29, 2002 Competition and Coexistence of Mobile Animals (A) (B) Log (#pixels, M) D=1.98 c= 0.19 D=1.37 c= 0.72 (C) 5 Random Fractal 4 3 2 M = cxD 1 0 -1 0 1 Log (x) 2 3 123 Fig. 5.6. Hypothetical resource distributions (dark areas) with identical density (15 % of landscape occupied), A random, B fractal. The fractal nature of distribution B is demonstrated in C by a plot of average number of occupied (dark) pixels within windows of length x surrounding occupied pixels (the sliding window method of Milne 1997). Distribution B shows a constant slope across two orders of magnitude in scale, but this slope, equal to the fractal dimension D, is less than 2, which is the slope of a similar plot for the random distribution A. The intercept at log(x)=0, x=1, is higher for the fractal distribution because occupied pixels in the fractal distribution are much more likely to have adjacent pixels occupied than those in the random distribution. If a distribution is fractal, then its quantity (M) can be described with the simple power law M=cxD where c is a prefactor that is proportional to both density and clustering framework for thinking about community structure and competitive coexistence. This framework incorporates two major factors, heterogeneity and scale, that influence mobile organisms. Fractal geometry can be used to describe complex, heterogeneous distributions of resources in space (Fig. 5.6). A species’ scale of perception influences its use of habitat and resources within this complex habitat. Thresholds of resource cluster size that different species use can generate exclusive resources available to multiple competing species. These choices of different cluster size, as constrained by size or morphology, reflect different scales of resolution, and influence the resource density detected by each (Fig. 5.5). These exclusive resources can define conditions for species’ persistence, regardless of the details of competitive dynamics, carrying capacities, and rates of resource consumption. In this way, the role of competition in structuring a community is applied across all species rather than particular pairs. As an example of this approach, Han Olff and I developed a model to predict the coexistence and abundance of species of different body size within communities that share a common resource (Ritchie and Olff 1999). These resources, however, were assumed to be contained in some other material we called food. We assumed that different-sized species perceived resources, F. Kröner, Heidelberg Ecological Studies Vol 161, page proofs as of Juli 29, 2002 124 M. Ritchie food-containing resources, and habitat at grains (scale of resolution) proportional to their body size. These different perceptions led to a predicted tradeoff: larger species require larger food patches but can tolerate lower resource concentrations within food, while smaller species can tolerate smaller food patch sizes but these must be of higher resource concentration. This trade-off emerges from the fundamental nature of scale-dependent foraging (Fig. 5.5) and generates exclusive resources for species of different size: each species has a unique set of food patches of a particular size and resource concentration (Fig. 5.7). Regardless of competitive dynamics with any of the other species, a given species can persist in a community if its exclusive resources are sufficiently available. Persistence thus depends on how far apart competing species are in size. Thus, species diversity and community structure can be predicted by calculating how many species can be “packed” into an environment (sensu MacArthur 1969). a Patch Size(P) Pmax P* T R* Rmax Resource Concentration(R) b log(R) log(P) P* R* Patch Size(P) c log(Scale) Tk Rk* Rj* Ri* Exclusive Niches Pk * Pj * Tj Pi* Ti Resource Concentration(R) F. Kröner, Heidelberg Fig. 5.7a–c. Graphic representation of the model of minimum acceptable food patch size (P) (food density per sampling volume) and resource concentration (R) for species with different foraging scale (grain) (Ritchie and Olff 1999). a Any given forager can match resource losses by consuming a minimum required resource amount. This requirement can be met by consuming large food patches that are low in resource concentration or small food patches that are high in resource concentration (trade-off curve T). If the forager simultaneously minimizes food patch size and resource concentration (R*, P*) along this tradeoff curve to avoid competition, then it will use all patches that exceed these minima in size and resource concentration. b The R*, P* for each species change in opposite directions with increasing foraging scale (grain) indicating a trade-off between food patch size and resource concentration for species of different body size. c Because of this trade-off, species of different size, and presumably different foraging scale (grain) have unique R*, P* values that give them an exclusive niche, that is, access to food patches of a particular size and resource concentration (shaded areas). These exclusive niches (species k, hatching; species j, shaded; species i, waves ) emerge because the trade-off curves for ever larger species occur ever farther from the origin. Intermediately sized species j coexists if its exclusive niche is sufficiently large, or if it sufficiently separated in size from species i and k Ecological Studies Vol 161, page proofs as of Juli 29, 2002 Competition and Coexistence of Mobile Animals 125 The model predicts patterns of body size ratios in communities, the distribution of diversity vs. body size, diversity-productivity relationships, speciesarea relationships and the effect of habitat fragmentation on diversity. For example, the model predicts left-skewed distributions of diversity vs. size (Fig. 5.8) for guilds, or species using the same resource type, that contrast with log-normal or even right-skewed distributions normally reported for regional or continental faunas in the literature. This left-skewed distribution arises from the fact that small food patches with high resource concentrations are statistically rare if both food and resources have a fractal distribution. This forces smaller species to be separated more in size than larger species. This prediction agrees surprisingly well with observed patterns of species diversity vs size for different guilds (Fig. 5.8). The other predictions about diversity-productivity, diversity-fragmentation and species-area relationships also # Species a ln(Size) Chihuahuan Desert Vertebrate Granivores b # Species 6 5 4 3 2 1 0 4 4.25 4.5 4.75 5 ln(Length(mm)) c # Species 6 5 Great Basin Vascular Plants 4 3 2 1 0 0 .5 1 1.5 2 2.5 3 ln(Crown Width(cm)) F. Kröner, Heidelberg 3.5 4 Fig. 5.8a–c. Size structure of locally coexisting guilds of species (those consuming the same resource) from the scale-dependent patch size and resource concentration model (Fig. 5.7). a Prediction, showing a strong left-skewed distribution in the number of species in different body size classes. b, c Observed diversity vs. size distributions for selected guilds from b body lengths for desert granivores (Brown and Davidson 1977; Brown et al. 1979; Davidson et al. 1980, 1985) and c average crown widths for herbaceous and woody plants from a sagebrush community in northern Utah (Ritchie, unpubl. data). For other similar patterns (not shown) for folivorous vertebrate herbivores from the Serengeti, East Africa and herbaceous plants in a Minnesota (USA) oak savanna, see Ritchie and Olff (1999) Ecological Studies Vol 161, page proofs as of Juli 29, 2002 126 M. Ritchie agree surprisingly well with observed data for species guilds (Ritchie and Olff 1999; Olff and Ritchie 2001). Other models that generate trade-offs and constraints on exclusive resources can make similar predictions. For example, Belovsky (1997; Fig. 5.2) derived trade-offs between food intake rate and digestive turnover rate with body size for herbivores to yield exclusive resources in competition. Tradeoffs between food patch size vs within-patch resource concentration may exist within granivorous rodent communities (Kotler and Brown 1999), as they did for marine snails (Wilson et al. 1999). In field tests in the Negev Desert, large gerbils (Gerbillus sp.) left patches (higher GUDs) with more seeds remaining than smaller gerbils, suggesting that larger foragers select only large seed patches and thus perceive the environment in a more coarsegrained manner than smaller rodents. These GUDs directly correspond to a minimum seed consumption rate, and thus could conceivably be used to calculate a minimum size similarity and community structure for a guild of granivorous species (Brown et al. 1994; Garb et al. 2000). 5.5 New Challenges A quarter century of field experiments shows that mobile animal species do compete, but not at all points in space and time, and that diet (resource) and habitat separation are major mechanisms of coexistence among pairs of species. Circumstantial evidence and a small number of experimental tests suggest that many pairs of species may have exclusive resources, and such resources effectively prevent competitive exclusion. This firming up of the existence and importance of competition places us back at the same intellectual forefront ecologists faced in the early 1970s. The question remains: how do the competitive interactions among species, when they are important, structure ecological communities? This question effectively refocuses attention on mechanistic community ecology, in that ecologists must determine how individual species traits influence their competitive dynamics with other species. Despite two decades of experimental studies of species interactions, predation, and indirect interactions (Wootton 1994; Schmitz et al. 2000) relatively little progress has been made in predicting community structure from species’ traits, particularly of mobile animals. Understanding coexistence among mobile species presents an array of challenges that have never been resolved despite the issue’s popularity in the 1960s and 1970s. The first challenge is deriving quantitative predictions of community structure from competitive and other species interactions. Despite well over a century of exploration of major patterns in species abundance, size structure, and diversity within ecological communities, the theory of community ecology remains fragmented and poorly able to explain these patterns in a unified F. Kröner, Heidelberg Ecological Studies Vol 161, page proofs as of Juli 29, 2002 Competition and Coexistence of Mobile Animals 127 way. Spatial scaling may be a critical axis of niche differentiation that contributes to exclusive resources and coexistence. If so, using fractal geometry to generate scale-dependent models of species coexistence (Palmer 1992; Milne et al. 1992; Brown 1995; Ritchie and Olff 1999) is a first step towards linking exploitative competition with community ecology. The ability of scale-dependent models to predict community-level patterns from first principles suggests new avenues of empirical research that explore patterns and experimentally test for relationships between body size differences among species, trade-offs in resource use, exclusive resources, and the diversity and abundance of multiple species in communities. The models resulting from this scaling approach should help ecologists more fully understand the role of spatial heterogeneity in influencing community structure and species diversity. More generally, ecologists need to expand the concept of “choice” to dispersal of sedentary organisms in space (Tilman 1994) and foraging of roots and leaves (Campbell et al. 1991). They also need to better understand the magnitude of temporal variation in resources. This will require matching life history scaling laws (Charnov 1993) with temporal dynamics of resources (Chesson 1994) and raises the possibility of temporal scales of resolution as axes for coexistence. Thinking of organism scale, whether spatial or temporal, in ways not related to body size, as I discussed earlier, may provide powerful new insights. Most of the attention in this chapter has focused on how species partition resources in ways that affect their resource intake rates. However, these choices can affect their loss rates of resources as well. Predation may vary in space, and prey species may modify their choices in habitats with high predation risk in order to balance the gain in fitness from resource consumption with the loss in fitness from predation. For example, foragers often increase their food GUD in riskier habitats because the higher rate of resource return from high within-patch food density is needed to balance the greater expected mortality rate from predation (Sih et al. 1985; Kotler and Brown 1999; Schmitz et al. 1997, 2000). In light of Morgan et al.’s (1997) results for fox squirrels, predation risk may influence habitat and food patch choice at different spatial scales, and may do so differently for larger vs smaller species that differ in their inherent predation risk. This area of research needs more explicitly developed hypotheses and experimental tests by comparing resource patch selection under conditions with high vs low predation risk. Similar types of trade-offs may also exist between varying abiotic conditions and food or resource patch size (Ritchie 2000). Although competition is but one species interaction that affects community structure, a new theory of community structure that incorporates scale, heterogeneity and the concept of exclusive resources should spark many new experiments and increased understanding of the simultaneous coexistence of multiple species. At the least, coexistence should not be seen as an anomaly, F. Kröner, Heidelberg Ecological Studies Vol 161, page proofs as of Juli 29, 2002 128 M. Ritchie and the question: “Why are there this many species?” should replace “Why are there so many species?” This new understanding could greatly help in conserving biodiversity. Such theory could predict which species and communities are most vulnerable to habitat loss and fragmentation (Olff and Ritchie 2001), which communities might be most easily invaded (Leibold 1996), and the necessary conditions for restored habitats to support high levels of diversity. Successful predictions of this sort would further the development of a comprehensive synthetic theory of biodiversity and rejuvenate efforts to conserve diversity worldwide. The multitude of diversity patterns at all spatial and temporal scales of data collection and observation may ultimately be unified as a single body of knowledge. Together with appropriate neutral models, and mechanisms such as predation, colonization, extinction and biogeographic history, the role of competition in species coexistence should once again be recognized and used to help understand controls on biodiversity. Acknowledgements. I thank the editors, Sebastian Diehl, Han Olff, Joel Brown, and an anonymous reviewer for comments on various aspects of the manuscript. My own work reported in this chapter was supported by the US National Science Foundation, the Utah State University Ecology Center and Utah Agriculture Experiment Station. References Abrams PA (1988) Resource productivity-consumer species diversity: simple models of competition in spatially heterogeneous environments. Ecology 69:1418–1433 Abrams PA (1990) Adaptive responses of generalist herbivores to competition: convergence or divergence. Evol Ecol 4:103–114 Ayala FJ, Gilpin ME, Ehrenfeld JG (1973) Competition between species: theoretical models and experimental tests. Theor Popul Biol 4:331–356 Barnsley M (1988) Fractals everywhere. Academic Press, New York Belovsky GE (1984) Moose and snowshoe hare competition and a mechanistic explanation from foraging theory. Oecologia 61:150–159 Belovsky GE (1986) Generalist herbivore foraging and its role in competitive interactions. Am Zool 26:51–69 Belovsky GE (1997) Optimal foraging and community structure: the allometry of herbivore food selection and competition. Evol Ecol 11:641–672 Brodman R (1999) Food and space dependent effects during the interactions of two species of larval salamanders. J Freshwater Ecol 14:431–438 Brown JH (1995) Macroecology. University of Chicago Press, Chicago Brown JH, Davidson DW (1977) Competition between seed-eating rodents and ants in desert ecosystems. Science 196:880–882 Brown JH, Davidson DW, Reichman OJ (1979) An experimental study of competition between seed-eating desert rodents and ants. Am Zool 19:1129–1143 Brown JS, Kotler BP, Mitchell WM (1994) Foraging theory, patch use, and the structure of a Negev Desert granivore community. Ecology 75:2286–2300 F. Kröner, Heidelberg Ecological Studies Vol 161, page proofs as of Juli 29, 2002 Competition and Coexistence of Mobile Animals 129 Campbell BD, Grime JP, Mackey JML (1991) A trade-off between scale and precision in resource foraging. Oecologia 87:532–538 Capizzi D, Luiseli L (1996) Feeding relationships and competitive interactions between phylogenetically unrelated predators (owls and snakes). Acta Oecol 17:265–284 Charnov EL (1976) Optimal foraging, the marginal value theorem. Theor Popul Biol 9:129–136Chase JM (1996) Differential competitive interactions and the included niche: an experimental test with grasshoppers. Oikos 76:103–112 Chesson P (1994) Multi-species competition in variable environments. Theor Popul Biol 45:227–276 Connell JH (1983) On the prevalence and relative importance of interspecific competition: evidence from field experiments. Am Nat 122:661–696 Davidson DW, Brown JH, Inouye RS (1980) Competition and the structure of granivore communities. Bioscience 30:233–238 Davidson DW, Samson DA, Inouye RS (1985) Granivory in the Chihuahuan desert: interactions within and between trophic levels. Ecology 66:486–502 Edwards GP, Croft DB, Dawson TJ (1996) Competition between red kangaroos (Macropus rufus) and sheep (Ovis aries) in the arid rangelands of Australia. Aust J Ecol 21:165–172 Evans EW (1995) Interactions among grasshoppers (Orthoptera: Acrididae) in intermountain grassland of western North America. Oikos 73:73–78 Fasola M, Caova L (2000) Asymmetrical competition between the bank vole and the wood mouse, a removal experiment. Acta Theriol 45:353–365 Fretwell SD (1972) Populations in a seasonal environment. Princeton University Press, Princeton Garb J, Kotler BP, Brown JS (2000) Foraging and community consequences of seed size for coexisting Negev Desert granivores. Oikos 88:291–300 Gause GF (1934) The struggle for existence. Hafner, New York Grime JP (1979) Plant strategies and vegetation processes. Wiley, Chichester Hairston NG (1981) An experimental test of a guild: salamander competition. Ecology 62:65–72 Hairston NG (1986) Species packing in Desmognathus salamanders: experimental demonstration of predation and competition. Am Nat 127:266–291 Heske EJ, Brown JH, Mistry S (1994) Long-term experimental study of a Chihuahuan Desert rodent community: 13 years of competition. Ecology 75:438–445 Huisman J, Jonker RR, Zonneveld C, Weissing FJ (1999) Competition for light between phytoplankton species: experimental tests of mechanistic theory. Ecology 80:211–222 Hutchinson GE (1959) Homage to Santa Rosalia: or why are there so many kinds of animals? Am Nat 93:145–159 Hutchinson GE, MacArthur RH (1959) A theoretical model of size distributions among species of animals. Am Nat 93:117–125 Kotler BP, Brown JS (1999) Mechanisms of coexistence of optimal foragers as determinants of local abundances and distributions of desert granivores. J Mammal 80:361–374 Leibold MA (1996) A graphical model of keystone predators in food webs: trophic regulation of abundance, incidence and diversity patterns in communities. Am Nat 147:784–812 Levins R (1962) A theory of fitness in a heterogeneous environment. I. The fitness set and adaptive function. Am Nat 96:361–373 Levins R (1968) Evolution in changing environments. Princeton University Press, Princeton Loeb SC, Hooper RG (1997) An experimental test of interspecific competition for Redcockaded woodpecker cavities. J Wildl Manage 61:1268–1280 F. Kröner, Heidelberg Ecological Studies Vol 161, page proofs as of Juli 29, 2002 130 M. Ritchie Losos JB, Spiller DA (1999) Differential colonization success and asymmetrical interactions between two lizard species. Ecology 80:252–258 Lotka AJ (1925) Elements of mathematical biology. Williams and Whitkins, New York (reprint 1956 by Dover, New York) MacArthur RH (1958) Population ecology of some warblers of northeastern coniferous forests. Ecology 39:599–619 MacArthur RH (1969) Species packing, and what interspecies competition minimizes. Proc Natl Acad Sci USA 64:1369–1371 Mandelbrot BB (1982) The fractal geometry of nature. Freeman, San Francisco Milne BT (1992) Spatial aggregation and neutral models in fractal landscapes. Am Nat 139:32–57 Milne BT (1997) Applications of fractal geometry in wildlife biology. In: Bissonette JA (ed) Wildlife and landscape ecology. Springer, Berlin Heidelberg New York, pp 32–69 Milne BT, Turner MG, Wiens JA, Johnson AR (1992) Interactions between fractal geometry of landscapes and allometric herbivory. Theor Popul Biol 41:337–353 Morgan RA, Brown JS, Thorson JM (1997) The effect of spatial scale on the functional response of fox squirrels. Ecology 78:1087–1097 Morris DW, Fox BJ, Luo J, Monamy V (2000) Habitat-dependent competition and the coexistence of Australian heathland rodents. Oikos 91:294–306 Olff H, Ritchie ME (2001) Fragmented nature: consequences for biodiversity. Landscape Urban Planning 58:83–92 Palmer MW (1992) The coexistence of species in fractal landscapes.Am Nat 139:375–397 Petren K, Case TJ (1996) An experimental demonstration of exploitation competition in an ongoing invasion. Ecology 77:118–132 Petren K, Case TJ (1998) Habitat structure determines competition intensity and invasion success in gecko lizards. Proc Natl Acad Sci USA 95:11739–11744 Ritchie ME (1998) Scale-dependent foraging and optimal patch choice in fractal environments. Evol Ecol 12:309–330 Ritchie ME (2000) Nitrogen limitation and trophic vs. abiotic influences on insect herbivores in a temperate grassland. Ecology 81:1601–1612 Ritchie ME, Olff H (1999) Spatial scaling laws yield a synthetic theory of biodiversity. Nature 400:557–560 Ritchie ME, Tilman D (1992) Interspecific competition among grasshoppers and their effect on plant abundance in experimental field environments. Oecologia 89:524–532 Ritchie ME, Tilman D (1993) Predictions of species interactions from consumerresource theory: experimental tests with grasshoppers and plants. Oecologia 94:516–527 Rosenzweig ML (1981) A theory of habitat selection. Ecology 62:327–335 Rosenzweig ML, Abramsky Z (1997) Two gerbils of the Negev: a long-term investigation of optimal habitat selection and its consequences. Evol Ecol 11:733–756 Rothhaupt KO (1988) Mechanistic resource competition theory applied to laboratory experiments with zooplankton. Nature 333:660–662 Schmitz OJ, Beckerman AP, O’Brien KM (1997) Behaviorally mediated trophic cascades: effects of predation risk on food web interactions. Ecology 78:1388–1399 Schmitz OJ, Hambäck PA, Beckerman AP (2000) Trophic cascades in terrestrial systems: a review of the effects of carnivore removals on plants. Am Nat 155:141–153 Schoener TW (1976) Alternatives to Lotka-Volterra competition: models of intermediate complexity. Theor Popul Biol 10:309–333 Schoener TW (1983) Field experiments on interspecific competition. Am Nat 122:240–285 Sih A, Crowley P, McPeek M, Petranka J, Strohmeier K (1985). Predation, competition and prey communities: a review of field experiments. Annu Rev Ecol Syst 16:269–311 F. Kröner, Heidelberg Ecological Studies Vol 161, page proofs as of Juli 29, 2002 Competition and Coexistence of Mobile Animals 131 Stephens DW, Krebs JR (1986) Foraging theory. Cambridge University Press, Cambridge Tilman D (1976) Ecological competition between algae: experimental confirmation of resource-based competition theory. Science 192:463–465 Tilman D (1982) Resource competition and community structure. Princeton University Press, Princeton Tilman D (1990) Constraints and trade-offs: toward a predictive theory of competition and succession. Oikos 58:3–15 Tilman D (1994) Competition and biodiversity in spatially structured habitats. Ecology 75:2–16 Van Soest P (1985) Nutritional ecology of the ruminant. Cornell University Press, Ithaca Vandermeer JH (1972) Niche theory. Annu Rev Ecol Syst 3:107–132 Volterra V (1926) Fluctuations in the abundance of a species considered mathematically. Nature 118:558–560 Werner EE, Hall DJ (1979) Foraging efficiency and habitat switching in competing sunfishes. Ecology 60:256–264 Wiens JA (1992) The ecology of bird communities. Cambridge University Press, Cambridge Wiens JA (1995) Habitat fragmentation: island vs. landscape perspectives on bird conservation. Ibis 137:S97–S104 Wilbur HM (1997) Experimental ecology of food webs: complex systems in temporary ponds. Ecology 78:2279–2302 Wilson WG, Osenberg CW, Schmitt RJ, Nisbet RM (1999) Complementary foraging behaviors allow coexistence of two consumers. Ecology 80:2358–2372 Wissinger SA, Sparks GB, Rouse GL, Brown WS, Steltzer H (1996) Intraguild predation and cannibalism among larvae of detritivorous caddisflies in subalpine wetlands. Ecology 77:2421–2430 Wootton JT (1994) Predicting direct and indirect effects: an integrated approach using experiments and path analysis. Ecology 75:151–165 F. Kröner, Heidelberg