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ecological complexity 3 (2006) 148–159 available at www.sciencedirect.com journal homepage: http://www.elsevier.com/locate/ecocom Evolution of body size, range size, and food composition in a predator–prey metapopulation C. Hui *, M.A. McGeoch Spatial, Physiological and Conservation Ecology Group, Department of Entomology, University of Stellenbosch, Private Bag X1, Matieland 7602, South Africa article info abstract Article history: Relationships among body size, range size, and food composition are central to community Received 25 August 2005 ecology. Utilizing a simple framework of allopatric speciation, a stochastic, cellular auto- Received in revised form maton model of predator–prey metapopulations in one- and two-dimensional patchy net- 12 December 2005 works are constructed. In the model, ecological processes, such as local extinction, Accepted 30 December 2005 recolonization, and predation, and evolutionary processes, such as mutation, influence Published on line 12 May 2006 the average body size or morphological value of a local population in a patch. Accumulating morphological divergence between local populations incurs allopatric speciation. Results of Keywords: the model, highly correlated with some experimental data (795 species totally in China: Allopatric speciation Tetrigoidea 139 species, Fringillidae 453 species, and Serpentes 203 species), show that Dietary niche breadth distribution of body size is right-skewed and multimodal. The right-skewed distribution Metacommunity arises from the proportionality assumption and multimodality is a result of adjacent Skewness colonization. Predation (the increase of tropic level) can decrease the skewness and increase Distribution the number of modes in the distribution. Distributions of range size and food composition Tropic level are also right-skewed. Species with small range size like to aggregate in space surrounding by widespread species, forming a fountain of allopatric speciation. Furthermore, two rough rules from these distributions about the proportion of prey numbers to predator numbers and food composition are represented, showing that the proportion is about 2.3 and the number of prey species in food is 4.3 with about 47% similar between neighboring predator species. Additionally, the relationship between range size and body size is triangular, implying that widespread species has medium body size and large or small species is always spatially restricted. Relationship between body size and food composition is also triangular and indicates that extreme body size, largest or smallest, is always accompanied with stenophagic, while species with medium body size can be either euryphagic or stenophagic. # 2006 Elsevier B.V. All rights reserved. 1. Introduction The evolution of life history characters is central to both ecological and evolutionary research. These characters range from body size and longevity, describing the organism itself (Brown, 1995; Gaston and Blackburn, 2000; Makarieva et al., 2004a, 2005a), to spatial distribution and food composition, indicating the relationship with its environment (McGeoch and Gaston, 2002; Hui et al., 2004). Traditional and classical approaches to life history evolution involve optimization under constraints and trade-offs (Roff, 1992; Stearns, 1992; Charnov, 1993; Kozlowski and Weiner, 1997). The realm of * Corresponding author. Tel.: +27 21 808 4775; fax: +27 21 808 4807. E-mail addresses: [email protected] (C. Hui), [email protected] (M.A. McGeoch). 1476-945X/$ – see front matter # 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ecocom.2005.12.003 ecological complexity 3 (2006) 148–159 most studies of life history theory encompasses a single, large, undisturbed, and spatially homogeneous population. Recently, owing to global rates of habitat destruction and fragmentation, as well as progress in computing techniques, spatial modelling, and analysis (Tilman and Kareiva, 1997), e.g. the dynamic complexity of metapopulations (Hui and Li, 2003), has become a key instrument in ecological research and biological conservation (Hanski, 1998). For example, using a spatial modeling approach, Hui and Li (2004) found a new equilibrium of the spatiotemporal population dynamics resulting in a ‘‘circumscription’’ distribution which cannot appear under the mean-field assumption (that is a single wellmixed population). Olivieri and Gouyon (1997) illustrated how disequilibrium and the spatial structure characteristic of metapopulations might significantly affect the evolution of life history traits, a phenomenon they called ‘‘the metapopulation effect’’. Populations in spatially structured habitats may generate an ‘‘ecological imprint’’, on the environment that leads to environmental heterogeneity and the distribution segregation of different species, and even an oscillation dynamics in community (Hui et al., 2004), which brings about the maintenance of polymorphism in natural population (Yue et al., 2004). All these studies show that spatial factors are essential to ecological patterns. However, studies of life history evolution in a metapopulation context remain rare compared to the explosion of metapopulation demographic studies (see review in Ronce and Olivieri, 2004). In this paper, spatial factors are introduced into a life history evolution model that reveals some spatial and scaling patterns of life history characters. Body size is one of the most important quantitative traits under evolutionary scrutiny, because it is strongly correlated with many physiological and fitness characters, and exhibits prominent general evolutionary and allometric patterns in many organisms (Blanckenhorn et al., 1999; Brown et al., 2004; Li et al., 2004; Makarieva et al., 2005a). Because the allometric scaling relationship between body size and metabolic rate (Huxley, 1932; Kleiber, 1932; Savage et al., 2004; Chown et al., 2004; West et al., 1999; Brown et al., 2004; Li et al., 2004), body size and allometry has become the focus in recently ecological and physiological debate. Within species, body size, determined by allometry and life history constraints (Kozlowski and Weiner, 1997; Charnov, 2002), can affect heritability (Leibowitz et al., 1995), niche breadth (Shine et al., 1998), spatial structure (Ward et al., 2002), and mating success (Jones and Purvis, 1997). Interspecific pattern of body size presents a rough rule (S L2, where S is the number of species and L the characteristic linear dimension) for animals on the land (May, 1978), and in the sea (Fenchel, 1993), except for the less knowledge about smaller organisms (L < 0.01 m). The ecological or evolutionary origins of this rule may result from future studies on allometric scaling relationships (Enquist et al., 1998; West et al., 1999; Gillooly et al., 2001; Makarieva et al., 2004b, 2005b,c,d,e) and branching vascular structure (Banavar et al., 1999; West et al., 1999; Makarieva et al., 2006). Compared with the above taxonomic rule, observations in a community always show a lumpy distribution of body size (Holling, 1992). This universal lumpy distribution may result from discontinuous texture of landscape (Raffaelli et al., 2000), and this landscape structure can result from many self-organizing 149 ecosystem processes such as fire, storm and water, and biological process (McNaughton et al., 1988; Naiman, 1988). Evidences reinforce the point that discontinuities in the geometry of vegetated landscape impose discontinuities on the morphology of animals (Morton, 1990). However, species richness and body size distribution in different tropic levels have been little investigated and compared. Several recent studies have modeled the joint dynamics of speciation, extinction, and colonization in a spatially explicit framework using phenomenological descriptions of speciation (Bramson et al., 1996; Durrett and Levin, 1996; Hubbell, 2001). Although these earlier approaches are heuristically very useful for the process of diversification in metapopulations and for providing a basis for additional numerical and analytical work, the phenomenological treatment of speciation they employ is not satisfactory (Gavrilets, 2004). In the point speciation model each new species starts with exactly one individual (Bramson et al., 1996; Durrett and Levin, 1996). In the random fission model, the new species gets a random proportion of individuals of the ancestral species (Hubbell, 2001). However, these studies do not consider underlying genetics and simply postulate that a new species with a certain number of individuals emerges with a certain probability out of the ancestral species. However, excluding processes such as polyploidy and major chromosomal changes, speciation does not occur instantaneously (Gavrilets, 2004). In the model presented here, the speciation process is based on a simple model of allopatric speciation (Gavrilets et al., 2000), which is closely related to several previous studies (Orr and Orr, 1996; Gavrilets, 1999). Allopatric speciation is the origin of two or more species resulting from divergent evolution of populations that are geographically isolated from one another. Speciation through reproductive isolation that is a consequence of incompatibilities between different genes and traits (Gavrilets, 2004) is utilized in most existing studies, which firstly expressed by Bateson (1909), Dobzhansky (1937), and Muller (1942). Growing experimental evidence supports this definition (Wu and Palopoli, 1994; Orr, 1995; Wu, 2001). By the metaphor of adaptive landscapes (Wright, 1932), populations diverge genetically along the ‘ridge’ of highly fit genotypes and become reproductively isolated species when they come to be on opposite sides of a ‘hole’ in a ‘holey’ adaptive landscape (Gavrilets, 1997; Gavrilets and Gravner, 1997). Therefore, quantitative characteristics, such as body size, determined by multi-locus genes evolve gradually and the morphological distance between two adult individuals is, to some extent, a reflection of the inner genetic differences, and can incur reproductive isolation if a threshold value is exceeded. Paleontologists have adopted the related morphological species concept, in which species are discerned by phenotypic differences (Benton and Pearson, 2001). The morphological species concept is that a species is defined by being sufficiently morphologically distinct from all others. The definition can include multivariate tests of the statistical distance between species centroids in relation to intraspecific variation about the centroids (Sneath and Sokal, 1973). It is assumed that, although morphological differentiation need not form part of reproductive isolation, populations will nonetheless diverge 150 ecological complexity 3 (2006) 148–159 genetically, and this will be reflected rapidly enough in the divergence of phenotypes that the point of splitting and detectable morphological differentiation effectively coincide. This might be true given that the finest geological timescales are generally in the order of hundreds or thousands of years (Benton and Pearson, 2001). The assumption that morphologically recognized species in the fossil record correspond to biological species is an essential underpinning of palaeontological studies of speciation (Benton and Pearson, 2001). Genetic and morphological differentiation need not coincide, but there is extensive evidence for such a coincidence at the temporal and spatial scales used in studies of fossils (Ereshevsky, 1992; Roth, 1992; Coyne, 1992). Here, we will simulate allopatric speciation in a metapopulation framework. This speciation is a consequence of accumulating morphological distance, e.g. body size differences. Ecological processes, such as local extinction, recolonization, and predation, as well as evolutionary processes, such as mutation, can affect this allopatric speciation as well as the frequency distribution of the life history characteristic in a patchy environment. For simplicity, we will call this quantitative character decided by multi-loci genes as body size in this paper. What patterns of these life history characters generated in a metapopulation structure and how predation and local space-competition (extinction–recolonization process) affects these life history patterns will be discussed. As the corollaries of the results, relationships among body size, range size, and dietary niche breath, i.e. food composition will also be discussed. Further, results from empirical data (795 species totally: Tetrigoidea 139 species, Fringillidae 453 species and Serpentes 203 species) are compared with the theoretical results of the model. 2. Models In 1968, Levins indicated that both the spatial and temporal organization of the environment might significantly affect the extent to which a population would rely on genetic polymorphism (Levins, 1968). Furthermore, Levins (1969) defined a metapopulation as a population consisting of many local populations or demes. Due to aggregated distributions of individuals (Weiher and Keddy, 1999), any species is, to some extent, a metapopulation influenced by ecological processes (such as local extinction and recolonization) and microevolutionary processes (such as selection and gene flow) (Hui and Yue, 2005). In a metapopulation, all local populations have a substantial probability of extinction, and hence longterm persistence of the species can only occur at the regional or metapopulation level (Hanski, 1998). The stochastic cellular automaton model (SCAM) here is based on the metapopulation framework. Here, we assume the phenotypic differences (such as the differences in body size) are a reflection of genetic differences, which will lead to reproductive isolation beyond a certain threshold. This assumption is consistent with the Bateson– Dobzhansky–Muller Model (Bateson, 1909; Dobzhansky, 1937; Muller, 1942; also see Gavrilets, 2004) and the shift from the two-dimensional rugged adaptive landscape (Wright, 1932) to the high-dimensional holey adaptive landscape that are extensive nearly neutral networks (Gavrilets and Gravner, 1997; Gavrilets, 1997; Reidys, 1997; Reidys et al., 1997). SCAM is constructed to investigate distributions and relationships mentioned above. The model will be run in a one-dimensional stepping-stone habitat (SCAM-1d) with n patches and in a two-dimensional patchy network (SCAM-2d) with n n patches. Periodic boundary condition that patches are located in a circle or a spherical surface is adopted to exclude the boundary effect. The ‘‘body size’’ of an individual can be measured by a morphological value, and hence every local population has its average morphological value. The morphological variation within populations is neglected (Gavrilets et al., 2000) since we only concentrate on evolutionary events and neglect the ecological ones (such as how a particular body size predominates in the local population). In each patch, there is a local prey population and a local predator population, with average morphological values m1(i) and m2(i), respectively, where i indicates the location of each patches. The average morphological values can be altered by mutation and metapopulation processes. Because most speciation events involve gradual or relatively smallscale changes (Strickberger, 2000), we assume that body size can only change from mk(i) to (1 b)mk(i) with probability u at each time step, where b is a parameter of mutation intensity. This assumption implies that the absolute morphological change of a large species by mutation will be larger than that of a small species (i.e. an elephant that is 1 m larger than the average becomes a new species, while a Fig. 1 – A schematic illustration of ecological speciation. (a) Punctuated speciation. (b) Classic phyletic gradualism speciation. A species located in a one-dimensional eight patches (bottom) is separated to two species (up with white and gray background) if the morphological difference between two local populations is larger than two. Numbers in square indicate the morphological value of local population in the patch, and numbers nearby the arrow is the average morphological values of different species. ecological complexity 3 (2006) 148–159 Table 1 – Algorithm of the simulation procedure in SCAM Step 1 ‘‘Lock-and-key’’ relationship of body size between prey and predator If jm2 ðiÞ H m1 ðiÞj B, extinction rates are e1 + d for prey and e2 for predator, else if extinction rates are e1 for prey and e2 + d for predator. Step 2 Metapopulation processes If the prey extinct, choose a prey in the neighborhood re-colonize the patch (and hence the new prey have the same body size as the neighbor). The same process for the predator. Step 3 Mutation processes If the prey mutate (mutation rate: u), m1(i) = (1 W b)m1(i), else if m1(i) = m1(i). The similar process for the predator. Step 4 Allopatric speciation processes If patch j is a neighbor of patch i and d1 ði; jÞ > b Dðm1 ðiÞþ m1 ð jÞÞ=2, there forms a reproductive isolation between the prey populations in these two patches and the populations belong to two different species according to the concept of allopatric speciation. The same process for the predator. Step 5 Go to step 1. 151 mouse just needs 1 cm larger to be a new species), which is analogous to the assumption of the model STEVE (Cumming and Havlicek, 2002). The gradual morphological change in speciation events is consistent with the concept of ecological speciation (Schluter, 2001; Hey, 2001). Ecological speciation might come about indirectly as a consequence of natural selection on morphological, physiological or behavioral traits, or it might include direct selection on pre-mating isolation (Schluter, 2001). This gradual morphological change in the sub-populations does not mean the gradual morphological change in speciation, but a combination between the classic phyletic gradualism model and the punctuated equilibrium model (Simpson, 1944; Eldredge, 1971; Eldredge and Gould, 1972; Benton and Pearson, 2001). As shown in Fig. 1, the gradual morphological change in local populations can lead to the punctuated speciation (Fig. 1a) and the classic phyletic gradualism speciation (Fig. 1b), which depends on the variability of the morphological values within the metapopulation. Evidences have shown that there is a ‘lock-and-key’ relationship between the body size of prey and that of Fig. 2 – Spatial structure of species border and body size in two-dimensional habitat after 2000 generations. (a) and (b) are species borders of prey and predator, respectively. Black curves indicate that the two adjacent populations are reproductively isolated. (c) and (d) are spatial structure of body sizes for prey and predator, respectively. Darkness represents the relatively morphological values of body size. Parameter values are n = 100, u = 0.05, b = 0.05, e1 = 0.1, e2 = 0.1, D = 5, d = 0.1, s = 0.5, H = 50, and B = 1. 152 ecological complexity 3 (2006) 148–159 predator (Morand et al., 2000). The relationship between mean prey size (Wprey) and predator size (Wpred), in kilograms, for mammals and birds of prey (large-prey eaters) and for lizards, amphibians, seabirds, and insectivorous birds (small-prey eaters) is consist with a positive power relationship (for 1:18 small-prey eaters, Wprey ¼ 0:0018Wpred , R2 = 0.75; for large-prey 2 1:16 eaters, Wprey ¼ 0:109Wpred , R = 0.74; for raptorial birds, 0:93 1:26 ; for codfish, Wprey ¼ 0:0035Wpred ) (A. Wprey ¼ 0:179Wpred Vézina, unpublished; Schoener, 1968; Ware, 1980; see also Peters, 1983). Hence, we assume that a predator population can only feed on prey populations with corresponding body sizes, jm2 ðiÞ H m1 ðiÞj B, where H is a constant depicting body size differences between prey and predator, and B indicates the body size range of available prey (e.g. if m2(i) = 100, H = 50, and B = 1, the body sizes of available prey are m1(i) = 49, 50, and 51). Because predation can profoundly affect the metapopulation processes (Taylor, 1991), the local extinction rates of prey and predator are e1 + d and e2, respectively, if the predator can find the available prey, and are e1 and e2 + s, respectively, if not. After extinction, individuals from one of the adjacent nonextinct populations can colonize the empty patch immediately (Durrett and Levin, 1996). Let the morphological difference between patch i and patch j is dk(i, j), where k is either 1 for prey or 2 for predator. This morphological difference represents genetic divergence between these populations and can result in reproductive isolation between these populations if it exceeds a threshold, dk ði; jÞ > b Dðmk ðiÞ þ mk ð jÞÞ=2, where D is the mutation steps needing for species separation. It implies that largebody populations need more morphological differences for diversification than small ones, although the mutation steps are the same. This speciation pattern is coincident with the speciation mechanism in a holey adaptive landscape (Gavrilets et al., 1998), which shows that speciation is an inevitable consequence of genetic divergence (Orr, 1995). According to the above rules, we can construct the SCAM (see Table 1 for the simulation procedure), a cellular automaton, which is one of the most prevalent approaches in spatial ecology (Tilman and Kareiva, 1997; Hui, 2004; Hui et al., 2005; Li et al., 2005). 3. Results The spatial structures of distribution border and body size of species are presented in Fig. 2, by SCAM-2d. Populations surrounded by closed species border are a new species in terms of allopatric speciation. We noticed that speciation always occur clustered, which implies that new species are always spatial restricted (small range size) and the spatially restricted species are clustered in space; moreover, the species richness of prey is larger than that of predator (Fig. 2(a) and (b)). The spatial structure of body size is a mosaic, and the fountain of speciation is the region that the morphological values intensively change between patches (i.e. the region of drastically fluctuation of gray-level in Fig. 2(c) and (d)). The fountain of speciation is consistent with the region that spatially restricted species distribute, which has important corollary in discussion. Because SCAM-2d is very time-costing, we only use it to describe the spatial Fig. 3 – Evolutionary dynamics of species border. (a) Border dynamics of prey species. (b) Border dynamics of predator species. Parameter values are the same as in Fig. 2. structure of allopatric speciation. More theoretical analysis will be based on the SCAM-1d. Using SCAM-1d, evolutionary dynamics can be presented (Fig. 3). Firstly, species borders of prey are more stable than those of predator, which means that species with high trophic level is more vulnerable to environmental changes, such as local extinction and species invasion, than species with low trophic level, which is accordance with the experiences of biological conservation (Taylor, 1991). Secondly, ecosystem needs a coalescence phase, about 500 generations, to construct its structure. According to Gavrilets’ estimation (Gavrilets et al., 2000), the coalescence phase is about T D/u. This result indicates that reconstructed artificial ecosystem can hardly generate stable structure and ecological complexity 3 (2006) 148–159 produce normal ecosystem service within short duration, which challenges the optimism in biological conservation. Thirdly, morphological values or body sizes are clumpy distributed in space even though the habitat is homogeneous. This clumpy pattern is a consequence of local colonization and the coarseness or lumpiness of body-size distribution is even amplified in higher trophic. Colonization between neighboring patches is the key to maintain the lumpy pattern and discrete distribution of body size in metapopulation communities. 4. 153 Discussion 4.1. Distributions of body size, range size and food composition Real-world data on body size are abundant, since it is the most fundamental measure of species. According to the data from Fauna Sinica (Li et al., 1982; Liang and Zheng, 1998), we show the body size distributions of grasshoppers (Tetrigoidea, 139 species) and finches (Fringillidae, 453 species) of China Fig. 4 – Distributions of body size, range size, and food composition of prey and predator. (A) and (B) are body-length distributions of Tetrigoidea and Fringillidae in China (data from Li et al., 1982; Liang and Zheng, 1998). (C) and (D) are body size distributions of prey and predator. (E) and (F) are range size distributions of prey and predator. (G) is the distribution of food composition of predator. Simulated data are obtained by SCAM-1d, sampling every 100 generations from 4000 to 5000 generations. Parameter values are the same as in Fig. 2 except n = 400 and u = 0.02. 154 ecological complexity 3 (2006) 148–159 (Fig. 4A and B). Simulated distributions of prey and predator are also presented for comparison (Fig. 4C and D). Simulated results, highly consistent to the results from taxonomy, imply that distributions of body size are right-skewed and multimodal both for prey and predator. The effect of predation, or tropic level, is a weakener of skewness and an amplifier of lumpiness. This right-skewed distribution in our work is a consequence of the proportional assumption that a genetic mutation can lead to more morphological variation in the organism of large body size than that in small one, and hence large organisms have a larger speciation threshold for morphological diversification. Right-skewed distribution of body size turns to normalized distribution without the proportional assumption. Therefore, this assumption, a certain result of allometric scaling relationships (Kozlowski and Weiner, 1997; Enquist et al., 1998), may be a kernel for pattern formation in communities, which needs additional experimental attestations. May (1978, 2001) indicated that the species-body size distribution could be described by a rough rule S L2 (L > 0.01 m). What are the ecological or evolutionary origins of this rough rule, which holds true over four or more orders-ofmagnitude in characteristic lengths of animals on land, and roughly similarly in the sea (Fenchel, 1993)? To what extent and why is the breakdown in this rule at small sizes real, and to what extent may it be a consequence of less knowledge about smaller things (May, 2001)? In Fig. 4, we analyzed the distribution of the right tail (from modal body size to maximal size) by the power– function regression and found that the relationships do not fit this rough rule very well (for Tetrigoidae in Fig. 4A, S L6.58, R2 = 0.74; for Fringillidae in Fig. 4B, S L8.1, R2 = 0.59; for the prey in Fig. 4C, S L4.97, R2 = 0.73; for the predator in Fig. 4D, S L3.98, R2 = 0.39). First, these relationships are consistent with the negative power equations; yet, the exponents in these equations are significantly different from the one in May’s formula. Second, the coefficient of determination R2 decreases with the tropic level, which indicates the uncertainty of the community structure in high tropic level. Kozlowski and Gawelcyk (2002) presented an excellent review about why body size distribution is skewed to the right. They indicated that skewness of body size distribution is influenced by geographic scale and explained by macroevolutionary models, the fractal character of the environment, or body size optimization (Kozlowski and Gawelcyk, 2002). For a broad range, distributions in a class are usually right-skewed; for a narrower scale, distributions remain right-skewed or become symmetric or even close to uniform (Kozlowski and Gawelcyk, 2002). Roy et al. (2000) analyzed the body size distribution of the north-eastern Pacific marine bivalves along a latitudinal gradient at the provincial level and found that the modal sizes and shapes of these distributions are invariant. They further indicated that the modal size is an evolutionary attractor over geological time (Roy et al., 2000). Yet, Knouft (2004) studied the regional communities of North American freshwater fishes and suggested that there is a negative correlation between latitude and regional community size distribution skewness, with size distributions becoming leftskewed at high latitudes. The reason of the commonness of right-skewed distribution of body size in a regional community is still not clear. Three mechanisms were presented to explain this character of body size distribution. First, the fractal nature of environment will straightforwardly leads to the right skewed distribution (Morse et al., 1985; see a review by Gaston and Blackburn, 2000). Yet, as Kozlowski and Gawelcyk (2002) indicated, the most serious problem is that the smallest sizeclass should always be most numerous, and this is never or almost never the case. Second, small-biased speciation and large-biased extinction can also lead to right skewness (McKinney, 1990; Maurer et al., 1992). Third, there might be an optimal body size, which will form the modal in the distributions (Brown et al., 1993; Charnov, 1993; Perrin and Sibly, 1993; Kozlowski, 1996; Chown and Gaston, 1997). Results here suggested that (1) the assumption of proportional morphological change to body size and (2) tropic level in community are also two important factors to the skewness of body size distribution. On the other hand, although textural discontinuity indeed generates lumpiness in distribution of body size (Holling, 1992; Cumming and Havlicek, 2002), it can also come from adjacent colonization even in homogenous patchy habitat, which can be amplified by trophic levels. Additionally, the top species (the largest species in body size) of prey is larger than the one of predator. This interesting result has been reported in dinosaurs by Burness et al. (2001), which show that the body size of the top species decreased in the sequence: ectothermic herbivore > endothermic herbivore > ectothermic carnivore > endothermic carnivore. Distributions of range size and food composition are also right-skewed in linear scale (Fig. 4E–G). Right-skewed distribution of range size has been reported in many real experiments (Gaston, 1994, 1996; also called occupancy frequency distribution in McGeoch and Gaston, 2002). While, there are also numerous evidences showing that the distribution of range size is hollow, i.e. bimodal (Blackburn et al., 1997; Tokeshi, 1992). In contrast to the unimodal, right-skewed distribution that is the norm for geographic range-size distributions, at finer scales bimodal and uniform occupancy distributions are not uncommon (Tokeshi, 1992), and at least eight forms of occupancy distribution have been distinguished in empirical studies (McGeoch and Gaston, 2002). Numerous mechanisms, such as sampling artefactual effects include sampling characteristics and biological mechanisms include organism niche-based and metapopulation models, have been proposed to give rise to range-size distributions of different shapes (see review in McGeoch and Gaston, 2002). An increase in sample number may bring about a reduction in the number of species in the core class, i.e. a change from bimodal to a unimodal (satellite-mode) occupancy distribution (Gotelli and Simberloff, 1987; Brown, 1995; Guo et al., 2000). The distribution will also change from bimodal to unimodal with the sample extent changing from local scales to geographic and continental scales (Brown, 1984; Gaston, 1998). Additionally, sampling coverage, intensity, and temporal factors also affects the shape of occupancy distributions (McGeoch and Gaston, 2002). Our results show that skewness of the range size distribution of prey is smaller than that of predator, which implies that there are relatively fewer widespread species in high trophic level. The distribution curves of range size vary from lognormal to hollow with the increase of trophic level. It ecological complexity 3 (2006) 148–159 is the trophic level that determines the types of range size distribution, either right-skewed or hollow (bimodal). Many works have focused on the species–area relationship (Bell, 2001; He and Legender, 2002), which can also be depicted by using different patch number in our model. However, we interests in the proportion of prey species number to predator species number, p, which is an important index to describe food–web structure. A rough result in simulation is that the species richness of prey and predator vibrate around equilibriums after coalescence phase. By all 50 possible combinations of parameters of SCAM-1d, we found that p 1:25 expð4bDÞ. It strongly suggests that this result could be obtained from basic considerations of diffusion process in the metapopulation. For example, parameter D in the power of the exponent corresponds to the number of steps needed to drive the morphological difference to the level of divergence between two species. Coefficient exp(4b) can be interpreted as the mean increment of species numbers per step. With the increase of the morphological difference threshold to incur reproductive isolation, species richness will decrease more rapidly with the tropic level. This result is insensitive to the mutation rate and the colonization–extinction rate, which means that it is an attractive equilibrium of community structure. Note that bD is the proportion of morphological difference for species diversification to average morphological values, which varies from 0% to 25% presumably. Therefore, the typical values of p vary from 1.25 to 3.40, which is accordance with the classical experiment in Florida Keys (Simberloff and Wilson, 1969; p = 1.53) and the data of Tetrigoidea and Fringillidae from 155 Fauna Sinica (Li et al., 1982; Liang and Zheng, 1998; p = 2.12). Further, it has been strongly argued that each plant or animal species in a food web typically is connected (eating or being eaten) with only three to five other species (May, 2001). Raymond et al. (2001) studied 18,223 individual lizards of 127 species and found that the dietary niche breadth in the whole world is from 1 to 10.45, with the mean 4.58 and the standard deviation 2.3. This rough rule, which reveals the proportion of stenophagic species to euryphagic ones, can be obtained from the SCAM-1d. The average number of species in food composition distribution is 4.3, which varies typically from 1 to 7. Therefore, we obtain a typical ecosystem pattern: species number of prey is about 2.3-times (average of p values) greater than that of predator, and each predator species feeds on 4.3 prey species, which means that two predator species have 53% different foods. 4.2. Relationships among body size, range size, and food composition Gaston and Blackburn (1996) and Blackburn et al. (1997) indicated that the relationship between body size and range size is triangular, which implies that large species always has large range and small species can be either widespread or spatially restricted. Note this triangular relationship between body size and range size as ‘‘ ’’ (breadth is range size, and height is body size). In general, range size is an increasing function of body size, or at least the minimum range size of species in a body size class increases with the mean body size of that class (Gaston, 1994). Species tend to fall within a Fig. 5 – (a) Relationships among body size, range size, and food composition of predator. (b) Relationship between body length and range size of Serpentes in China (~, male; *, female). Range size is measured by the number of county or region in China, where the snake is found. Data from Fauna Sinica (Zhao et al., 1998). Data are obtained by SCAM-1d with similar parameters as in Fig. 4. 156 ecological complexity 3 (2006) 148–159 roughly triangular region of range size–body size space, with species with small range sizes tending to have small body sizes (Gaston, 1994). Some studies indicated that there are no significant correlations between range size and body size (Juliano, 1983); others even found a negative interaction between range size and body size, such as for North American Peromyscus (Glazier, 1980). The explanations of this vague correlation are based on energetic constraints (Damuth, 1987; Maurer and Brown, 1988; Root, 1991), but still inadequate (Lawton, 1991; Nee et al., 1991; Gaston, 1994). Using SCAM-1d, we reveal that the relationship is indeed triangular, but with different form, " (Fig. 5(a)). This result implies that species with medium body size, not large one, is widespread, and the largest or the smallest species is always spatially restricted in an evolutionary lineage. Our deduction is validated by the relationship of Serpentes in China, including five families and 203 species (Fig. 5(b); data from Zhao et al., 1998). The most widespread snake in China, Rhabdophis tigrinus, inhabited in 207 counties, has a medium body length about 751 mm for male and 900 for female. The largest serpent Ophiophagus hannah, with 3906 mm on domestic record, just inhabits in 39 counties, and the smallest snake Ramphotyphlops braminus, with only 100 mm body length in general, inhabits in 27 counties. The average body lengths of the most spatially restricted snake, inhabited in only one county, vary from 125 to 2686 mm. The relationship between body size and food composition also presents triangular-like (Fig. 5(c)). This result implies that species with medium body size could be either stenophagic or euryphagic. Largest or smallest species always has restricted dietary niche breadth. Brändle et al. (2002) have also discussed the relationship between body size and food composition (called dietary niche breadth in their work). They suggested that range size of species in Eastern Germany did not correlate with dietary niche breadth. Although body size has no correlation with food composition in their work, we found that the data points in the plane of body size and dietary niche breadth indeed distribute triangularly (Fig. 1(c) in Brändle et al., 2002; also see Brändle and Brandl, 2001). Therefore, the relationship between body size and food composition, in spite of no linear correlation, is also ‘‘"’’-like triangular. The most obvious result is that food composition is positive correlated with range size (Fig. 5(d)). Widespread predator species, i.e. euryoecious species, always have larger morphological variability within species than the stenoecious one, and hence can be euryphagic with wider dietary niche breadth. Therefore, in the fountain of speciation (Fig. 2(a) and (b)), the stenoecious always lead to stenophagic with narrow dietary niche breadth, which also means that stenophagic species are likely aggregated spatially restricted in habitats surrounding by euryoecious species with wide dietary niche breadth. 4.3. Muller, 1942; also see Kauffman, 1993), in which reproductive isolation is a consequence of ‘‘incompatibilities’’ between different genes and traits. In this model, the populations are not required to cross any adaptive valleys to evolve reproductive isolation, as they simply follow a ridge of high fitness values (Kauffman, 1993; Gavrilets, 1999). This model is to response to the improbability of high fitness ridge in a twodimensional rugged adaptive landscape (Wright, 1932). Analyses have shown that the properties of the three-dimensional adaptive landscape implicit in Wright’s metaphor are a rather poor indicator when describing genetic systems with thousands of loci (Gavrilets and Gravner, 1997; Gavrilets, 1997). A prominent feature of adaptive landscapes of very high dimensionality is extensive nearly neutral network (Gavrilets, 2004). Connected networks of genotypes with very similar fitnesses that expand throughout the genotype space (Gavrilets and Gravner, 1997; Gavrilets, 1997; Reidys, 1997; Reidys et al., 1997). Existing data on the genetics of reproductive isolation support this assumption that typically there are many different loci underlying reproductive isolation (Wu and Palopoli, 1994; Naveira and Masida, 1998; Wu, 2001). This founding makes the assumption in this paper appropriate that reproductive isolation and ordinary phenotypic differences tend to go hand-in-hand (Orr, 2001). Speciation in spatially structured networks has been studied. Bramson et al. (1996) and Durrett and Levin (1996) considered the individual based model in a two-dimensional networks. Their model has similar extinction–recolonization process as in this model. The difference is that their model is a point speciation model that new species starts from a mutation in one individual, which seems like not true, because there are numerous loci involved in the speciation event (Gavrilets, 1997). Hubbell (2001) also studied the evolutionary dynamics in a metacommunity (that is, a community consisting of many local populations with different competitive species). The speciation in his ‘‘random fission model’’ is also a probable event (Hubbell, 2001). In fact, the speciation in their models is a particular situation here that when D = 1. From Fig. 1, we can see that the speciation adopted here consists of the phyletic gradualism speciation and the punctuated equilibrium speciation. Classic palaeontological studies adopts the phyletic gradualism speciation (Ereshevsky, 1992; Roth, 1992; Coyne, 1992); yet theoretical ecologists like to choose the punctuated speciation (Eldredge, 1971; Eldredge and Gould, 1972), which is also adopted in the studies of community structure (Bramson et al., 1996; Durrett and Levin, 1996; Barraclough and Vogler, 2000; Hoelzer, 2001; Hubbell, 2001). Moreover, up to now, there is no other paper studying the coevolution of predator and prey in a metapopulation framework. The model here opens the door to study the evolutionary dynamics of predator–prey in metapopulations. Speciation in metapopulations 5. Here, we have build the stochastic cellular automaton based on allopatric speciation, predator–prey process and extinction–recolonization process in metapopulation framework. The theoretical foundation of this model is the Bateson– Dobzhansky–Muller Model (Bateson, 1909; Dobzhansky, 1937; Conclusion In conclusion, predation can profoundly affect speciation dynamics and community patterns. Skewness and lumpiness of distributions are changing with tropic level. Metapopulation processes, especially adjacent recolonization, can deeply ecological complexity 3 (2006) 148–159 influence the spatial structure of community and allopatric speciation. Although there are no obviously linear relationships between body size and range size, and between body size and food composition, these relationships are in fact ‘‘"’’-like triangular. Only dietary niche breadth is positive correlated with distribution range. Therefore, predation and colonization are the most important factors influencing the community patterns, which can be depicted soundly by body size, range size, and food composition. The particular spatial model used here has properties that are likely to exemplify a broad of models, and the assumptions of model are made largely on the basis of analytical convenience. This pregnant model can amplify the effects of spatial factors and interspecific interactions on dynamics, distribution and competition, and reveal the mechanisms underlying distinctly. In realistic ecosystem, this model needs specializing, and the substitution of ecological and evolutionary processes comprising more factors for the simply assumption here is inevitable. Acknowledgments We are very grateful to S. Gavrilets, J. Kozlowski, Z. Li, B. Laniewski, B.L. Li, and anonymous reviewers for their helpful comments, and F. Zhang and X.Z. Han for the data collection from Fauna Sinica. This work was partially supported as a fellowship for C.H. by the National Research Foundation of South Africa (GUN2053618) and the University of Stellenbosch. references Banavar, J.R., Maritan, A., Rinaldo, A., 1999. 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