Metapopulation dynamics and distribution, and ... - Semantic Scholar

Ecological Modelling 177 (2004) 107–118

Metapopulation dynamics and distribution, and environmental heterogeneity induced by niche construction Cang Hui1 , Zizhen Li∗ , Dong-xia Yue2 State Key Laboratory of Arid Agroecology, Lanzhou University, Tianshui Road, Lanzhou, Gansu 730000, China Received 10 March 2003; received in revised form 18 November 2003; accepted 25 November 2003

Abstract Niche construction means that all organisms modify their environments, also known as ecosystem engineering. Organism– environmental relations induced by niche construction profoundly influence the dynamics, competition, and diversity of metapopulations. Single-species model shows a positive feedback between metapopulation and environmental resources, which leads to threshold phenomena in dynamics. Lattice model suggests that ‘ecological imprint’ is formed by niche construction in spatial habitat. Ecological imprint leads to the self-organized spatial heterogeneity of environments and species’ distribution limits. In competitive systems, niche construction leads to alternative competitive consequences, which implies that trade-offs between the abilities of competition, colonization, and niche construction are important to competitive coexistence. Ecological imprint in competitive systems can weaken the spatial competitive intensity by spatial heterogeneity and segregation of species’ distributions. In metapopulation community, positive niche construction leads to exclusion of intermediate species with odd-numbered species richness and oscillation with even-numbered species richness; negative niche construction has opposite results. These results suggest that species richness may be critical to community’s dynamics and structure. Extinction of some species can lead to dramatic change of dynamical stability, oscillations or exclusions, or even chain reactions that damage the community structure. © 2004 Elsevier B.V. All rights reserved. Keywords: Niche construction; Metapopulation dynamics; Ecological imprint; Diversity; Distribution limit; Heterogeneity

1. Introduction Ecology is the study of relationships between organisms and the environment (May, 1981). However, studies are accumulated in the responses of organisms to the variations in environments, the center of which implies that the survival of organisms has depended upon how well organisms could adapt to its environ∗ Corresponding author. Tel.: +86-931-8913370; fax: +86-931-8912823. E-mail addresses: [email protected] (C. Hui), [email protected] (Z. Li), [email protected] (D.-x. Yue). 1 Tel.: +86-931-8631147; fax: +86-931-8912823. 2 Tel.: +86-931-8912106; fax: +86-931-8912823.

ments (Molles, 2000). It is a curious fact that though organisms have influences on their environments, this counter-interaction has received much less attention from ecologists than routine interaction. Recent studies may reverse this situation. Niche construction that all organisms modify their environments (Laland et al., 1999), elsewhere described as ecosystem engineering (Jones et al., 1994), is a process with increasing recognition (Odling-Smee et al., 1996; Jørgensen, 1997). Organism not only is a passive inductor selected by nature, but also is an active ‘engineer’ that modifies its environments. The most obvious example is humans, the most important power changing the ecosystems on earth (Vitousek et al., 1997). In natural world, there are also

0304-3800/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolmodel.2003.11.016

108

C. Hui et al. / Ecological Modelling 177 (2004) 107–118

numerous examples of organisms choosing or changing their habitats. Orb-web spiders construct webs (Hansell, 1984). Ants can regulate temperature by adjusting the height or shape of their mounds (Hölldobler and Wilson, 1995). Many mammals construct burrow systems (Nowak, 1991). For vegetation, niche construction, however, does not involve the building of artifacts but merely the modification of habitats (Odling-Smee et al., 1996). Whitford et al. (1997) also indicated that desert shrubs not only could enrich the soil nutrients but also have influence on the infiltration and deposition of precipitation. Plants can change the chemical nature, the pattern of nutrient cycling, the temperature, the humidity, the fertility, the acidity, and the salinity of their soils and the patterns of light and shade in their habitats (Willis et al., 1997). Mechanism of niche construction, or ecosystem engineering, is a positive feedback between organisms and their environment. Although positive feedback is a destabilized force, it can incur multiple stable states in ecosystems, which is important to the survival of organisms in the adverse and stressing environments, such as the diatom–silt interactions of a tidal flat in the Westerschelde (Van de Koppel et al., 2001) and the vegetation–soil relationship in the early postglacial in northeastern Hungary (Willis et al., 1997). The trait that altars the environment in a manner that is favorable to growth tends to be reinforced (Lenton, 1998) and this positive feedback can further, to a certain extent, modify the selection pressure on itself (Jørgensen, 1997). As Lewontin (1979) points out, the growth in complexity of organisms goes hand in hand with a concurrent growth in complexity of environments and thus of organism–environment relations. Besides selecting their environments, organisms also determine and modify the environmental features that are most relevant to their own survival. Hitherto, studies of niche construction or ecosystem engineering are accumulated in single-species system (e.g., Flecker, 1996; Van de Koppel et al., 2001), while multi-species system has been scarcely discussed. In this paper, we attempt to illuminate the ecological consequences of niche construction in multi-species metapopulations with interspecific competition. We first construct organism–environmental relationships in terms of Levins’ patch occupant model (Levins, 1969) and Tilman’s interspecific competitive model (Tilman, 1994). Based on these relationships, we

reveal the threshold phenomena, alternative states, spatial heterogeneity, and species’ distribution limit induced by niche construction. We also test the ecological consequence of niche construction in metapopulation community. Finally, we discuss the pattern of natural selection at different scales, ecological imprint, and the significance of species richness in community. Our work will suggest that ecological models based only on population dynamics may not reveal the underlying mechanism and depict actual situations; models concerned about organism–environmental relationships could predigest the complexity of analysis and generate new phenomena.

2. Niche construction in metapopulation models 2.1. Dynamics of a single-species and persistence threshold Metapopulation describe a ‘population’ consisting of many local populations (Levins, 1969). All the local populations have a substantial probability of extinction, and hence the long-term persistence of the species can only occur at the regional or metapopulation level (Hanski, 1998). Owing to habitat destruction and fragmentation around the world, metapopulation model has become an essential instrument in the research of conservation and landscape ecology (Hui and Li, 2003). The classical metapopulation framework is based on Levins’ patch occupant model dp = cp(1 − p) − ep, dt

(1)

where p is the fraction of patches occupied by the species; c and e, respectively, the colonization rate and extinction rate. The non-trivial equilibrium p¯ = 1−(e/c) is globally stable as long as e < c. This model has been a fundamental framework of spatial ecology and is a potent metaphor for population dynamics in patchy environments (Tilman and Kareiva, 1997). Niche construction has been defined as “the capacity of organisms to modify sources of natural selection in their environment” (Laland et al., 1999). This concept is analogous to that of ‘ecosystem engineering,’ which is defined as “the physical modification, maintenance, or creation of habitats by organisms” (Jones et al., 1997). For metapopulation model, we assume


109

that the population’s capacity for niche construction is influenced by the fraction of occupied patches, i.e., the metapopulation size. For simplicity, we also assume that the resource is scarce, which means we only consider resource dissipation but neglect resource recovery. Hence, the dynamical function of environmental resource should have the following form dR = αp − βR, dt

(2)

where R is the resource content; α, coefficient of niche construction; and β, dissipation rate. Noted resource will be depleted without niche construction. Furthermore, we assume that colonization rate is a function of the amount of environmental resources, c = c R, where c is a coefficient. This treatment of the interaction between the metapopulation and the resource is extremely simple. A more realistic treatment would involve general distributions of the resource, more complex dynamics of resource and metapopulation, and ecological models that take the density of niche constructors into account (DeAngelis, 1992; Silvertown and Doust, 1993). However, this simple treatment can soundly reveal the mechanism underlying niche construction. Combining Eqs. (1) and (2), we set up the single-species metapopulation model subject to niche construction. According to the analysis of null isoclines and Lyapunov’s theorem (Murray, 1999), we obtain the necessary condition for metapopulation persistence α>

4βe . c2

(3)

This is a persistence threshold for the ability of niche construction. If inequality (3) is satisfied, two equilibriums appear: a stable node and an unstable saddle (see Fig. 1). The separatrix of saddle point divides the phase plane into two parts: extinction part and persistence part. Trajectories only starting from persistence part can limit to stable equilibrium. These results show that a metapopulation can survive if and only if it satisfies the threshold condition and initial condition. Spatial patterns of resources and metapopulations are simulated by lattice model with Neumann neighborhood and non-periodic boundary (Scheffer et al., 1995; Keitt, 1997; Tilman and Kareiva, 1997). If there is a patch being occupied, the increasing rate of resource in the patch will be described by Eq. (2) with

Fig. 1. The zero-change isoclines of resource (dashed line) and metapopulation (solid curve) in the resource-metapopulation phase plane. Solid circles represent stable equilibriums; open circle represent unstable equilibrium (saddle point). The separatrix of unstable equilibrium divides the phase plane into two parts: extinction part (gray region) and persistence part (white region). Trajectories starting from extinction part will incline to the stable point of intersections of coordinate axes. Trajectories starting from persistence part will tend to the stable point of intersections of isoclines.

p = 1; if the patch is empty, the resource dynamics will be modeled by Eq. (2) with p = 0. A relatively stable distribution pattern of resource content is formed in simulations (Fig. 2). This spatial heterogeneity of environmental resources results from the niche construction, which is an “ecological imprint” of organisms on environments. The distribution of metapopulation is closely correlated with this ecological imprint. Therefore, the distribution of resource content inosculates with the one of metapopulation. Populations select the patches with high resource content to colonize, which improves the content of resource in these patches and attracts more populations to colonize. It suggests that environmental heterogeneity and species distribution may be deeply influenced by the effect of ecological imprint. 2.2. Competitive metapopulations and trade-off One of the most important results obtained from metapopulation models is the mechanism of competitive coexistence in homogeneous habitat. Hutchinson (1961) noted that the open, seemingly well-mixed waters of lakes and oceans might contain a hundred

110


species 2 is the inferior competitor. Tilman’s model describes the dynamics of two spatial structured populations competing for the suitable patches in the spatial habitat. Even though the best competitor immediately displaces the other locally, these two competing metapopulation can stably coexist in an implicitly spatial homogeneous environment, which requires both an interspecific trade-off in competitive ability versus dispersal ability and a limit to similarity of these traits (Tilman and Kareiva, 1997). In brief, the inferior competitor must be a superior colonizer, which means for example, c2 > c12 /e1 if e1 = e2 . This competition–colonization trade-off is the key to the interspecific coexistence in spatial habitat (Lehman and Tilman, 1997; Yu and Wilson, 2001). If niche construction impacts on interspecific interaction, dynamics and consequences of competing system will be profoundly influenced. Because superior competitor cannot apperceive inferior one, we only consider the niche construction by inferior species, which can affect the resource content and further determine fitness of species 1 in patches. Therefore, we assume that the dynamics of resource has the following form Fig. 2. Spatial distribution patterns of resource content in two-dimensional space of 30 × 30 patches. Parameter values: α = 0.1, β = 0.2, c = 0.5, and e = 0.1; the number of initial local populations is 350, which are randomly distributed in space. Time generations of plot (a) and (b) are 100 and 200, respectively.

or more species of phytoplanktonic algae. Space seemed to have the potential of providing a solution to this paradox of diversity (Horn and MacArthur, 1972; Levin and Paine, 1974; Platt and Weis, 1977; Hastings, 1980; Nee and May, 1992). In this part, we use Tilman’s model for spatially interspecific competition of metapopulations (Tilman, 1994; Tilman et al., 1994; Lehman and Tilman, 1997) dp1 = c1 p1 (1 − p1 ) − e1 p1 , dt

(4A)

dp2 = c2 p2 (1 − p1 − p2 ) − e2 p1 p2 − c1 p1 p2 . dt (4B) Here p, c, and e have the same meaning as in Eq. (1), except now they are indexed by species numbers 1 and 2. Species 1 is the superior competitor, and

dR = αp2 − βR + γ, dt

(5)

where R, α, and β have the same meaning as in Eq. (2), and γ is a coefficient that determines the degree of independent renewal. If there is no niche construction (α = 0), the equilibrium of resource content is given by R0 = γ/β. To depict the effect of niche construction more distinctively, we introduce the concept of niche fitness into this section. Niche fitness is defined as the closeness degree between optimum niche point in hypervolume and actual resource state (Li and Lin, 1997). We assume that the resource constructed by species 2 can affect the niche fitness of species 1, by which the colonization rate of species 1 is determined. Using the simplest form of resource utilization spectrum (single-humped curve; May, 1981), we may assume that the optimum resource content of species 1 is the equilibrium of resource content without niche construction, R0 , and hence the colonization rate of species 1 has the following form c1 = c exp(−δ(R − R0 )2 ),

(6)


where 1/δ is a coefficient of niche breadth and c is a constant. Furthermore, there is always a limited amount of time, energy, and other resources to spend on growth, maintenance and reproduction, so an organism must allocate its resources among these alternative demands (Silvertown and Doust, 1993). For metapopulation, conflicting demands lead to trade-off between abilities of niche construction and colonization. Therefore, we assume that c2 + µα = 1, where µ is the proportional coefficient. Combining Eqs. (4), (5) and (6), we can analyze the ecological consequences influenced by niche construction. First, species 2 can exclude species 1 with moderate ability of niche construction. This result implies that inferior competitor can defeat superior one if it can influence the resource that determines the colonization ability of superior competitor. Second, trade-off reaches optimum effect at moderate abilities. If niche construction is too feeble (e.g., α = 0 or 0.2 in Fig. 3), species 2 has scarce influences on environmental resources and hence can hardly depress the fitness of species 1. If niche construction is too strong (e.g., α = 0.8 or 1 in Fig. 3), the colonization rate is too small

111

due to trade-off, which exceeds the benefit from decreasing fitness of species 1. Therefore, moderate decrease of colonization rate of inferior competitor may be a better life history strategy to alleviate and resist the competitive pressure from superior competitor. Examples are abundant in plant community (Gilbert, 1985; Hunter and Aarssen, 1988), such as the competition of Artemisia ordosica and Caragana korshinskii (Li and Lin, 1997; Li et al., 2002). The nitrogen fixation and water holding of C. korshinskii can profoundly affect the growing and competitive ability of A. ordosica. Lattice model with Neumann neighborhood and non-periodic boundary is again applied to the study of spatial pattern (Fig. 4). If there is a patch occupied by specie 2, the increasing rate of resource in the patch will be described by Eq. (5) with p = 1; if the patch is empty or occupied by species 1, the resource dynamics will be modeled by Eq. (5) with p = 0. Through comparison of spatial patterns with and without niche construction, two results can be obtained. First, the distribution of two species with niche construction is more segregated than the one without niche construction. Resource content in the distribution region of inferior competitor is altered by niche construction, which reduces the colonization rate of superior competitor in this region and leads to the segregation of distributions. Second, the distribution of species with niche construction is more immovable than the one without niche construction, which is in accordance with the result of single-species system (Fig. 2). Hence, ecological imprint can segregate and fix the distributions of two species. It implies that we cannot explain species’ distribution limit in terms of environmental heterogeneity, for the reason that spatial heterogeneity in space and species’ distribution limit may appear by cooperative interactions of organisms and environments, i.e., selforganization. 2.3. Multi-species model of metapopulations and diversity

Fig. 3. Competitive consequences of metapopulations subject to niche construction. Parameter values: β = 0.35, γ = 0.1, c = 0.2, δ = 3, R0 = γ/β = 0.286, e1 = e2 = 0.1, µ = 1, c2 = 1 − α, and the values of parameters α are marked near the trajectories. The six trajectories are all starting from p1 (0) = p2 (0) = 0.05 and R(0) = 0.3.

Recently, community structure and biodiversity have once again become the core of ecological studies (Bell, 2001). According to Tilman’s model for interspecific competition among individual plants (Tilman, 1994; Lehman and Tilman, 1997), Eq. (4)

112


Fig. 4. Distribution of metapopulations with and without niche construction. Gray patches in (a–c) depict species 2, and black patches depict species 1. Darkness in (d) represents the ecological imprint. Lattice model is calculated in two-dimensional space of 50 × 50 patches with 400 randomly located initial local populations for each species. (a) Distribution after 100 generations without niche construction (α = 0); (b) distribution after 50 generations from (a) without niche construction (α = 0); (c) distribution after 50 generations from (a) with niche construction (α = 0.2); and (d) is the spatial distribution of resource content of (c). Parameter values: β = 0.2, γ = 0.1, c = 0.31, δ = 3, e1 = e2 = 0.2, and c2 = 0.4.

can be expanded into the following form   i i−1 dpi pj  − e i pi − c j pi p j . = ci pi 1 − dt j=1

(7)

j=1

This equation predicts that any number of species can stably coexist in an implicitly spatial homogeneous environment through competition–colonization trade-off, which may be the underlying mechanism in many terrestrial vegetation communities and seem to explain biodiversity in many animal and plant communities (Tilman et al., 1994).

With niche construction, this dynamics will be profoundly influenced. For simplicity, we assume that the number of species is n. We only consider that species n influences resource content with the similar dynamics as Eq. (5), and the resource content influences the ability of colonization rate of species 1 (c1 = cR, where c is a constant coefficient). Additionally, the ability of niche construction α can be positive which means species n improves resource content and hence increases the colonization rate of species 1, and negative, indicating species n depletes resource and decreases the colonization rate of species 1. Other interspecific niche construction is neglected for simplicity.


113

Fig. 5. Dynamics of multi-species model of metapopulations with niche construction. (a) and (b) are three-species system with parameter values: β = 0.2, γ = 0.1, c = 0.038, c2 = 0.04, c3 = 0.09, e1 = e2 = e3 = 0.01, and α = −0.35 for (a) and α = 0.1 for (b). (c) and (d) are four-species system with the same parameter values as in (a) and (d) except: c = 0.03, c3 = 0.1, c4 = 0.4, and α = −0.1 for (c) and α = 0.34 for (d). Metapopulation size start from: p1 (0) = 0.1, p2 (0) = 0.2, p3 (0) = 0.3, and p4 (0) = 0.4.

Three- and four-species systems are numerically simulated (Fig. 5). In three-species system, negative niche construction can lead to oscillations (Fig. 5(a)); and positive niche construction can result in the competing exclusion of intermediate species (species 2 in Fig. 5(b)). In four-species system, negative niche construction leads to competing exclusion of intermediate species (species 3 in Fig. 5(c)), while positive niche construction leads to oscillations (Fig. 5(d)). The reason may be distinct. If a system has oddnumber species (n) with positive interspecific niche construction, species n construct environmental resource and improves the colonization ability of species 1, the superior competitor. Species 1 suppresses species 2, and hence supports spices 3. Analogically, species n will be improved. Hence, positive niche construction forms a positive feedback in systems with odd-number species. Some intermediate species in these systems will be suppressed and may be elimi-

nated. In an odd-number species system with negative interspecific niche construction, species n depletes environmental resource and reduces the colonization rate of species 1, which will ultimately suppress species n itself. This suppression will further lead to the increases of colonization rate of species 1, and spur the oscillated dynamics of metapopulation sizes. Similar reason goes to even-number species system.

3. Discussion We have constructed the metapopulation models by the continuous dynamical systems (CDS, also called ordinary differential equations) and the stochastic cellular automata (CA) based on the lattice model. The CDS is the classical approach to study the population dynamics in mathematical biology (Murray, 1999), from which we can determine the transition rules for

114


patch states in the CA model (e.g., Hui and Li, 2003). The CA is one of the most important approaches to reveal the spatial patterns in modern ecology (McGlade, 1999), especially in metapopulation ecology (Hanski, 1999) and spatial ecology (Tilman and Kareiva, 1997). The CA model has been widely used in plant ecology, indicating neighborhood effects and the importance of different forms of competition between plants (Hendry et al., 1996), taking into account the fact that abiotic factors could trigger premature senescence which could then be accelerated by biotic agents (Jeltsch and Wissel, 1994), examining the effects of tree size and distribution on gap phase dynamics, the role of spatial location on the nature of competition and the effect of morphology on spatial occupancy (Williams, 1996), describing plant distributions in alpine communities (Humphries et al., 1996). The CA model has also been used to examine territorial behavior and the population consequences of kinship in red grouse (Lagopus lagopus scoticus) (Hendry et al., 1997). The study of spider predatory foraging strategies on prey captures and spider fecundity can also be based on CA (Provencher and Reichert, 1995). These models always assume an invariant homogeneous habitat, compared to our model here that incurs a spatial heterogeneity in habitat. Assumption of heterogeneous habitat has also been found. Keitt (1997) examined the consequences of introducing spatial heterogeneity into uniform and non-uniform lattice models and found that local interactions resulted in more species-rich food webs. Koh et al. (1997) explored the effect of environmental pollutants on organisms. However, our model focuses on the spatial heterogeneity incurred by biological population, which in turn influences its own survival. Spatial patterns are often found where the movement, or range of influence, of individuals is small compared with the habitat they occupy (Keeling, 1999). These local correlations can lead to sweeping waves of infection that are characteristic of diseases in many spatially distributed hosts, such as fungal disease in trees (Maddison et al., 1996). Most spatial patterns can be considered as being generated by one of four basic processes: aggregation, spatial instabilities, multiple stable solutions or complex local dynamics (Keeling, 1999). The simplest source of spatial patterning is aggregation and local correlations due to the directed movement of individuals (Swart and

Lawes, 1996; Wu et al., 1996). These are the causes of many common spatial phenomena such as shoals of fish and insect swarms (Reuter and Breckling, 1994). Besides the aggregation resulting from local interactions, our results are primarily incurred by the multiple stable states in metapopulations. We will attempt to reveal the implications of these results in the following. 3.1. Patterns and scales The mathematical analysis presented in this paper indicates that the generally observed functional relationship between environmental resources and single-species metapopulation can lead to the threshold phenomena. The ability of niche construction must be larger than a threshold (formula (3)) to generate a stable equilibrium in resource-metapopulation phase plane. The threshold phenomena imply that nature will select the species with larger ability of niche construction. This is a directional selection incurred by niche construction. Hitherto, evidences have been accumulated at the scales of gene (Laland et al., 1999), individual (Whitford et al., 1997), population (Li et al., 2002), community (known as ecosystem engineering; Flecker, 1996; Van de Koppel et al., 2001), and even biosphere (called Gaia theory; Lenton, 1998). The mechanism of niche construction at gene scale reveals the relationship between resource content and particular genotype (Laland et al., 1999). Whitford et al. (1997) observed that high mineral concentrations in stemflow may be due to the activity of stem micro-organisms and the collection of “dust” from the air, all of which may add to the “fertile island” effect of soil under creosotebushes. Li et al. (2002) found that resource contents (including soil moisture, organic matter, hydrolytic nitrogen, P2 O5 and K2 O) have positive correlation with the coverage of saksaul forests (Haloxylon ammodendron) in arid and desert zone. At population scales, there is a minimum planting density or coverage, and high cover will lead to low extinction rate for plant populations. Flecker (1996) reported the phenomenon of ecosystem engineering by a dominant detritivore in a diverse tropical stream. Van de Koppel et al. (2001) revealed the positive feedback between growth of benthic diatoms and erosion of silt in tidal flat systems. At biosphere scale,


Gaia theory indicates that the Earth self-regulates at a state that is tolerated by life (Lenton, 1998). All the evidences of niche construction show that there is a positive feedback between organisms and its environments. Although mechanisms of niche construction are similar, different patterns of ecological and evolutionary dynamics are found at different scales. At gene scale, niche construction generates selection for particular genotype. At individual scale, niche construction generates selection for larger individual. At population or community scale, niche construction generates selection for higher cover rate or density. Because cover rate or density is generally negatively correlated with individual biomass (White, 1981), directions of selection are opposite at individual scale and population scale. Traditionally, selection unit is the individual with genetic differences (Johnson, 1976). While, our results show that selection unit may be altered at different scales. Different ecological and evolutionary patterns may appear at different scales with similar underlying mechanism. Therefore, niche construction is a potent evolutionary agent by generating alternative stable states and diverse ecological or evolutionary consequences (Odling-Smee et al., 1996). Same mechanism of niche construction can lead to different patterns at different scales, which may be the prevalent mode in ecology (Levin, 1992). 3.2. Ecological imprint and species’ distribution limit Understanding the factors that lead to the current distribution limits of species is a fundamental goal of ecological biogeography (Keitt et al., 2001). Mainstream ecologists focus on the role of broad scale gradients or interspecific interactions. The factor that limits a species’ range is itself spatially delimited, and so the realized range limit reflects real spatial heterogeneity in the circumstances facing a species (Keitt et al., 2001). The physical environment limits the geographic distribution of species (Molles, 2000). Along a gradient, local habitat condition may become unsuitable, such that populations are no longer sustained by recruitment (Holt and Keitt, 1999). Anyway, spatial heterogeneity as well as niche theory, indicating that species can only grow, survive and reproduce in particular range of environmental

115

gradients, become the best explanation of species’ borders. Traditionally, spatial heterogeneity arises from geographical and geological interactions. However, our results imply that spatial heterogeneity and species’ distribution limit may be the byproducts of ecological imprint at small scale. Ecological imprint means that niche construction will affect not only dynamics of present population, but also the dynamics and distribution of future generations. In single-species system, niche construction of present population improves the resource content and forms an ecological imprint in habitat. This ecological imprint will increase the probability of successful colonization in next generation and deepen the imprint on habitat further. Hence, descended population will be likely to distribute in the patches that have ever been occupied. The habitat, initially unsuitable to survive, forms a self-organized spatial heterogeneity, and population will survive in the imprinted region. Therefore, ecological imprint forms a positive feedback between species’ borders and spatial heterogeneity. In competing system, spatial heterogeneity induced by ecological imprint forms a distribution region of inferior competitor, where the colonization ability of superior competitor is weakened and hence the competitive intensity is weakened too. This makes the species’ borders more distinct. Niche construction bridging the spatial heterogeneity and biotic interactions may be an important factor leading to environmental gradient and species’ distribution limit, especially in adverse environmental system, such as the spatial distribution of benthic diatoms on tidal flats (Van de Koppel et al., 2001). Self-organization may be a primary characteristic of the development of ecosystem (Jørgensen, 1997; many example can be found in Kauffman, 2000). 3.3. Trade-offs and coexistence in metapopulations Trade-off between the ability of colonization and competition is the key to coexistence of metapopulations in homogeneous patchy environments (Tilman, 1994). Tilman’s model provides an excellent explanation for the high species richness of many communities of sessile organisms. However, Tilman’s model depicts a completely asymmetric interspecific competition, which hardly exists in the nature. The multi-species model developed here demonstrates

116


that niche construction has profound influences on competing consequences (Fig. 3). Species do alter the environmental resources, especially the resource that is closely related to its survival. Interspecific niche construction decreases the resource content necessary for other species’ survival and hence reduces the intensity of competition and improves stable coexistence. Mechanism of niche construction may be a potential metaphor to account for the competitive coexistence in many communities. Hitherto, factors encouraging stable coexistence have been well documented. Neighborhood interactions and local dispersal increase intraspecific competition relative to interspecific (Pacala, 1986; Ives, 1988). Spatial subdivision and local dispersal can cause intriguing spatial dynamics and stabilize predator–prey dynamics (Hassell et al., 1991). Trade-offs between the abilities of colonization and competition forms a stable coexistence of a competitor and a fugitive (MacArthur and Wilson, 1967; Horn and MacArthur, 1972; Tilman, 1994). Our results imply that spatial coexistence can arise from the appropriate three-way interspecific trade-offs among competitive ability, colonization ability and niche-construction ability. Models that combine the population dynamics and environmental dynamics may be the best explanation to competing coexistence. Invariant-environmental assumption should be challenged and displaced by inter-feedback between variant environments and biotic interactions. 3.4. Biodiversity and entangling community Species richness, abundances, and heterogeneity of their spatial or temporal distributions in a given area are the central subjects of community ecology (He and Legendre, 2002). Neutral community model and numerous experiments have been applied into community ecology to explain the mechanism underlying (see review in Bell, 2001). The function and significance of biodiversity may be the key to this central subjects, which is still in vagueness, especially the relationship between ecosystem stability and biodiversity (Naeem and Li, 1997; Tilman et al., 1996). May (2001) indicated that value of biological diversity is narrowly utilitarian (benefits already derived from natural products), diffusely utilitarian (that the interactions between biological and physical processes cre-

ated and maintained the earth’s biosphere as a place where life can flourish) and an ethical impetration. Through interspecific niche construction, competition is not the only factor influencing the structure and dynamics of communities. Superior competitor interfere the survival of the inferior, while inferior competitor can alter the necessary resource level of superior competitor. Our results show that the influence of niche construction is alternatively positive (P) and negative (N) with competitive rank (. . . PNPN. . . ). Flourish of species i will lead to the decline of species i + 1, and the rest may be deduced by analogy. Although only niche construction from species n to species 1 is concerned, it implies that species richness is important to the dynamics and consequences of communities, and chain reactions may be potential in ecosystems. Species richness can profoundly influence community’s dynamics and structure. Community is an entangling system with biotic interactions and organism–environmental relationships, and needs additional researches. The particular model we use has properties that are likely to exemplify a broad class of models, and our assumptions concerning resource dynamics are made largely on the basis of analytical convenience. This pregnant model can amplify the effects of niche construction on dynamics, distribution and competition, and reveal the mechanisms underlying distinctly. In realistic ecosystem, this model needs specializing, such as the displacement of Levins’ model with spatially explicit model of spatial structured population (e.g., the incidence function model; Hanski, 1999) and the substitution of resource dynamics comprising more factors, such as diffusive rate and the niche construction by the superior competitor, for the simply dynamics of resources.

Acknowledgements This work was supported by the National Natural Science Foundation of China (grant nos. 39970135 and 30070139) and the National Key Basic Research Program (grant nos. G2000018603 and 2002CCA00300). We are grateful to Dr. Xue Tan, Dr. Xiao-zhuo Han, and Dr. Feng Zhang for their constructive comments and kind help with the English of this manuscript. We also thank the help comments


received from two anonymous reviewers and the editors. References Bell, G., 2001. Neutral macroecology. Science 293, 2413–2418. DeAngelis, D.L., 1992. Dynamics of Nutrient Cycling and Food Webs. Chapman & Hall, London. Flecker, A.S., 1996. Ecosystem engineering by a dominant detritivore in a diverse tropical stream. Ecology 77, 1845–1854. Gilbert, B., 1985. A tree too tough to kill. Audubon 87, 84–96. Hansell, M., 1984. Animal Architecture and Building Behavior. Longman, New York. Hanski, I., 1998. Metapopulation dynamics. Nature 396, 41–49. Hanski, I., 1999. Metapopulation Ecology. Oxford University Press, Oxford. Hassell, M.P., Comins, H.N., May, R.M., 1991. Spatial structure and chaos in insect population dynamics. Nature 353, 255–258. Hastings, A., 1980. Disturbance, coexistence, history, and competition for space. Theor. Popul. Biol. 18, 363–373. He, F., Legendre, P., 2002. Species diversity patterns derived from species–area models. Ecology 83, 1185–1198. Hendry, R., McGlade, J.M., Weiner, J., 1996. A coupled map lattice model of the growth of plant monocultures. Ecol. Model. 84, 81–90. Hendry, R., Bacon, P.J., Moss, R., Palmer, S.C.F., McGlade, J.M., 1997. A two-dimensional individual-based model of territorial behaviour: possible population consequences of kinship in Red Grouse. Ecol. Model. 105, 23–39. Hölldobler, B., Wilson, E.O., 1995. Journey to the Ants: a Story of Scientific Exploration. Belknap, Cambridge. Holt, R.D., Keitt, T.H., 1999. Alternative causes for range limits: a metapopulation perspective. Ecol. Lett. 3, 41–47. Horn, H.S., MacArthur, R.H., 1972. Competition among fugitive species in a harlequin environment. Ecology 53, 749–752. Hui, C., Li, Z., 2003. Dynamical complexity and metapopulation persistence. Ecol. Model. 164, 201–209. Humphries, H.C., Coffin, D.P., Lauernroth, W.K., 1996. An individual-based model of alpine plant distributions. Ecol. Model. 84, 99–126. Hunter, A.F., Aarssen, L.W., 1988. Plants helping plants. BioScience 38, 34–40. Hutchinson, G.E., 1961. The paradox of the plankton. Am. Nat. 95, 137–147. Ives, A.R., 1988. Covariance, coexistence and the population dynamics of two competitors using a patchy resource. J. Theor. Biol. 133, 345–361. Jeltsch, F., Wissel, C., 1994. Modelling dieback phenomena in natural forests. Ecol. Model. 75/76, 111–121. Johnson, C., 1976. Introduction to Natural Selection. University Park Press, Baltimore. Jones, C.G., Lawton, J.H., Shachak, M., 1994. Organisms as ecosystem engineers. Oikos 69, 373–386. Jones, C.G., Lawton, J.H., Shachak, M., 1997. Positive and negative effects of organisms as physical ecosystem engineers. Ecology 78, 1946–1957.

117

Jørgensen, S.E., 1997. Integration of Ecosystem Theories: a Pattern. Kluwer Academic Publishers, Boston. Kauffman, S.A., 2000. Investigations. Oxford University Press, Oxford. Keeling, M., 1999. Spatial models of interacting populations. In: McGlade, J.M. (Ed.), Advanced Ecological Theory: Principles and Applications. Blackwell, Oxford, pp. 64–99. Keitt, T.H., 1997. Stability and complexity on a lattice: co-existence of species in an individual-based food web model. Ecol. Model. 102, 243–258. Keitt, T.H., Lewis, M.A., Holt, R.D., 2001. Allee effects, invasion pinning, and species’ borders. Am. Nat. 157, 203–216. Koh, H.L., Hallam, T.G., Lee, H.L., 1997. Combined effects of environmental and chemical stressors on a model Daphnia population. Ecol. Model. 103, 19–32. Laland, K.N., Odling-Smee, F.J., Feldman, M.W., 1999. Evolutionary consequences of niche construction and their implications for ecology. Proc. Natl. Acad. Sci. USA 96, 10242– 10247. Lehman, C.L., Tilman, D., 1997. Competition in spatial habitats. In: Tilman, D., Kareiva, P. (Eds.), Spatial Ecology: the Role of Space in Population Dynamics and Interspecific Interactions. Princeton University Press, Princeton, pp. 185–203. Lenton, T.M., 1998. Gaia and natural selection. Nature 394, 439– 447. Levin, S.A., 1992. The problem of patterns and scales in ecology. Ecology 73, 1943–1967. Levin, S.A., Paine, R.T., 1974. Disturbance, patch formation, and community structure. Proc. Natl. Acad. Sci. USA 71, 2744– 2747. Levins, R., 1969. Some demographic and genetic consequences of environmental heterogeneity for biological control. Bull. Entomol. Soc. Am. 15, 237–240. Lewontin, R., 1979. Sociobiology as an adaptationist program. Behav. Sci. 24, 5–14. Li, Z., Lin, H., 1997. The niche-fitness model of crop population and its application. Ecol. Model. 104, 199–203. Li, Z., Hui, C., Xu, Z.M., Liu, F.M., 2002. Mathematical model of niche construction for desert vegetation and its applications. J. Glaciol. Geocryol. 24, 387–392. MacArthur, R.H., Wilson, E.O., 1967. The Theory of Island Biogeography. Princeton University Press, Princeton. Maddison, A.C., Holt, J., Jeger, M.J., 1996. Spatial dynamics of a monocyclic disease in a perennial crop. Ecol. Model. 88, 45–52. May, R.M., 1981. Theoretical Ecology: Principles and Applications. Blackwell, Oxford. May, R.M., 2001. Biological Diversity: Causes, Consequences, and Conservation. The Asahi Glass Foundation, Tokyo. McGlade, J.M., 1999. Advanced Ecological Theory: Principles and Applications. Blackwell, Oxford. Molles, M.C., 2000. Ecology: Concepts and Applications. McGraw-Hill, New York. Murray, J.D., 1999. Mathematical Biology. Springer-Verlag, Berlin. Naeem, S., Li, S., 1997. Biodiversity enhances ecosystem reliability. Nature 390, 507–509. Nee, S., May, R.M., 1992. Dynamics of metapopulations: habitat destruction and competitive coexistence. J. Anim. Ecol. 61, 37–40.

118


Nowak, R.M., 1991. Walker’s Mammals of the World. John Hopkins University Press, Baltimore. Odling-Smee, F.J., Laland, K.N., Feldman, M.W., 1996. Niche construction. Am. Nat. 147, 641–648. Pacala, S.W., 1986. Neighborhood models of plant population dynamics: Part 4. Single-species and multispecies models of annuals with dormant seeds. Am. Nat. 128, 859–878. Platt, W., Weis, I., 1977. Resource partitioning and competition within a guild of fugitive prairie plants. Am. Nat. 111, 479–513. Provencher, L., Reichert, S.E., 1995. Theoretical comparisons of individual success between phenotypically pure and mixed generalist predator populations. Ecol. Model. 82, 175–191. Reuter, H., Breckling, B., 1994. Self organization of fish schools: an object oriented model. Ecol. Model. 75, 147–159. Scheffer, M., Baveco, J.M., DeAngelis, D.L., Rose, K.A., van Nes, E.H., 1995. Super-individuals a simple solution for modelling large populations on an individual basis. Ecol. Model. 80, 161– 170. Silvertown, J.W., Doust, J.L., 1993. Introduction to Plant Population Biology. Blackwell, Oxford. Swart, J., Lawes, M.J., 1996. The effects of habitat patch connectivity on samango monkey (Cercopithecus mitis) metapopulation persistence. Ecol. Model. 93, 57–74. Tilman, D., Kareiva, P., 1997. Spatial Ecology: the Role of Space in Population Dynamics and Interspecific Interactions. Princeton University Press, Princeton. Tilman, D., 1994. Competition and biodiversity in spatially structured habitats. Ecology 75, 2–16.

Tilman, D., May, R.M., Lehman, C.L., Nowak, M.A., 1994. Habitat destruction and the extinction debt. Nature 371, 65– 66. Tilman, D., Wedon, D., Knops, J., 1996. Productivity and sustainability influenced by biodiversity in grassland ecosystems. Nature 379, 718–720. Van de Koppel, J., Herman, P.M.J., Thoolen, P., Help, C.A., 2001. Do alternative stable states occur in natural ecosystems? Evidence from a tidal Flat. Ecology 82, 3449–3461. Vitousek, P.M., Mooney, H.A., Lubchenco, J., Melillo, J.M., 1997. Human domination of earth’s ecosystems. Science 277, 494– 499. White, J., 1981. The allometric interpretation of the self-thinning rule. J. Theor. Biol. 89, 475–500. Whitford, W.G., Anderson, J., Rice, P.M., 1997. Stemflow contribution to the fertile island effect in creosobush, larrea tridentat. J. Arid Environ. 35, 451–457. Williams, M., 1996. A three-dimensional model of forest development and competition. Ecol. Model. 89, 73–98. Willis, K.J., Braun, M., Sumegi, P., Tóth, A., 1997. Does soil change cause vegetation change or vice versa? A temporal perspective from hungary. Ecology 78, 740–750. Wu, Y.G., Sklar, F.H., Gopu, K., Rutchey, K., 1996. Fire simulations in the everglades landscape using parallel programming. Ecol. Model. 93, 113–124. Yu, D.W., Wilson, H.B., 2001. The competition–colonization tradeoff is dead long live the competition–colonization trade-off. Am. Nat. 158, 49–63.