利用元胞自动机研究一类捕食食饵模型中的斑块扩散现象

利用概率元胞自动机模型对空间隐式的、食饵具Allee效应的一类捕食食饵模型进行模拟,发现随着相关参数的变化,种群的空间扩散前沿由连续的扩散波逐渐转变为一种相互隔离的斑块向外扩散,这种斑块扩散现象与以往的扩散模式有所不同。研究结果表明：(1)在斑块扩散的情况下,相关参数的微小变化会导致种群灭绝或者形成连续的扩散波,即斑块扩散发生在种群趋于灭绝和连续扩散之间;(2)当种群的空间扩散方式为斑块扩散时,种群的扩散速度会变慢,与其他扩散方式下的速度有着明显的区别。该研究结果对生物入侵控制和外来物种监测有重要的启发和指导作用。     

Patterns of Patchy Spread in Deterministic and Stochastic Models of Biological Invasion and Biological Control

A few spatiotemporal models of population dynamics are considered in relation to biological invasion and biological control. The patterns of spread in one and two spatial dimensions are studied by means of extensive numerical simulations. We show that, in the case that population multiplication is damped by the strong Allee effect (when the population growth rate becomes negative for small population density), in a certain parameter range the spread can take place not via the intuitively expected circular expanding population front but via motion and interaction of separate patches. Alternatively, the patchy spread can take place in a system without Allee effect as a result of strong environmental noise. We then show that the phenomenon of deterministic patchy invasion takes place ‘at the edge of extinction’ so that a small change of controlling parameters either brings the species to extinction or restores the travelling population fronts. Moreover, we show that the regime of patchy invasion in two spatial dimensions actually takes place when the species go extinct in the corresponding 1-D system.     

Patterns of patchy spread in multi-species reaction–diffusion models

Spread of populations in space often takes place via formation, interaction and propagation of separated patches of high species density, without formation of continuous fronts. This type of spread is called a ‘patchy spread’. In earlier models, this phenomenon was considered to be a result of a pronounced environmental or/and demographic stochasticity. Recently, it was found that a patchy spread can arise in a fully deterministic predator–prey system and in models of infectious diseases; in each case the process takes place in a homogeneous environment. It is well recognized that the observed patterns of patchy spread in nature are a result of interplay between stochastic and deterministic factors. However, the models considering deterministic mechanism of patchy spread are developed and studied much less compared to those based on stochastic mechanisms. A further progress in the understanding of the role of deterministic factors in the patchy spread would be extremely helpful. Here we apply multi-species reaction–diffusion models of two spatial dimensions in a homogeneous environment. We demonstrate that patterns of patchy spread are rather common for the considered approach, in particular, they arise both in mutualism and competition models influenced by predation. We show that this phenomenon can occur in a system without a strong Allee effect, contrary to what was assumed to be crucial in earlier models. We show, as well, a pattern of patchy spread having significantly different speeds in different spatial directions. We analyze basic features of spatiotemporal dynamics of patchy spread common for the reaction–diffusion approach. We discuss in which ecosystems we would observe patterns of deterministic patchy spread due to the considered mechanism.     

Allee effect makes possible patchy invasion in a predator–prey system

The dynamics of interacting ecological populations results from the interplay between various deterministic and stochastic factors and this is particularly the case for the phenomenon of biological invasion. Whereas the spread of invasive species via propagation of a population front was shown to appear as a result of deterministic processes, the spread via formation, interaction and movement of separate patches has been recently attributed to the influence of environmental stochasticity. An appropriate understanding of the comparative importance of deterministic and stochastic mechanisms is still lacking, however. In this paper, we show that the patchy invasion appears to be possible also in a fully deterministic predator–prey model as a result of the Allee effect.     

Bacterial predator–prey dynamics in microscale patchy landscapes

Soil is a microenvironment with a fragmented (patchy) spatial structure in which many bacterial species interact. Here, we explore the interaction between the predatory bacterium Bdellovibrio bacteriovorus and its prey Escherichia coli in microfabricated landscapes. We ask how fragmentation influences the prey dynamics at the microscale and compare two landscape geometries: a patchy landscape and a continuous landscape. By following the dynamics of prey populations with high spatial and temporal resolution for many generations, we found that the variation in predation rates was twice as large in the patchy landscape and the dynamics was correlated over shorter length scales. We also found that while the prey population in the continuous landscape was almost entirely driven to extinction, a significant part of the prey population in the fragmented landscape persisted over time. We observed significant surface-associated growth, especially in the fragmented landscape and we surmise that this sub-population is more resistant to predation. Our results thus show that microscale fragmentation can significantly influence bacterial interactions.     

A functional response model of a predator population foraging in a patchy habitat

1. Functional response models (e.g. Holling's disc equation) that do not take the spatial distributions of prey and predators into account are likely to produce biased estimates of predation rates. 2. To investigate the consequences of ignoring prey distribution and predator aggregation, a general analytical model of a predator population occupying a patchy environment with a single species of prey is developed. 3. The model includes the density and the spatial distribution of the prey population, the aggregative response of the predators and their mutual interference. 4. The model provides explicit solutions to a number of scenarios that can be independently combined: the prey has an even, random or clumped distribution, and the predators show a convex, sigmoid, linear or no aggregative response. 5. The model is parameterized with data from an acarine predator-prey system consisting of Phytoseiulus persimis and Tetranychus urticae inhabiting greenhouse cucumbers. 6. The model fits empirical data quite well and much better than if prey and predators were assumed to be evenly distributed among patches, or if the predators were distributed independently of the prey. 7. The analyses show that if the predators do not show an aggregative response it will always be an advantage to the prey to adopt a patchy distribution. On the other hand, if the predators are capable of responding to the distribution of prey, then it will be an advantage to the prey to be evenly distributed when its density is low and switch to a more patchy distribution when its density increases. The effect of mutual interference is negligible unless predator density is very high. 8. The model shows that prey patchiness and predator aggregation in combination can change the functional response at the population level from type II to type III, indicating that these factors may contribute to stabilization of predator-prey dynamics.     

Revising the Role of Species Mobility in Maintaining Biodiversity in Communities with Cyclic Competition

One of the most crucial tasks faced by biologists today is revealing the mechanisms which account for biodiversity, yet we are still far from a full understanding of these mechanisms, and in particular the role of spatially heterogeneous population distributions. Recently, the spatially heterogeneous coexistence seen in cyclic competition models-in which species compete as in the game rock-paper-scissors-has brought them to the fore as a paradigm for biodiversity. Research into cyclic competition has so far been focused almost exclusively on stochastic lattice models with discrete space, which ignore several key dynamical aspects. In particular, such models usually assume that species disperse at the same speed. This paper aims to extend our understanding of cyclic competition by applying a reaction-diffusion Lotka-Volterra scheme to the problem, which allows us to vary the mobility of each species, and lets us take into account cyclic competition with more complex underlying mechanisms. In this paper we reveal an entirely new kind of cyclic competition-'conditional' cyclic competition, with a different underlying mechanism to 'classic' cyclic competition-and we show that biodiversity in communities with cyclic competition in fact depends heavily on the ratios between the species mobilities. Furthermore, we show that this dependence can be completely different for conditional and classic cyclic competition. We also present a wide range of spatiotemporal patterns which are formed in the system, including spiral and target waves, spiralling patches, and irregular chaotic patches. We show that the previously unknown case of conditional cyclic competition is host to a scenario of patchy co-invasion, where the spread of the population front takes place via the formation, splitting and propagation of patches of high species density. This is also an example of invasional meltdown because one competitor facilitates the invasion of the other, but unlike well-known cases of invasional meltdown the co-invaders in this system are not mutualists but antagonistic competitors, and the overall result mitigates, rather than amplifies, the damage done to the native ecosystem.     

An exactly solvable model of population dynamics with density-dependent migrations and the Allee effect

We consider a single-species model of population dynamics allowing for migrations and the Allee effect. Two types of migration are taken into account: one caused by environmental factors (e.g., a passive transport with the wind or water current) and the other associated with biological mechanisms. While the first type is apparently density-independent, the speed of migration in the second one can depend on the population density. Mathematically, this model consists of a non-linear partial differential equation of advection-diffusion-reaction type. Using an appropriate change of variables, we obtain an exact solution of the equation describing propagation of travelling population fronts. We show that, depending on parameter values and thus on the relative intensity of density-dependent and density-independent factors, the direction of the propagation can be different thus describing either species invasion or species retreat.     

Transient dynamics limit the effectiveness of keystone predation in bringing about coexistence

We analyze the transient dynamics of simple models of keystone predation, in which a predator preferentially consumes the dominant of two (or more) competing prey species. We show that coexistence is unlikely in many systems characterized both by successful invasion of either prey species into the food web that lacks it and by a stable equilibrium with high densities of all species. Invasion of the predator-resistant consumer species often causes the resident, more vulnerable prey to crash to such low densities that extinction would occur for many realistic population sizes. Subsequent transient cycles may entail very low densities of the predator or of the initially successful invader, which may also preclude coexistence of finite populations. Factors causing particularly low minimum densities during the transient cycles include biotic limiting resources for the prey, limited resource partitioning between the prey, a highly efficient predator with relatively slow dynamics, and a vulnerable prey whose population dynamics are rapid relative to the less vulnerable prey. Under these conditions, coexistence of competing prey via keystone predation often requires that the prey's competitive or antipredator characteristics fall within very narrow ranges. Similar transient crashes are likely to occur in other food webs and food web models.     

Invasion of an intermediate predator: the dynamics of fish populations in the mathematical model of a trophic chain (as applied to the Syamozero lake)

We present a mathematical model of the dynamics of a spatially heterogeneous predator-prey population system. A prototype of the model system is the Syamozero lake fish community. We study the impact of the invader, an intermediate predator, on the dynamics of the fish community. We show that the invasion can lead to the appearance of chaotic oscillations in the population density. We show also that different dynamical regimes resulting from the invasion, i.e., stationary, non-chaotic oscillatory and chaotic ones, can coexist. The "choice" of a specific regime therewith depends on the initial invader density. Our analysis of solutions of the mathematical models shows that the successful invasion of the alien species takes place solely in the absence of the competition between the invaders and the native species.     

Metapopulation dynamics for spatially extended predator–prey interactions

Traditional metapopulation theory classifies a metapopulation as a spatially homogeneous population that persists on neighboring habitat patches. The fate of each population on a habitat patch is a function of a balance between births and deaths via establishment of new populations through migration to neighboring patches. In this study, we expand upon traditional metapopulation models by incorporating spatial heterogeneity into a previously studied two-patch nonlinear ordinary differential equation metapopulation model, in which the growth of a general prey species is logistic and growth of a general predator species displays a Holling type II functional response. The model described in this work assumes that migration by generalist predator and prey populations between habitat patches occurs via a migratory corridor. Thus, persistence of species is a function of local population dynamics and migration between spatially heterogeneous habitat patches. Numerical results generated by our model demonstrate that population densities exhibit periodic plane-wave phenomena, which appear to be functions of differences in migration rates between generalist predator and prey populations. We compare results generated from our model to results generated by similar, but less ecologically realistic work, and to observed population dynamics in natural metapopulations.     

Community structure and the evolution of aposematic coloration

Studies on the evolution of aposematic coloration (prey coloration advertising for unpalatability) have mainly focused on predator psychology in simplified single-prey species systems. We chose, instead, to model population dynamics on the community level. We studied the invasion by an aposematic phenotype in the presence and absence of another prey species. The single-prey and two-prey models differed in two major ways. First, with two prey species the invasion was possible only with a weak aposematic signal, whereas with a single prey species there was no such an upper limit for signal strength. Second, with a single prey species, increase of the aposematic phenotype always resulted in rapid extinction of the predator. Resource value and growth rate of the alternative prey species affected the invasion. These results suggest that community structure is an important determinant of the conditions for invasion of aposematism, and may have contributed to its initial evolution.     

Regional and local scale metapopulation dynamics in the interaction between Callosobruchus maculatus and Anisopteromalus calandrae

Habitat structure increases the persistence of many extinction‐prone resource–consumer interactions. Metapopulation theory is one of the leading approaches currently used to explain why local, ephemeral populations persist at a regional scale. Central to the metapopulation concept is the amount of dispersal occurring between patches, too much or too little can result in regional extinction. In this study, the role of dispersal on the metapopulation dynamics of an over‐exploitative host–parasitoid interaction is assessed. In the absence of the parasitoid the highly vagile bruchid, Callosobruchus maculatus, can maintain a similar population size regardless of the permeability of the inter‐patch matrix and exhibits strong negative density‐dependence. After the introduction of the parasitoid the size of the bruchid population decreases with a corresponding increase in the occurrence of empty patches. In this case, limiting the dispersal of both species decouples the interaction to a greater extent and results in larger regional bruchid populations. Given the disparity between the dispersal rates of the two species, it is proposed that the more dispersive host benefits from the reduction in landscape permeability by increasing the opportunity to colonise empty patches and rescue extinction prone populations. Associated with the introduction of the parasitoid is a shift in the strength of density‐dependence as the population moves from bottom–up towards top–down regulation. The importance of local and regional scale measurements is apparent when the role of individual patches on regional dynamics is considered. By only taking regional dynamics into account the importance of dispersal regime on local dynamics is overlooked. Similarly, when local dynamics were examined, patches were found to have different influences on regional dynamics depending on dispersal regime and patch location.     

Predation and the evolutionary dynamics of species ranges

Gene flow that hampers local adaptation can constrain species distributions and slow invasions. Predation as an ecological factor mainly limits prey species ranges, but a richer array of possibilities arises once one accounts for how predation alters the interplay of gene flow and selection. We extend previous single-species theory on the interplay of demography, gene flow, and selection by investigating how predation modifies the coupled demographic-evolutionary dynamics of the range and habitat use of prey. We consider a model for two discrete patches and a complementary model for species along continuous environmental gradients. We show that predation can strongly influence the evolutionary stability of prey habitat specialization and range limits. Predators can permit prey to expand in habitat or geographical range or, conversely, cause range collapses. Transient increases in predation can induce shifts in prey ranges that persist even if the predator itself later becomes extinct. Whether a predator tightens or loosens evolutionary constraints on the invasion speed and ultimate size of a prey range depends on the predator effectiveness, its mobility relative to its prey, and the prey's intraspecific density dependence, as well as the magnitude of environmental heterogeneity. Our results potentially provide a novel explanation for lags and reversals in invasions.     

Invasion of an intermediate predator: Fish population dynamics in a mathematical model of a trophic chain (As applied to Syamozero lake)

A mathematical model is presented for the dynamics of a spatially heterogeneous predator-prey population system; a prototype is the Syamozero lake fish community. We show that the invasion of an intermediate predator can evoke chaotic oscillations in the population densities. We also show that different dynamic regimes (stationary, nonchaotic oscillatory, and chaotic) can coexist. The “choice” of a particular regime depends on the initial invader density. Analysis of the model solutions shows that invasion of an alien species is successful only in the absence of competition between the juvenile invaders and the native species.     

On the importance of dimensionality of space in models of space-mediated population persistence

Spatially explicit models have become widely used in today's mathematical ecology to study persistence of populations. For the sake of simplicity, population dynamics is often analyzed with 1-D models. An important question is: how adequate is such 1-D simplification of 2-D (or 3-D) dynamics for predicting species persistence. Here we show that dimensionality of the environment can play a critical role in the persistence of predator-prey interactions. We consider 1-D and 2-D dynamics of a predator-prey model with the prey growth damped by the Allee effect. We show that adding a second space coordinate into the 1-D model results in a pronounced increase of size of the domain in the parametric space where predator-prey coexistence becomes possible. This result is due to the possibility of formation of a number of 2-D patterns, which is impossible in the 1-D model. The 1-D and the 2-D models exhibit different qualitative responses to variations of system parameters. We show that in ecosystems having a narrow width (e.g. mountain valleys, vegetation patterns along canals in dry areas, etc.), extinction of species is more probable compared to ecosystems having a pronounced second dimension. In particular, the width of a long narrow natural reserve should be large enough to guarantee nonextinction of species via interaction of 2-D population patches.     

Regimes of biological invasion in a predator-prey system with the Allee effect

Spatiotemporal dynamics of a predator-prey system is considered under the assumption that prey growth is damped by the strong Allee effect. Mathematically, the model consists of two coupled diffusion-reaction equations. The initial conditions are described by functions of finite support which corresponds to invasion of exotic species. By means of extensive numerical simulations, we identify the main scenarios of the system dynamics as related to biological invasion. We construct the maps in the parameter space of the system with different domains corresponding to different invasion regimes and show that the impact of the Allee effect essentially increases the system spatiotemporal complexity. In particular, we show that, as a result of the interplay between the Allee effect and predation, successful establishment of exotic species may not necessarily lead to geographical spread and geographical spread does not always enhance regional persistence of invading species.     

Biodiversity as both a cause and consequence of resource availability: a study of reciprocal causality in a predator-prey system

1. One of the oldest questions in ecology is how species diversity in any given trophic level is related to the availability of essential resources that limit biomass (e.g. water, nutrients, light or prey). Researchers have tried to understand this relationship by focusing either on how diversity is influenced by the availability of resources, or alternatively, how resource abundance is influenced by species diversity. These contrasting perspectives have led to a seeming paradox '... is species diversity the cause or the consequence of resources that limit community biomass?' 2. Here we present results of an experiment that show it is possible for species diversity and resource density to exhibit reciprocal causal relationships in the same ecological system. Using a guild of ladybeetle predators and their aphid prey, we manipulated the number of predator species in field enclosures to examine how predator diversity impacts prey population size. At the same time, we manipulated the abundance of aphid prey in discrete habitat patches within each enclosure to determine how smaller-scale spatial variation in resource abundance affects the number of co-occurring predator species. 3. We found that the number of ladybeetle species added to enclosures had a significant impact on aphid population dynamics because interference competition among the predators reduced per capita rates of predation and, in turn, the overall efficiency of the predator guild. At the same time, spatial variation in aphid abundance among smaller habitat patches generated variation in the observed richness of ladybeetles because more species occurred in patches where predators aggregated in response to high aphid density. 4. The results of our experiment demonstrate that it is possible for species diversity to simultaneously be a cause and a consequence of resource density in the same ecological system, and they shed light on how this might occur for groups of mobile consumers that exhibit rapid responses to spatial and temporal variation in their prey.     

The dynamics of predation and competition in patchy environments

The model of N. D. Atkinson and B. Shorrocks (J. Anim. Ecol. 50, 461–471 (1981)) as two competing species distributing their progeny amongst patches according to independent negative binomial distributions. The resulting separation of the species increases the likelihood of coexistence. We have assumed a much simpler distribution of the competitors which has enabled us to explore analytically the dynamics of interactions with two competing species and a shared natural enemy in a patchy environment. Two types of natural enemy have been considered: a generalist predator whose dynamics are uncoupled from those of the two prey species, and a specialist (e.g., a parasitoid) whose dynamics are entirely coupled to those of its two prey. The following conclusions emerge. Non-aggregating generalist predators causing random predation across patches are generally destabilizing (although asymmetrical predation may in some case enhance coexistence as a result of preferential predation on the superior competitor). Predator aggregation in patches of high prey density, however, produces a switching effect which tends to promote stability. Coexistence is now even possible with high degrees of correlation in the distribution of the two prey and in situations of extreme competition where the competition coefficients exceed one. The main difference in the models with a specialist parasitoid as the natural enemy is a reduction in stability compared with the equivalent generalist-prey interaction. But stable coexistence can still readily occur if the natural enemies aggregate markedly in patches of high prey density.     

From simple rules to cycling in community assembly

Simulation studies of community assembly have frequently observed two related phenomena: (1) the humpty dumpty effect in which communities can not be reconstructed by "sequential" invasions (i.e. single species invasions separated by long intervals of time) and (2) cycling between sub-communities. To better understand the mechanisms underlying these phenomena, we analyze a system consisting of two predators and two prey competing for a shared resource. We show how simple dominance rules (i.e. R^* and P^* rules) lead to cycling between sub-communities consisting of predator–prey pairs; predator and prey invasions alternatively lead to prey displacement via apparent competition and predator displacement via exploitative competition. We also show that these cycles are often dynamically unstable in the population phase space. More specifically, while for too slow invasion rates (i.e. "sequential" invasions) the system cycles indefinitely, faster invasion rates lead to coexistence of all species. In the later case, the assembly dynamics exhibit transient cycling between predator-prey subcommunities and the length of these transients decreases with the invasion rate and increases with habitat productivity.