基于个体的空间显性模型和遥感技术模拟入侵植物扩张机制

基于个体的空间显性模型和遥感技术,以互花米草为例,模拟了自1997到2010年的种群扩张动态,揭示了土地利用变化与潮间带高程的影响;并通过全局敏感性分析揭示了种子扩散、成体存活率、有性和无性繁殖等种群统计学特征对互花米草种群扩张的相对重要性。研究结果发现:1)有性繁殖与无性繁殖共同决定互花米草种群快速扩张;2)潮间带高程和土地利用变化显著影响模型预测的精度,对互花米草种群扩张有非常重要的影响;3)成体存活率与种子长距离扩散是影响互花米草种群扩张速度最重要的因素;无性繁殖比有性繁殖对种群扩张的影响更大;种子长距离扩散比本地扩散更为重要,同时,小概率的种子长距离扩散事件对种群扩张有非常重要的影响。为了经济有效地控制外来入侵植物的扩张,应该抑制种子的长距离扩散和移除种子长距离扩散形成的位于入侵前沿的小斑块。     

Coexistence of cycling and dispersing consumer species: Armstrong and McGehee in space

Two competing consumer species may coexist using a single homogeneous resource when the more efficient consumer--the one having the lowest equilibrium resource density--has a more nonlinear functional response that generates consumer-resource cycles. We extend this model of nonequilibrium coexistence, as proposed by Armstrong and McGehee, by putting the interaction into a spatial context using two frameworks: a spatially explicit individual-based model and a spatially implicit metapopulation model. We find that Armstrong and McGehee's mechanism of coexistence can operate in a spatial context. However, individual-based simulations suggest that decreased dispersal restricts coexistence in most cases, whereas differential equation models of metapopulations suggest that a low rate of dispersal between subpopulations often increases the coexistence region. This difference arises in part because of two potentially opposing effects on coexistence due to the asynchrony in the temporal dynamics at different locations. Asynchrony implies that the less efficient species is more likely to be favored in some spatial locations at any given time, which broadens the conditions for coexistence. On the other hand, asynchrony and dispersal can also reduce the amplitude of local population cycles, which restricts coexistence. The relative influence of these two effects depends on details of the population dynamics and the representation of space. Our results also demonstrate that coexistence via the Armstrong-McGehee mechanism can occur even when there is little variation in the global densities of either the consumers or the resource, suggesting that empirical studies of the mechanisms should measure densities on several spatial scales.     

Exploring stable pattern formation in models of tussock moth populations

1. The western tussock moth ( Orgyia vetusta ) at the University of California Bodega Marine Reserve (Sonoma County, California, USA) exhibits dense, localized populations in the midst of extensive habitats where variation in host plant quality or predator abundance is unable to explain the restricted extent of the outbreaks.
2. Two primary features suggest that the host patterning is intrinsically generated: (i) female tussock moths are wingless, producing a low effective dispersal distance for the hosts; and (ii) the tussock moth population is attacked by several species of widely dispersing wasp and fly parasitoids.
3. We consider a set of spatially explicit host–parasitoid models to examine whether intrinsically generated patterns are possible within this system. These models include a spatially extended Nicholson–Bailey model to examine general features of pattern formation in host–parasitoid systems, and two system-specific models, an individual-based simulation and a population-level analytic model, to examine the details of this empirical system.
4. Both stable patterning and rapid extinction of the host population are initial-condition dependent outcomes of the general and specific models, implying that an intrinsically generated stable host pattern is feasible within the tussock moth system.
5. Stable patterning is enhanced by a large parasitoid-to-host dispersal ratio, local host resource limitation, and increased parasitism at the host patch's edge.     

Relationships between migration rates and landscape resistance assessed using individual-based simulations

Linking landscape effects on gene flow to processes such as dispersal and mating is essential to provide a conceptual foundation for landscape genetics. It is particularly important to determine how classical population genetic models relate to recent individual-based landscape genetic models when assessing individual movement and its influence on population genetic structure. We used classical Wright-Fisher models and spatially explicit, individual-based, landscape genetic models to simulate gene flow via dispersal and mating in a series of landscapes representing two patches of habitat separated by a barrier. We developed a mathematical formula that predicts the relationship between barrier strength (i.e., permeability) and the migration rate (m) across the barrier, thereby linking spatially explicit landscape genetics to classical population genetics theory. We then assessed the reliability of the function by obtaining population genetics parameters (m, F(ST) ) using simulations for both spatially explicit and Wright-Fisher simulation models for a range of gene flow rates. Next, we show that relaxing some of the assumptions of the Wright-Fisher model can substantially change population substructure (i.e., F(ST) ). For example, isolation by distance among individuals on each side of a barrier maintains an F(ST) of ～0.20 regardless of migration rate across the barrier, whereas panmixia on each side of the barrier results in an F(ST) that changes with m as predicted by classical population genetics theory. We suggest that individual-based, spatially explicit modelling provides a general framework to investigate how interactions between movement and landscape resistance drive population genetic patterns and connectivity across complex landscapes.     

Immigration,Local Dispersal Limitation,and the Repeatability of Community Composition under Neutral and Niche Dynamics

Repeatability of community composition has been a critical aspect for community structure, which is closely associated with community stability, predictability, conservation biology and ecological restoration. It has been shown that both immigration and local dispersal limitation can affect the community composition in both neutral and niche model. Hence, we use a spatially explicit individual-based model to investigate the potential influence of immigration rate and strength of local dispersal limitation on repeatability in both neutral and niche models. Similarity measures are used to quantify repeatability. We examine the repeatability of community composition among replicate communities (which means the same community repeats many times), and between niche and neutral replicate communities. We find the correlation between repeatability and immigration rate is positive in the neutral model and an inverted unimodal in the niche model. The correlation between repeatability and local dispersal distance is positive in the niche model and negative in the neutral model. High repeatability between niche communities and neutral communities is observed with high immigration rates or when high local dispersal distance appears in the niche model or low local dispersal distance in the neutral model. Our results show that repeatability of community composition is not only dependent on the types of community models (niche vs. neutrality) but also strongly determined by immigration rates and local dispersal limitation.     

Mutation accumulation in space and the maintenance of sexual reproduction

The maintenance of sexual reproduction remains one of the major puzzles of evolutionary biology, since, all else being equal, an asexual mutant should have a twofold fitness advantage over the sexual wildtype. Most theories suggest that sex helps either to purge deleterious mutations, or to adapt to changing environments. Both mechanisms have their limitations if they act in isolation because they require either high genomic mutation rates or very virulent pathogens, and it is therefore often thought that they must act together to maintain sex. Typically, however, these theories have in common that they are not based on spatial processes. Here, we show that local dispersal and local competition can explain the maintenance of sexual reproduction as a means of purging deleterious mutations. Using a spatially explicit individual-based model, we find that even with reasonably low genomic mutation rates and large total population sizes, asexual clones cannot invade a sexual population. Our results demonstrate how spatial processes affect mutation accumulation such that it can fully erode the twofold benefit of asexuality faster than an asexual clone can take over a sexual population. Thus, the cost of sex is generally overestimated in models that ignore the effects of space on mutation accumulation.     

Linking the allee effect, sexual reproduction, and temperature-dependent sex determination via spatial dynamics

We develop a spatially explicit, two-sex, individual-based model (IBM) and a derived spatially homogeneous model (SHM) to describe the Allee effect due to scarcity of mating possibilities at low population sizes or densities. The SHM, based on coupled difference equations, represents the first spatially homogeneous approach to this phenomenon, which differentiates between sexes and relies only on measurable population parameters. The IBM reinforces the findings of the SHM by adopting more realistic mate search strategies of diffusive movement and active search. Both models are characterized by a hyperbolic-shaped extinction boundary in the male-female state space, which contrasts with a linear boundary in one-dimensional models of the Allee effect. We examine how the position of the extinction boundary depends on population demography (primary sex ratio, reproduction and mortality probabilities) and adopted mate search strategies. The investigation of different phases in the IBM dynamics emphasizes the differences between local and global densities and shows the importance of scale when assessing the Allee effect. To demonstrate the potential application of our models, we combine the SHM and available data to predict the impact of environmental temperature changes on two turtle species with temperature-dependent sex determination.     

Stabilizing effects in spatial parasitoid-host and predator-prey models: a review

We review the literature on spatial host-parasitoid and predator-prey models. Dispersal on its own is not stabilizing and can destabilize a stable local equilibrium. We identify three mechanisms whereby limited dispersal of hosts and parasitoids combined with other features, such as spatial and temporal heterogeneity, can promote increased persistence and stability. The first mechanisms, "statistical stabilization", is simply the statistical effect that summing a number of out-of-phase population trajectories results in a relatively constant total population density. The second mechanism involves decoupling of immigration from local density, such that limited dispersal between asynchronous patches results in an effect that mimics density-dependence at the local patch level. The third mechanism involves altering spatially averaged parameter values resulting from spatial heterogeneity in density combined with non-linear responses to density. Persistence in spatially explicit models with local dispersal frequently associated with self-organized spatial patterning.     

Attractivity of coherent manifolds in metapopulation models

The likelihood that coupled dynamical systems will completely synchronize, or become “coherent”, is often of great applied interest. Previous work has established conditions for local stability of coherent solutions and global attractivity of coherent manifolds in a variety of spatially explicit models. We consider models of communities coupled by dispersal and explore intermediate regimes in which it can be shown that states in phase space regions of positive measure are attracted to coherent solutions. Our methods yield rigorous and practically useful coherence criteria that facilitate useful analyses of ecological and epidemiological problems.     

Temporal self-similarity created by spatial individual-based population dynamics

We report an individual-based single-species model producing temporal scale-free, self-similar dynamics in time. Individuals in the population renew in an explicit space with a large number of loci. We show that reproduction, subsequent dispersal of the offspring, and mortality will organise population fluctuations such that the emerging dynamics represent power law and scale-free structures. Further, we show that spatially structured population dynamics may show red frequency spectra, a property that the simple nonlinear population models are generally lacking.     

Intraguild predation with spatially structured interactions

Consumer–resource interactions with intraguild predation (IGP) were studied in a spatial setting (i.e., predators catch prey and individuals reproduce within local neighborhoods only). Pair approximation (a method for deriving ordinary differential equations that approximate the dynamics of a community that interacts in a lattice environment) was used to study the effect of spatially structured species interactions. An individual-based computer simulation was used to extend the study to a case with spatially variable resource densities. The qualitative results of the pair approximation model were similar to those of the corresponding non-spatial model. However, the spatial model predicted coex((istence over a wider range of parameters than the non-spatial model when intraguild prey are nutritionally valuable to intraguild predators. Spatially heterogeneous resource distributions and spatially structured interaction could overturn the qualitative predictions of non-spatial models.     

Spreading speed, traveling waves, and minimal domain size in impulsive reaction-diffusion models

How growth, mortality, and dispersal in a species affect the species' spread and persistence constitutes a central problem in spatial ecology. We propose impulsive reaction-diffusion equation models for species with distinct reproductive and dispersal stages. These models can describe a seasonal birth pulse plus nonlinear mortality and dispersal throughout the year. Alternatively, they can describe seasonal harvesting, plus nonlinear birth and mortality as well as dispersal throughout the year. The population dynamics in the seasonal pulse is described by a discrete map that gives the density of the population at the end of a pulse as a possibly nonmonotone function of the density of the population at the beginning of the pulse. The dynamics in the dispersal stage is governed by a nonlinear reaction-diffusion equation in a bounded or unbounded domain. We develop a spatially explicit theoretical framework that links species vital rates (mortality or fecundity) and dispersal characteristics with species' spreading speeds, traveling wave speeds, as well as minimal domain size for species persistence. We provide an explicit formula for the spreading speed in terms of model parameters, and show that the spreading speed can be characterized as the slowest speed of a class of traveling wave solutions. We also give an explicit formula for the minimal domain size using model parameters. Our results show how the diffusion coefficient, and the combination of discrete- and continuous-time growth and mortality determine the spread and persistence dynamics of the population in a wide variety of ecological scenarios. Numerical simulations are presented to demonstrate the theoretical results.     

The role of landscape-dependent disturbance and dispersal in metapopulation persistence

The fundamental processes that influence metapopulation dynamics (extinction and recolonization) will often depend on landscape structure. Disturbances that increase patch extinction rates will frequently be landscape dependent such that they are spatially aggregated and have an increased likelihood of occurring in some areas. Similarly, landscape structure can influence organism movement, producing asymmetric dispersal between patches. Using a stochastic, spatially explicit model, we examine how landscape-dependent correlations between dispersal and disturbance rates influence metapopulation dynamics. Habitat patches that are situated in areas where the likelihood of disturbance is low will experience lower extinction rates and will function as partial refuges. We discovered that the presence of partial refuges increases metapopulation viability and that the value of partial refuges was contingent on whether dispersal was also landscape dependent. Somewhat counterintuitively, metapopulation viability was reduced when individuals had a preponderance to disperse away from refuges and was highest when there was biased dispersal toward refuges. Our work demonstrates that landscape structure needs to be incorporated into metapopulation models when there is either empirical data or ecological rationale for extinction and/or dispersal rates being landscape dependent.     

The evolution of parasite manipulation of host dispersal

We investigate the evolution of manipulation of host dispersal behaviour by parasites using spatially explicit individual-based simulations. We find that when dispersal is local, parasites always gain from increasing their hosts' dispersal rate, although the evolutionary outcome is determined by the costs-to-benefits ratio. However, when dispersal can be non-local, we show that parasites investing in an intermediate dispersal distance of their hosts are favoured even when the manipulation is not costly, due to the intrinsic spatial dynamics of the host-parasite interaction. Our analysis highlights the crucial importance of ecological spatial dynamics in evolutionary processes and reveals the theoretical possibility that parasites could manipulate their hosts' dispersal.     

Selection for intermediate mortality and reproduction rates in a spatially structured population

How local interactions influence both population and evolutionary dynamics is currently a key topic in theoretical ecology. We use a 'well-mixed' analytical model and spatially explicit individual-based models to investigate a system where a population is subject to rare disturbance events. The disturbance can only propagate through regions of the population where the density of individuals is sufficiently high and individuals affected by the disturbance die shortly after. We find that populations where individuals are sessile often exhibit very different dynamic behaviour when compared to populations where individuals are mobile and spatially well mixed. When mutations are allowed which affect either offspring birth rates or mortality rates, the well-mixed populations always evolve to a state where a single disturbance event leads to extinction. Populations often persist substantially longer if individuals are sessile and they disperse their offspring locally. We also find that for sessile populations selection may favour short-lived individuals with limited offspring production. Population dynamics are found to be strongly influenced by the host characters that are evolving and the rate at which host variation is introduced into the system.     

Reid's paradox revisited: the evolution of dispersal kernels during range expansion

Current approaches to modeling range advance assume that the distribution describing dispersal distances in the population (the "dispersal kernel") is a static entity. We argue here that dispersal kernels are in fact highly dynamic during periods of range advance because density effects and spatial assortment by dispersal ability ("spatial selection") drive the evolution of increased dispersal on the expanding front. Using a spatially explicit individual-based model, we demonstrate this effect under a wide variety of population growth rates and dispersal costs. We then test the possibility of an evolved shift in dispersal kernels by measuring dispersal rates in individual cane toads (Bufo marinus) from invasive populations in Australia (historically, toads advanced their range at 10 km/year, but now they achieve >55 km/year in the northern part of their range). Under a common-garden design, we found a steady increase in dispersal tendency with distance from the invasion origin. Dispersal kernels on the invading front were less kurtotic and less skewed than those from origin populations. Thus, toads have increased their rate of range expansion partly through increased dispersal on the expanding front. For accurate long-range forecasts of range advance, we need to take into account the potential for dispersal kernels to be evolutionarily dynamic.     

cdpop: A spatially explicit cost distance population genetics program

Spatially explicit simulation of gene flow in complex landscapes is essential to explain observed population responses and provide a foundation for landscape genetics. To address this need, we wrote a spatially explicit, individual-based population genetics model (cdpop). The model implements individual-based population modelling with Mendelian inheritance and k-allele mutation on a resistant landscape. The model simulates changes in population and genotypes through time as functions of individual based movement, reproduction, mortality and dispersal on a continuous cost surface. This model will be a valuable tool for the study of landscape genetics by increasing our understanding about the effects of life history, vagility and differential models of landscape resistance on the genetic structure of populations in complex landscapes.     

Diffusion-limited predator-prey dynamics in Euclidean environments: an allometric individual-based model

We claim that diffusion-limited rates of reaction can be an explanation for the altered population dynamics predicted by models incorporating local interactions and limited individual mobility. We show that the predictions of a spatially explicit, individual-based model result from reduced rates of predation and reproduction caused by limited individual mobility and patchiness. When these reduced rates are used in a mean-field model, there is better agreement with the predictions of the simulation model incorporating local interactions. We also explain previous findings regarding the effects of dimensionality on population dynamics in light of diffusion-limited reactions and Pólya random walks. In particular, we demonstrate that 3D systems are better "stirred" than 2D systems and consequently have a reduced tendency for diffusion-limited interaction rates.