Structured models of metapopulation dynamics

I develop models of metapopulation dynamics that describe changes in the numbers of individuals within patches. These models are analogous to structured population models, with patches playing the role of individuals. Single species models which do not include the effect of immigration on local population dynamics of occupied patches typically lead to a unique equilibrium. The models can be used to study the distributions of numbers of individuals among patches, showing that both metapopulations with local outbreaks and metapopulations without outbreaks can occur in systems with no underlying environmental variability. Distributions of local population sizes (in occupied patches) can vary independently of the total population size, so both patterns of distributions of local population sizes are compatible with either rare or common species. Models which include the effect of immigration on local population dynamics can lead to two positive equilibria, one stable and one unstable, the latter representing a threshold between regional extinction and persistence.     

The effect of metapopulation dynamics on the survival and spread of a novel, conspicuous prey

Animals that deploy chemical defences against predators often signal their unprofitability using bright colouration. This pairing of toxicity and conspicuous patterning is known as aposematism.Explaining the evolution and spread of aposematic traits in previously cryptic species has been the focus of much empirical and theoretical work over the last two decades. Existing research concerning the initial evolution of aposematism does not however properly consider that many aposematic species (such as members of the hymenoptera, the lepidoptera, and amphibia) are highly mobile. We argue in this paper that the evolution of aposematic displays is therefore often best understood within a metapopulation framework; hence in this paper we present the first explicit metapopulation model of the evolution of aposematism. Our most general finding is that migration tends to reduce the probability that an aposematic prey can increase from rarity and spread across a large population. Hence, the best case scenarios for the spread of aposematism required fixation of the aposematic form in one or more isolated sub-habitats prior to some event which subsequently enabled migration. We observed that changes in frequency of new aposematic forms within source habitats are likely to be nonmonotonic. First, aposematic prey tend to decline in frequency as they migrate outwards from the source habitat to neighbouring sink habitats, but subsequently they increase in relative abundance in the source, as the descendents of earlier migrants migrate back from newly converted sub-populations. This pattern of initial loss and subsequent gain between new source and neighbouring sink habitats is then repeated as the aposematic form spreads via a moving cline.     

The effect of conspecific attraction on metapopulation dynamics

Random dispersal direction is assumed in all current metapopulation models. This assumption is called into question by recent experiments demonstrating that some species disperse preferentially to sites occupied by conspecifies. We incorporate conspecific attraction into two metapopulation models which differ in type of dispersal, the Levins model and a two-dimensional stepping-stone model. In both models, conspecific attraction lowers the proportion of occupied habitat patches within a metapopulation at equilibrium.     

Chaotic dynamics of allele frequencies in condition-dependent mating systems

I study the dynamics of allele frequencies in sexually reproducing populations where the choosy sex has a preference for condition-dependent displays of the opposite sex. The condition of an individual is assumed to be shaped by frequency-dependent selection. For sufficiently strong preferences the dynamics becomes increasingly complex, and periodic orbits and chaos are observed. Moreover, multiple attractors can exist simultaneously. The results hold also when the choosy sex is allowed to maintain a moderate level of assortative mating. Complex dynamics, a well studied phenomenon in a purely ecological setting, has been rarely observed in ecologically motivated population genetic models.     

Evolutionary aspects of the metapopulation dynamics of Biomphalaria pfeifferi,the intermediate host of Schistosoma mansoni

Combining genetic and demographic data is a powerful approach to study adaptation process and evolutionary forces acting in natural populations. We focus on the freshwater snail Biomphalaria pfeifferi, the intermediate host of Schistosoma mansoni. Twenty‐one populations sampled in the south of Madagascar were genotyped at six microsatellite loci. Demographic parameters and parasitic prevalence were estimated monthly over the year preceding the genetic sampling. Our results indicate that populations experience recurrent bottlenecks and size fluctuations, which strongly depresses the genetic diversity within population. The recolonization of depleted sites involves genetically differentiated immigrants. We detected frequent migration events along rivers and rare migration events between watersheds. This explains the high level of differentiation observed among populations. The negative regression observed between the prevalence of S. mansoni and the genetic diversity of B. pfeifferi populations indicates that host consanguinity may affect prevalence through the genetic mechanisms involved in resistance. Coevolutionary outcomes are also influenced by the relative migration rates of snails and flukes, but the parasite local adaptation may be prevented by rare long distance dispersal in snails and the phylogeographical patterns of colonization of both hosts and snails.     

Testing metapopulation dynamics using genetic, demographic and ecological data

The metapopulation concept is a cornerstone in the recent history of ecology and evolution. However, determining whether a natural system fits a metapopulation model is a complex issue. Extinction-colonization dynamics are indeed often difficult to quantify because species detectability is not always 100%, resulting in an imperfect record of extinctions. Here, we explore whether combining population genetics with demographic and ecological surveys can yield more realistic estimates of metapopulation dynamics. We apply this approach to the freshwater snail Drepanotrema depressissimum in a fragmented landscape of tropical ponds. In addition to studying correlations between genetic diversity and demographical or ecological characteristics, we undertake, for the first time, a detailed search for genetic signatures of extinction-recolonization events using temporal changes in allele frequencies within sites. Surprisingly, genetic data indicate that extinction is much rarer than suggested by demographic surveys. Consequently, this system is better described as a set of populations with different sizes and immigration rates than as a true metapopulation. We identify several cases of apparent extinction owing to nondetection of low-density populations, and of aestivating individuals in desiccated ponds. More generally, we observed a frequent mismatch between genetic and demographical/ecological information at small spatial and temporal scales. We discuss the causes of these discrepancies and show how these two types of data provide complementary information on population dynamics and history, especially when temporal genetic samples are available.     

Habitat shape, metapopulation processes and the dynamics of multispecies predator-prey interactions

1. The effects of habitat shape, connectivity and the metapopulation processes of persistence and extinction are explored in a multispecies resource-consumer interaction. 2. The spatial dynamics of the indirect interaction between two prey species (Callosobruchus chinensis, Callosobruchus maculatus) and a predator (Anisopteromalus calandrae) are investigated and we show how the persistence time of this interaction is altered in different habitat configurations by the presence of an apparent competitor. 3. Habitat structure has differential effects on the dynamics of the resource-consumer interaction. Across all habitat types, the pairwise interaction between C. chinensis and A. calandrae is highly prone to extinction, while the interaction between C. maculatus and A. calandrae shows sustained long-term fluctuations. Contrary to expectations from theory, habitat shape has no significant effect on persistence time of the full, three-species resource-consumer assemblage. 4. A stochastic metapopulation model for a range of habitat configurations, incorporating different forms of regulatory processes, highlights that it is the spatially explicit population dynamics rather than the shape of the metapopulation that is the principal determinant of interaction persistence time.     

The effect of emigration and immigration on the dynamics of a discrete-generation population

The recent paper of Sinha and Parthasarathy investigated the effect of modifying the Ricker and logistic population models to simulate the effects of immigration to, and emigration from, the population. Immigration of a fixed number of individuals was shown to reduce the probability of observing chaos in the Ricker model but not the logistic one. Here, isocline analysis is used to investigate why these effects occur. The stabilization effect for the Ricker equation occurs over a wide range of values of the immigration parameter. There are no values of the parameter, however, which increase the stability of the logistic equation substantially. In contrast density-dependent immigration is found to destabilize both the Ricker and logistic models. Density-dependent emigration serves to reduce the propensity of both models to exhibit chaos.     

The effect of migration on metapopulation stability is qualitatively unaffected by demographic and spatial heterogeneity

Coupled map lattices (CMLs), using two coupled logistic equations, have been extensively used to model the dynamics of two-patch ecological systems. Such studies have revealed that migration rate plays an important role in determining the dynamics of the system, particularly when the two maps differ in their intrinsic growth rate parameter, r. However, under more realistic assumptions, a metapopulation can be expected to consist of more than two subpopulations, each with its own demographic parameters, which will in part be a function of the environment of that patch. The role of the spatial arrangement of heterogeneous (i.e. with different r values) subpopulations in shaping the dynamics of such a metapopulation has rarely been investigated. Here, we study the effect of demographic and spatial heterogeneity on the stability of one- and two-dimensional systems of 64 coupled Ricker maps with different r values, under periodic and absorbing boundary conditions. We show that the effects of migration rate on metapopulation stability do not depend upon either the precise spatial arrangement of the subpopulations in the lattice, or on the presence of a moderate proportion of vacant (uninhabitable) patches in the lattice. The results, thus, suggest that metapopulation models are robust to variation in spatial arrangement of patch quality and, hence, of demographic parameters. We also show that for any given arrangement of the patches, maximum stability of the metapopulation occurs when the migration levels are intermediate, a result that agrees well with previous studies on two-map CML systems.     

Gene network dynamics controlling keratinocyte migration

Translation of large‐scale data into a coherent model that allows one to simulate, predict and control cellular behavior is far from being resolved. Assuming that long‐term cellular behavior is reflected in the gene expression kinetics, we infer a dynamic gene regulatory network from time‐series measurements of DNA microarray data of hepatocyte growth factor‐induced migration of primary human keratinocytes. Transferring the obtained interactions to the level of signaling pathways, we predict in silico and verify in vitro the necessary and sufficient time‐ordered events that control migration. We show that pulse‐like activation of the proto‐oncogene receptor Met triggers a responsive state, whereas time sequential activation of EGF‐R is required to initiate and maintain migration. Context information for enhancing, delaying or stopping migration is provided by the activity of the protein kinase A signaling pathway. Our study reveals the complex orchestration of multiple pathways controlling cell migration.     

Climate change effects on migration phenology may mismatch brood parasitic cuckoos and their hosts

Phenological responses to climate change vary among taxa and across trophic levels. This can lead to a mismatch between the life cycles of ecologically interrelated populations (e.g. predators and prey), with negative consequences for population dynamics of some of the interacting species. Here we provide, to our knowledge, the first evidence that climate change might disrupt the association between the life cycles of the common cuckoo (Cuculus canorus), a migratory brood parasitic bird, and its hosts. We investigated changes in timing of spring arrival of the cuckoo and its hosts throughout Europe over six decades, and found that short-distance, but not long-distance, migratory hosts have advanced their arrival more than the cuckoo. Hence, cuckoos may keep track of phenological changes of long-distance, but not short-distance migrant hosts, with potential consequences for breeding of both cuckoo and hosts. The mismatch to some of the important hosts may contribute to the decline of cuckoo populations and explain some of the observed local changes in parasitism rates of migratory hosts.     

SIR传染病模型的混沌跟踪控制

研究了一类疾病传染率受季节因素影响的SIR传染病模型的混沌运动,并采用轨迹跟踪控制方法对传染病模型中的混沌运动进行控制,设计状态反馈控制器,控制系统输出跟踪某一理想状态,使染病者数量渐近趋于零,从而,达到消除疾病的目的．仿真结果表明该方法的有效性．     

In vitro dynamics of chromatin organization and migration

The organization of eukaryotic chromatin is not static but changes as a function of cell status during processes such as proliferation, differentiation, and migration. DNA quantification has not been used extensively to investigate chromatin dynamics in combination with cellular migration. In this context, an optimized DNA-specific, nonperturbant method has been developed for studying chromatin organization, using the fluorescent vital bisbenzimidazole probe Hoechst 33342: this property has been described by Hamori et al. (1980). Computer-assisted image analysis was used to follow migratory activity and chromatin organization of L929 fibroblasts during in vitro wound healing. Cell movements were analyzed using an optical flow technique, which consists in the calculation of the velocity field of cells and nuclear movements in the frame. This system allows the correlation of cell migration and position in the cell cycle. It makes it possible to study chromatin dynamics using a quantitative analysis of nuclear differentiation reorganization (nuclear texture) and to correlate this with migration characteristics. The present system would be of interest for studying cell-extracellular matrix interactions using differing substrates, and also the migratory response to chemotactic factors. Such a model is a prerequisite for gaining better understanding of drug action.     

On the role of body size in a tri-trophic metapopulation model

 A particular tri-trophic (resource, prey, predator) metapopulation model with dispersal of preys and predators is considered in this paper. The analysis is carried out numerically, by finding the bifurcations of the equilibria and of the limit cycles with respect to prey and predator body sizes. Two routes to chaos are identified. One is characterized by an intriguing cascade of flip and tangent bifurcations of limit cycles, while the other corresponds to the crisis of a strange attractor. The results are summarized by partitioning the space of body sizes in eight subregions, each one of which is associated to a different asymptotic behavior of the system. Emphasis is put on the possibility of having different modes of coexistence (stationary, cyclic, and chaotic) and/or extinction of the predator population. Received 1 August 1995; received in revised form 8 January     

Eco-evolutionary metapopulation dynamics and the spatial scale of adaptation

We construct a model that combines extinction-colonization dynamics with the dynamics of local adaptation in a network of habitat patches of dissimilar qualities. We derive a deterministic approximation for the stochastic model that allows the calculation of patch-specific incidences of occupancy and levels of adaptation at steady state. Depending on (i) the strength of local selection, (ii) the amount of genetic variance, (iii) the demographic cost of maladaptation, (iv) the spatial scale of gene flow, and (v) the amount of habitat heterogeneity, the model predicts adaptation at different spatial scales. Local adaptation is predicted when there is much genetic variance and strong selection, while network-level adaptation occurs when the demographic cost of maladaptation is low. For little genetic variance and high cost of maladaptation, the model predicts network-level habitat specialization in species with long-range migration but an intermediate scale of adaptation (mosaic specialization) in species with short-range migration. In fragmented landscapes, the evolutionary dynamics of adaptation may both decrease and enhance metapopulation viability in comparison with no evolution. The model can be applied to real patch networks with given sizes, qualities, and spatial positions of habitat patches.     

Long-term dynamics in a metapopulation of the American pika

A 20-yr study of a metapopulation of the American pika revealed a regional decline in occupancy in one part of a large network of habitat patches. We analyze the possible causes of this decline using a spatially realistic metapopulation model, the incidence function model. The pika metapopulation is the best-known mammalian example of a classical metapopulation with significant population turnover, and it satisfies closely the assumptions of the incidence function model, which was parameterized with data on patch occupancy. The model-predicted incidences of patch occupancy are consistent with observed incidences, and the model predicts well the observed turnover rate between four metapopulation censuses. According to model predictions, the part of the metapopulation where the decline has been observed is relatively unstable and prone to large oscillations in patch occupancy, whereas the other part of the metapopulation is predicted to be persistent. These results demonstrate how extinction-colonization dynamics may produce spatially correlated patterns of patch occupancy without any spatially correlated processes in local dynamics or extinction rate. The unstable part of the metapopulation gives an empirical example of multiple quasi equilibria in metapopulation dynamics. Phenomena similar to those observed here may cause fluctuations in species' range limits.