Finite metapopulation models with density-dependent migration and stochastic local dynamics

The effects of small density-dependent migration on the dynamics of a metapopulation are studied in a model with stochastic local dynamics. We use a diffusion approximation to study how changes in the migration rate and habitat occupancy affect the rates of local colonization and extinction. If the emigration rate increases or if the immigration rate decreases with local population size, a positive expected rate of change in habitat occupancy is found for a greater range of habitat occupancies than when the migration is density-independent. In contrast, the reverse patterns of density dependence in respective emigration and immigration reduce the range of habitat occupancies where the metapopulation will be viable. This occurs because density-dependent migration strongly influences both the establishment and rescue effects in the local dynamics of metapopulations.     

Stabilizing dispersal delays in predator-prey metapopulation models

Time delays produced by dispersal are shown to stabilize Lotka-Volterra predator-prey models. The models are formulated as integrodifferential equations that describe local predator-prey dynamics and either intrapatch or interpatch dispersal. Dispersing individuals may (or may not) differ in the duration of their trips; these differences are captured via a distributed delay in the models. Our results include those of previous studies as special cases and show that the stabilizing effect continues to operate when the dispersal process is modeled more realistically.     

Simple discrete-time metapopulation models of patch occupancy

Simple models in theoretical ecology have a long-standing history of being used to understand how specific processes influence population dynamics as well as providing a foundation for future endeavors. The Levins model is the seminal example of this for continuous-time metapopulation dynamics. However, many natural populations have a distinct separation between processes and data is not collected continuously leading to the need for using a discrete-time model. Our goal is to develop a simple discrete-time metapopulation model of patch occupancy using difference equations. In our formulation, we consider the two fundamental processes of colonization and extinction that will be treated as sequential events and will only consider patch occupancy. To achieve this, we use a composition of two functions where one will reflect the extinction process and the other for the colonization process. Under some mild assumptions, we are able determine the dynamic behavior of the metapopulation. In addition, we provide numerous examples for the functions used to emulate the colonization and extinction processes. Our results illustrate that the dynamics of the model are tied to properties such as convexity and monotonicity of the colonization and extinction functions. In particular, if the model is non-monotone, then complex dynamics can arise such as cyclic and even chaotic behavior. Overall, our approach shows how certain properties of the colonization and extinction functions can influence metapopulation dynamics.     

Spatially discrete metapopulation models with directional dispersal

We use an age-structured discrete-time metapopulation model linking two sub-populations through larval transport and directed movements of adults to study the implications of linkages among subpopulations for the stability and resilience of exploited species. Our two-habitat model, a generalization of Fogarty's inshore-offshore lobster population model, includes isolated habitats under compensatory (monotone) or overcompensatory (oscillatory) dynamics [M.J. Fogarty, Implications of migration and larval interchange in American lobster (Homarus americanus) stocks: spatial structure and resilience, in: G.S. Jamieson, A. Campbell (Eds.), Proc. of North Pacific Symposium on Invertebrate Stock Assessment and Management, Can. Spec. Publ. Fish. Aquat. Sci. 125 (1998) 273]. Pre-migration local dynamics are selected from general classes of functions that capture the effects of competition for resources via contest (compensatory) and scramble (overcompensatory) intraspecific competitions. We explore the implications of these mechanisms on the long-term survival of exploited species. In particular, we use threshold parameters R(d)1 for Habitat 1 and R(d)2 for Habitat 2 together with precise mathematical definitions to prove that species persistence is possible at high levels of fishing in one habitat and low to moderate levels of fishing in the other. Our results support Fogarty's conclusion that conservative management of larval source populations could contribute to the resilience of exploited species.     

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.     

Spatially structured metapopulation models: global and local assessment of metapopulation capacity

We model metapopulation dynamics in finite networks of discrete habitat patches with given areas and spatial locations. We define and analyze two simple and ecologically intuitive measures of the capacity of the habitat patch network to support a viable metapopulation. Metapopulation persistence capacity lambda(M) defines the threshold condition for long-term metapopulation persistence as lambda(M)>delta, where delta is defined by the extinction and colonization rate parameters of the focal species. Metapopulation invasion capacity lambda(I) sets the condition for successful invasion of an empty network from one small local population as lambda(I)>delta. The metapopulation capacities lambda(M) and lambda(I) are defined as the leading eigenvalue or a comparable quantity of an appropriate "landscape" matrix. Based on these definitions, we present a classification of a very general class of deterministic, continuous-time and discrete-time metapopulation models. Two specific models are analyzed in greater detail: a spatially realistic version of the continuous-time Levins model and the discrete-time incidence function model with propagule size-dependent colonization rate and a rescue effect. In both models we assume that the extinction rate increases with decreasing patch area and that the colonization rate increases with patch connectivity. In the spatially realistic Levins model, the two types of metapopulation capacities coincide, whereas the incidence function model possesses a strong Allee effect characterized by lambda(I)=0. For these two models, we show that the metapopulation capacities can be considered as simple sums of contributions from individual habitat patches, given by the elements of the leading eigenvector or comparable quantities. We may therefore assess the significance of particular habitat patches, including new patches that might be added to the network, for the metapopulation capacities of the network as a whole. We derive useful approximations for both the threshold conditions and the equilibrium states in the two models. The metapopulation capacities and the measures of the dynamic significance of particular patches can be calculated for real patch networks for applications in metapopulation ecology, landscape ecology, and conservation biology.     

Landscape dynamics and evolution of colonizer syndromes: interactions between reproductive effortand dispersal in a metapopulation

The evolutionary consequences of changes in landscape dynamics for the evolution of life history syndromes are studied using a metapopulation model. We consider in turn the long-term effects of a change in the local disturbance rate, in the maximal local population persistence, in habitat productivity, and in habitat fragmentation. We examine the consequences of selective interactions between dispersal and reproductive effort by comparing the outcome of joint evolution to a situation where the species has lost the potential to evolve either its reproductive effort or its dispersal rate. We relax the classical assumption that any occupied site in the metapopulation reaches its carrying capacity immediately after recolonization. Our main conclusions are the following: (1) genetic diversity modifies the range of landscape parameters for which the metapopulation is viable, but it alters very little the qualitative evolutionary trends observed for each trait within this range. Although they are both part of a competition/colonization axis, reproductive effort and dispersal are not substitutable traits: their evolution reflects more directly the change in the landscape dynamics, than a selective interaction among them. (2) no general syndrome of covariation between reproductive effort and dispersal can be predicted: the pattern of association between the two traits depends on the type of change in landscape dynamics and on the saturation level. We review empirical evidence on colonizer syndromes and suggest lines for further empirical work. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

Measuring dispersal in a metapopulation using stable isotope enrichment: high rates of sex-biased dispersal between patches in a mayfly metapopulation

Dispersal affects a wide array of ecological and evolutionary processes, but has been difficult to estimate empirically. A ¹⁵Nitrogen stable isotope enrichment technique was used to passively mark all developing Callibaetis ferrugineus hageni (Eaton) mayfly larvae in a beaver pond that had previously been shown to be a patch in a source-sink metapopulation. After enrichment during the larval stages, dispersal among ponds by adult females was demonstrated by the presence of unmarked females ovipositing in the labeled pond, and marked females in an unlabeled pond. Observed frequencies of marked females suggested incomplete mixing between ponds. In contrast, males rarely dispersed from their natal pond, which was consistent with the unusual mating system in this species – adult Callibaetis are short-lived, do not feed, and females are sexually receptive immediately after emerging from the larval habitat. The frequent dispersal demonstrated using the stable isotope technique was a critical component of the source-sink dynamic observed in this metapopulation, and further use of this technique will provide insights into patterns of dispersal in spatially structured habitats.     

Modelling mortality and dispersal: consequences of parameter generalisation on metapopulation dynamics

Modelling dispersal is a fundamental step in the design of population viability analyses. Here, we address the question of the generalisation of population viability analysis models across landscapes by comparing dispersal between two metapopulations of the bog fritillary butterfly ( Proclossiana eunomia ) living in similar highly fragmented landscapes (<1% of suitable habitat in 9 km²). Differences in dispersal patterns were investigated using the virtual migration (VM) model, which was parameterised with capture–mark–recapture data collected during several years in both landscapes. The VM model allows the estimation of 6 parameters describing dispersal and mortality as well as the simulation of dispersal in the landscapes. The model revealed large differences in the VM parameter estimates between the two landscapes and consequently, simulations indicated differential rates of emigration and dispersal mortality. Furthermore, results from crossed-simulations i.e. simulations performed in one of the landscape but using parameter estimates from the other landscape emphasize that dispersal parameters are very specific to each metapopulation and to their landscape. Hence, we urge conservation biologists to be cautious with such parameter generalisations, even for the same species in comparable landscapes.     

Seed dispersal in heterogeneous environments: bridging the gap between mechanistic dispersal and forest dynamics models

Seed dispersal is an important determinant of vegetation composition. We present a mechanistic model of seed dispersal by wind that incorporates heterogeneous vegetation structure. Vegetation affects wind speeds, a primary determinant of dispersal distance. Existing models combine wind speed and fall velocity of seeds. We expand on them by allowing vegetation, and thus wind profiles, to vary along seed trajectories, making the model applicable to any wind-dispersed plant in any community. Using seed trap data on seeds dispersing from forests into adjacent sites of two distinct vegetation structures, we show that our model was unbiased and accurate, even though dispersal patterns differed greatly between the two structures. Our spatially heterogeneous model performed better than models that assumed homogeneous vegetation for the same system. Its sensitivity to vegetation structure and ability to predict seed arrival when vegetation structure was incorporated demonstrates the model's utility for providing realistic estimates of seed arrival in realistic landscapes. Thus, we begin to bridge mechanistic seed dispersal and forest dynamics models. We discuss the merits of our model for incorporation into forest simulators, applications where such incorporation has been or is likely to be especially fruitful, and future model refinements to increase understanding of seed dispersal by wind.     

Non-random dispersal in the butterfly Maniola jurtina: implications for metapopulation models

The dispersal patterns of animals are important in metapopulation ecology because they affect the dynamics and survival of populations. Theoretical models assume random dispersal but little is known in practice about the dispersal behaviour of individual animals or the strategy by which dispersers locate distant habitat patches. In the present study, we released individual meadow brown butterflies (Maniola jurtina) in a non-habitat and investigated their ability to return to a suitable habitat. The results provided three reasons for supposing that meadow brown butterflies do not seek habitat by means of random flight. First, when released within the range of their normal dispersal distances, the butterflies orientated towards suitable habitat at a higher rate than expected at random. Second, when released at larger distances from their habitat, they used a non-random, systematic, search strategy in which they flew in loops around the release point and returned periodically to it. Third, butterflies returned to a familiar habitat patch rather than a non-familiar one when given a choice. If dispersers actively orientate towards or search systematically for distant habitat, this may be problematic for existing metapopulation models, including models of the evolution of dispersal rates in metapopulations.     

Single-species metapopulation dynamics: concepts, models and observations

This paper outlines a conceptual and theoretical framework for single-species metapopulation dynamics based on the Levins model and its variants. The significance of the following factors to metapopulation dynamics are explored: evolutionary changes in colonization ability; habitat patch size and isolation; compensatory effects between colonization and extinction rates; the effect of immigration on local dynamics (the rescue effect); and heterogeneity among habitat patches. The rescue effect may lead to alternative stable equilibria in metapopulation dynamics. Heterogeneity among habitat patches may give rise to a bimodal equilibrium distribution of the fraction of patches occupied in an assemblage of species (the core-satellite distribution). A new model of incidence functions is described, which allows one to estimate species' colonization and extinction rates on islands colonized from mainland. Four distinct kinds of stochasticity affecting metapopulation dynamics are discussed with examples. The concluding section describes four possible scenarios of metapopulation extinction.     

Joint evolution of altruistic cooperation and dispersal in a metapopulation of small local populations

We investigate the joint evolution of public goods cooperation and dispersal in a metapopulation model with small local populations. Altruistic cooperation can evolve due to assortment and kin selection, and dispersal can evolve because of demographic stochasticity, catastrophes and kin selection. Metapopulation structures resulting in assortment have been shown to make selection for cooperation possible. But how does dispersal affect cooperation and vice versa, when both are allowed to evolve as continuous traits? We found four qualitatively different evolutionary outcomes. (1) Monomorphic evolution to full defection with positive dispersal. (2) Monomorphic evolution to an evolutionarily stable state with positive cooperation and dispersal. In this case, parameter changes selecting for increased cooperation typically also select for increased dispersal. (3) Evolutionary branching can result in the evolutionarily stable coexistence of defectors and cooperators. Although defectors could be expected to disperse more than cooperators, here we show that the opposite case is also possible: Defectors tend to disperse less than cooperators when the total amount of cooperation in the dimorphic population is low enough. (4) Selection for too low cooperation can cause the extinction of the evolving population. For moderate catastrophe rates dispersal needs to be initially very frequent for evolutionary suicide to occur. Although selection for less dispersal in principle could prevent such evolutionary suicide, in most cases this rescuing effect is not sufficient, because selection in the cooperation trait is typically much stronger. If the catastrophe rate is large enough, a part of the boundary of viability can be evolutionarily attracting with respect to both strategy components, in which case evolutionary suicide is expected from all initial conditions.     

The effects of small dispersal rates on extinction times in structured metapopulation models

Habitat destruction is a critical factor that affects persistence in several taxa, including Pacific salmon. Salmon are noted for their ability to home to their natal streams for reproduction. Since straying (i.e., spawners reproducing in nonnatal streams) is typically low in salmon, its effects have not been appreciated. In this article, we develop both a general analytical model and a simple simulation model describing structured metapopulations to study how weak connections between subpopulations affect the ability of a species to tolerate habitat destruction and/or declines in habitat quality. Our goals are to develop general principles and to relate these principles to salmon population dynamics. The analytical model describes the dynamics of two density-dependent subpopulations, connected by dispersal, whose growth rates fluctuate in response to environmental and demographic stochasticity. We find that, for moderate levels of environmental variability, small dispersal rates can significantly increase mean extinction times. This effect declines with increasing habitat quality, increasing temporal correlation, and increasing spatial correlation, but it is still significant for realistic parameter values. The simulation model shows there is a threshold rate of dispersal that minimizes extinction probabilities. These results cannot be seen in classical metapopulation models and provide new insights into the rescue effect.     

From individual behavior to metapopulation dynamics: unifying the patchy population and classic metapopulation models

Spatially structured populations in patchy habitats show much variation in migration rate, from patchy populations in which individuals move repeatedly among habitat patches to classic metapopulations with infrequent migration among discrete populations. To establish a common framework for population dynamics in patchy habitats, we describe an individual-based model (IBM) involving a diffusion approximation of correlated random walk of individual movements. As an example, we apply the model to the Glanville fritillary butterfly (Melitaea cinxia) inhabiting a highly fragmented landscape. We derive stochastic patch occupancy model (SPOM) approximations for the IBMs assuming pure demographic stochasticity, uncorrelated environmental stochasticity, or completely correlated environmental stochasticity in local dynamics. Using realistic parameter values for the Glanville fritillary, we show that the SPOMs mimic the behavior of the IBMs well. The SPOMs derived from IBMs have parameters that relate directly to the life history and behavior of individuals, which is an advantage for model interpretation and parameter estimation. The modeling approach that we describe here provides a unified framework for patchy populations with much movements among habitat patches and classic metapopulations with infrequent movements.     

Interplay between microtubule dynamics and intracellular organization

Microtubules are hollow tubes essential for many cellular functions such as cell polarization and migration, intracellular trafficking and cell division. They are polarized polymers composed of α and β tubulin that are, in most cells, nucleated at the centrosome at the center of the cell. Microtubule plus-ends are oriented towards the periphery of the cell and explore the cytoplasm in a very dynamic manner. Microtubule alternate between phases of growth and shrinkage in a manner described as dynamic instability. Their dynamics is highly regulated by multiple factors: tubulin post-translational modifications such as detyrosination or acetylation, and microtubule-associated proteins, among them the plus-tip tracking proteins. This regulation is necessary for microtubule functions in the cell. In this review, we will focus on the role of microtubules in intracellular organization. After an overview of the mechanisms responsible for the regulation of microtubule dynamics, the major roles of microtubules dynamics in organelle positioning and organization in interphase cells will be discussed. Conversely, the role of certain organelles, like the nucleus and the Golgi apparatus as microtubule organizing centers will be reviewed. We will then consider the role of microtubules in the establishment and maintenance of cell polarity using few examples of cell polarization: epithelial cells, neurons and migrating cells. In these cells, the microtubule network is reorganized and undergoes specific and local regulation events; microtubules also participate in the intracellular reorganization of different organelles to ensure proper cell differentiation.     

Evolution of density-dependent dispersal in a structured metapopulation

We study the evolution of density-dependent dispersal in a structured metapopulation subject to local catastrophes that eradicate local populations. To this end we use the theory of structured metapopulation dynamics and the theory of adaptive dynamics.The set of evolutionarily possible dispersal functions (i.e., emigration rates as a function of the local population density) is derived mechanistically from an underlying resource-consumer model. The local resource dynamics is of a flow-culture type and consumers leave a local population with a constant probability per unit of time κ when searching for resources but not when handling resources (i.e., eating and digesting). The time an individual spends searching (as opposed to handling) depends on the local resource density, which in turn depends on the local consumer density, and so the average per capita emigration rate depends on the local consumer density as well.The derived emigration rates are sigmoid functions of local consumer population density. The parameters of the local resource-consumer dynamics are subject to evolution. In particular, we find that there exists a unique evolutionarily stable and attracting dispersal rate κ^∗ for searching consumers. The κ^∗ increases with local resource productivity and decreases with resource decay rate. The κ^∗ also increases with the survival probability during dispersal, but as a function of the catastrophe rate it reaches a maximum before dropping off to zero again.     

Allee-like effects in metapopulation dynamics

The existences of the Allee effect at the local population level and of the Allee-like effect at the metapopulation level are important for both ecology and conservation. Although there have been a great many papers on the Allee effect, they have mainly referred to only local populations and have not dealt with the relationship between the two. In this paper, we begin with local population dynamics and then construct a model including both local population and metapopulation dynamics. Then we simulate with computer at these two levels. The results indicate that the Allee-like effect in a metapopulation may emerge from the imposed Allee effect at the local population level. This threshold fraction of occupied patches below which the metapopulation goes extinct is seriously affected by the per capita migration rate, the survival rate during migration and the initial population size on the occupied patches. We also find that severe demographic stochasticity may compound the metapopulation extinction risk posed by the Allee effect. These conclusions are helpful for nature conservation, especially for the preservation of rare species.