A metapopulation model for the introgression from genetically modified plants into their wild relatives

Most models on introgression from genetically modified (GM) plants have focused on small spatial scales, modelling gene flow from a field containing GM plants into a single adjacent population of a wild relative. Here, we present a model to study the effect of introgression from multiple plantations into the whole metapopulation of the wild relative. The most important result of the model is that even very low levels of introgression and selection can lead to a high probability that the transgene goes to fixation in the metapopulation. Furthermore, the overall frequency of the transgene in the metapopulation, after a certain number of generations of introgression, depends on the population dynamics. If there is a high rate of migration or a high rate of population turnover, the overall transgene frequency is much higher than with lower rates. However, under an island model of population structure, this increased frequency has only a very small effect on the probability of fixation of the transgene. Considering these results, studies on the potential ecological risks of introgression from GM plants should look not only at the rate of introgression and selection acting on the transgene, but also at the metapopulation dynamics of the wild relative.

Stochastic dynamics in exotic and native blowflies: an analysis combining laboratory experiments and a two-patch metapopulation model

In this study we explored the stochastic population dynamics of three exotic blowfly species, Chrysomya albiceps, Chrysomya megacephala and Chrysomya putoria, and two native species, Cochliomyia macellaria and Lucilia eximia, by combining a density-dependent growth model with a two-patch metapopulation model. Stochastic fecundity, survival and migration were investigated by permitting random variations between predetermined demographic boundary values based on experimental data. Lucilia eximia and Chrysomya albiceps were the species most susceptible to the risk of local extinction. Cochliomyia macellaria, C. megacephala and C. putoria exhibited lower risks of extinction when compared to the other species. The simultaneous analysis of stochastic fecundity and survival revealed an increase in the extinction risk for all species. When stochastic fecundity, survival and migration were simulated together, the coupled populations were synchronized in the five species. These results are discussed, emphasizing biological invasion and interspecific interaction dynamics.

A stochastic metapopulation model accounting for habitat dynamics

A stochastic metapopulation model accounting for habitat dynamics is presented. This is the stochastic SIS logistic model with the novel aspect that it incorporates varying carrying capacity. We present results of Kurtz and Barbour, that provide deterministic and diffusion approximations for a wide class of stochastic models, in a form that most easily allows their direct application to population models. These results are used to show that a suitably scaled version of the metapopulation model converges, uniformly in probability over finite time intervals, to a deterministic model previously studied in the ecological literature. Additionally, they allow us to establish a bivariate normal approximation to the quasi-stationary distribution of the process. This allows us to consider the effects of habitat dynamics on metapopulation modelling through a comparison with the stochastic SIS logistic model and provides an effective means for modelling metapopulations inhabiting dynamic landscapes.

Conservation of a threatened European tree frog (Hyla arborea) metapopulation

Summary: Amphibians are among the most vulnerable animals of the world. One third of all species are currently threatened with extinction. Habitat loss is the major menace to pond- and stream-breeding species in the old world. In highly urbanized landscape like the Swiss Plateau, most species suffer from habitat reduction and fragmentation. Among all indigenous species, the European tree frog (Hyla arborea L., 1758) is one of the most endangered. It experienced an alarming decline during the last century and its regional long-term persistence is not guaranteed. We developed a monitoring framework based on calling male counts which included multiple visits to each wetland during the reproduction period in order to precisely determine its distribution on the Lemanic coast. Our results indicate that visiting populations 3 limes under suitable climatic conditions (temperature >20°C) provides reliable presence/absence data. Based on our monitoring data, we analyzed the species requirements regarding its breeding habitat. It appeared that anthropogenic activities had paradoxical effects on the species. On one hand, urbanization, traffic and intensive agriculture had a strong detrimental effect on tree frog distribution. On the other hand, large tree frog populations were frequently associated with gravel pits and military training grounds. Our results allowed us to create a habitat suitability map taking into account detrimental landscape elements around ponds (>1100m away from urban areas and >500m away from first class roads). In parallel, we developed a metapopulation model of the European tree frog in order to identify the critical threats to the long term persistence of the species. Our results indicated that suitable pond density is at the low end of the species requirements. Pond creation must therefore be considered an essential complementary approach to pond conservation and restoration. Our model also provided a mapping solution permitting the location of the must suitable area for pond creation from a metapopulation perspective. As many other amphibians, the European tree frog is not only exposed to an aquatic habitat (breeding and larval period), but also to a terrestrial stage (summer and overwintering habitats). Unfortunately, animals in their terrestrial phase are less conspicuous and, as a consequence, their terrestrial needs are relatively unknown. Using a recent tracking method (the Harmonic Direction Finder), we followed post-breeding frogs and identified favored terrestrial habitats, thus providing another practical conservation tool. We conclude that only the combination of multiple spatially explicit approaches (landscape-scale habitat suitability, metapopulation dynamics and terrestrial needs) is likely to provide wildlife managers with effective tools for the conservation of highly endangered amphibians. Résumé: Les amphibiens font partie des animaux les plus vulnérables du monde. Un tiers des espèces est actuellement menacé d'extinction. Dans l'ancien monde, la disparition des habitats constitue la principale menace pour les grenouilles, crapauds, tritons et salamandres. Dans les paysages fortement urbanisés comme le Plateau Suisse, la plupart des espèces souffrent d'une réduction et d'une fragmentation de leurs habitats. Parmi toutes les espèces indigènes, la rainette verte (Hyla arborea L., 1758) est l'une des plus menacée. Sa distribution a régressé de manière alarmante durant le siècle passé et sa survie régionale à long terme n'est pas assurée. Nous avons développé une méthode de suivi des populations se basant sur le comptage des mâles chanteurs durant la période de reproduction. Cette méthode requiert plusieurs visites à chaque plan d'eau de manière à déterminer précisément la distribution de l'espèce. Nos résultats démontrent que 3 visites par population dans des conditions climatiques favorable (température >20°C) permettent d'obtenir des données de présence/ absence valables. Sur la base de nos comptages sur la Côte lémanique, nous avons analysé les exigences de l'espèce concernant ses sites de reproduction. Il est apparu que les activités humaines avaient un effet paradoxal sur l'espèce. D'une part, l'urbanisation, le trafic routier et l'intensification de l'agriculture ont un effet fortement préjudiciable, tandis que d'autre part les plus grandes populations sont souvent associées à des gravières et autres places d'armes. Nos résultats ont permis de créer une carte de qualité d'habitat prenant en compte les éléments paysagers préjudiciables à la rainette (situé à plus de 1100m de zones urbaines et à plus de 500m de routes de première classe). En parallèle, nous avons développé un modèle métapopulationnel (incluant l'ensemble des populations) de manière à identifier les menaces prépondérantes sur la survie à long terme de l'espèce. Nos résultats ont permis de déterminer que la densité actuelle de plans d'eau adéquats est à la limite inférieure des exigences de l'espèce. La création d'étangs doit donc être considérée comme une approche indispensable et complémentaire à la protection et à la restauration des sites existants. Notre modèle a également fourni des résultats cartographiables permettant l'identification des sites les plus appropriés dans une perspective métapopulationnelle. Comme de nombreux autres amphibiens, la rainette verte est exposée à un habitat aquatique (reproduction et développement larvaire) ainsi qu'à un habitat terrestre (été et hiver). Les animaux étant particulièrement cryptiques dans cette seconde phase, leurs besoins terrestres sont relativement mal connus. Nous avons donc développé une nouvelle méthode de télémétrie basée sur le goniomètre harmonique. Cette méthode nous a permis de suivre des rainettes dans leurs migrations jusqu'à leurs habitats d'été et d'établir ainsi des recommandations pratiques pour la conservation de la rainette. Nous concluons que la combinaison de multiples approches spatialement explicites (qualité d'habitat, dynamique de métapopulation et habitats terrestres) est seule à même de produire des outils efficaces pour la conservation des espèces menacées d'amphibiens.

Genetic drift and within-host metapopulation dynamics of HIV-1 infection

Most HIV replication occurs in solid lymphoid tissue, which has prominent architecture at the histological level, which separates groups of productively infected CD4+ cells. Nevertheless, current population models of HIV assume panmixis within lymphoid tissue. We present a simple “metapopulation” model of HIV replication, where the population of infected cells is comprised of a large number of small populations, each of which is established by a few founder viruses and undergoes turnover. To test this model, we analyzed viral genetic variation of infected cell subpopulations within the spleen and demonstrated the action of founder effects as well as significant variation in the extent of genetic differentiation between subpopulations among patients. The combination of founder effects and subpopulation turnover can result in an effective population size much lower than the actual population size and may contribute to the importance of genetic drift in HIV evolution despite a large number of infected cells.

The role of habitat disturbance and recovery in metapopulation persistence

Classical metapopulation theory assumes a static landscape. However, empirical evidence indicates many metapopulations are driven by habitat succession and disturbance. We develop a stochastic metapopulation model, incorporating habitat disturbance and recovery, coupled with patch colonization and extinction, to investigate the effect of habitat dynamics on persistence. We discover that habitat dynamics play a fundamental role in metapopulation dynamics. The mean number of suitable habitat patches is not adequate for characterizing the dynamics of the metapopulation. For a fixed mean number of suitable patches, we discover that the details of how disturbance affects patches and how patches recover influences metapopulation dynamics in a fundamental way. Moreover, metapopulation persistence is dependent not only oil the average lifetime of a patch, but also on the variance in patch lifetime and the synchrony in patch dynamics that results from disturbance. Finally, there is an interaction between the habitat and metapopulation dynamics, for instance declining metapopulations react differently to habitat dynamics than expanding metapopulations. We close, emphasizing the importance of using performance measures appropriate to stochastic systems when evaluating their behavior, such as the probability distribution of the state of the. metapopulation, conditional on it being extant (i.e., the quasistationary distribution).

Optimal release strategies for biological control agents: an application of stochastic dynamic programming to population management

1. Establishing biological control agents in the field is a major step in any classical biocontrol programme, yet there are few general guidelines to help the practitioner decide what factors might enhance the establishment of such agents. 2. A stochastic dynamic programming (SDP) approach, linked to a metapopulation model, was used to find optimal release strategies (number and size of releases), given constraints on time and the number of biocontrol agents available. By modelling within a decision-making framework we derived rules of thumb that will enable biocontrol workers to choose between management options, depending on the current state of the system. 3. When there are few well-established sites, making a few large releases is the optimal strategy. For other states of the system, the optimal strategy ranges from a few large releases, through a mixed strategy (a variety of release sizes), to many small releases, as the probability of establishment of smaller inocula increases. 4. Given that the probability of establishment is rarely a known entity, we also strongly recommend a mixed strategy in the early stages of a release programme, to accelerate learning and improve the chances of finding the optimal approach.

The use of stochastic dynamic programming in optimal landscape reconstruction for metapopulations

A decision theory framework can be a powerful technique to derive optimal management decisions for endangered species. We built a spatially realistic stochastic metapopulation model for the Mount Lofty Ranges Southern Emu-wren (Stipiturus malachurus intermedius), a critically endangered Australian bird. Using diserete-time Markov,chains to describe the dynamics of a metapopulation and stochastic dynamic programming (SDP) to find optimal solutions, we evaluated the following different management decisions: enlarging existing patches, linking patches via corridors, and creating a new patch. This is the first application of SDP to optimal landscape reconstruction and one of the few times that landscape reconstruction dynamics have been integrated with population dynamics. SDP is a powerful tool that has advantages over standard Monte Carlo simulation methods because it can give the exact optimal strategy for every landscape configuration (combination of patch areas and presence of corridors) and pattern of metapopulation occupancy, as well as a trajectory of strategies. It is useful when a sequence of management actions can be performed over a given time horizon, as is the case for many endangered species recovery programs, where only fixed amounts of resources are available in each time step. However, it is generally limited by computational constraints to rather small networks of patches. The model shows that optimal metapopulation, management decisions depend greatly on the current state of the metapopulation,. and there is no strategy that is universally the best. The extinction probability over 30 yr for the optimal state-dependent management actions is 50-80% better than no management, whereas the best fixed state-independent sets of strategies are only 30% better than no management. This highlights the advantages of using a decision theory tool to investigate conservation strategies for metapopulations. It is clear from these results that the sequence of management actions is critical, and this can only be effectively derived from stochastic dynamic programming. The model illustrates the underlying difficulty in determining simple rules of thumb for the sequence of management actions for a metapopulation. This use of a decision theory framework extends the capacity of population viability analysis (PVA) to manage threatened species.

Interacting populations in heterogeneous environments

To optimally manage a metapopulation, managers and conservation biologists can favor a type of habitat spatial distribution (e.g. aggregated or random). However, the spatial distribution that provides the highest habitat occupancy remains ambiguous and numerous contradictory results exist. Habitat occupancy depends on the balance between local extinction and colonization. Thus, the issue becomes even more puzzling when various forms of relationships - positive or negative co-variation - between local extinction and colonization rate within habitat types exist. Using an analytical model we demonstrate first that the habitat occupancy of a metapopulation is significantly affected by the presence of habitat types that display different extinction-colonization dynamics, considering: (i) variation in extinction or colonization rate and (ii) positive and negative co-variation between the two processes within habitat types. We consequently examine, with a spatially explicit stochastic simulation model, how different degrees of habitat aggregation affect occupancy predictions under similar scenarios. An aggregated distribution of habitat types provides the highest habitat occupancy when local extinction risk is spatially heterogeneous and high in some places, while a random distribution of habitat provides the highest habitat occupancy when colonization rates are high. Because spatial variability in local extinction rates always favors aggregation of habitats, we only need to know about spatial variability in colonization rates to determine whether aggregating habitat types increases, or not, metapopulation occupancy. From a comparison of the results obtained with the analytical and with the spatial-explicit stochastic simulation model we determine the conditions under which a simple metapopulation model closely matches the results of a more complex spatial simulation model with explicit heterogeneity.

Parallel declines in species and genetic diversity driven by anthropogenic disturbance: a multispecies approach in a French Atlantic dune system.

Numerous studies assess the correlation between genetic and species diversities, but the processes underlying the observed patterns have only received limited attention. For instance, varying levels of habitat disturbance across a region may locally reduce both diversities due to extinctions, and increased genetic drift during population bottlenecks and founder events. We investigated the regional distribution of genetic and species diversities of a coastal sand dune plant community along 240 kilometers of coastline with the aim to test for a correlation between the two diversity levels. We further quantify and tease apart the respective contributions of natural and anthropogenic disturbance factors to the observed patterns. We detected significant positive correlation between both variables. We further revealed a negative impact of urbanization: Sites with a high amount of recreational infrastructure within 10 km coastline had significantly lowered genetic and species diversities. On the other hand, a measure of natural habitat disturbance had no effect. This study shows that parallel variation of genetic and species diversities across a region can be traced back to human landscape alteration, provides arguments for a more resolute dune protection, and may help to design priority conservation areas.

Theory for designing nature reserves for single species

We examine the question of the optimal number of reserves that should be established to maximize the persistence of a species. We assume that the mean time to extinction of a single population increases as a power of the habitat area, that there is a certain amount of habitat to be reserved, and that the aim is to determine how this habitat is most efficiently divided. The optimal configuration depends on whether the management objective is to maximize the mean time to extinction or minimize the risk of extinction. When maximizing the mean time to extinction, the optimal number of independent reserves does not depend on the amount of available habitat for the reserve system. In contrast, the risk of extinction is minimized when individual reserves are equal to the optimal patch size, making the optimal number of reserves linearly proportional to the amount of available habitat. A model that includes dispersal and correlation in the incidence of extinction demonstrates the importance of considering the relative rate at which these two factors decrease with distance between reserves. A small number of reserves is optimal when the mean time to extinction increases rapidly with habitat area or when risks of extinction are high.

A new method for conservation planning for the persistence of multiple species

Although the aim of conservation planning is the persistence of biodiversity, current methods trade-off ecological realism at a species level in favour of including multiple species and landscape features. For conservation planning to be relevant, the impact of landscape configuration on population processes and the viability of species needs to be considered. We present a novel method for selecting reserve systems that maximize persistence across multiple species, subject to a conservation budget. We use a spatially explicit metapopulation model to estimate extinction risk, a function of the ecology of the species and the amount, quality and configuration of habitat. We compare our new method with more traditional, area-based reserve selection methods, using a ten-species case study, and find that the expected loss of species is reduced 20-fold. Unlike previous methods, we avoid designating arbitrary weightings between reserve size and configuration; rather, our method is based on population processes and is grounded in ecological theory.

Accounting for uncertainty in marine reserve design

Ecosystems and the species and communities within them are highly complex systems that defy predictions with any degree of certainty. Managing and conserving these systems in the face of uncertainty remains a daunting challenge, particularly with respect to developing networks of marine reserves. Here we review several modelling frameworks that explicitly acknowledge and incorporate uncertainty, and then use these methods to evaluate reserve spacing rules given increasing levels of uncertainty about larval dispersal distances. Our approach finds similar spacing rules as have been proposed elsewhere - roughly 20-200 km - but highlights several advantages provided by uncertainty modelling over more traditional approaches to developing these estimates. In particular, we argue that uncertainty modelling can allow for (1) an evaluation of the risk associated with any decision based on the assumed uncertainty; (2) a method for quantifying the costs and benefits of reducing uncertainty; and (3) a useful tool for communicating to stakeholders the challenges in managing highly uncertain systems. We also argue that incorporating rather than avoiding uncertainty will increase the chances of successfully achieving conservation and management goals.

Stochastic models for mainland-island metapopulations in static and dynamic landscapes

This paper has three primary aims: to establish an effective means for modelling mainland-island metapopulations inhabiting a dynamic landscape: to investigate the effect of immigration and dynamic changes in habitat on metapopulation patch occupancy dynamics; and to illustrate the implications of our results for decision-making and population management. We first extend the mainland-island metapopulation model of Alonso and McKane [Bull. Math. Biol. 64:913-958,2002] to incorporate a dynamic landscape. It is shown, for both the static and the dynamic landscape models, that a suitably scaled version of the process converges to a unique deterministic model as the size of the system becomes large. We also establish that. under quite general conditions, the density of occupied patches, and the densities of suitable and occupied patches, for the respective models, have approximate normal distributions. Our results not only provide us with estimates for the means and variances that are valid at all stages in the evolution of the population, but also provide a tool for fitting the models to real metapopulations. We discuss the effect of immigration and habitat dynamics on metapopulations, showing that mainland-like patches heavily influence metapopulation persistence, and we argue for adopting measures to increase connectivity between this large patch and the other island-like patches. We illustrate our results with specific reference to examples of populations of butterfly and the grasshopper Bryodema tuberculata.

A landscape-scale test of the predictive ability of a spatially explicit model for population viability analysis

1. Although population viability analysis (PVA) is widely employed, forecasts from PVA models are rarely tested. This study in a fragmented forest in southern Australia contrasted field data on patch occupancy and abundance for the arboreal marsupial greater glider Petauroides volans with predictions from a generic spatially explicit PVA model. This work represents one of the first landscape-scale tests of its type. 2. Initially we contrasted field data from a set of eucalypt forest patches totalling 437 ha with a naive null model in which forecasts of patch occupancy were made, assuming no fragmentation effects and based simply on remnant area and measured densities derived from nearby unfragmented forest. The naive null model predicted an average total of approximately 170 greater gliders, considerably greater than the true count (n = 81). 3. Congruence was examined between field data and predictions from PVA under several metapopulation modelling scenarios. The metapopulation models performed better than the naive null model. Logistic regression showed highly significant positive relationships between predicted and actual patch occupancy for the four scenarios (P = 0.001-0.006). When the model-derived probability of patch occupancy was high (0.50-0.75, 0.75-1.00), there was greater congruence between actual patch occupancy and the predicted probability of occupancy. 4. For many patches, probability distribution functions indicated that model predictions for animal abundance in a given patch were not outside those expected by chance. However, for some patches the model either substantially over-predicted or under-predicted actual abundance. Some important processes, such as inter-patch dispersal, that influence the distribution and abundance of the greater glider may not have been adequately modelled. 5. Additional landscape-scale tests of PVA models, on a wider range of species, are required to assess further predictions made using these tools. This will help determine those taxa for which predictions are and are not accurate and give insights for improving models for applied conservation management.