Stochastic Patch Occupancy Model Research Articles

Broadening applications of stochastic patch occupancy models over three decades

AbstractAimStochastic patch occupancy models (SPOMs) are a type of spatial population simulation. They are arguably well‐suited to guide conservation in human‐altered landscapes, but their appropriateness for a wide range of species and landscape types has often been questioned. Here, we provide an overview of how SPOM research has expanded over the last three decades and discuss the untapped potential for these models to inform current conservation strategies.LocationWorldwide.MethodsWe carried out a systematic review of studies that have fitted SPOMs to real species and landscapes. We assessed temporal trends in SPOMs' use in conservation and management studies, their taxonomic and geographic coverage, and the attributes of studied landscapes. We quantitatively and qualitatively evaluated whether the authors' modelling choices reflected the perceived advantages and disadvantages of SPOMs.ResultsThe proportion of SPOMs used to answer conservation questions has increased over time. Questions of where, when and how to conserve have all been addressed, sometimes considering additional aspects such as cost‐effectiveness and climate change. Taxonomic diversity coverage has increased over time, and SPOMs have been used in landscapes with a higher proportion of suitable habitat. They have, however, been predominantly applied in temperate biomes. Few studies have explored parameter extrapolation in taxonomically and ecologically related species with mixed results.Main ConclusionsOver the past three decades, authors have exploited the simplicity and flexibility of SPOMs to answer a broad range of questions with practical implications. The use of SPOMs in less fragmented landscapes, and for an increasing range of taxa, suggests that the strictest definitions of their applicability can be challenged. Stochastic patch occupancy models have untapped potential for informing conservation under climate change. Given the urgent need to plan for large numbers of species with limited data for fitting, SPOMs could better fulfil their potential to guide conservation if parameters could be extrapolated to data‐deficient landscapes and species.

Extinction threshold and large population limit of a plant metapopulation model with recurrent extinction events and a seed bank component

We introduce a new model for plant metapopulations with a seed bank component, living in a fragmented environment in which local extinction events are frequent. This model is an intermediate between population dynamics models with a seed bank component, based on the classical Wright–Fisher model, and Stochastic Patch Occupancy Models (SPOMs) used in metapopulation ecology. Its main feature is the use of “ghost” individuals, which can reproduce but with a very strong selective disadvantage against “real” individuals, to artificially ensure a constant population size. We show the existence of an extinction threshold above which persistence of the subpopulation of “real” individuals is not possible, and investigate how the seed bank characteristics affect this extinction threshold. We also show the convergence of the model to a SPOM under an appropriate scaling, bridging the gap between individual-based models and occupancy models.

Dynamic spatio-temporal patterns of metapopulation occupancy in patchy habitats.

Spatio-temporal dynamics in habitat suitability and connectivity among mosaics of heterogeneous wetlands are critical for biological diversity and species persistence in aquatic patchy landscapes. Despite the recognized importance of stochastic hydroclimatic forcing in driving wetlandscape hydrological dynamics, linking such effects to emergent dynamics of metapopulation poses significant challenges. To fill this gap, we propose here a dynamic stochastic patch occupancy model (SPOM), which links parsimonious hydrological and ecological models to simulate spatio-temporal patterns in species occupancy in wetlandscapes. Our work aims to place ecological studies of patchy habitats into a proper hydrologic and climatic framework to improve the knowledge about metapopulation shifts in response to climate-driven changes in wetlandscapes. We applied the dynamic version of the SPOM (D-SPOM) framework in two wetlandscapes in the US with contrasting landscape and climate properties. Our results illustrate that explicit consideration of the temporal dimension proposed in the D-SPOM is important to interpret local- and landscape-scale patterns of habitat suitability and metapopulation occupancy. Our analyses show that spatio-temporal dynamics of patch suitability and accessibility, driven by the stochasticity in hydroclimatic forcing, influence metapopulation occupancy and the topological metrics of the emergent wetlandscape dispersal network. D-SPOM simulations also reveal that the extinction risk in dynamic wetlandscapes is exacerbated by extended dry periods when suitable habitat decreases, hence limiting successful patch colonization and exacerbating metapopulation extinction risks. The proposed framework is not restricted only to wetland studies but could also be applied to examine metapopulation dynamics in other types of patchy habitats subjected to stochastic external disturbances.

Porównawcza ocena programów analizy żywotności populacji (PVA) w rankingu scenariuszy przekształceń krajobrazu = A comparative assessment of PVA software packages applied to rank the landscape management scenarios

Because of the scale and speed of species extinctions conservationists require methods that facilitate decision making. Therefore, a wide range of habitat and population viability analysis (PVA) software has been developed. Given the diversity of available programs it is currently challenging to decide which program is the most appropriate for a particular problem and what has to be considered when interpreting and comparing results from different approaches. Previous comparisons of PVA software addressed more generic questions such as data requirements, assumptions and predictive accuracy. In contract, we focus on a more applied problem that is still unresolved: how do simple habitat models and PVA software packages affect the ranking of alternative management scenarios? We addressed this problem by comparing different packages (LARCH, META-X, VORTEX and RAMAS GIS). As a test case, we studied the impact of alternative landscape development scenarios (river regulation, grassland restoration, reforestation and renaturalisation) for the Vistula valley, Poland, on the natterjack toad (Bufo calamita). In this context we also aimed to assess whether the use of at least two different PVA packages can enable users to better understand the differences in model predictions, which would imply a greater awareness and critical use of the packages. Our model selection represents different approaches to population viability analysis, including habitat, local population and stochastic patch occupancy models. The models can be evaluated in regard to the complexity of parameters and to the way the landscape is handled. We used RAMAS GIS to create a habitat model (RAMASh) and a detailed spatially explicit stochastic metapopulation model (RAMASp) which combined served as a complete “virtual” dataset for parameterisation of other programs. As an example of a stochastic patch occupancy model, we selected the META-X software. For a more independent comparison we added VORTEX – another package that includes explicit population dynamics, similar to RAMAS. Additionally, we included the habitat model LARCH because this type of model is often used by policy makers. We compared the metapopulation structure produced by RAMASh and LARCH. Scenario ranking according to the predicted carrying capacity in both programs was exactly the same, because the quantitative results for each scenario were almost identical in both programs. However, the metapopulation structure showed big differences between the programs, especially in the number of small populations. The analyses of results of different PVA programs (RAMASp, VORTEX and META-X) showed that absolute values of viability measures partly differed among these programs. Slight differences in population growth rate in RAMASp and VORTEX were amplified by stochasticity and resulted in visibly lower values of final abundance in VORTEX than in RAMASp. Also the absolute values of intrinsic mean time to extinction showed some discrepancies in VORTEX and META-X. These results are in agreement with findings of previous PVA comparisons, which emphasizes that absolute values of viability measures produced by any single model should be treated with caution. Nevertheless, despite these differences the rankings of the scenarios were the same in all three programs. However the order of the scenarios was different than in habitat models. In addition, these rankings were robust to the choice of viability measure. Taken together, these results emphasize that scenario ranking delivered by PVA software is robust and thus very useful for conservation management. Furthermore, we recommend using at least two PVA software packages in parallel, as this forces user to scrutinize the simplifying assumptions of the underlying models and of the viability metrics used.

Normal approximations for discrete-time occupancy processes

We study normal approximations for a class of discrete-time occupancy processes, namely, Markov chains with transition kernels of product Bernoulli form. This class encompasses numerous models which appear in the complex networks literature, including stochastic patch occupancy models in ecology, network models in epidemiology, and a variety of dynamic random graph models. Bounds on the rate of convergence for a central limit theorem are obtained using Stein’s method and moment inequalities on the deviation from an analogous deterministic model. As a consequence, our work also implies a uniform law of large numbers for a subclass of these processes.

Integrating social and ecological data to model metapopulation dynamics in coupled human and natural systems.

Understanding how metapopulations persist in dynamic working landscapes requires assessing the behaviors of key actors that change patches as well as intrinsic factors driving turnover. Coupled human and natural systems (CHANS) research uses a multidisciplinary approach to identify the key actors, processes, and feedbacks that drive metapopulation and landscape dynamics. We describe a framework for modeling metapopulations in CHANS that integrates ecological and social data by coupling stochastic patch occupancy models of metapopulation dynamics with agent-based models of land-use change. We then apply this framework to metapopulations of the threatened black rail (Laterallus jamaicensis) and widespread Virginia rail (Rallus limicola) that inhabit patchy, irrigation-fed wetlands in the rangelands of the California Sierra Nevada foothills. We collected data from five diverse sources (rail occupancy surveys, land-use change mapping, a survey of landowner decision making, climate and reservoir databases, and mosquito trapping and West Nile virus testing) and integrated them into an agent-based stochastic patch occupancy model. We used the model to (1) quantify the drivers of metapopulation dynamics, and the potential interactions and feedbacks among them; (2) test predictions of the behavior of metapopulations in dynamic working landscapes; and (3) evaluate the impact of three policy options on metapopulation persistence (irrigation district water cutbacks during drought, incentives for landowners to create wetlands, and incentives for landowners to protect wetlands). Complex metapopulation dynamics emerged when landscapes functioned as CHANS, highlighting the importance of integrating human activities and other ecological processes into metapopulation models. Rail metapopulations were strongly top-down regulated by precipitation, and the black rail's decade-long decline was caused by the combination of West Nile virus and drought. Theoretical predictions of the two metapopulations' responses to dynamic landscapes and incentive programs were complicated by heterogeneity in patch quality and CHANS couplings, respectively. Irrigation cutbacks during drought posed a serious extinction risk that neither incentive policy effectively ameliorated.

Use of stochastic patch occupancy models in the California red-legged frog for Bayesian inference regarding past events and future persistence.

Assessing causes of population decline is critically important to management of threatened species. Stochastic patch occupancy models (SPOMs) are popular tools for examining spatial and temporal dynamics of populations when presence–absence data in multiple habitat patches are available. We developed a Bayesian Markov chain method that extends existing SPOMs by focusing on past environmental changes that may have altered occupancy patterns prior to the beginning of data collection. Using occupancy data from 3 creeks, we applied the method to assess 2 hypothesized causes of population decline—in situ die‐off and residual impact of past source population loss—in the California red‐legged frog. Despite having no data for the 20–30 years between the hypothetical event leading to population decline and the first data collected, we were able to discriminate among hypotheses, finding evidence that in situ die‐off increased in 2 of the creeks. Although the creeks had comparable numbers of occupied segments, owing to different extinction–colonization dynamics, our model predicted an 8‐fold difference in persistence probabilities of their populations to 2030. Adding a source population led to a greater predicted persistence probability than did decreasing the in situ die‐off, emphasizing that reversing the deleterious impacts of a disturbance may not be the most efficient management strategy. We expect our method will be useful for studying dynamics and evaluating management strategies of many species.

Abundance-based detectability in a spatially-explicit metapopulation: a case study on a vulnerable beetle species in hollow trees

In many fragmented habitats, the detectability of a population in a habitat patch closely depends on the local abundance of individuals. However, metapopulation studies rarely connect abundance and detectability. We propose a framework for using abundance-based estimates of detectability in the analysis of a spatially-explicit stochastic patch occupancy model (SPOM). We illustrate our approach with the example of Tenebrio opacus, a beetle inhabiting hollows in old trees, and have based it on a 6-year monitoring programme of adult beetles in an area harbouring a high density of old oaks. We validated our abundance-based methodology by showing that the estimates of detectability were positively and significantly correlated with those obtained from presence/absence data (Pearson r = 0.54, p < 2E−16) in our study system. We further showed that the height of the hollow on the tree and the area of its entrance hole, the living status and girth of the host tree, and the time of survey significantly affected the detectability of beetle populations. Median detectability was 51% for one survey. The SPOM analysis revealed a high but heterogeneous extinction risk among trees, suggesting a metapopulation dynamics between the “classic” and “mainland–island” paradigms. However, it also indicated unexplained beetle colonization of trees in our study, despite the fact that we included limited detectability in our estimation procedure. This may have been due to the cryptic larval stage of T. opacus and may thus invalidate the use of a classic SPOM in our study system.

Using metapopulation models to assess species conservation–ecosystem restoration trade-offs

Ecological restoration is needed to counter global-scale ecosystem degradation, but can conflict with endangered species conservation when restoration impacts habitat quality. In such cases, prioritizing long-vacant patches for restoration is an intuitively appealing strategy for minimizing the effects on endangered species. Metapopulation models grounded in empirical data potentially provide a rigorous framework for developing theoretical “patch vacancy thresholds” (i.e., duration of vacancy required before implementing restoration) and assessing the implications of such criteria for restoration objectives. We develop such a model for spotted owls (Strix occidentalis), which embody the species–ecosystem dilemma given their preference for closed-canopy forests that are also susceptible to severe fire and drought and hence the center of debates about forest restoration intended to reduce fire and drought risk. We leveraged a >20-year territory occupancy dataset to parameterize a Stochastic Patch Occupancy Model (SPOM) to assess relative risk to a metapopulation of owls in California under alternative conservation guidelines, including a range of vacancy thresholds. Territories with greater amounts of owl habitat were more likely to be recolonized and less likely to go extinct. Importantly, the probability of a vacant owl territory becoming recolonized declined as length of vacancy increased; territories vacant for 1 and 10 years had annual recolonization probabilities of 0.34 and 0.06, respectively. Based on our SPOM, projected territory occupancy rates declined as the vacancy threshold decreased and as habitat within territories was impacted by restoration. However, more liberal territory vacancy thresholds were projected to increase the proportion of territories (and thus landscape) that could be restored and that restored conditions could be maintained with repeated treatments. Reintroducing natural disturbance regimes, which eliminated the need for repeated treatments, was projected to reduce risk to owls, particularly with relaxed vacancy thresholds. We provide a simple, yet novel, metapopulation framework for quantifying how alternative conservation guidelines might impact owl occupancy and influence forest restoration guidelines. Similar analyses could facilitate restoration efforts in other systems by more explicitly quantifying tradeoffs between species–ecosystem objectives.

When Group Dispersal and Allee Effect Shape Metapopulation Dynamics

The dispersal ability of a species will be critical for how population dynamics are realized in spatially structured systems. To date, the effect of group dispersal on metapopulation dynamics is poorly understood. Here, we investigate how group dispersal and Allee effects shape metapopulation dynamics identifying conditions in which group dispersal can be an advantage over independent dispersal. We approach this question by building and analysing a Markovian random walk for metapopulation dynamics including group dispersal and Allee effect. This Markovian random walk is analogous to the discrete-time Stochastic Patch Occupancy Model (SPOM). We find that intermediate group sizes may lead to larger and more sustainable metapopulations in the presence of an Allee effect. Hence, understanding how group size variation and realized (meta)population dynamics are linked offers an exciting future venue for research that is expected to yield key insights into the ecology and evolution of populations occupying spati...

When environmentally persistent pathogens transform good habitat into ecological traps.

Habitat quality plays an important role in the dynamics and stability of wildlife metapopulations. However, the benefits of high-quality habitat may be modulated by the presence of an environmentally persistent pathogen. In some cases, the presence of environmental pathogen reservoirs on high-quality habitat may lead to the creation of ecological traps, wherein host individuals preferentially colonize high-quality habitat, but are then exposed to increased infection risk and disease-induced mortality. We explored this possibility through the development of a stochastic patch occupancy model, where we varied the pathogen’s virulence, transmission rate and environmental persistence as well as the distribution of habitat quality in the host metapopulation. This model suggests that for pathogens with intermediate levels of spread, high-quality habitat can serve as an ecological trap, and can be detrimental to host persistence relative to low-quality habitat. This inversion of the relative roles of high- and low-quality habitat highlights the importance of considering the interaction between spatial structure and pathogen transmission when managing wildlife populations exposed to an environmentally persistent pathogen.

Evaluating the combined effects of climate and land‐use change on tree species distributions

Summary A large proportion of the world's biodiversity is reportedly threatened by habitat loss and climate change. However, there are few studies that investigate the interaction between these two threats using empirical data. Here, we investigate interactions between climate change and land‐use change in the future distribution of 23 dominant tree species in mainland Spain. We simulated changes up to year 2100 using a climate‐dependent Stochastic Patch Occupancy Model, parameterized with colonization and extinction events recorded in 46 596 survey plots. We estimated that the distribution of 17 out of 23 tree species are expanding and hence not at equilibrium with the climate. However, climate change will make the future occupancy of 15 species to be lower than expected if climate, and habitat, remained stable (baseline scenario). Climate change, when combined with the loss of 20% of the habitat, was estimated to reduce species occupancies (relative to baseline projections) by an average of 23% if habitat loss was spatially clumped, and by 35% if it was scattered. If habitat loss occurred in areas already impacted by human activities, species occupancies would be reduced by 26%. Land‐use changes leading to habitat gain (i.e. creation through reforestation) could slightly mitigate the effects of climate change, but a 20% increment in habitat would reduce climate change‐driven losses in species occupancies by only ∼3%. Synthesis and applications. The distributions of the most common tree species in mainland Spain are expanding, but climate change threatens to reduce this expansion by ∼18% for 15 of the 23 studied species. Moreover, if the habitat of these species is simultaneously lost, the occupancies of all of them will be reduced further, with variation depending on the spatial pattern of the lost habitats. However, we did not detect synergies between climate change and habitat loss. The combined effect (with 20% habitat loss) was 5–13% less than what it would be if the effects were additive. Importantly, reforestation could partially offset the negative effects of climate change, but complete mitigation would require an increase in forested land of ∼80%, and the prioritization of territories that are less impacted by human activities.

Simple models, complex models, useful models: can we tell them from the flap of a butterfly's wings?

The strategy of scientific model building is the strategy of abstraction. An abstraction is devised to explain the workings of certain mechanistic principles and, as subjective constructs they are neither right nor wrong. Rather, abstractions obscure or enlighten the process under study, yielding useless or useful models (Levins, 2006). Two opposing approaches are usually followed in the process of ecological model construction as a route to understanding (Evans et al., 2013). In the first one, a model is worked out from theoretical principles and a set of testable predictions are then confronted with data from real systems. In the second approach, it is the detailed knowledge of the natural history of a particular system what drives the level of complexity of a mechanistic model used to fit empirical data, and this model is further used to reproduce the dynamics of the original system and, ideally, of other systems. Given the current challenges in the study of population dynamics (Oro, 2013), which abstraction is more useful? The paper by Harrison et al. (2011) is a salient example of the second approach. Using 17-year time series data from a metapopulation of the Glanville fritillary butterfly (Melitaea cinxia Figure 1) inhabiting 72 meadows in Finland, they fit a mechanistic Individual-Based Model (IBM) to spatial biannual counts of larval groups. With the aim of assessing the desirability of complex models with respect to simpler ones in explaining the observed metapopulation dynamics, they also derived a simpler, Stochastic Patch Occupancy Model (SPOM), and fit it to the presence or absence of local populations across time and space. Interestingly, the overall fitting of both models was rather similar, and the bold result is the same with either model: variation in habitat quality influenced patch occupancy mainly through the effects on movement behavior at patch edges. The question immediately arises: does it pay to have expensive, individual-based

The limiting behaviour of a stochastic patch occupancy model

Metapopulation models have been used to better understand the conditions necessary for the persistence of the metapopulation. In this paper, we study a stochastic patch occupancy model that incorporates variation in quality and connectivity of the habitat patches. Two important assumptions are imposed in our analysis. Firstly, the distance between patches has a special form. This amounts to assuming that migrating individuals follow certain pathways. Secondly, the area of the habitat patches is assumed to scale with the number of patches in the metapopulation. Under these assumptions, a deterministic limit is obtained as the number of patches goes to infinity. Using the deterministic limiting process, a condition for persistence of the metapopulation is derived.

Persistence of black‐tailed prairie‐dog populations affected by plague in northern Colorado, USA

The spatial distribution of prairie dog (Cynomys ludovicianus) colonies in North America has changed from large, contiguous populations to small, isolated colonies in metapopulations. One factor responsible for this drastic change in prairie-dog population structure is plague (caused by the bacterium Yersinia pestis). We fit stochastic patch occupancy models to 20 years of prairie-dog colony occupancy data from two discrete metapopulations (west and east) in the Pawnee National Grassland in Colorado, USA, that differ in connectivity among suitable habitat patches. We conducted model selection between two hypothesized modes of plague movement: independent of prairie-dog dispersal (colony-area) vs. plague movement consistent with prairie-dog dispersal (connectivity to extinct colonies). The best model, which fit the data well (area under the curve [AUC]: 0.94 west area; 0.79 east area), revealed that over time the proportion of extant colonies was better explained by colony size than by connectivity to extinct (plagued) colonies. The idea that prairie dogs are not likely to be the main vector that spreads Y. pestis across the landscape is supported by the observation that colony extinctions are primarily caused by plague, prairie-dog dispersal is short range, and connectivity to extinct colonies was not selected as a factor in the models. We also conducted simulations with the best model to examine long-term patterns of colony occupancy and persistence of prairie-dog metapopulations. In the case where the metapopulations persist, our model predicted that the western metapopulation would have a colony occupancy rate approximately 2.5 times higher than that of the eastern metapopulation (-50% occupied colonies vs. 20%) in 50 years, but that the western metapopulation has -80% chance of extinction in 100 years while the eastern metapopulation has a less than 25% chance. Extinction probability of individual colonies depended on the frequency with which colonies of the same size class occurred in the metapopulation. Thus, the long-term persistence of prairie-dog metapopulations depended on specific details of the metapopulation.

A Bayesian model of metapopulation viability, with application to an endangered amphibian

AbstractAimPopulation viability analysis (PVA) is used to quantify the risks faced by species under alternative management regimes. Bayesian PVAs allow uncertainty in the parameters of the underlying population model to be easily propagated through to the predictions. We developed a Bayesian stochastic patch occupancy model (SPOM) and used this model to assess the viability of a metapopulation of the growling grass frog (Litoria raniformis) under different urbanization scenarios.LocationMelbourne, Victoria, Australia.MethodsWe fitted a Bayesian model that accounted for imperfect detection to a multiseason occupancy dataset for L. raniformis collected across northern Melbourne. The probability of extinction was modelled as a function of effective wetland area, aquatic vegetation cover and connectivity, using logistic regression. The probability of colonization was modelled as a function of connectivity alone. We then simulated the dynamics of a metapopulation of L. raniformis subject to differing levels of urbanization and compensatory wetland creation. Uncertainty was propagated by conducting simulations for 5000 estimates of the parameters of the models for extinction and colonization.ResultsThere was considerable uncertainty in both the probability of quasi‐extinction and the minimum number of occupied wetlands under most urbanization scenarios. Uncertainty around the change in quasi‐extinction risk and minimum metapopulation size increased with increasing habitat loss. For our focal metapopulation, the analysis revealed that significant investment in new wetlands may be required to offset the impacts of urbanization.Main conclusionsBayesian approaches to PVA allow parametric uncertainty to be propagated and considered in management decisions. They also provide means of identifying parameters that represent critical uncertainties, and, through the use of informative priors, can easily assimilate new data to reduce parametric uncertainty. These advantages, and the ready availability of software to run Bayesian analyses, will ensure that Bayesian approaches are used increasingly for PVAs.

Coherence, conservation and patch‐occupancy analysis

Spatial coherence (synchrony) among subpopulations poses a danger to the metacommunity, as it increases the risk of regional extinction. When this effect is significant, the use of inference techniques based on the stochastic patch occupancy model (SPOM) may be inadequate, since SPOMs assume that each habitat patch is either occupied or empty, thereby neglecting the intra‐patch dynamics. Here we suggest a general classification of the dynamics that allows the identification, in a model‐independent manner, of the regimes where coherence effects are strong. We also present a new technique, based on patch occupancy (presence/absence) data, for identifying the role of spatial coherence in the stabilization of a metapopulation. If the chance of a local extinction grows with the connectivity, this implies that spatial synchronization is too strong and that regional‐scale extinction becomes possible. When this scenario occurs, a decrease in the movement of individuals (habitat fragmentation, reduced dispersal rates) has a positive effect on the sustainability of the spatially distributed population. The results of individual based simulations of a spatially structured population are analyzed with SPOM and the regime where the two‐state approximation fails is identified.

Impact of species-specific dispersal and regional stochasticity on estimates of population viability in stream metapopulations

Species dispersal is a central component of metapopulation models. Spatially realistic metapopulation models, such as stochastic patch-occupancy models (SPOMs), quantify species dispersal using estimates of colonization potential based on inter-patch distance (distance decay model). In this study we compare the parameterization of SPOMs with dispersal and patch dynamics quantified directly from empirical data. For this purpose we monitored two metapopulations of an endangered minnow, redside dace (Clinostomus elongatus), using mark-recapture techniques across 43 patches, re-sampled across a 1 year period. More than 2,000 fish were marked with visible implant elastomer tags coded for patch location and dispersal and patch dynamics were monitored. We found that species-specific dispersal and distance decay models provided qualitatively similar rankings of viable patches; however, there were differences of several orders of magnitude in the estimated intrinsic mean times to extinction, from 24 and 148 years to 362 and >100,000 years, depending on the population. We also found that the rate of regional stochasicity had a dramatic impact for the estimate of species viability, and in one case altered the trajectory of our metapopulation from viable to non-viable. The divergent estimates in time to extinction times were likely due to a combination species-specific behavior, the dendritic nature of stream metapopulations, and the rate of regional stochasticity. We demonstrate the importance of developing comparative analyses using species- and patch-specific data when determining quantitative estimates for mean time to extinction, which in the case of redside dace, were highly sensitive to different estimates of dispersal.

Bayesian state-space modeling of metapopulation dynamics in the Glanville fritillary butterfly

The complexity of mathematical models of ecological dynamics varies greatly, and it is often difficult to judge what would be the optimal level of complexity in a particular case. Here we compare the parameter estimates, model fits, and predictive abilities of two models of metapopulation dynamics: a detailed individual-based model (IBM) and a population-based stochastic patch occupancy model (SPOM) derived from the IBM. The two models were fitted to a 17-year time series of data for the Glanville fritillary butterfly (Melitaea cinxia) inhabiting a network of 72 small meadows. The data consisted of biannual counts of larval groups (IBM) and the annual presence or absence of local populations (SPOM). The models were fitted using a Bayesian state-space approach with a hierarchical random effect structure to account for observational, demographic, and environmental stochasticities. The detection probability of larval groups (IBM) and the probability of false zeros of local populations (SPOM) in the observati...

Metapopulation dynamics and a landscape approach to conservation of lowland water voles (Arvicola amphibius)

Effective conservation management for species that function as metapopulations requires an understanding of population dynamics at the landscape scale. The water vole, Arvicola amphibius, is one such species. Water voles have recently undergone a significant decline in the UK, as a result of habitat loss and predation from the introduced American mink, Neovison vison. Large reed bed and grazing marsh sites can provide refuge habitats for water voles from mink predation, in which case populations within these sites could sustain metapopulations in the surrounding landscape where conditions are less favourable. We carried out a study using a stochastic patch occupancy model to determine the long term viability of water vole metapopulations in the wider landscape around a series of extensive reed bed and grazing marsh sites designated as National Key Sites for water voles. The results of our model simulations show that a large protected core site, or mainland, is essential in maintaining the long term viability of these systems. Our results also show how these metapopulations could be enhanced by increasing patch numbers through habitat creation and/or restoration and suggest what the minimum effective size of created or restored patches should be. The study shows how population modelling can provide insight into some effective practical ways of enhancing the viability of water vole metapopulations at the landscape scale. Furthermore it demonstrates that extensive wetlands are an appropriate focus for water vole conservation measures.