Patch Occupancy Model Research Articles

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. BayesianPVAs 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 forL. raniformiscollected 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 ofL. raniformissubject 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 toPVAallow 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 forPVAs.

Inferring contemporary dispersal processes in plant metapopulations: comparison of direct and indirect estimates of dispersal for the annual species Crepis sancta

Analyzing population dynamics in changing habitats is a prerequisite for population dynamics forecasting. The recent development of metapopulation modeling allows the estimation of dispersal kernels based on the colonization pattern but the accuracy of these estimates compared with direct estimates of the seed dispersal kernel has rarely been assessed. In this study, we used recent genetic methods based on parentage analysis (spatially explicit mating models) to estimate seed and pollen dispersal kernels as well as seed and pollen immigration in fragmented urban populations of the plant species Crepis sancta with contrasting patch dynamics. Using two independent networks, we documented substantial seed immigration and a highly restricted dispersal kernel. Moreover, immigration heterogeneity among networks was consistent with previously reported metapopulation dynamics, showing that colonization was mainly due to external colonization in the first network (propagule rain) and local colonization in the second network. We concluded that the differences in urban patch dynamics are mainly due to seed immigration heterogeneity, highlighting the importance of external population source in the spatio-temporal dynamics of plants in a fragmented landscape. The results show that indirect and direct methods were qualitatively consistent, providing a proper interpretation of indirect estimates. This study provides attempts to link genetic and demographic methods and show that patch occupancy models may provide simple methods for analyzing population dynamics in heterogeneous landscapes in the context of global change.

Chasing a moving target: projecting climate change‐induced shifts in non‐equilibrial tree species distributions

Summary The geographic distributions of plant species show marked correlations with the current climate, suggesting that they are likely to shift if climate changes. However, before projecting any such shifts, it is important to establish whether distributions are at equilibrium with the current climate. If they are not, distributional shifts could occur even without climate change, making it difficult to tease apart climate‐induced shifts from shifts occurring naturally without climate change. We forecast the geographical distributions of the 10 most common trees occurring in the Iberian Peninsula using a new method that relaxes the species–climate equilibrium assumption implicit in most species distributions models. For each species, we developed a spatially explicit patch occupancy model (SPOM) with climate‐dependent extinction rates and with colonization rates that depend on both climate and local seed dispersal. Bayesian methods were used to estimate the colonization, extinction and seed dispersal functions against observed colonization and extinction events recorded in repeat surveys of 46 596 forest plots in the Spanish Forest Inventories (1986–96 and 1997–2007). We then simulated distributional changes between the years 2000–2100. Without climate change, 9 of the 10 species substantially increased in regional frequency. These increases occurred primarily within current ranges, although some species also expanded across their range edges. With climate change, one temperate conifer species and two sub‐Mediterranean species would reduce their frequency of occurrence across the studied region, whereas temperate broad‐leaved species were unaffected and Mediterranean species were either unaffected or increased their frequency of occurrence. Synthesis. The analysis suggests that these species are substantially out of equilibrium, such that abundances and ranges would increase without climate change. Climate change may increase, decrease, stabilize or shift distributions, in a way that can only be understood by comparing predictions against baseline scenarios that account for these non‐equilibrium range dynamics.

Habitat association in populations on landscapes with continuous-valued heterogeneous habitat quality

We explore a spatially implicit patch-occupancy model of a population on a landscape with continuous-valued heterogeneous habitat quality, primarily considering the case where the habitat quality of a site affects the mortality rate but not the fecundity of individuals at that site. Two analytical approaches to the model are constructed, by summing over the sites in the landscape and by integrating over the range of habitat quality. We obtain results relating the equilibrium population density and all moments of the probability distribution of the habitat quality of occupied sites, and relating the probability distributions of total habitat quality and occupied habitat quality. Special cases are considered for landscapes where habitat quality has either a uniform or a linear probability density function. For these cases, we demonstrate habitat association, where the quality of occupied sites is higher than the overall mean quality of all sites; the discrepancy between the two is reduced at larger population densities. The variance of the quality of occupied sites may be greater or less than the overall variance of habitat quality, depending on the distribution of habitat quality across the landscape. Increasing the variance of habitat quality is also shown to increase the ability of a population to persist on a landscape.

Organism-induced habitat restoration leads to bi-stability in metapopulations

Following Levins’ patch occupancy model, we presented a differential-equation model, in which both the metapopulation dynamics and the dynamics of the fraction of suitable patches in the habitat are characterized. Habitat restoration induced by organism itself (internal restoration) and by other organisms or/and abiotic causes (external restoration) were incorporated in the model, together with habitat destruction. Stability analysis revealed the existence of alternative equilibriums (i.e., bi-stability) in the system. The internal restoration of habitat was identified as the trigger for the bi-stability, whereas the external restoration, in contrast, can eliminate the bi-stability from the system. The results, thus, emphasize the important role of the organism-environment feedback in biological conservation.

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.

General methods for sensitivity analysis of equilibrium dynamics in patch occupancy models

Sensitivity analysis is a useful tool for the study of ecological models that has many potential applications for patch occupancy modeling. Drawing from the rich foundation of existing methods for Markov chain models, I demonstrate new methods for sensitivity analysis of the equilibrium state dynamics of occupancy models. Estimates from three previous studies are used to illustrate the utility of the sensitivity calculations: a joint occupancy model for a prey species, its predators, and habitat used by both; occurrence dynamics from a well-known metapopulation study of three butterfly species; and Golden Eagle occupancy and reproductive dynamics. I show how to deal efficiently with multistate models and how to calculate sensitivities involving derived state variables and lower-level parameters. In addition, I extend methods to incorporate environmental variation by allowing for spatial and temporal variability in transition probabilities. The approach used here is concise and general and can fully account for environmental variability in transition parameters. The methods can be used to improve inferences in occupancy studies by quantifying the effects of underlying parameters, aiding prediction of future system states, and identifying priorities for sampling effort.

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.

The implications of metapopulation dynamics on the design of vaccination campaigns.

Control programmes for vaccine preventable diseases typically operate under logistic constraints such as limited resources and in spatially structured populations where the assumption of homogeneous mixing is invalid. It is unclear, therefore, how to maximise the effectiveness of campaigns in such populations. We investigate how to deploy vaccine in metapopulations by comparing the effectiveness of alternative vaccination strategies on reducing disease occurrence (presence/absence), using canine rabies as a model system, and a domestic dog population within a Tanzanian district divided into sub-populations corresponding to villages. We use patch-occupancy models to quantify the contribution of sub-populations to disease occurrence ("risk") and model allocation strategies for a limited number of vaccine doses that prioritize villages based on their size, risk, or the reduction in risk for the entire population that would result from vaccination. We assume that a maximum of 70% of susceptible individuals in a village could be vaccinated, and that only susceptible dogs are vaccinated. The most effective strategy maximised the reduction in risk of the entire population, and was up to 62% more effective than the other strategies. Large, single-pulse campaigns provided the greatest short-term protection, but higher frequencies of smaller pulses were more effective at reducing long-term disease occurrence. Vaccine allocation on a per-dose basis was substantially more effective than a per-village strategy, indicating that operational constraints can reduce control effectiveness. The spatial distribution and abundance of hosts have an important influence on disease dynamics and these results demonstrate that metapopulation models can be used to substantially improve the effectiveness of vaccination campaigns and optimize the allocation of limited control resources.

Habitat selection by adult walleye during spawning season in irrigation reservoirs: a patch occupancy modeling approach

Recruitment of walleye (Sander vitreus Mitchill) is limited in irrigation reservoirs of the Republican River basin in southwestern Nebraska. The causal mechanism for this limited recruitment is unknown, but may be related to a lack of suitable spawning habitat. Patch occupancy models were developed to describe variation in detection probability and habitat selection during spawning season using shoreline electrofishing data. Detection of adult walleye was negatively affected by water temperature, silt substrate, and woody cover. Adult walleye selected sites with cooler water temperatures and greater fetch at Enders Reservoir, and large rock substrate and no cover at Hugh Butler Lake; these characteristics are limited to areas on or near the riprap dams in both reservoirs. Walleye eggs were also only found in these areas. We conclude that patch occupancy modeling provided valuable information when considering habitat improvement projects and propose a management approach for the addition of walleye spawning habitat in irrigation reservoirs.

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.

Habitat selection by adult walleye during spawning season in irrigation reservoirs: a patch occupancy modeling approach

Recruitment of walleye (Sander vitreus Mitchill) is limited in irrigation reservoirs of the Republican River basin in southwestern Nebraska. The causal mechanism for this limited recruitment is unknown, but may be related to a lack of suitable spawning habitat. Patch occupancy models were developed to describe variation in detection probability and habitat selection during spawning season using shoreline electrofishing data. Detection of adult walleye was negatively affected by water temperature, silt substrate, and woody cover. Adult walleye selected sites with cooler water temperatures and greater fetch at Enders Reservoir, and large rock substrate and no cover at Hugh Butler Lake; these characteristics are limited to areas on or near the riprap dams in both reservoirs. Walleye eggs were also only found in these areas. We conclude that patch occupancy modeling provided valuable information when considering habitat improvement projects and propose a management approach for the addition of walleye spawning habitat in irrigation reservoirs.

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.

Prevalence of Influenza A Antibodies in Yellow-Legged Gull (Larus michahellis) Eggs and Adults in Southern Tunisia

Investigating the prevalence of anti-influenza A viruses (AIV) antibodies in wild birds can provide important information for the understanding of bird exposure to AIV, as well as for prevention purposes. We investigated AIV exposure in nature by measuring the prevalence of anti-AIV antibodies in the nests and adults of an abundant and anthropophilic waterbird species common around the Mediterranean sea, the yellow-legged gull (Larus michahellis). Sampling took place in two colonies located in the gulf of Gabès in southern Tunisia: Sfax and Djerba. Antibodies were detected in the two sites, with higher prevalence in adults, eggs, and nests at Sfax than Djerba. Across both colonies, clutches that were laid later in the season, and, thus, more likely by younger parents, showed lower prevalence. Using patch occupancy modeling applied to egg clutches, we found that it is unnecessary to sample all the eggs in a given nest; nest status (antibody positive or negative) can be reliably estimated from a single egg. Differences in the density of birds, notably Larids, between the two sites may explain the observed differences in prevalence. The higher concentration of Larids in the Sfax colony could favor the transmission of AIV to yellow-legged gulls. This study highlights the importance of further developing ecological-based approaches to the factors determining the circulation of infectious agents in species such as the yellow-legged gull, which exist at the interface between diverse biological communities and human activities.

The limiting behaviour of a mainland-island metapopulation

Stochastic patch occupancy models (SPOMs) are a class of discrete time Markov chains used to model the presence/absence of a population in a collection of habitat patches. This class of model is popular with ecologists due to its ability to incorporate important factors of the habitat patch network such as connectivity and distance between patches as well as heterogeneity in patch characteristics. We present an asymptotic examination of a simple type of SPOM called the mainland-island model. In this model a single patch called the mainland is connected to a large number of smaller patches called islands and each island is only connected to the mainland. We discuss the limiting behaviour of the SPOM as the number of islands increases and the size of the islands decrease relative to the mainland. We demonstrate that a variety of limiting behaviours is possible depending on the scaling of the island size and on the heterogeneity of habitat quality.

Refining logistic regression models for wildlife habitat suitability modeling—A case study with muntjak and goral in the Central Himalayas, India

High quality habitat suitability maps are indispensable for the management and planning of wildlife reserves. This is particularly important for megadiverse developing countries where shortages in skilled manpower and funding may preclude the use of mathematically complex modeling techniques and resource-intensive field surveys. In this study, we propose a simulation based k-fold partitioning and re-substitution approach to refine and update logistic regression models that are widely used for habitat suitability assessment and modeling. We test the modeling strategy using data from a rapid field survey conducted for habitat suitability assessment for muntjak ( Muntiacus muntjak) and goral ( Naemorrhaedus goral) in the central Himalayas, India. Results obtained from simulations match expectations in terms of model behavior and in terms of published habitat associations of the investigated species. Qualitative comparisons with predictions from the GARP, MaxEnt and Bioclimatic Envelopes modeling systems also show broad agreement with predictions obtained from the proposed technique. The proposed technique is suggested as a rapid-assessment precursor to detailed habitat studies such as patch occupancy modeling in situations where funds or trained manpower are not available.

Colonization and extinction dynamics of an annual plant metapopulation in an urban environment

The metapopulation framework considers that the spatiotemporal distribution of organisms results from a balance between the colonization and extinction of populations in a suitable and discrete habitat network. Recent spatially realistic metapopulation models have allowed patch dynamics to be investigated in natural populations but such models have rarely been applied to plants. Using a simple urban fragmented population system in which favourable habitat can be easily mapped, we studied patch dynamics in the annual plant Crepis sancta (Asteraceae). Using stochastic patch occupancy models (SPOMs) and multi‐year occupancy data we dissected extinction and colonization patterns in our system. Overall, our data were consistent with two distinct metapopulation scenarios. A metapopulation (sensu stricto) dynamic in which colonization occurs over a short distance and extinction is lowered by nearby occupied patches (rescue effect) was found in a set of patches close to the city centre, while a propagule rain model in which colonization occurs from a large external population was most consistent with data from other networks. Overall, the study highlights the importance of external seed sources in urban patch dynamics. Our analysis emphasizes the fact that plant distributions are governed not only by habitat properties but also by the intrinsic properties of colonization and dispersal of species. The metapopulation approach provides a valuable tool for understanding how colonization and extinction shape occupancy patterns in highly fragmented plant populations. Finally, this study points to the potential utility of more complex plant metapopulation models than traditionally used for analysing ecological and evolutionary processes in natural metapopulations.

A robust-design formulation of the incidence function model of metapopulation dynamics applied to two species of rails

The incidence function model (IFM) uses area and connectivity to predict metapopulation dynamics. However, false absences and missing data can lead to underestimates of the number of sites contributing to connectivity, resulting in overestimates of dispersal ability and turnovers (extinctions plus colonizations). We extend estimation methods for the IFM by using a hierarchical Bayesian model to account both for false absences due to imperfect detection and for missing data due to sites not surveyed in some years. We compare parameter estimates, measures of metapopulation dynamics, and forecasts using stochastic patch occupancy models (SPOMs) among three IFM models: (1) a Bayesian formulation assuming no false absences and omitting site-year combinations with missing data; (2) a hierarchical Bayesian formulation assuming no false absences but incorporating missing data; and (3) a hierarchical Bayesian formulation allowing for imperfect detection and incorporating missing data. We fit the models to multiyear data sets of occupancy for two bird species that differ in body size and presumed dispersal ability but inhabit the same network of sites: the small Black Rail (Laterallus jamaicensis) and the medium-sized Virginia Rail (Rallus limicola). Incorporating missing data affected colonization parameters and led to lower estimates of dispersal ability for the Black Rail. Detection rates were high for the Black Rail in most years but moderate for the Virginia Rail. Incorporating imperfect detection resulted in higher occupancy and lower turnover rates for both species, with largest effects for the Virginia Rail. Forecasts using SPOMs were sensitive to both missing data and false absences; persistence in models assuming no false absences was more optimistic than from robust models. Our results suggest that incorporating false absences and missing data into the IFM can improve (1) estimates of dispersal ability and the effect of connectivity on colonization, (2) the scaling of extinction risk with patch area, and (3) forecasts of occupancy and turnover rates.

Landscape Composition Influences the Restoration of Subtropical Coastal Dune Forest

Successional processes should increase habitat complexity, and increase resources available for forest‐associated species. However, according to the theory of Island Biogeography, the size, amount of edge, and isolation of a habitat patch will influence the probability of successful colonization. If this is true for restoring patches of coastal dune forest, then restoration managers need to mitigate for spatial characteristics.We used patch occupancy models to assess correlations between the probability of forest birds and trees being present in a patch and patch characteristics that measured age, area, isolation, and the amount of edge. We surveyed birds and trees in an unmined coastal dune forest, remnant patches within the mine lease, and regenerating patches, some of which were being rehabilitated by a mining company. Contrary to expectations patch age only explained the patch occupancy of 6 of 21 birds and 11 of 25 woody plant species. Landscape spatial parameters, measuring edge, isolation, and area explained the patch occupancy of the remaining 15 birds and 14 woody plant species. However, responses to patch characteristics were varied and idiosyncratic. These varied responses may be related to species habitat affinities, dispersal abilities, and establishment constraints. For restoration to succeed, managers need to consider the spatial configuration of the landscape to facilitate colonization of rehabilitating patches.