A General Model of Metapopulation Dynamics

Aim Geographical variations in species richness are strongly related to temperature and precipitation. On ecological time-scales, these variations in species richness should reflect rates of immigration and local extinction (extirpation). Here we ask whether the probability of local extinction in passerine birds covaries with climate. Specifically, we test whether local extinctions increase with climatic harshness or with the climatic distance from a species' optimal climate. Location USA and Canada. Methods We obtained bird counts from the North American Breeding Bird Survey (BBS) from 1967 to 2012. For each BBS route, we calculated the probability of interannual local extinction for each of 206 passerine birds. We then used linear mixed-effects models and structural equation modelling to relate local extinction rates to our hypothesized predictor variables: temperature, precipitation and their distance from the species' most occupied temperature and precipitation. Results We found that local extinctions are nearly independent of temperature and precipitation: no climate is inherently more extinction-prone than any other. Similarly, the climatic distance from a species' maximally occupied temperature and precipitation has only an extremely weak positive effect on the probability of local extinction. We found that only abundance has a strong negative effect on the probability of local extinction. Main conclusions Although variations in local extinctions are typically spatially structured, we conclude that they are not related to contemporary climate in a consistent way among species. Broad-scale geographical gradients of species richness are unlikely to be driven by higher extinction rates in climatically harsh areas.

From a theoretical viewpoint, nature management basically has two options to prolong metapopulation persistence: decreasing local extinction probabilities and increasing colonization probabilities. This article focuses on those options with a stochastic, single-species metapopulation model. We found that for most combinations of local extinction probabilities and colonization probabilities, decreasing the former increases metapopulation extinction time more than does increasing the latter by the same amount. Only for relatively low colonization probabilities is an effort to increase these probabilities more beneficial, but even then, decreasing extinction probabilities does not seem much less effective. Furthermore, we found the following rules of thumb. First, if one focuses on extinction, one should preferably decrease the lowest local extinction probability. Only if the extinction probabilities are (almost) equal should one prioritize decreases in the local extinction probability of the patch with the best direct connections to and from other patches. Second, if one focuses on colonization, one should preferably increase the colonization probability between the patches with the lowest local extinction probability. Only if the local extinction probabilities are (almost) equal should one instead prioritize increases in the highest colonization probability (unless extinction probabilities and colonization probabilities are very low). The rules of thumb have an important common denominator: the local extinction process has a greater bearing on metapopulation extinction time than colonization.

Aim Based ona priorihypotheses, we developed predictions about how avian communities might differ at the edges vs. interiors of ecoregions. Specifically, we predicted lower species richness and greater local turnover and extinction probabilities for regional edges. We tested these predictions using North American Breeding Bird Survey (BBS) data across nine ecoregions over a 20‐year time period.Location Data from 2238 BBS routes within nine ecoregions of the United States were used.Methods The estimation methods used accounted for species detection probabilities < 1. Parameter estimates for species richness, local turnover and extinction probabilities were obtained using the program COMDYN. We examined the difference in community‐level parameters estimated from within exterior edges (the habitat interface between ecoregions), interior edges (the habitat interface between two bird conservation regions within the same ecoregion) and interior (habitat excluding interfaces). General linear models were constructed to examine sources of variation in community parameters for five ecoregions (containing all three habitat types) and all nine ecoregions (containing two habitat types).Results Analyses provided evidence that interior habitats and interior edges had on average higher bird species richness than exterior edges, providing some evidence of reduced species richness near habitat edges. Lower average extinction probabilities and turnover rates in interior habitats (five‐region analysis) provided some support for our predictions about these quantities. However, analyses directed at all three response variables, i.e. species richness, local turnover, and local extinction probability, provided evidence of an interaction between habitat and region, indicating that the relationships did not hold in all regions.Main conclusions The overall predictions of lower species richness, higher local turnover and extinction probabilities in regional edge habitats, as opposed to interior habitats, were generally supported. However, these predicted tendencies did not hold in all regions.

Summary The effect that the surrounding landscape matrix has on the loss of species from fragmented patches remains largely unknown. To determine whether there were differences in the persistence of plants inhabiting remnant patches in contrasting landscape types we examined the local extinction of grassland plants along an urban–rural gradient in western Victoria, Australia. Thirty small grassland remnants that had been comprehensively surveyed between 1979 and 1990 were intensively re‐surveyed. A total of 289 (26%) of the 1104 plant populations present in the 1980s were not relocated and were presumed to be locally extinct. The proportion of populations lost differed along the gradient, with higher local extinction rates at patches in urban (37%) and peri‐urban landscapes (27%) than those in the rural landscape (20%). We calculated the probability of local extinction of species in urban, peri‐urban and rural landscapes using Bayesian logistic regression models. Across all plant functional traits examined, species had a consistently higher probability of local extinction in the urban landscape. Species that were geophytes or hemicryptophytes with a flat rosette and species with seeds dispersed by wind or ants had substantially increased risks of extinction in the urban landscape. Low seed mass, the lack of vegetative reproduction and the presence of a soil‐stored seed bank increased the probability of local extinction in all landscapes. Regionally rare species had a higher probability of local extinction in rural and peri‐urban landscapes but rarity had little influence on extinction risk in urban landscapes. Urbanization has a strong influence on the species composition of urban grasslands and substantially increases the probability of local extinction of plants with particular combinations of functional traits.

Despite the increasing sophistication of ecological models with respect to the size and spatial arrangement of habitat, there is relatively little empirical documentation of how species dynamics change as a function of habitat size and the fraction of habitat occupied. In an assemblage of tidepool fishes, I used maximum-likelihood estimation to test whether models which included habitat size provided a better fit to empirical data on extinction and colonization probabilities than models that assumed constant probabilities over all habitats. I found species differences in how extinction and colonization probabilities scaled with habitat size (and hence local population size). However, there was little evidence for a relationship between extinction and colonization probabilities and the fraction of occupied tidepools, as assumed in simple metapopulation models. Instead, colonization and extinction were independent of the fraction of occupied tidepools, favoring a MacArthur-Wilson island-mainland model. When I incorporated declines in extinction probability with tidepool volume in a simple simulation model, I found that predicted occupancy could change greatly, especially when colonization was low. However, the predicted fraction of occupied patches in the simulation model changed little when I incorporated the range of values reported here for extinction and colonization and the rate at which they scale with habitat size. Quantifying extinction and colonization patterns of natural populations is fundamental to understanding how species are distributed spatially and whether metapopulation models of species occupancy provide explanatory power for field populations.

We investigated the site occupancy dynamics of greater prairie‐chickens at Konza Prairie Biological Station, a protected site in northeastern Kansas that is managed for ecological research. We surveyed the site during mid‐Mar to mid‐May, 1981–2008, and recorded detections of birds in a grid of 6.3 ha survey plots (n = 187 plots). We used multiseason occupancy models to estimate the probabilities of occupancy (ψ) and detection (p), and tested whether land cover in woody vegetation, and land use with prescribed fire or grazing management influenced the dynamic processes of site colonization and local extinction. Probability of detection per site was consistently <1 and varied among years (p = 0.12–0.82). Site occupancy of prairie‐chickens declined 40% over the study period from a high of ψ = 0.19 ± 0.02 SE in 1981 to a low of 0.11 ± 0.03 in 2008, despite protection from disturbance at leks and losses to harvest. We found that different sets of environmental factors impacted the probabilities of colonization and local extinction. Probability of colonization for an unoccupied site was negatively associated with the proportion of site occupied by woodland cover (β = −1.25), and was lower for grazed sites (β = −0.62). In contrast, probability of local extinction was affected by a weak interaction between grazing and average frequency of prescribed fire (β = −1.01), but model‐averaged slope coefficients were not statistically different than 0. To conserve prairie‐chickens, we recommend prairies be managed with combinations of prescribed fire and grazing that maintain a heterogeneous mosaic of prairie habitats, while preventing woody encroachment. To assess biotic responses to land management practices, field sampling should be based on occupancy models or similar techniques that account for imperfect detection. © 2011 The Wildlife Society.

Perturbation analysis is a powerful tool to study population and community dynamics. This article describes expressions for sensitivity metrics reflecting changes in equilibrium occupancy resulting from small changes in the vital rates of patch occupancy dynamics (i.e., probabilities of local patch colonization and extinction). We illustrate our approach with a case study of occupancy dynamics of Golden Eagle (Aquila chrysaetos) nesting territories. Examination of the hypothesis of system equilibrium suggests that the system satisfies equilibrium conditions. Estimates of vital rates obtained using patch occupancy models are used to estimate equilibrium patch occupancy of eagles. We then compute estimates of sensitivity metrics and discuss their implications for eagle population ecology and management. Finally, we discuss the intuition underlying our sensitivity metrics and then provide examples of ecological questions that can be addressed using perturbation analyses. For instance, the sensitivity metrics lead to predictions about the relative importance of local colonization and local extinction probabilities in influencing equilibrium occupancy for rare and common species.

Metapopulation ecology is a field that is richer in theory than in empirical results. Many existing empirical studies use an incidence function approach based on spatial patterns and key assumptions about extinction and colonization rates. Here we recast these assumptions as hypotheses to be tested using 18 years of historic detection survey data combined with four years of data from a new monitoring program for the Lower Keys marsh rabbit. We developed a new model to estimate probabilities of local extinction and colonization in the presence of nondetection, while accounting for estimated occupancy levels of neighboring patches. We used model selection to identify important drivers of population turnover and estimate the effective neighborhood size for this system. Several key relationships related to patch size and isolation that are often assumed in metapopulation models were supported: patch size was negatively related to the probability of extinction and positively related to colonization, and estimated occupancy of neighboring patches was positively related to colonization and negatively related to extinction probabilities. This latter relationship suggested the existence of rescue effects. In our study system, we inferred that coastal patches experienced higher probabilities of extinction and colonization than interior patches. Interior patches exhibited higher occupancy probabilities and may serve as refugia, permitting colonization of coastal patches following disturbances such as hurricanes and storm surges. Our modeling approach should be useful for incorporating neighbor occupancy into future metapopulation analyses and in dealing with other historic occupancy surveys that may not include the recommended levels of sampling replication.

Relationships between local annual immigration and extinction rates of plant species and total species richness were determined from long-term data in permanent plots in tallgrass and shortgrass prairies in Kansas. Combining plots resulted in higher equilibrium numbers of species as predicted from immigration and extinction rates. Immigration and extinction rates also increased with scale. Extinction rates are higher because the regional scale supports more rare species which, in turn, have high probabilities of extinction. We also tested the hypotheses that extinction rates would be higher on burned versus unburned grasslands, and that immigration rates would be higher on grazed versus ungrazed grasslands. Extinction rates were positively correlated with the number of species at a site, and this relationship was not altered by burning or grazing. Immigration rates were variable, but were sometimes positively correlated with growing season precipitation. Immigration rates decreased in years sites were burned. Therefore, after fire, the number of species going locally extinct was still dependent on earlier species richness, but the number of species added to the site was reduced. Variances in immigration and extinction rates were high, therefore, confident predictions regarding the effects of burning or grazing regimes on species richness could not be made. Variance in rates of immigration and extinction results in a range of values within which the equlibrium number of species fluctuates randomly.

All gibbon species (Family: Hylobatidae) are considered threatened with extinction and recognized on the International Union for Conservation of Nature Red List of Threatened Species. Because gibbons are one of the most threatened families of primates, monitoring their status is now critically important. Long-term monitoring programs applying occupancy approaches, in addition to assessing occurrence probability, improves understanding of other population parameters such as site extinction or colonization probabilities, which elucidate temporal and spatial changes and are therefore important for guiding conservation efforts. In this study, we used multiple season occupancy models to monitor occurrence, extinction, and colonization probabilities for northern yellow-cheeked crested gibbon Nomascus annamensis in three adjacent protected areas in the Central Annamites mountain range, Vietnam. We collected data at 30 listening posts in 2012, 2014, and 2016 using the auditory point count method. Occurrence probabilities were highest in 2012 (0.74, confidence interval [CI]: 0.56-0.87) but slightly lower in 2014 (0.66, CI: 0.51-0.79) and 2016 (0.67, CI: 0.49-0.81). Extinction probabilities during the 2012-2014 and 2014-2016 intervals were 0.26 (0.14-0.44) and 0.25 (0.12-0.44), respectively. Colonization probabilities during 2012-2014 were 0.44 (0.19-0.73) and between 2014 and 2016 was 0.51 (0.26-0.75). Although local site extinctions have occurred, high recolonization probability helped to replenish the unoccupied sites and kept the occurrence probability stable. Long-term monitoring programs which use occurrence probability alone might not fully reveal the true dynamics of gibbon populations. We strongly recommend including multiple season occupancy models to monitor occurrence, extinction, and colonization probabilities in long-term gibbon monitoring programs.

Critical information for evaluating the effectiveness of management strategies for species of concern include distinguishing seldom occupied (or low‐quality) habitat from habitat that is frequently occupied and thus contributes substantially to population trends. Using multi‐season models that account for imperfect detection and a long‐term (1981–2002) dataset on migratory Arctic Peregrine FalconsFalco peregrinus tundriusnesting along the Colville River, Alaska, we quantified the effects of previous year's productivity (i.e. site quality), amount of prey habitat, topography, climate, competition and year on occupancy dynamics across two spatial scales (nest‐sites, cliffs) during recovery of the population. Initial occupancy probability was positively correlated with area of surrounding prey habitat and height of nest‐sites above the Colville River. Colonization probability was positively correlated with nest height and negatively correlated with date of snowmelt. Local extinction probability was negatively correlated with productivity, area of prey habitat and nest height. Colonization and local extinction probabilities were also positively and negatively correlated, respectively, with year. Our results suggest that nest‐sites (or cliffs) along the Colville River do not need equal protection measures. Nest‐sites and cliffs with historically higher productivity were occupied most frequently and had lower probability of local extinction. These sites were on cliffs high above the river drainage, surrounded by adequate prey habitat and with southerly aspects associated with early snowmelt and warmer microclimates in spring. Protecting these sites is likely to encourage continued occupancy by Arctic Peregrine Falcons along the Colville River and other similar areas. Our findings also illustrate the importance of evaluating fitness parameters along with climate and habitat features when analysing occupancy dynamics, particularly with a long‐term dataset spanning a range of annual climate variation.

AimWe incorporate diversity‐dependent colonization and extinction rates into process‐based models of species geographic range dynamics to explore their effects on species richness gradients, and on extent and occupancy of species ranges. In particular, we investigate whether diversity dependence promotes or inhibits the emergence of mid‐domain effects (MDEs) in homogeneous environments.LocationA theoretical one‐dimensional domain.MethodsWe formulated diversity‐independent (DI) and diversity‐dependent (DD) models that simulated colonization, local extinction and speciation within a homogenous domain. In the DD model, colonization and extinction probabilities were functions of diversity, whereas in the DI model, they were constants. For a wide range of parameter values, we examined local and regional species richness gradients and species range size frequency distributions (RSFDs).ResultsIn contrast to the DI model, for which MDEs only occurred in a very narrow parameter range, the DD model generated a MDE in regional richness (range overlap) that was robust to colonization and extinction parameters, over a broad range of speciation rates. However, neither model could produce gradients in local richness (patch occupancy). The DD model also produced more realistic RSFDs than the DI model. In the latter, all species generally either became highly pandemic or went globally extinct, depending on the balance of colonization and extinction probabilities.Main conclusionsDiversity‐dependent colonization and extinction rates can have strong effects on species richness gradients and distributions of range extent and occupancy. Models with such diversity dependence amplify MDEs in regional richness, but largely eliminate MDEs in local richness, relative to DI models. DD models also generate more realistic RSFDs. These findings suggest that diffuse species interactions can strongly influence patterns of range size and overlap, but also that environmental gradients are likely to be necessary to explain many species richness patterns in nature, which exhibit both local and regional diversity gradients.

Aim The study of the spatial dynamics of invasive species is a key issue in invasion ecology. While mathematical models are useful for predicting the extent of population expansions, they are not suitable for measuring and characterizing spatial patterns of invasion unless the probability of detection is homogeneous across the distribution range. Here, we apply recently developed statistical approaches incorporating detection uncertainty to characterize the spatial dynamics of an invasive bird species, the Eurasian collared dove (Streptopelia decaocto).Location France.Methods Data on presence/absence of doves were recorded from 1996 to 2004 over 1045 grid cells (28 × 20 km) covering the entire country. Each grid cell included five point counts spaced along a route, which was visited twice a year, allowing for an estimation of detection probability. Each route was assigned to one of six geographical regions. We used robust design occupancy analysis to assess spatial and temporal variation in parameters related to the spatial dynamics of the species. These parameters included occupancy rate, colonization and local extinction probabilities. Our inference approach was based on the selection of the most parsimonious model among competitive models parametrized with conditional probabilities.Results The probability of detecting the presence of doves on a given route was high. However, we found evidence to incorporate detection uncertainty in inference processes about spatial dynamics, since detection probability was neither perfect (i.e. it was < 1), nor constant over space and time. Results showed a clear positive trend in occupancy rate over the study period, increasing from 55% in 1996 to 76% in 2004. In addition, occupancy rate differed among regions (range: 37–79%) and further analysis showed that colonization probability by region was positively related to occupancy rate. Finally, local extinction probability was lower than colonization probability and showed a tendency to decrease over the study period.Main conclusions Our results emphasize the importance of estimating detection probabilities in order to draw proper inferences about the spatial and temporal dynamics of the invasion pattern of the collared dove. In contrast to the perceived spatial dynamics from national atlas surveys, we provide evidence that the range of this species is currently increasing in France. Other results, such as regional specificity in colonization probabilities and time variation in local extinction are consistent with expectations from invasion and metapopulation theory.

Understanding the risk of extinction of a single population is an important problem in both theoretical and applied ecology. Local extinction risk depends on several factors, including population size, demographic or environmental stochasticity, natural catastrophe, or the loss of genetic diversity. The probability of local extinction may also be higher in low-quality sink habitats than in high-quality source habitats. We tested this hypothesis by comparing local extinction rates of 15 species of Odonata (dragonflies and damselflies) between 1930-1975 and 1995-2003 in central Finland. Local extinction rates were higher in low-quality than in high-quality habitats. Nevertheless, for the three most common species there were no differences in extinction rates between low- and high-quality habitats. Our results suggest that a good understanding of habitat quality is crucial for the conservation of species in heterogeneous landscapes.

This paper presents a metapopulation study of the bush cricket, Metrioptera bicolor , living in a recently fragmented landscape. The species inhabits grass and heathland patches of varying area and isolation. Analyses are made of how these geometrical factors affect local population size and density, distribution pattern, and the probability of local extinction and colonization. The proportion of available patches occupied varied between 72 and 79% during 1985–1990. Unoccupied patches were smaller and more isolated than those that were occupied. Patches where populations became extinct during this period were smaller than those with persisting populations. Since local population size was well correlated with patch area, it was clear that stochastic extinctions only occurred in small populations. Critical patch size for population extinction was approximately half a hectare. Colonized patches were less isolated than those that had not been colonized. Critical inter‐patch distance for colonization was about 100 meters. The turnover was restricted to an identifiable share of the available patches. Only 33% of the patches were so small that extinction due to stochastic causes could be considered highly probable. This metapopulation will therefore most likely persist over a considerable period in its present spatial structure. There are apparent threats of further fragmentation, however, and nothing is known about the likelihood of large‐scale extinctions resulting from extremely unfavorable weather conditions. Nevertheless, our results show that it is appropriate to include geometrical factors in metapopulation models.