A model for behavioral regulation of metapopulation dynamics

Habitat fragmentation can decrease local population persistence by reducing connectivity, which is a function of dispersal of individuals among habitat fragments. Dispersal is often treated as diffusion in population models, even though for many species it is a result of a series of behavioral decisions. We developed a metapopulation model to explore the potential importance of dispersal behaviors in driving metapopulation dynamics. We incorporated types of behavior that affect dispersal—colonization inhibiting, colonization enhancing, extinction inhibiting, extinction enhancing, rescue enhancing, rescue inhibiting—into Levins’ (1969) metapopulation model and projected occupancy rates for a variety of parameter values. Examples from the literature of behaviors associated with each of these parameters are provided. Our model simplifies into previously published metapopulation models that incorporate only a single behavior, and we present a density-dependent rescue function that leads to multiple non-zero equilibria. We found a variety of behavioral effects on metapopulations. Rescue enhancement fills patches faster than does colonization enhancement or extinction inhibition, and declines in patch occupancy are moderate with extinction enhancement, but colonization inhibition causes metapopulation extinction. We also found that with colonization and extinction inhibitions, equilibrium patch occupancy is inversely related to patch turnover rate. With density-dependent rescue, persistence depends not only on the strength of the strong rescue effect, but also on having a sufficient initial fraction of patches occupied; the stronger the rescue effect, the lower this fraction can be. This study suggests that dispersal behavior can have strong influences on metapopulation dynamics. It confirms the importance of understanding the relationship between landscape structure and dispersal behavior in understanding population persistence.     

Influence of habitat quality, population size, patch size, and connectivity on patch-occupancy dynamics of the middle spotted woodpecker

Despite extensive research on the effects of habitat fragmentation, the ecological mechanisms underlying colonization and extinction processes are poorly known, but knowledge of these mechanisms is essential to understanding the distribution and persistence of populations in fragmented habitats. We examined these mechanisms through multiseason occupancy models that elucidated patch-occupancy dynamics of Middle Spotted Woodpeckers (Dendrocopos medius) in northwestern Spain. The number of occupied patches was relatively stable from 2000 to 2010 (15-24% of 101 patches occupied every year) because extinction was balanced by recolonization. Larger and higher quality patches (i.e., higher density of oaks >37 cm dbh [diameter at breast height]) were more likely to be occupied. Habitat quality (i.e., density of large oaks) explained more variation in patch colonization and extinction than did patch size and connectivity, which were both weakly associated with probabilities of turnover. Patches of higher quality were more likely to be colonized than patches of lower quality. Populations in high-quality patches were less likely to become extinct. In addition, extinction in a patch was strongly associated with local population size but not with patch size, which means the latter may not be a good surrogate of population size in assessments of extinction probability. Our results suggest that habitat quality may be a primary driver of patch-occupancy dynamics and may increase the accuracy of models of population survival. We encourage comparisons of competing models that assess occupancy, colonization, and extinction probabilities in a single analytical framework (e.g., dynamic occupancy models) so as to shed light on the association of habitat quality and patch geometry with colonization and extinction processes in different settings and species.     

Geometrical Factors and Metapopulation Dynamics of the Bush Cricket, Metrioptera bicolor Philippi (Orthoptera: Tettigoniidae)

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.     

An analysis of water level dynamics in Esteros del Ibera wetland

In an apparent violation of Gause’s principle of competitive exclusion, many metapopulation models of interspecific competition make the claim that identical species can coexist in spatially structured habitats. In these models, it is assumed that extinction and colonization parameters are always the same for both species, independent of the relative abundance of the two species in doubly occupied patches. We show that it is this simplifying assumption that gives an unfair advantage to the regionally rarer species. More realistic assumptions in these models would lead to different conclusions, which indicate that two identical species cannot coexist regionally in a network of many habitat patches.     

Populations in small, ephemeral habitat patches may drive dynamics in a Daphnia magna metapopulation

Migration is the key process to understand the dynamics and persistence of a metapopulation. Many metapopulation models assume a positive correlation between habitat patch size or stability and the number of emigrants. However, few empirical data exist, and habitat patch size and habitat stability may affect dispersal differently than they affect local persistence. Here, we studied the production of the migration stage (i.e., resting eggs called ephippia) of the cladoceran Daphnia magna in a metapopulation consisting of 530 rock pool habitat patches over 25 years. Earlier, the functioning of this metapopulation was explained with a Levins-type metapopulation model or with a mainland-island metapopulation model, based on local extinction and colonization data or time series data, respectively. We used pool volume, hydroperiod length, and number of desiccation events to calculate per-pool production of ephippia (i.e., migration stages). We estimated that populations in small and ephemeral habitat patches produced more than half of the 250 000 to 1 million ephippia that were produced in the metapopulation as a whole per year between 1982 and 2006. Furthermore, these small populations contributed approximately 90% of the ephippia exposed during desiccation events, while the contribution of the long-lived populations in large pools was minimal. We term this an "inverse mainland-island" type metapopulation and propose that populations in small, ephemeral habitat patches may also be the driving force for metapopulation dynamics in other systems.     

The Quantitative Incidence Function Model and Persistence of an Endangered Butterfly Metapopulation

The incidence function model is derived from a linear first-order Markov chain of the presence or absence of a species in a habitat patch. The model can be parameterized with "snapshot" presence/absence data from a patch network. Using the estimated parameter values the Markov chain can be iterated in the same or in some other patch network to generate quantitative predictions about transient metapopulation dynamics and the stochastic steady state. We tested the ability of the incidence function model to predict patch occupancy using extensive data on an endangered butterfly, the Glanville fritillary ( Melitaea cinxia ) Parameter values were estimated with data collected from a 50-patch network in 1991. In 1993 we surveyed the entire geographic range of the species in Finland, within an area of 50 × 70 km², with 1502 habitat patches (dry meadows) of which 536 were occupied. Model predictions were generated for the 1502 patches and were compared with the observed pattern of occupancy in 1993. The model predicted patch occupancy well in more than half of the study area, but prediction was poor for one quarter of the area, probably because of regional variation in habitat quality and because metapopulations may have been perturbed away from the steady state. The incidence function model provides a practical tool for making quantitative predictions about metapopulation dynamics of species living in fragmented landscapes.     

Comparison of Two Types of Metapopulation Models in Real and Artificial Landscapes

Abstract: Application of metapopulation models is becoming increasingly widespread in the conservation of species in fragmented landscapes. We provide one of the first detailed comparisons of two of the most common modeling techniques, incidence function models and stage-based matrix models, and test their accuracy in predicting patch occupancy for a real metapopulation. We measured patch occupancies and demographic rates for regional populations of the Florida scrub lizard (   Sceloporus woodi ) and compared the observed occupancies with those predicted by each model. Both modeling strategies predicted patch occupancies with good accuracy ( 77–80%) and gave similar results when we compared hypothetical management scenarios involving removal of key habitat patches and degradation of habitat quality. To compare the two modeling approaches over a broader set of conditions, we simulated metapopulation dynamics for 150 artificial landscapes composed of equal-sized patches (2–1024 ha) spaced at equal distances (50–750 m). Differences in predicted patch occupancy were small to moderate (<20%) for about 74% of all simulations, but 22% of the landscapes had differences openface> 50%. Incidence function models and stage-based matrix models differ in their approaches, assumptions, and requirements for empirical data, and our findings provide evidence that the two models can produce different results. We encourage researchers to use both techniques and further examine potential differences in model output. The feasibility of obtaining data for population modeling varies widely among species and limits the modeling approaches appropriate for each species. Understanding different modeling approaches will become increasingly important as conservation programs undertake the challenge of managing for multiple species in a landscape context.     

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.     

Habitat-quality effects on metapopulation dynamics in greater white-toothed shrews, Crocidura russula

The effects of patch size and isolation on metapopulation dynamics have received wide empirical support and theoretical formalization. By contrast, the effects of patch quality seem largely underinvestigated, partly due to technical difficulties in properly assessing quality. Here we combine habitat-quality modeling with four years of demographic monitoring in a metapopulation of greater white-toothed shrews (Crocidura russula) to investigate the role of patch quality on metapopulation processes. Together, local patch quality and connectivity significantly enhanced local population sizes and occupancy rates (R2 = 14% and 19%, respectively). Accounting for the quality of patches connected to the focal one and acting as potential sources improved slightly the model explanatory power for local population sizes, pointing to significant source-sink dynamics. Local habitat quality, in interaction with connectivity, also increased colonization rate (R2 = 28%), suggesting the ability of immigrants to target high-quality patches. Overall, patterns were best explained when assuming a mean dispersal distance of 800 m, a realistic value for the species under study. Our results thus provide evidence that patch quality, in interaction with connectivity, may affect major demographic processes.     

Inferring Metapopulation Dynamics from Patch-Level Incidence of Florida Scrub Plants

Spatial structure and dynamics of multiple populations may explain species distribution patterns in patchy communities with heterogeneous disturbance regimes, especially when species have poor dispersal. The endemic-rich Florida (U.S.A.) rosemary scrub occupies about 4% of the west portion of Archbold Biological Station and occurs scattered within a matrix of less xeric vegetation. Longer fire-return times and higher frequency of open patches in rosemary scrub provide favorable habitat for many plant species. Occupancy of 123 species of vascular plants and ground lichens in 89 patches was determined by repeated site surveys. About two-thirds of the species occurring at more than 14 patches had a significant logistic regression of presence on time-since-fire, patch size, patch isolation, or their interactions. Species with presence related to the interaction between patch isolation and patch size were primarily herbs and small shrubs specializing in rosemary scrub. These results suggest the importance of spatial characteristics of the landscape for population turnover of these species. An incidence-based metapopulation model was used to predict extinction and colonization probabilities of those species with presence in rosemary scrub patches related to the studied spatial variables. This is the first attempt to apply incidence-based metapopulation models to plants. The results showed stronger effects of patch size and patch isolation on extinction probabilities of herbs than on those of woody species. Because of their effect on spatial heterogeneity and habitat availability, fire suppression and habitat destruction may decrease persistence probabilities for these rosemary scrub specialists, many of which are endangered species.     

Metacommunity dynamics over 16 years in a pyrogenic shrubland

Metacommunity theory allows predictions about the dynamics of potentially interacting species' assemblages that are linked by dispersal, but strong empirical tests of the theory are rare. We analyzed the metacommunity dynamics of Florida rosemary scrub, a patchily distributed pyrogenic community, to test predictions about turnover rates, community nestedness, and responses to patch size, arrangement, and quality. We collected occurrence data for 45 plant species from 88 rosemary scrub patches in 1989 and 2005 and used growth form, mechanism of regeneration after fire, and degree of habitat specialization to categorize species by life history. We tested whether patch size, fire history, and structural connectivity (a measure of proximity and size of surrounding patches) could be used to predict apparent extinctions and colonizations. In addition, we tested the accuracy of incidence-function models built with the patch survey data from 1989. After fire local extinction rates were higher for herbs than woody plants, higher for species that regenerated only from seed than species able to resprout, and higher for generalist than specialist species. Fewer rosemary specialists and a higher proportion of habitat generalists were extirpated on recently burned patches than on patches not burned between 1989 and 2005. Nestedness was highest for specialists among all life-history groups. Estimated model parameters from 1989 predicted the observed (1989-2005) extinction rates and the number of patches with persistent populations of individual species. These results indicate that species with different life-history strategies within the same metacommunity can have substantially different responses to patch configuration and quality. Real metacommunities may not conform to certain assumptions of simple models, but incidence-function models that consider only patch size, configuration, and quality can have significant predictive accuracy.     

The role of habitat disturbance and recovery in metapopulation persistence

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

The effect of migration on the viability,dynamics and structure of two coexisting metapopulations

Two species of butterflies, Euphydryas aurinia and Melitaea phoebe, coexist as two metapopulations in a 38-patch network in Hebei Province, China. A Markovian model, whose transition matrix is the product of two matrices which represent the local extinction and recolonization process respectively, is used to describe the metapopulation dynamics. The application of this model to the metapopulation, consisting of 12 local populations in the northern subregion, shows that the expected life times of E. aurinia and M. phoebe are 160 and 121 years respectively and usually nearly half of the patches are occupied by E. aurinia, while only 1–3 patches are occupied by M. phoebe. We claim that E. aurinia can persist for a long time while M. phoebe faces relatively big extinction risk. By comparing the population dynamics with and without migration, we find M. phoebe benefits much more from migration than E. aurinia. Most patches are occupied mainly by local populations for E. aurinia, while by immigrants from the 8th patch for M. phoebe, meaning that E. aurinia has a classical metapopulation structure while M. phoebe has a source–sink metapopulation structure.     

The Application of Neutral Landscape Models in Conservation Biology

Neutral landscape models, derived from percolation theory in the field of landscape ecology, are grid-based maps in which complex habitat distributions are generated by random or fractal algorithms. This grid-based representation of landscape structure is compatible with the raster-based format of geographical information systems (GIS), which facilitates comparisons between theoretical and real landscapes. Neutral landscape models permit the identification of critical thresholds in connectivity, which can be used to predict when landscapes will become fragmented. The coupling of neutral landscape models with generalized population models, such as metapopulation theory, provides a null model for generating predictions about population dynamics in fragmented landscapes. Neutral landscape models can contribute to the following applications in conservation: (1) incorporation of complex spatial patterns in (meta)population models; (2) identification of species' perceptions of landscape structure; (3) determination of landscape connectivity; (4) evaluation of the consequences of habitat fragmentation for population subdivision; (5) identification of the domain of metapopulation dynamics; (6) prediction of the occurrence of extinction thresholds; ( 7) determination of the genetic consequences of habitat fragmentation; and (8) reserve design and ecosystem management. This generalized, spatially explicit framework bridges the gap between spatially implicit, patch-based models and spatially realistic GIS applications which are usually parameterized for a single species in a specific landscape. Development of a generalized, spatially explicit framework is essential in conservation biology because we will not be able to develop individual models for every species of management concern.     

Metapopulation dynamics in the butterfly Hipparchia semele changed decades before occupancy declined in The Netherlands

The survival of many species in human-dominated, fragmented landscapes depends on metapopulation dynamics, i.e., on a dynamic equilibrium of extinctions and colonizations in patches of suitable habitat. To understand and predict distributional changes, knowledge of these dynamics can be essential, and for this, metapopulation studies are preferably based on long-time-series data from many sites. Alas, such data are very scarce. An alternative is to use opportunistic data (i.e., collected without applying standardized field methods), but these data suffer from large variations in field methods and search intensity between sites and years. Dynamic site-occupancy models offer a general approach to adjust for variable survey effort. These models extend classical metapopulation models to account for imperfect detection of species and yield estimates of the probabilities of occupancy, colonization, and survival of species at sites. By accounting for detection, they fully correct for among-year variability in search effort. As an illustration, we fitted a dynamic site-occupancy model to 60 years of presence-absence data (more precisely, detection-nondetection) of the heathland butterfly Hipparchia semele in The Netherlands. Detection records were obtained from a database containing volunteer-based data from 1950-2009, and nondetection records were deduced from database records of other butterfly species. Our model revealed that metapopulation dynamics of Hipparchia had changed decades before the species' distribution began to contract. Colonization probability had already started to decline from 1950 onward, but this was counterbalanced by an increase in the survival of existing populations, the result of which was a stable distribution. Only from 1990 onward was survival not sufficient to compensate for the further decrease of colonization, and occupancy started to decline. Hence, it appears that factors acting many decades ago triggered a change in the metapopulation dynamics of this species, which ultimately led to a severe decline in occupancy that only became apparent much later. Our study emphasizes the importance of knowledge of changes in survival and colonization of species in modern landscapes over a very long time scale. It also demonstrates the power of site-occupancy modeling to obtain important population dynamics information from databases containing opportunistic sighting records.     

A Habitat-Based Metapopulation Model of the California Gnatcatcher

We present an analysis of the metapopulation dynamics of the federally threatened coastal California Gnatcatcher (Polioptila c. californica) for an approximately 850 km² region of Orange County, California. We developed and validated a habitat suitability model for this species using data on topography, vegetation, and locations of gnatcatcher pair observations. Using this habitat model, we calculated the spatial structure of the metapopulation, including size and location of habitat patches and the distances among them. We used data based on field studies to estimate parameters such as survival, fecundity, dispersal, and catastrophes, and combined these parameters with the spatial structure to build a stage-structured, stochastic, spatially-explicit metapopulation model. The model predicted a fast decline and high risk of population extinction with most combinations of parameters. Results were most sensitive to density-dependent effects, the probability of weather-related catastrophes, adult survival, and adult fecundity. Based on data used in the model, the greatest difference in results was given when the simulation's time horizon was only a few decades, suggesting that modeling based on longer or shorter time horizons may underestimate the effects of alternative management actions.     

Modelling dispersal with diffusion and habitat selection: Analytical results for highly fragmented landscapes

Quantifying dispersal is crucial both for understanding ecological population dynamics, and for gaining insight into factors that affect the genetic structure of populations. The role of dispersal becomes pronounced in highly fragmented landscapes inhabited by spatially structured populations. We consider a landscape consisting of a set of habitat patches surrounded by unsuitable matrix, and model dispersal by assuming that the individuals follow a random walk with parameters that may be specific to the habitat type. We allow for spatial variation in patch quality, and account for edge-mediated behavior, the latter meaning that the individuals bias their movement towards the patches when close to an edge between a patch and the matrix. We employ a diffusion approximation of the random walk model to derive analytical expressions for various characteristics of the dispersal process. For example, we derive formulae for the time that an individual is expected to spend in its current patch i, and for the time that it will spend in the matrix, both conditional on the individual hitting next a given patch j before hitting any of the other patches or dying. The analytical formulae are based on the assumptions that the landscape is infinitely large, that the patches are circularly shaped, and that the patches are small compared to interpatch distances. We evaluate the effect of these assumptions by comparing the analytical results to numerical results in a real patch network that violates all of the three assumptions. We then consider a landscape that fulfills the assumptions, and show that in this case the analytical results are in a very good agreement with the numerical results. The results obtained here allow the construction of computationally efficient dispersal models that can be used as components of metapopulation models.     

Simple rules for ranking and optimally managing metapopulations

We present two ‘rules of thumb’ for metapopulation management. The first identifies an explicit formula for the persistence time of the population, and thus enables the population manager to form a priority species ranking by identifying those species most at risk of extinction. The second identifies an optimal management strategy that gives direction on how to alter the colonisation rate (creation or improvement of habitat corridors) and local extinction rate (restoring habitat quality or expanding habitat) in order to maximise the persistence time under a budgetary constraint. We employ a simple stochastic version of Levins (1969) metapopulation model, which is first calibrated to a more realistic spatial model. Our rules are tested on computer-generated patch networks and a model for malleefowl (Leipoa ocellata) in the Bakara region of South Australia.     

Assessing hypotheses about nesting site occupancy dynamics

Hypotheses about habitat selection developed in the evolutionary ecology framework assume that individuals, under some conditions, select breeding habitat based on expected fitness in different habitat. The relationship between habitat quality and fitness may be reflected by breeding success of individuals, which may in turn be used to assess habitat quality. Habitat quality may also be assessed via local density: if high-quality sites are preferentially used, high density may reflect high-quality habitat. Here we assessed whether site occupancy dynamics vary with site surrogates for habitat quality. We modeled nest site use probability in a seabird subcolony (the Black-legged Kittiwake, Rissa tridactyla) over a 20-year period. We estimated site persistence (an occupied site remains occupied from time t to t+1) and colonization through two subprocesses: first colonization (site creation at the timescale of the study) and recolonization (a site is colonized again after being deserted). Our model explicitly incorporated site-specific and neighboring breeding success and conspecific density in the neighborhood. Our results provided evidence that reproductively "successful" sites have a higher persistence probability than "unsuccessful" ones. Analyses of site fidelity in marked birds and of survival probability showed that high site persistence predominantly reflects site fidelity, not immediate colonization by new owners after emigration or death of previous owners. There is a negative quadratic relationship between local density and persistence probability. First colonization probability decreases with density, whereas recolonization probability is constant. This highlights the importance of distinguishing initial colonization and recolonization to understand site occupancy. All dynamics varied positively with neighboring breeding success. We found evidence of a positive interaction between site-specific and neighboring breeding success. We addressed local population dynamics using a site occupancy approach integrating hypotheses developed in behavioral ecology to account for individual decisions. This allows development of models of population and metapopulation dynamics that explicitly incorporate ecological and evolutionary processes.