Models Of Metapopulation Dynamics Research Articles

The spatial extent and the dispersal strategy of species shape the occupancy frequency distribution of stream insect assemblages.

Several theoretical models have been proposed as the underlying mechanisms behind occupancy frequency distribution (OFD) patterns. For instance, the metapopulation dynamic model predicts bimodal OFD pattern indicating the dominance of dispersal processes in structuring the assemblages, while the niche-based model predicts unimodal right-skewed OFD pattern, and thus assemblages are driven mostly by niche processes. However, it is well known that the observed OFD pattern reflects the interplay of several other factors (e.g. habitat heterogeneity, species specificity and sampling protocol parameters). It follows that the individual contribution of each factor to the OFD pattern is rather complicated to explore. Our main objective was to examine the role of the spatial extent of the sampling and the dispersal strategies of species in shaping OFD pattern. For this, we collected samples of stream insect assemblages inhabiting near-natural streams in the Pannon Ecoregion. We formed groups of species representing contrasting dispersal strategies (referred to as dispersal groups). Applying a computer program algorithm, we produced samples with different spatial extent. We found that with increasing spatial extent, the OFD pattern changed from bimodal to unimodal for active dispersers. Insect groups with different dispersal strategies differed in the strength of support for OFD patterns within all spatial extent. Furthermore, the strength of support for OFD patterns varied across dispersal groups differently as the spatial extent increased. Our results reflected underlying changes in mechanisms structuring assemblages along an increasing spatial extent. We also assumed that the stream insect dispersal strategy influences the relative role of dispersal and niche processes particularly as spatial extent increases from stream reaches to the extent of adjacent valleys. We could define spatial extents and dispersal strategies within which unique metacommunity processes could underlie the organisation of assemblages.

Dispersal in Kentish Plovers (Charadrius alexandrinus): adult females perform furthest movements

Dispersal is an important behavioral process that plays a significant role in, among others, speciation, population viability, and individual fitness. Despite progress in avian dispersal research, there are still many knowledge gaps. For example, it is of interest to study how dispersal propensity relates to age- and/or sex-specific patterns. Here, we investigated the role of sex and life stage on natal (i.e., movement from birth site to first breeding site) and breeding dispersal (i.e., movement between sequential breeding sites) in the Kentish Plover (Charadrius alexandrinus) for dispersal events of more than 10 km. This small and inconspicuous wader is characterized by flexible mating behavior that includes monogamy, and serial polygynandry. Using a continent-wide dataset of ringing and re-encounter data throughout the species’ range in Europe, we found that adult females generally dispersed further than adult males between seasons, but we detected no sex difference in natal dispersal distances and no general difference between natal and breeding dispersal distances. Furthermore, females were the main group exhibiting ‘long-distance’ breeding dispersal, which we defined as dispersal greater than ≥ 108 km, i.e., the upper 10% percentile of our dataset. The data set included dispersal of two females that first bred in the Mediterranean before being detected breeding at the North Sea in the subsequent year, having dispersed 1290 and 1704 km, respectively. These observations represent the longest breeding dispersal observed within the genus Charadrius. Our long-distance dispersal records are consistent with low genetic differentiation between mainland populations shown in previous work. The dispersal of the Kentish Plover is likely linked to its breeding behavior: polyandrous females exhibit extensive mate searching and habitat prospecting. We recommend that the dispersal traits of Kentish Plover be incorporated into the species’ conservation and management planning to more accurately inform models of population connectivity and metapopulation dynamics.

Limited temporal variability in natural mortality for juvenile American plaice on the Grand Bank of Newfoundland

Increases in natural mortality have been suggested as a potential driver for both the collapse and lack of recovery for the American plaice (Hippoglossoides platessoides) population on the Grand Bank of Newfoundland in NAFO Divisions 3LNO. However, natural mortality is among the most difficult parameters to estimate since it can be confounded with other parameters and model misspecifications. One method used to avoid this confounding involves modeling unfished components of a population where total mortality and natural mortality are equal. Here, we use a state-space metapopulation dynamics model to investigate whether there is evidence that natural mortality rates for unfished juvenile American plaice have varied since the population collapse. In addition, our model examined the degree of synchrony in age-1 recruitment signals between each management Division. The best fitting model included temporal variability in natural mortality rates, but estimates did not frequently differ from zero. This indicates that change in natural mortality rates is not an important driver of current juvenile 3LNO American plaice stock dynamics. Instead, this model identified that juvenile stock dynamics were mainly affected by variations in age-1 recruitment. Furthermore, a correlation analysis of the temporal variations in recruitment showed that trends were somewhat dissimilar between NAFO Divisions 3L and 3NO. Overall, although increases in M have been suggested by recent studies, we did not find strong evidence for this in juvenile fish.

Macroinvertebrate species occupancy frequency distribution patterns in eutrophic lakes

Metacommunity models describe species occupancy frequency distribution (hereinafter ‘SOFD’). Our goal is to present how the differences in eight macroinvertebrate orders dispersal ability affect SOFD patterns. A total of 293 species from eight macroinvertebrate orders were observed in 14 eutrophic lakes in southern Finland. Species occupancy ranged from 1 to 14. About 30% (89 out of 293) of the species were found in only one lake, yielding a surprisingly high number of rare species. So, there were few widely distributed common species and numerous rare species with a restricted distribution. Combined data from eight macroinvertebrate orders supported the bimodal truncated SOFD pattern. Similarly, the low dispersal ability orders, watermites and mayflies, fitted the bimodal truncated SOFD pattern. However, bimodal symmetric SOFD pattern also fitted relatively well to the dragonflies and damselflies with high dispersal ability. It seems that differences in dispersal ability among different macroinvertebrate orders may partly explain observed differences. Moreover, our results supported slightly more a niche-based model rather than a metapopulation dynamics model in eutrophic lakes littoral macroinvertebrate metacommunities. Our results highlight that the dispersal ability is important trait for species conservation in patchily distributed habitat.

Metapopulation dynamics on double graphs for mediated infectious disease in patchy environment

We study the metapopulation dynamics of such mediated infectious disease as mosquito-borne infection in a patchy environment. The action range and habitat of mediators (e.g. mosquito) are different from those of humans. We focus on the effect of the difference on epidemic spreading in a patchy environment. The patchy environment and migration paths are represented by double graph: the first graph is for human and the second graph for mediators. We present a metapopulation dynamic model on homogeneous and heterogeneous double graphs; a subpopulation (patch) is represented by a node on a graph and a link represents a migration path between patches. Mobile individuals move by random walk through a link between nodes. Each individual is either susceptible human (S), infected human (I), susceptible mediator (M) or infected mediator (D). We extend SIS epidemic model to taking into account mediated infection. The reaction–diffusion equations on double graphs are presented for four species of S, I, M, and D. To evaluate the infection risk of each patch (node), we obtain the solutions of reaction–diffusion equations on double graphs numerically. It is shown that the densities of infected individuals depend highly on both action range and graph structure. The infection threshold is controlled by the density of mediators and their living area.

Diffusively-Coupled Rock-Paper-Scissors Game with Mutation in Scale-Free Hierarchical Networks

We present a metapopulation dynamic model for the diffusively-coupled rock-paper-scissors (RPS) game with mutation in scale-free hierarchical networks. We investigate how the RPS game changes by mutation in scale-free networks. Only the mutation from rock to scissors (R-to-S) occurs with rate μ. In the network, a node represents a patch where the RPS game is performed. RPS individuals migrate among nodes by diffusion. The dynamics are represented by the reaction-diffusion equations with the recursion formula. We study where and how species coexist or go extinct in the scale-free network. We numerically obtained the solutions for the metapopulation dynamics and derived the transition points. The results show that, with increasing mutation rate μ, the extinction of P species occurs and then the extinction of R species occurs, and finally only S species survives. Thus, the first and second dynamical phase transitions occur in the scale-free hierarchical network. We also show that the scaling law holds for the population dynamics which suggests that the transition points approach zero in the limit of infinite size.

Odonate species occupancy frequency distribution and abundance-occupancy relationship patterns in temporal and permanent water bodies in a subtropical area.

This paper investigates species richness and species occupancy frequency distributions (SOFD) as well as patterns of abundance–occupancy relationship (SAOR) in Odonata (dragonflies and damselflies) in a subtropical area. A total of 82 species and 1983 individuals were noted from 73 permanent and temporal water bodies (lakes and ponds) in the Pampa biome in southern Brazil. Odonate species occupancy ranged from 1 to 54. There were few widely distributed generalist species and several specialist species with a restricted distribution. About 70% of the species occurred in <10% of the water bodies, yielding a surprisingly high number of rare species, often making up the majority of the communities. No difference in species richness was found between temporal and permanent water bodies. Both temporal and permanent water bodies had odonate assemblages that fitted best with the unimodal satellite SOFD pattern. It seems that unimodal satellite SOFD pattern frequently occurred in the aquatic habitats. The SAOR pattern was positive and did not differ between permanent and temporal water bodies. Our results are consistent with a niche‐based model rather than a metapopulation dynamic model.

Chimpanzee (Pan troglodytes schweinfurthii) Population Spans Multiple Protected Areas in the Albertine Rift

We used mitochondrial DNA to examine gene flow in a region of western Uganda that has received little attention regarding chimpanzee population dynamics. The area is critical to gene flow between isolated Democratic Republic of Congo populations and the rest of East Africa. None of the chimpanzees in each of the 4 protected areas under consideration (Toro-Semliki Wildlife Reserve, Semuliki National Park, Rwenzori Mountains National Park and Itwara Central Forest Reserve) are fully habituated. Therefore, it is not clear whether one or more populations have historically used this fragmented landscape for (1) regular ranging and/or (2) infrequent dispersal. We incorporated the published sequences of the first hypervariable region of the D-loop of the mitochondrial genome from 3 previously sampled sites (n = 39) while also contributing the first extensive genetic sampling of chimpanzees in Toro-Semliki (n = 80). Our goal was to generate a historical baseline model of metapopulation dynamics in this region and determine which, if any, of these protected areas forms a fragmented landscape for a single chimpanzee population. According to a discriminant analysis of principal components, the haplotypes at Toro-Semliki form a central cluster, and Itwara is its nearest genetic neighbor. Rwenzori Mountains National Park is the most distant neighbor of all protected areas. We performed an analysis of molecular variance for 14 different population models that divided the samples from the 4 protected areas into 2, 3 or 4 populations. The best fit model included 3 populations: Toro-Semliki Wildlife Reserve and Itwara Forest Reserve comprised a single population; Semuliki National Park and Rwenzori Mountains National Park formed 2 additional separate populations (variance among = 9%, p = 0.014). The results indicated that some protected areas comprised distinctive populations, while others formed a fragmented landscape for a population’s ranging for foraging purposes. Therefore, the edges of a protected area do not always define a chimpanzee population. We propose a closer examination of those dynamics through renewed sampling. Advances in DNA extraction and next-generation sequencing will allow us to compare thousands of single nucleotide polymorphisms in the genomes of unhabituated chimpanzees living in each of these protected areas.

Diffusively-Coupled Prey-Predator Dynamics in Scale-Free and Self-Similar Networks

We present a metapopulation dynamic model for a diffusively-coupled prey-predator system in hierarchical networks with scale-free and self-similar properties. A node represents a patch where prey a...

Forest cover and open land drive the distribution and dynamics of the breeding sites for urban-dwelling Northern Goshawks

Land cover change accompanying large-scale and rapid urbanization has caused major losses to biodiversity, with urban planning that incorporates biodiversity conservation being urgently needed. Understanding how land cover impacts the distribution and dynamics of breeding sites of biodiversity indicator species could facilitate the creation of long-term, landscape-scale urban planning to enhance biodiversity. Here, we identified land cover factors that influence the distribution and dynamics of the breeding sites of goshawks, a biodiversity indicator species, in the urban areas of Kanagawa, Japan. We analyzed how breeding site presence and absence data were correlated with land cover factors using a logistic regression model. To evaluate the dynamics in breeding site distribution, a meta-population dynamics model was used to analyze the relationship between breeding site occupancy history and land cover factors over 6 years. Forest cover, open land, and highly vegetated urban cover positively affected the distribution of goshawk breeding sites. However, the relative importance of highly vegetated urban cover was not as high as forest cover or open land. Forest cover negatively affected local extinction probability, while forest cover and open areas positively affected local colonization probability. In comparison, highly vegetated urban cover had low relative importance for the distribution of breeding sites, with no relationship being detected for breeding site distribution dynamics. The importance of forest cover and open land for both the distribution and dynamics of goshawk breeding sites emphasizes the importance of these land cover types for the breeding of urban-dwelling goshawks. Therefore, managers should focus on maintaining forests and open land to conserve goshawk breeding sites in urban areas to facilitate their long-term viability. Highly vegetated urban cover was considered to be less important for the long-term viability of goshawk breeding sites.

Spatiotemporal variations in juvenile mortality and cohort strength of Atlantic cod (Gadus morhua) off Newfoundland and Labrador

Juvenile mortality is an important factor affecting the spatiotemporal dynamics of fish recruitment, but estimation of the spatiotemporal variations in juvenile mortality rates remains challenging. We developed a state-space metapopulation dynamics model to simultaneously estimate spatiotemporal variations in juvenile mortality rates and cohort strength and applied this general modelling framework to data from multiple surveys for juvenile (ages 2–5) Atlantic cod (Gadus morhua) stocks off Newfoundland and Labrador (NL). We found large-scale synchronized dynamics of decreasing juvenile mortality rates and increasing cohort strength from offshore surveys off eastern and southeastern NL, suggesting improving reproduction and survival rates for juvenile cod. No synchronized patterns of juvenile mortality rates and cohort strength were detected for cod stocks off southern and western NL, indicating more complex cod population spatial structures in those areas. Our study demonstrates the potential of juvenile mortality to cause temporally variable and spatially synchronized dynamics of fish recruitment, and the spatial patterns of juvenile mortality and cohort strength indicate some potential mismatch between cod population structure and current management units off NL.

Infection promotes species coexistence: Rock–paper–scissors game with epidemic on graphs

We combine the rock–paper–scissors (RPS) game with SIS epidemic model. We study the effect of infection on population dynamics of RPS games with epidemic by using the metapopulation dynamic model on graphs. Via infection, an individual R changes to I with infection rate β. An infected individual I returns to R with recovery rate γ. All agents move by random walk between patches (subpopulations) and the RPS game with epidemic is performed in each patch. The dynamics are represented by the reaction–diffusion equations in diffusively coupled reactors. We obtain the solutions of the reaction–diffusion equations for the mean-field dynamics in a single patch analytically. The numerical solutions are obtained for metapopulation dynamics on graphs with three nodes. The analytical solutions are also obtained for metapopulation dynamics on complete graph. When the recovery rate is lower than the critical value, infected individuals survive, the dynamics exhibit stable focuses, and all species coexist. Infection promotes the coexistence of species.

T. cruzi and T. gondii ex vivo infection of Human, Canine and Ovine Placental Explant induces specific miRNA profiles

When the action range of infected individuals is restricted in a patchy environment, epidemic spreading changes due to the restricted migration. We focus on the effect of the restricted migration of infected individuals to epidemic spreading in a patchy environment. Each individual is either susceptible (S) or infected (I). The restricted migration is represented by the double graphs. We present a metapopulation dynamic model on double graphs; a subpopulation (patch) is represented by a node on the double graphs, a link on the first graph represents a migration path between patches for susceptible individuals, and a link on the second graph represents a migration path between patches for infected individuals. Susceptible and infected individuals move by random walk through a link on the first graph and through a link on the second graph respectively. Two kinds of reaction–diffusion equations are presented as the differential equations for susceptible and infected individuals respectively. To evaluate the infection risk of each patch (node), we obtain the solutions of reaction–diffusion equations numerically. The infected densities change greatly by the restricted migration on double graphs. It is shown that the densities of infected individuals depend highly on the structure of double graphs. In specific double graphs, there exist infected individuals only on the hub (subpopulation with highest degree) and disappear on other subpopulations.

Restricted migration of infected individuals in epidemic metapopulation model on double graphs

When the action range of infected individuals is restricted in a patchy environment, epidemic spreading changes due to the restricted migration. We focus on the effect of the restricted migration of infected individuals to epidemic spreading in a patchy environment. Each individual is either susceptible (S) or infected (I). The restricted migration is represented by the double graphs. We present a metapopulation dynamic model on double graphs; a subpopulation (patch) is represented by a node on the double graphs, a link on the first graph represents a migration path between patches for susceptible individuals, and a link on the second graph represents a migration path between patches for infected individuals. Susceptible and infected individuals move by random walk through a link on the first graph and through a link on the second graph respectively. Two kinds of reaction–diffusion equations are presented as the differential equations for susceptible and infected individuals respectively. To evaluate the infection risk of each patch (node), we obtain the solutions of reaction–diffusion equations numerically. The infected densities change greatly by the restricted migration on double graphs. It is shown that the densities of infected individuals depend highly on the structure of double graphs. In specific double graphs, there exist infected individuals only on the hub (subpopulation with highest degree) and disappear on other subpopulations.

Allee effect with time-varying migration on heterogeneous graphs

The behavior of animals during day and night can be demonstrated as time-varying migration. We study the effect of the temporal migration in a diffusively coupled Allee model on heterogeneous graphs. We present the metapopulation dynamic model for temporally heterogeneous graphs using the Allee effect of mobile individuals. We consider the small graphs with three and four nodes, and the star graphs with N nodes. A subpopulation (patch) is represented by a node on a graph. A link represents a temporal migration path between subpopulations. Mobile individuals move temporally by random walk through a link between nodes. Individuals grow or die out according to the Allee population dynamics within each subpopulation. The population dynamics in the metapopulation model are presented by reaction–diffusion equations with time-dependent diffusion coefficients. To evaluate the population size of each subpopulation (node), we obtain the solutions of the reaction–diffusion equations numerically for the small graphs and star graphs. The temporal migration path induces complex behavior for the Allee dynamics. The period (the inverse of frequency) of this temporal path has an important effect on the Allee dynamics.

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.

A minimalist model of extinction and range dynamics of virtual mountain species driven by warming temperatures.

A longstanding question in ecology concerns the prediction of the fate of mountain species under climate change, where climatic and geomorphic factors but also endogenous species characteristics are jointly expected to control species distributions. A significant step forward would single out reliably landscape effects, given their constraining role and relative ease of theoretical manipulation. Here, we address population dynamics in ecosystems where the substrates for ecological interactions are mountain landscapes subject to climate warming. We use a minimalist model of metapopulation dynamics based on virtual species (i.e. a suitable assemblage of focus species) where dispersal processes interact with the spatial structure of the landscape. Climate warming is subsumed by an upward shift of species habitat altering the metapopulation capacity of the landscape and hence species viability. We find that the landscape structure is a powerful determinant of species survival, owing to the specific role of the predictably evolving connectivity of the various habitats. Range shifts and lags in tracking suitable habitat experienced by virtual species under warming conditions are singled out in different landscapes. The range of parameters is identified for which these virtual species (characterized by comparable viability thus restricting their possible fitnesses and niche widths) prove unable to cope with environmental change. The statistics of the proportion of species bound to survive is identified for each landscape, providing the temporal evolution of species range shifts and the related expected occupation patterns. A baseline dynamic model for predicting species fates in evolving habitats is thus provided.

Drought-mediated extinction of an arid-land amphibian: insights from a spatially explicit dynamic occupancy model.

Understanding how natural and anthropogenic processes affect population dynamics of species with patchy distributions is critical to predicting their responses to environmental changes. Despite considerable evidence that demographic rates and dispersal patterns vary temporally in response to an array of biotic and abiotic processes, few applications of metapopulation theory have sought to explore factors that explain spatiotemporal variation in extinction or colonization rates. To facilitate exploring these factors, we extended a spatially explicit model of metapopulation dynamics to create a framework that requires only binary presence-absence data, makes few assumptions about the dispersal process, and accounts for imperfect detection. We apply this framework to 22yr of biannual survey data for lowland leopard frogs, Lithobates yavapaiensis, an amphibian that inhabits arid stream systems in the southwestern United States and northern Mexico. Our results highlight the importance of accounting for factors that govern temporal variation in transition probabilities, as both extinction and colonization rates varied with hydrologic conditions. Specifically, local extinctions were more frequent during drought periods, particularly at sites without reliable surface water. Colonization rates increased when larval and dispersal periods were wetter than normal, which increased the probability that potential emigrants metamorphosed and reached neighboring sites. Extirpation of frogs from all sites in one watershed during a period of severe drought demonstrated the influence of site-level features, as frogs persisted only in areas where most sites held water consistently and where the amount of sediment deposited from high-elevation wildfires was low. Application of our model provided novel insights into how climate-related processes affected the distribution and population dynamics of an arid-land amphibian. The approach we describe has application to a wide array of species that inhabit patchy environments, can improve our understanding of factors that govern metapopulation dynamics, and can inform strategies for conservation of imperiled species.

Diffusively coupled Allee effect on heterogeneous and homogeneous graphs

We study how the Allee effect with diffusion changes depending on the graph topology. We present the metapopulation dynamic model on heterogeneous and homogeneous graphs for the Allee effect of mobile individuals. We consider the small graphs with three and four nodes and the star and complete graphs with N nodes. A subpopulation (patch) is represented by a node on a graph. A link represents a migration path between subpopulations. Mobile individuals move by random walk through a link between nodes. Individuals grow or die out according to Allee population dynamics within each subpopulation. The population dynamics in the metapopulation model are presented by reaction–diffusion equations. To evaluate the population size of each subpopulation (node), we obtain the solutions of the reaction–diffusion equations numerically for the small graphs, star graphs, and complete graphs. The equilibrium points of the Allee metapopulation model depend highly on the network topology. The dependence of the critical Allee parameter on the number of nodes is derived for star and complete graphs.

Epidemic spreading of random walkers in metapopulation model on an alternating graph

Much literature exists on temporal networks for epidemic spreading. We present a metapopulation dynamic model on a temporal network; a subpopulation (patch) is represented by a node on a graph, and a link represents a migration path between patches. We consider the alternating graph as a temporal network. It alternates between star and complete graphs, where the nodes do not change but links vary temporally and periodically. Mobile individuals move by random walk through a link between nodes. Each individual is either susceptible (S) or infected (I). The reaction–diffusion equations are presented as ordinary differential equations with time-dependent coefficients. To evaluate the infection risk of each patch (node), we obtain the solutions of reaction–diffusion equations numerically. The temporal behavior of infected individuals depends highly on the frequency of the alternating graph. At low frequency, infected densities exhibit an oscillating behavior, while they keep a constant value at high frequencies. The crossover occurs from the oscillating state to the frozen state with increasing frequency. The SIS epidemic threshold is derived for the alternating graph. The epidemic threshold is lower than that on the star graph and higher than that on the complete graph.