Models Of Metapopulation Dynamics Research Articles

A probe mechanism to couple spatially explicit agents and landscape models in an integrated modelling framework

Many environmental, ecological, and social problems require investigation using a mixture of landscape models, individual‐based models, and some level of interaction between them. Few simulation‐modelling frameworks are structured to handle both styles of model in an integrated fashion. ECO‐COSM is a framework that is capable of handling complex models with both landscape and agent components. Its Probe‐based architecture allows model components to have controlled access to the state of other components. The ProbeWrapper is a modification of this common design approach which allows alterations to the state retrieved from the model and is a critical component of ECO‐COSM's broad modelling capability. It allows agents to apply perceptual filters or measurement errors to their observations of the landscape, or apply decision‐making strategies in the face of incomplete or uncertain observations. ECO‐COSM is demonstrated with a landscape model of metapopulation dynamics, an agent model of squirrel dispersal, and a coupled landscape‐agent model to evaluate field‐data‐acquisition strategies for identifying nutrient or contaminant hotspots.

Effects of patch quality and network structure on patch occupancy dynamics of a yellow‐bellied marmot metapopulation

1. The presence/absence of a species at a particular site is the simplest form of data that can be collected during ecological field studies. We used 13 years (1990-2002) of survey data to parameterize a stochastic patch occupancy model for a metapopulation of the yellow-bellied marmot in Colorado, and investigated the significance of particular patches and the influence of site quality, network characteristics and regional stochasticity on the metapopulation persistence. 2. Persistence of the yellow-bellied marmot metapopulation was strongly dependent on the high quality colony sites, and persistence probability was highly sensitive to small changes in the quality of these sites. 3. A relatively small number of colony sites was ultimately responsible for the regional persistence. However, lower quality satellite sites also made a significant contribution to long-term metapopulation persistence, especially when regional stochasticity was high. 4. The northern network of the marmot metapopulation was more stable compared to the southern network, and the persistence of the southern network depended heavily on the northern network. 5. Although complex models of metapopulation dynamics may provide a more accurate description of metapopulation dynamics, such models are data-intensive. Our study, one of the very few applications of stochastic patch occupancy models to a mammalian species, suggests that stochastic patch occupancy models can provide important insights into metapopulation dynamics using data that are easy to collect.

SPOMSIM: software for stochastic patch occupancy models of metapopulation dynamics

Classical metapopulations are groups of local populations living in networks of spatially distinct habitat patches in a balance between local extinctions and recolonizations of empty habitat. Models are needed for understanding and predicting metapopulation dynamics in changing landscapes. One particularly important question is what is the effect of habitat loss to the persistence of a metapopulation. A class of metapopulation models that have been successfully used in practical applications are called stochastic patch occupancy models (SPOMs), which model the presence/absence of the species on habitat patches as a Markov chain. The presence–absence assumption makes the model relatively parameter sparse, facilitates empirical data collection, and enables rigorous parameter estimation. This study reviews theory of SPOMs and describes a computational tool, called SPOMSIM, which allows one to simulate SPOMs and estimate parameters for them. SPOMSIM offers a range of choices for submodels; alternatives are provided for the functional forms of local extinction, the dispersal kernel, computation of connectivity, the colonization function, the implementation of the rescue effect and the implementation of regional stochasticity. SPOMSIM includes also, among other things, a utility based on hierarchical clustering for the analysis of the structure of a patch network, a reserve network optimization algorithm, and a patch system editor which makes it possible to investigate the consequences of changes in landscape structure. Potential uses for SPOMSIM include scientific metapopulation studies, teaching and conservation management.

Using pattern‐oriented modeling for revealing hidden information: a key for reconciling ecological theory and application

We suggest that the conscious use of information that is “hidden” in distinct structures in nature itself and in data extracted from nature (=pattern) during the process of modeling (=pattern‐oriented modeling) can substantially improve models in ecological application and conservation. Observed patterns, such as time‐series patterns and spatial patterns of presence/absence in habitat patches, contain a great deal of data on scales, site‐history, parameters and processes. Use of these data provides criteria for aggregating the biological information in the model, relates the model explicitly to the relevant scales of the system, facilitates the use of helpful techniques of indirect parameter estimation with independent data, and helps detect underlying ecological processes. Additionally, pattern‐oriented models produce comparative predictions that can be tested in the field. We developed a step‐by‐step protocol for pattern‐oriented modeling and illustrate the potential of this protocol by discussing three pattern‐oriented population models: (1) a population viability analysis for brown bears (Ursusarctos) in northern Spain using time‐series data on females with cubs of the year to adjust unknown model parameters; (2) a savanna model for detecting underlying ecological processes from spatial patterns of tree distribution; and (3) the incidence function model of metapopulation dynamics as an example of process integration and model generalization. We conclude that using the pattern‐oriented approach to its full potential will require a major paradigm shift in the strategies of modeling and data collection, and we argue that more emphasis must be placed on observing and documenting relevant patterns in addition to attempts to obtain direct estimates of model parameters.

A test of the metapopulation model of the species–area relationship

Abstract Aim The species–area relationship is a ubiquitous pattern. Previous methods describing the relationship have done little to elucidate mechanisms producing the pattern. Hanski & Gyllenberg (Science, 1997, 275, 397) have shown that a model of metapopulation dynamics yields predictable species–area relationships. We elaborate on the biological interpretation of this mechanistic model and test the prediction that communities of species with a higher risk of extinction caused by environmental stochasticity should have lower species–area slopes than communities experiencing less impact of environmental stochasticity.Methods We develop the mainland–island version of the metapopulation model and show that the slope of the species–area relationship resulting from this model is related to the ratio of population growth rate to variability in population growth of individual species. We fit the metapopulation model to five data sets, and compared the fit with the power function model and Williams's (Ecology, 1995, 76, 2607) extreme value function model. To test that communities consisting of species with a high risk of extinction should have lower slopes, we used the observation that small‐bodied species of vertebrates are more susceptible to environmental stochasticity than large‐bodied species. The data sets were divided into small and large bodied species and the model fit to both.Results and main conclusions The metapopulation model showed a good fit for all five data sets, and was comparable with the fits of the extreme value function and power function models. The slope of the metapopulation model of the species–area relationship was greater for larger than for smaller‐bodied species for each of five data sets. The slope of the metapopulation model of the species–area relationship has a clear biological interpretation, and allows for interpretation that is rooted in ecology, rather than ad hoc explanation.

Community assembly and the emergence of ecosystem pattern

A fundamental problem challenging natural scientists is to understand how macroscopic patterns, such as population abundance distributions and element ratios, emerge and are sustained in ecosystems, given that evolution typically operates most strongly at the level of individuals and their genomes. How do such patterns persist in the face of evolutionary innovation? In this paper, we explore this issue through dynamical models of community assembly and metapopulation dynamics in dynamic landscapes, and discuss individual-based approaches to the control of element cycles.

MOVEMENT IN CORRIDORS: ENHANCEMENT BY PREDATION THREAT, DISTURBANCE, AND HABITAT STRUCTURE

Movement by stream fish is known to be strongly influenced by abiotic factors such as floods and temperature, but roles of biotic factors, such as predation threat, and interactions of abiotic and biotic factors are less clear. Predation threat is known to fragment populations of killifish, Rivulus hartii, in Trinidad rivers by rendering habitat inhospitable. We asked whether such spatial fragmentation was accompanied by reduced movement by fish in the predator-occupied zone of a river, relative to a zone free of the strong piscivore, Hoplias malabaricus, that causes the fragmentation. We used a 19-mo marking study in a river with a predator barrier, field experiments in the river, and mesocosms to evaluate four hypotheses: (1) the predator reduces prey movement in the river; (2) for the special case of prey leaving refugia, the predator increases movement; (3) movement positively cor- relates with water level in the predator's presence; and (4) complex physical structure in hazardous habitat promotes prey movement. We marked 1467 Rivulus in the natural study areas and had 1015 recaptures. Contrary to Hypothesis 1 but in support of Hypothesis 2, prey showed greater movement along the river in the presence of the predator, regardless of whether the fish resided in a refuge at its previous capture. An experiment with introduced fish confirmed the findings that move- ment was elevated in the predator's presence. Effects of an abiotic factor (water level, Hypothesis 3) and a phenotypic trait (body size) depended upon whether the predator was present: movement was independent of water level and body size in the absence of the predator, but positively related to both variables in the predator's presence. Emigration from the river to tributaries was also independent of body size in the predator's absence, but positively size-dependent in the predator's presence. Complex physical structure (Hy- pothesis 4), in the form of cobble added to experimental pools, enhanced the transit of fish through hazardous pools. This study shows that spatial fragmentation does not necessarily imply that movement between fragments will be impeded (dynamical fragmentation). Rather, it is possible that movement among spatial fragments may be enhanced by the same factor, predation threat, that produced the spatial fragmentation in the first place. Because of the context-dependent effects of an abiotic factor (water level) and a phenotypic variable (body size) on movement, the study also emphasizes the need to clarify the exact role of predation as an agent promoting or retarding movement, and it suggests a need for incorporating such parameters into models of movement and metapopulation dynamics.

Extension of ideal free resource use to breeding populations and metapopulations

The concept of an ideal and free use of limiting resources is commonly invoked in behavioural ecology as a null model for predicting the distribution of foraging consumers across heterogeneous habitat. In its original conception, however, its predictions were applied to the longer timescales of habitat selection by breeding birds. Here I present a general model of ideal free resource use, which encompasses classical deterministic models for the dynamics in continuous time of feeding aggregations, breeding populations and metapopulations. I illustrate its key predictions using the consumer functional response given by Holling's disc equation. The predictions are all consistent with classical population dynamics, but at least two of them are not usually recognised as pertaining across all scales. At the fine scale of feeding aggregations, the steady state of an equal intake for all ideal free consumers may be intrinsically unstable, if patches are efficiently exploited by individuals with a non‐negligible handling time of resources. At coarser scales, classical models of population and metapopulation dynamics assume exploitation of a homogeneous environment, yet they can yield testable predictions for heterogeneous environments too under the assumption of ideal free resource use.

Test of mathematical assumptions behind the `incidence function' estimation process of metapopulations' dynamic parameters

I question Hanski's [I. Hanski, A practical model of metapopulation dynamics, J. Animal Ecol. 63 (1994) 151] assumption that incidence functions are relevant approximations of the equilibrium dynamics of stochastic metapopulation models to estimate models' parameters based on snapshot data. Based on ten different metapopulation models, this assumption is found to be at least partly unjustified when referring to the asymptotic behaviour of the models. This leads me to recommend the use of explicit extinction–colonisation transition probabilities and process data (rather than snapshot data) in the estimation process of metapopulation models.

PATCH OCCUPANCY MODELS OF METAPOPULATION DYNAMICS: EFFICIENT PARAMETER ESTIMATION USING IMPLICIT STATISTICAL INFERENCE

The practical value of a predictive metapopulation model is much affected by the amount of data required for parameter estimation. Some metapopulation models require information on population turnover events for parameterization, whereas other models, such as the incidence function model that is used in this study, can be parameterized with spatial data on patch occupancy. The latter data are more readily available. The original method of using spatial pattern data to parameterize the incidence function and other patch models has been criticized for involving potentially troublesome assumptions, such as the independence of habitat patches and constant colonization probabilities. This study describes an improved parameter estimation method that is not affected by these problems. The proposed method is based on Monte Carlo inference for implicit statistical models, and it can be adapted to any stochastic patch occupancy model of metapopulation dynamics. As an additional advantage, the new method allows the estimation of the amplitude of regional stochasticity. Tested with simulated data, the new method was found to produce substantially more accurate parameter estimates than the original method. The new approach is applied to two empirical metapopulations, the false heath fritillary butterfly in Finland and the American pika at Bodie, California.

Patch Occupancy Models of Metapopulation Dynamics: Efficient Parameter Estimation Using Implicit Statistical Inference

The practical value of a predictive metapopulation model is much affected by the amount of data required for parameter estimation. Some metapopulation models require information on population turnover events for parameterization, whereas other models, such as the incidence function model that is used in this study, can be parameterized with spatial data on patch occupancy. The latter data are more readily available. The original method of using spatial pattern data to parameterize the incidence function and other patch models has been criticized for involving potentially troublesome assumptions, such as the independence of habitat patches and constant colonization probabilities. This study describes an improved parameter estimation method that is not affected by these problems. The proposed method is based on Monte Carlo inference for implicit statistical models, and it can be adapted to any stochastic patch occupancy model of metapopulation dynamics. As an additional advantage, the new method allows the estimation of the amplitude of regional stochasticity. Tested with simulated data, the new method was found to produce substantially more accurate parameter estimates than the original method. The new approach is applied to two empirical metapopulations, the false heath fritillary butterfly in Finland and the American pika at Bodie, California.

Development of a systematic classification scheme of marine habitats to facilitate regional management and mapping of Caribbean coral reefs

Most coastal habitat mapping is conducted on an ad hoc basis with little consistency in terminology and ambiguous documentation. These limitations obstruct interpretation and integration of maps for coral reef science and management, particularly at regional (international) scales where standardisation is urgently required. This paper advocates an objective, systematic approach to habitat classification which couples coastal geomorphology and benthic cover. Benthic classes are derived and described objectively using agglomerative hierarchical classification of field data and Similarity Percentage analysis of resulting clusters. The scheme has a hierarchical structure to accommodate various user requirements, variable availability of data, and the spatial scales of most remote sensing methods. We illustrate our approach with a scheme based on extensive field data from the Turks and Caicos Islands and Belize. While the scheme will not represent all habitats of the Caribbean, it provides a useful basis for a regional classification and illustrates the systematic approach. Standardised regional maps of coastal habitats will help development of predictive models of coral metapopulation dynamics, aid the identification of larval source and sink areas, and facilitate strategic transboundary planning of protected areas to maximise species, habitat, and ecosystem conservation. Habitats might also be interpreted to reflect ecosystem processes such as productivity and trophic guild structure, thereby allowing the ecosystem function to be examined at larger scales. ©

Density dependence in resource exploitation: empirical test of Levins’ metapopulation model

Levins’ model of metapopulation dynamics is modified to incorporate variable degrees of density dependence in the per capita exploitation of resource patches. We demonstrate a simple means of testing for this density dependence in a sample of metapopulations, each at its equilibrium balance of local colonization to extinction. The fraction of habitable unoccupied patches equilibrates to a constant number under the null model of density independent colonization, and to a constant proportion under strong density dependence. We compare the null model to two density dependent alternatives, using data on exploitation of nest boxes by collared flycatchers Ficedula albicollis. The analysis shows how predicted trends in the equilibrium unoccupied fraction are similar for both spatial interference and net immigration. This needs to be recognized, since the null hypothesis of a constant unused resource applies also to the dynamics of consumable resources, where it is expressed in a constant stock of uneaten prey at the dynamic equilibrium of predators to prey.

Connecting the Parameters of Local Extinction and Metapopulation dynamics

This paper explores the correspondence between the parameters of an extinction model analysed by Lande, Foley and Middleton et al. and the parameters of the incidence function model of metapopulation dynamics. The parameters of the extinction model, the intrinsic rate of population increase (r), its variance (v) and the population ceiling (K), can be mapped to the parameters of the incidence function model describing the scaling of the probability of local extinction (E) with patch area (A), E = eA X, via the equations s = x and r = eDs/s, where s = 2r/v, D is population density and K= DA. I explore this correspondence with two empirical examples, a mainlandisland metapopulation of the European common shrew (Sorex araneus) on islands in lakes and a classical metapopulation of the American pika (Ochotona princess. The most robust result is the correspondence x = 2r/v, which value decreases with increasing strength of environmental stochasticity. Thus the impact of environmental stochasticity on population dynamics can, in principle, be inferred from the pattern of habitat patch occupancy in a metapopulation.

THE MAINTENANCE OF GYNODIOECY AND ANDRODIOECY IN A METAPOPULATION.

Males and females are at a selective disadvantage relative to hermaphrodites (cosexuals) in species with a colonizing habit, as only cosexuals are able to establish new colonies on their own. The implications of this disadvantage are assessed by means of a computer model of metapopulation dynamics, in which individual colonies are established through different rates of immigration and suffer different rates of local extinction. Results are given for simulations of an island model, a stepping-stone model, and for a partial analysis of the island model with simplifying assumptions. It is shown that: (1) unisexual frequencies in a metapopulation can be reasonably approximated by a linear function of the logarithm of the ratio of the immigration rate to the colony extinction rate; (2) metapopulation dynamics favor the maintenance of females (gynodioecy) over males (androdioecy) with cosexuals when they would otherwise be equally likely in a panmictic situation; (3) the way in which extinction and immigration rates affect unisexual frequencies at metapopulation equilibrium interacts with whether sterility is determined by a dominant or a recessive allele; and (4) unisexual frequencies are affected in a qualitatively similar way by the dynamics of a metapopulation when cosexuals are self-incompatible to when they are self-compatible, although only in the former case are high frequencies of unisexuals maintained when extinction and colonization rates approach the threshold at which the metapopulation goes extinct. These results are discussed with reference to existing data from species with nuclear male or female sterility.

A Stochastic Metapopulation Model with Variability in Patch Size and Position

Analytically tractable metapopulation models usually assume that every patch is identical, which limits their application to real metapopulations. We describe a new single species model of metapopulation dynamics that allows variation in patch size and position. The state of the metapopulation is defined by the presence or absence of the species in each patch. For a system of n patches, this gives 2n possible states. We show how to construct and analyse a matrix describing transitions between all possible states by first constructing separate extinction and colonisation matrices. We illustrate the model′s application to metapopulations by considering an example of malleefowl, Leipoa ocellata, in southern Australia, and calculate extinction probabilities and quasi-stationary distributions. We investigate the relative importance of modelling the particular arrangement of patches and the variation in patch sizes for this metapopulation and we use the model to examine the effects of further habitat loss on extinction probabilities.

A General Model of Metapopulation Dynamics

Metapopulation models describe the colonization and extinction of populations in a landscape of connected patches. Levins modeled the fraction of population sites occupied as a balance between the rate of successful immigration into empty sites and the rate of extinction in occupied sites. Several variants of Levins'model have been proposed that assume the probability of local colonization or extinction is either dependent or independent of regional occurrence. We show that the models of Levins, Hanski, and Gotelli are extreme cases of a single metapopulation model, which predicts the equilibrium fraction of sites occupied as a function of 4 parameters, 2 for colonization and 2 for extinction. We tested this model using single-species and multi-species data on patch occupancy

Effects of patch connectivity and arrangement on animal metapopulation dynamics: a simulation study

We constructed a simulation model of metapopulation dynamics consisting of two or three habitat patches using STELLA. our simulations show that, given the assumptions of the deterministic model, the metapopulation is doomed to global extinction with or without interpatch immigration when all local populations are below minimum viable population (MVP) size. This suggests that for a cluster of scattered small populations, it is preferable to focus on augmenting individual population sizes rather than enhancing interpatch immigration. In the case when at least one of the subpopulations is above the MVP size, there is a critical size for that subpopulation above which the metapopulation persists and otherwise collapses. Also, when a metapopulation system is composed of more than two patches, the spatial configuration in terms of patch connection and the relative position of the above-MVP subpopulation will have significant effects on metapopulation dynamics and persitence. All simulation results from the three-patch animal metapopulation model suggest that both the number of interpatch connections and the magnitude represented by them are crucial for overall patch connectivity. The magnitude of interpatch immigration is positively related to the minimum size of the above-MVP subpopulation in both the two- and three-patch metapopulation systems due to population sink effect. The phenomenon is especially significant when subpopulations in sink patches are well below MVP. Appropriate introduction of stochastic components into the model may increase its realism especially for the cases where all subpopulations are well below MVP. Although the current version of the model involves no more than three patches, it may serve as a general conceptual framework and a specific simulator for modeling metapopulation dynamics incorporating a variety of spatial arrangements of habitat patches.

Structured models of metapopulation dynamics

I develop models of metapopulation dynamics that describe changes in the numbers of individuals within patches. These models are analogous to structured population models, with patches playing the role of individuals. Single species models which do not include the effect of immigration on local population dynamics of occupied patches typically lead to a unique equilibrium. The models can be used to study the distributions of numbers of individuals among patches, showing that both metapopulations with local outbreaks and metapopulations without outbreaks can occur in systems with no underlying environmental variability. Distributions of local population sizes (in occupied patches) can vary independently of the total population size, so both patterns of distributions of local population sizes are compatible with either rare or common species. Models which include the effect of immigration on local population dynamics can lead to two positive equilibria, one stable and one unstable, the latter representing a threshold between regional extinction and persistence.

Metapopulation dynamics: Does it help to have more of the same?

With the interest in conservation biology shifting towards processes from patterns, and to populations from communities, the theory of metapopulation dynamics is replacing the equilibrium theory of island biogeography as the population ecology paradigm in conservation biology. The simplest models of metapopulation dynamics make predictions about the effects of habitat fragmentation - size and isolation of habitat patches - on metapopulation persistence. The simple models may be enriched by considerations of the effects of demographic and environmental stochasticity on the size and extinction probability of local populations. Environmental stochasticity affects populations at two levels: it makes local extinctions more probable, and it also decreases metapopulation persistence time by increasing the correlation of extinction events across populations. Some controversy has arisen over the significance of correlated extinctions, and how they may affect the optimal subdivision of metapopulations to maximize their persistence time.