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Results for “spatially explicit population models”

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PubMed2005

Terrestrial metapopulation dynamics: a nonlinear bioeconomic model analysis.

This paper presents a spatially explicit bioeconomic analysis of species conservation in agricultural areas. Wild species in fragmented agricultural landscapes are best approached as metapopulations consisting of a finite number of local populations. Economic analysis of species conservation in fragmented habitat needs to deal with metapopulation theory and its theoretical implications. This paper presents a spatially explicit bioeconomic model consisting of a straightforward economic land use model and an applied metapopulation model. This paper demonstrates that multiple equilibria and multiple local optima in metapopulations might lead to nonconvexities in the production possibilities set of agricultural profits and species conservation.

Agriculture↗

PubMed2000

Diffusion-limited predator-prey dynamics in Euclidean environments: an allometric individual-based model.

We claim that diffusion-limited rates of reaction can be an explanation for the altered population dynamics predicted by models incorporating local interactions and limited individual mobility. We show that the predictions of a spatially explicit, individual-based model result from reduced rates of predation and reproduction caused by limited individual mobility and patchiness. When these reduced rates are used in a mean-field model, there is better agreement with the predictions of the simulation model incorporating local interactions. We also explain previous findings regarding the effects of dimensionality on population dynamics in light of diffusion-limited reactions and Pólya random walks. In particular, we demonstrate that 3D systems are better "stirred" than 2D systems and consequently have a reduced tendency for diffusion-limited interaction rates.

Animals↗

PubMed2003

The linear process of somatic evolution.

Cancer is the consequence of an unwanted evolutionary process. Cells receive mutations that alter their phenotype. Especially dangerous are those mutations that increase the net reproductive rate of cells, thereby leading to neoplasia and later to cancer. The standard models of evolutionary dynamics consider well mixed populations of individuals in symmetric positions. Here we introduce a spatially explicit, asymmetric stochastic process that captures the essential architecture of evolutionary dynamics operating within tissues of multicellular organisms. The "linear process" has the property of cancelling out selective differences among cells yet retaining the protective function of apoptosis. This design can slow down the rate of somatic evolution dramatically and therefore delay the onset of cancer.

Animals↗

PubMedDate not supplied

Is pertussis actually reemerging? Insights from an individual-based model.

In this paper, we introduce a spatially explicit, individual-based model developed to simulate the dynamics of pertussis in a small population. With this simulation approach, complex epidemic systems can be built using information on parasite population structure (strain diversity, virulence diversity, etc.), human population structure (individual risk, age structure, interaction matrices, immune response, etc.), as well as mechanisms of evolution and learning. We parameterized our model to describe pertussis in an age-structured community. Pertussis or whooping cough is an acute infection of the respiratory tract caused by Bordetella pertussis. Despite wide-scale vaccination in many countries, this disease is reemerging throughout the world in both adults and children. Emergence has been explained by many factors: wane of vaccine and natural immunity, increase of asymptomatic carriers, and/or natural selection of non-vaccine strains. Here, we model these hypotheses and analyze their potential impact on the observed increase of pertussis notification.

Adolescent↗

PubMed2005

Land-cover change trajectories in northern Ghana.

Land-cover change trajectories are an emergent property of complex human-environment systems such as the land-use system. An understanding of the factors responsible for land change trajectories is fundamental for land-use planning and the development of land-related policies. The aims of this study were to characterize and identify the spatial determinants of agricultural land-cover change trajectories in northern Ghana. Land-cover change trajectories were defined using land-cover maps prepared from Landsat Thematic Mapper dataset acquired in 1984, 1992, and 1999. Binary logistic regression was used to model the probability of observing the trajectories as a function of spatially explicit biophysical and socioeconomic independent variables. Population densities generally increased along the continuum of land-use intensity, whereas distance from market and roads generally decreased along this continuum. Apparently, roads and market serve as incentives for settlement and agricultural land use. An increase in population density is an important spatial determinant only for trajectories where the dominant change process is agricultural extensification. A major response to population growth is an increase in cultivation frequency around the main market. Agricultural intensification is highly sensitive to accessibility by roads. The increase in land-use intensity is also associated with low soil quality. These results suggest the need for policies to restore soil fertility for agricultural sustainability. The models also provide a means for identifying functional relationships for in-depth analyses of land-use change in Ghana.

Agriculture↗

PubMed1999

Nucleation and relaxation from meta-stability in spatial ecological models.

We study a model for competing species that explicitly accounts for effects due to discreteness, stochasticity and spatial extension of populations. If a species does better locally than the other by an amount epsilon, the global outcome depends on the initial densities (uniformly distributed in space), epsilon and the size of the system. The transition point moves to lower values of the initial density of the superior species with increasing system size. Away from the transition point, the dynamics can be described by a mean-field approximation. The transition zone is dominated by formation of clusters and is characterized by nucleation effects and relaxation from meta-stability. Following cluster formation, the dynamics are dominated by motion of cluster interfaces through a combination of planar wave motion and motion through mean curvature. Clusters of the superior species bigger than a certain critical threshold grow whereas smaller clusters shrink. The reaction-diffusion system obtained from the mean-field dynamics agrees well with the particle system. The statistics of clusters at an early time soon after cluster-formation follow a percolation-like diffusive scaling law. We derive bounds on the time-to-extinction based on cluster properties at this early time. We also deduce finite-size scaling from infinite system behavior.

Animals↗

PubMed2000

Canonical functions for dispersal-induced synchrony.

Two processes are universally recognized for inducing spatial synchrony in abundance: dispersal and correlated environmental stochasticity. In the present study we seek the expected relationship between synchrony and distance in populations that are synchronized by density-independent dispersal. In the absence of dispersal, synchrony among populations with simple dynamics has been shown to echo the correlation in the environment. We ask what functional form we may expect between synchrony and distance when dispersal is the synchronizing agent. We formulate a continuous-space, continuous-time model that explicitly represents the time evolution of the spatial covariance as a function of spatial distance. Solving this model gives us two simple canonical functions for dispersal-induced covariance in spatially extended populations. If dispersal is rare relative to birth and death, then covariances between nearby points will follow the dispersal distance distribution. At long distances, however, the covariance tails off according to exponential or Bessel functions (depending on whether the population moves in one or two dimensions). If dispersal is common, then the covariances will follow the mixture distribution that is approximately Gaussian around the origin and with an exponential or Bessel tail. The latter mixture results regardless of the original dispersal distance distribution. There are hence two canonical functions for dispersal-induced synchrony

Animals↗

PubMed2003

Spatially-explicit matrix models. A mathematical analysis of stage-structured integrodifference equations.

This paper is concerned with mathematical analysis of the 'critical domain-size' problem for structured populations. Space is introduced explicitly into matrix models for stage-structured populations. Movement of individuals is described by means of a dispersal kernel. The mathematical analysis investigates conditions for existence, stability and uniqueness of equilibrium solutions as well as some bifurcation behaviors. These mathematical results are linked to species persistence or extinction in connected habitats of different sizes or fragmented habitats; hence the framework is given for application of such models to ecology. Several approximations which reduce the complexity of integrodifference equations are given. A simple example is worked out to illustrate the analytical results and to compare the behavior of the integrodifference model to that of the approximations.

Algorithms↗

PubMed1998

"Critical slowing down" in time-to-extinction: an example of critical phenomena in ecology.

We study a model for two competing species that explicitly accounts for effects due to discreteness, stochasticity and spatial extension of populations. The two species are equally preferred by the environment and do better when surrounded by others of the same species. We observe that the final outcome depends on the initial densities (uniformly distributed in space) of the two species. The observed phase transition is a continuous one and key macroscopic quantities like the correlation length of clusters and the time-to-extinction diverge at a critical point. Away from the critical point, the dynamics can be described by a mean-field approximation. Close to the critical point, however, there is a crossover to power-law behavior because of the gross mismatch between the largest and smallest scales in the system. We have developed a theory based on surface effects, which is in good agreement with the observed behavior. The course-grained reaction-diffusion system obtained from the mean-field dynamics agrees well with the particle system.

Animals↗

PubMed2006

Plugging space into predator-prey models: an empirical approach.

Extrapolating ecological processes from small-scale experimental systems to scales of natural populations usually entails a considerable increase in spatial heterogeneity, which may affect process rates and, ultimately, population dynamics. We demonstrate how information on the heterogeneity of natural populations can be taken into account when scaling up laboratory-derived process functions, using the technique of moment approximation. We apply moment approximation to a benthic crustacean predator-prey system, where a laboratory-derived functional response is made spatial by including correction terms for the variance in prey density and the covariance between prey and predator densities observed in the field. We also show how moment approximation may be used to incorporate spatial information into a dynamic model of the system. While the nonspatial model predicts stable dynamics, its spatial equivalent also produces bounded fluctuations, in agreement with observed dynamics. A detailed analysis shows that predator-prey covariance, but not prey variance, destabilizes the dynamics. We conclude that second-order moment approximation may provide a useful technique for including spatial information in population models. The main advantage of the method is its conceptual value: by providing explicit estimates of variance and covariance effects, it offers the possibility of understanding how heterogeneity affects ecological processes.

Amphipoda↗

PubMed2006

An ESS for the height of a plant population, or an optimal height for an individual?--Rethinking game-theoretic models for plant height.

Plants only interact with neighbors over restricted distances, so local conditions are of great significance for plants. It is therefore important to consider spatial structure and neighborhood effects if we are to understand plants' strategies. We constructed a spatially-explicit, game theory model to explore optimal height growth at the individual-level. In the model, there is no ESS for height growth at the population level, because there is an "instantaneous" optimal height growth strategy for the individual plant that changes depending on the local light environment. The optimal strategy is plasticity in response to local conditions. Game-theoretic models for plant phenotypic traits should move from "mean-field approximations" towards explicit modeling of local interactions.

Ecosystem↗

PubMed2006

Inferring evolutionary signals from ecological data in a plant-pathogen metapopulation.

We followed the dynamics of local epidemics in three populations of a natural plant-pathogen system for four sequential years. We characterize the overwintering process with spatial statistics and use a stochastic, spatially explicit, modeling approach with Bayesian parameter estimation to study the spread of the infection during the growing season. Our modeling approach allows us to infer coevolutionary signals from spatiotemporal data on pathogen prevalence. Most importantly, we are able to assess the distribution of resistant hosts within the distribution of all host plants. We show that resistant hosts occur in areas with high pathogen encounter rates, and that the occurrence of resistance correlates with overwintering probability of the pathogen. The estimates for essentially all model parameters are characterized by a large amount of variation over the years and the populations. While the variation in the fraction of resistant hosts and in the force of infection is to a large extent explained by the population, the other model parameters (two parameters describing the shape of the dispersal kernel) vary essentially in an unpredictable manner, suggesting that much of the variation may occur at very fine spatial and temporal scales.

Bayes Theorem↗

PubMed2002

Class of self-limiting growth models in the presence of nonlinear diffusion.

The source term in a reaction-diffusion system, in general, does not involve explicit time dependence. A class of self-limiting growth models dealing with animal and tumor growth and bacterial population in a culture, on the other hand, are described by kinetics with explicit functions of time. We analyze a reaction-diffusion system to study the propagation of spatial front for these models.

Animals↗

PubMed2001

Two-sex population dynamics in space: effects of gestation time on persistence.

Most single-species population models assume either that one sex dominates the growth dynamics (usually the female), or that the life cycles of the two sexes are identical; however, sexual differences in ontogenetic features can render this assumption invalid. Further, the interaction between sexes is necessarily nonlinear, and the dependence of dynamic behavior on sexual interactions can be complicated. Here we examine a two-sex population model, related to the well-known logistic model, with explicit sexual interactions. The model is bistable and, by the addition of diffusion, admits traveling wave solutions. Dominance of states via this spatial dynamic are examined. A simple condition for neutral dominance is obtained; sexual interactions inhibit the dominance of the nonzero population, making persistence more difficult.

Animals↗

PubMed2006

Pollen dispersal in spatially aggregated populations.

We perform a theoretical study of effective pollen dispersal within plant populations exhibiting intraspecific spatial aggregation. We simulate nonuniform distributions of individuals by means of a Poisson cluster process and use an individual-based spatially explicit model of pollen dispersal to assess the effects of different aggregation patterns on the effective pollen pool size (N(ep)) and the axial variance of pollen dispersal (sigma (p)). Results show clear interactions between clumping and both N(ep) and sigma (p), whose precise form and intensity depend on the relative spatial scale of aggregation to pollen dispersal range. If clump size is small relative to dispersal range, clumping results in lower N(ep) and sigma (p) than in randomly distributed populations. Interestingly, by contrast, aggregation may actually enlarge N(ep) and has minimum impact on sigma (p) if clump size is near or above the scale of dispersal. High intraclump to global density ratios enhance the sensitivity of both N(ep) and sigma (p) to clumping, while leptokurtic pollen dispersal generates sharper reductions of both N(ep) and sigma (p) for small clump sizes and stronger increments of N(ep) for larger clump sizes. Overall, our results indicate that isolation-by-distance models in plants should not ignore the effects of intraspecific spatial aggregation on effective dispersal.

Computer Simulation↗

PubMed2005

Population-level assessment of risks of pesticides to birds and mammals in the UK.

It is generally acknowledged that population-level assessments provide a better measure of response to toxicants than assessments of individual-level effects. Population-level assessments generally require the use of models to integrate potentially complex data about the effects of toxicants on life-history traits, and to provide a relevant measure of ecological impact. Building on excellent earlier reviews we here briefly outline the modelling options in population-level risk assessment. Modelling is used to calculate population endpoints from available data, which is often about individual life histories, the ways that individuals interact with each other, the environment and other species, and the ways individuals are affected by pesticides. As population endpoints, we recommend the use of population abundance, population growth rate, and the chance of population persistence. We recommend two types of model: simple life-history models distinguishing two life-history stages, juveniles and adults; and spatially-explicit individual-based landscape models. Life-history models are very quick to set up and run, and they provide a great deal of insight. At the other extreme, individual-based landscape models provide the greatest verisimilitude, albeit at the cost of greatly increased complexity. We conclude with a discussion of the implications of the severe problems of parameterising models.

Animals↗

PubMed2006

A functional response model of a predator population foraging in a patchy habitat.

1. Functional response models (e.g. Holling's disc equation) that do not take the spatial distributions of prey and predators into account are likely to produce biased estimates of predation rates. 2. To investigate the consequences of ignoring prey distribution and predator aggregation, a general analytical model of a predator population occupying a patchy environment with a single species of prey is developed. 3. The model includes the density and the spatial distribution of the prey population, the aggregative response of the predators and their mutual interference. 4. The model provides explicit solutions to a number of scenarios that can be independently combined: the prey has an even, random or clumped distribution, and the predators show a convex, sigmoid, linear or no aggregative response. 5. The model is parameterized with data from an acarine predator-prey system consisting of Phytoseiulus persimis and Tetranychus urticae inhabiting greenhouse cucumbers. 6. The model fits empirical data quite well and much better than if prey and predators were assumed to be evenly distributed among patches, or if the predators were distributed independently of the prey. 7. The analyses show that if the predators do not show an aggregative response it will always be an advantage to the prey to adopt a patchy distribution. On the other hand, if the predators are capable of responding to the distribution of prey, then it will be an advantage to the prey to be evenly distributed when its density is low and switch to a more patchy distribution when its density increases. The effect of mutual interference is negligible unless predator density is very high. 8. The model shows that prey patchiness and predator aggregation in combination can change the functional response at the population level from type II to type III, indicating that these factors may contribute to stabilization of predator-prey dynamics.

Animals↗

PubMed2004

Stabilizing effects in spatial parasitoid-host and predator-prey models: a review.

We review the literature on spatial host-parasitoid and predator-prey models. Dispersal on its own is not stabilizing and can destabilize a stable local equilibrium. We identify three mechanisms whereby limited dispersal of hosts and parasitoids combined with other features, such as spatial and temporal heterogeneity, can promote increased persistence and stability. The first mechanisms, "statistical stabilization", is simply the statistical effect that summing a number of out-of-phase population trajectories results in a relatively constant total population density. The second mechanism involves decoupling of immigration from local density, such that limited dispersal between asynchronous patches results in an effect that mimics density-dependence at the local patch level. The third mechanism involves altering spatially averaged parameter values resulting from spatial heterogeneity in density combined with non-linear responses to density. Persistence in spatially explicit models with local dispersal frequently associated with self-organized spatial patterning.

Animals↗