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Results for “spatially explicit population models”

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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↗

PubMed1989

On growth and dispersal of population.

In his unpublished Master's thesis of 1921, the young Hotelling invented an ingenious model of population growth and diffusion. The contribution remained widely unknown until Waldo Tobler and Alan Wilson edited it as an article in 1978. Not even then did it trigger any outburst of contributions. Meanwhile, in 1951, Skellam invented the same model for non-human populations. Unlike in economics, it was a great success in ecology. In a recent contribution, Skellam is named Father of Ecological Diffusion and more than 1000 articles on the subject are listed. There were many attempts at solving the equation, but none were quite successful. The Hotelling and Skellam models both assumed a given saturation population that nature could support. In 1985 the present author suggested that an explicit production function be introduced in the Hotelling model, as a man produces his own means of subsistence. Moreover, it was proposed that diffusion be related to spatial differences in per capita productivity, rather than to those in population density. The present contribution is a rejoinder. It is shown that the stationary solutions to the original Hotelling model are periodic and dip into negative populations, whereas this is avoided by the modified model suggested. It can thus be used to show how agglomerative structures may evolve.

Demography↗

PubMed2005

Simulating the spatial dynamics of foot and mouth disease outbreaks in feral pigs and livestock in Queensland, Australia, using a susceptible-infected-recovered cellular automata model.

We describe an approach to modelling the spatio-temporal spread of foot and mouth disease through feral animal and unfenced livestock populations. We used a susceptible-infected-recovered model, implemented in a cellular automata framework, to assess the spread of FMD across two regions of Queensland, Australia. Following a sensitivity analysis on the infectious states, scenario analyses were conducted using feral pigs only as the susceptible population, and then with the addition of livestock, and initiated in the wet season and in the dry season. The results indicate that, depending on the season the outbreak is initiated, and without the implementation of control measures, an outbreak of Foot and Mouth Disease around Winton could continue unchecked, while an outbreak around Cape York may die out naturally. The approach explicitly incorporates the spatial relationships between the populations through which the disease spreads and provides a framework by which the spread of disease outbreaks can be explored through varying the model parameters. It highlights the emergence and importance of spatio-temporal patterns, something that previous modelling of FMD in feral animal and unfenced livestock populations has lacked.

Animals↗

PubMed2001

Cooperative boundary populations: the evolution of cooperation on mortality risk gradients.

Cooperative or altruistic behavior is known to be vulnerable to destructive exploitation in the absence of spatial segregation and perceptual discrimination on the part of cooperators. In this study, a non-standard, agent-based, spatially explicit model of the evolution of cooperation shows that spatial gradients of increasing individual mortality risk can allow cooperative subpopulations to persist among players randomly matched for one-shot Prisoner's Dilemma. Further, the dynamically stable cooperator population formed on the gradient at the boundary of the survivable non-cooperative range provides ideal conditions for the evolution of discriminating strategies such as tit-for-tat. It is suggested that such gradients may commonly exist at the boundaries of the ranges of existing populations, providing a new basic mechanism for the evolution of cooperation.

Animals↗

PubMed2000

Generating probabilistic spatially-explicit individual and population exposure estimates for ecological risk assessments.

Exposure to chemical contaminants in various media must be estimated when performing ecological risk assessments. Exposure estimates are often based on the 95th-percentile upper confidence limit on the mean concentration of all samples, calculated without regard to critical ecological and spatial information about the relative relationship of receptors, their habitats, and contaminants. This practice produces exposure estimates that are potentially unrepresentative of the ecology of the receptor. This article proposes a habitat area and quality-conditioned exposure estimator, E[HQ], that requires consideration of these relationships. It describes a spatially explicit ecological exposure model to facilitate calculation of E[HQ]. The model provides (1) a flexible platform for investigating the effect of changes in habitat area, habitat quality, foraging area, and population size on exposure estimates, and (2) a tool for calculating E[HQ] for use in actual risk assessments. The inner loop of a Visual Basic program randomly walks a receptor over a multicelled landscape--each cell of which contains values for cell area, habitat area, habitat quality, and concentration--accumulating an exposure estimate until the total area foraged is less than or equal to a given foraging area. An outer loop then steps through foraging areas of increasing size. This program is iterated by Monte Carlo software, with the number of iterations representing the population size. Results indicate that (1) any single estimator may over- or underestimate exposure, depending on foraging strategy and spatial relationships of habitat and contamination, and (2) changes in exposure estimates in response to changes in foraging and habitat area are not linear.

Animals↗

PubMed2000

Development of nerve connections under the control of neurotrophic factors: parallels with consumer-resource systems in population biology.

The development of connections between neurons and their target cells involves competition between axons for target-derived neurotrophic factors. Although the notion of competition is commonly used in neurobiology, the process is not well understood, and only a few formal models exist. In population biology, in contrast, the concept of competition is well developed and has been studied by means of many formal models of consumer-resource systems. Here we show that a recently formulated model of axonal competition can be rewritten as a general consumer-resource system. This allows neurobiological phenomena to be interpreted in population biological terms and, conversely, results from population biology to be applied to neurobiology. Using findings from population biology, we have studied two extensions of our axonal competition model. In the first extension, the spatial dimension of the target is explicitly taken into account. We show that distance between axons on their target mitigates competition and permits the coexistence of axons. The model can account for the fact that in many types of neurons a positive correlation exists between the size of the dendritic tree and the number of innervating axons surviving into adulthood. In the second extension, axons are allowed to respond to more than one neurotrophic factor. We show that this permits competitive exclusion among axons of one type, while at the same time there is coexistence with axons of another type innervating the same target. The model offers an explanation for the innervation pattern found on cerebellar Purkinje cells, where climbing fibres compete with each other until only a single one remains, which coexists with parallel fibre input to the same Purkinje cell.

Animals↗

PubMed2005

Spatial mosaic formation through frequency-dependent selection in Müllerian mimicry complexes.

Although contemporary models of Müllerian mimicry have considered the movement of interfacial boundaries between two distinct mimetic forms, and even the possibility of polymorphisms in two patch systems, no model has considered how multiple forms of Müllerian mimics might evolve and be maintained over large geographical areas. A spatially explicit individual-based model for the evolution of Müllerian mimicry is presented, in which two unpalatable species are distributed over discrete cells within a regular lattice. Populations in each cell are capable of genetic drift and experience localized dispersal as well as frequency-dependent selection by predators. When each unpalatable prey species was introduced into a random cell and allowed to spread, then mimicry evolved throughout the system in the form of a spatial mosaic of phenotypes, separated by narrow "hybrid zones". The primary mechanism generating phenotypic diversity was the occasional establishment of new mutant forms in unoccupied cells and their subsequent maintenance (and spread) through frequency-dependent selection. The mean number of discrete clusters of the same morph that formed in the lattice was higher the higher the intensity of predation, and higher the lower the dispersal rate of unpalatable prey. Under certain conditions the hybrid zones moved, in a direction dependent on the curvature of their interfacial boundaries. However, the mimetic mosaics were highly stable when the intensity of predation was high and the rate of prey dispersal was low. Overall, this model highlights how a stable mosaic of different mimetic forms can evolve from a range of starting conditions through a combination of chance effects and localized frequency-dependent selection.

Adaptation, Biological↗

PubMed1997

Using Moment Equations to Understand Stochastically Driven Spatial Pattern Formation in Ecological Systems

Spatial patterns in biological populations and the effect of spatial patterns on ecological interactions are central topics in mathematical ecology. Various approaches to modeling have been developed to enable us to understand spatial patterns ranging from plant distributions to plankton aggregation. We present a new approach to modeling spatial interactions by deriving approximations for the time evolution of the moments (mean and spatial covariance) of ensembles of distributions of organisms; the analysis is made possible by "moment closure," neglecting higher-order spatial structure in the population. We use the growth and competition of plants in an explicitly spatial environment as a starting point for exploring the properties of second-order moment equations and comparing them to realizations of spatial stochastic models. We find that for a wide range of effective neighborhood sizes (each plant interacting with several to dozens of neighbors), the mean-covariance model provides a useful and analytically tractable approximation to the stochastic spatial model, and combines useful features of stochastic models and traditional reaction-diffusion-like models. Copyright 1997 Academic Press. Copyright 1997 Academic Press

Journal Article↗

PubMed2004

Emergent trade-offs and selection for outbreak frequency in spatial epidemics.

Nonspatial theory on pathogen evolution generally predicts selection for maximal number of secondary infections, constrained only by supposed physiological trade-offs between pathogen infectiousness and virulence. Spread of diseases in human populations can, however, exhibit large scale patterns, underlining the need for spatially explicit approaches to pathogen evolution. Here, we show, in a spatial model where all pathogen traits are allowed to evolve independently, that evolutionary trajectories follow a single relationship between transmission and clearance. This trade-off relation is an emergent system property, as opposed to being a property of pathogen physiology, and maximizes outbreak frequency instead of the number of secondary infections. We conclude that spatial pattern formation in contact networks can act to link infectiousness and clearance during pathogen evolution in the absence of any physiological trade-off. Selection for outbreak frequency offers an explanation for the evolution of pathogens that cause mild but frequent infections.

Biological Evolution↗

PubMed2005

Dynamic patterns of adaptive radiation.

Adaptive radiation is defined as the evolution of ecological and phenotypic diversity within a rapidly multiplying lineage. When it occurs, adaptive radiation typically follows the colonization of a new environment or the establishment of a "key innovation," which opens new ecological niches and/or new paths for evolution. Here, we take advantage of recent developments in speciation theory and modern computing power to build and explore a large-scale, stochastic, spatially explicit, individual-based model of adaptive radiation driven by adaptation to multidimensional ecological niches. We are able to model evolutionary dynamics of populations with hundreds of thousands of sexual diploid individuals over a time span of 100,000 generations assuming realistic mutation rates and allowing for genetic variation in a large number of both selected and neutral loci. Our results provide theoretical support and explanation for a number of empirical patterns including "area effect," "overshooting effect," and "least action effect," as well as for the idea of a "porous genome." Our findings suggest that the genetic architecture of traits involved in the most spectacular radiations might be rather simple. We show that a great majority of speciation events are concentrated early in the phylogeny. Our results emphasize the importance of ecological opportunity and genetic constraints in controlling the dynamics of adaptive radiation.

Adaptation, Biological↗

PubMed2004

Processes leading to a spatial aggregation of Echinococcus multilocularis in its natural intermediate host Microtus arvalis.

The small fox tapeworm (Echinococcus multilocularis) shows a heterogeneous spatial distribution in the intermediate host (Microtus arvalis). To identify the ecological processes responsible for this heterogeneity, we developed a spatially explicit simulation model. The model combines individual-based (foxes, Vulpes vulpes) and grid-based (voles) techniques to simulate the infections in both intermediate and definite host. If host populations are homogeneously mixed, the model reproduces field data for parasite prevalence only for a limited number of parameter combinations. As ecological parameters inevitably vary to a certain degree, we discarded the homogeneous mixing model as insufficient to gain insight into the ecology of the fox tapeworm cycle. We analysed five different model scenarios, each focussing on an ecological process that might be responsible for the heterogeneous spatial distribution of E. mulitlocularis in the intermediate host. Field studies revealed that the prevalence ratio between intermediate and definite host remains stable over a wide range of ecological conditions. Thus, by varying the parameters in simulation experiments, we used the robustness of the agreement between field data and model output as quality criterion for the five scenarios. Only one of the five scenarios was found to reproduce the prevalence ratio over a sufficient range of parameter combinations. In the accentuated scenario most tapeworm eggs die due to bad environmental conditions before they cause infections in the intermediate host. This scenario is supported by the known sensitivity of tapeworm eggs to high temperatures and dry conditions. The identified process is likely to lead to a heterogeneous availability of infective eggs and thus to a clumped distribution of infected intermediate hosts. In conclusion, areas with humid conditions and low temperatures must be pointed out as high risk areas for human exposure to E. multilocularis eggs as well.

Animals↗

PubMed2004

Competition between near and far dispersers in spatially structured habitats.

Competitive interactions and invasibility between short- and long-distance dispersal was investigated in a population on a heterogeneous landscape with spatial correlations in habitat types, and where the driving interaction between individuals is competition for space. Stochastic spatially explicit simulations were used, along with differential equation models based on pair approximations. Conditions under which either dispersal strategy can successfully invade the other were determined, as a function of the amount and clustering of suitable habitat and the relative costs involved in the two dispersal strategies. Long-distance dispersal, which reduces intraspecific competition, is sometimes advantageous even where aggregation of suitable habitat would otherwise favor short-distance dispersal, although certain habitat distributions can lead to either strategy being dominant. Coexistence is also possible on some landscapes, where the spatial structure of the populations partitions suitable sites according to the number of suitable neighboring sites. Mutual competitive exclusion, where whichever strategy is established first cannot be invaded, is also possible. All of these results are observed even when there is no intrinsic difference in the two strategies' costs, such as mortality or competitive abilities.

Animals↗

PubMed2004

Spatial heterogeneity, social structure and disease dynamics of animal populations.

Social groupings, population dynamics and population movements of animals all give rise to spatio-temporal variations in population levels. These variations may be of crucial importance when considering the spread of infectious diseases since infection levels do not increase unless there is a sufficient pool of susceptible individuals. This paper explores the impact of social groupings on the potential for an endemic disease to develop in a spatially explicit model system. Analysis of the model demonstrates that the explicit inclusion of space allows asymmetry between groups to arise when this was not possible in the equivalent spatially homogeneous system. Moreover, differences in movement behaviours for susceptible and infected individuals gives rise to different spatial profiles for the populations. These profiles were not observed in previous work on an epidemic system. The results are discussed in an ecological context with reference to furious and dumb strains of infectious diseases.

Animal Diseases↗

PubMed2002

Cyclic dynamics in simulated plant populations.

Despite the general interest in nonlinear dynamics in animal populations, plant populations are supposed to show a stable equilibrium that is attributed to fundamental differences compared with animals. Some studies find more complex dynamics, but empirical studies usually are too short and most modelling studies ignore important spatial aspects of local competition and establishment. Therefore, we used a spatially explicit individual-based model of a hypothetical, non-clonal perennial to explore which mechanisms might generate complex dynamics, i.e. cycles. The model is based on the field-of-neighbourhood approach that describes local competition and establishment in a phenomenological manner. We found cyclic population dynamics for a wide spectrum of model variants, provided that mortality is determined by local competition and recruitment is virtually completely suppressed within the zone of influence of established plants. This destabilizing effect of local processes within plant populations might have wide-ranging implications for the understanding of plant community dynamics and coexistence.

Ecosystem↗

PubMed2006

A new method for conservation planning for the persistence of multiple species.

Although the aim of conservation planning is the persistence of biodiversity, current methods trade-off ecological realism at a species level in favour of including multiple species and landscape features. For conservation planning to be relevant, the impact of landscape configuration on population processes and the viability of species needs to be considered. We present a novel method for selecting reserve systems that maximize persistence across multiple species, subject to a conservation budget. We use a spatially explicit metapopulation model to estimate extinction risk, a function of the ecology of the species and the amount, quality and configuration of habitat. We compare our new method with more traditional, area-based reserve selection methods, using a ten-species case study, and find that the expected loss of species is reduced 20-fold. Unlike previous methods, we avoid designating arbitrary weightings between reserve size and configuration; rather, our method is based on population processes and is grounded in ecological theory.

Animals↗

PubMed2006

Local population size in a flightless insect: importance of patch structure-dependent mortality.

In spatially heterogeneous systems, utilizing population models to integrate the effects of multiple population rates can yield powerful insights into the relative importance of the component rates. The relative importance of demographic rates and dispersal in shaping the distribution of the western tussock moth (Orgyia vetusta) among patches of its host plant was explored using stage-structured population models. Tussock moth dispersal occurs passively in first-instar larvae and is poor or absent in all other life stages. Spatial surveys suggested, however, that moth distribution is not well explained by passive dispersal; moth populations were greater on small patches and on isolated ones. Further analysis showed that several local demographic rates varied significantly with patch characteristics. Two mortality factors in particular may explain the observed patterns. First, crawler mortality both increased with patch size and was density-dependent. A single-patch difference equation model showed mortality related to patch size is strong enough to overcome the homogenizing effect of density dependence; greater equilibrium densities were predicted for smaller patches. Second, although three rates were found to vary with local patch density, only pupal parasitism by a chalcid wasp could potentially account for higher moth abundances on isolated patches. A spatially explicit simulation model of the multiple-patch system showed that spatial variation in pupal parasitism is indeed strong enough to generate such a pattern. These results demonstrate that habitat spatial structure can affect multiple population processes simultaneously, and even relatively low attack rates imposed on a reproductively valuable life stage of the host can have a dominant effect on population distribution among habitat patches.

Animals↗

PubMed2006

Predicting outbreaks: a spatial risk assessment of West Nile virus in British Columbia.

BACKGROUND: West Nile virus (WNv) has recently emerged as a health threat to the North American population. After the initial disease outbreak in New York City in 1999, WNv has spread widely and quickly across North America to every contiguous American state and Canadian province, with the exceptions of British Columbia (BC), Prince Edward Island and Newfoundland. In this study we develop models of mosquito population dynamics for Culex tarsalis and C. pipiens, and create a spatial risk assessment of WNv prior to its arrival in BC by creating a raster-based mosquito abundance model using basic geographic and temperature data. Among the parameters included in the model are spatial factors determined from the locations of BC Centre for Disease Control mosquito traps (e.g., distance of the trap from the closest wetland or lake), while other parameters were obtained from the literature. Factors not considered in the current assessment but which could influence the results are also discussed. RESULTS: Since the model performs much better for C. tarsalis than for C. pipiens, the risk assessment is carried out using the output of C. tarsalis model. The result of the spatially-explicit mosquito abundance model indicates that the Okanagan Valley, the Thompson Region, Greater Vancouver, the Fraser Valley and southeastern Vancouver Island have the highest potential abundance of the mosquitoes. After including human population data, Greater Vancouver, due to its high population density, increases in significance relative to the other areas. CONCLUSION: Creating a raster-based mosquito abundance map enabled us to quantitatively evaluate WNv risk throughout BC and to identify the areas of greatest potential risk, prior to WNv introduction. In producing the map important gaps in our knowledge related to mosquito ecology in BC were identified, as well, it became evident that increased efforts in bird and mosquito surveillance are required if more accurate models and maps are to be produced. Access to real time climatic data is the key for developing a real time early warning system for forecasting vector borne disease outbreaks, while including social factors is important when producing a detailed assessment in urban areas.

Animals↗

PubMed2002

Random walk models of worker sorting in ant colonies.

Sorting can be an important mechanism for the transfer of information from one level of biological organization to another. Here we study the algorithm underlying worker sorting in Leptothorax ant colonies. Worker sorting is related to task allocation and therefore to the adaptive advantages associated with an efficient system for the division of labour in ant colonies. We considered four spatially explicit individual-based models founded on two-dimensional correlated random walk. Our aim was to establish whether sorting at the level of the worker population could occur with minimal assumptions about the behavioural algorithm of individual workers. The behaviour of an individual worker in the models could be summarized by the rule "move if you can, turn always". We assume that the turning angle of a worker is individually specific and negatively dependent on the magnitude of an internal parameter micro which could be regarded as a measure of individual experience or task specialization. All four models attained a level of worker sortedness that was compatible with results from experiments onLeptothorax ant colonies. We found that the presence of a sorting pivot, such as the nest wall or an attraction force towards the centre of the worker population, was crucial for sorting. We make a distinction between such pivots and templates and discuss the biological implications of their difference.

Algorithms↗