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Results for “spatially explicit population models”

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PubMed2002

Spatially explicit models of Turelli-Hoffmann Wolbachia invasive wave fronts.

This paper examines different mathematical models of insect dispersal and infection spread and compares these with field data. Reaction-diffusion and integro-difference equation models are used to model the spatio-temporal spread of Wolbachia in Drosophila simulans populations. The models include cytoplasmic incompatibility between infected females and uninfected males that creates a threshold density, similar to an Allee effect, preventing increase from low incidence of infection in the host population. The model builds on an earlier model (Turelli & Hoffmann, 1991) by incorporating imperfect maternal transmission. The results of simulations of the models using the same parameter values produce different dynamics for each model. These differences become very marked in the integro-difference equation models when insect dispersal patterns are assumed to be non-Gaussian. The success or failure of invasion by Wolbachia in the simulations may be attributed to the insect dispersal mechanism used in the model rather than the parameter values. As the models predict very different outcomes for the integro-difference models depending on the underlying assumptions of insect dispersal patterns, this emphasizes that good field data on real (rather than idealized) dispersal patterns need to be collected before models such as these can be used for predictive purposes.

Animals↗

PubMed2006

Spatial scaling of consumer-resource interactions in advection-dominated systems.

Ecologists studying consumer-resource interactions in advection-dominated systems such as streams and rivers frequently seek to link the results of small-scale experiments with larger-scale patterns of distribution and abundance. Accomplishing this goal requires determining the characteristic scale, termed the response length, at which there is a shift from local dynamics dominated by advective dispersal to larger-scale dynamics dominated by births and deaths. Here, we model the dynamics of consumer-resource systems in a spatially variable, advective environment and show how consumer-resource interactions alter the response length relative to its single-species value. For one case involving a grazer that emigrates in response to high predator density, we quantify the changes using published data from small-scale experiments on aquatic invertebrates. Using Fourier analysis, we describe the responses of advection-dominated consumer-resource systems to spatially extended environmental variability in a way that involves explicit consideration of the response length. The patterns we derive for different consumer-resource systems exhibit important similarities in how component populations respond to spatial environmental variability affecting dispersal as opposed to demographic parameters.

Ecosystem↗

PubMed2000

The ESS under spatial variation with applications to sex allocation.

I derive a new approximation which uses the backward Kolmogorov equation to describe evolution when individuals have variable numbers of offspring. This approximation is based on an explicit fixed population size assumption and therefore differs from previous models. I show that for individuals to accept an increase in the variance of offspring number, they must be compensated by an increase in mean offspring number. Based on this model and any given set of feasible alleles, an evolutionary stable strategy (ESS) can be found. Four types of ESS are possible and can be discriminated by graphical methods. These ESS values depend on population size, but population size can be reinterpreted as deme size in a structured population. I adapt this theory to the problem of sex allocation under variable returns to male and female function and derive the ESS sex allocation strategy. I show that allocation to the more variable sexual function should be reduced, but that this effect decreases as population size increases and as variability decreases. These results are compared with results from exact matrix models and computer simulations, all of which show strong congruence.

Animals↗

PubMed2004

"What" and "where" in visual working memory: a computational neurodynamical perspective for integrating FMRI and single-neuron data.

Single-neuron recordings, functional magnetic resonance imaging (fMRI) data, and the effects of lesions indicate that the prefrontal cortex (PFC) is involved in some types of working memory and related cognitive processes. Based on these data, two different models of the topographical and functional organization of the PFC have been proposed: organization-by-stimulus-domain, and organization-by-process. In this article, we utilize an integrate-and-fire network to model both single-neuron and fMRI data on short-term memory in order to understand data obtained in topologically different parts of the PFC during working memory tasks. We explicitly model the mechanisms that underlie working memory-related activity during the execution of delay tasks that have a "what"-then-"where" design (with both object and spatial delayed responses within the same trial). The model contains different populations of neurons (as found experimentally) in attractor networks that respond in the delay period to the stimulus object, the stimulus position, and to combinations of both object and position information. The pools are arranged hierarchically and have global inhibition through inhibitory interneurons to implement competition. It is shown that a biasing attentional input to define the current relevant information (object or location) enables the system to select the correct neuronal populations during the delay period in what is a biased competition model of attention. The processes occurring at the AMPA and NMDA synapses are dynamically modeled in the integrate-and-fire implementation to produce realistic spiking dynamics. It is shown that the fMRI data characteristic of the dorsal PFC and linked to spatial processing and manipulation of items can be reproduced in the model by a high level of inhibition, whereas the fMRI data characteristic of the ventral PFC and linked to object processing can be produced by a lower level of inhibition, even though the network is itself topographically homogeneous with no spatial topology of the neurons. This article, thus, not only presents a model for how spatial versus object short-term memory could be implemented in the PFC, but also shows that the fMRI BOLD signal measured during such tasks from different parts of the PFC could reflect a higher level of inhibition dorsally, without this dorsal region necessarily being primarily spatial and the ventral region object-related.

Algorithms↗

PubMed2000

An explicit approach to evolutionarily stable dispersal strategies: no cost of dispersal.

The evolution of dispersal is examined by looking at evolutionarily stable strategies (ESS) for dispersal parameters in discrete time multisite models without any cost of dispersal. ESS are investigated analytically, based on explicit results on sensitivity analysis of matrix models. The basic model considers an arbitrary number of sites and a single age class. An ESS for dispersal parameters is obtained when the spatial reproductive values, calculated at the density-dependent population equilibrium, are equal across sites. From this basic formulation, one derives equivalently that all local populations should be at equilibrium in the absence of migration, and that dispersal between sites should be balanced, i.e., the numbers of individuals arriving to and leaving a site are equal. These results are then generalized to a model with several age classes. Equal age-specific reproductive values do not however imply balanced dispersal in this case. Our results generalize to any number of sites and age classes those available ¿M. Doebeli, Dispersal and dynamics, Theoret. Popul. 47 (1995) 82 for two sites and one age class.

Age Distribution↗

PubMed1986

From basic network principles to neural architecture: emergence of spatial-opponent cells.

The functional architecture of mammalian visual cortex has been elucidated in impressive detail by experimental work of the past 20-25 years. The origin of many of the salient features of this architecture, however, has remained unexplained. This paper is the first of three (the others will appear in subsequent issues of these Proceedings) that address the origin and organization of feature-analyzing (spatial-opponent and orientation-selective) cells in simple systems governed by biologically plausible development rules. I analyze the progressive maturation of a system composed of a few layers of cells, with connections that develop according to a simple set of rules (including Hebb-type modification). To understand the prenatal origin of orientation-selective cells in certain primates, I consider the case in which there is no external input, with the first layer exhibiting random spontaneous electrical activity. No orientation preference is specified to the system at any stage, and none of the basic developmental rules is specific to visual processing. Here I introduce the theory of "modular self-adaptive networks," of which this system is an example, and explicitly demonstrate the emergence of a layer of spatial-opponent cells. This sets the stage for the emergence, in succeeding layers, of an orientation-selective cell population.

Animals↗

PubMed2006

Simulating the influences of various fire regimes on caribou winter habitat.

Caribou are an integral component of high-latitude ecosystems and represent a major subsistence food source for many northern people. The availability and quality of winter habitat is critical to sustain these caribou populations. Caribou commonly use older spruce woodlands with adequate terrestrial lichen, a preferred winter forage, in the understory. Changes in climate and fire regime pose a significant threat to the long-term sustainability of this important winter habitat. Computer simulations performed with a spatially explicit vegetation succession model (ALFRESCO) indicate that changes in the frequency and extent of fire in interior Alaska may substantially impact the abundance and quality of winter habitat for caribou. We modeled four different fire scenarios and tracked the frequency, extent, and spatial distribution of the simulated fires and associated changes to vegetation composition and distribution. Our results suggest that shorter fire frequencies (i.e., less time between recurring fires) on the winter range of the Nelchina caribou herd in eastern interior Alaska will result in large decreases of available winter habitat, relative to that currently available, in both the short and long term. A 30% shortening of the fire frequency resulted in a 3.5-fold increase in the area burned annually and an associated 41% decrease in the amount of spruce-lichen forest found on the landscape. More importantly, simulations with more frequent fires produced a relatively immature forest age structure, compared to that which currently exists, with few stands older than 100 years. This age structure is at the lower limits of stand age classes preferred by caribou from the Nelchina herd. Projected changes in fire regime due to climate warming and/or additional prescribed burning could substantially alter the winter habitat of caribou in interior Alaska and lead to changes in winter range use and/or population dynamics.

Alaska↗

PubMed2003

Resistance may be futile: dispersal scales and selection for disease resistance in competing plants.

If a host species shares a pathogen with competing species, the disease may provide a net benefit. Selection for resistance will depend on the trade-off between the damage done by the disease and the positive effects resulting from infection of competitors. This paper presents a simple, spatially explicit model of a plant that shares a disease with a superior competitor. The phenotypic evolution of cost-free resistance is studied by using the method of pair approximation to analyse the small-scale spatial structure of the interacting populations. Selection favors lower resistance when disease transmission is spatially local and the damage to the competitor is sufficient to outweigh the direct effects of infection. This suggests that local spatial structure may be critical in determining the coevolution of host-host-pathogen systems.

Competitive Behavior↗

PubMed2006

Gene flow and functional connectivity in the natterjack toad.

Functional connectivity is a key factor for the persistence of many specialist species in fragmented landscapes. However, connectivity estimates have rarely been validated by the observation of dispersal movements. In this study, we estimated functional connectivity of a real landscape by modelling dispersal for the endangered natterjack toad (Bufo calamita) using cost distance. Cost distance allows the evaluation of 'effective distances', which are distances corrected for the costs involved in moving between habitat patches in spatially explicit landscapes. We parameterized cost-distance models using the results of our previous experimental investigation of natterjack's movement behaviour. These model predictions (connectivity estimates from the GIS study) were then confronted to genetic-based dispersal rates between natterjack populations in the same landscape using Mantel tests. Dispersal rates between the populations were inferred from variation at six microsatellite loci. Based on these results, we conclude that matrix structure has a strong effect on dispersal rates. Moreover, we found that cost distances generated by habitat preferences explained dispersal rates better than did the Euclidian distances, or the connectivity estimate based on patch-specific resistances (patch viscosity). This study is a clear example of how landscape genetics can validate operational functional connectivity estimates.

Animals↗

PubMed2000

A Reevaluation of Density-Dependent Population Cycles in Open Systems.

Studies motivated by consideration of barnacle populations have led to the prediction of two different dynamic states for space-limited open populations subject to density-dependent mortality. Population densities may cycle or fluctuate stochastically around a mean value. Despite the potential generality of the associated theory, there are few examples of population cycling in open systems that have been shown to be driven by density-dependent effects. This may be because settlement and growth processes are generally too slow or too variable to generate consistent cycles. An alternative explanation is examined in this article using spatially explicit simulations. Even under conditions of consistent settlement and growth, the cycles predicted in at least one previous study are shown to represent a special case. Clear population cycles are only observed when the density-dependent disturbances are constrained to reoccur in exactly the same location. In the more general case, where density-dependent disturbances respond to local variations in population density, the cycling predicted from simple models is difficult to detect. Hence, a failure to detect cycling in population density does not refute a role for density dependence. Density-dependent disturbances can create a characteristic spatial structure consisting of a mosaic of cohorts.

barnacles↗

PubMed2006

Independent effects of fragmentation on forest songbirds: an organism-based approach.

The degree to which spatial patterns influence the dynamics and distribution of populations is a central question in ecology. This question is even more pressing in the context of rapid habitat loss and fragmentation, which threaten global biodiversity. However, the relative influence of habitat loss and landscape fragmentation, the spatial patterning of remaining habitat, remains unclear. If landscape pattern affects population size, managers may be able to design landscapes that mitigate habitat loss. We present the results of a mensurative experiment designed to test four habitat loss vs. fragmentation hypotheses. Unlike previous studies, we measured landscape structure using quantitative, spatially explicit habitat distribution models previously developed for two species: Blackburnian Warbler (Dendroica fusca) and Ovenbird (Seiurus aurocapilla). We used a stratified sampling design that reduced the confounding of habitat amount and fragmentation variables. Occurrence and reoccurrence of both species were strongly influenced by characteristics at scales greater than the individual territory, indicating little support for the random-sample hypothesis. However, the type and spatial extent of landscape influence differed. Both occurrence and reoccurrence of Blackburnian Warblers were influenced by the amount of poor-quality matrix at 300- and 2000-m spatial extents. The occurrence and reoccurrence of Ovenbirds depended on a landscape pattern variable, patch size, but only in cases when patches were isolated. These results support the hypothesis that landscape pattern is important for some species only when the amount of suitable habitat is low. Although theoretical models have predicted such an interaction between landscape fragmentation and composition, to our knowledge this is the first study to report empirical evidence of such nonlinear fragmentation effects. Defining landscapes quantitatively from an organism-based perspective may increase power to detect fragmentation effects, particularly in forest mosaics where boundaries between patches and matrix are ambiguous. Our results indicate that manipulating landscape pattern may reduce negative impacts of habitat loss for Ovenbird, but not Blackburnian Warbler. We emphasize that most variance in the occurrence of both species was explained by local scale or landscape composition variables rather than variables reflecting landscape pattern.

Animals↗

PubMed2003

Modeling habitat suitability for moose in coastal northern Sweden: empirical vs process-oriented approaches.

Habitat models may provide viable tools for co-management of large ungulates and forest resources, yet their applicability has not been comprehensively evaluated in managed forest. We examined 2 inherently different approaches to model the relative winter habitat suitability for moose (Alces alces) in the coastal area of northern Sweden. An empirical approach based on GPS positions of 15 female moose was used to scrutinize the assumptions and functional mechanisms of a process-oriented, conceptual approach, based on published material on the species' preferences for habitat components related to food and cover. For both model approaches habitat was described using estimates of forest-stand characteristics based on satellite imagery. The empirical model also included variables relating to topographic properties of the landscape as well as distances to landscape features. The output from both models was a habitat suitability index (HSI) score, enabling the models to be compared with each other. The models showed different results, highlighting the need to include the spatially explicit distribution of environmental variables in future conceptual, process-oriented models.

Animals↗

PubMed1979

Fission models of population variability.

Most models in population genetics are models of allele frequency, making implicit or explicit assumptions of equilibrium or constant population size. In recent papers, we have attempted to develop more appropriate models for the analysis of rare variant data in South American Indian tribes; these are branching process models for the total number of replicates of a variant allele. The spatial distribution of a variant may convey information about its history and characteristics, and this paper extends previous models to take this factor into consideration. A model of fission into subdivisions is superimposed on the previous branching process, and variation between subdivisions is considered. The case where fission is nonrandom and the locations of like alleles are initially positively associated, as would happen were a tribal cluster or village to split on familial lines, is also analyzed. The statistics developed are applied to Yanomama Indian data on rare genetic variants. Due to insufficient time depth, no definitive new inferences can be drawn, but the analysis shows that this model provides results consistent with previous conclusions, and demonstrates the general type of question that may be answered by the approach taken here. In particular, striking confirmation of a higher-than-average growth rate, and hence smaller-than-previously-estimated age, is obtained for the Yan2 serum albumen variant.

Biological Evolution↗

PubMed2004

Evaluation of syndromic surveillance systems--design of an epidemic simulation model.

INTRODUCTION: The paucity of outbreak data from biologic terrorism and emerging infectious diseases limits the evaluation of syndromic surveillance systems. Evaluation using naturally occurring outbreaks of proxy disease (e.g., influenza) is one alternative but does not allow for rigorous evaluation. Another approach is to inject simulated outbreaks into real background data, but existing simulation models generally do not account for such factors as spatial mobility and do not explicitly incorporate knowledge of the disease agent. OBJECTIVE: The objective of this analysis was to design a simulated anthrax epidemic injection model that accounts for the complexity of the background data and enables sensitivity analyses based on uncertain disease-agent characteristics. MODEL REQUIREMENTS AND ASSUMPTIONS: Model requirements are described and used to limit the scope of model development. Major assumptions used to limit model complexity are also described. Available literature on inhalational anthrax is reviewed to ensure that the level of model detail reflects available disease knowledge. MODEL DESIGN: The model is divided into four components: 1) agent dispersion, 2) infection, 3) disease and behavior, and 4) data source. The agent-dispersion component uses a Gaussian plume model to compute spore counts on a fine grid. The infection component uses a cohort approach to identify infected persons by residential zip code, accounting for demographic covariates and spatial mobility. The disease and behavior component uses a discrete-event approach to simulate progression through disease stages and health-services utilization. The data-source component generates records to insert into background data sources. CONCLUSIONS: An epidemic simulation model was designed to enable evaluation of syndromic surveillance systems. The model addresses limitations of existing simulation approaches by accounting for such factors as spatial mobility and by explicitly modeling disease knowledge. Subsequent work entails software implementation and model validation.

Anthrax↗

PubMed2005

Reserve selection using nonlinear species distribution models.

Reserve design is concerned with optimal selection of sites for new conservation areas. Spatial reserve design explicitly considers the spatial pattern of the proposed reserve network and the effects of that pattern on reserve cost and/or ability to maintain species there. The vast majority of reserve selection formulations have assumed a linear problem structure, which effectively means that the biological value of a potential reserve site does not depend on the pattern of selected cells. However, spatial population dynamics and autocorrelation cause the biological values of neighboring sites to be interdependent. Habitat degradation may have indirect negative effects on biodiversity in areas neighboring the degraded site as a result of, for example, negative edge effects or lower permeability for animal movement. In this study, I present a formulation and a spatial optimization algorithm for nonlinear reserve selection problems in grid-based landscapes that accounts for interdependent site values. The method is demonstrated using habitat maps and nonlinear habitat models for threatened birds in the Netherlands, and it is shown that near-optimal solutions are found for regions consisting of up to hundreds of thousands grid cells, a landscape size much larger than those commonly attempted even with linear reserve selection formulations.

Algorithms↗

PubMed2005

Position, direction of movement, and speed tuning of cerebellar Purkinje cells during circular manual tracking in monkey.

The cerebellum plays an essential role in pursuit tracking with the eye and with the hand. During smooth pursuit eye movements, both tracking position and velocity are signaled by Purkinje cells. Purkinje cell simple spike discharge is also modulated by direction and speed during linear manual tracking. This study evaluated how all three parameters, position, movement direction, and speed, are signaled in the simple spike discharge of Purkinje cells during circular manual tracking. Three rhesus monkeys intercepted and then tracked a target moving in a circle in both counterclockwise and clockwise directions across a range of constant target speeds. Two sets of analyses of the simple spike firing of 97 Purkinje cells examined the effects of position, movement direction, and speed. The first approach was the incremental improvement of regression models, initially modeling a pure position dependence, then incorporating movement direction, and finally incorporating speed dependence. The second was a model-independent approach, without any explicit assumptions about the character of the directional tuning or speed effects. Both analyses revealed the same three results: (1) Purkinje cell discharge is spatially tuned, to both the position and direction of movement, and (2) this spatial tuning is not altered by the speed, except (3) the speed scales the average firing and/or depth of modulation. The results suggest that the population of Purkinje cells forms a representation of the entire position-direction space of arm movements, and that the speed modulates the scale of that representation. This speed scaling provides insights into the cerebellar processing of movement-related timing.

Action Potentials↗

PubMed2004

Spatially explicit analyses unveil density dependence.

Density-dependent processes are fundamental in the understanding of species population dynamics. Whereas the benefits of considering the spatial dimension in population biology are widely acknowledged, the implications of doing so for the statistical detection of spatial density dependence have not been examined. The outcome of traditional tests may therefore differ from those that include ecologically relevant locational information on both the prey species and natural enemy. Here, we explicitly incorporate spatial information on individual counts when testing for density dependence between an insect herbivore and its parasitoids. The spatially explicit approach used identified significant density dependence more frequently and in different instances than traditional methods. The form of density dependence detected also differed between methods. These results demonstrate that the explicit consideration of patch location in density-dependence analyses is likely to significantly alter current understanding of the prevalence and form of spatial density dependence in natural populations.

Animals↗

PubMed2006

Effects of temporal and spatial heterogeneities created by consumer-driven nutrient recycling on algal diversity.

A spatially explicit plant-herbivore model composed of planktonic herbivores, algal preys and nutrients was constructed to examine the effects of consumer-driven nutrient recycling (CNR) on the algal species richness with and without spatial structure. The model assumed that either of two essential nutrients (N and P) limited growth of algal populations and that consumer individuals moved randomly in the lattice and grazed all the algal species with the same efficiency. The results showed that when there was no CNR, the number of persistent algal species was affected by neither supply rates of external nutrients nor spatial structure and was consistently low. When consumers recycled nutrients according to their stoichiometry, the algal species richness changed with supply rates of external nutrients depending on spatial structure: the algal species richness decreased with increasing nutrient loadings when there were no spatial structure because CNR increased the probability of stochastic extinction of algal species by amplifying the oscillation of algae-consumer dynamics. However, when spatial structures were created by the migration of consumers, CNR increased the algal species richness in a range of nutrient loadings because spatial variation of grazing pressure functioned to stabilize the algal-consumer dynamics. The present study suggests that through grazing and nutrient recycling, consumer individuals can create ephemeral heterogeneity in growth environments for algal species and that this ephemerality is one of the keys to understanding algal species in nature.

Animals↗