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Results for “spatially explicit population models”

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PubMed2006

Building statistical models to analyze species distributions.

Models of the geographic distributions of species have wide application in ecology. But the nonspatial, single-level, regression models that ecologists have often employed do not deal with problems of irregular sampling intensity or spatial dependence, and do not adequately quantify uncertainty. We show here how to build statistical models that can handle these features of spatial prediction and provide richer, more powerful inference about species niche relations, distributions, and the effects of human disturbance. We begin with a familiar generalized linear model and build in additional features, including spatial random effects and hierarchical levels. Since these models are fully specified statistical models, we show that it is possible to add complexity without sacrificing interpretability. This step-by-step approach, together with attached code that implements a simple, spatially explicit, regression model, is structured to facilitate self-teaching. All models are developed in a Bayesian framework. We assess the performance of the models by using them to predict the distributions of two plant species (Proteaceae) from South Africa's Cape Floristic Region. We demonstrate that making distribution models spatially explicit can be essential for accurately characterizing the environmental response of species, predicting their probability of occurrence, and assessing uncertainty in the model results. Adding hierarchical levels to the models has further advantages in allowing human transformation of the landscape to be taken into account, as well as additional features of the sampling process.

Bayes Theorem↗

PubMed1982

On population growth of cities in a region: a stochastic nonlinear model.

"A stochastic migration model describing the population dynamics in a region is investigated. The model is described by a pair of coupled differential equations with state-dependent stochasticity. Explicit expressions for the time evolution of the moments for the population sizes of cities are obtained from the Fokker-Planck equation. The Stratonovich calculus is employed in the analysis."

Demography↗

PubMed1998

The Unit of Selection in Viscous Populations and the Evolution of Altruism.

Group selection can overcome individual selection for selfishness and favour altruism if there is variation among the founders of the spatially distinct groups, and groups with many altruists become substantially larger (or exist longer) than groups with few. Whether altruism can evolve in populations that do not have an alternation of local population growth and global dispersal ("viscous populations") has been disputed for some time. Limited dispersal protects the altruists from the non-altruists, but also hinders the export of altruism. In this article, we used the Pair Approximation technique (tracking the dynamics of pairs of neighbours instead of single individuals) to derive explicit invasion conditions for rare mutants in populations with limited dispersal. In such viscous populations, invading mutants form clusters, and ultimately, invasion conditions depend on the properties of such clusters. Thus there is selection on a higher level than that of the individual; in fact, invasion conditions define the unit of selection in viscous populations. We treat the evolution of altruism as a specific example, but the method is of more general interest. In particular, an important advantage is that the spatial aspects can be incorporated into game theory in a straightforward fashion; we will specify the ESS for a more general model. The invasion condition can be interpreted in terms of inclusive fitness. In contrast with Hamilton's model, the coefficient of relatedness is not merely a given genetical constant but depends on local population dynamical processes (birth, dispersal and death of individuals). With a simple birth rate function, Hamilton's rule is recovered: the cost to the donor should be less than the benefit to the recipient weighted with the coefficient of relatedness. As the coefficient of relatedness is roughly proportional to an individual's number of neighbours, benefits to the recipient must be substantial to outweigh the costs, confirming earlier studies. We discuss the consequences for the evolution of dispersal and outline how the method may be extended to study evolution in interacting populations.Copyright 1998 Academic Press

Journal Article↗

PubMedDate not supplied

[Explicit model for searching behavior of predator].

The authors present an approach for explicit modeling of spatio-temporal dynamics of predator-prey community. This approach is based on a reaction-diffusion-adjection PD (prey dependent) system. Local kinetics of population is determined by logistic reproduction function of prey, constant natural mortality of predator and Holling type 2 trophic function. Searching behavior of predator is described by the advective term in predator balance equation assuming the predator acceleration to be proportional to the prey density gradient. The model was studied with zero-flux boundary conditions. The influence of predator searching activity on the community dynamics, in particular, on the emergence of spatial heterogeneity, has been investigated by linear analysis and numerical simulations. It has been shown how searching activity may effect the persistence of species, stabilizing predator-prey interactions at very low level of pest density. It has been demonstrated that obtaining of such dynamic regimes does not require the use of complex trophic functions.

Animals↗

PubMed2002

A Bayesian model for spatial wildlife disease prevalence data.

The analysis of the geographical distribution of disease on the scale of geographic areas such as administrative boundaries plays an important role in veterinary epidemiology. Prevalence estimates of wildlife population surveys are often based on regional count data generated by sampling animals shot by hunters. The observed disease rate per spatial unit is not an useful estimate of the underlying disease prevalence due to different sample sizes and spatial dependencies between neighbouring areas. Therefore, it is necessary to account for extra-sample variation and spatial correlations in the data to produce more accurate maps of disease incidence. The detection of spatial patterns is complicated by missing data in many of the geographical areas as the complete coverage of all areas is nearly impossible in wildlife surveys. For this purpose a hierarchical Bayesian model in which structured and unstructured over dispersion is modelled explicitly in terms of spatial and non-spatial components was implemented by Markov chain Monte Carlo methods. The model was empirically compared with the results of a non-spatial beta-binomial model using surveillance data of pseudorabies virus infections of European wild boars (Sus scrofa scrofa L.) in the Federal State of Brandenburg, Germany.

Animal Diseases↗

PubMed1997

Model with distributed vectorial premotor bursters accounts for the component stretching of oblique saccades.

During oblique saccades, the durations of the horizontal and vertical components are stretched until they are approximately equal. Models of the saccadic system have been proposed that provide a mechanism for that stretching. However, they fail to simulate the pattern of activity recorded from premotor medium lead burst neurons (MLBNs) in the brain stem. A new model of the saccadic system is proposed that accounts for both the component stretching of oblique movements and the pattern of activity recorded in MLBNs. MLBNs that project to horizontal (or vertical) motoneurons actually have a wide span of on-directions (the direction associated with the largest discharge) around the cardinal direction. We infer from the wide span of their on-directions that, at the level of individual MLBNs, the vectorial signal present in spatially organized structures (e.g., the superior colliculus) is not decomposed into the separate horizontal and vertical components represented by the motoneurons. Nonetheless, all prior models of the saccadic system have decomposed the vectorial premotor command into horizontal and vertical commands at the level of the MLBNs. That decomposition was explicit, because individual MLBNs, with a sine- or cosine-shaped directional tuning curve, were used. We propose here that the decomposition into horizontal and vertical commands is carried out only at the level of the motoneurons. This decomposition is implicit, because no single MLBN encodes the horizontal or vertical command; the command only exists implicitly in the activity of the population of MLBNs. The new vectorial burster model correctly simulates the pattern of activity recorded in primate MLBNs, and the components of its oblique saccades are stretched. Two mechanisms contribute to this stretching: the distribution of MLBN tuning curves and the inhibition exerted by the contralateral population of MLBNs. In contrast, feedback control of the saccade contributes negligibly to the stretching. Even though the vectorial burster model predicts a component stretching, it is not constrained to produce perfectly straight oblique saccades because no trajectory control is implemented. The amount of curvature depends on the similarity of the horizontal and vertical systems (both neural and mechanical). In this model, stretching is interpreted simply as a side effect of the properties of the MLBNs' tuning curves. The distributed MLBNs of the vectorial burster model forces the general organization of the saccadic system to be reconsidered. We propose that a distributed architecture in which several different neural systems cooperate is needed.

Computer Simulation↗

PubMed1999

A Tridimensional Self-Thinning Model for Multilayered Intertidal Mussels.

Intertidal mussels usually form complex multilayered matrices with density-dependent effects on survival and growth, and self-thinning scaling between biomass (B) and density (N) is expected. This article develops a tridimensional model of space-driven self-thinning that in addition to B-N explicitly includes the degree of packing of the mussels, measured as the number of layers (L). The structure of our model (B-N-L) encompasses previous bidimensional models (B-N) of self-thinning as special cases and enables comparisons between mono- and multilayered populations. We contrast the predictions of the bi- and tridimensional models using data obtained from Perumytilus purpuratus mussel beds on the rocky shores of central Chile monitored during a 28-mo period. The tridimensional model suggests that density dependence is much more frequent than hitherto indicated by bidimensional models. We propose that our space-driven tridimensional model may be applied not only to mussels but also to other species where spatial overlapping configurations occur.

food driven↗

PubMed2003

Coevolution between hosts and parasites with partially overlapping geographic ranges.

Many host species interact with a specific parasite within only a fraction of their geographical range. Where host and parasite overlap geographically, selection may be reciprocal constituting a coevolutionary hot spot. Host evolution, however, may be driven primarily by selection imposed by alternative biotic or abiotic factors that occur outside such hot spots. To evaluate the importance of coevolutionary hot spots for host and parasite evolution, we analyse a spatially explicit genetic model for a host that overlaps with a parasite in only part of its geographical range. Our results show that there is a critical amount of overlap beyond which reciprocal selection leads to a coevolutionary response in the host. This critical amount of overlap depends upon the explicit spatial configuration of hot spots. When the amount of overlap exceeds this first critical level, host-parasite coevolution commonly generates stable allele frequency clines rather than oscillations. It is within this region that one of the primary predictions of the geographic mosaic theory is realized, and local maladaptation is prevalent in both species. Past a further threshold of overlap between the species oscillations do evolve, but allele frequencies in both species are spatially synchronous and local maladaptation is absent in both species. A consequence of such transitions between coevolutionary dynamics is that parasite adaptation is inversely proportional to the fraction of its host's range that it occupies. Hence, as the geographical range of a parasite increases, it becomes increasingly maladapted to the host. This suggests a novel mechanism through which the geographical range of parasites may be limited.

Animals↗

PubMed2006

The comparative evidence relating to functional and neutral interpretations of biological communities.

Neutral and functional theories provide rival interpretations of community patterns involving distribution, abundance, and diversity. One group of patterns describes the overall properties of species or sites, and derives principally from the frequency distribution of abundance among species. According to neutral theory, these patterns are determined by the number of individuals of novel type appearing each generation in the community, whereas functional theory relates them to the distribution of the extent of niches. A second group of patterns describes the spatial attributes of communities, and derives principally from the decay of similarity in species composition with distance. Neutral theory interprets these patterns as consequences of local dispersal alone, whereas the functional interpretation is that more distant sites are likely to be ecologically different. Neutral theory often provides good predictions of community patterns, yet is at variance with a wide range of experimental results involving the manipulation of environments or communities. One explanation for this discrepancy is that spatially explicit models where selection is generally weak, or where selection acts strongly on only a few species at each site, have essentially the same output as neutral models with respect to the distribution of abundance and the decay of similarity. Detecting a non-neutral signal in survey data requires careful spatial or phylogenetic analysis; we emphasize the potential utility of incorporating phylogenetic information in order to detect functional processes that lead to ecological variation among clades.

Biodiversity↗

PubMed2002

Spreading speed and linear determinacy for two-species competition models.

One crucial measure of a species' invasiveness is the rate at which it spreads into a competitor's environment. A heuristic spread rate formula for a spatially explicit, two-species competition model relies on 'linear determinacy' which equates spread rate in the full nonlinear model with spread rate in the system linearized about the leading edge of the invasion. However, linear determinacy is not always valid for two-species competition; it has been shown numerically that the formula only works for certain values of model parameters when the model is diffusive Lotka-Volterra competition [2]. This paper derives a set of sufficient conditions for linear determinacy in spatially explicit two-species competition models. These conditions can be interpreted as requiring sufficiently large dispersal of the invader relative to dispersal of the out-competed resident and sufficiently weak interactions between the resident and the invader. When these conditions are not satisfied, spread rate may exceed linearly determined predictions. The mathematical methods rely on the application of results established in a companion paper [11].

Animals↗

PubMed2004

Coexistence of cycling and dispersing consumer species: Armstrong and McGehee in space.

Two competing consumer species may coexist using a single homogeneous resource when the more efficient consumer--the one having the lowest equilibrium resource density--has a more nonlinear functional response that generates consumer-resource cycles. We extend this model of nonequilibrium coexistence, as proposed by Armstrong and McGehee, by putting the interaction into a spatial context using two frameworks: a spatially explicit individual-based model and a spatially implicit metapopulation model. We find that Armstrong and McGehee's mechanism of coexistence can operate in a spatial context. However, individual-based simulations suggest that decreased dispersal restricts coexistence in most cases, whereas differential equation models of metapopulations suggest that a low rate of dispersal between subpopulations often increases the coexistence region. This difference arises in part because of two potentially opposing effects on coexistence due to the asynchrony in the temporal dynamics at different locations. Asynchrony implies that the less efficient species is more likely to be favored in some spatial locations at any given time, which broadens the conditions for coexistence. On the other hand, asynchrony and dispersal can also reduce the amplitude of local population cycles, which restricts coexistence. The relative influence of these two effects depends on details of the population dynamics and the representation of space. Our results also demonstrate that coexistence via the Armstrong-McGehee mechanism can occur even when there is little variation in the global densities of either the consumers or the resource, suggesting that empirical studies of the mechanisms should measure densities on several spatial scales.

Animal Migration↗

PubMed1980

Diffusion model for genotype-dependent migration.

A diffusion model for the joint action of genotype-dependent migration and genotype-independent population regulation is derived and investigated. The diploid, monoecious population occupies a finite chain of equally spaced colonies; generations are discrete and nonoverlapping; mating is random in each colony. A boundary-value problem is deduced for the gene frequencies at a multiallelic locus in the absence of mutation, selection, and random drift. This problem is studied for two alleles and constant and uniform population density and drift and diffusion coefficients. All equilibria are shown to be monotone, and explicit conditions for a protected polymorphism are established. Two examples of asymptotically stable clines are presented. It is demonstrated that genotype dependence of the mean displacements is necessary to produce or maintain spatial differentiation of gene frequencies.

Journal Article↗

PubMed1978

Predicting the response time of an urban ambulance system.

Response time, i.e., the time from dispatch of an ambulance to its arrival at the scene of an emergency, is an important measure of performance in an urban ambulance system. We developed a model that predicts the entire distribution of response time, explicitly accounting for the rate and spatial distribution of demand, variable ambulance velocities, and queueing effects. We tested the model using data sampled from 3,936 ambulance runs in Houston and achieved close agreement between empirical and predicted distributions of response time. Our use of probability theory to predict response times yielded a model that complements those previously reported for planning and evaluating urban ambulance systems.

Ambulances↗

PubMed2006

Interactive effects of natural and human disturbances on vegetation dynamics across landscapes.

Accurate measures of human effects on landscape processes require consideration of both the direct impacts from human activities and the indirect consequences of the interactions between humans and the landscape. This is particularly evident in systems experiencing regular natural disturbances such as in the mountainous areas of southwestern China, where the remaining population of giant pandas (Ailuropoda melanoleuca) is supported. Here the spatiotemporal patterns of human impacts, forests, and bamboo episodic die-offs combine to determine the distribution of panda habitat. To study the complex interactions of humans and landscapes, we developed an integrated spatiotemporally explicit model of household activities, natural vegetation dynamics, and their impacts on panda habitat. Using this model we examined the direct consequences of local fuelwood collection and household creation on areas of critical giant panda habitat and the indirect impacts when coupled with vegetation dynamics. Through simulations, we found that over the next 30 years household impacts would result in the loss of up to 30% of the habitat relied on by pandas during past bamboo die-offs. The accumulation and spatial distribution of household impacts would also have a considerable indirect influence on the spatial distribution of understory bamboo. While human impacts influence both bamboo die-off and regeneration, over 19% of pre-existing low-elevation bamboo habitat may be lost following an episodic die-off depending on the severity of the impacts and timing of the die-offs. Our study showed not only the importance of the spatial distribution of direct household impacts on habitat, but also the far-reaching effects of the indirect interactions between humans and the landscapes they are modifying.

Animals↗

PubMed2006

The effects of prey patchiness, predator aggregation, and mutual interference on the functional response of Phytoseiulus persimilis feeding on Tetranychus urticae (Acari: Phytoseiidae, Tetranychidae).

The spatial distributions of two-spotted spider mites Tetranychus urticae and their natural enemy, the phytoseiid predator Phytoseiulus persimilis, were studied on six full-grown cucumber plants. Both mite species were very patchily distributed and P. persimilis tended to aggregate on leaves with abundant prey. The effects of non-homogenous distributions and degree of spatial overlap between prey and predators on the per capita predation rate were studied by means of a stage-specific predation model that averages the predation rates over all the local populations inhabiting the individual leaves. The empirical predation rates were compared with predictions assuming random predator search and/or an even distribution of prey. The analysis clearly shows that the ability of the predators to search non-randomly increases their predation rate. On the other hand, the prey may gain if it adopts a more even distribution when its density is low and a more patchy distribution when density increases. Mutual interference between searching predators reduces the predation rate, but the effect is negligible. The stage-specific functional response model was compared with two simpler models without explicit stage structure. Both unstructured models yielded predictions that were quite similar to those of the stage-structured model.

Animals↗

PubMed2005

Pair statistics clarify percolation properties of spatially explicit simulations.

Dispersal is a fundamental control on the spatial structure of a population. We investigate the precise mechanism by which a mixed strategy of short- and long-distance dispersal affects spatial patterning. Using techniques from pair approximation and percolation theory, we demonstrate that dispersal controls the extent to which a population is completely connected by modulating the proportion of neighboring sites which are simultaneously occupied. We show that near the percolation threshold this pair statistic, rather than other metrics proposed earlier, best explains clustering, and we suggest more general circumstances under which this may hold.

Cluster Analysis↗

PubMed2006

The impact of exploiting grazers (Scaridae) on the dynamics of Caribbean coral reefs.

Coral reefs provide a number of ecosystem services including coastal defense from storms, the generation of building materials, and fisheries. It is increasingly clear that the management of reef resources requires an ecosystem approach in which extractive activities are weighed against the needs of the ecosystem and its functions rather than solely those of the fishery. Here, I use a spatially explicit simulation model of a Caribbean coral reef to examine the ecosystem requirements for grazing which is primarily conducted by parrotfishes (Scaridae). The model allows the impact of fishing grazers to be assessed in the wider context of other ecosystem processes including coral-algal competition, hurricanes, and mass extinction of the herbivorous urchin Diadema antillarum. Using a new analytical model of scarid grazing, it is estimated that parrotfishes can only maintain between 10% and 30% of a structurally complex forereef in a grazed state. Predictions from this grazing model were then incorporated into a broader simulation model of the ecosystem. Simulations predict that scarid grazing is unable to maintain high levels of coral cover (> or = 30%) when severe hurricanes occur on a decadal basis, such as occurs in parts of the northern Caribbean. However, reefs can withstand such intense disturbance when grazing is undertaken by both scarids and the urchin Diadema. Scarid grazing is predicted to allow recovery from hurricanes when their incidence falls to 20 years or less (e.g., most of Central and South America). Sensitivity analyses revealed that scarid grazing had the most acute impact on model behavior, and depletion led to the emergence of a stable, algal-dominated community state. Under conditions of heavy grazer depletion, coral cover was predicted to decline rapidly from an initial level of 30% to less than 1% within 40 years, even when hurricane frequency was low at 60 years. Depleted grazers caused a population bottleneck in juvenile corals in which algal overgrowth caused elevated levels of postsettlement mortality and resulted in a bimodal distribution of coral sizes. Several new hypotheses were generated including a region-wide change in the spatial heterogeneity of coral reefs following extinction of Diadema. The management of parrotfishes on Caribbean reefs is usually approached implicitly through no-take marine reserves. The model predicts that depletion of grazers in nonreserve areas can severely limit coral accretion. Other studies have shown that low coral accretion can reduce the structural complexity and therefore quality of the reef habitat for many organisms. A speculative yet rational inference from the model is that failure to manage scarid populations outside reserves will have a profoundly negative impact on the functioning of the reserve system and status of non-reserve reefs.

Animals↗

PubMed1992

Migration decisions and site-specific attributes of public policy: microeconomic evidence from the NLSY.

The authors examine the linkage between household location decisions in the United States and county-level public sector attributes. "This paper demonstrates a relationship between migration and public policy and suggests a role for migration in regional development.... We link migration to public policy by treating tax and expenditure variables as site attributes in a utility maximization model. We find that public sector attributes, through their effect on migration, are among the determinants of regional development.... An additional contribution of this paper is to suggest that if taxes and public expenditures influence migration, then a general theory of local or regional policy aimed at economic development must include explicit consideration of migration." Microdata from the 1984-1985 U.S. National Longitudinal Survey of Youth (NLSY) are analyzed.

Adolescent↗