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Results for “spatially explicit population models”

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PubMed2002

Neutral evolution in spatially continuous populations.

We introduce a general recursion for the probability of identity in state of two individuals sampled from a population subject to mutation, migration, and random drift in a two-dimensional continuum. The recursion allows for the interactions induced by density-dependent regulation of the population, which are inevitable in a continuous population. We give explicit series expansions for large neighbourhood size and for low mutation rates respectively and investigate the accuracy of the classical Malécot formula for these general models. When neighbourhood size is small, this formula does not give the identity even over large scales. However, for large neighbourhood size, it is an accurate approximation which summarises the local population structure in terms of three quantities: the effective dispersal rate, sigma(e); the effective population density, rho(e); and a local scale, kappa, at which local interactions become significant. The results are illustrated by simulations.

Alleles↗

PubMed2003

A spatially explicit model simulating western corn rootworm (Coleoptera: Chrysomelidae) adaptation to insect-resistant maize.

A stochastic spatially explicit computer model is described that simulates the adaptation by western corn rootworm, Diabrotica virgifera virgifera LeConte, to rootworm-resistance traits in maize. The model reflects the ecology of the rootworm in much of the corn belt of the United States. It includes functions for crop development, egg and larval mortality, adult emergence, mating, egg laying, mortality and dispersal, and alternative methods of rootworm control, to simulate the population dynamics of the rootworm. Adaptation to the resistance trait is assumed to be controlled by a monogenic diallelic locus, whereby the allele for adaptation varies from incompletely recessive to incompletely dominant, depending on the efficacy of the resistance trait. The model was used to compare the rate at which the adaptation allele spread through the population under different nonresistant maize refuge deployment scenarios, and under different levels of crop resistance. For a given refuge size, the model indicated that placing the nonresistant refuge in a block within a rootworm-resistant field would be likely to delay rootworm adaptation rather longer than planting the refuge in separate fields in varying locations. If a portion of the refuge were to be planted in the same fields or in-field blocks each year, rootworm adaptation would be delayed substantially. Rootworm adaptation rates are also predicted to be greatly affected by the level of crop resistance, because of the expectation of dependence of functional dominance on dose. If the dose of the insecticidal protein in the maize is sufficiently high to kill >90% of heterozygotes and approximately 100% of susceptible homozygotes, the trait is predicted to be much more durable than if the dose is lower. A partial sensitivity analysis showed that parameters relating to adult dispersal affected the rate of pest adaptation. Partial validation of the model was achieved by comparing output of the model with field data on population dynamics, and with field data documenting rootworm adaptation to cyclodienes and organophosphates.

Adaptation, Physiological↗

PubMed2006

Fast approximate calculation of multiply scattered lidar returns.

An efficient method is described for the approximate calculation of the intensity of multiply scattered lidar returns. It divides the outgoing photons into three populations, representing those that have experienced zero, one, and more than one forward-scattering event. Each population is parameterized at each range gate by its total energy, its spatial variance, the variance of photon direction, and the covariance of photon direction and position. The result is that for an N-point profile the calculation is O(N2) efficient and implicitly includes up to N-order scattering, making it ideal for use in iterative retrieval algorithms for which speed is crucial. In contrast, models that explicitly consider each scattering order separately are at best O(Nm/m!) efficient for m-order scattering and often cannot be performed to more than the third or fourth order in retrieval algorithms. For typical cloud profiles and a wide range of lidar fields of view, the new algorithm is as accurate as an explicit calculation truncated at the fifth or sixth order but faster by several orders of magnitude.

Journal Article↗

PubMed2002

When and where was the most recent common ancestor?

The structured coalescent is investigated for single-locus, digenic samples in the diffusion limit of the unidimensional stepping-stone model for homogeneous, isotropic migration and random genetic drift. Let T denote the scaled time to the most recent common ancestor (MRCA) of the two genes, and let Z designate the scaled deviation of the position of the MRCA from the average position of the two genes. The joint probability density of T and Z is evaluated explicitly. Both the marginal and conditional distributions of T have infinite expectation, as does the marginal distribution of Z. Conditioned on T = tau, the distribution of Z is Gaussian with mean zero and variance 2tau. The main results are extended to anisotropic migration. The results establish the existence of and define in the diffusion limit a retrospective stochastic process for digenic samples in one spatial dimension.

Animals↗

PubMed2002

Small-scale structure of nonlinearly interacting species advected by chaotic flows.

We study the spatial patterns formed by interacting biological populations or reacting chemicals under the influence of chaotic flows. Multiple species and nonlinear interactions are explicitly considered, as well as cases of smooth and nonsmooth forcing sources. The small-scale structure can be obtained in terms of characteristic Lyapunov exponents of the flow and of the chemical dynamics. Different kinds of morphological transitions are identified. Numerical results from a three-component plankton dynamics model support the theory, and they serve also to illustrate the influence of asymmetric couplings. (c) 2002 American Institute of Physics.

Journal Article↗

PubMed2006

Mathematical modelling of the loss of tissue compression responsiveness and its role in solid tumour development.

This paper presents a mathematical model of normal and abnormal tissue growth. The modelling focuses on the potential role that stress responsiveness may play in causing proliferative disorders which are at the basis of the development of avascular tumours. In particular, we study how an incorrect sensing of its compression state by a cell population can represent a clonal advantage and can generate hyperplasia and tumour growth with well-known characteristics such as compression of the tissue, structural changes in the extracellular matrix, change in the percentage of cell type (normal or abnormal), extracellular matrix and extracellular liquid. A spatially independent description of the phenomenon is given initially by a system of non-linear ordinary differential equations which is explicitly solved in some cases of biological interest showing a first phase in which some abnormal cells simply replace the normal ones, a second phase in which the hyper-proliferation of the abnormal cells causes a progressive compression within the tissue itself and a third phase in which the tissue reaches a compressed state, which presses on the surrounding environment. A travelling wave analysis is also performed which gives an estimate of the velocity of the growing mass.

Cadherins↗

PubMed2005

Does quasi-local competition lead to pattern formation in metapopulations? An explicit resource competition model.

In metapopulations, competitive interactions may extend beyond the confines of the local population such that members of neighbouring habitat patches affect each other adversely (quasi-local competition). We derive a model for quasi-local competition from first principles, assuming that individuals compete for shared resources and members of a population spend a certain fraction of their foraging time in the adjacent populations. Contrary to the results of Doebeli and Killingback [2003. Theor. Popul. Biol. 64, 397-416], our model does not produce spatial patterns of population densities in homogeneous environments. Quasi-local competition nevertheless contributes to pattern formation by amplifying the effect of heterogeneities in the external environment, and this amplification can be extremely strong when dispersal is absent. We discuss why apparently similar models lead to contrasting results.

Competitive Behavior↗

PubMed2006

Contrasting patterns in the small-scale heterogeneity of human helminth infections in urban and rural environments in Brazil.

Marked heterogeneity exists in the patterns of parasitic infection between individuals, households and communities. Analysis of parasite distributions within populations is complicated by the fact that parasite distributions are highly aggregated and few studies have explicitly incorporated this distribution when investigating small-scale spatial heterogeneities. This study aimed to quantify the small-scale (within- and between-household) heterogeneity of helminth infection in an area of Minas Gerais State, Brazil, with rural and urban sectors. Parasitological data from a cross-sectional survey of 1,249 individuals aged 0-86 years from 242 households were analysed. Within-household clustering of infection was assessed using random effect logistic regression models and between-household spatial heterogeneity was assessed using a Bayesian negative binomial spatial model. The overall prevalence of hookworm (Necator americanus) was 66.9%, the prevalence of Schistosoma mansoni was 44.9% and the prevalence of Ascaris lumbricoides was 48.8%. Statistical analysis indicated significant (within) household and (between household) spatial clustering of hookworm in both rural and urban areas and of S. mansoni in rural areas. There was no evidence of either household or spatial clustering of S. mansoni in urban areas. The spatial correlation of S. mansoni was estimated to reduce by half over a distance of 700 m in the rural area. Rural hookworm had a much smaller half-distance (28 m) and urban hookworm showed an even smaller half-distance (12 m). We suggest that such species-specific differences in patterns of infection by environment are primarily due to variation in exposure and parasite life cycle, although host genetic factors cannot be ruled out.

Adolescent↗

PubMed1975

A theoretical note on sex linkage and race differences in spatial visualization ability.

Evidence on the poorer spatial visualization ability in various Negro populations compared to the white populations and on the direction and magnitude of sex difference in spatial ability relative to other abilities suggests the genetic hypothesis that spatial ability is enhanced by a sex-linked recessive gene and that, since the 20-30 percent admixture of Caucasian genes in American Negroes came mostly from male white ancestors, relatively fewer X-linked than autosomal Caucasian genes were transmitted to the American Negro gene pool. The genetic model as explicitly formulated indicates the kinds of data which could substantiate or disporve the theory, but which do not now exist.

Aptitude↗

PubMed2003

Taking malaria transmission out of the bottle: implications of mosquito dispersal for vector-control interventions.

Most malaria transmission models assume enclosed systems of people, parasites, and vectors in which neither emigration nor immigration of mosquitoes is considered. This simplification has facilitated insightful analyses but has substantial limitations for evaluating control measures in the field. Here we show that mosquito dispersal can confound conventional approaches to evaluating malaria vector-control interventions, and explore this association with a model of two villages between which mosquito subpopulation exchange occurs. Exchange of mosquitoes between such subpopulations can readily explain the discrepancy between experimental efficacy measurements for insecticide-treated nets and their much lower apparent effectiveness when in use. Our results indicate that current approaches to assessing malaria interventions that confer community-level protection may be severely compromised by mosquito dispersal in many endemic settings. The true effectiveness of many vector-control methods may be much greater than previously appreciated and the application of such interventions should be consolidated into larger contiguous spatial units so that more effective local suppression of malaria can be achieved. Spatially explicit modelling formats that consider vector dispersal as a determinant of malaria transmission and control are needed urgently for rational planning and evaluation of efforts to roll back malaria.

Animals↗

PubMed2004

Adult female voxel models of different stature and photon conversion coefficients for radiation protection.

This paper describes the construction of three adult female voxel models, two whole-body and one from head to thighs, from computed tomographic data of 3 women of different stature. Voxel models (also called phantoms) are human models based on computed tomographic or magnetic resonance images obtained from high resolution continuous scans of a single individual. The gray-scale data or information content of the medical images are interpreted into tissues (i.e., organs), a process known as segmentation. The phantoms, consisting of millions of volume elements, called voxels, provide a three-dimensional representation of the human body and the spatial form of its constituent organs and structures. They were initially developed for radiation protection purposes to estimate the organ and effective doses and hence the risk to a person or population due to an irradiation. This paper also presents conversion coefficients for idealized geometries of external photon exposures of energies 10 keV-1 MeV for the three female models, calculated with a Monte Carlo code. Until now there were not any published data on conversion coefficients for explicit female voxel models. Such sets of conversion coefficients exist for voxel adult males or for MIRD-type male, female, and hermaphrodite models. Numerical differences of the calculated conversion coefficients for the voxel female models and MIRD-type models can amount up to 60% or more for external exposures and are due to the improved anatomical realism of the voxel models. The size of the model also has an effect on the conversion coefficients, particularly for deeper lying organs and energies below 200 keV. The three separate sets of conversion coefficients allow one to choose the most suitable model according to the size of the individual as well as to study the dosimetric variations due to the size of the model.

Adult↗

PubMed2004

Spatial flows and the regulation of ecosystems.

Spatial flows of materials and organisms across ecosystem boundaries are ubiquitous. Understanding the consequences of these flows should be a basic goal of ecosystem science, and yet it has received scant theoretical treatment to date. Here, using a simple, open, nutrient-limited ecosystem model with trophic interactions, we explore theoretically how spatial flows affect the functioning of local ecosystems, how physical mass-balance constraints interact with biological demographic constraints in the regulation of this functioning, and how failure to consider these constraints explicitly can lead to models that are ecologically inconsistent. In particular, we show that standard prey-dependent models for trophic interactions may lead to implausible outcomes when embedded in an ecosystem context with appropriate mass flows and mass-balance constraints. Our analysis emphasizes the need for integration of population, community, and ecosystem perspectives in ecology and the critical consequences of assuming closed versus open systems.

Food Chain↗

PubMed2004

Platelet-wall interactions in continuum models of platelet thrombosis: formulation and numerical solution.

A model is developed to describe the formation of platelet thrombi in coronary-artery-sized blood vessels. It involves interactions among a viscous, incompressible fluid; populations of non-activated and activated platelets; activating chemicals; and the vessel walls. Adhesion of platelets to the injured wall and cohesion between activated platelets is modelled using distributions of elastic links which generate stresses that can influence the fluid motion. The first version of the model presented involves two spatial scales: the microscale of the platelets and the macroscale of the vessel. A closure approximation is introduced that allows essential microscale behaviour to be computed while eliminating the necessity to explicitly track events on this scale. Computational methods are presented that meet the diverse challenges posed by the coupled nonlinear partial differential equations of the model and by the complex geometry of the constricted vessels in which the thrombosis simulations are carried out. Simulation results demonstrate that the model can produce thrombi that grow to occlude the vessel, that shear-stress exerted by the fluid on the thrombi can modify their subsequent growth and cause remodelling of their shape through small-scale local changes or large-scale structural breakup.

Blood Platelets↗

PubMed2004

The evolution of reproductive restraint through social communication.

The evolution of altruistic behavior through group selection is generally viewed as possible in theory but unlikely in reality, because individual selection favoring selfish strategies should act more rapidly than group selection favoring cooperation. Here we demonstrate the evolution of altruism, in the form of conditional reproductive restraint based on an explicitly social mechanism, modulated by intrapopulation communication comprising signal and evolved response, in a spatially distributed predatory/parasitic/pathogenic model system. The predatory species consistently comes to exploit a signal implying overcrowding, individuals constraining their reproduction in response, with a corresponding increase in equilibrium reproduction rate in the absence of signal. This signaled restraint arises in a robust way for a range of model spatial systems; it outcompetes non-signal-based restraint and is not vulnerable to subversion by noncooperating variants. In these systems, communication is used to evaluate population density and regulate reproduction accordingly, consistent with central ideas of Wynne-Edwards [Wynne-Edwards, V. C. (1962) Animal Dispersion in Relation to Social Behavior (Hafner, New York)], whose claims about the evolutionary importance of group selection helped ignite decades of controversy. This quantitative simulation model shows how the key evolutionary transition from solitary living to sociality can occur. The process described here of cooperation evolving through communication may also help to explain other major evolutionary transitions such as intercellular communication leading to multicellular organisms.

Altruism↗

PubMed2003

Applicability of the Fisher equation to bacterial population dynamics.

The applicability of the Fisher equation, which combines diffusion with logistic nonlinearity, to population dynamics of bacterial colonies is studied with the help of explicit analytic solutions for the spatial distribution of a stationary bacterial population under a static mask. The mask protects bacteria from ultraviolet light. The solution, which is in terms of Jacobian elliptic functions, is used to provide a practical prescription to extract Fisher equation parameters from observations and to decide on the validity of the Fisher equation.

Bacteria↗

PubMed2004

Intrinsic scaling complexity in animal dispersion and abundance.

Ecological theory related to animal distribution and abundance is at present incomplete and to some extent naive. We suggest that this may partly be due to a long tradition in the field of model development for choosing mathematical and statistical tools for convenience rather than applicability. Real population dynamics are influenced by nonlinear interactions, nonequilibrium conditions, and scaling complexity from system openness. Thus, a coherent theory for individual-, population-, and community-level processes should rest on mathematical and statistical methods that explicitly confront these issues in a manner that satisfies principles from statistical mechanics for complex systems. Instead, ecological theory is traditionally based on premises from simpler statistical mechanical theory for memory-free, scale-specific, random-walk, and diffusion processes, while animals from many taxa generally express strategic homing, site fidelity, and conspecific attraction in direct violation of primary model assumptions. Thus, the main challenge is to generalize the theory for memory-free physical, many-body systems to include a more realistic memory-influenced framework that better satisfies ecological realism. We describe, simulate, and discuss three testable aspects of a model for multiscaled habitat use at the individual level: (1) scale-free distribution of movement steps under influence of self-reinforcing site fidelity, (2) fractal spatial dispersion of intra-home range relocations, and (3) nonasymptotic expansion of observed intra-home range patch use with increasing set of relocations. Examples of literature data apparently supporting the conjecture that multiscaled, strategic space use is widespread among many animal taxa are also described. We suggest that the present approach, which provides a protocol to test for influence from scale-free, memory-dependent habitat use at the individual level, may also point toward a guideline for development of a generalized theoretical framework for complex population kinetics and spatiotemporal population dynamics.

Animal Migration↗

PubMed2004

The effects of spatial movement and group interactions on disease dynamics of social animals.

The effects of spatial movements of infected and susceptible individuals on disease dynamics is not well understood. Empirical studies on the spatial spread of disease and behaviour of infected individuals are few and theoretical studies may be useful to explore different scenarios. Hence due to lack of detail in empirical studies, theoretical models have become necessary tools in investigating the disease influence in host-pathogen systems. In this paper we developed and analysed a spatially explicit model of two interacting social groups of animals of the same species. We investigated how the movement scenarios of susceptible and infected individuals together with the between-group contact parameter affect the survival rate of susceptible individuals in each group. This work can easily be applied to various host-pathogen systems. We define bounds on the number of susceptibles which avoid infection once the disease has died out as a function of the initial conditions and other model parameters. For example, once disease has passed through the populations, a larger diffusion coefficient for each group can result in higher population levels when there is no between-group interaction but in lower levels when there is between-group interaction. Numerical simulations are used to demonstrate these bounds and behaviours and to describe the different outcomes in ecological terms.

Animals↗

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↗