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PubMed2006

Putting the "landscape" in landscape genetics.

Landscape genetics has emerged as a new research area that integrates population genetics, landscape ecology and spatial statistics. Researchers in this field can combine the high resolution of genetic markers with spatial data and a variety of statistical methods to evaluate the role that landscape variables play in shaping genetic diversity and population structure. While interest in this research area is growing rapidly, our ability to fully utilize landscape data, test explicit hypotheses and truly integrate these diverse disciplines has lagged behind. Part of the current challenge in the development of the field of landscape genetics is bridging the communication and knowledge gap between these highly specific and technical disciplines. The goal of this review is to help bridge this gap by exposing geneticists to terminology, sampling methods and analysis techniques widely used in landscape ecology and spatial statistics but rarely addressed in the genetics literature. We offer a definition for the term "landscape genetics", provide an overview of the landscape genetics literature, give guidelines for appropriate sampling design and useful analysis techniques, and discuss future directions in the field. We hope, this review will stimulate increased dialog and enhance interdisciplinary collaborations advancing this exciting new field.

Animals↗

PubMed1987

Long-run urban growth with agglomeration economies.

"It is widely recognized that agglomeration economies are a crucially important factor in explaining the existence and growth of urban areas, and therefore should be explicitly taken into consideration in long-run urban growth analysis. Once such economies are introduced, however, the urban economy tends to diverge from a steady state equilibrium and may 'explode' without limit. A possible way to solve this dilemma is shown. First, a simple urban growth model with production and factor migration functions in the presence of agglomeration economies is set up....Then, land is introduced to show that the availability of the third factor of production will make it more likely to achieve a steady growth equilibrium in the presence of agglomeration economies. Last, the model is generalized to include many factors of production."

Agriculture↗

PubMed1998

Pattern formation in a patch occupancy metapopulation model: a cellular automata approach.

The explicit consideration of space in ecological research is of paramount importance to understand the structure and functioning of ecological systems. In this paper we develop a simple spatially explicit metapopulation model in which colonization is constant and independent of the number of occupied patches (i.e. propagule-rain effect, Gotelli, 1991). Extinction, on the other hand, is modelled as a stochastic process whose intensity depends on the number of occupied patches in the neighborhood of each focal patch. Our model is the CA counterpart of two classical patch occupancy metapopulation models. We analytically prove this by showing that our CA converges to the differential equation in the mean-field approximation. The asymptotic behaviour of the system, expressed as the proportion of occupied patches, agrees with the equilibrium proportion of patches derived by using ODEs. In both models, the existence of a rescue-effect increases the range of extinction and colonization parameters over which the system attains complete occupancy of patches. However, in our model this result is strongly influenced by the degree of coupling among patches and is apparent only for local interactions. With local interactions and particular parameter values of colonization and extinction, self-organized spatio-temporal patterns emerge with a fractal-like clustering, even though the environment is spatially homogeneous. Our results point out that the importance of being spatial and discrete (Durrett & Levin, 1994a) in our model is a result of local interactions.

Ecology↗

PubMed2006

A spatially explicit resource-based approach for managing stream fishes in riverscapes.

The article describes a riverscape approach based on landscape ecology concepts, which aims at studying the multiscale relationships between the spatial pattern of stream fish habitat patches and processes depending on fish movements. A review of the literature shows that few operational methods are available to study this relationship due to multiple methodological and practical challenges inherent to underwater environments. We illustrated the approach with literature data on a cyprinid species (Barbus barbus) and an actual riverscape of the Seine River, France. We represented the underwater environment of fishes for different discharges using two-dimensional geographic information system-based maps of the resource habitat patches, defined according to activities (feeding, resting, and spawning). To quantify spatial patterns at nested levels (resource habitat patch, daily activities area, subpopulation area), we calculated their composition, configuration, complementation, and connectivity with multiple spatial analysis methods: patch metrics, moving-window analysis, and least cost modeling. The proximity index allowed us to evaluate habitat patches of relatively great value, depending on their spatial context, which contributes to the setting of preservation policies. The methods presented to delimit potential daily activities areas and subpopulation areas showed the potential gaps in the biological connectivity of the reach. These methods provided some space for action in restoration schemes.

Animals↗

PubMed2006

Predicting the epidemiological impact of antiretroviral allocation strategies in KwaZulu-Natal: the effect of the urban-rural divide.

Antiretroviral therapy (ART) is becoming available in South Africa. Demand will exceed supply; thus, difficult decisions will have to be made in allocating ART. The majority of those treated for HIV are likely to be in cities, because health infrastructure and personnel are concentrated in urban centers. We predict the epidemiological impact of drug allocation strategies (DAS) by using a spatially explicit model that links urban and rural epidemics. We parameterize our model by using data from the KwaZulu-Natal province in South Africa. We model the South African government's treatment plan from 2004-2008, and we predict the consequences of one DAS that allocates drugs only to Durban and of two DAS that allocate drugs to both urban and rural areas. All three strategies would treat 500,000 people by 2008. Not surprisingly, the Durban-only DAS would prevent the greatest number of infections (an additional 15,000 infections by 2008). However, it may have been expected that this DAS would generate the highest levels of transmitted resistance, because it concentrates ART in one location. Paradoxically, we found that this DAS would generate the lowest levels of transmitted resistance. Concentrating treatment in Durban would also avert the greatest number of AIDS-related deaths. We discuss the difference between using the principle of treatment equity versus using the principle of utilitarianism/efficiency to allocate ART. Decisions about allocating scarce drugs should consider treatment equity as well as epidemiological consequences. Notably, a Durban-only DAS would lead to new disparities in healthcare between urban and rural areas in KwaZulu-Natal.

Anti-Retroviral Agents↗

PubMed1999

Spatial autocorrelation analysis of individual multiallele and multilocus genetic structure.

Population genetic theory predicts that plant populations will exhibit internal spatial autocorrelation when propagule flow is restricted, but as an empirical reality, spatial structure is rarely consistent across loci or sites, and is generally weak. A lack of sensitivity in the statistical procedures may explain the discrepancy. Most work to date, based on allozymes, has involved pattern analysis for individual alleles, but new PCR-based genetic markers are coming into vogue, with vastly increased numbers of alleles. The field is badly in need of an explicitly multivariate approach to autocorrelation analysis, and our purpose here is to introduce a new approach that is applicable to multiallelic codominant, multilocus arrays. The procedure treats the genetic data set as a whole, strengthening the spatial signal and reducing the stochastic (allele-to-allele, and locus-to-locus) noise. We (i) develop a very general multivariate method, based on genetic distance methods, (ii) illustrate it for multiallelic codominant loci, and (iii) provide nonparametric permutational testing procedures for the full correlogram. We illustrate the new method with an example data set from the orchid Caladenia tentaculata, for which we show (iv) how the multivariate treatment compares with the single-allele treatment, (v) that intermediate frequency alleles from highly polymorphic loci perform well and rare alleles poorly, (vi) that a multilocus treatment provides clearer answers than separate single-locus treatments, and (vii) that weighting alleles differentially improves our resolution minimally. The results, though specific to Caladenia, offer encouragement for wider application.

Alleles↗

PubMed2006

Predictors of concentrations of nitrogen dioxide, fine particulate matter, and particle constituents inside of lower socioeconomic status urban homes.

Air pollution exposure patterns may contribute to known spatial patterning of asthma morbidity within urban areas. While studies have evaluated the relationship between traffic and outdoor concentrations, few have considered indoor exposure patterns within low socioeconomic status (SES) urban communities. In this study, part of a prospective birth cohort study assessing asthma etiology in urban Boston, we collected indoor and outdoor 3-4 day samples of nitrogen dioxide (NO2) and fine particulate matter (PM2.5) in 43 residences across multiple seasons from 2003 to 2005. Homes were chosen to represent low SES households, including both cohort and non-cohort residences in similar neighborhoods, and consisted almost entirely of multiunit residences. Reflectance analysis and X-ray fluorescence spectroscopy were performed on the particle filters to determine elemental carbon (EC) and trace element concentrations, respectively. Additionally, information on home characteristics (e.g. type, age, stove fuel) and occupant behaviors (e.g. smoking, cooking, cleaning) were collected via a standardized questionnaire. The contributions of outdoor and indoor sources to indoor concentrations were quantified with regression analyses using mass balance principles. For NO2 and most particle constituents (except outdoor-dominated constituents like sulfur and vanadium), the addition of selected indoor source terms improved the model's predictive power. Cooking time, gas stove usage, occupant density, and humidifiers were identified as important contributors to indoor levels of various pollutants. A comparison between cohort and non-cohort participants provided another means to determine the influence of occupant activity patterns on indoor-outdoor ratios. Although the groups had similar housing characteristics and were located in similar neighborhoods, cohort members had significantly higher indoor concentrations of PM2.5 and NO2, associated with indoor activities. We conclude that the effect of indoor sources may be more pronounced in high-density multiunit dwellings, and that future epidemiological studies in these populations should explicitly consider these sources in assigning exposures.

Female↗

PubMed2006

Using habitat suitability index and particle dispersion models for early detection of marine invaders.

Eradication and control of invasive species are often possible only if populations are detected when they are small and localized. To be efficient, detection surveys should be targeted at locations where there is the greatest risk of incursions. We examine the utility of habitat suitability index (HSI) and particle dispersion models for targeting sampling for marine pests. Habitat suitability index models are a simple way to identify suitable habitat when species distribution data are lacking. We compared the performance of HSI models with statistical models derived from independent data from New Zealand on the distribution of two nonindigenous bivalves: Theora lubrica and Musculista senhousia. Logistic regression models developed using the HSI scores as predictors of the presence/absence of Theora and Musculista explained 26.7% and 6.2% of the deviance in the data, respectively. Odds ratios for the HSI scores were greater than unity, indicating that they were genuine predictors of the presence/ absence of each species. The fit and predictive accuracy of each logistic model were improved when simulated patterns of dispersion from the nearest port were added as a predictor variable. Nevertheless, the combined model explained, at best, 46.5% of the deviance in the distribution of Theora and correctly predicted 56% of true presences and 50% of all cases. Omission errors were between 6% and 16%. Although statistical distribution models built directly from environmental predictors always outperformed the equivalent HSI models, the gain in model fit and accuracy was modest. High residual deviance in both types of model suggests that the distributions realized by Theora and Musculista in the field data were influenced by factors not explicitly modeled as explanatory variables and by error in the environmental data used to project suitable habitat for the species. Our results highlight the difficulty of accurately predicting the distribution of invasive marine species that exhibit low habitat occupancy and patchy distributions in time and space. Although the HSI and statistical models had utility as predictors of the likely distribution of nonindigenous marine species, the level of spatial accuracy achieved with them may be well below expectations for sensitive surveillance programs.

Animals↗

PubMed1998

BacSim, a simulator for individual-based modelling of bacterial colony growth.

The generic, quantitative, spatially explicit, individual-based model BacSim was developed to simulate growth and behaviour of bacteria. The potential of this approach is in relating the properties of microscopic entities - cells - to the properties of macroscopic, complex systems such as biofilms. Here, the growth of a single Escherichia coli cell into a colony was studied. The object-oriented program BacSim is an extension of Gecko, an ecosystem dynamics model which uses the Swarm toolkit for multi-agent simulations. The model describes bacterial properties including substrate uptake, metabolism, maintenance, cell division and death at the individual cell level. With the aim of making the model easily applicable to various bacteria under different conditions, the model uses as few as eight readily obtainable parameters which can be randomly varied. For substrate diffusion, a two-dimensional diffusion lattice is used. For growth-rate-dependent cell size variation, a conceptual model of cell division proposed by Donachie was examined. A mechanistic version of the Donachie model led to unbalanced growth at higher growth rates, whereas including a minimum period between subsequent replication initiations ensured balanced growth only if this period was unphysiologically long. Only a descriptive version of the Donachie model predicted cell sizes correctly. For maintenance, the Herbert model (constant specific rate of biomass consumption) and for substrate uptake, the Michaelis-Menten or the Best equations were implemented. The simulator output faithfully reproduced all input parameters. Growth characteristics when maintenance and uptake rates were proportional to either cell mass or surface area are compared. The authors propose a new generic measure of growth synchrony to quantify the loss of synchrony due to random variation of cell parameters or spatial heterogeneity. Variation of the maximal uptake rate completely desynchronizes the simulated culture but variation of the volume-at-division does not. A new measure for spatial heterogeneity is introduced: the standard deviation of substrate concentrations as experienced by the cells. Spatial heterogeneity desynchronizes population growth by subdividing the population into parts synchronously growing at different rates. At a high enough spatial heterogeneity, the population appears to grow completely asynchronously.

Algorithms↗

PubMed2006

The distribution of positive and negative species interactions across environmental gradients on a dual-lattice model.

There has been considerable recent interest in understanding the role of positive inter-specific interactions within ecology, and significant progress has been made both empirically and theoretically. Similarly, considerable progress has been made in improving our understanding of the mechanisms that limit species' ranges. In this contribution, we seek to understand the setting of species' borders when some species within the assemblage exhibit positive inter-specific interactions. We use a spatially explicit dual-lattice simulation model to explore the distribution of different interactions across environmental gradients. We first simulate community dynamics when there is either a gradient in reproductive rate or in mortality. We then consider what happens when gradients in reproduction and mortality run in parallel or perpendicular to one another. If the stress gradient impacts on reproductive potential, positive interactions are found where there is high abiotic stress. In this instance, the mutualists are able to tolerate an environment that the cheaters cannot. However, when the stress gradient influences mortality, we find that the mutualists occur as a stripe surrounded by cheaters both towards the better and the harsher ends of the gradient. Previous theory and most empirical evidence tend to indicate that net positive interactions are likely to occur in environments characterized by high abiotic stress. However, evidence from some stress gradients suggests that the distribution of positive and negative interactions can be more complex, with the most stressful environments being occupied by individuals engaging in negative rather than positive interactions. Our results provide a potential theoretical explanation for these recent field observation, and highlight the need for further theoretical and empirical work to better our understanding of how positive and negative interactions act to determine the limits to species' ranges.

Animals↗

PubMed1985

Representation of cooperative firing activity among simultaneously recorded neurons.

Simultaneous and separable extracellular recording of substantial populations of neurons under chronic and behavioral conditions is becoming experimentally feasible. We have recently described a conceptual transformation of such multiple spike train data that allows the experimenter to analyze the entire network of observed neurons as an entity rather than as a summation of neuron pairs. The basic transformation represents each of N neurons as a particle in an N-space. Each particle is given a "charge" that is related to the spike train of the corresponding neuron. The resulting forces on the N particles cause aggregation of those particles that represent neurons with time-related firing. The present paper extends the visualization and possibilities of this way of analyzing properties of neuronal assemblies. Data are taken from computer-simulated neuronal networks in order to provide known properties. We demonstrate projection of particle positions from the N space to a plane. Under the right conditions the spatial arrangement of the particles forms a Venn diagram of functional relationships in the entire neural network. We introduce revised force rules in the transformation that allow detection and study of inhibitory connections among the observed neurons. Sensitivity is lower than for excitatory connections. We introduce revised "charge" rules that improve "signal-to-noise" properties and in addition allow inference of directed connectivity. The original transformation only allows identification of neurons with time-related firing. The two-charge transformation allows explicit identification of presynaptic and postsynaptic neurons. Finally we examine sensitivity of the transformation to individual and near-coincident firing rates. Some criteria are presented for choice of charge normalization rules in the transformation.

Action Potentials↗

PubMed2006

The wave speed of intergradation zone in two-species lattice Müllerian mimicry model.

A spatially explicit model is studied to analyse the movement of coupled clines in two-species Müllerian mimicry system as exemplified by the comimicking helicoiine butterflies in Central-South America Heliconius erato and Heliconius melpomene. In this system, a pair of comimicking wing patterns of two species (mimicry ring) is found in a geographical region but another pair of wing patterns is found in a different geographical region. The distribution of mimicry rings thus forms a spatial mosaic in a large geographical scale, and the mechanism responsible for their stable maintenance has been a long-standing question in evolutionary biology. We here examine the speed of the movement of boundaries that divide the regions inhabited by different mimetic morphs in each comimicking species, by assuming coupled two-state stochastic cellular automatons where the flipping rate of the site occupied by a mimetic morph depends on the local density of the same morph and of the comimicking morph in the other species. The speed of cline movement shows a complex dependence on the coupling parameter between mimetic species--greater coupling of comimicking morphs between species slows down the cline movement only when the reduction in predation rate exhibits diminishing return to the increase of local mimetic morph density. The analytical predictions are confirmed by the results of Monte Carlo simulations. The speed of advance is quite different from that predicted from the conventional reaction-diffusion model, indicating that demographic stochasticity plays a critical role in determining the speed of cline movement. We also examine if the spatial heterogeneity in migration rate can stably maintain clines.

Animals↗