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Disease risk near point sources: statistical issues for analyses using individual or spatially aggregated data.

STUDY OBJECTIVE: To examine the statistical issues involved in the analysis of disease risk near point sources of environmental pollution, where data are held at both the individual and group (areal) level. To explore these issues with reference to possible socioeconomic confounding. DESIGN: Statistical review. SETTING: Point sources of environmental pollution. MAIN RESULTS: Except in very specific circumstances unlikely to hold in practice, aggregation of data to the areal level will lead to bias in the estimation of disease risk. CONCLUSIONS: There is no easy solution to the analysis of spatial data when some covariates (for example, age and sex of cases) are known at individual level, whereas others (for example, populations, age-sex distributions, small area deprivation indices) are known only at the areal (ecological) level. The underlying assumptions inherent in the analysis of these data need to be explicitly recognised in order to understand better the limitations of the available methodology as well as to inform interpretation of results. Ideally, the data should be kept as disaggregated as possible, to maximise the information available and minimise potential for bias.

Bias↗

Biodiversity in urban habitat patches.

We examined the biodiversity of urban habitats in Birmingham (England) using a combination of field surveys of plants and carabid beetles, genetic studies of four species of butterflies, modelling the anthropochorous nature of the floral communities and spatially explicit modelling of selected mammal species. The aim of the project was to: (i) understand the ecological characteristics of the biota of cities model, (ii) examine the effects of habitat fragment size and connectivity upon the ecological diversity and individual species distributions, (iii) predict biodiversity in cities, and (iv) analyse the extent to which the flora and fauna utilise the 'urban greenways' both as wildlife corridors and as habitats in their own right. The results suggest that cities provide habitats for rich and diverse range of plants and animals, which occur sometimes in unlikely recombinant communities. The studies on carabids and butterflies illustrated the relative importance of habitat quality on individual sites as opposed to site location within the conurbation. This suggests that dispersal for most of our urban species is not a limiting factor in population persistence, although elements of the woodland carabid fauna did appear to have some geographical structuring. Theoretical models suggested that dormice and water voles may depend on linear habitats for dispersal. The models also indicated that other groups, such as small and medium sized mammals, may use corridors, although field-based research did not provide any evidence to suggest that plants or invertebrates use urban greenways for dispersal. This finding indicates the importance of identifying a target species or group of species for urban greenways intended as dispersal routeways rather than as habitat in their own right. Their importance for most groups is rather that greenways provide a chain of different habitats permeating the urban environment. We suggest that planners can have a positive impact on urban biodiversity by slowing the pace of redevelopment and by not hurrying to tidy up and redevelop brownfield sites.

Animals↗

Spatial mechanisms for coexistence of species sharing a common natural enemy.

We examine the conditions under which spatial structure can mediate coexistence of apparent competitors. We use a spatially explicit, host-parasitoid metapopulation model incorporating local dynamics of Nicholson-Bailey type and global dispersal. Depending on the model parameters, the resulting system displays a plethora of asynchronous dynamical behaviors for which permanent or transient coexistence is observed. We identify a number of spatially mediated tradeoffs which apparent competitors can utilize and demonstrate that the dynamics of spatial coexistence can typically be understood from consideration of two and three patch systems. The phase relationships of species abundances are different for our model than for some other mechanisms of spatial coexistence. We discuss the implications of our findings relative to issues of community organization and biological conservation.

Animals↗

Spatially structured superinfection and the evolution of disease virulence.

When pathogen strains differing in virulence compete for hosts, spatial structuring of disease transmission can govern both evolved levels of virulence and patterns in strain coexistence. We develop a spatially detailed model of superinfection, a form of contest competition between pathogen strains; the probability of superinfection depends explicitly on the difference in levels of virulence. We apply methods of adaptive dynamics to address the interplay of spatial dynamics and evolution. The mean-field approximation predicts evolution to criticality; any small increase in virulence capable of dynamical persistence is favored. Both pair approximation and simulation of the detailed model indicate that spatial structure constrains disease virulence. Increased spatial clustering reduces the maximal virulence capable of single-strain persistence and, more importantly, reduces the convergent-stable virulence level under strain competition. The spatially detailed model predicts that increasing the probability of superinfection, for given difference in virulence, increases the likelihood of between-strain coexistence. When strains differing in virulence can coexist ecologically, our results may suggest policies for managing diseases with localized transmission. Comparing equilibrium densities from the pair approximation, we find that introducing a more virulent strain into a host population infected by a less virulent strain can sometimes reduce total host mortality and increase global host density.

Adaptation, Physiological↗

Out of the tropics: evolutionary dynamics of the latitudinal diversity gradient.

The evolutionary dynamics underlying the latitudinal gradient in biodiversity have been controversial for over a century. Using a spatially explicit approach that incorporates not only origination and extinction but immigration, a global analysis of genera and subgenera of marine bivalves over the past 11 million years supports an "out of the tropics" model, in which taxa preferentially originate in the tropics and expand toward the poles without losing their tropical presence. The tropics are thus both a cradle and a museum of biodiversity, contrary to the conceptual dichotomy dominant since 1974; a tropical diversity crisis would thus have profound evolutionary effects at all latitudes.

Animals↗

Demographic-economic analysis in a multi-zonal region: a case study of Nordrhein-Westfalen.

"This paper develops a series of spatially-disaggregated demographic-economic models, based on an extended Leontief type input-output model. Travel between residence and place of work and residence and place of shopping is included in the models, and a detailed decomposition of a range of multipliers identified. A model explicitly involving travel to work is developed empirically for the state of Nordrhein-Westfalen in West Germany, and sets of multipliers presented which relate changes in demographic and economic variables in particular zones of the state with changes in economic output and employment-related variables in other zones."

Behavior↗

A spatially explicit neutral model of beta-diversity in tropical forests.

To represent species turnover in tropical rain forest, we use a neutral model where a tree's fate is not affected by what species it belongs to, seeds disperse a limited distance from their parents, and speciation is in equilibrium with random extinction. We calculate the similarity function, the probability F(r) that two trees separated by a distance r belong to the same species, assuming that the dispersal kernel P(r), the distribution of seeds about their parents and the prospects of mortality and reproduction, are the same for all trees regardless of their species. If P(r) is radially symmetric Gaussian with mean-square dispersal distance sigma, F(r) can be expressed in closed form. If P(r) is a radially symmetric Cauchy distribution, then, in two-dimensional space, F(r) is proportional to 1/r for large r. Analytical results are compared with individual-based simulations, and the relevance to field observations is discussed.

Ecosystem↗

Recovering the geographic origin of early modern humans by realistic and spatially explicit simulations.

Most genetic and archeological evidence argue in favor of a recent and unique origin of modern humans in sub-Saharan Africa, but no attempt has ever been made at quantifying the likelihood of this model, relative to alternative hypotheses of human evolution. In this paper, we investigate the possibility of using multilocus genetic data to correctly infer the geographic origin of humans, and to distinguish between a unique origin (UO) and a multiregional evolution (ME) model. We introduce here an approach based on realistic simulations of the genetic diversity expected after an expansion process of modern humans into the Old World from different possible areas and their comparison to observed data. We find that the geographic origin of the expansion can be correctly recovered provided that a large number of independent markers are used, and that precise information on past demography and potential places of origins is available. In that case, it is also possible to unambiguously distinguish between a unique origin and a multiregional model of human evolution. Application to a real human data set of 377 STR markers tested in 22 populations points toward a unique but surprising North African origin of modern humans. We show that this result could be due to ascertainment bias in favor of markers selected to be polymorphic in Europeans. A new estimation modeling this bias explicitly reveals that East Africa is the most likely place of origin for modern humans.

Africa↗

The intermediate dispersal principle in spatially explicit metapopulations.

Aim of this paper is to assess the fate of metapopulations described by spatially explicit models. To this end, we first present an interacting particle system (IPS) where individuals of a single species compete logistically at the local scale and can move among patches according to various dispersal kernels. As the IPS is a complex stochastic system, it is impossible to determine the persistence-extinction boundaries in any relevant parameter space with analytical methods or numerical continuation techniques. We thus resort to a heuristic method that lets us determine the boundaries as space-time percolation thresholds with a relatively modest computational effort. Such boundaries are qualitatively consistent with those we obtained with spatial implicit modelling. In particular, we find that the intermediate dispersal principle, namely that globally persistent metapopulations correspond to dispersal rates that are neither too low nor too high, turns out to be very robust even in this explicit context. However, the quantification of the boundaries strongly depends upon the number of patches, the dispersal kernels and the border conditions. Finally, we show that there exists a scaling law that relates the number of species lost in a fragmented landscape to the number of patches. Thus, the law allows a rough estimation of the cost of destroying a patch.

Animals↗

Stability in a metapopulation model with density-dependent dispersal.

A spatially explicit metapopulation model with positive density-dependent migration is analysed. We obtained conditions under which a previously stable system can be driven to instability caused by a density-dependent migration mechanism. The stability boundary depends on the rate of increase of the number of migrants on each site at local equilibrium, on the intrinsic rate of increase at local level, on the number of patches, and on topological aspects regarding the connectivity between patches. A concrete example is presented illustrating the dynamics on the dispersal-induced unstable regime.

Animals↗

Foraging in a tidally structured environment by Red Knots (Calidris canutus): ideal, but not free.

Besides the "normal" challenge of obtaining adequate intake rates in a patchy and dangerous world, shorebirds foraging in intertidal habitats face additional environmental hurdles. The tide forces them to commute between a roosting site and feeding grounds, twice a day. Moreover, because intertidal food patches are not all available at the same time, shorebirds should follow itineraries along the best patches available at a given time. Finally, shorebirds need additional energy stores in order to survive unpredictable periods of bad weather, during which food patches are covered by extreme tides. In order to model such tide-specific decisions, we applied stochastic dynamic programming in a spatially explicit context. Two assumptions were varied, leading to four models. First, birds had either perfect (ideal) or no (non-ideal) information about the intake rate at each site. Second, traveling between sites was either for free or incurred time and energy costs (non-free). Predictions were generated for three aspects of foraging: area use, foraging routines, and energy stores. In general, non-ideal foragers should feed most intensely and should maintain low energy stores. If traveling for such birds is free, they should feed at a random site; otherwise, they should feed close to their roost. Ideal foragers should concentrate their feeding around low tide (especially when free) and should maintain larger energy stores (especially when non-free). If traveling for such birds is free, they should feed at the site offering the highest intake rate; otherwise, they should trade off travel costs and intake rate. Models were parameterized for Red Knots (Calidris canutus) living in the Dutch Wadden Sea in late summer, an area for which detailed, spatially explicit data on prey densities and tidal heights are available. Observations of radio-marked knots (area use) and unmarked knots (foraging routines, energy stores) showed the closest match with the ideal/non-free model. We conclude that knots make state-dependent decisions by trading off starvation against foraging-associated risks, including predation. Presumably, knots share public information about resource quality that enables them to behave in a more or less ideal manner. We suggest that our modeling approach may be applicable in other systems where resources fluctuate in space and time.

Animals↗

Dos and don'ts of spatially explicit ecological risk assessments.

Location affects exposure and response to stressors at scales ranging from small sites to large regions. Tools such as geographic information systems (GIS) make it feasible to conduct spatially explicit ecological risk assessments (ERAs). However, no tools provide a panacea, and complex models based on sparse data can be inappropriate and misleading. Operations such as an interpolation within a GIS are models, and so they contain assumptions and uncertainties. Errors can propagate easily as numerous operations are performed, and the resulting uncertainties should be made explicit. Analysts should assure that space actually matters by using explanatory data prior to investigating spatial correlation. Exposure and risk estimates from experimental plots or monitoring stations may require scaling factors if they are to be used for larger watersheds or regional analyses. Maps are useful because they present complex spatial information in a manner that is easily interpreted. However, they must be prepared and interpreted with caution because they can suggest that there is a great deal more information than actually exists. In addition to presenting maps of predicted risks, maps of the spatial patterns in the uncertainties in these risk estimates should be included in risk assessments.

Animals↗

The curse of the pharaoh in space: free-living infectious stages and the evolution of virulence in spatially explicit populations.

The idea that parasites with long-lived infective stages may evolve higher virulence has received considerable attention. This idea is called 'the curse of the pharaoh' because of the hypothesis that the death of Lord Carnavon was caused by very long-lived propagules of a highly virulent infectious disease. Here, we examined the evolution of diseases that transmit via free-living stages in a spatial context. We show that, if virulence evolves independently of transmission, long-lived infective stages can select for higher virulence. There is always the evolution of a finite transmission rate, which becomes higher when the infective stages are shorter lived. When a trade-off occurs between transmission and virulence, we show that there is no evidence for the curse of the pharaoh. Indeed, higher transmission and therefore virulence may be selected for by shorter rather than long-lived infective stages.

Animals↗

Individual-based spatially-explicit model of an herbivore and its resource: the effect of habitat reduction and fragmentation.

We present an individual-based, spatially-explicit model of the dynamics of a small mammal and its resource. The life histories of each individual animal are modeled separately. The individuals can have the status of residents or wanderers and belong to behaviorally differing groups of juveniles or adults and males or females. Their territory defending and monogamous behavior is taken into consideration. The resource, green vegetation, grows depending on seasonal climatic characteristics and is diminished due to the herbivore's grazing. Other specifics such as a varying personal energetic level due to feeding and starvation of the individuals, mating preferences, avoidance of competitors, dispersal of juveniles, as a result of site overgrazing, etc., are included in the model. We determined model parameters from real data for the species Microtus ochrogaster (prairie vole). The simulations are done for a case of an enclosed habitat without predators or other species competitors. The goal of the study is to find the relation between size of habitat and population persistence. The experiments with the model show the populations go extinct due to severe overgrazing, but that the length of population persistence depends on the area of the habitat as well as on the presence of fragmentation. Additionally, the total population size of the vole population obtained during the simulations exhibits yearly fluctuations as well as multi-yearly peaks of fluctuations. This dynamics is similar to the one observed in prairie vole field studies.

Animal Feed↗

Evolution of density- and patch-size-dependent dispersal rates.

Based on a marginal value approach, we derive a nonlinear expression for evolutionarily stable (ES) dispersal rates in a metapopulation with global dispersal. For the general case of density-dependent population growth, our analysis shows that individual dispersal rates should decrease with patch capacity and-beyond a certain threshold-increase with population density. We performed a number of spatially explicit, individual-based simulation experiments to test these predictions and to explore further the relevance of variation in the rate of population increase, density dependence, environmental fluctuations and dispersal mortality on the evolution of dispersal rates. They confirm the predictions of our analytical approach. In addition, they show that dispersal rates in metapopulations mostly depend on dispersal mortality and inter-patch variation in population density. The latter is dominantly driven by environmental fluctuations and the rate of population increase. These conclusions are not altered by the introduction of neighbourhood dispersal. With patch capacities in the order of 100 individuals, kin competition seems to be of negligible importance for ES dispersal rates except when overall dispersal rates are low.

Adaptation, Biological↗

Neuronal population codes and the perception of object distance in weakly electric fish.

Weakly electric fish use an electric sense to navigate and capture prey in the dark. Objects in the surroundings of the fish produce distortions in their self-generated electric field; these distortions form a two-dimensional Gaussian-like electric image on the skin surface. To determine the distance of an object, the peak amplitude and width of its electric image must be estimated. These sensory features are encoded by a neuronal population in the early stages of the electrosensory pathway, but are not represented with classic bell-shaped neuronal tuning curves. In contrast, bell-shaped tuning curves do characterize the neuronal responses to the location of the electric image on the body surface, such that parallel two-dimensional maps of this feature are formed. In the case of such two-dimensional maps, theoretical results suggest that the width of neural tuning should have no effect on the accuracy of a population code. Here we show that although the spatial scale of the electrosensory maps does not affect the accuracy of encoding the body surface location of the electric image, maps with narrower tuning are better for estimating image width and those with wider tuning are better for estimating image amplitude. We quantitatively evaluate a two-step algorithm for distance perception involving the sequential estimation of peak amplitude and width of the electric image. This algorithm is best implemented by two neural maps with different tuning widths. These results suggest that multiple maps of sensory features may be specialized with different tuning widths, for encoding additional sensory features that are not explicitly mapped.

Algorithms↗

Development aspects of migration in third world settings: a simulation, with implications for urbanization.

A simulation of the interrelationships between development and migration in developing countries is presented. "Development is represented as the diffusion of demographic transition, employment opportunities, and formal and communication channels, which in turn affect informal communications and the overall economic base. The simulation falls within the genre of neoclassical development models, but, unlike many, explicitly explores the long-run aspects of landscape evolution." The results generally "conform with expectations hypothesized in earlier research, including phenomena such as polarization reversal, converging regional disparities, and low-level equilibrium traps at small remote places where continual resource drain thwarts the agglomeration economies necessary for sustained growth. [The authors] also find that the initial urban system configuration has little effect on the final configuration, and that only urban size diseconomies are likely to alter significantly the size, spatial distribution, and spatial characteristics of the urban system."

Demography↗

Rift Valley fever in West Africa: the role of space in endemicity.

Rift Valley fever is an endemic vector-borne disease in West Africa, which mainly affects domestic ruminants and occasionally humans. The aetiological mechanisms of its endemicity remain under debate. We used a simple spatially explicit model to assess the possibility of endemicity without wild animals providing a permanent virus reservoir. Our model takes into account the vertical transmission in some mosquito species, the rainfall-driven emergence of their eggs and local and distant contacts because of herd migration. Endemicity without such a permanent virus reservoir would be impossible in a single site except when there is a strictly periodic rainfall pattern; but it would be possible when there are herd movements and sufficient inter-site variability in rainfall, which drives mosquito emergence.

Aedes↗