Pathogen transmission at stage-structured infectious patches: Killers and vaccinators.

Spatial localization of an obligate-killing, free-living pathogen generates a landscape of patches where new infections occur. As an infectious patch ages, both pathogen exposure at the patch and the probability of lethal infection following exposure can decline. We model stage-structured infectious patches, where non-lethal exposure can naturally "vaccinate" susceptible hosts.

Spatial Competition: Roughening of an Experimental Interface.

Limited dispersal distance generates spatial aggregation. Intraspecific interactions are then concentrated within clusters, and between-species interactions occur near cluster boundaries. Spread of a locally dispersing invader can become motion of an interface between the invading and resident species, and spatial competition will produce variation in the extent of invasive advance along the interface.

Environmentally transmitted parasites: Host-jumping in a heterogeneous environment.

Groups of chronically infected reservoir-hosts contaminate resource patches by shedding a parasite׳s free-living stage. Novel-host groups visit the same patches, where they are exposed to infection. We treat arrival at patches, levels of parasite deposition, and infection of the novel host as stochastic processes, and derive the expected time elapsing until a host-jump (initial infection of a novel host) occurs.

Restoration ecology: two-sex dynamics and cost minimization.

We model a spatially detailed, two-sex population dynamics, to study the cost of ecological restoration. We assume that cost is proportional to the number of individuals introduced into a large habitat. We treat dispersal as homogeneous diffusion in a one-dimensional reaction-diffusion system.

Extraordinary sex ratios: cultural effects on ecological consequences.

We model sex-structured population dynamics to analyze pairwise competition between groups differing both genetically and culturally. A sex-ratio allele is expressed in the heterogametic sex only, so that assumptions of Fisher's analysis do not apply. Sex-ratio evolution drives cultural evolution of a group-associated trait governing mortality in the homogametic sex.

Interference competition and invasion: spatial structure, novel weapons and resistance zones.

Certain invasive plants may rely on interference mechanisms (e.g., allelopathy) to gain competitive superiority over native species.

Preemptive spatial competition under a reproduction-mortality constraint.

Spatially structured ecological interactions can shape selection pressures experienced by a population's different phenotypes. We study spatial competition between phenotypes subject to antagonistic pleiotropy between reproductive effort and mortality rate. The constraint we invoke reflects a previous life-history analysis; the implied dependence indicates that although propagation and mortality rates both vary, their ratio is fixed.

Ecological invasion, roughened fronts, and a competitor's extreme advance: integrating stochastic spatial-growth models.

Both community ecology and conservation biology seek further understanding of factors governing the advance of an invasive species. We model biological invasion as an individual-based, stochastic process on a two-dimensional landscape. An ecologically superior invader and a resident species compete for space preemptively.

Stage-structured infection transmission and a spatial epidemic: a model for Lyme disease.

A greater understanding of the rate at which emerging disease advances spatially has both ecological and applied significance. Analyzing the spread of vector-borne disease can be relatively complex when the vector's acquisition of a pathogen and subsequent transmission to a host occur in different life stages. A contemporary example is Lyme disease.

Free-living pathogens: life-history constraints and strain competition.

Many pathogen life histories include a free-living stage, often with anatomical and physiological adaptations promoting persistence outside of host tissues. More durable particles presumably require that the pathogen metabolize more resources per particle. Therefore, we hypothesize functional dependencies, pleiotropic constraints, between the rate at which free-living particles decay outside of host tissues and other pathogen traits, including virulence, the probability of infecting a host upon contact, and pathogen reproduction within host tissues.

Invasive advance of an advantageous mutation: nucleation theory.

For sedentary organisms with localized reproduction, spatially clustered growth drives the invasive advance of a favorable mutation. We model competition between two alleles where recurrent mutation introduces a genotype with a rate of local propagation exceeding the resident's rate. We capture ecologically important properties of the rare invader's stochastic dynamics by assuming discrete individuals and local neighborhood interactions.

Spatiotemporal Bayesian analysis of Lyme disease in New York state, 1990-2000.

Mapping ordinarily increases our understanding of nontrivial spatial and temporal heterogeneities in disease rates. However, the large number of parameters required by the corresponding statistical models often complicates detailed analysis. This study investigates the feasibility of a fully Bayesian hierarchical regression approach to the problem and identifies how it outperforms two more popular methods: crude rate estimates (CRE) and empirical Bayes standardization (EBS).

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.

Epidemic and spatial dynamics of Lyme disease in New york State, 1990-2000.

Lyme disease (LD) occurrence in New York State (NYS) has not only increased over time but also spread throughout the state from the original disease focus in southeastern NYS. Few studies have investigated this epidemic and spatial dynamic in great detail. Using data from the NYS Department of Health Lyme Registry Surveillance System, we summarized epidemic and spatial characteristics of LD in NYS for the 11-yr time period from 1990 through 2000.

Spatial dynamics of invasion: the geometry of introduced species.

Many exotic species combine low probability of establishment at each introduction with rapid population growth once introduction does succeed. To analyse this phenomenon, we note that invaders often cluster spatially when rare, and consequently an introduced exotic's population dynamics should depend on locally structured interactions. Ecological theory for spatially structured invasion relies on deterministic approximations, and determinism does not address the observed uncertainty of the exotic-introduction process.