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Louis J Gross

Publications and source records attributed to Louis J Gross.

3 recordsLinked to original sources
PubMed2006

Modeling tick-borne disease: a metapopulation model.

Recent increases in reported outbreaks of tick-borne diseases have led to increased interest in understanding and controlling epidemics involving these transmission vectors. Mathematical disease models typically assume constant population size and spatial homogeneity. For tick-borne diseases, these assumptions are not always valid. The disease model presented here incorporates non-constant population sizes and spatial heterogeneity utilizing a system of differential equations that may be applied to a variety of spatial patches. We present analytical results for the one patch version and find parameter restrictions under which the populations and infected densities reach equilibrium. We then numerically explore disease dynamics when parameters are allowed to vary spatially and temporally and consider the effectiveness of various tick-control strategies.

Animals↗
PubMed2006

Overyielding and species diversity: what should we expect?

Recent empirical studies have found evidence of increased biomass production ('overyielding') in species mixtures relative to monoculture, but the interpretation of these results remains controversial, in part, because of the lack of a theoretical expectation. Here, we examined the expected frequency and stability of overyielding species mixtures using Lotka-Volterra models of species dynamics in two- and four-species systems in conjunction with community, population, and specific rate of biomass production (SRP) definitions of overyielding. Overyielding plant mixtures represented > 55% of potential species assemblages under community definitions and approximately 100% of species were either overyielding or underyielding under the population definition. Our species simulations approached their equilibria in 1-2 yr, supporting the relevancy of an equilibrial analysis. The range of parameter space that we explored produced realistic values of plot biomass, supporting their biological relevance. We show that overyielding is expected to be common under community definitions and population definitions. Overyielding, under community or population definitions, does not imply an actual increase in the specific rate of biomass production. In addition, assemblages of overyielding and underyielding species under all three definitions can be stable over time with underyielding species persisting in the presence of overyielding species.

Biodiversity↗