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J Dushoff

Publications and source records attributed to J Dushoff.

7 recordsLinked to original sources
PubMed2001

Phenotypic diversity and ecosystem functioning in changing environments: a theoretical framework.

Biodiversity plays a vital role for ecosystem functioning in a changing environment. Yet theoretical approaches that incorporate diversity into classical ecosystem theory do not provide a general dynamic theory based on mechanistic principles. In this paper, we suggest that approaches developed for quantitative genetics can be extended to ecosystem functioning by modeling the means and variances of phenotypes within a group of species. We present a framework that suggests that phenotypic variance within functional groups is linearly related to their ability to respond to environmental changes. As a result, the long-term productivity for a group of species with high phenotypic variance may be higher than for the best single species, even though high phenotypic variance decreases productivity in the short term, because suboptimal species are present. In addition, we find that in the case of accelerating environmental change, species succession in a changing environment may become discontinuous. Our work suggests that this phenomenon is related to diversity as well as to the environmental disturbance regime, both of which are affected by anthropogenic activities. By introducing new techniques for modeling the aggregate behavior of groups of species, the present approach may provide a new avenue for ecosystem analysis.

Biomass↗
PubMed2000

Carrying capacity and demographic stochasticity: scaling behavior of the stochastic logistic model.

The stochastic logistic model is the simplest model that combines individual-level demography with density dependence. It explicitly or implicitly underlies many models of biodiversity of competing species, as well as non-spatial or metapopulation models of persistence of individual species. The model has also been used to study persistence in simple disease models. The stochastic logistic model has direct relevance for questions of limiting similarity in ecological systems. This paper uses a biased random walk heuristic to derive a scaling relationship for the persistence of a population under this model, and discusses its implications for models of biodiversity and persistence. Time to extinction of a species under the stochastic logistic model is approximated by the exponential of the scaling quantity U=(R-1)(2) N/R(R+1), where N is the habitat size and R is the basic reproductive number.

Animals↗
PubMed1999

Local frequency dependence and global coexistence.

In sessile organisms such as plants, interactions occur locally so that important ecological aspects like frequency dependence are manifest within local neighborhoods. Using probabilistic cellular automata models, we investigated how local frequency-dependent competition influenced whether two species could coexist. Individuals of the two species were randomly placed on a grid and allowed to interact according to local frequency-dependent rules. For four different frequency-dependent scenarios, the results indicated that over a broad parameter range the two species could coexist. Comparisons between explicit spatial simulations and the mean-field approximation indicate that coexistence occurs over a broader region in the explicit spatial simulation.

Ecosystem↗
PubMed1999

Host heterogeneity and disease endemicity: a moment-based approach.

This paper investigates the possibility of understanding the effects of host heterogeneity on disease levels through the use of moment approximations. The approach is to avoid assumptions about the distribution of mixing rates (or other parameters) in the population, by treating the low-order moments of the distribution as estimable parameters. This approach, while approximate, can greatly reduce the number of parameters needed to explore the effects of population heterogeneity on disease dynamics. This makes the approach useful for both inference and prediction, and also for gaining insight into the qualitative effects of heterogeneity on the spread of disease. This paper focuses on populations with variations in mixing rate and random mixing. It is shown that moment-based approximations can provide good quantitative estimates of disease dynamics, as well as aiding in qualitative under- standing, over a respectable range of parameters. It is hoped that this approach will provide a useful complement to more traditional box models of heterogeneity.

Communicable Diseases↗
PubMed1996

Incorporating immunological ideas in epidemiological models.

Many diseases show important interactions between epidemiology and immunology. Both models and data suggest that epidemiologically controlled variables, like frequency and intensity of exposure, can affect immunological outcomes in a wide variety of diseases. Conversely, the results of the immunological "battle" between host and parasite determine the ability of the parasite to spread. I present a simple model with two possible states of infection, which assumes that higher exposure to infection is correlated with likelihood of acquiring a more severe infection. For some parameter values, this model leads to simultaneous stability of the disease-free equilibrium and an endemic equilibrium, implying that the disease might be able to persist in a population that it could not invade. I also derive a simple and interpretable sufficient condition for multiple stable states. The "cartoon" model presented here shows that interaction between epidemiology and immunology can have important effects on the invasion and persistence of diseases. In particular, it raises the possibility that this mechanism can lead to mathematical "catastrophe" and to long-term cycles in disease prevalence.

Epidemiology↗
PubMedDate not supplied

The effects of population heterogeneity on disease invasion.

The incorporation of population heterogeneity is a central issue in theoretical biology, and it has received considerable attention in epidemiology recently. This paper presents general conclusions and interpretations about the effects of heterogeneity, with and without positive assortative mating, on the ability of a disease to establish itself. We show that the invasion of a disease into a population with random mixing is determined by an average of reproductive numbers for each subgroup, weighted by the total amount of mixing activity of the subgroup. In particular, if the mixing rate is constant across the population, invasion occurs if and only if the average reproductive number for the population exceeds 1. In the case of "preferred mixing," one can find a critical number for each subgroup such that invasion occurs if and only if a suitably defined average over subgroups exceeds 1.

Epidemiologic Methods↗