Showing papers by "Donald L. DeAngelis published in 2016"

Dispersal and spatial heterogeneity: single species.

Abstract: A recent result for a reaction-diffusion equation is that a population diffusing at any rate in an environment in which resources vary spatially will reach a higher total equilibrium biomass than the population in an environment in which the same total resources are distributed homogeneously. This has so far been proven by Lou for the case in which the reaction term has only one parameter, $$m(x)$$ , varying with spatial location $$x$$ , which serves as both the intrinsic growth rate coefficient and carrying capacity of the population. However, this striking result seems rather limited when applies to real populations. In order to make the model more relevant for ecologists, we consider a logistic reaction term, with two parameters, $$r(x)$$ for intrinsic growth rate, and $$K(x)$$ for carrying capacity. When $$r(x)$$ and $$K(x)$$ are proportional, the logistic equation takes a particularly simple form, and the earlier result still holds. In this paper we have established the result for the more general case of a positive correlation between $$r(x)$$ and $$K(x)$$ when dispersal rate is small. We review natural and laboratory systems to which these results are relevant and discuss the implications of the results to population theory and conservation ecology.

Prediction of Plant Vulnerability to Salinity Increase in a Coastal Ecosystem by Stable Isotope Composition (δ18O) of Plant Stem Water: A Model Study

Abstract: Sea level rise and the subsequent intrusion of saline seawater can result in an increase in soil salinity, and potentially cause coastal salinity-intolerant vegetation (for example, hardwood hammocks or pines) to be replaced by salinity-tolerant vegetation (for example, mangroves or salt marshes). Although the vegetation shifts can be easily monitored by satellite imagery, it is hard to predict a particular area or even a particular tree that is vulnerable to such a shift. To find an appropriate indicator for the potential vegetation shift, we incorporated stable isotope 18O abundance as a tracer in various hydrologic components (for example, vadose zone, water table) in a previously published model describing ecosystem shifts between hammock and mangrove communities in southern Florida. Our simulations showed that (1) there was a linear relationship between salinity and the δ18O value in the water table, whereas this relationship was curvilinear in the vadose zone; (2) hammock trees with higher probability of being replaced by mangroves had higher δ18O values of plant stem water, and this difference could be detected 2 years before the trees reached a tipping point, beyond which future replacement became certain; and (3) individuals that were eventually replaced by mangroves from the hammock tree population with a 50% replacement probability had higher stem water δ18O values 3 years before their replacement became certain compared to those from the same population which were not replaced. Overall, these simulation results suggest that it is promising to track the yearly δ18O values of plant stem water in hammock forests to predict impending salinity stress and mortality.

Effects of diffusion on total biomass in heterogeneous continuous and discrete-patch systems

Abstract: Theoretical models of populations on a system of two connected patches previously have shown that when the two patches differ in maximum growth rate and carrying capacity, and in the limit of high diffusion, conditions exist for which the total population size at equilibrium exceeds that of the ideal free distribution, which predicts that the total population would equal the total carrying capacity of the two patches However, this result has only been shown for the Pearl-Verhulst growth function on two patches and for a single-parameter growth function in continuous space Here, we provide a general criterion for total population size to exceed total carrying capacity for three commonly used population growth rates for both heterogeneous continuous and multi-patch heterogeneous landscapes with high population diffusion We show that a sufficient condition for this situation is that there is a convex positive relationship between the maximum growth rate and the parameter that, by itself or together with the maximum growth rate, determines the carrying capacity, as both vary across a spatial region This relationship occurs in some biological populations, though not in others, so the result has ecological implications