How trait distributions evolve in populations with parametric heterogeneity

Natural gradient ascent in evolutionary games

We consider evolutionary games with a continuous trait space where the replicator dynamics are restricted to the manifold of multivariate Gaussian distributions. We demonstrate that replicator dynamics are gradient flows with respect to the Fisher information metric. The potential function for these gradient flows is closely related to the mean fitness. Our findings extend previous results on natural gradient ascent in evolutionary games with a finite strategy set. Throughout the paper we pursue an information-geometric point of view on evolutionary games. This sheds a new light on the replicator dynamics as a learning process, realizing the compromise between maximization of the mean fitness and preservation of the diversity.

The effect of using fresh farmyard manure (animal manure) on the severity of Fusarium verticilioides in soil, root, stem, and kernels as well as lodging and borer incidence of maize plants

Fusarium verticillioides, an important maize pathogen, produce fumonisins, causes stalk rot and consequentially reduce crop growth and yield. Therefore, herein we aimed to evaluate the potential use of two farmyard soil organic manures, i.e., fresh (5-6 days old) and stored (5-6 months old) organic manure, to manage F. verticillioides infections as well as borer incidence and lodging in maize plants. After 30, 60, and 90 days of sowing, samples of soil, roots, and stems were collected to isolate F. verticillioides. Moreover, we estimated ear and kernel rot induced by F. verticillioides at the final harvest. Fresh organic manure treatment increased infection rates of F. verticillioides in soil, roots, stem and kernels compared to the control treatment. In contrast, stored organic manure plots treatments decrease F. verticillioides frequency. At 90 days after sowing, stored organic manure suppressed the survival of F. verticillioides, which reduced the F. verticillioides incidence percent. These results were similar to the effect of herbicides-and insecticide-treated plots demonstrated, which show a significant decrease in F. verticillioides incidence rates. Mycological analysis on symptomless kernels revealed a higher % of pathogen infection in opened husks variety (Balady) than closed husks variety (SC10). Compared with stored organic manure, the stem borer incidence and lodging percentage were the highest in fresh organic manure plots. Finally, these results demonstrated that storing organic manure within five to six months as farmyard manure led to high-temperature centigrade within organic manure, thereby destroying spores of F. verticillioides, whereas fresh organic manure did not.

A systematic procedure for incorporating separable static heterogeneity into compartmental epidemic models

In this paper, we show how to modify a compartmental epidemic model, without changing the dimension, such that separable static heterogeneity is taken into account. The derivation is based on the Kermack-McKendrick renewal equation.

Heterogeneity in susceptibility dictates the order of epidemic models

The fundamental models of epidemiology describe the progression of an infectious disease through a population using compartmentalized differential equations, but typically do not incorporate population-level heterogeneity in infection susceptibility. Here we combine a generalized analytical framework of contagion with computational models of epidemic dynamics to show that variation strongly influences the rate of infection, while the infection process simultaneously sculpts the susceptibility distribution. These joint dynamics influence the force of infection and are, in turn, influenced by the shape of the initial variability. We find that certain susceptibility distributions (the exponential and the gamma) are unchanged through the course of the outbreak, and lead naturally to power-law behavior in the force of infection; other distributions are often sculpted towards these "eigen-distributions" through the process of contagion. The power-law behavior fundamentally alters predictions of the long-term infection rate, and suggests that first-order epidemic models that are parameterized in the exponential-like phase may systematically and significantly over-estimate the final severity of the outbreak. In summary, our study suggests the need to examine the shape of susceptibility in natural populations as part of efforts to improve prediction models and to prioritize interventions that leverage heterogeneity to mitigate against spread.