Shift-inducible [transgenerational] increase in recombination rate as an evolving strategy in a periodic environment: a numerical model

Numerous empirical studies have witnessed a plastic increase in meiotic recombination rate in organisms experiencing physiological stress due to unfavourable environmental conditions. Yet, it is not clear enough which characteristics of an ecological factor (intensity, duration, variability, etc.) make it stressogenic and therefore recombinogenic for an organism. Several previous theoretical models proceeded from the assumption that organisms increase their recombination rate when the environment becomes more severe, and demonstrated the evolutionary advantage of such recombination strategy. Here we explore another stress-associated recombination strategy, implying a reversible increase in recombination rate each time when the environment alternates. We allow such plastic changes in the organisms, grown in an environment different from that of their parents, and, optionally, also in their offspring. We show that such shift-inducible recombination is always favoured over intermediate constant optimal recombination. Besides, it sometimes outcompetes also zero and free optimal constant recombination, therefore making selection on recombination less polarized. Shift-inducible strategies with a longer, transgenerational plastic effect, are favoured under slightly stronger selection and longer period. These results hold for both panmixia and partial selfing, although selfing makes the dynamics of recombination modifier alleles faster. Our results suggest that epigenetic factors, presumably underlying the environmental plasticity of recombination, may play an important evolutionary role.

Modeling the dengue fever transmission in a periodic environment

A mathematical model for dengue fever transmission is analyzed, which incorporates relevant biological and ecological factors: vertical transmission and seasonality in the interaction between the vector (Aedes aegypti females) and the host (human). The existence and uniqueness of a positive disease-free periodic solution is proved; the global stability of the disease-free solution and the effect of periodic migrations of mosquitoes carrying the virus on the transmission of dengue are analyzed utilizing the mathematical definition of the Basic Reproductive Number in periodic environments; finally, it is numerically corroborated with the help of the Basic Reproductive Number that dengue cannot invade the disease-free state if it is less than one and can invade if it is greater than one, however, in both threshold conditions when vertical transmission occurs, the number of infected people and carrier vectors rises, representing a mechanism for the persistence of dengue cases in a community throughout a natural year.

Periodic Solutions for Stochastic Differential Equations Driven by General Counting Processes: Application to Malaria

In this paper, a class of periodic stochastic differential equations driven by general counting processes (SDEsGp) is studied. First, an existence-uniqueness result for the solution of general SDEsGp based on Poisson processes with т-periodic stochastic intensity of time t has been given, for some  т> 0. Then, using the properties of periodic Markov processes, sufficient conditions for the existence and uniqueness of a periodic solution of the considered equations are obtained. We will then apply the obtained results to the propagation of malaria in a periodic environment.

On the dynamics of the impulsive predator-prey systems with Beddington – DeAngelis type functional response

UDC 517.9 In this study, the two-dimensional predator-prey system with Beddington–DeAngelis type functional response with impulses is considered in a periodic environment. For this special case, necessary and sufficient conditions are found for the considered system when it has at least one -periodic solution. This result is mainly based on the continuation theorem in the coincidence degree theory and to get the globally attractive -periodic solution of the given system, an inequality is given as the necessary and sufficient condition by using the analytic structure of the system.

Species coexistence and temporal environmental fluctuations: a quantitative comparison between stochastic and seasonal variations.

Temporal environmental variations may promote diversity in communities of competing populations. Here we compare the effect of environmental stochasticity with the effect of periodic (e.g., seasonal) cycles, using analytic solutions and individual-based Monte-Carlo simulations. Even when stochasticity facilitates coexistence it still allows for rare sequences of bad years that may drive a population to extinction, therefore the stabilizing effect of periodic variations is stronger. Correspondingly, the mean time to extinction grows exponentially with community size in periodic environment and switch to power-law dependence under stochastic fluctuations. On the other hand, the number of temporal niches in periodic environment is typically lower, so as diversity increases stochastic temporal variations may support higher species richness.

Dynamics for a non-autonomous fall armyworm-maize interaction model with a saturation functional response

<abstract><p>In this study, we present a non-autonomous model with a Holling type II functional response, to study the complex dynamics for fall armyworm-maize biomass interacting in a periodic environment. Understanding how seasonal variations affect fall armyworm-maize dynamics is critical since maize is one of the most important cereals globally. Firstly, we study the dynamical behaviours of the basic model; that is, we investigate positive invariance, boundedness, permanence, global stability and non-persistence. We then extended the model to incorporate time dependent controls. We investigate the impact of reducing fall armyworm egg and larvae population, at minimal cost, through traditional methods and use of chemical insecticides. We noted that seasonal variations play a significant role on the patterns for all fall armyworm populations (egg, larvae, pupae and moth). We also noted that in all scenarios, the optimal control can greatly reduce the sizes of fall armyworm populations and in some scenarios, total elimination may be attained. The modeling approach presented here provides a framework for designing effective control strategies to manage the fall armyworm during outbreaks.</p></abstract>