Evolutionarily Stable Coevolution Between a Plastic Lytic Virus and Its Microbial Host

Hosts influence and are influenced by viral replication. Cell size, for example, is a fundamental trait for microbial hosts that can not only alter the probability of viral adsorption, but also constrain the host physiological processes that the virus relies on to replicate. This intrinsic connection can affect the fitness of both host and virus, and therefore their mutual evolution. Here, we study the coevolution of bacterial hosts and their viruses by considering the dependence of viral performance on the host physiological state (viral plasticity). To this end, we modified a standard host-lytic phage model to include viral plasticity, and compared the coevolutionary strategies emerging under different scenarios, including cases in which only the virus or the host evolve. For all cases, we also obtained the evolutionary prediction of the traditional version of the model, which assumes a non-plastic virus. Our results reveal that the presence of the virus leads to an increase in host size and growth rate in the long term, which benefits both interacting populations. Our results also show that viral plasticity and evolution influence the classic host quality-quantity trade-off. Poor nutrient environments lead to abundant low-quality hosts, which tends to increase viral infection time. Conversely, richer nutrient environments lead to fewer but high-quality hosts, which decrease viral infection time. Our results can contribute to advancing our understanding of the microbial response to changing environments. For instance, both cell size and viral-induced mortality are essential factors that determine the structure and dynamics of the marine microbial community, and therefore our study can improve predictions of how marine ecosystems respond to environmental change. Our study can also help devise more reliable strategies to use phage to, for example, fight bacterial infections.

The replicator dynamics of generalized Nash games

Generalized Nash Games are a powerful modelling tool, first introduced in the 1950's. They have seen some important developments in the past two decades. Separately, Evolutionary Games were introduced in the 1960's and seek to describe how natural selection can drive phenotypic changes in interacting populations. In this paper, we show how the dynamics of these two independently formulated models can be linked under a common framework and how this framework can be used to expand Evolutionary Games. At the center of this unified model is the Replicator Equation and the relationship we establish between it and the lesser known Projected Dynamical System.

An Analytic Framework for Effective Public Health Program Design Using Correctional Facilities

We present a decision analytic framework that uses a mathematical model of Chlamydia trachomatis transmission dynamics in two interacting populations using ordinary differential equations. A public health survey informs model parametrization, and analytical findings guide the computational design of the decision-making process. The potential impact of jail-based screen-treat (S-T) programs on community health outcomes is presented. Numerical experiments are conducted for a case study population to quantify the effect and evaluate the cost-effectiveness of considered interventions. Numerical experiments show the effectiveness of increased jail S-T rates on community cases when resources for a community S-T program stays constant. Although this effect decreases when higher S-T rates are in place, jail-based S-T programs are cost-effective relative to community-based programs. Summary of Contribution: Public health programs have been developed to control community-wide infectious diseases and to reduce prevalence of sexually transmitted diseases (STD). These programs can consist of screening and treatment of diseases and behavioral interventions. Public correctional facilities play an important role in operational execution of these public health programs. However, because of lack of capacity and resources, public health programs using correctional facilities are questioned by policy-makers in terms of their costs and benefits. In this article, we present an analytical framework using a computational epidemiology model for supporting public health policy making. The system represents the dynamics of Chlamydia trachomatis transmission in two interacting populations, with an ordinary differential equations-based simulation model. The theoretical epidemic control conditions are derived and numerically tested, which guide the design of simulation experiments. Then cost-effectiveness of the potential policies is analyzed. We also present an extensive sensitivity analyses on model parameters. This study contributes to the computational epidemiology literature by presenting an analytical framework to guide effective simulation experimentation for policy decision making. The presented methodology can be applied to other complex policy and public health problems.

HOW DO PARTIALLY HIDING BEHAVIOR AND COMPLETELY HIDING BEHAVIOR IMPACT INTERACTING POPULATIONS?

As the two main behaviors of prey populations in ecological systems, the partially hiding behavior (PHB) and the completely hiding behavior (CHB) play a significant role in determining the dynamics of predator–prey models. This work examines to the dynamical consequences of predator–prey systems with the PHB and the CHB. Previous research has independently studied the two behaviors, and the general conclusions are that the two behaviors can have positive and/or negative impacts on the considered population models. However, to our knowledge, no study has combined and compared the two behaviors in studying the dynamical consequences of predation interactions. Motivated by this, we investigated the dynamical consequences induced by the PHB and the CHB. From a mathematical point of view, the dynamical behaviors are studied and the corresponding sufficient conditions are given. Our findings are general and some published models are special cases of ours. From an ecological point of view, we find that the size of the ecological regions is mainly determined by the two behaviors, and which one is ecologically beneficial for the health coexistence of the interacting populations are primarily determined by the functional response and the attack coefficient of predators. Moreover, we conclude that the evolutionary and optimal choices of prey behavior (PHB or CHB) depend on the predators attack coefficient (large or small attack coefficient) and the resource level (abundant or pool resource level).

Models for large ecological communities—a random matrix approach

Lotka and Volterra were among the first to attempt to mathematize the dynamics of interacting populations. While their work had a profound influence on ecology, leading to many of the results that were covered in the preceding chapters, their approach is difficult to generalize to the case of many interacting species. When the number of species in a community is sufficiently large, there is little hope of obtaining analytical results by carefully studying the system of dynamical equations describing their interactions. Here, we introduce an approach based on the theory of random matrices that exploits the very large number of species to derive cogent mathematical results. We review basic concepts in random matrix theory by illustrating their applications to the study of multispecies systems. We introduce tools that can be used to yield new insights into community ecology and conclude with a list of open problems.