Title: The overlooked implications of density dependence in evolutionary epidemiology

Since pathogens tend to affect their host environment in radical ways, selection pressures usually depend on the types of pathogens and hosts that are established in an infected population. Evolutionary consequences of this dependence cannot be captured by the traditional approach of predicting outcomes of disease evolution by maximizing the disease's basic reproduction ratio. In this talk I will outline the theory of adaptive dynamics as a versatile tool for investigating the evolution and coevolution of pathogen-host interactions under conditions of frequency-dependent selection. The great variety of biological mechanisms leading to density-dependent demographic rates, and thus to frequency-dependent selection pressures, will be highlighted. On this basis, examples will be given to illustrate how classic methods and the new models presented here result in quantitatively and qualitatively different predictions about the evolution of infectious diseases.

Title: Evolutionary and ecological dynamics of host-pathogen interactions

Coevolution between hosts and pathogens is fundamental to the evolutionary epidemiology of infectious diseases. The melding of evolutionary, ecological and epidemiological theory can yield insights into the dynamics of host-pathogen interactions that could not be revealed through these disciplines on their own, as will be demonstrated with examples from my research. Four examples of the repercussions of host-mediated selection on pathogens will be discussed. The selective pressure to evade host immunity may be strong enough to compensate for the two-fold cost of sex in some parasites will be discussed. Host immunity also influences the coexistence of parasite strains and the distribution of infection intensity, with implications for the evolution of drug resistance and the control of disease. Additionally, selection from host immunity can drive the emergence of new viral strains and determine phylogenetic patterns of antigenic evolution, as illustrated by the human influenza virus. In turn, the phylogenetic patterns of influenza can be used to identify emergent strains with epidemic potential. Pathogen-mediated selection on the host can also be a potent evolutionary force, which will be discussed in relation to the CCR5-32 HIV resistance allele in humans. Thus, the talk will highlight that combining evolutionary ecology and epidemiology has widespread potential for answering evolutionary questions, informing public health policy and explaining empirical observations.

Title: On the interplay of community ecology and evolution in emerging diseases

Predicting the emergence of novel infectious disesases is a significant scientific and societal challenge. A pervasive aspect of global change is the disruption of natural predator-prey interactions, due to the reduction and even elimination of top predators. I use simple food web models to suggest that one consequence should often be an upsurge of infectious diseases, and an increased likelihood of transmission across species. In some systems, the latter may pose extinction risks for certain host species. I further argue that these ecological effects of predator removal can lead to evolutionary shifts in virulence and host range for infectious diseases, leading to a kind of evolutionary compounding of the cascading ecological effects of predator reduction.

Title: Linking dynamical and population genetic models of persistent viral infection

We develop a theoretical framework to link dynamical and population genetic models of persistent viral infection. This linkage is useful because, while the dynamical and population genetic theories have developed independently, the biological processes they describe are completely inter-related. Parameters of the dynamical models are important determinants of evolutionary processes such as natural selection and genetic drift. We develop analytical methods, based on coupled differential equations and Markov chain theory, to predict the accumulation of genetic diversity within the viral population as a function of dynamical parameters. These methods are first applied to the standard model of viral dynamics and then generalized to consider the infection of multiple host cell types by the viral population. Each cell type is characterized by specific parameter values. Inclusion of multiple cell types increases the likelihood of persistent infection and can increase the amount of genetic diversity within the viral population. However, the overall rate of gene sequence evolution may actually be reduced. Most recently, we have developed a statistical variant of the theory to analyze gene sequence data from viral pathogens. An application of these models to data from HIV indicates that "divergence stabilization", the reduction in evolutionary rate towards the end of infection, is likely due to a succession of immune-mediated selection.

Title: Dynamics and genealogy of strains in spatially extended host-pathogen models

We examine the dynamics of evolution in a generic spatial model of a pathogen infecting a population of hosts. When transmissibility can evolve by mutation, strains of intermediate transmissibility dominate even though high-transmissibility mutants have a short-term reproductive advantage. Mutant strains continually arise and grow rapidly for many generations but eventually go extinct before dominating the system. We find that, after a number of generations, the mutant pathogen characteristics strongly impact the spatial distribution of their local host environment, even when there are diverse types coexisting. Extinction is due to the depletion of susceptibles in the local environment of these mutant strains. Studies of spatial and genealogical relatedness reveal the self-organized spatial clustering of strains that enables their impact on the local environment. Thus we find that selection acts against the high-transmissibility strains on long time scales as a result of the feedback due to environmental change. Our study shows that averages over space or time should not be assumed to adequately describe the evolutionary dynamics of spatially-distributed host-pathogen systems.

Title: An endemic model with variable re-infection rate and application to influenza

An epidemic model is considered, where immunity is not absolute, but individuals that have recovered from the disease can be re-infected at a rate which depends on the time that has passed since their recovery (recovery age). Such a model, e.g., can account for the genetic drift in the influenza virus. In the special case that the model has no vital dynamics, there is no obvious disease-free equilibrium and so the model lacks the usual interplay between the basic replacement ratio being greater than 1 and the disease-free equilibrium being unstable. One can show, however, that if the basic replacement ratio is greater than one, the disease is uniformly strongly persistent, i.e., the number of infectives is ultimately bounded away from 0 with the bound not depending on the initial data. We derive various conditions for the local and global stability of the endemic equilibrium in terms of the re-infection rate. For instance, the endemic equilibrium is likely to be locally asymptotically stable if the re-infection rate is a highly sub-homogeneous function of recovery age. Conversely, if the re-infection rate is a step function which is zero at small recovery age, the endemic equilibrium can be unstable.