Immunity-driven evolution of virulence and diversity in respiratory diseases.

The time-honored paradigm in the theory of virulence evolution assumes a positive relation between infectivity and harmfulness. However, the etiology of respiratory diseases yields a negative relation, with diseases of the lower respiratory tract being less infective and more harmful. We explore the evolutionary consequences in a simple model incorporating cross-immunity between disease strains that diminishes with their distance in the respiratory tract, assuming that docking rate follows the match between the local mix of cell surface types and the pathogen's surface and cross-immunity the similarity of the pathogens' surfaces. The assumed relation between fitness components causes virulent strains infecting the lower airways to evolve to milder more transmissible variants. Limited cross-immunity, generally, causes a readiness to diversify that increases with host population density. In respiratory diseases that diversity will be highest in the upper respiratory tract. More tentatively, emerging respiratory diseases are likely to start low and virulent, to evolve up, and become milder. Our results extend to a panoply of realistic generalizations of the disease's ecology to including additional epitope axes. These extensions allow us to apply our results quantitatively to elucidate the differences in diversification between rhino- and coronavirus caused common colds.

The importance of ecological dynamics in evolutionary processes: A host-bacteriophage model revisited.

A recent study of adaptive dynamics of lysis propensity in temperate phages suggested that full lysogeny emerges as the outcome of bacteriophage evolution in a simple host-phage system. The conclusion is based on the premise that mutant strains necessarily appear in equilibrium host-phage environments. Revisiting the model, we show that the ecological system exhibits richer asymptotic dynamics and that, in a certain parameter regime, evolution may in fact drive lysis propensity towards an evolutionary singularity in which a non-zero proportion of phages initiate infection in a lytic cycle. These singularities act as points of evolutionary diversification, leading to periodic coexistence of two distinct phage strains on the evolutionary time-scale. One of the two strains in the dimorphic evolutionary singularity is fully lysogenic (in the sense that cell infection always leads to lysogeny), while the other is partially lytic. Our study thus highlights the importance of ecological interactions as a driver of evolution.

Evolution of mate-finding Allee effect in prey.

The search for mates is often accompanied with conspicuous behaviour or morphology that can be exploited by predators. Here we explore the evolutionary consequences of a trade-off that arises naturally between mate acquisition and risk of predation and study evolution of the rate at which male prey search for mates in a population subject to a mate-finding Allee effect and exposed to either generalist or specialist predators. Since we show that the mate search rate determines the strength of the mate-finding Allee effect, we can alternatively view this as evolution of the mate-finding Allee effect in prey. We contrast two different life histories and find that, predominantly, male prey either evolve towards the maximal mate search rate yielding the weakest possible mate-finding Allee effect (thus showing no adaptive response in mating behaviour to predation risk) or evolutionary bi-stability occurs. In the latter case, males evolve a relatively low mate search rate (hence a relatively strong mate-finding Allee effect, interpreted as an adaptive response of male prey to predation) when initially slow or the maximal mate search rate when initially fast. Disruptive selection does not occur in populations exposed to generalist predators but is possible when predators are specialists. The dimorphic phase, in which fast and conspicuous male prey coexist with slow and cryptic ones, is however but a transient in evolutionary dynamics as one branch goes extinct while the other evolves towards the maximal mate search rate.

Evolutionary suicide through a non-catastrophic bifurcation: adaptive dynamics of pathogens with frequency-dependent transmission.

Evolutionary suicide is a riveting phenomenon in which adaptive evolution drives a viable population to extinction. Gyllenberg and Parvinen (Bull Math Biol 63(5):981-993, 2001) showed that, in a wide class of deterministic population models, a discontinuous transition to extinction is a necessary condition for evolutionary suicide. An implicit assumption of their proof is that the invasion fitness of a rare strategy is well-defined also in the extinction state of the population. Epidemic models with frequency-dependent incidence, which are often used to model the spread of sexually transmitted infections or the dynamics of infectious diseases within herds, violate this assumption. In these models, evolutionary suicide can occur through a non-catastrophic bifurcation whereby pathogen adaptation leads to a continuous decline of host (and consequently pathogen) population size to zero. Evolutionary suicide of pathogens with frequency-dependent transmission can occur in two ways, with pathogen strains evolving either higher or lower virulence.

An extension of the classification of evolutionarily singular strategies in Adaptive Dynamics.

The existing classification of evolutionarily singular strategies in Adaptive Dynamics (Geritz et al. in Evol Ecol 12:35-57, 1998; Metz et al. in Stochastic and spatial structures of dynamical systems, pp 183-231, 1996) assumes an invasion exponent that is differentiable twice as a function of both the resident and the invading trait. Motivated by nested models for studying the evolution of infectious diseases, we consider an extended framework in which the selection gradient exists (so the definition of evolutionary singularities extends verbatim), but where the invasion fitness may lack the smoothness necessary for the classification à la Geritz et al. We derive the classification of singular strategies with respect to convergence stability and invadability and determine the condition for the existence of nearby dimorphisms. In addition to ESSs and invadable strategies, we observe what we call one-sided ESSs: singular strategies that are invadable from one side of the singularity but uninvadable from the other. Studying the regions of mutual invadability in the vicinity of a one-sided ESS, we discover that two isoclines spring in a tangent manner from the singular point at the diagonal of the mutual invadability plot. The way in which the isoclines unfold determines whether these one-sided ESSs act as ESSs or as branching points. We present a computable condition that allows one to determine the relative position of the isoclines (and thus dimorphic dynamics) from the dimorphic as well as from the monomorphic invasion exponent and illustrate our findings with an example from evolutionary epidemiology.

Evolution of pathogen virulence under selective predation: a construction method to find eco-evolutionary cycles.

We investigate eco-evolutionary cycles in the joint dynamics of pathogen virulence and predator population density when hosts carrying virulent infections are exposed to increased risk of predation. We introduce a new technique to find trade-off functions under which the model exhibits limit cycles; this technique provides a constructive proof that the system is able to generate limit cycles, and can be applied to other eco-evolutionary models as well. We also study a concrete example to confirm that eco-evolutionary cycles occur in a significant part of the parameter space and to briefly explore other evolutionary outcomes in the same model.

A construction method to study the role of incidence in the adaptive dynamics of pathogens with direct and environmental transmission.

We study the adaptive dynamics of virulence of a pathogen transmitted both via direct contacts between hosts and via free pathogens that survive in the environment. The model is very flexible with a number of trade-off functions linking virulence to other pathogen-related parameters and with two incidence functions that describe the contact rates between hosts and between a host and free pathogens. Instead of making a priori particular assumptions about the shapes of these functions, we introduce a construction method to create specific pairs of incidence functions such that the model becomes an optimization model. Unfolding the optimization model leads to coexistence of pathogen strains and evolutionary branching of virulence. The construction method is applicable to a wide range of eco-evolutionary models.

On the evolutionary dynamics of pathogens with direct and environmental transmission.

A number of ecologically and economically important pathogens exhibit a complex transmission dynamics that involves distinct transmission modes. In this paper, we study the evolutionary dynamics of pathogens for which transmission includes direct host-to-host as well as indirect environmental transmission. Different routes of infection spread require specific adaptations of the parasite, which may result in conflicting selection pressures. Using the framework of Adaptive dynamics, we investigate how these conflicting selection pressures are resolved in the course of evolution and determine the conditions for evolutionary diversification of pathogen strains. We show that evolutionary branching and subsequent evolution of specialist strains occurs in wide parameter regions but evolutionary bistability and evolution of generalist pathogens are possible as well. Our analysis reveals that the relative contributions of direct and environmental transmission, as well as the underlying ecological dynamics, play a crucial role in shaping the course of pathogen evolution. Our findings may explain the coexistence of high and low virulence strains observed in several pathogenic organisms using different transmission modes (e.g., influenza viruses) and highlight the importance of considering ecological dynamics in virulence management.

Persistence and spread of gastro-intestinal infections: the case of enterotoxigenic Escherichia coli in piglets.

Several gastro-intestinal infections in animal husbandry not only greatly reduce the well-being of animals, but also have the potential to cause large economical damage. Understanding of the dynamics of such diseases is thus of great importance. In this paper, we focus on within-host dynamics and present a model describing the dynamics of pathogens in the intestine of a single host. Our motivation to study the problem stems from the case of enterotoxigenic Escherichia coli in newly weaned piglets, but the models we present offer an acceptable description of within-host dynamics of several other gastro-intestinal infections. We begin by studying the case where infection is a one-time event and derive an explicit expression for the distribution of pathogens inside the intestine at an arbitrary time after the infection took place. Since farm animals often come into contact with faeces, we furthermore investigate the reinfection case, in which a fraction of the shed pathogens is reintroduced into the intestine. We find the condition that guarantees persistence of colonization in the reinfection case and determine when the microbial distribution in the intestine obeys the so called asynchronous exponential growth. We outline possibilities for infection control and point out some challenges for further research on the subject.

Superinfections can induce evolutionarily stable coexistence of pathogens.

Parasites reproduce and are subject to natural selection at several different, but intertwined, levels. In the recent paper, Gilchrist and Coombs (Theor. Popul. Biol. 69:145-153, 2006) relate the between-host transmission in the context of an SI model to the dynamics within a host. They demonstrate that within-host selection may lead to an outcome that differs from the outcome of selection at the host population level. In this paper we combine the two levels of reproduction by considering the possibility of superinfection and study the evolution of the pathogen's within-host reproduction rate p. We introduce a superinfection function phi = phi(p,q), giving the probability with which pathogens with trait q, upon transmission to a host that is already infected by pathogens with trait p, "take over" the host. We consider three cases according to whether the function q --> phi(p,q) (i) has a discontinuity, (ii) is continuous, but not differentiable, or (iii) is differentiable in q = p. We find that in case (i) the within-host selection dominates in the sense that the outcome of evolution at the host population level coincides with the outcome of evolution in a single infected host. In case (iii), it is the transmission to susceptible hosts that dominates the evolution to the extent that the singular strategies are the same as when the possibility of superinfections is ignored. In the biologically most relevant case (ii), both forms of reproduction contribute to the value of a singular trait. We show that when phi is derived from a branching process variant of the submodel for the within-host interaction of pathogens and target cells, the superinfection functions fall under case (ii). We furthermore demonstrate that the superinfection model allows for steady coexistence of pathogen traits at the host population level, both on the ecological, as well as on the evolutionary time scale.