Why have parasites promoting mating success been observed so rarely?

Host manipulation by sexually transmitted parasites which increases host mating rate and thus parasite transmission rate has long been viewed as a plausible parasite adaptation. However, empirical evidence for it is rare. Here, using an adaptive dynamics approach to evolution, we explore conditions under which such disease-induced mating enhancement is (or is not) likely to occur. We find that increased mating success is less likely to evolve if the host reproduction rate, or the baseline disease transmission rate, is reduced, and the parasite affects just one sex, compared to when it affects both. We also find that it is less likely to evolve if the virulence-transmission trade-off curve is stronger, since we assume that enhanced disease transmission can only be achieved at the cost of increased virulence and as this trade-off is concave. In addition, we demonstrate that if disease-induced mating enhancement is equally acting in both sexes the mating system has no effect on evolutionary outcomes. On the contrary, if disease-induced mating enhancement is acting in just one sex, the potential for its evolution increases with the degree of polygyny in the host population. To study the examined phenomenon in greater detail we encourage further empirical research on this apparently less explored impact of sexually transmitted parasites on host fitness.

The impact of sexually abstaining groups on persistence of sexually transmitted infections in populations with ephemeral pair bonds.

Individuals often stop reproducing some time before they die. In this paper we compose and analyze a logistic two-sex population model in which individuals form pairs just to mate (i.e. pair bonds are ephemeral) and later move on to sexually abstaining groups. Using this model, we study the impact of sexually abstaining groups on persistence of a benign sexually transmitted infection (STI) in populations with such ephemeral pair bonds. We observe that the presence of sexually abstaining groups cannot prevent an STI from invasion or eliminate it when already present if the transition rates to the sexually abstaining groups are independent of the infection status of individuals (susceptible or infected). On the other hand, if they depend on that status, the presence of sexually abstaining groups can prevent an STI from invasion or eliminate it when present. Specifically, in the simple case of sex-independent vital parameters, this happens if the transition rate of the infected individuals to the sexually abstaining group is higher than the transition rate of the susceptible ones. These results contrast the earlier results based on assuming long-term, stable pair bonds, in which case one is capable of preventing or eliminating the disease with the same isolation rate for the susceptible and infected individuals.

A two-sex demographic model with single-dependent divorce rate.

Divorce appears to be one of the least studied demographic processes, both empirically and in two-sex demographic models. In this paper, we study mathematical as well as biological implications of the assumption that the divorce rate is positively affected by the amount of single (i.e., unmarried/unpaired) individuals in the population. We do that by modifying the classical exponential two-sex model accounting for pair formation and separation. We model the divorce rate as an increasing function of the single population size and show that the single population pressure on the established couples alters the exponential behavior of the classical model in which the divorce rate is assumed constant. In particular, the total population size becomes bounded and a unique positive equilibrium exists. In addition, a Hopf bifurcation analysis around the positive equilibrium shows that the modified model may exhibit sustained oscillations.

Global stability of the coexistence equilibrium for a general class of models of facultative mutualism.

Many models of mutualism have been proposed and studied individually. In this paper, we develop a general class of models of facultative mutualism that covers many of such published models. Using mild assumptions on the growth and self-limiting functions, we establish necessary and sufficient conditions on the boundedness of model solutions and prove the global stability of a unique coexistence equilibrium whenever it exists. These results allow for a greater flexibility in the way each mutualist species can be modelled and avoid the need to analyse any single model of mutualism in isolation. Our generalization also allows each of the mutualists to be subject to a weak Allee effect. Moreover, we find that if one of the interacting species is subject to a strong Allee effect, then the mutualism can overcome it and cause a unique coexistence equilibrium to be globally stable.

A note on 'A generalized two-sex logistic model'.

We re-visit the recently published paper on a generalization of the two-sex logistic model by Maxin and Sega [A generalized two-sex logistic model, J. Biol. Dyn. 7(1) (2013), pp. 302-318]. We show that the logistic assumption of a non-increasing birth rate can be replaced by a more general assumption of a non-increasing ratio between the female/male birth and mortality rate. In this note we indicate the changes necessary in the proofs of the theorems in [D. Maxin and L. Sega, A generalized two-sex logistic model, J. Biol. Dyn. 7(1) (2013), pp. 302--318] and discuss several situations where this new assumption is useful.

The effect of risk-taking behaviour in epidemic models.

We study an epidemic model that incorporates risk-taking behaviour as a response to a perceived low prevalence of infection that follows from the administration of an effective treatment or vaccine. We assume that knowledge about the number of infected, recovered and vaccinated individuals has an effect in the contact rate between susceptible and infectious individuals. We show that, whenever optimism prevails in the risk behaviour response, the fate of an epidemic may change from disease clearance to disease persistence. Moreover, under certain conditions on the parameters, increasing the efficiency of vaccine and/or treatment has the unwanted effect of increasing the epidemic reproductive number, suggesting a wider range of diseases may become endemic due to risk-taking alone. These results indicate that the manner in which treatment/vaccine effectiveness is advertised can have an important influence on how the epidemic unfolds.

A generalized two-sex logistic model.

We provide a generalization of the logistic two-sex model with ephemeral pair-bonds and with stable couples without assuming any specific mathematical form for fertility, mortality and the mating function. In particular, we establish a necessary and sufficient condition on the fertility/mortality density-dependent ratio that ensures the existence of the logistic behaviour. Several differences and similarities between the two models are also provided.