The aim of this project is to investigate the hydra effect occurring in a population infected by a disease. First, I will explain what exactly the hydra effect is. Intuitively, higher mortality rate applied to a population will decrease the size of that population, but this is not always the case. Under some circumstances the population size might increase with higher mortality, causing the phenomenon called by Abrams and Matsuda (2005) the 'hydra effect', after the mythological beast, who grew two heads in place of one removed. Abrams (2009) lists in a few mechanisms underlying the hydra effect from which the one I will focus onis a temporal separation of mortality and density dependence.
Most work on the hydra effect involved explicit increase of a death rate, for example by harvesting. The idea of this thesis is to investigate the existence of the hydra effect due to mortality increased not explicitly, but through a lethal disease. Such an approach has not been shown in any published work so far. Instead of harvesting, we will have a virulence, the disease-induced mortality.
In this project, I fi rst briefly explain some theory underlying my model. In chapter 2 I look at disease-free population and bifurcation analysis when varying the birth rate. In chapter 3 I propose the model and continue with population dynamics analysis. I look at bifurcations of equilibria when varying birth rate, virulence and transmission rate. Then in section 3.4 I investigate whether it is possible to observe the hydra effect if there exists a trade-off between virulence and transmission rate, and derive a condition for transcritical and fold bifurcation to occur. In chapter 4 I focus on evolution of traits. First I study evolution of the pathogen, assuming the same trade-off as earlier. Finally I look at evolution of host's traits, immunity and birth rate, using Adaptive Dynamics framework (Geritz et al. 1998). I compare two possible trade-off functions and show that with a concave trade-off, the host will evolve to getting rid of the disease despite increasing its immunity.
