Evolution of searching and life history characteristics in individual-based models of host-parasitoid-microbe associations

In this paper we develop a novel discrete, individual-based mathematical model of the evolution of life history, dispersal and other behavioural characteristics in insect host-parasitoid-microbe associations, and use it to investigate their evolutionary dynamics. For any individual characteristic the model begins with an even, rectangular distribution of characteristic values. Selection is then allowed to act, and the change in the distribution of the characteristic values is observed. Evolutionary change in the population variance of the characteristic value is also observed, since we would expect this to decline under selection in most cases. The paper, therefore, introduces a general framework for modeling problems of evolution in stochastic, spatially structured environments, where movement and dispersal are under selection. The model then extends this approach to include the sex-distorting bacterium Wolbachia in order to investigate aspects of its horizontal and vertical transmission under different levels of superparasitism by parasitoids. The model also includes a neutral genetic marker, in order to be able to detect changes in phenotype frequency caused by genetic drift, as well as a simplified simulation of sexual reproduction so as to allow the possibility of recombination between genotypes. Key results from the model simulations show that: (i) the refractory time after oviposition affects the value of superparasitism, with short refractory times favouring high rates of superparasitism; (ii) variable levels of superparasitism do not affect the stable proportion of the population of parasitoids infected with Wolbachia, but this is achieved by different evolutionary pathways under low and high superparasitism, respectively. In the case of low superparasitism Wolbachia spreads mainly by vertical transmission, leading to population replacement, whereas when superparasitism rates are high there is significant horizontal transfer.