Experimental evolution in silico: a custom-designed mathematical model for virulence evolution of Bacillus thuringiensis

Abstract

Most mathematical models on the evolution of virulence are based on epidemiological models that assume parasite transmission follows the mass action principle. In experimental evolution, however, mass action is often violated due to controlled infection protocols. This "theory-experiment mismatch" raises the question whether there is a need for new mathematical models to accommodate the particular characteristics of experimental evolution. Here, we explore the experimental evolution model system of Bacillus thuringiensis as a parasite and Caenorhabditis elegans as a host. Recent experimental studies with strict control of parasite transmission revealed that one-sided adaptation of B. thuringiensis with non-evolving hosts selects for intermediate or no virulence, sometimes coupled with parasite extinction. In contrast, host-parasite coevolution selects for high virulence and for hosts with strong resistance against B. thuringiensis. In order to explain the empirical results, we propose a new mathematical model that mimics the basic experimental set-up. The key assumptions are: (i) controlled parasite transmission (no mass action), (ii) discrete host generations, and (iii) context-dependent cost of toxin production. Our model analysis revealed the same basic trends as found in the experiments. Especially, we could show that resistant hosts select for highly virulent bacterial strains. Moreover, we found (i) that the evolved level of virulence is independent of the initial level of virulence, and (ii) that the average amount of bacteria ingested significantly affects the evolution of virulence with fewer bacteria ingested selecting for highly virulent strains. These predictions can be tested in future experiments. This study highlights the usefulness of custom-designed mathematical models in the analysis and interpretation of empirical results from experimental evolution.

Keywords: Bacillus thuringiensis; Evolution of virulence; Experimental evolution; Mass action principle; Mathematical modelling.