Mathematical Models of Microbial Evolution: Cooperative Systems

Abstract

Microbes usually live in large communities, where they interact with other organisms and species. These interactions include cooperation, when individuals facilitate each others growth and reproduction. Such cooperation has been for instance observed within pathogens in the process of infection. Therefore, given the number and the frequency of infectious diseases, understanding the nature and the dynamics of microbial cooperation may be a crucial step in modern medicine. Microbes often secrete costly enzymes which extracellularly metabolise resources available in the environment. This external metabolism is a form of ’public good cooperation’, in which individuals invest their energy in producing ’public goods’, available to other organisms. To study this phenomenon we deploy mathematical models which are based on biologically relevant assumptions. Our models not only aim to capture the dynamics of studied microbial communities, but also to remove the natural complexity arising in the empirical studies and thus to provide a mechanistic understanding of their results. We first recover and explain the recent empirical finding, about mixed strain infections, showing that an addition of a low virulent strain which does not produce public goods (termed ’cheat’) may counter-intuitively enhance the total population virulence. What drives this result turns out to be an interaction of two different cooperative traits and the presence of spatial structure. Next we study the competition between the strains that do and do not produce public goods. Our results depend on environmental conditions, such as resource concentration and population density, but they are also determined by the degree of spatial structure - the ecological trait which so far has been treated only as a binary variable. Finally, we identify some environmental threats for the external metabolism feeding strategy, and we examine its competitiveness in comparison to ’internal metabolism’, in which the costly enzymes are private.