A resource based model for the competition of two species with different metabolic pathways

The evolution of cooperation is one of the most intriguing conundrum in evolutionary biology. Natural selection favours traits that increase individual?s ability to reproduce or survive. One individual is said to be cooperative if it provides a benefit to another individual or to a group at the expense of its own relative fitness. According to evolutionary theory, such cooperative behaviour is detrimental to the individual and should be counter-selected. Instead, the selfish behaviour is expected to rise and invade in a group of cooperators. However, cooperation is observed everywhere. Despite the greater attention the issue has received in the last decades our understanding about the underlying mechanisms that explain the emergence and maintenance of cooperation is still poor. Here we combine the frameworks of resource-based modeling and evolutionary game theory to study the conditions under which cooperative strains can thrive in the context of metabolic pathways.

Heterotrophic organisms can produce adenosine triphosphate (ATP) from two different mechanisms: inefficient (high rate) in which high amount of resources is consumed or efficient (high yield) with less resource consumption. Despite cells with a higher rate but lower yield of ATP production may have a selective advantage compared with high yield cells, the latter is abundant in nature. To be well succeeded the high yield cells behave as a cooperative organism while high rate cells are non-cooperative. This problem can be posed in terms of competition between cooperative and selfish cells. Here we investigate the probability that a cooperative trait can invade a population of defectors (high rate of consumption, but low yield of conversion of research into energy) by using multilevel selection, where individuals (cells) are organised into groups. Selection occurs at both individual and group levels. Selection at the group level stems from differentiated growth rates that vary according to the group's composition. We show in what conditions high yield cells can invade a population of high rate metabolic cells. One of the motivation to study this problem is understanding the transition of unicellular organism (high rate) to multicellular (high yield).