Directed migration shapes cooperation in spatial ecological public goods games

From the microscopic to the macroscopic level, biological life exhibits directed migration in response to environmental conditions. Chemotaxis enables microbes to sense and move towards nutrient-rich regions or to avoid toxic ones. Socio-economic factors drive human populations from rural to urban areas. However, migration affects the quantity and quality of desirable resources. The effect of collective movement is especially significant when in response to the generation of public goods. Microbial communities can, for instance, alter their environment through the secretion of extracellular substances. Some substances provide antibiotic-resistance, others provide access to nutrients or promote motility. However, in all cases the maintenance of such public goods requires costly cooperation and is consequently susceptible to exploitation. The threat of exploitation becomes even more acute with motile individuals as defectors can avoid the consequences of their cheating. Here, we propose a model to investigate the effects of targeted migration based on the production of ecological public goods and analyze the interplay between social conflicts and migration. In particular, individuals can locate attractive regions by moving towards higher cooperator densities or avoid unattractive regions by moving away from defectors. Both migration patterns not only shape an individual’s immediate environment but also affects the population as a whole. For example, defectors hunting cooperators in search of the public good have a homogenizing effect on population densities. They limit the production of the public good and hence inhibit the growth of the population. In contrast, aggregating cooperators promote the spontaneous formation of heterogeneous density distributions. The positive feedback between cooperator aggregation and public goods production, however, poses analytical and numerical challenges due to its tendency to develop discontinuous distributions. Thus, different modes of directed migration bear the potential to enhance or inhibit the emergence of complex and sometimes dynamic spatial arrangements. Interestingly, whenever patterns emerge in the form of heterogeneous density distributions, cooperation is promoted, on average, population densities rise, and the risk of extinction is reduced. Author summary The production and maintenance of shared environmental resources such as access to nutrients in microbial communities or potable water in human societies require the cooperation of groups of individuals. However, cooperation is costly and prone to exploitation. If too many individuals follow selfish interests and spoil their environment, the group and possibly the entire population suffers. Nevertheless, many forms of biological life – from humans to microbes – migrate in response to resource availability. Here, we analyze the interplay of the social conflict in public goods production and targeted migration. In particular, we find that aggregation of cooperators can enhance or trigger the spontaneous formation of heterogeneous spatial distributions, which promote cooperation and result in higher population densities. Conversely, attempts to avoid defectors increases the risk of extinction because it tends to homogenize population distributions and lower population densities.