Stirring does not make populations well mixed

In evolutionary dynamics, the notion of a ‘well-mixed’ population is usually associated with all-to-all interactions at all times. This assumption simplifies the mathematics of evolutionary processes, and makes analytical solutions possible. At the same time the term ‘well-mixed’ suggests that this situation can be achieved by physically stirring the population. Using simulations of populations in chaotic flows, we show that in most cases this is not true: conventional well-mixed theories do not predict fixation probabilities correctly, regardless of how fast or thorough the stirring is. We propose a new analytical description in the fast-flow limit. This approach is valid for processes with global and local selection, and accurately predicts the suppression of selection as competition becomes more local. It provides a modelling tool for biological or social systems with individuals in motion.FHA thanks Consejo Nacional de Ciencia y Tecnología (CONACyT, Mexico) for support. VPM acknowledges support by Ministerio de Economía y Competitividad and Xunta de Galicia (MAT2015-71119-R, GPC2015/014), contributions by COST Action MP1305 and CRETUS Strategic Partnership (AGRUP2015/02)S