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2018 ; 8
(1
): 4068
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Stirring does not make populations well mixed
#MMPMID29511246
Herrerías-Azcué F
; Pérez-Muñuzuri V
; Galla T
Sci Rep
2018[Mar]; 8
(1
): 4068
PMID29511246
show ga
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.