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Open Access Highly Accessed Research article

Selection for altruism through random drift in variable size populations

Bahram Houchmandzadeh* and Marcel Vallade

Author affiliations

Univ. Grenoble 1/CNRS, LIPhy UMR 5588, Grenoble, F-38401, France

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Citation and License

BMC Evolutionary Biology 2012, 12:61  doi:10.1186/1471-2148-12-61

Published: 10 May 2012



Altruistic behavior is defined as helping others at a cost to oneself and a lowered fitness. The lower fitness implies that altruists should be selected against, which is in contradiction with their widespread presence is nature. Present models of selection for altruism (kin or multilevel) show that altruistic behaviors can have ‘hidden’ advantages if the ‘common good’ produced by altruists is restricted to some related or unrelated groups. These models are mostly deterministic, or assume a frequency dependent fitness.


Evolutionary dynamics is a competition between deterministic selection pressure and stochastic events due to random sampling from one generation to the next. We show here that an altruistic allele extending the carrying capacity of the habitat can win by increasing the random drift of “selfish” alleles. In other terms, the fixation probability of altruistic genes can be higher than those of a selfish ones, even though altruists have a smaller fitness. Moreover when populations are geographically structured, the altruists advantage can be highly amplified and the fixation probability of selfish genes can tend toward zero. The above results are obtained both by numerical and analytical calculations. Analytical results are obtained in the limit of large populations.


The theory we present does not involve kin or multilevel selection, but is based on the existence of random drift in variable size populations. The model is a generalization of the original Fisher-Wright and Moran models where the carrying capacity depends on the number of altruists.

Frequency independent fitness; Genetic drif; Fixation probabilities; Non-structured populations