TY - JOUR
T1 - Natural selection of altruism in inelastic viscous homogeneous populations
AU - Grafen, Alan
AU - Archetti, Marco
N1 - Funding Information:
The paper is a development of important insights of Taylor et al. (2007a) , and we are very grateful to Peter Taylor, Troy Day and Geoff Wild for sight of the manuscript of that paper. Laurent Lehmann, Laurent Keller and David Sumpter generously allowed us sight of a MS of Lehmann et al. (2007a) . We are grateful to the authors of both those papers, and to Martin Nowak, for helpful discussions about inclusive fitness on graphs. Laurent Lehmann, Peter Taylor, Andy Gardner, Stu West and Laurent Keller made extremely useful comments on the manuscript. The counter-example in Fig. B1 was pointed out to us by Colin McDiarmid and Peter Cameron, who kindly gave us permission to include it here, and we are grateful to Philip Maini for passing the problem on to them. The very neat formulation for compensated relatednesses in Eq. (4) and following equations was acutely and generously suggested by one referee. The other very rightly encouraged a better attempt to make connections to the literature on structured populations that predates the graph theory approach. We are grateful to them both. M.A. is supported by a long-term fellowship of the Human Frontier Science Program Organization.
Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2008/6/21
Y1 - 2008/6/21
N2 - Biological explanations are given of three main uninterpreted theoretical results on the selection of altruism in inelastic viscous homogeneous populations, namely that non-overlapping generations hinder the evolution of altruism, fecundity effects are more conducive to altruism than survival effects, and one demographic regime (so-called death-birth) permits altruism whereas another (so-called birth-death) does not. The central idea is 'circles of compensation', which measure how far the effects of density dependence extend from a focal individual. Relatednesses can then be calculated that compensate for density dependence. There is very generally a 'balancing circle of compensation', at which the viscosity of the population slows up selection of altruism, but does not affect its direction, and this holds for altruism towards any individual, not just immediate neighbours. These explanations are possible because of recent advances in the theory of inclusive fitness on graphs. The assumption of node bitransitivity in that recent theory is relaxed to node transitivity and symmetry of the dispersal matrix, and new formulae show how to calculate relatedness from dispersal and vice versa.
AB - Biological explanations are given of three main uninterpreted theoretical results on the selection of altruism in inelastic viscous homogeneous populations, namely that non-overlapping generations hinder the evolution of altruism, fecundity effects are more conducive to altruism than survival effects, and one demographic regime (so-called death-birth) permits altruism whereas another (so-called birth-death) does not. The central idea is 'circles of compensation', which measure how far the effects of density dependence extend from a focal individual. Relatednesses can then be calculated that compensate for density dependence. There is very generally a 'balancing circle of compensation', at which the viscosity of the population slows up selection of altruism, but does not affect its direction, and this holds for altruism towards any individual, not just immediate neighbours. These explanations are possible because of recent advances in the theory of inclusive fitness on graphs. The assumption of node bitransitivity in that recent theory is relaxed to node transitivity and symmetry of the dispersal matrix, and new formulae show how to calculate relatedness from dispersal and vice versa.
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U2 - 10.1016/j.jtbi.2008.01.021
DO - 10.1016/j.jtbi.2008.01.021
M3 - Article
C2 - 18371985
AN - SCOPUS:44449127028
VL - 252
SP - 694
EP - 710
JO - Journal of Theoretical Biology
JF - Journal of Theoretical Biology
SN - 0022-5193
IS - 4
ER -