weak selection - senecio7の日記

Ohtsuki H 2010 Evolutionary games in Wright's island model: kin selection meets evolutionary game theory. Evolution 64:3344-3353.

it has been argued that nonadditivity of social interaction (or termed synergistic effect) is not captured well by inclusive fitness hence kin selection theory applies only to a special class of game models
other authors argue that nonadditivity can be studied in the framework of kin selection
one reason for this discrepancy is because those two fields have adopted different approaches
evolutionary game theory usually explores games described by payoff matrices and investigates dynamic properties of the system
it pays relatively little attention to its precise genetic background
kin selection theory, on the other hand, usually assumes weak selection and/or additivity of several effects
I will show that genetic association between two individuals is not enough but that genetic association between three individuals is sufficient to solve the nonadditivity issue

the assumption of weak selection (i.e., δ ≪ 1) guarantees that those quantities can be calculated under neutrality, δ = 0, for the use in equation (5)
see Appendix S1

juveniles produced in the FI's deme, to whom the FI is related by R₂^R on average, suffer from the increased competition
through using strategy k, the FI can cause an extra increase in kin competition in its natal deme, only when the FI is related to its game-opponent and the synergistic effect, (a_kk − a_k● − a_●k − a_●● + 2a_●○), is produced
this increase in competition becomes a kin-selected indirect cost to the FI only when juveniles produced in the FI's natal deme are related to the FI
this event occurs with probability R₃^RN

traditional inclusive fitness theory has often focused on the case in which the payoff (or fecundity) is additively determined by behaviors of two interactants
under such a scenario R₃ does not appear
all we need is genetic correlations between two individuals
when the model describes the competition between two strategies (biallelic model), one can reproduce a frequency-dependent inclusive fitness
for more general nonadditive games, however, the coefficient of triplet relatedness appears
genetic correlations among three individuals must be taken into account
a primary reason why the coefficient of triplet relatedness, R₃ appears in my basic equation is because one's fitness is affected by results of the game between two other players in the same deme
we need to take into account the genetic association between an FI and two other players engaged in a game in the same deme

it has been argued that inclusive fitness can deal with only a special class of games or games with two strategies
for additive games genetic association between two individuals is sufficient to describe evolutionary game dynamics
for nonadditive games we need up to triplet genetic association to study the full dynamics
the theoretical framework provided in this article extends traditional inclusive fitness to incorporate triplet relatedness such that we can study a general matrix-form game with any number of strategies played in the Wright's island model
it is now clear that triplet genetic association solves the long-lasting nonadditivity issue