2011-19_Kin - EVOLUTION (11:704-486) KIN SELECTION SMOUSE...

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EVOLUTION (11:704-486) – KIN SELECTION S MOUSE – SPRING 2011 1 Kin Selection Inclusive Fitness I want to pick up on this idea of kin selection. The idea goes something like this (Hamilton W, 1964, J Theo Biol 7 :1-52). My fitness, in the absence of interactions with anyone else, is a i (I’m the i th individual). We index other individuals in the population by j = 1, . . . , N . My fitness value is denoted W i = a i , in the absence of interactions among individuals, i.e., if I just “mind my own business.” The fitness values of others are denoted as W j = a j , assuming they are also minding their own business. I’ll win if a i > a j for all the j i , everything else equal. On the other hand, if I do anything altruistic for someone else, that reduces my fitness by a cost figure c i , but I increase the fitness of anyone else (say the j th individual) whom I choose to help. The increase in fitness to the j th individual is b j , so that Fitness of i th individual (me): W i = ( a i c i ) Fitness of j th individual (you): W j = ( a j + b j ) Now, if you and I are related, it might be worth the cost to me to increase your fitness. It depends on how much mine (W i ) goes down, how much yours (W j ) goes up, the degree to which we are related ( r ij ), and how many of you there are that I am benefiting ( N ). I would do more for offspring than for cousins, and more for full-sibs than for half-sibs. What Hamilton did was to come up with a simple model. My inclusive fitness , he said, is simply my fitness, minus the cost to me, plus the benefit to you, weighted by the degree of relationship between us (where r jj ) is the degree of genetic relationship between us. Inclusive Fitness =  b r c a j N j ij i i i 1 W Relationship - My full-sibs / parents / progeny all have r ij = ½. Any allele I have has a 50% chance of being found in a parent, a full-brother or a full-sister. My half-sibs have r ij = ¼, or a 25% chance of sharing any particular allele with me. My full cousins have r ij = 1/8, or one chance 8 of sharing any particular allele I have. With the rest of you, I share almost nothing. If I die in keeping two 1 st degree relatives alive, who would otherwise have died, I can break even. If I can die and keep four 2 nd degree relatives alive, I can break even. I am going to need 8 cousins to make it a fair trade, and the of you are out of luck. Futuyma describes the relationships between various types of individuals. He covers both the standard diploid case and the haplo-diploid case that works for hymenoptera (haploid males, diploid females). We can treat mitochondria, chloroplasts, X and Y chromosomes in similar fashion. The details vary with genetic transmission; the principle does not. I may offer aid rather indiscriminantly to individuals in my own social group, but I can
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This note was uploaded on 08/18/2011 for the course ECOLOGY 301 taught by Professor Staff during the Spring '11 term at Rutgers.

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2011-19_Kin - EVOLUTION (11:704-486) KIN SELECTION SMOUSE...

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