{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

2011-19_Kin

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

This preview shows pages 1–2. Sign up to view the full content.

E VOLUTION (11:704-486) K IN S ELECTION S MOUSE S PRING 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 get away with that, provided the group is heavily infiltrated with my own kin. I’ve made the point that small populations are highly related internally. Small groups are really ‘kin groups’. Most everyone is related; ‘group selection’ is really ‘kin selection’, in disguise.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 8

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online