Group vs. Individual selection

Transcription

1 Group vs. Individual selection There can be a tension between within groupselection, which favors X, and between-group selection, which favors A. Suppose that groups with two or more Xs do not survive. But within successful groups, X is more fit than A. Can you think of an example? 1

2 Let zi be the breeding value of the i th individual in the th group. Members mean breading value mean fitness covi, zi) group 1 z11 to zn1 z1 1 covi1,zi1) group 2 z12 to zn2 z2 2 covi2,zi2) group 3 z13 to zn3 z3 3 covi3,zi3) Mean of groups z E[covi,zi)] hat is the between group effect? hat is the within group effect local host competition?) 2

3 The Price equation. Let s start with selection at the level of the group. Suppose we have groups, each with I individuals per group. Let z be the average breeding value over all groups. By the full Price equation, we have = cov'z, * +!, where is the frequency of groups having group fitness, where is absolute group fitness Multiply both sides by to get: = covz, *+E * where the second term on the RHS is the mean of the products: 3

4 = covz, *+E * Now let pi equal the frequency of individuals in population with breeding value i. As such, E# ' =E cov#z i, i '+E#Δz i i ' where i is the absolute fitness of individual i in group. Thus the whole puppy containing selection within and between groups is: w = covz, ++E-covz i, i ++EΔz i i +/ Assuming no transmission bias during meiosis e.g., no meiotic drive) the Expectation term within brackets is zero i.e., E#Δz i i = 0). Hence for two levels of selection, we get 4

5 = covz, *+E,covz i, i *. where the first covariance term on the Right Hand Side is selection between groups, and the second covariance term on the RHS is selection within groups averaged over all groups). Note that the two terms could have different signs, selection among groups is positive, and selection within groups is negative. If there is only one group, we get Δz = cov'z i, i * Δz cov'z = i, i * Δz β,z = var'z *! since z is a breeding value, the varz) is the variance in breeding values, which is the additive genetic variance. Thus we recover the breeder s equation division by bar gives relative fitness, which is what we used previously for delta zbar) 5

6 Finally, if the trait is fitness, we have Δ var& ' =! where var) is the variance in breeding values for fitness, which gives Fisher s fundamental theorem of natural selection: the change in mean fitness is equal to the additive genetic variance for fitness divided by mean absolute fitness). Hamilton s rule can also be derived from the Price equation How to derive the Price equation? 6

7 = z z = q ' z 'z = q 'z + 'z q = 'z + 'z q = q 'z + ' 'z = z 1 + = z ) z )+ ' now multiply both side by bar 'Δz 1 7

8 Δz = z ) z )+ Δz = E'z z )+ ' Δz = cov ',z +E' 'Δz 1 Note: in the second to last line, the first term on the RHS is the mean of the products. The second term on the RHS is the product of the means. The mean of the products minus the product of the means is a covariance. The third term on the RHS is the mean or E for expectation) of the product of and delta z. The last line can be rewitten to give the first equation on page 1: = cov'z, * + 8