4.1 Phylogeny and Evolution

33

The social insects (cf. Sect. 14.4.1) form a nice example of this rule in operation. ¹³

Actually, group selection and kin selection are formally equivalent ¹⁴ and there

seems to be little justification for the sometimes acrimonious disputes favouring one

or the other mechanism.

The Price equation describes the effect of selection:

Delta upper Q equals Cov left parenthesis z comma q right parenthesis divided by z overbarΔQ = Cov(z, q)/¯z

(4.2)

whereDelta upper QΔQ is the difference in gene frequency (or, probably better, phenotypic value)

in consecutive generations, zz is the number of offspring of individuals, qq is the

genetic or phenotypic value of individuals,z overbar¯z is the arithmetic mean ofzz in the parent

generation, and assuming that random drift averages out to zero. If that assumption

does not hold, then a “transmission effect” is added to Eq. 4.2:

Delta upper Q equals Cov left parenthesis z comma q right parenthesis divided by z overbarΔQ = Cov(z, q)/¯z +

Σ

i

ziΔqi(N ¯z)

(4.3)

where upper NN is the population size and Delta q Subscript i BaselineΔqi is parent-offspring difference of qq. The

equation states, in effect, that natural selection is a product of the gradient of relative

reproductive success (z divided by z overbarz/¯z, i.e., fitness) v. genetic or phenotypic valueqq for the indi-

vidual, and the (genetic or phenotypic) variance of the trait in the population. Price

considered that the relationship between fitness andqq is linear. This is, however, too

simplistic; very likely it is concave, and Stearns (2000), drawing on D. Bernoulli’s

1738 paper (cf. Sect. 6.2.1) shows how for a risk-averse population (the relationship

is concave-down) selection should act to reduce variance in the trait, whereas for a

risk-prone population (the relationship is concave-up) selection should act to increase

variance in the trait.

Temporal variance in fitness constitutes evolutionary risk, to capture which the

geometric rather than the arithmetic mean of reproductive success should be taken

(fitness is multiplicative, cf. Sect. 9.3.4). ¹⁵ The phenomenology of life histories and

evolutionary genetics are thus more complex than captured by the Price equation. For

example, local (in the parental habitat) settlement of offspring is risk-prone; broad

dispersal is risk-averse. Stearns gives further examples.

Clearly there are trade-offs between means and variances of multiple traits to ulti-

mate evolutionary success. One such trade-off is between competition and coöpera-

tion, which brings us back to eusociality.

13 A related phenomenon is eusociality, in which some individuals diminish their own lifetime

potential by raising the offspring of compeers—see Nowak et al. (2010) and critiques in Abbot

et al. (2011), Boomsma et al. (2011) and Ferrière and Michod (2011).

14 Marshall (2011).

15 They are simply related, for example:

Delta upper Q equals Cov left parenthesis z comma q right parenthesis divided by z overbar˜z ≈(¯z² −Var(z))^1/2

(4.4)

wherez overTilde˜z is the geometric mean (the Latané approximation).