When does the good of the group override the advantage of the individual?

In a system of N populations of n reproductive individuals apiece, in which each population has constant variance v² and lasts L generations, group selection on a quantitative character has a reasonable chance of overriding selection within populations if (and only if) the populations never exchange migrants, each population is founded by colonists from a single parent population, and the number of populations exceeds the effective number of reproductive individuals per population. If each population derives from a single parent population, then the exchange of a single successful migrant per population per L generations can triple the strength of group selection required to overcome a given selection within populations. If populations exchange no migrants, then the derivation of one in every N populations from two equally represented parents (while the others all derive from a single parent) doubles the strength of group selection required to prevail. Group selection is accordingly likely to be effective only in certain categories of parasites.