In certain species only the dominant male gets to mate (or given strong preference), and yet the sex ratio remains 1:1. (I'm thinking in particular of gorillas). How does this happen? It doesn't seem like Fisher's argument should apply in this case.
Fisher's principle applies to such cases as much as it does to species where only pairs mate. Consider a species where a successful male has exclusive mating with a harem of 20 females, and for each such male, 19 other males are not able to mate. A female has 100% chance of mating, and a male has a 5% (1 in 20) chance of mating. Assume a female has two offspring.
In this scenario, an equal sex ratio would mean having a female offspring would lead to an expected number of grand-offspring of 2 (100% chance of 2 offspring from that female). Having a male offspring would also lead to an expected number of 2 grand-offspring (95% times 0 offspring plus 5% times 20 harem females each having 2 offspring).
What would happen if the ratio of births was off from 1 to 1, say 5 females were born for each male? Then expected number of grand offspring would be for a female is still 2, but for a male it is 25% (chance of taking a harem of 20 females against the 3 other males born alongside those 20 females) x 40 (20 harem matings x 2 offspring) = 10. Hence with a lopsided sex ratio in this situation, having a male is much more valuable genetically than having a female. If a mutant arose which produced more male offspring in this imbalanced situation, it would have success until the population sex ratio became close to 1:1.Tweet