# In the Selfish Gene, the chapter about ESS, how do the doves spread their genes?

In his explanation of the Evolutionary Stable Strategy, in the Selfish Gene, Richard Dawkins repeats a couple of times, that a population of hawk-type males would make the ground for a dove-type individual to spreat his genes, because the dove always retreats against a hawk and if an average hawk loses every second match, than he'll be worse off than the dove that always retreats and stays unhurt.

My question is - how dose a male, that does not win a single contest for a mate and therefore doesn't get to mate at all, spreat his genes? Does the ESS imply that there are ways to breed bypassing the contest?

• I don't know enough about the model to really give an answer, but I guess that if a dove keeps trying he might eventually come across a mate who isn't being protected by a hawk. The dove's strategy isn't winning fights, but in finding opportunities where there won't be a fight. – user137 Apr 9 '18 at 1:23

Game theory

Your question is not as specific to biology as you may think. The hawk-dove game is a type of game in game theory, a field of mathematics. Game theory is used in biology, in economics, in psychology and many other disciplines.

The hawk-dove game is often called the chicken game. If a game is defined as a chicken game, then it has an equilibrium different from 0 or 1. Otherwise, it may not.

You need to fully specify the scenario of interest to figure our what type of game we're dealing with to know what type of game we're dealing with and what are the possible equilibriums.

For more information, have a look at the mathematical field of game theory.

You specific scenario

The scenario as written in your post is not fully discribed. In your question, you define the doves such as they have a fitness (or a payoff in game theory terms) of 0, whatever is the state of the population. For such case, of course, a frequency of doves of 1 cannot be an ESS. However, under such case, you are not dealing with a hawk-dove game. I suspect you misunderstood the game as defined by Dawkins (it is also possible that Dawkins did not fully define the game he's talking about).

In short...

In short, I can't say much else than just "read more about game theory". However, you might want to cite exactly Dawkins so that we can understand exactly how he describes the specific game at play and comment on the expected outcome.

A male that does not mate will not spread his genes. Females might, if they have the option to reproduce asexually. However, this is probably not the answer you are after though. What you need to do is to look at the assumptions behind the game theory model being used.

For instance, some of the assumptions in a basic ESS-analysis are usually:

1. that the population size is infinite.

2. that the game payoffs are fitness modifiers and do not determine absolute levels of fitness.

Point 1 means that the game payoffs refer to the average payoff of individuals in each type of encounter. Point 2 means that there is always a baseline level of fitness, so all strategies are able to reproduce. Sometimes, assumption 2 is reformulated in terms of asexual populations, which means that all individuals will be able to reproduce (so the hawk-dove game will strictly not the modelling access to mates).

Therefore, doves (which never escalate a contest) will be able to "spread their genes" (win the contest) 50% of the times when there is a dove-dove contest (here is a description of what appears to be the normal version of the hawk-dove game). A single dove that enters a population will also be able to reproduce, even though it will never win contests (based on assumption 2). Again, remember that the game payoffs are fitness modifiers and does not determine the absolute level of fitness.

This means that individuals that play the dove strategy will still be able to spread their genes to later generations, but this doesn't preclude that certain dove individuals never get the chance to reproduce. This also means that there isn't any need for "ways to breed bypassing the contest", since one of the assumptions is that all strategies can reproduce, and in this case all strategies also have a payout option where they sometimes win the contest (which is the case for the hawk-dove game).

You are adding assumptions that are not there.

You assume not winning equals not mating, it doesn't, if a dove meets a female by herself they mate. The example of elephant seals he uses shows this, some males fight others wait for unattended females.

• Oh, didn't notice that.. – Shanidze Apr 11 '18 at 19:34