You should read the selfish gene. He has a chapter on this question.
The answer is that the time period depends upon the longevity (in generations) of the piece of DNA that you take as your “basic unit of selection”; the gene isn’t a precisely defined concept, rather Darwinian theory is parametric over the length of the basic unit of selection. In this case, it doesn’t really matter.
For most purposes, selection should be on the long time scale. If the environment is uniform, long-term fitness should be the same as short-term fitness (though less random). If there are occasional catastrophes and population bottlenecks, then being adapted to them may be more important than being adapted to the usual environment. Even with a uniform environment, there may be a long tail to male fitness which is not easily observed in the short-term. Genghis Khan demonstrates that there is, at least occasionally, a long tail to human male reproductive success. If genetic factors were relevant and the opportunity arose reasonably often, then we should expect those genes to spread, even if they impede normal reproduction.
I don’t understand this question
Is selection for having the most grandchildren, or is it for having the most descendants a millennium later?
I’m not sure that’s a real distinction, but I’m not sure that it isn’t, either.
You should read the selfish gene. He has a chapter on this question.
The answer is that the time period depends upon the longevity (in generations) of the piece of DNA that you take as your “basic unit of selection”; the gene isn’t a precisely defined concept, rather Darwinian theory is parametric over the length of the basic unit of selection. In this case, it doesn’t really matter.
For most purposes, selection should be on the long time scale. If the environment is uniform, long-term fitness should be the same as short-term fitness (though less random). If there are occasional catastrophes and population bottlenecks, then being adapted to them may be more important than being adapted to the usual environment. Even with a uniform environment, there may be a long tail to male fitness which is not easily observed in the short-term. Genghis Khan demonstrates that there is, at least occasionally, a long tail to human male reproductive success. If genetic factors were relevant and the opportunity arose reasonably often, then we should expect those genes to spread, even if they impede normal reproduction.