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An equation to determine the minimum offspring required per group of species to continue on without extinction?

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I know that genetic mutations are a major part in allowing the next generation to continue on because in order for there to be the "choice" of an offspring that can be fit for a certain environment there must be multiple "choices" available for that species to live on. However, I assume there must be a particular amount of offspring to allow the needed gene to move onto the next generation. I also assume that there is a required amount of that particular species(parents) to allow the probabilities to allow that particular offspring to be born and carry on with the gene.

 

If all my assumptions are correct, and correct them if they are wrong, is there an equation to determine what the minimum amount of offspring needed to allow this gene to move on to the next generation, given the amount of parents needed is already met? I can clarify if this doesn't make sense.

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The problem can and has been modeled, the complexity of the model depending upon the assumptions one makes regarding the population and the nature of the mutation.

 

The simplest cases are probably those that were first investigated by Fisher back in the 1920s. However, I think the work of Ken-ichi Kojima is more what you are looking for.

 

Unfortunately, there is no simple equation and each case has to be modeled individually, each giving a probability of survival for a given generation.

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