Evolution Requires Reduction in Genetic Diversity

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I disagree. If a new allele arises it can only be passed on if the whole of the individual is selected for.

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This is incorrect, though whether the error is one of terminology or of concept I'm not sure. A new allele can be passed on even if the individual who carries it has lower fitness than other individuals in the population. In particular, it can be passed on even if the new allele is responsible for the lower fitness. This is identical to saying that it is passed on despite being selected against.

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A most excellent mutation will be stopped dead if it pops up first in an individual whose remaining genome causes the individual to get caught in the sieve of natural selection.

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A most excellent mutation, occurring in an individual with nothing but excellent alleles, can still be stopped dead if the individual is hit by a truck -- or simply fails to pass on that allele to any of its descendants. There is a large amount of randomness in the transmission of alleles that has nothing to do with selection.