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Decius comments on Does evolution select for mortality? - Less Wrong
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... Except that it strongly selects FOR organisms that have an infinite number of offspring, regardless of other pressures.
Depends on when the reproduction happens. Say the organism becomes sexually mature in 20 years, then as far as evolution is concerned the organism 40 year old self is the equivalent of two addition offspring in the first litter. And that's assuming the organism is as good at reproducing at 40 as at 20.
It's all about the death rate from things other than aging, or how much immortality extends expected lifespan. Side effects of immortality which reduce competitiveness aren't inherent with immortality.