In a constant environment, asexuality is the most efficient and reliable form of reproduction, as it directly copies the genomes of parents who survive to reproduce. Asexuality also avoids the many costs of finding and attracting a mate, not to mention sexually transmitted diseases. If the world were constant, organisms would likely be asexual.
The world is, however, ever-changing. Species must continually adapt in the face of environmental shifts, fires and other catastrophes, as well as constantly evolving parasites, prey, and predators.
Asexual populations are very much limited in their evolutionary potential by the genomes currently present within a population, while sexual populations can evolve much further by mixing and matching genes initially present in different individuals. Sexual reproduction shuffles genetic variants throughout the entire genome, providing an almost limitless variety for evolution to act upon, even with a limited number of individuals within a species. Models of this combinatoric problem have indeed found that genes increasing the amount of sex can spread.
The bottom line: In our changing world, more sexual individuals leave descendants with a greater variety of genomes, the best of which is most likely to survive, spreading the genes that make sex so common.
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