An evolutionary cycle …

Rescan, Lenormand and Roze (2016) recently published new models on the evolution of life cycles in The American Naturalist.
An evolutionary cycle - A bicycle emerges from the water after evolving from two amoeba
Most animals and protists have diploid life cycles in which the haploid stage is reduced to a single-celled gamete.
Other organisms, such as charophytes and dinoflagellates, have a haploid life cycle in which the diploid phase is reduced to the zygote and meiosis occurs before any mitotic development.
There’s a third type of life cycle, that regular TME readers may have stumbled across with my posts: haploid-diploidy in which somatic development occurs in both haploid and diploid stages. In seed plants, the haploid stage is rather limited, but in fungi, mosses and macroalgae, the haploid stage is much more important.

[Due to the difference in duration of one phase and the corresponding limits to selection], the problem of the evolution of life cycles (i.e., the relative degrees of development of the haploid and diploid phases) is often recast in terms of the opportunity of selection within each phase.

One model suggests diploids may benefit from the masking of deleterious mutations. But, this assumes deleterious mutations have the same effect in both haploids and homozygous diploids. Recent transcriptomic studies in haploid-diploid species, such as Coelho et al. (2007), have demonstrated some genes are only expressed in one policy and mutations in these genes would have no effect in the other stage as they are not expressed.
Moreover, these genetic models cannot explain the evolutionary stability of haploid-diploid life cycles without considering additional mechanisms, such as ecological niche differentiation (Hughes and Otto 1999).
Rescan et al. (2016) explored

the interplay between ecological and genetic effects on the evolution of life cycles, [using a simple demographic model].

They found ecological niche differentiation between haploid and diploid phases can lead to a continuum of life cycle types from haploid-only to diploid-only and everything in between, just like Hughes and Otto (1999). However, when deleterious mutations are introduced and when the ecological component of selection is strong enough to favor biphasic life cycles, populations eventually evolve

to a state where alleles coding for fully haploid [i.e., haploid only, such as in charophytes] and fully diploid [i.e., diploid only, such as in animals] life cycles stably coexist.

Niche differentiation is not sufficient by itself to explain the maintenance of truly biphasic life cycles. Rather, additional mechanisms that favor this obligatory alternation are necessary, such as temporal variability in the environment, as explored by Rescan et al. (2016).
Coelho et al. 2007. Complex life cycles of multicellular eukaryotes: new approaches based on the use of model organisms. Gene 406: 152-170.
Hughes and Otto 1999. Ecology and the evolution of biphasic life cycles. The American Naturalist 154: 306-320.
Rescan et al. 2016. Interactions between genetic and ecological effects on the evolution of life cycles. The American Naturalist 187: 19-34.

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