The sexual has several parameters at its disposal, in the sense that selection could mold its sexual cycle in any of several different directions (increased fusion, decreased splitting, etc.). We have seen that if damage is low there is a tradeoff between sexuality and asexuality, but that haploids generally beat the diploid due to their superior replication rates. If a sexual uses more fusion than necessary, it relinquishes its superiority to an outcome of competitive coexistence with the diploid (if the haploid is absent). In competition with the haploid, selection might eliminate a "fusion-happy, sexual, perhaps by back-mutation to a haploid in that case.
The asexual haploid cannot cope with high damage. So, when damage is high, only the sexual can compete with a diploid. The sexual cycle must maintain a minimum level of activity before the sexual can even begin to compete with the diploid. If this condition is met, then initial conditions give the outcome to one or the other of the two species or to competitive coexistence. The actual outcome is a function of initial conditions. Our computer experiments have failed to produce interesting dynamical behavior (periodic limit cycles or chaos), and we believe it unlikely that such behavior is possible in this system (for biologically reasonable parameter values) in spite of the large number of free parameters and dimensions. - in Origin of sex for error repair. I. Sex, diploidy, and haploidy.