To confirm the generality of the simulations, we derived an analytic solution for the initial spread or decline of a rare recessive fertilization mutation (additional file 2).
Researchers have thought that the animals' long penises, which wave around until they find a neighbor and eject sperm into an egg-bearing cavity, were their only means of solving the problem, aside from a few rare cases of self-fertilization.
Identical parent-offspring haplotypes could be a result of either repeated inbreeding or possibly self-fertilization of rare bisexual individuals.
Self-fertilization is also rare.
We examined intra-and interspecific variation in potential for self-fertilization among four rare fern species, of which two were diploids and two were tetraploids: Asplenium scolopendrium (2n), Asplenium trichomanes subsp. quadrivalens (4n), Polystichum setiferum (2n) and Polystichum aculeatum (4n).
However, there are two observations that suggest that, at least in plants, self-fertilization or double reduction may rarely affect results: first, of the established autotetraploid plant species that have been documented and studied, multivalent formation (and thus the possibility of double reduction) and self-fertilization are both rare.
Apogamous reproduction, the formation of a sporophyte from a gametophyte without fertilization, is not a rare reproductive mode in ferns [32].
Previous research indicated moral considerations related to stage 2 or 3 are rather frequent, whereas anecdotal information points towards only rare reservations against methods working before fertilization [ 2, 9].
Self-fertilization, however, is probably rare.
The higher extinction rate in outcrossing populations was likely due to the fact that outcrossing hermaphrodites had no opportunity to escape extinction through self-fertilization when they became rare in populations, allowing females to rise to fixation.
