A population dynamic model for facultative agamosperms

Plants that can reproduce both sexually and agamically are called facultative apomicts. Some species, such as Taraxacum, contain both sexual diploids and triploid facultative apomicts. Triploids produce seeds without gamete fusion and recombination, and can also produce pollen and fertilize diploids. We present a population dynamic model that deals with gene flow and competition between diploids and triploids, with differing allocation towards reproductive investment in seeds and pollen. This paper examines whether diploids and triploids of plants with facultative agamospermy can coexist within a single population. We analyse the global behavior of such a dynamic system. Features of the system are significantly affected by the germination rates of diploids and triploids. Either diploids or triploids persist alone when the germination rate of diploids is sufficiently larger or smaller than that of triploids, respectively. Competitive exclusion occurs when both germination rates are sufficiently large. Coexistence is possible under certain specific conditions when: (I) the germination rates of both diploid sexuals and triploids are not sufficiently large, and (II) triploids produce sufficient pollen. When diploid sexuals and triploids coexist, triploids cannot exist alone, implying that the pollen of triploids is necessary to exploit diploid ovules.