A simple stochastic mathematical model is developed and investigated for early human immunodeficiency virus type-1 (HIV-1) population dynamics. The model, which is a multi-dimensional diffusion process, includes activated uninfected CD4 + T cells, latently and actively infected CD4 + T cells and fre
A Population Dynamic Model for Facultative Agamosperms
β Scribed by YUU NAKAYAMA; HIROMI SENO; HIROYUKI MATSUDA
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 251 KB
- Volume
- 215
- Category
- Article
- ISSN
- 0022-5193
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β¦ Synopsis
Plants that can reproduce both sexually and agamically are called facultative apomicts. Some species, such as ΒΉaraxacum, 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 #ow and competition between diploids and triploids, with di!ering 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 signi"cantly a!ected by the germination rates of diploids and triploids. Either diploids or triploids persist alone when the germination rate of diploids is su$ciently larger or smaller than that of triploids, respectively. Competitive exclusion occurs when both germination rates are su$ciently large. Coexistence is possible under certain speci"c conditions when: (I) the germination rates of both diploid sexuals and triploids are not su$ciently large, and (II) triploids produce su$cient pollen. When diploid sexuals and triploids coexist, triploids cannot exist alone, implying that the pollen of triploids is necessary to exploit diploid ovules.
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