Coletti, Cristian F.; Marić, Nevena; Rodriguez, Pablo M. On the role of reduced habitat in the phase transition of a stochastic model for seed dispersal. (English) Zbl 1529.60059 Math. Methods Appl. Sci. 46, No. 9, 10540-10553 (2023). Summary: Habitat loss is one of the biggest threats facing plant species nowadays. We formulate a simple mathematical model of seed dispersal on reduced habitats to discuss survival of the species in relation to the habitat size and seeds production rate. Seeds get dispersed around the mother plant via several agents in a random way. In our model, seeds landing sites are distributed according to a homogeneous Poisson point process with a constant rate on \(\mathbb{R}\). We will assume that each seed will successfully germinate and grow into a new plant with the same characteristics as the mother plant. The time is discrete, scaled according to generations of plants, or can represent years, since annual plants go through an entire growing cycle during 1 year. Then we will assume there are two symmetric barriers with respect to the origin and consider that the growth cannot evolve past the barriers. Imposing barriers correspond to the physical limitation of the habitat. We appeal to tools of probability theory to formalize and study such a model, which can be seen as a discrete-time one-dimensional branching random walk with barriers. By means of coupling techniques and the comparison with suitably constructed multitype branching processes, we localize the critical parameter of the process around which there is survival with positive probability or extinction almost surely. In addition, we consider a discrete-space version of the model for which exact results are also obtained.{© 2023 John Wiley & Sons, Ltd.} MSC: 60J80 Branching processes (Galton-Watson, birth-and-death, etc.) 60J85 Applications of branching processes 92D25 Population dynamics (general) Keywords:branching process; branching random walk; critical parameter; phase transition; population dynamics × Cite Format Result Cite Review PDF Full Text: DOI arXiv References: [1] C.Parmesan, Ecological and evolutionary responses to recent climate change, Annu. Rev. Ecol. Evol. Syst.37 (2006), 637-669. [2] M.Tejo, S.Niklitschek‐Soto, C.Vásquez, and P. A.Marquet, Single species dynamics under climate change, Theoret. Ecol.10 (2017), 181-193. [3] M.Tejo, C.Quiñinao, R.Rebolledo, and P. A.Marquet, Coexistence, dispersal and spatial structure in metacommunities: A stochastic model approach, Theoret. Ecol.14 (2021), no. 2, 279-302. [4] A.Abdullahi, S.Shohaimi, A.Kilicman, and M. 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