“Using Branching Processes to Explain Survival of Populations”.
RESUMEN: “Branching processes have been intensively studied during the last decades; classical references are the books of Harris (1963), Sevastyanov (1971), Athreya and Ney (1972) and Jagers (1975). With a special emphasis on applications, recent books are Axelrood and Kimmel (2002) and Haccou, Jagers and Vatutin (2005). Throughout the literature it is possible to find several examples of how these processes have been successfully used to solve important problems arising in different sciences such as medicine, biology, ecology, physics and even computer science.
In this work we were particularly interested in describing how populations that are, in principle, doomed to extinction manage to survive. This is usually achieved through the appearance of certain types of individuals that give an “advantage” to the initial population. For example:
i) virus placed in a new and hostile environment often develop mutations.
ii) stochastic introgression, which is the process whereby a specified gene.
In this talk we describe how (multitype) branching processes can be used to model the evolution of the populations described above and provide answers to some of the most relevant questions arising in them.First we present the basic definitions and some elementary results on the theory of branching processes. Then we proceed with the presentation of recent results on problems i) and ii) described above. Finally we will present some proposals for future research.