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Resource-dependent branching process
open-in-new
<p>A <a href="/facts/Branching_process/JzdGdWrQ">branching process</a> (BP) (see e.g. Jagers (1975)) is a mathematical model to describe the development of a population. Here population is meant in a general sense, including a human population, animal populations, bacteria and others which reproduce in a biological sense, cascade process, or particles which split in a physical sense, and others. Members of a BP-population are called individuals, or particles. </p><p>If the times of reproductions are discrete (usually denoted by 1,2, ...) then the totality of individuals present at time n and living to time n+1 excluded are thought of as forming the nth generation. Simple BPs are defined by an initial state (number of individuals at time 0) and a law of reproduction, usually denoted by pk, k = 1,2,.... </p><p>A resource-dependent branching process (RDBP) is a discrete-time BP which models the development of a population in which individuals are supposed to have to work in order to be able to live and to reproduce. The population decides on a society form which determines the rules how available resources are distributed among the individuals. For this purpose a RDBP should incorporate at least four additional model components, namely the individual demands for resources, the creation of new resources for the next generation, the notion of a policy to distribute resources, and a control option for individuals for interactions with the society. </p>