Editing Population process (section)

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{{Use American English|date=December 2024}}

In [[applied probability]], a '''population process''' is a [[Markov chain]] in which the state of the chain is analogous to the number of individuals in a population (0, 1, 2, etc.), and changes to the state are analogous to the addition or removal of individuals from the population. Typical population processes include [[birth–death process]]es and [[birth, death and catastrophe process]]es.<ref name="transact">{{cite book |editor1-last=Priami |editor1-first=Corrado |editor2-last=de Vink |editor2-first=Erik |editor3-last=Petre |editor3-first=Ion |title=Transactions on Computational Systems Biology XIV |date=28 November 2012 |publisher=Springer Berlin Heidelberg |isbn=9783642355240 |pages=4–5 |url=https://books.google.com/books?id=7lO5BQAAQBAJ |access-date=17 April 2023}}</ref>

Although named by analogy to [[biology|biological]] populations from [[population dynamics]], population processes find application in a much wider range of fields than just [[ecology]] and other biological sciences.  These other applications include [[telecommunications]] and [[queueing theory]], [[chemical kinetics]] and [[financial mathematics]], and hence the ''population'' could be of [[packet switching|packet]]s in a [[computer network]], of [[molecule]]s in a [[chemical reaction]], or even of units in a [[stock market index|financial index]].  

Population processes are typically characterized by processes of birth and immigration, and of death, emigration and catastrophe, which correspond to the basic [[demography|demographic]] processes and broad [[natural environment|environment]]al effects to which a population is subject.  However, population processes are also often equivalent to other processes that may typically be characterized under other [[paradigm]]s (in the literal sense of "patterns").  [[queueing theory|Queues]], for example, are often characterized by an arrivals process, a service process, and the number of servers.  In appropriate circumstances, however, arrivals at a queue are functionally equivalent to births or immigration and the service of waiting "customers" is equivalent to death or emigration.