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applied probability Applied probability is the application of probability theory to statistical problems and other scientific and engineering domains. Scope Much research involving probability is done under the auspices of applied probability. However, while such res ...

, a population process is a

Markov chain A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happen ...

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. Although named by analogy to

biological Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary ...

populations from

population dynamics Population dynamics is the type of mathematics used to model and study the size and age composition of populations as dynamical systems. History Population dynamics has traditionally been the dominant branch of mathematical biology, which has ...

, population processes find application in a much wider range of fields than just

ecology Ecology () is the study of the relationships between living organisms, including humans, and their physical environment. Ecology considers organisms at the individual, population, community, ecosystem, and biosphere level. Ecology overl ...

and other biological sciences. These other applications include

telecommunication Telecommunication is the transmission of information by various types of technologies over wire, radio, optical, or other electromagnetic systems. It has its origin in the desire of humans for communication over a distance greater than tha ...

s and

queueing theory Queueing theory is the mathematical study of waiting lines, or queues. A queueing model is constructed so that queue lengths and waiting time can be predicted. Queueing theory is generally considered a branch of operations research because the ...

chemical kinetics Chemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is to be contrasted with chemical thermodynamics, which deals with the direction in ...

and

financial mathematics Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. In general, there exist two separate branches of finance that require ...

, and hence the "population" could be of

packet Packet may refer to: * A small container or pouch ** Packet (container), a small single use container ** Cigarette packet ** Sugar packet * Network packet, a formatted unit of data carried by a packet-mode computer network * Packet radio, a form ...

s in a

computer network A computer network is a set of computers sharing resources located on or provided by network nodes. The computers use common communication protocols over digital interconnections to communicate with each other. These interconnections ar ...

, of

molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bio ...

s in a

chemical reaction A chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the positions of electrons in the forming and break ...

, or even of units in a

financial index In Statistics, Economics and Finance, an index is a statistical measure of change in a representative group of individual data points. These data may be derived from any number of sources, including company performance, prices, productivity, and ...

. Population processes are typically characterized by processes of birth and immigration, and of death, emigration and catastrophe, which correspond to the basic

demographic Demography () is the statistical study of populations, especially human beings. Demographic analysis examines and measures the dimensions and dynamics of populations; it can cover whole societies or groups defined by criteria such as edu ...

processes and broad

environment Environment most often refers to: __NOTOC__ * Natural environment, all living and non-living things occurring naturally * Biophysical environment, the physical and biological factors along with their chemical interactions that affect an organism or ...

al effects to which a population is subject. However, population processes are also often equivalent to other processes that may typically be characterised under other paradigms (in the literal sense of "patterns"). Queues, for example, are often characterised 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. Typical population processes include

birth–death process The birth–death process (or birth-and-death process) is a special case of continuous-time Markov process where the state transitions are of only two types: "births", which increase the state variable by one and "deaths", which decrease the state ...

es and birth, death and catastrophe processes.

See also