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How is population growth rate calculated from births deaths immigration and emigration?

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Common wildebeest — population ecology A herd of common wildebeest (*Connochaetes taurinus*) migrating across a dusty savanna in Africa. The animal is a keystone species (i.e., a species with a disproportionately large effect on its biological community) in plains and acacia savanna ecosystems from southeastern Africa to central Kenya.

In population ecology, the population growth rate is a measure of how the number of individuals in a species changes over a specific period. While some models focus on natural increase (births minus deaths), a comprehensive calculation for an open population must account for migration.123

Calculating Population Change

To determine the change in population size for an open population, you can use the following relationship:

Population at the end of an interval = Population at the beginning + Births - Deaths + Immigration - Emigration3

In this context, population growth rates are calculated by subtracting the combined rates of loss—mortality and emigration—from the combined rates of gain, which include fertility (births) and immigration.1

Key Considerations

Closed vs. Open Populations: A closed population is one where migration does not occur, meaning size changes only through births and deaths. Most natural populations are open, requiring the inclusion of in-migration and out-migration data.3
Intrinsic Growth: Biologists also use the intrinsic rate of natural increase (r), which represents the birth rate minus the death rate per generation time, to compare the growth potential of different species.4