Population growth ($\dot{N}=B-D+I-E$)

Population growth is change in population abundance through births, deaths and movement. For a stated region, the accounting identity iswhere the terms are birth, death, immigration and emigration counts per unit time. A growing local population need not have more births than deaths if immigration supplies the difference.

In a closed population with constant per-capita birth and death rates $b,d$, the identity becomes $\dot{N}=(b-d)N=rN$, giving exponential growth $N(t)=N_0{e}^{rt}$. For $r>0$ the doubling time is $\log 2/r$; a negative $r$ gives exponential decline. These are assumptions about rates, not a universal prediction for every biological population.

The logistic growth equation instead uses $\dot{N}=rN(1-N/K)$ with carrying capacity $K$. Its per-capita growth decreases with abundance, representing one form of negative density dependence. Resource limitation, age structure and environmental variation can require other mechanisms. In particular, two populations with equal present abundance but different reproductive age distributions need not have equal future population growth.