Population growth
= Population growth
{title2=$\dot N=B-D+I-E$}
<Population growth> is change in population abundance through births, deaths and movement. For a stated region, the accounting identity is
$$
\frac{dN}{dt}=B-D+I-E,
$$
where 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> $N(t)=N_0e^{rt}$. For $r>0$ the doubling time is $\log2/r$; 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>.