Practice question

In a closed population with no migration, the instantaneous per-capita growth rate can be written r = b − d, where b is the per-capita birth rate and d is the per-capita death rate measured over the same time unit. Their difference is the intrinsic or instantaneous rate of increase under the stated conditions. Substitution into dN/dt = rN shows how individual-level demographic rates scale to total population change. A positive difference produces growth, zero gives demographic balance, and a negative difference produces decline. Net reproductive rate R0 is different: it is the expected number of daughters produced per female over a lifetime and is dimensionless per generation. Per-capita mortality is represented by d alone, not by the difference. “Exponential growth constant” is sometimes used informally for r, but intrinsic rate of increase is the biologically precise term because r integrates births and deaths into net per-capita performance. In open populations, immigration and emigration must also be included or treated separately, so b − d alone may not predict observed local change.