Practice question

For a population observed at discrete time intervals, the finite rate of increase is λ = N(t+1)/N(t). A value of 1 means that each census contains the same number of individuals as the preceding census, so abundance is stable rather than rising or falling. Equivalently, births plus immigration exactly balance deaths plus emigration over the interval. This does not imply that no individuals are born or die; demographic turnover may be substantial while net population change remains zero. In an age-structured population, λ = 1 is the long-term result after the stable age distribution has been reached, even though particular age classes may temporarily change in size. Values above 1 indicate multiplication, whereas values below 1 indicate decline. The corresponding continuous intrinsic rate is r = ln λ, making λ = 1 equivalent to r = 0. Stability also refers to expected size under the model; environmental and demographic stochasticity can still produce fluctuations around that expectation.