Ungulate

3.9 Estimating Rates of Population Change

Virtually all analyses of the dynamics of wild populations involve the concept of a rate of increase or population change. Sinclair and Grimsdell (1978) provide an excellent introduction to calculating rates of change from a time series of population estimates, and van Ballenberghe (1983) discusses estimating rate of change in moose populations.

The rate of population change (increase or decline) is estimated from 2 or more population estimates (or relative abundance indices) over time. The rate estimator depends on the trajectory of the population growth curve, e.g., linear growth, exponential growth, or logistic growth. If the time series is relatively short, then exponential or geometric growth is usually assumed. While there are numerous formulae for calculating l, the finite rate of population change, population rates of change are most easily obtained by log-linear regression of abundance versus time in years, i.e.,

which is of the general form of the usual linear regression equation, y = a + bx, with N t the number of individuals (or population index) in year t, N 0 is the number of individuals in the initial year or year zero, and l is the finite rate of change (slope b = log e l = r where r is the exponential rate of increase, e r = l, and e is the base of natural logarithms [2.7182818]).

If both the population estimate and the variance is known, then the formulae outlined by Gasaway et al. (1986:67) should be used to calculate rate of change, its associated variance and CI's. Gasaway and Dubois (1987) note that meaningful rates of change can best be estimated when a population makes a statistically significant change. Therefore, before estimating rates of change, determine if initial and final population estimates differ statistically with appropriate statistical tests (see Section 3.8).

Gerrodette (1993) has provided software to facilitate the assessment of trend lines from annual estimates or indices of population abundance. Program TRENDS can be used to determine: (1) how many years monitoring should continue to detect a change; (2) how precise the survey data must be; (3) how large a change can be detected; and (4) what is the probability of detecting a change (obtaining a significant slope to the regression line), given that change really is occurring?

[Back to TOC] [Previous] [Next]

Published by the Resources Inventory Committee