3.8 Detecting Changes in Abundance
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Detecting changes in abundance is vital for both monitoring populations and evaluating management programs (e.g., impact of forest harvesting or hunting regulations). In total count surveys, all animals are assumed to be counted, and thus any difference in numbers indicates a change in abundance. However, in virtually all cases these surveys do not provide exact measures of abundance, and statistical procedures which adjust for sightability are required to detect changes in abundance.
The most common statistical procedure for determining the probability that two population estimates differ in size is the Student's t test. Gasaway et al. (1986:61-66) provides an excellent discussion for detecting changes in moose populations using the t-statistic (t'), and standard statistical texts discuss the procedure as well (e.g., Zar 1984:126). The null hypothesis is: there is no change in abundance between the two surveys. t' is calculated as
where T 1 estimates and T 2 are population estimates from the two surveys, and V(T 1) and V(T 2) are the associated variances. The degrees of freedom (df t) is calculated as:
where df 1 and df 2 are the degrees of freedom associated with each survey estimate.
Gasaway et al. (1986:63) point out that if you do not detect a significant decline, then you should determine if the null hypothesis can be accepted with a tolerable probability of committing a Type 2 error (probability of concluding no change in abundance when a change occurred). This involves calculation of statistical power (1- b), or the probability of rejecting a false null hypothesis. Usually, it is difficult to statistically detect changes over a short periods because of imprecision in census estimates, e.g., 1 or 2 years. For example, Gasaway and Dubois (1987) indicate that with confidence intervals of + 20%, a population must increase or decline about 20% to detect a significant (p<0.05) change in abundance. If the population is increasing 3.7% per year, then 5 years would be required between surveys to detect a significant difference. Gasaway et al. (1986:65) discuss planning surveys to detect specified population changes and provide formula for estimating the required precision from a second survey, after the first survey has been completed.
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