3.7 Detecting Changes in Sex and Age Composition
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The number of animals in particular sex or age categories is one of the most common statistics reported from ungulate inventories. These statistics are typically expressed as age and sex (e.g., bull/100 cow and calf/100 cow) ratios, which provide information on herd composition and recruitment. However, to be meaningful, sex/age ratios should be based on statistically reliable sample sizes, and should be reported with 90% confidence intervals. Statistical tests should also be conducted to determine if two or more ratios are significantly different.
Four basic approaches have been used to measure population ratios and statistical variance. The simplest approach has been to treat individual animals as the sampling unit and assume that individuals are independently and randomly sampled from the population (Czaplewski et al. 1983). This assumption is almost always violated with ungulates, and it is generally recognized that a better approach is to use cluster sampling which treats groups of animals as the sampling unit (Bowden et al. 1984). If absolute abundance is measured through a stratified random survey design then the procedures outlined by Gasaway et al. (1986) can be used to estimate sex/age ratios and their statistical precision. A limitation of Gasaway's method is that it does not explicitly account for differential visibility of age or sex classes when calculating ratios or their variance. An alternative estimation procedure has been developed by Samuel et al. (1992) that considers both errors associated with survey design (either simple or stratified random sampling) and visibility bias.
Although generally not recommended, classification or reconnaissance surveys may be used to estimate sex/age ratios and confidence limits using Czaplewski's method. Sample sizes should be determined prior to the survey, based upon desired levels of precision and allowable error (Section 3.2.1) and an estimate of the ratio of interest:
where:
n is the required number of animals to be classified (e.g., bucks and does to determine buck:doe ratios),
p is the proportion of the sample comprising the sex/age class of interest (e.g., bucks/[bucks+does]),
q is 1 - p,
N is the estimated population size (bucks and does),
z is the 2-tailed value from the normal distribution, and
e is the allowable error (as a proportion of p).
Significant differences in ratios or percentages can be tested using chi-square contingency tables (Zar 1984). Yates correction for continuity should be used for 2x2 contingency tables. Often it is desirable to conduct a second survey to determine if a significant change in sex/age composition has occurred (e.g., increase in % caribou calves following wolf control). Snedecor and Cochrane (1978:221-223) describe a method for calculating the required sample size for the second survey in order to test for a differences between 2 population ratios (e.g., % calves). That requires identifying both Type 1 and Type 2 errors (see Section 3.2.1).
If the composition of each animal group is recorded, which is recommended, then cluster sampling formulas can and should be used to estimate population ratios and confidence intervals (Bowden et al. 1984; Cochrane 1977:65-68). Required sample sizes and confidence limits may be based on simple random sampling of animal groups (Schaeffer et al. 1979), or using a 2-stage sampling design where land units (e.g., blocks, quadrats, transects) constitute the first-stage sampling units, and groups of animals located within each sample unit comprise the second-stage (Bowden et al. 1984).
Population surveys incorporating stratified random sampling should use the procedure outlined by Gasaway et al. (1986:83) to estimate sex/age composition and confidence intervals (available in program MOOSEPOP).
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