FINDING CONFIDENCE-LIMITS ON POPULATION-GROWTH RATES - MONTE-CARLO TEST OF A SIMPLE ANALYTIC METHOD

Estimates of population growth rates are subject to uncertainties because of errors incurred in estimating the individual rates of fecundity, survival and growth. However, the non-linear relationship between the population growth rate and the vital rates makes this a difficult task, and confidence limits are rarely assigned to growth rate estimates. The mean and standard error of the population growth rate may be approximated using a Taylor's series expansion. Assuming a particular type of sampling distribution for the population rate, one may use this analytic estimate to assign confidence limits. Available simulations do not enable generalizations concerning the performance of this analytic approach, especially for estimates obtained for age or stage-structured populations. In this paper we: (1) extend the analytic formula for the variance of estimates of population growth rates to allow for correlations between the errors in matrix entries; and (2) we test the performance of this analytic approximation by developing a Monte Carlo simulation model of a population whose density-independent dynamics is readily described with matrix models. We used examples that encompass a wide range of life-cycle types, and tested the effects that the magnitude, distribution type and correlation of errors in estimates of vital rates may have on the performance of the analytic approach. We found that previous Monte Carlo evaluations were flawed because they failed to account for the effects of truncating the distribution of matrix errors so that only biologically possible values occur (e.g., no negative fecundities). We found that the analytic method to find approximate confidence intervals on population growth rates is reliable for all cases tested if coefficients of variation of estimates of matrix entries are not very high (<50%). When dealing with matrices with high coefficients of variation, the analytic approximation may still be used to assign rough confidence intervals if a Monte Carlo simulation cannot be performed.