Estimating Uncertainty in Population Growth Rates: Jackknife vs. Bootstrap Techniques

Although per capita rates of increase (r) have been calculated by population biologists for decades, the inability to estimate uncertainty (variance) associated with r values has until recently precluded statistical comparisons of population growth rates. In this study, we used two computerintensive techniques, Jackknifing and Bootstrapping, to estimate bias, standard errors, and sampling distributions of r for real and hypothetical populations of cladocerans. Results generated using the two techniques, using data on laboratory cohorts of Daphnia pulex, were almost identical, as were results for a hypothetical D. pu!e,u population whose sampling distribution was approximately normal. However, for another hypothetical population whose sampling distribution was negatively skewed due to high juvenile mortality, Bootstrap and full-sample estimates of r were negatively biased by 3.3 and 1.8%, respectively. A bias adjustment reduced the bias in the Bootstrap estimate and produced estimates of r and sE(r) almost identical to those of the Jackknife technique. In general, our simulations show that the Jackknife will provide more cost-effective point and interval estimates of r for cladoceran populations, except when juvenile mortality is high (at least >25%). Coefficients of variation in the mean of r within laboratory cohorts of D. pulex were one-half to one-third the magnitude of the corresponding coef@ients of variation in the mean of total reproduction and in the mean day to death (range of values ofcv[r] = 1.6 to 3.8%). This suggests that extremes in reproductive output and survival of individuals tend to be dampened at the population level, and that within-cohort variability in r is not explosive. Moreover, between-cohort Variability in r can be much greater than within-cohort variability, as indicated by a statistically significant difference of 30% (P K .Ol) between the high and low r values that were computed for four cohorts of D. pulex born during a I-mo period from the same laboratory stock population. Based on variability in per capita rates of increase that have been estimated for several cladoceran species, we suggest that the precision for reporting r values should in most cases be limited to two significant figures.