Statistical Inference in Life-Table Experiments: The Finite Rate of Increase

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Abstract
Life-table experiments are frequently used to examine the effects of food level, toxicants, and other experimental treatments on a population's finite rate of increase λ. Although methods for computing the variance of λ have been suggested, the sampling distribution of λ, which is needed for statistical inference, has not been described. We used Monte Carlo procedures to simulate sampling distributions of λ for a variety of assumptions regarding survivorship and fecundity schedules and initial cohort sizes. The distribution of λ can be bimodal when cohort size is small and when juvenile mortality is large. Under these circumstances the probability that none of the initial cohort members reproduces is high enough to produce a significant frequency of zero values for λ. Zero therefore becomes the lower mode of the distribution. Many commonly observed mortality schedules and commonly used cohort sizes yield distributions of λ that are skewed toward low values. Although the skewness and variance of distributions of λ decrease as cohort size increases, these distributions are asymptotically non-normal. Normal-based statistical procedures for comparing experimental estimates of λ may therefore be misleading. To compare estimates of λ obtained from life-table experiments, we recommend using a Monte Carlo approach to generate sampling distributions of λ and then comparing these distributions directly. We illustrate this procedure with life-table data from Daphnia pulex cohorts raised at different levels of pH. We also show that a Taylor series variance estimator yields confidence intervals for λ that approximate those obtained from simulations. This variance estimator is less conservative, and therefore more useful, than a previous estimator derived by Lenski and Service (1982. Ecology 63: 655–662).