Analysis of life table response experiments II. Alternative parameterizations for size- and stage-structured models

Life table response experiments (LTREs) are studies that quantify the population-level effects of environmental factors by measuring a set of vital rates (a life table) under two or more conditions (treatments). The vital rates are incorporated into a demographic model and the population growth rate λ is calculated to summarize the treatment effects at the population level. A previous paper introduced a way to measure the contribution of each vital rate to the overall treatment effect on λ. Here, I generalize this method from age-classified models to models based on size or stage. I present methods for three parameterizations (in terms of the matrix entries, in terms of lower-level vital rates, and in terms of the life cycle graph, including age at maturity) of size- or stage-classified models. In each case, the contributions are calculated from the treatment effects on the vital rates and the sensitivity of λ to changes in the vital rates. Examples are presented of the effects of fire on a tropical grass, of geographical location on killer whales (orcas), and of pollutants on a marine polychaete. In analyzing LTREs, it is not safe to assume that the most obvious treatment effects on the vital rates are the most important.