Analysis of life table response experiments .2. 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 lambda 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 lambda. 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 lambda 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.