1. Life table response experiment (LTRE) analyses have been widely used to examine the sources of differences in the long-termdeterministic growth rate (r = logk) of stage-structured populations that live in spatially distinct habitats or under distinct experimental conditions. However, existing methods for LTRE analysis ignore the fact that persistent temporal variation in matrix elements results in a long-term stochastic growth rate (a = log ks) that is different from the deterministic growth rate (r) and thus do not take into account environmental stochasticity. 2. Here, we develop a stochastic extension of LTRE methods that can be used to compare stochastic growth rates among populations that differ in the observed variability of their matrix elements over time. We illustrate our method with actual data and explore a range of questions that may be addressed with these new tools. Specifically, we investigate how variability in weather conditions affected the population dynamics of the short-lived perennial plant species Anthyllis vulneraria and examine how differences in stochastic growth rates (a) are determined by contributions of mean matrix elements and variability in matrix elements. 3. We find that, consistent with the life history of the species, differences in mean fertility and growth made the largest contribution to differences in a, whereas in terms of variability fertility made the largest contribution in most populations. However, we also find that in all populations, the magnitude of the total contribution of mean matrix elements outweighed that of variability. Finally, increasing soil depth significantly lowered contributions of variability in matrix elements, but it was not related to contributions of differences in mean matrix elements. 4. Synthesis. Stochastic life table response experiment analysis described here provides the first systematic way of incorporating observed differences in temporal variability into the comparison of natural populations.Akey finding fromthis study is that populations occurring on relatively deeper soils were better buffered against climatic variation than populations occurring on shallow soils. We expect this new approach to analyse temporal variability to prove especially useful in the analysis of natural populations experiencing environmental change.
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