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Abstract Life table response experiments (LTREs) decompose differences in population growth rate between environments into separate contributions from each underlying demographic rate. However, most LTRE analyses make the unrealistic assumption that the relationships between demographic rates and environmental drivers are linear and independent, which may result in diminished accuracy when these assumptions are violated. We extend regression LTREs to incorporate nonlinear (second‐order) terms and compare the accuracy of both approaches for three previously published demographic datasets. We show that the second‐order approach equals or outperforms the linear approach for all three case studies, even when all of the underlying vital rate functions are linear. Nonlinear vital rate responses to driver changes contributed most to population growth rate responses, but life history changes also made substantial contributions. Our results suggest that moving from linear to second‐order LTRE analyses could improve our understanding of population responses to changing environments. 

research on ways to monitor populations 

The dynamics of colonizing populations may be strongly influenced by both extrinsic (e.g., climate and competition) and intrinsic (e.g., density) forces as well as demographic and environmental stochasticity. Understanding the impacts of these effects is crucial for predicting range expansions, trailing edge dynamics, and the viability of rare species, but the general importance of each of these forces remains unclear. Here, we assemble establishment time and spatial locations of most individuals that have reached maturity in six isolated, establishing populations of two pine species. These data allow us to quantify the relative importance of multiple factors in controlling growth of these populations. We found that climate, density, site, and demographic stochasticity were of varying importance both within and across species, but that no driver appeared to dominate dynamics across all populations and time periods. Indeed, exclusion of any one of these effects greatly reduced predictive power of our population growth models. Given the similarity in the abiotic characteristics of these sites, the varying importance of these classes of effects was surprising but speaks to the need to consider multiple effects when predicting the dynamics of small and colonizing populations.