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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.