Generalized Single Index Models and Jensen Effects on Reproduction and Survival

Environmental variability often has substantial impacts on natural populations and communities through its effects the performance of individuals. Because organisms’ responses to environmental conditions are nonlinear (e.g., decreasing both sides an optimal temperature), mean response is different from in environment. Ye et al. (Ann Appl Stat 14(3):1326–12341, 2020) proposed testing for presence such variance individual or population growth rates by estimating “Jensen Effect”, difference average under varying versus fixed environments, functional single index models growth. In this paper, we extend analysis reproduction survival, which have count binary outcomes. standard generalized linear used analyze data direction Jensen Effect tacitly assumed a priori model’s link function. Here methods (2020) using model test whether contradicted data. We show that our reasonable power mild alternatives, but requires sample sizes larger than available. demonstrate long-term time series plant ground cover Idaho sagebrush steppe.