Fig. 1.

Nonlinear and interaction responses to environment. (A) Nonlinear response of species $s$ to a temperature gradient ($x_1$) is fitted with a model containing a quadratic term, $x_1^2$. (B) Combined effects of temperature and land cover ($x_2$) are fitted with an additional interaction term, $x_1\times x_2$, where response to temperature might differ in forests and fields. (C) Alternatively, nonlinear and interaction responses enter indirectly though products with other species $s\prime$ (blue and brown) that depend on temperature $x_1$, but require the time dimension. The background shading in C describes Hutchinson’s concept of the fundamental niche that might be realized by species $s$ in the absence of other species.