  Inspired by recent studies associating shifting temperature conditions with
changes in the efficiency of predator species in converting their prey to
offspring, we propose a predator-prey model of reaction-diffusion type to
analyze the consequence of such effects on the population dynamics and spread
of species. In the model, the predator conversion efficiency is represented by
a spatially heterogeneous function depending on the variable $\xi=x-c_1t$ for
some given $c_1>0$. Using the Hamilton-Jacobi approach, we provide explicit
formulas for the spreading speed of the predator species. When the conversion
function is monotone increasing, the spreading speed is determined in all cases
and non-local pulling is possible. When the function is monotone decreasing, we
provide formulas for the spreading speed when the rate of shift of the
conversion function is sufficiently fast or slow.
