Gavrilets, S. and Scheiner S. 1993. ``The genetics of phenotypic plasticity. V. Evolution of reaction norm shape.'' *Journal of Evolutionary Biology* **6**: 31-48.
** ABSTRACT **

We present a general quantitative genetic model for the evolution
of reaction norms. This model goes beyond previous models by
simultaneously permitting any shaped reaction norm and allowing for the
imposition of genetic constraints. Earlier models are shown to be
special cases of our general model; we discuss in detail models
involving just two macroenvironments, linear reaction norms, and
quadratic reaction norms. The model predicts that, for the case of a
temporally varying environment, a population will converge on (1) the
genotype with the maximum mean geometric fitness over all environments,
(2) a linear reaction norm whose slope is proportional to the covariance
between the environment of development and the environment of selection,
and (3) a linear reaction norm even if nonlinear reaction norms are
possible. An examination of experimental studies finds some limited
support for these predictions. We discuss the limitations of our model
and the need for more realistic gametic models and additional data on
the genetic and developmental bases of plasticity.