  The inheritance of characteristics induced by the environment has often been
opposed to the theory of evolution by natural selection. Yet, while evolution
by natural selection requires new heritable traits to be produced and
transmitted, it does not prescribe, per se, the mechanisms by which this is
operated. The mechanisms of inheritance are not, however, unconstrained, since
they are themselves subject to natural selection. We introduce a general,
analytically solvable mathematical model to compare the adaptive value of
different schemes of inheritance. Our model allows for variations to be
inherited, randomly produced, or environmentally induced, and, irrespectively,
to be either transmitted or not during reproduction. The adaptation of the
different schemes for processing variations is quantified for a range of
fluctuating environments, following an approach that links quantitative
genetics with stochastic control theory.
