The ®tness threshold model: Random environmental change alters adaptive landscapes

We used a probabilistic optimization model to explore the joint evolutionary e€ects of random phenotypic and environmental variation. Two forms of environmental noise were de®ned in which the optimal phenotype remained constant but all organisms experienced either the same proportionate or the same absolute ®tness gains and losses. There was no evolutionary e€ect of proportionate ®tness ̄uctuations. In contrast, the optimal genotype varied with absolute ®tness ̄uctuations, despite the environmental e€ect being phenotypeindependent. We refer to such phenotype-independent ̄uctuation in absolute ®tness as the `®tness threshold model', because shared ®tness e€ects determine the zero-®tness points (i.e. the baseline) on an intrinsic ®tness function. Thus, environmental e€ects that are unrelated to a focal trait can cause peak shifts in the genetic optimum for the trait. Changes in the ®tness threshold not only changed peak locations, but also altered the slopes de®ning the peaks, and so should alter the rate of evolution towards optima. This model pertains to evolution in any system, unless there is no phenotypic or environmental variance, or the selection function and distribution of phenotypic error assume similar shapes. Our results have many basic and applied implications for topics such as the maintenance of genetic variation, the canalization of development and the management of natural populations.