Comparison between the Fitness Function and Its Best Quadratic Approximation

Abstract

The standard method to estimate the fitness landscape is the approach of Lande and Arnold, which has been very widely used and has over 1000 citations. Basically, what they do is to estimate the actual fitness function as its best quadratic approximation (BQA) given data which is a set of phenotypic character variables and observed fitness such as the number of off springs. We show that the “best” quadratic approximation is futile and does not provide the true information a fitness function can convey, because it often approximates the true fitness function only poorly. More often than not, we would find that the BQA displays artifacts rather than the actual characteristic of fitness landscape of biological interest.