A geometrical model of adaptation and the derived estimates of complexity. A) A geometric model of adaptation is used as a reference to characterize complexity. In this model, an organism is defined by a number of idealized independent phenotypes (here 3). The number of phenotypes is what we will call phenotypic complexity. The model assumes the existence of an optimal combination of phenotype having maximal fitness. The more organisms are distant from that optimal combination, the lower is their fitness. B) To estimate phenotypic complexity, one can analyze a set of fitness-linked-phenotypes in a collection of mutants and perform a principal component analysis (PCA). The distribution of variance explained by the different axes of the PCA is directly linked to phenotypic complexity. For instance, if there is indeed a single phenotype (case 1), a single axis will explain all variance, while if complexity is indeed 2 or 3, 2 or 3 axis will be necessary to explain the phenotypic variance of mutants. C) Mathematical derivation from the geometric model have proved the existence of some fitness equilibrium and that the fitness at these equilibrium is a direct function of the effective population size and the phenotypic complexity. Hence if we record the average fitness of populations of different population size at equilibrium, we can estimate phenotypic complexity.
Le Nagard et al. BMC Evolutionary Biology 2011 11:326 doi:10.1186/1471-2148-11-326