Why there are so many definitions of fitness in models

Evolutionary "fitness" is operationalized in many different ways in models. Its role is to quantify that which is favored by natural selection. Generally, short-term ability to survive and reproduce (e.g. expected number of surviving offspring) is assigned to genotypes or phenotypes and used to non-trivially derive longer-term quantities (e.g. invasion rate or fixation probability) that provide insight as to which organismal strategies tend to evolve due to natural selection. Assigned fitness operationalizations either explicitly or implicitly specify organismal vital rates (i.e. births, deaths, organismal growth). Derived operationalizations also depend on assumptions regarding demographic stochasticity; environmental stochasticity; feedbacks whereby births, deaths, and organismal growth cause environmental change; and the impact of migration and niche construction on which environment is experienced. The choice of derived operationalization can impact conclusions, as we illustrate for the evolution of bet hedging when treated by invasion probability vs expected Malthusian parameter within an adaptive dynamics approach. After reviewing existing derived fitness operationalizations, we propose a new one that meets the particular challenges posed by balancing selection. Population genetic models generally sidestep ultra-high-dimensional phenotype and genotype spaces by deriving the long-term evolutionary fate/fitness of a lower-dimensional set of genetically encoded "strategies." Strategies (e.g. costly developmental commitment to producing armaments) are causally upstream from realized phenotypes (e.g. armament size), but downstream from how an organism's early environment (e.g. maternal effects) might inform developmental commitments. While selection is best understood in terms of differences in organismal vital rates, its derived outcomes are most easily understood as properties of genetic lineages.