Defining fitness in evolutionary models

Abstract

The analysis of evolutionary models requires an appropriate definition for fitness. In this paper, I review such definitions in relation to the five major dimensions by which models may be described, namely (i) finite versus infinite (or very large) population size, (ii) type of environment (constant, fixed length, temporally stochastic, temporally predictable, spatially stochastic, spatially predictable and social environment), (iii) density-independent or density-dependent, (iv) inherent population dynamics (equilibrium, cyclical and chaotic), and (v) frequency dependent or independent. In simple models, the Malthusian parameter 'r' or the net reproductive rate R(0) may be satisfactory, but once density-dependence or complex population dynamics is introduced the invasion exponent should be used. Defining fitness in a social environment or when there is frequency-dependence requires special consideration.

Evolution of alternative insect life histories in stochastic seasonal environments

“…Only individuals that follow the diapause pathway and complete the prediapause development of duration rt larva (rounded to the nearest integer) before the end of the season will survive winter. Annual fitness is calculated as the number of surviving descendants produced within a season, R (annual rate of increase; assuming no winter mortality), which is appropriate for temperate insects when only a few generations are completed within a season (Roff 1980, 1983, 2008; Kivelä et al. 2013).…”

“…2013). Long‐term fitness is defined as the geometric mean, G , of the annual rates of increase, as it is an appropriate fitness currency in stochastic environments without density‐dependent selection (Dempster 1955; Gillespie 1977; Yoshimura and Jansen 1996; Roff 2002, 2008). Across n years (see “Analyses” section for deriving the years to be analyzed), G can be calculated as $G=e^{\frac{1}{n}{\sum }_{i=1}^n\ln false(R_{i}false)}$where R i is the rate of increase in year i .…”

Experimental determination of invasive fitness in Caenorhabditis elegans

“…To estimate the intrinsic growth rate, the invading genotype must be rare, so that interactions between individuals with that genotype are negligible, and the overall dynamics of the population, which are determined by the resident genotypes, do not change 20 . Under those these circumstances the selection coefficient of the invader genotype reflects its long-term per capita growth rate relative to resident genotype and determine the probability of a successful invasion 7 .…”

“…Finally, even when the relative fitness of a new allele is known, its fixation in the population is contingent on it not being lost by drift while it is still rare 3,4 . Drift is an important determinant of the probability of a genotype to invade and become established in a population characterized by other genotypes 5,6 and, ultimately, a key outcome to evaluate in order to understand the role of fitness in evolution 7 .…”

Bet hedging based cooperation can limit kin selection and form a basis for mutualism

“…This is done by introducing a stochastically varying environment, which allows some individuals to obtain resources at a time when other individuals are lacking resources. Evolution in such a varying environment is the domain of bet hedging theory (Lewontin and Cohen, 1969;Philippi and Seger, 1989;Frank and Slatkin, 1990;Grafen, 2000;Kussell and Leibler, 2005;Roff, 2008;Ellner, 2009) and therefore relations from that field can be used to describe cooperation and mutualism. This gives new insight into how mutualism can stabilize groups, under which conditions it can outcompete kin selection, and how an initial mutualistic relation can evolve to generate specialized partners.…”