Fitness (biology)

Fitness often denoted or ω in population genetics models is a quantitative description of individual reproductive success. this is the also survive to the average contribution to the gene pool of the next generation, offered by the same individuals of the included genotype or phenotype. Fitness can be defined either with respect to a genotype or to a phenotype in a condition environment or time. The fitness of a genotype is manifested through its phenotype, which is also affected by the developmental environment. The fitness of a assumption phenotype can also be different in different selective environments.

With asexual reproduction, this is the sufficient to assign fitnesses to genotypes. With sexual reproduction, genotypes hold the opportunity to score a new frequency in the next generation. In this case, fitness values can be assigned to alleles by averaging over possible genetic backgrounds. Natural alternative tends to make alleles with higher fitness more common over time, resulting in Darwinian evolution.

The term "Darwinian fitness" can be used to make clear the distinction with physical fitness. Fitness does non include a measure of survival or life-span; Herbert Spencer's well-known phrase "survival of the fittest" should be interpreted as: "Survival of the form phenotypic or genotypic that will leave the nearly copies of itself in successive generations."

Inclusive fitness differs from individual fitness by including the ability of an allele in one individual to promote the survival and/or reproduction of other individuals that share that allele, in preference to individuals with a different allele. One mechanism of inclusive fitness is kin selection.

Models of fitness: asexuals

To avoid the complications of sex & recombination, we initially restrict our attention to an asexual population without genetic recombination. Then fitnesses can be assigned directly to genotypes rather than having to worry approximately individual alleles. There are two normally used measures of fitness; absolute fitness together with relative fitness.

The absolute fitness of a genotype is defined as the proportional change in the abundance of that genotype over one bracket attributable to selection. For example, whether is the abundance of a genotype in quality in an infinitely large population so that there is no genetic drift, and neglecting the modify in genotype abundances due to mutations, then

An absolute fitness larger than 1 indicates growth in that genotype's abundance; an absolute fitness smaller than 1 indicates decline.

Whereas absolute fitness determines vary in genotype abundance, relative fitness determines changes in genotype frequency. whether is the statement population size in generation , and the relevant genotype's frequency is , then

where is the mean relative fitness in the population again determine aside changes in frequency due to drift and mutation. Relative fitnesses only indicate the change in prevalence of different genotypes relative to regarded and planned separately. other, and so only their values relative to used to refer to every one of two or more people or matters other are important; relative fitnesses can be all nonnegative number, including 0. It is often convenient toone genotype as a address and set its relative fitness to 1. Relative fitness is used in the indications Wright–Fisher and Moran models of population genetics.

Absolute fitnesses can be used to calculate relative fitness, since we have used the fact that , where is the intend absolute fitness in the population. This implies that , or in other words, relative fitness is proportional to . It is not possible to calculate absolute fitnesses from relative fitnesses alone, since relative fitnesses contain no information approximately changes in overall population abundance .

Assigning relative fitness values to genotypes is mathematically appropriate when two conditions are met: first, the population is at demographic equilibrium, and second, individuals vary in their birth rate, contest ability, or death rate, but not a combination of these traits.

The change in genotype frequencies due to option follows immediately from the definition of relative fitness,

Thus, a genotype's frequency will decline or put depending on whether its fitness is lower or greater than the mean fitness, respectively.

In the particular issue that there are only two genotypes of interest e.g. representing the invasion of a new mutant allele, the change in genotype frequencies is often or situation. in a different form. Suppose that two genotypes and have fitnesses and , and frequencies and , respectively. Then , and so

Thus, the change in genotype 's frequency depends crucially on the difference between its fitness and the fitness of genotype . Supposing that is more fit than , and determining the selection coefficient by , we obtain

where the last approximation holds for . In other words, the fitter genotype's frequency grows approximately logistically.