# Fitness (biology)

(Redirected from Mean fitness)

Fitness (often denoted $w$ in population genetics models) is a central idea in evolutionary theory. It can be defined either with respect to a genotype or to a phenotype in a given environment. In either case, it describes the ability to both survive and reproduce, and is equal to the average contribution to the gene pool of the next generation that is made by an average individual of the specified genotype or phenotype. The term "Darwinian fitness" is often used to make clear the distinction with physical fitness.[1] If differences between alleles of a given gene affect Darwinian fitness, then the frequencies of the alleles will change across generations; the alleles with higher fitness become more common. This process is called natural selection.

An individual's fitness is manifested through its phenotype. The phenotype is affected by the developmental environment as well as by genes, and the fitness of a given phenotype can be different in different environments. The fitnesses of different individuals with the same genotype are therefore not necessarily equal. However, since the fitness of the genotype is an averaged quantity, it will reflect the reproductive outcomes of all individuals with that genotype in a given environment or set of environments.

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.

## Fitness is a propensity

Fitness is often defined as a propensity or probability, rather than the actual number of offspring. For example, according to Maynard Smith, "Fitness is a property, not of an individual, but of a class of individuals — for example homozygous for allele A at a particular locus. Thus the phrase ’expected number of offspring’ means the average number, not the number produced by some one individual. If the first human infant with a gene for levitation were struck by lightning in its pram, this would not prove the new genotype to have low fitness, but only that the particular child was unlucky." [2] Equivalently, "the fitness of the individual - having an array x of phenotypes — is the probability, s(x), that the individual will be included among the group selected as parents of the next generation."[3]

## Measures of fitness

There are two commonly used measures of fitness; absolute fitness and relative fitness.

### Absolute fitness

Absolute fitness ($w_{\mathrm{abs}}$) of a genotype is defined as the ratio between the number of individuals with that genotype after selection to those before selection. It is calculated for a single generation and must be calculated from absolute numbers. When the absolute fitness is larger than 1, the number of individuals bearing that genotype increases; an absolute fitness smaller than 1 indicates an absolute fall in the number of individuals bearing the genotype. If the number of individuals in a population stays constant, then the average absolute fitness must be equal to 1.

${w_{\mathrm{abs}}} = {{N_{\mathrm{after}}} \over {N_{\mathrm{before}}}}$

Absolute fitness for a genotype can also be calculated as the product of the probability of survival multiplied by the average fecundity. Absolute fitness is used in Fisher's fundamental theorem.

### Relative fitness

Relative fitness is quantified as the average number of surviving progeny of a particular genotype compared with average number of surviving progeny of competing genotypes after a single generation, i.e. one genotype is normalized at $w=1$ and the fitnesses of other genotypes are measured with respect to that genotype. Relative fitness can therefore take any nonnegative value, including 0. Relative fitness is used in the standard Wright-Fisher and Moran models of population genetics.

The two concepts are related, as can be seen by dividing each by the mean fitness, which is weighted by genotype frequencies.

${\frac{w_{abs}}{\overline{w}_{abs}} = \frac{w_{rel}}{\overline{w}_{rel}}}$

## History

Herbert Spencer (27 April 1820 - 8 December 1903) was an English philosopher.

The British sociologist Herbert Spencer coined the phrase "survival of the fittest" (though originally, and perhaps more accurately, "survival of the best fitted") in his 1864 work Principles of Biology to characterise what Charles Darwin had called natural selection.

The British biologist J.B.S. Haldane was the first to quantify fitness, in terms of the modern evolutionary synthesis of Darwinism and Mendelian genetics starting with his 1924 paper A Mathematical Theory of Natural and Artificial Selection. The next further advance was the introduction of the concept of inclusive fitness by the British biologist W.D. Hamilton in 1964 in his paper on The Evolution of Social Behavior.

## Fitness landscape

Natural selection pushes fitness towards nearby peaks, but lacks the foresight to select the highest peak.

A fitness landscape, first conceptualized by Sewall Wright, is a way of visualising fitness in terms of a high-dimensional surface. Height indicates fitness, while each of the other dimensions may represent allele identity at one gene, allele frequency at one gene, or one phenotypic trait. These options represent three different ways in which the term fitness landscape is used.[4] Peaks correspond to local fitness maxima; it is often said that natural selection always progresses uphill but can only do so locally. This can result in suboptimal local maxima becoming stable, because natural selection cannot return to the less-fit "valleys" of the landscape on the way to reach higher peaks.

Genetic load measures the average fitness of a population of individuals, relative to a hypothetical population in which the most fit genotype has become fixed.

Genetic load is the probability that an average individual will die or fail to reproduce because of its harmful genes. It is a number between 0 and 1 that measures the extent to which the average individual is inferior to the best individual.[5]

If there are a number of genotypes in a population, each with its characteristic fitness; the genotype with the highest fitness is called Wopt. The average fitness of the whole population is the fitness of each genotype multiplied by its frequency: this is called mean fitness. V symbolizes mean fitness. The formula for genetic load (L) is as follows:

L = (Wopt-V)/(Wopt)

If all the individuals in the population have the optimal genotype, then v = Wopt and the load is zero. If all but one have a genotype of zero fitness then v = 0 and L = 1.[5]