Fitness (biology)

{{Short description|Expected reproductive success}} {{evolutionary biology}} '''Fitness''' (often denoted '''<math>w</math>''' or '''ω''' in [[population genetics]] models) is a [[Numerical data|quantitative]] representation of individual [[reproductive success]]. It is also equal to the [[expected value|average contribution]] to the [[gene pool]] of the next generation, made by the same individuals of the specified genotype or phenotype. Fitness can be defined either with respect to a [[genotype]] or to a [[phenotype]] in a given 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 given phenotype can also be different in different selective environments.

With [[asexual reproduction]], it is sufficient to assign fitnesses to genotypes. With [[sexual reproduction]], recombination scrambles [[allele]]s into different genotypes every generation; in this case, fitness values can be assigned to alleles by averaging over possible genetic backgrounds. Natural selection tends to make alleles with higher fitness more common over time, resulting in [[Darwinism|Darwinian]] evolution.

The term "Darwinian fitness" can be used to make clear the distinction with [[physical fitness]].<ref>Wassersug, J. D., and R. J. Wassersug, 1986. Fitness fallacies. Natural History 3:34–37.</ref> Fitness does not 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 most 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. To avoid double counting, inclusive fitness excludes the contribution of other individuals to the survival and reproduction of the focal individual. One mechanism of inclusive fitness is [[kin selection]].

==Fitness as 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."<ref>Maynard-Smith, J. (1989) ''Evolutionary Genetics'' {{ISBN|978-0-19-854215-5}}</ref>

Alternatively, "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."<ref>Hartl, D. L. (1981) ''A Primer of Population Genetics'' {{ISBN|978-0-87893-271-9}}</ref>

== Models of fitness == In order to avoid the complications of sex and recombination, the concept of fitness is presented below in the restricted setting of an asexual population without [[genetic recombination]]. Thus, fitnesses can be assigned directly to genotypes. There are two commonly used operationalizations of fitness – absolute fitness and relative fitness.

===Absolute fitness=== The absolute fitness (<math>W</math>) of a genotype is defined as the proportional change in the abundance of that genotype over one generation attributable to selection. For example, if <math> n(t) </math> is the abundance of a genotype in generation <math>t</math> in an infinitely large population (so that there is no [[genetic drift]]), and neglecting the change in genotype abundances due to [[mutation]]s, then<ref>{{cite book|last1=Kimura|first1=James F. Crow, Motoo|title=An introduction to population genetics theory|date=1970|publisher=Blackburn Press|location=New Jersey|isbn=978-1-932846-12-6|pages=5|edition=[Reprint]}}</ref>

:<math>n(t+1)=Wn(t)</math>.

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

===Relative fitness=== Whereas absolute fitness determines changes in genotype abundance, relative fitness (<math>w</math>) determines changes in genotype [[Allele frequency|frequency]]. If <math>N(t)</math> is the total population size in generation <math>t</math>, and the relevant genotype's frequency is <math>p(t)=n(t)/N(t)</math>, then

:<math>p(t+1)=\frac{w}{\overline{w}}p(t)</math>,

where <math>\overline{w}</math> is the mean relative fitness in the population (again setting aside changes in frequency due to drift and mutation). Relative fitnesses only indicate the change in prevalence of different genotypes relative to each other, and so only their values relative to each other are important; relative fitnesses can be any nonnegative number, including 0. It is often convenient to choose one genotype as a reference and set its relative fitness to 1. Relative fitness is used in the standard [[Genetic drift#Wright–Fisher model|Wright–Fisher]] and [[Moran process|Moran model]]s of population genetics.

Absolute fitnesses can be used to calculate relative fitness, since <math>p(t+1)=n(t+1)/N(t+1)=(W/\overline{W})p(t)</math> (we have used the fact that <math>N(t+1)=\overline{W} N(t) </math>, where <math>\overline{W}</math> is the mean absolute fitness in the population). This implies that <math>w/\overline{w}=W/\overline{W}</math>, or in other words, relative fitness is proportional to <math>W/\overline{W}</math>. It is not possible to calculate absolute fitnesses from relative fitnesses alone, since relative fitnesses contain no information about changes in overall population abundance <math>N(t)</math>.

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.<ref>{{cite journal |last1=Bertram |first1=Jason |last2=Masel |first2=Joanna |title=Density-dependent selection and the limits of relative fitness |journal=Theoretical Population Biology |date=January 2019 |volume=129 |pages=81–92 |doi=10.1016/j.tpb.2018.11.006|pmid=30664884 |doi-access=free |bibcode=2019TPBio.129...81B }}</ref>

=== Change in genotype frequencies due to selection === [[File:Selective sweep, frequency vs time.jpg|thumb|Increase in frequency over time of genotype <math>A</math>, which has a 1% greater relative fitness than the other genotype present, <math>B</math>]]

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

:<math>\Delta p = p(t+1)-p(t)=\frac{w-\overline{w}}{\overline{w}}p(t) </math>.

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

In the particular case 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 written in a different form. Suppose that two genotypes <math> A </math> and <math> B </math> have fitnesses <math>w_A</math> and <math>w_B</math>, and frequencies <math>p</math> and <math>1-p</math>, respectively. Then <math>\overline{w}=w_A p + w_B (1-p)</math>, and so

:<math>\Delta p = \frac{w-\overline{w}}{\overline{w}}p = \frac{w_A-w_B}{\overline{w}}p(1-p) </math>.

Thus, the change in genotype <math>A</math>'s frequency depends crucially on the difference between its fitness and the fitness of genotype <math>B</math>. Supposing that <math>A</math> is more fit than <math>B</math>, and defining the [[selection coefficient]] <math>s</math> by <math>w_A=(1+s)w_B</math>, we obtain

:<math>\Delta p = \frac{w-\overline{w}}{\overline{w}}p = \frac{s}{1+sp}p(1-p)\approx sp(1-p) </math>,

where the last approximation holds for <math>s\ll 1</math>. In other words, the fitter genotype's frequency grows approximately [[Logistic function|logistically]].

== History == [[File:Herbert Spencer.jpg|thumb|[[Herbert Spencer]]]] The [[United Kingdom|British]] [[sociologist]] [[Herbert Spencer]] coined the phrase "[[survival of the fittest]]" in his 1864 work ''Principles of Biology'' to characterise what [[Charles Darwin]] had called [[natural selection]].<ref name="sotf">{{cite web | url=http://www.darwinproject.ac.uk/entry-5140#back-mark-5140.f5 | title=Letter 5140 – Wallace, A. R. to Darwin, C. R., 2 July 1866 | publisher=Darwin Correspondence Project | access-date=12 January 2010}}<br />{{cite web | url=http://www.darwinproject.ac.uk/entry-5145#mark-5145.f3 | title=Letter 5145 – Darwin, C. R. to Wallace, A. R., 5 July (1866) | publisher=Darwin Correspondence Project | access-date=12 January 2010}}<br /> ^ "Herbert Spencer in his ''Principles of Biology'' of 1864, vol. 1, p. 444, wrote: 'This survival of the fittest, which I have here sought to express in mechanical terms, is that which Mr. Darwin has called "natural selection", or the preservation of favoured races in the struggle for life.'" {{Citation | url=http://works.bepress.com/cgi/viewcontent.cgi?article=1000&context=maurice_stucke | title=Better Competition Advocacy | access-date=29 August 2007 | author=Maurice E. Stucke}}, citing HERBERT SPENCER, THE PRINCIPLES OF BIOLOGY 444 (Univ. Press of the Pac. 2002.)</ref>

The British-Indian biologist [[J.B.S. Haldane]] was the first to quantify fitness, in terms of the [[Modern synthesis (20th century)|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 Genetical Evolution of Social Behaviour]]''.

== Genetic load == {{Main|Genetic load}} [[Genetic load]] measures the average fitness of a population of individuals, relative either to a theoretical genotype of optimal fitness, or relative to the most fit genotype actually present in the population.<ref>{{cite book|last1=Ewens|first1=Warren J.|title=Mathematical population genetics.|url=https://archive.org/details/springer_10.1007-978-0-387-21822-9|date=2003|publisher=Springer|location=New York|isbn=978-0-387-20191-7|edition=2nd|pages=[https://archive.org/details/springer_10.1007-978-0-387-21822-9/page/n95 78]–86}}</ref> Consider n genotypes <math> \mathbf{A} _1 \dots \mathbf{A} _n</math>, which have the fitnesses <math>w_1 \dots w_n</math> and the [[genotype frequency|genotype frequencies]] <math>p_1 \dots p_n</math> respectively. Ignoring [[frequency-dependent selection]], then genetic load (<math>L</math>) may be calculated as:

:<math>L = {{w_\max - \bar w}\over w_\max}</math>

Genetic load may increase when deleterious mutations, migration, [[inbreeding depression|inbreeding]], or [[outbreeding depression|outcrossing]] lower mean fitness. Genetic load may also increase when beneficial mutations increase the maximum fitness against which other mutations are compared; this is known as the [[Haldane's dilemma|substitutional load or cost of selection]].

== See also == {{portal |Evolutionary biology}} * [[Gene-centered view of evolution]] * [[Inclusive fitness]] * [[Lineage selection]] * [[Natural selection]] * [[Reproductive success]] * [[Selection coefficient]] * [[Universal Darwinism]] * [[Differential fitness]]

== Notes and references == {{Reflist|2}}

==Bibliography== * [[Elliott Sober|Sober, E.]] (2001). The Two Faces of Fitness. In R. Singh, D. Paul, C. Krimbas, and J. Beatty (Eds.), ''Thinking about Evolution: Historical, Philosophical, and Political Perspectives''. Cambridge University Press, pp. 309–321. [https://web.archive.org/web/20110718075456/http://philosophy.wisc.edu/sober/tff.pdf Full text] * {{cite journal |author=Orr HA |title=Fitness and its role in evolutionary genetics |journal=Nat. Rev. Genet. |volume=10 |issue=8 |pages=531–539 |date=August 2009 |pmid=19546856 |doi=10.1038/nrg2603 |pmc=2753274}}

== External links == * [https://www.youtube.com/watch?v=4pdiAneMMhU Video: Using fitness landscapes to visualize evolution in action] * [http://beacon-center.org/blog/2012/10/08/evolution-101-fitness-landscapes/ BEACON Blog--Evolution 101: Fitness Landscapes] * [http://pleiotropy.fieldofscience.com/2012/07/crossing-valleys-in-fitness-landscapes.html Pleiotrophy Blog--an interesting discussion of Sergey Gavrilets's contributions] * [http://www.blackwellpublishing.com/ridley/a-z/Fitness.asp Evolution A-Z: Fitness] * [http://plato.stanford.edu/entries/fitness/ Stanford Encyclopedia of Philosophy entry]

[[Category:Evolutionary biology concepts]] [[Category:Genetics concepts]] [[Category:Modern synthesis (20th century)]] [[Category:Population genetics]] [[Category:Sexual selection]] [[Category:Natural selection]] [[Category:Darwinism]]