genetic load

Consider n genotypes $\backslash mathbf\{A\}\; \_1,\; \backslash dots,\; \backslash mathbf\{A\}\; \_n$, which have the fitnesses $w\_1,\; \backslash dots,\; w\_n$ and frequencies $p\_1,\; \backslash dots,\; p\_n$, respectively. Ignoring frequency-dependent selection, the genetic load $L$ may be calculated as:

:$L\; =\; \{\{w\_\backslash max\; -\; \backslash bar\; w\}\backslash over\; w\_\backslash max\}$

where $w\_\backslash max$ is either some theoretical optimum, or the maximum fitness observed in the population. In calculating the genetic load, $w\_1\; \backslash dots\; w\_n$ must be actually found in at least a single copy in the population, and $\backslash bar\; w$ is the average fitness calculated as the mean of all the fitnesses weighted by their corresponding frequencies:

:$\backslash bar\; w\; =\; \{\backslash sum\_\{i=1\}^n\; \{p\_i\; w\_i\}\}$

where the $i^\backslash mathrm\{th\}$ genotype is $\backslash mathbf\{A\}\_i$ and has the fitness and frequency $w\_i$ and $p\_i$ respectively.

One problem with calculating genetic load is that it is difficult to evaluate either the theoretically optimal genotype, or the maximally fit genotype actually present in the population.{{cite journal|last1=Agrawal|first1=Aneil F.|last2=Whitlock|first2=Michael C. |year=2012 |title=Mutation load: the fitness of individuals in populations where deleterious alleles are abundant |journal=Annual Review of Ecology, Evolution, and Systematics |volume=43 |issue=1 |pages=115–135 |doi=10.1146/annurev-ecolsys-110411-160257}} This is not a problem within mathematical models of genetic load, or for empirical studies that compare the relative value of genetic load in one setting to genetic load in another.

Deleterious mutation load is the main contributing factor to genetic load overall.{{cite journal|last1=Klekowski|first1=EdwardJ. |year=1988 |title=Genetic load and its causes in long-lived plants |journal=Trees |volume=2 |issue=4 |pages=195–203 |doi=10.1007/BF00202374|bibcode=1988Trees...2..195K |s2cid=24058154 }} The Haldane-Muller theorem of mutation–selection balance says that the load depends only on the deleterious mutation rate and not on the selection coefficient.{{cite journal|last1=Bürger|first1=Reinhard|journal=Genetica|date=1998|volume=102/103|pages=279–298|doi=10.1023/a:1017043111100|title=Mathematical properties of mutation-selection models|s2cid=22885529}} Specifically, relative to an ideal genotype of fitness 1, the mean population fitness is $\backslash exp(-U)$ where U is the total deleterious mutation rate summed over many independent sites. The intuition for the lack of dependence on the selection coefficient is that while a mutation with stronger effects does more harm per generation, its harm is felt for fewer generations.

A slightly deleterious mutation may not stay in mutation–selection balance but may instead become fixed by genetic drift when its selection coefficient is less than one divided by the effective population size.{{cite journal|last1=Lande|first1=Russell|title=Risk of Population Extinction from Fixation of New Deleterious Mutations|journal=Evolution|date=October 1994|volume=48|issue=5|pages=1460–1469|doi=10.2307/2410240|pmid=28568413|jstor=2410240}} Over time, drift load can seriously impact the fitness of a population.{{Citation |last=Whitlock |first=Mc |title=Genetic Load |date=2011 |work=eLS |url=https://onlinelibrary.wiley.com/doi/10.1002/9780470015902.a0001787.pub2 |access-date=2025-03-17 |publisher=John Wiley & Sons, Ltd |language=en |doi=10.1002/9780470015902.a0001787.pub2 |isbn=978-0-470-01590-2 |last2=Davis |first2=B|url-access=subscription }}{{Cite journal |last=Whitlock |first=Michael C. |date=2000-12-01 |title=FIXATION OF NEW ALLELES AND THE EXTINCTION OF SMALL POPULATIONS: DRIFT LOAD, BENEFICIAL ALLELES, AND SEXUAL SELECTION |url=https://academic.oup.com/evolut/article-abstract/54/6/1855/6758002?redirectedFrom=fulltext |journal=Evolution |volume=54 |issue=6 |pages=1855–1861 |doi=10.1111/j.0014-3820.2000.tb01232.x |issn=0014-3820}} In asexual populations, the stochastic accumulation of mutation load is called Muller's ratchet, and occurs in the absence of beneficial mutations, when after the most-fit genotype has been lost, it cannot be regained by genetic recombination. Deterministic accumulation of mutation load occurs in asexuals when the deleterious mutation rate exceeds one per replication.{{cite journal | doi = 10.1038/336435a0 | last1 = Kondrashov | first1 = A. S. | author-link = Alexey Kondrashov | year = 1988| title = Deleterious mutations and the evolution of sexual reproduction | journal = Nature | volume = 336 | issue = 6198| pages = 435–440 | pmid=3057385| bibcode = 1988Natur.336..435K| s2cid = 4233528 }} Sexually reproducing species are expected to have lower genetic loads.{{cite thesis |author=Marriage, Tara N. |year=2009 |title=Mutation, asexual reproduction and genetic load: A study in three parts |publisher=University of Kansas |type=Ph.D. thesis |url=https://kuscholarworks.ku.edu/handle/1808/5949}} This is one hypothesis for the evolutionary advantage of sexual reproduction. Purging of deleterious mutations in sexual populations is facilitated by synergistic epistasis among deleterious mutations.{{cite journal|last1=Crow|first1=James F.|title=The high spontaneous mutation rate: Is it a health risk?|journal=Proceedings of the National Academy of Sciences|date=5 August 1997|volume=94|issue=16|pages=8380–8386|language=en|issn=0027-8424|doi=10.1073/pnas.94.16.8380|pmid=9237985|pmc=33757|bibcode=1997PNAS...94.8380C|doi-access=free}}

High load can lead to a small population size, which in turn increases the accumulation of mutation load, culminating in extinction via mutational meltdown.{{cite journal|last1=Lynch|first1=Michael|last2=Conery|first2=John|last3=Burger|first3=Reinhard|title=Mutational Meltdowns in Sexual Populations|journal=Evolution|date=December 1995|volume=49|issue=6|pages=1067–1080|doi=10.2307/2410432|pmid=28568521|jstor=2410432}}{{cite journal|last1=Lynch|first1=Michael|last2=Conery|first2=John|last3=Burger|first3=Reinhard|title=Mutation Accumulation and the Extinction of Small Populations|journal=The American Naturalist|date=1 January 1995|volume=146|issue=4|pages=489–518|jstor=2462976|doi=10.1086/285812|bibcode=1995ANat..146..489L |s2cid=14762497}}

The accumulation of deleterious mutations in humans has been of concern to many geneticists, including Hermann Joseph Muller,{{cite journal|last1=Muller|first1=H. J.|title=Our load of mutations|journal=American Journal of Human Genetics|date=1 June 1950|volume=2|issue=2|pages=111–176|pmc=1716299|issn=0002-9297|pmid=14771033}} James F. Crow, Alexey Kondrashov,{{cite journal|last1=Kondrashov|first1=Alexey S.|title=Contamination of the genome by very slightly deleterious mutations: why have we not died 100 times over?|journal=Journal of Theoretical Biology|date=21 August 1995|volume=175|issue=4|pages=583–594|doi=10.1006/jtbi.1995.0167|pmid=7475094|bibcode=1995JThBi.175..583K |doi-access=free}} W. D. Hamilton,{{cite book|last1=Hamilton|first1=W.D.|title=Narrow Roads of Gene Land vol. 2: Evolution of Sex|pages=449–463}} and Michael Lynch.{{cite journal|last1=Lynch|first1=M.|title=Mutation and Human Exceptionalism: Our Future Genetic Load|journal=Genetics|date=7 March 2016|volume=202|issue=3|pages=869–875|doi=10.1534/genetics.115.180471|pmid=26953265|pmc=4788123}}

In sufficiently genetically loaded populations, new beneficial mutations create fitter genotypes than those previously present in the population. When load is calculated as the difference between the fittest genotype present and the average, this creates a substitutional load. The difference between the theoretical maximum (which may not actually be present) and the average is known as the "lag load".{{cite journal|last1=Smith|first1=J. Maynard|title=What Determines the Rate of Evolution?|journal=The American Naturalist|date=1 January 1976|volume=110|issue=973|pages=331–338|jstor=2459757|doi=10.1086/283071|bibcode=1976ANat..110..331S |s2cid=85575105}} Motoo Kimura's original argument for the neutral theory of molecular evolution was that if most differences between species were adaptive, this would exceed the speed limit to adaptation set by the substitutional load.{{cite journal |last=Kimura |first=Motoo |year=1968 |title= Evolutionary rate at the molecular level |journal= Nature |volume=217 |pages=624–626 |url= http://www.blackwellpublishing.com/ridley/classictexts/kimura.pdf |doi= 10.1038/217624a0 |pmid=5637732 |issue=5129|bibcode = 1968Natur.217..624K |s2cid=4161261 }} However, Kimura's argument confused the lag load with the substitutional load, using the former when it is the latter that in fact sets the maximal rate of evolution by natural selection.{{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=978-0387201917|edition=2nd|page=[https://archive.org/details/springer_10.1007-978-0-387-21822-9/page/n95 78]}}

More recent "travelling wave" models of rapid adaptation derive a term called the "lead" that is equivalent to the substitutional load, and find that it is a critical determinant of the rate of adaptive evolution.{{cite journal |last1=Desai |first1=M. M. |last2=Fisher |first2=D. S. |title=Beneficial Mutation Selection Balance and the Effect of Linkage on Positive Selection |journal=Genetics |date=4 May 2007 |volume=176 |issue=3 |pages=1759–1798 |doi=10.1534/genetics.106.067678|pmid=17483432 |pmc=1931526 }}{{cite journal |last1=Bertram |first1=J |last2=Gomez |first2=K |last3=Masel |first3=J |title=Predicting patterns of long-term adaptation and extinction with population genetics |journal=Evolution |date=February 2017 |volume=71 |issue=2 |pages=204–214 |doi=10.1111/evo.13116|pmid=27868195 |arxiv=1605.08717 |s2cid=4705439 }}

Inbreeding increases homozygosity. In the short run, an increase in inbreeding increases the probability with which offspring get two copies of a recessive deleterious alleles, lowering fitnesses via inbreeding depression.{{cite journal|last1=Saccheri|first1=I. J.|last2=Lloyd|first2=H. D.|last3=Helyar|first3=S. J.|last4=Brakefield|first4=P. M. |year=2005 |title=Inbreeding uncovers fundamental differences in the genetic load affecting male and female fertility in a butterfly|journal=Proceedings of the Royal Society B: Biological Sciences |volume=272 |issue=1558 |pages=39–46 |doi=10.1098/rspb.2004.2903 |pmid=15875568 |pmc=1634945}} In a species that habitually inbreeds, e.g. through self-fertilization, a proportion of recessive deleterious alleles can be purged.{{cite journal|last1=Byers|first1=D. L.|last2=Waller|first2=D. M. |year=1999 |title=Do plant populations purge their genetic load? Effects of population size and mating history on inbreeding depression |journal=Annual Review of Ecology and Systematics |volume=30 |issue=1 |pages=479–513 |doi=10.1146/annurev.ecolsys.30.1.479|bibcode=1999AnRES..30..479B }}{{cite journal|last1=Barrett |first1=S. C. H. |last2=Charlesworth |first2=D. |year=1991 |title=Effects of a change in the level of inbreeding on the genetic load |journal=Nature |volume=352 |issue=6335 |pages=522–524 |doi=10.1038/352522a0 |pmid=1865906|bibcode=1991Natur.352..522B |s2cid=4240051 }}

Likewise, in a small population of humans practicing endogamy, deleterious alleles can either overwhelm the population's gene pool, causing it to become extinct, or alternately, make it fitter.{{cite journal|last1=Pala |first1=M. |last2=Zappala |first2=Z. |last3=Marongiu|first3=M.|year=2017 |title=Population and individual-specific regulatory variation in Sardinia |journal=Nature Genetics |volume=49| pages=700–707 |issue= 5|doi=10.1038/ng.3840|pmid= 28394350|pmc=5411016 |bibcode= |s2cid=4240051 }}

Combinations of alleles that have evolved to work well together may not work when recombined with a different suite of coevolved alleles, leading to outbreeding depression. Segregation load occurs in the presence of overdominance, i.e. when heterozygotes are more fit than either homozygote. In such a case, the heterozygous genotype gets broken down by Mendelian segregation, resulting in the production of homozygous offspring. Therefore, there is segregation load as not all individuals have the theoretical optimum genotype. Recombination load arises through unfavorable combinations across multiple loci that appear when favorable linkage disequilibria are broken down.{{cite journal |last1=Haag |first1=C. R. |last2=Roze |first2=D. |year=2007 |title=Genetic load in sexual and asexual diploids: segregation, dominance and genetic drift |journal=Genetics |volume=176 |issue=3 |pages=1663–1678 |doi=10.1534/genetics.107.073080 |pmid=17483409 |pmc=1931546}} Recombination load can also arise by combining deleterious alleles subject to synergistic epistasis, i.e. whose damage in combination is greater than that predicted from considering them in isolation.{{cite journal|last1=King |first1=J. |year=1966 |title=The gene interaction component of the genetic load |journal=Genetics |volume=53 |issue=3 |pages=403–413 |doi=10.1093/genetics/53.3.403 |pmid=5919323 |url=http://www.genetics.org/content/53/3/403.short |pmc=1211027}} Evidence was reviewed indicating that meiosis reduces recombination load, thus providing a selective advantage of sexual reproduction.Gorelick R and Villablanca FX (2018) Meiosis decreases recombination load; mitosis increases recombination load. Ideas in Ecology and Evolution 11: 19-28

Migration load is hypothesized to occur when maladapted non-native organisms enter a new environment.{{cite journal|last1=Bolnick|first1=Daniel I. |year=2007 |title=Natural selection in populations subject to a migration load |journal=Evolution |volume=61 |issue=9 |pages=2229–2243 |doi=10.1111/j.1558-5646.2007.00179.x|pmid=17767592|s2cid=25685919|doi-access= }}

On one hand, beneficial genes from migrants can increase the fitness of local populations.{{cite journal|last1=Hu|first1=Xin-Sheng|last2=Li|first2=Bailian |year=2003 |title=On migration load of seeds and pollen grains in a local population |journal=Heredity |volume=90 |issue=2 |pages=162–168 |doi=10.1038/sj.hdy.6800212 |pmid=12634823|doi-access=free }} "Gene flow can homogenize the genetic divergence among populations. On the one hand, effects of genetic drift in small local populations can be effectively reduced when the average number of migrants is greater than one (Wright, 1969), beneficial immigrant genes can shift local populations to a higher fitness peak (Barton and Whitlock, 1997). On the other hand, gene flow between populations adapted to different environments can cause maladaptation in a recipient population, resulting in migration load, a reduction in population fitness. If the migration rate is much greater than the selection coefficient, migrant alleles can even swamp out locally adaptive alleles (Wright, 1969)." On the other hand, migration may reduce the fitness of local populations by introducing maladaptive alleles. This is hypothesized to occur when the migration rate is "much greater" than the selection coefficient.

Migration load may occur by reducing the fitness of local organisms, or through natural selection imposed on the newcomers, such as by being eliminated by local predators.{{harvnb|Bolnick|2007|ps=: "A second consequence of migration–selection balance is known as “migration load” (Garcia-Ramos and Kirkpatrick 1997). This is the loss in mean fitness of a population that results from immigration of locally maladapted alleles. Migration load is analogous to the “mutation load” that arises when mutation inputs new alleles that, on average, are expected to be less fit than existing alleles. Although both migration and mutation have the potential to import locally beneficial novel alleles that promote adaptation (Kawecki 2000), immigrants from other environments may frequently carry alleles that are less fit in the local habitat. Consequently, in addition to constraining divergence among populations, migration displaces recipient populations from their local adaptive peaks. For Mendelian traits, this entails a reduction in the frequency of locally favored alleles that otherwise would be at or near fixation, whereas quantitative traits may be displaced from the mean value favored by selection."}}{{harvnb|Bolnick|2007|ps=:"Given this life history, the homogenizing effects of migration are expected to be most obvious early in a generation, after which natural selection by visual predators presumably eliminates many immigrants."}} Most studies have only found evidence for this theory in the form of selection against immigrant populations, however, one study found evidence for increased mutational burden in recipient populations, as well.{{harvnb|Bolnick|2007|ps=: To date, support for migration load has generally been confined to studies of individual populations, in which selection operates against immigrants (King 1992; Sandoval 1994a; Hendry et al. 2002; Moore and Hendry 2005).}}

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