Genetic load

Genetic load is the difference between the fitness of an average genotype in a population and the fitness of some reference genotype, which may be either the best present in a population, or may be the theoretically optimal genotype. The average individual taken from a population with a low genetic load will generally, when grown in the same conditions, have more surviving offspring than the average individual from a population with a high genetic load.^[1][2] Genetic load can also be seen as reduced fitness at the population level compared to what the population would have if all individuals had the reference high-fitness genotype.^[3] High genetic load may put a population in danger of extinction.

Fundamentals

Consider n genotypes ${\displaystyle \mathbf {A} _{1},\dots ,\mathbf {A} _{n}}$, which have the fitnesses ${\displaystyle w_{1},\dots ,w_{n}}$ and frequencies ${\displaystyle p_{1},\dots ,p_{n}}$, respectively. Ignoring frequency-dependent selection, the genetic load ${\displaystyle L}$ may be calculated as:

${\displaystyle L={{w_{\max }-{\bar {w}}} \over w_{\max }}}$

where ${\displaystyle w_{\max }}$ is either some theoretical optimum, or the maximum fitness observed in the population. In calculating the genetic load, ${\displaystyle w_{1}\dots w_{n}}$ must be actually found in at least a single copy in the population, and ${\displaystyle {\bar {w}}}$ is the average fitness calculated as the mean of all the fitnesses weighted by their corresponding frequencies:

${\displaystyle {\bar {w}}={\sum _{i=1}^{n}{p_{i}w_{i}}}}$

where the ${\displaystyle i^{\mathrm {th} }}$ genotype is ${\displaystyle \mathbf {A} _{i}}$ and has the fitness and frequency ${\displaystyle w_{i}}$ and ${\displaystyle p_{i}}$ 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.^[4] 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.

Causes

Deleterious mutation

Deleterious mutation load is the main contributing factor to genetic load overall.^[5] 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.^[6] Specifically, relative to an ideal genotype of fitness 1, the mean population fitness is ${\displaystyle \exp(-U)}$ 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. But see the section below, The genetic load paradox, for a counter argument regarding mutations with low levels of selection.

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.^[7] Over time, drift load can seriously impact the fitness of a population.^[8][9] 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.^[10] Sexually reproducing species are expected to have lower genetic loads.^[11] 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.^[12]

High load can lead to a small population size, which in turn increases the accumulation of mutation load, culminating in extinction via mutational meltdown.^[13][14]

The accumulation of deleterious mutations in humans has been of concern to many geneticists, including Hermann Joseph Muller,^[15] James F. Crow,^[12] Alexey Kondrashov,^[16] W. D. Hamilton,^[17] and Michael Lynch.^[18]

Beneficial mutation

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".^[19] 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.^[20] 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.^[21]

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.^[22][23]

Inbreeding

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.^[24] In a species that habitually inbreeds, e.g. through self-fertilization, a proportion of recessive deleterious alleles can be purged.^[25][26]

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.^[27]

Recombination/segregation

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.^[28] 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.^[29] Evidence was reviewed indicating that meiosis reduces recombination load, thus providing a selective advantage of sexual reproduction.^[30]

Migration

Migration load is hypothesized to occur when maladapted non-native organisms enter a new environment.^[31]

On one hand, beneficial genes from migrants can increase the fitness of local populations.^[32] 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.^[32]

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.^[33][34] 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.^[35]

The genetic load paradox

As noted above, the Haldane-Muller model for natural selection against deleterious mutations leads to a population fitness of e^-U, where U is the total mutation rate summed over all loci.   For high values of U, it predicts intolerably low overall fitness.

Human mutation rates are now known through direct DNA sequencing.  It is likely that each newborn contains around 100 new mutations^[18].  Many of these mutations, perhaps the majority, will have no effect on fitness.  But if a sizeable proportion do have a deleterious effect, even 5% of mutations, then application of the e^-U formula predicts that the overall fitness will be very low, 0.007 if there are 5 new deleterious mutations.  Are such low values realistic?

A potential answer to this paradox has been proposed ^{[36] [37][38]}, albeit for a different form of deleterious selection, where all homozygotes are less fit than heterozygotes.  The principle is, however, the same for deleterious mutation.

How does this work?  Deleterious mutations of small effect do not necessarily lead directly to death or infertility, in contrast to mutations of lethal effect.  But each such mutation will have a small effect that decreases the fitness, either through lower viability or lower fertility.  Death, or failure to produce offspring, is not caused directly by the genotype.  It is caused, instead, by a lowering of competitive ability compared to other individuals in the population.  This has been termed ‘soft selection’ ^[39], as opposed to hard selection where the genotype directly ‘causes’ the death or infertility.

The soft selection model provides a different lens for looking at genetic load.  Genetic load would not be a load at all if populations had the resources to expand indefinitely, such that all individuals could reproduce.

The arithmetical differences between the soft selection and hard selection models are also striking. The most ‘efficient’ type of selection is one which gives the highest selection against individual mutations for a given overall death rate (or failure to reproduce).  Clearly it is achieved when selection is concentrated against the individuals in the population with the highest number of deleterious mutations^[40],

It has been estimated that each individual carries, on average, around 400 deleterious mutations^[41].  If the 10% of individuals with the highest number of deleterious mutations fail to reproduce, an extreme form of ‘soft’ selection, it can be calculated that each deleterious mutation in the population would be at a selective disadvantage of around 1%.  Under the hard selection model, the ‘death rate’ in the population to produce 1% selection for each deleterious mutation would need to be 1.0 - 0.99⁴⁰⁰.  This comes to around 98%, as opposed to 10% for soft selection.

Under the Haldane-Muller model, each deleterious mutation, regardless of severity, requires one ‘genetic death’ to remove it.  If, as predicted by the soft selection model, natural selection acts based on the overall genotype rather than each mutation independently, each genetic death removes multiple deleterious mutations from the population.

In summary, if there are many mutations, each of small deleterious effect, extreme genetic loads are not a necessary consequence of the action of natural selection.