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The gene for total baldness is epistatic to those for blond hair or red hair. The baldness phenotype supersedes genes for hair colour and so the effects are non-additive.

Epistasis is a phenomenon that consists of the effect of one gene being dependent on the presence of one or more 'modifier genes' (genetic background). Similarly, epistatic mutations have different effects in combination than individually. It was originally a concept from genetics but is now used in biochemistry, population genetics, computational biology and evolutionary biology. It arises due to interactions, either between genes, or within them leading to non-additive effects. Epistasis has a large influence on the shape of evolutionary landscapes which leads to profound consequences for evolution and evolvability of traits.


  • History 1
  • Classification 2
    • Additivity 2.1
    • Magnitude epistasis 2.2
    • Sign epistasis 2.3
    • Haploid organisms 2.4
    • Diploid organisms 2.5
  • Genetic and molecular causes 3
    • Additivity 3.1
    • Epistasis between genes 3.2
    • Epistasis within genes 3.3
      • Heterozygotic epistasis 3.3.1
  • Evolutionary consequences 4
    • Fitness landscapes and evolvability 4.1
    • Evolution of sex 4.2
  • Methods and model systems 5
    • Regression analysis 5.1
    • Double mutant cycles 5.2
    • Statistical coupling analysis 5.3
    • Computational prediction 5.4
  • See also 6
  • References 7
  • External links 8


Understanding of epistasis has changed considerably through the history of genetics and so too has the use of the term. In early models of natural selection devised in the early 20th century, each gene was considered to make its own characteristic contribution to fitness, against an average background of other genes. Some introductory courses still teach population genetics this way. Because of the way that the science of population genetics was developed, evolutionary geneticists have tended to think of epistasis as the exception. However, in general, the expression of any one allele depends in a complicated way on many other alleles.

In classical genetics, if genes A and B are mutated, and each mutation by itself produces a unique phenotype but the two mutations together show the same phenotype as the gene A mutation, then gene A is epistatic and gene B is hypostatic. For example, the gene for male pattern baldness is epistatic to the gene for red hair. In this sense, epistasis can be contrasted with genetic dominance, which is an interaction between alleles at the same gene locus. As the study of genetics developed, and with the advent of molecular biology, epistasis started to be studied in relation to Quantitative Trait Loci (QTL) and polygenic inheritance.

The effects of genes are now commonly quantifiable by assaying the magnitude of a phenotype (e.g. height, pigmentation or growth rate) or by biochemically assaying protein activity (e.g. binding or catalysis). Increasingly sophisticated computational and evolutionary biology models aim to describe the effects of epistasis on a genome-wide scale and the consequences of this for evolution.[1][2]

Since identification of epistatic pairs is challenging in terms of computationally and also statistical, there are also some studies which tries to prioritize epistatic pairs. [3][4]


Quantitative trait values after two mutations either alone (Ab and aB) or in combination (AB). Bars contained in the grey box indicate the combined trait value under different circumstances of epistasis. Upper panel indicates epistasis between beneficial mutations (blue).[5][6] Lower panel indicates epistasis between deleterious mutations (red).[7][8]
Since, on average, mutations are deleterious, random mutations to an organism cause a decline in fitness. If all mutations are additive, fitness will fall proportionally to mutation number (black line). When deleterious mutations display negative epistasis, they are more deleterious in combination than individually and so fitness falls faster (lower, blue line). When mutations display positive epistasis, effects of mutations are less severe in combination than individually and so fitness falls less quickly (upper, red line).[7][8][9][10]

Terminology about epistasis can vary between scientific fields. Geneticists often refer to wild type and mutant alleles where the mutation is implicitly deleterious and may talk in terms of genetic enhancement, synthetic lethality and genetic suppressors. Conversely, a biochemist may more frequently focus on beneficial mutations and so explicitly state the effect of a mutation and use terms such as reciprocal sign epistasis and compensatory mutation.[11] Additionally, there are differences when looking at epistasis within a single gene (biochemistry) and epistasis within a haploid or diploid genome (genetics). In general, epistasis is used to denote the departure from 'independence' of the effects of different genetic loci. Confusion often arises due to the varied interpretation of 'independence' among different branches of biology.[12] The classifications below attempt to cover the various terms and how they relate to one another.


Two mutations are considered to be purely additive if the effect of the double mutation is the sum of the effects of the single mutations. This occurs when genes do not interact with each other, for example by acting through different metabolic pathways. Simple, additive traits were studied early on in the history of genetics, however they are relatively rare, with most genes exhibiting at least some level of epistatic interaction.[13][14]

Magnitude epistasis

When the double mutation has a fitter phenotype than either single mutation, it is referred to as positive or synergistic epistasis. Positive epistasis between beneficial mutations generates greater improvements in function than expected.[5][6] Positive epistasis between deleterious mutations protects against the negative effects to cause a less severe fitness drop.[8]

Conversely, when two mutations together have a smaller effect than expected from their effects when alone, it is called negative or antagonistic epistasis.[15][16] Negative epistasis between beneficial mutations cause smaller than expected fitness improvements, whereas negative epistasis between deleterious mutations cause greater-than-additive fitness drops.[7]

The term genetic enhancement is sometimes used when a double (deleterious) mutant has a more severe phenotype than the additive effects of the single mutants. Strong positive epistasis is sometimes referred to by creationists as irreducible complexity (although most examples are misidentified).

Sign epistasis

Sign epistasis[17] occurs when one mutation has the opposite effect when in the presence of another mutation. This occurs when a mutation that is deleterious on its own can enhance the effect of a particular beneficial mutation.[12] For example, a large and complex

  • INTERSNP - a software for genome-wide interaction analysis (GWIA) of case-control and case-only SNP data, including analysis of quantitative traits.
  • Science Aid: Epistasis High school (GCSE, Alevel) resource.

External links

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  2. ^ Edlund, JA; Adami, C (Spring 2004). "Evolution of robustness in digital organisms.". Artificial life 10 (2): 167–79.  
  3. ^ Ayati, Marzieh; Koyutürk, Mehmet (2014-01-01). "Prioritization of Genomic Locus Pairs for Testing Epistasis". Proceedings of the 5th ACM Conference on Bioinformatics, Computational Biology, and Health Informatics. BCB '14 (New York, NY, USA: ACM): 240–248.  
  4. ^ Piriyapongsa, Jittima; Ngamphiw, Chumpol; Intarapanich, Apichart; Kulawonganunchai, Supasak; Assawamakin, Anunchai; Bootchai, Chaiwat; Shaw, Philip J.; Tongsima, Sissades (2012-12-13). "iLOCi: a SNP interaction prioritization technique for detecting epistasis in genome-wide association studies". BMC Genomics 13 (Suppl 7): S2.  
  5. ^ a b Phillips, PC (November 2008). "Epistasis--the essential role of gene interactions in the structure and evolution of genetic systems.". Nature reviews. Genetics 9 (11): 855–67.  
  6. ^ a b Domingo, E; Sheldon, J; Perales, C (June 2012). "Viral quasispecies evolution.". Microbiology and molecular biology reviews : MMBR 76 (2): 159–216.  
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  8. ^ a b c He, X; Qian, W; Wang, Z; Li, Y; Zhang, J (March 2010). "Prevalent positive epistasis in Escherichia coli and Saccharomyces cerevisiae metabolic networks.". Nature Genetics 42 (3): 272–6.  
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  12. ^ a b Cordell, Heather J. (2002). "Epistasis: what it means, what it doesn't mean, and statistical methods to detect it in humans".  
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  16. ^ Bonhoeffer S, Chappey C, Parkin NT, Whitcomb JM, Petropoulos CJ (2004). "Evidence for positive epistasis in HIV-1". Science 306 (5701): 1547–50.  
  17. ^ Weinreich, Daniel M.; Watson, Richard A.; Chao, Lin (June 2005). "Perspective: Sign Epistasis and Genetic Constraint on Evolutionary Trajectories". Evolution 59 (6): 1165–1174.  
  18. ^ Poelwijk, Frank J.; Kiviet, Daniel J.; Weinreich, Daniel M.; Tans, Sander J. (January 2007). "Empirical fitness landscapes reveal accessible evolutionary paths.". Nature 445 (7126): 383–386.  
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  21. ^ Lunzer, M; Miller, SP; Felsheim, R; Dean, AM (Oct 21, 2005). "The biochemical architecture of an ancient adaptive landscape.". Science 310 (5747): 499–501.  
  22. ^ Shakhnovich, BE; Deeds, E; Delisi, C; Shakhnovich, E (Mar 2005). "Protein structure and evolutionary history determine sequence space topology.". Genome Research 15 (3): 385–92.  
  23. ^ Harms, MJ; Thornton, JW (Aug 2013). "Evolutionary biochemistry: revealing the historical and physical causes of protein properties.". Nature reviews. Genetics 14 (8): 559–71.  
  24. ^ Witt, D. (2008). "Recent developments in disulfide bond formation".  
  25. ^ Bershtein, S; Segal, M; Bekerman, R; Tokuriki, N; Tawfik, DS (Dec 14, 2006). "Robustness-epistasis link shapes the fitness landscape of a randomly drifting protein.". Nature 444 (7121): 929–32.  
  26. ^ Halabi, N; Rivoire, O; Leibler, S; Ranganathan, R (Aug 21, 2009). "Protein sectors: evolutionary units of three-dimensional structure.". Cell 138 (4): 774–86.  
  27. ^ Neet, KE; Koshland DE, Jr (Nov 1966). "The conversion of serine at the active site of subtilisin to cysteine: a "chemical mutation".". Proceedings of the National Academy of Sciences of the United States of America 56 (5): 1606–11.  
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  29. ^ Sigal, IS; Harwood, BG; Arentzen, R (Dec 1982). "Thiol-beta-lactamase: replacement of the active-site serine of RTEM beta-lactamase by a cysteine residue.". Proceedings of the National Academy of Sciences of the United States of America 79 (23): 7157–60.  
  30. ^ Phillips PC (November 2008). "Epistasis--the essential role of gene interactions in the structure and evolution of genetic systems". Nat. Rev. Genet. 9 (11): 855–67.  
  31. ^ Poelwijk, Frank J.; Tănase-Nicola, Sorin; Kiviet, Daniel J.; Tans, Sander J. (March 2011). "Reciprocal sign epistasis is a necessary condition for multi-peaked fitness landscapes.". Journal of Theoretical Biology 272 (1): 141–144.  
  32. ^ Reetz, MT; Sanchis, J (Sep 22, 2008). "Constructing and analyzing the fitness landscape of an experimental evolutionary process.". Chembiochem : a European journal of chemical biology 9 (14): 2260–7.  
  33. ^ Weinreich, DM; Delaney, NF; Depristo, MA; Hartl, DL (Apr 7, 2006). "Darwinian evolution can follow only very few mutational paths to fitter proteins.". Science 312 (5770): 111–4.  
  34. ^ Gong, LI; Suchard, MA; Bloom, JD (2013). "Stability-mediated epistasis constrains the evolution of an influenza protein.". eLife 2: e00631.  
  35. ^ Lobkovsky, AE; Wolf, YI; Koonin, EV (Dec 2011). "Predictability of evolutionary trajectories in fitness landscapes.". PLoS computational biology 7 (12): e1002302.  
  36. ^ Bridgham, JT; Ortlund, EA; Thornton, JW (Sep 24, 2009). "An epistatic ratchet constrains the direction of glucocorticoid receptor evolution.". Nature 461 (7263): 515–9.  
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See also

Computational prediction

Statistical coupling analysis

When assaying epistasis within a gene, site-directed mutagenesis can be used to generate the different genes and the expressed proteins can be assayed (e.g. for stability or catalytic activity). This is sometimes called a double mutant cycle and involves producing and assaying the wild type protein, the two single mutants and the double mutant. Epistasis is measured as the difference between the effects of the mutations together versus the sum of their individual effects.[41] This can be expressed as a free energy of interaction. The same methodology can be used to investigate the interactions between larger sets of mutations but all combinations have to be produced and assayed. For example, there are 120 different combinations of 5 mutations, some or all of which may show epistasis.

Double mutant cycles

Quantitative genetics focuses on genetic variance due to genetic interactions. Any two locus interactions at a particular gene frequency can be decomposed into eight independent genetic effects using a weighted regression. In this regression, the observed two locus genetic effects are treated as dependent variables and the "pure" genetic effects are used as the independent variables. Because the regression is weighted, the partitioning among the variance components will change as a function of gene frequency. By analogy it is possible to expand this system to three or more loci, or to cytonuclear interactions[40]

Regression analysis

Methods and model systems

However, the evidence for this hypothesis has not always been straightforward and the model proposed by Kondrashov has been criticized for assuming mutation parameters far from real world observations.[38] In addition, in those tests which used artificial gene networks, negative epistasis is only found in more densely connected networks,[15] whereas empirical evidence indicates that natural gene networks are sparsely connected,[39] and theory shows that selection for robustness will favor more sparsely connected and minimally complex networks.[39]

Negative epistasis and sex are thought to be intimately correlated. Experimentally, this idea has been tested in using digital simulations of asexual and sexual populations. Over time, sexual populations move towards more negative epistasis, or the lowering of fitness by two interacting alleles. It is thought that negative epistasis allows individuals carrying the interacting deleterious mutations to be removed from the populations efficiently. This removes those alleles from the population, resulting in an overall more fit population. This hypothesis was proposed by Alexey Kondrashov, and is sometimes known as the deterministic mutation hypothesis[37] and has also been tested using artificial gene networks.[15]

Evolution of sex

Rugged, epistatic fitness landscapes also affect the 'predictability' of evolution. When a mutation has a large number of epistatic effects, each accumulated mutations drastically changes the set of available beneficial mutations. Therefore the evolutionary trajectory followed depends highly on which early mutations were accepted. Therefore repeats of evolution from the same starting point tend to diverge to different local maxima rather than converge on a single global maximum as they would in a smooth, additive landscape.[35][36]

Consequently, high epistasis is usually considered a constraining factor on evolution, and improvements in a highly epistatic trait are considered to have lower evolvability. This is because, in any given genetic background, very few mutations will be beneficial, even though many mutations may need to occur to eventually improve the trait. The lack of a smooth landscape makes it harder for evolution to access fitness peaks. In highly rugged landscapes, fitness valleys block access to some genes, and even if ridges exist that allow access, these may be rare or prohibitively long.[34]

If all mutations are additive, they can be acquired in any order and still give a continuous uphill trajectory. The landscape is perfectly smooth, with only be one peak (local maxima in the fitness landscape having acquired mutations in the 'wrong' order.[32] For example, a variant of TEM1 β-lactamase with 5 mutations is able to cleave cefotaxime (a third generation antibiotic).[33] However, of the 120 possible pathways to this 5-mutant variant, only 7% are accessible to evolution as the remainder passed through fitness valleys where the combination of mutations reduces activity.

A fitness landscape is a representation of the fitness where all genotypes are arranged in 2D space and the fitness of each genotype is represented by height on a surface. It is frequently used as a visual metaphor for understanding evolution as the process of moving uphill from one genotype to the next, nearby, fitter genotype.[13]

In evolutionary genetics, the sign of epistasis is usually more significant than the magnitude of epistasis. This is because magnitude epistasis (positive and negative) simply affects how beneficial mutations are together, however sign epistasis affects whether mutation combinations are beneficial or deleterious.[30]

The top row indicates interactions between two genes that are either additive (a), show positive epistasis (b) or reciprocal sign epistasis (c). Below are fitness landscapes which display greater and greater levels of global epistasis between large numbers of genes. Purely additive interactions lead to a single smooth peak (d), as increasing numbers of genes exhibit epistasis, the landscape becomes more rugged (e) and when all genes interact epistatically the landscape becomes so rugged that mutations have seemingly random effects (f).

Fitness landscapes and evolvability

Evolutionary consequences

heterozygous / heteroallelic), the two different copies of the allele may interact with each other to cause epistasis. This is sometimes called allelic complementation, or interallelic complementation. It may be caused by several mechanisms, for example transvection, where an enhancer from one allele acts in trans to activate transcription from the promoter of the second allele. Alternately, trans-splicing of two non-functional RNA molecules may produce a single, functional RNA. Similarly, at the protein level, proteins that function as dimers may form a heterodimer composed of one protein from each alternate gene and may display different properties to the homodimer of one or both variants.

Heterozygotic epistasis

[29][28][27] In

Proteins are held in their tertiary structure by a distributed, internal network of cooperative interactions (hydrophobic, polar and covalent).[22] Epistatic interactions occur whenever one mutation alters the local environment of another residue (either by directly contacting it, or by inducing changes in the protein structure).[23] For example in a disulphide bridge, a single cysteine has no effect on protein stability until a second is present at the correct location at which point the two cysteines form a chemical bond which enhances the stability of the protein.[24] This would be observed as positive epistasis where the double-cysteine variant had a much higher stability than either of the single-cysteine variants. Conversely, when deleterious mutations are introduced, proteins often exhibit mutational robustness whereby as stabilising interactions are destroyed the protein still functions until it reaches some stability threshold at which point further destabilising mutations have large, detrimental effects as the protein can no longer fold. This leads to negative epistasis whereby mutations that have little effect alone, have a large, deleterious effect together.[25]

Just as mutations in two separate genes can be non-additive if those genes interact, mutations in two codons within a gene can be non-additive. In genetics this is sometimes called intragenic complementation when one deleterious mutation can be compensated for by a second mutation within that gene. This occurs when the amino acids within a protein interact. Due to the complexity of protein folding and activity, additive mutations are rare.

Epistasis within genes

Epistasis within the genomes of organisms occurs due to interactions between the genes within the genome. This interaction may be direct if the genes encode proteins that, for example, are separate components of a multi-component protein (such as the ribosome), inhibit each other's activity, or if the protein encoded by one gene modifies the other (such as by phosphorylation). Alternatively the interaction may be indirect, where the genes encode components of a metabolic pathway or network, developmental pathway, signalling pathway or transcription factor network. For example, the gene encoding the enzyme that synthesizes penicillin is of no use to a fungus without the enzymes that synthesize the necessary precursors in the metabolic pathway.

Epistasis between genes

[14][13] with hundreds or thousands of other genes.interact It is now considered that strict additivity is the exception, rather than the rule, since most genes [21] This can be the case when multiple genes act in parallel to achieve the same effect. For example, when an organism is in need of


Genetic and molecular causes

Additive A locus Additive B locus Dominance A locus Dominance B locus
aa aA AA aa aA AA aa aA AA aa aA AA
bb 1 0 –1 bb 1 1 1 bb –1 1 –1 bb –1 –1 –1
bB 1 0 –1 bB 0 0 0 bB –1 1 –1 bB 1 1 1
BB 1 0 –1 BB –1 –1 –1 BB –1 1 –1 BB –1 –1 –1
Additive by Additive Epistasis Additive by Dominance Epistasis Dominance by Additive Epistasis Dominance by Dominance Epistasis
aa aA AA aa aA AA aa aA AA aa aA AA
bb 1 0 –1 bb 1 0 –1 bb 1 –1 1 bb –1 1 –1
bB 0 0 0 bB –1 0 1 bB 0 0 0 bB 1 –1 1
BB –1 0 1 BB 1 0 –1 BB –1 1 –1 BB –1 1 –1

Epistasis in heterozygotes. For a two locus, two allele system, there are eight independent types of gene interaction.[20]

Diploid organisms

Interaction type ab Ab aB AB
No epistasis (additive)  0 1 1 2 AB = Ab + aB + ab 
Positive (synergistic) epistasis 0 1 1 3 AB > Ab + aB + ab 
Negative (antagonistic) epistasis 0 1 1 1 AB < Ab + aB + ab 
Sign epistasis 0 1 -1 2 AB has opposite sign to Ab or aB
Reciprocal sign epistasis 0 -1 -1 2 AB has opposite sign to Ab and aB

In a loci) ab, Ab, aB or AB, we can think different forms of epistasis as affecting the magnitude of a phenotype upon mutation individually (Ab and aB) or in combination (AB).

Haploid organisms

When two mutations are viable alone but lethal in combination, it is called Synthetic lethality or unlinked non-complementation.[19]

Reciprocal sign epistasis also leads to genetic suppression whereby two deleterious mutations are less harmful together than either one on its own, i.e. one

. competing organisms by killing fitness alone can waste energy, but producing both can improve toxin exporter, and producing a bacterium alone can kill a toxin occurs when two deleterious genes are beneficial when together. For example, producing a [18]

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