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Conceived and designed the experiments: WH MG PV. Analyzed the data: WH PV. Wrote the paper: WH MG PV.

The authors have declared that no competing interests exist.

The relative proportion of additive and non-additive variation for complex traits is important in evolutionary biology, medicine, and agriculture. We address a long-standing controversy and paradox about the contribution of non-additive genetic variation, namely that knowledge about biological pathways and gene networks imply that epistasis is important. Yet empirical data across a range of traits and species imply that most genetic variance is additive. We evaluate the evidence from empirical studies of genetic variance components and find that additive variance typically accounts for over half, and often close to 100%, of the total genetic variance. We present new theoretical results, based upon the distribution of allele frequencies under neutral and other population genetic models, that show why this is the case even if there are non-additive effects at the level of gene action. We conclude that interactions at the level of genes are not likely to generate much interaction at the level of variance.

Genetic variation in quantitative or complex traits can be partitioned into many components due to additive, dominance, and interaction effects of genes. The most important is the additive genetic variance because it determines most of the correlation of relatives and the opportunities for genetic change by natural or artificial selection. From reviews of the literature and presentation of a summary analysis of human twin data, we show that a high proportion, typically over half, of the total genetic variance is additive. This is surprising as there are many potential interactions of gene effects within and between loci, some revealed in recent QTL analyses. We demonstrate that under the standard model of neutral mutation, which leads to a U-shaped distribution of gene frequencies with most near 0 or 1, a high proportion of additive variance would be expected regardless of the amount of dominance or epistasis at the individual loci. We also show that the model is compatible with observations in populations undergoing selection and results of QTL analyses on F2 populations.

Complex phenotypes, including quantitative traits and common diseases, are controlled by many genes and by environmental factors. How do these genes combine to determine the phenotype of an individual? The simplest model is to assume that genes act additively with each other both within and between loci, but of course they may interact to show dominance or epistasis, respectively. A long standing controversy has existed concerning the importance of these non-additive effects, involving both Fisher

An understanding of the nature of complex trait variation is important in evolutionary biology, medicine and agriculture and has gained new relevance with the ability to map genes for complex traits, as demonstrated by the recent burst of papers that report genome-wide association studies between complex traits and thousands of single nucleotide polymorphisms (SNPs)

The genetic variance _{G} can be partitioned into additive (_{A}), dominance (_{D}), and a combined epistatic component (_{I}), which itself can be partitioned into two locus (_{AA}, _{AD}, and _{DD}) and multiple locus components (_{AAA}, etc.)

In an extremely large data set with very many different kinds of relationships present, it is possible in principle to partition variation into many components using modern statistical methods such as residual maximum likelihood _{AA}/16 for half-sibs), so estimates have high sampling error and there is little power to distinguish _{A} from, say, _{AA}. Selection, assortative mating, and non-genetic covariances also confound estimates. Consequently, there are few accurate estimates of non-additive variance components but there is indirect evidence. For instance, a narrow sense heritability value (^{2} = _{A}/_{P}) of one-half, typical for many traits, implies that dominance, all the vast number of epistatic components, and the environmental component, collectively contribute no more than _{A}. Similarly if the heritability is only a little less than the repeatability (the phenotypic correlation of repeated measures), all non-additive genetic variances and the permanent environmental variance together comprise this small difference. With these caveats we summarise data of various types.

The extensive data on experimental organisms show a range of heritability, higher for morphological than fitness associated traits, averaging as follows

There have been extensive estimates of heritability for traits of livestock. For example, for beef cattle, these averaged: post-weaning weight gain 0.31, market weight for age 0.41, backfat thickness 0.44

There are a number of cases where it can be shown directly that _{A} contributes almost all of _{G} and indeed almost all of _{P}. For bristle number in _{G}/_{P}, is only a little higher than the heritability, indicating that _{A}/_{G}∼0.8 _{A}/

There are rarely good direct estimates of epistatic or dominance variance because these variance components are usually estimated from full-sibs and therefore confounded with the common environment shared by full sibs. However, if the heritability is high, the space for them is limited.

Experiments on inbreeding depression provide some evidence on the importance of non-additive effects. Inbreeding depression implies directional dominance in gene effects but, for a given rate of inbreeding depression, as the number of loci increases and the gene frequencies move toward 0 or 1.0, the dominance variance decreases towards zero. Consequently, the importance of inbreeding depression for traits related to fitness is not evidence that the dominance variance is large. The observed linearity of inbreeding depression with inbreeding co-efficient is easiest to explain with directional dominance but not with DD or higher order epistatic effects because these would cause non-linearity unless they happened to exactly cancel each other out.

In contrast to studies of sibs and more distant relatives, identical twins can provide estimates of _{G}. The classical twin design of samples of monozygotic (MZ) and dizygotic (DZ) twin pairs has been used extensively to estimate variance components for a wide range of phenotypes in human populations. The primary statistics from these studies are the correlations between MZ pairs (_{MZ}) and between DZ pairs (_{DZ}). If twin resemblance due to common environmental factors is the same for MZ and DZ twins then _{MZ}>_{DZ} implies that part of the resemblance is due to genetic factors and _{MZ}>2_{DZ} implies the importance of non-additive genetic effects. Conversely, _{MZ}<2_{DZ} implies that common environmental factors cause some of the observed twin resemblance. Sophisticated variance component partitioning methods to estimate components of additive, non-additive and common environmental effects are used widely

We summarised the MZ and DZ correlations for a wide variety of phenotypes from published twin studies from a single productive laboratory in Australia (genepi.qimr.edu.au). The criteria were that each study must have more than 100 MZ and more than 100 DZ pairs and that the study subjects were Australian twins. For non-continuous traits, studies were included only if they reported polychoric or tetrachoric correlations. In total, 86 phenotypes qualified of which 42 were clinical measures of quantitative traits (including, for example, blood pressure, biochemical measures in blood, body-mass-index, height, tooth dimensions; a full list of phenotypes is available upon request). The MZ and DZ correlations are summarised in _{MZ}−2_{DZ} across all 86 phenotypes is shown in

Data are from published papers by N.G. Martin and colleagues of the Queensland Institute of Medical Research, Brisbane (

Group | All phenotypes | Clinically measured phenotypes | ||

No. traits | No. traits | |||

MZ females | 58 | 0.61 | 24 | 0.76 |

MZ males | 48 | 0.65 | 24 | 0.75 |

DZ females | 58 | 0.34 | 24 | 0.45 |

DZ males | 48 | 0.36 | 24 | 0.43 |

OS pairs |
46 | 0.29 | 23 | 0.36 |

All MZ | 86 | 0.58 | 42 | 0.67 |

All DZ | 86 | 0.29 | 42 | 0.35 |

MZ−2DZ | 86 | 0.00 | 42 | −0.04 |

These show the correlations (

Data from published papers by N.G. Martin and colleagues of the Queensland Institute of Medical Research, Brisbane (

Opposite sex

In view of the apparent conflict between the observations of high proportions of additive genetic variance (often half or more of the phenotypic variance, and even more of the total genetic variance) and the recent reports of epistasis at quantitative trait loci (QTL)

Genetic variance components depend on the mean value of each genotype and the allele frequencies at the genes affecting the trait

These analyses assume a gene frequency distribution which is relevant to no selection. For a more limited range of examples we consider the impact of selection on the partition of variance. We consider a limited range of genetic models, some simple classical ones and others based on published models of metabolic pathways or results of QTL mapping experiments.

Thus

Genetic variance components are obtained by integration of expressions for the variance as a function of _{A}) to genotypic variance (_{G}).

Consider a single biallelic locus with genotypic values for CC, Cc and cc of +

For the

Hence E(_{A}) = ^{2}/3 +^{2}/15 and E(_{D}) = 2^{2}/15, giving E(V_{A})/E(V_{G}) = 1−2^{2}/(5^{2}+3^{2}).

For the _{A})∼(^{2}+^{2}/3)/_{D})∼^{2}/(3_{A})/E(_{G}) = 1−^{2}/(3^{2}+2^{2}).

A simple additive × additive epistatic model has these genotypic values:

Assuming the frequency of B is

Mean =

The average effect of substitution of allele B is given by

_{A} = 2^{2}[^{2}+^{2}] = ^{2}(_{p}_{q}_{p}H_{q}

The AA epistatic effect is given by (_{BC} = ¼ d^{2}

Hence _{AA} = 4^{2}^{2} = ^{2}_{p}H_{q}_{G}^{2}(_{p}_{q}_{p}H_{q}

_{A}) = 2^{2}/9, E(_{AA}) = ^{2}/9, E(_{G}) = ^{2}/3

Similarly E(_{AA}) = ^{2}/(4_{A})/E(_{G}) = (2−4/_{AA}.

A simple epistatic model involving all epistatic components for two loci is the following:

For an arbitrary number (

For _{i}_{G} = ^{2}[(½)^{2L}−(¼)^{2L}], _{A} = ^{2}^{4L−1} and _{A}/_{G} = 2^{2L}−1). For two loci, _{A}/_{G} = 4/15.

For two loci, E(_{A})/E(_{G}) = 9/16 and declines to 0 as

For two loci

For large _{A}) /E(_{G}) → 4/5 and for very many loci E(_{A}) /E(_{G}) → 0

Another simple epistatic model involving all components is the following:_{i}_{A}/_{G} = 0.56; with the uniform distribution, E(_{A})/E(_{G}) = 2/3; and with the ‘U’ distribution

For two-locus models in which the genotypic values were not functions of simple parameters, the genotypic values were entered as data, and _{A} and _{G} calculated as functions of the gene frequencies _{A}(^{10} or higher power of 2 as necessary for adequate convergence. Results were computed for some models of metabolic pathways

Many general points are illustrated by two simple examples, the single locus model with dominance and the two locus model with AA interaction, so we consider these in more detail. For the single locus model with genotypic values for CC, Cc and cc of +_{A} = 2^{2} and _{D} = 4^{2}(1−^{2}^{2}. For _{A} = 8^{3}^{2} and _{D} = 4^{2}(1−^{2}^{2} and thus: at _{A} = (2/3)_{G}; if the dominant allele is rare (i.e. _{G} → 8_{A}/_{G} → 1, and if it is common, _{G} → 4^{2} and _{A}/_{G} → 0. Note, however, that _{G} and _{A} are much higher when the dominant allele is at low frequency, e.g. 0.1, than are _{G} and _{D} when the recessive is at low frequency, e.g. ^{2} = E(_{A})/E(_{G}), an equivalent to narrow sense heritability if _{E} = 0. For the ‘U’ distribution, ^{2} = 1−^{2}/(3^{2}+2^{2}) and for the uniform distribution, ^{2} = 1−2^{2}/(5^{2}+3^{2}). Hence, for a completely dominant locus, ^{2} = 0.8 and ^{2} = 0.75 respectively; whereas _{A}/_{G} = 0.67 for

Genetic model | Distribution of allele frequencies | |||

Uniform | ‘U’ ( |
‘U’ ( |
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Dominance without epistasis |
0.89 | 0.91 | 0.93 | 0.93 |

Dominance without epistasis |
0.67 | 0.75 | 0.80 | 0.80 |

Dominance without epistasis |
0.00 | 0.33 | 0.50 | 0.50 |

A × A without dominance | 0.00 | 0.67 | 0.87 | 0.92 |

Duplicate factor 2 loci | 0.27 | 0.56 | 0.71 | 0.75 |

Duplicate factor 100 loci | 0.00 | 0.00 | 0.00 | 0.00 |

Complementary 2 loci | 0.57 | 0.67 | 0.74 | 0.76 |

Models defined in Methods section

Population size

The genotypic values (see Theory section) for the simple AA model for double homozygotes BBCC and bbcc are +2_{A}/_{G} = 1−_{p}H_{q}_{p}_{q}_{p}H_{q}_{p}_{q}_{A}/_{G} → 1 if _{A}/_{G} = 0.88, 0.69, 0.43 and 0.14. For the uniform distribution ^{2} = 2/3, and for the ‘U’ distribution, the variances are a function of the population size, because more extreme frequencies are possible at larger population sizes. Thus ^{2} = (2−4/^{2} → 1 for large _{AA}.

These two examples, the single locus and A × A model, illustrate what turns out to be the fundamental point in considering the impact of the gene frequency distribution. When an allele (say C) is rare, so most individuals have genotype Cc or cc, the allelic substitution or average effect of C vs. c accounts for essentially all the differences found in genotypic values; or in other words the linear regression of genotypic value on number of C genes accounts for the genotypic differences (see _{G} is accounted for by _{A}.

With the ‘U’ distribution, most genes have one rare allele and so most variance is additive. Further examples (_{A} for the ‘U’ distribution for a few loci but the proportion of the variance which is additive genetic declines as the number increases. With many loci, however, such extreme models do not explain the covariance of sibs (i.e. any heritability) or the approximate linearity of inbreeding depression with inbreeding coefficient,

We also analysed a well-studied systems biology model of flux in metabolic pathways _{G} that is accounted for by _{A} is large (

Activities | Flux relative to wildtype, _{BBCC} = 1 |
E(_{A})/E(_{G}) |
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_{bb} |
_{cc} |
_{BbCc} |
_{bbCC} |
_{BBcc} |
_{bbcc} |
Distribution of allele frequencies | |||

0.5 | Uni |
U100 |
U1000 |
||||||

1 | 0.1 | 0.92 | 1 | 0.53 | 0.53 | 0.81 | 0.86 | 0.88 | 0.88 |

0.5 | 0.1 | 0.90 | 0.91 | 0.53 | 0.50 | 0.81 | 0.85 | 0.88 | 0.88 |

0.1 | 0.1 | 0.86 | 0.53 | 0.53 | 0.36 | 0.77 | 0.82 | 0.86 | 0.87 |

0.1 | 0.01 | 0.85 | 0.53 | 0.09 | 0.09 | 0.72 | 0.79 | 0.83 | 0.84 |

Enzyme activities are _{i}_{BB} = _{CC} = 1, values of _{bb} and _{cc} are listed, and heterozygotes are intermediate, e.g. _{Cc} = ½(1+_{cc}), assuming gene frequency distributions as in

Uniform

U-shaped with population size of 100

U-shaped with population size of 1000

A number of QTL analyses using crosses between populations (some inbred, some selected) have been published in which particular pairs (or more) of loci have been identified to have substantial epistatic effects

Model |
Genotypic values | E(_{A})/E(_{G}) |
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BBCC | BbCC | bbCC | BBCc | BbCc | bbCc | BBcc | Bbcc | bbcc | Distribution of allele frequencies | ||||

0.5 | Uni |
U100 |
U1000 |
||||||||||

DomEp | 4 | 10 | 15 | 11 | 8 | 7 | 10 | 8 | 7 | 0.05 | 0.52 | 0.73 | 0.78 |

Co-ad | 39.0 | 38.7 | 35.7 | 37.6 | 38.9 | 37.7 | 36.8 | 39.6 | 40.4 | 0.11 | 0.62 | 0.81 | 0.85 |

D × D | 4 | 13 | 6 | 13 | 7 | 11 | 5 | 13 | 6 | 0.00 | 0.15 | 0.37 | 0.42 |

Values obtained from tables or by interpolation from Box 1c–e of Carlborg and Haley

Uniform.

U-shaped with population size of 100.

U-shaped with population size of 1000.

The formulae we have given have been for the quantities E(_{A}), E(_{G}) and the ratio E(_{A})/E(_{G}). The quantity actually observed is _{A}/_{G} = Σ_{i}V_{Ai}/Σ_{Gi} where the expression denotes the sums over loci (_{A}/_{G}) ≠ E(_{A})/E(_{G}), we need to consider the relevance of the quantities calculated. Whilst it would be possible to obtain approximations using statistical differentiation

Uniform distribution | |||||

E(_{A})/E(_{G}) |
E(_{A}/_{G}) from simulation |
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Loci |
64 | 16 | 4 | 1 | |

0.750 | 0.749 | 0.747 | 0.734 | 0.609 | |

0.333 | 0.335 | 0.337 | 0.348 | 0.430 | |

A × A | 0.667 | 0.667 | 0.666 | 0.660 | 0.646 |

Dupl. factor | 0.562 | 0.559 | 0.549 | ||

‘U’ distribution with |
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E(_{A})/E(_{G}) |
E(_{A}/_{G}) from simulation |
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Loci* | 64 | 16 | 4 | 1 | |

0.800 | 0.798 | 0.796 | 0.773 | 0.561 | |

0.500 | 0.502 | 0.516 | 0.585 | 0.800 | |

A × A | 0.918 | 0.918 | 0.919 | 0.925 | 0.945 |

Dupl. factor | 0.746 | 0.743 | 0.733 |

Number of loci for non-epistatic cases (complete dominance

Not computed as _{G} = 0 in some replicates.

In this analysis we have assumed there is Hardy-Weinberg equilibrium (HWE) and linkage equilibrium among the loci. As departures from HWE are transient with random mating, they can be ignored, but LD can persist, and hence the estimated effects at locus C depend on those fitted at B and vice versa. The effect of LD is to reduce the number of haplotypes that segregate in the population so what would be epistatic variance becomes additive or dominance variance. For example, consider the A × A model and complete LD, i.e. equal frequencies at B and C loci and both loci segregating but with only two haplotypes present. Then only Bc and bC haplotypes are present, and genotypic values are 0 for homozygous classes and

In these models we have considered solely biallelic loci, appropriate for low mutation rates. Multiallelic loci, in terms of their effects on the trait, can arise from mutations at different structural or control sites. Predictions are complicated by the need to consider _{A} than does the overdominance model at

The analysis we have given for estimating effects of dominance and epistasis is for the classical method using simple averages over genotypes weighted by their frequencies, which are the least squares estimates in the balanced case and the basis for the analysis of variance

The ‘U’ and indeed uniform gene frequency distributions are limiting cases applying in the absence of selection on loci affecting the quantitative trait. The results for a wide range of models can be summarised as follows: gene frequencies that cause _{A}/_{G} to be small also cause _{G} to be small. Consequently, when _{A} and _{G} are summed over a full range of frequencies, _{A}/_{G} is large. This conclusion is dependent on the distribution of gene frequencies being symmetrical, so that cases with large _{G} and large _{A}/_{G} are as common as cases with small _{G} and small _{A}/_{G}. The impact of selection will depend on how it acts on the trait or traits analysed and also on other aspects of fitness, so we need to consider whether the findings are robust to selection.

Stabilising selection on the trait, such that individuals with phenotype closest to an optimum are most fit, leads to maintenance of the population mean at or close to the optimum, so that mutants are at a disadvantage if they increase or decrease trait values. Consequently the gene frequency distribution is still broadly U-shaped, but with much more concentration near 0 or 1

Under the neutral mutation or stabilising selection models where gene frequency distributions have extreme U shape, subsequent directional selection will lead to either rapid fixation or increase to intermediate frequency of genes affecting the trait. Even if the distribution of allele frequencies is initially symmetric, a net increase in variance over generations might thus be expected

Other types of selection do lead to an asymmetrical distribution of allele frequencies because the unfavourable allele will typically be at a low frequency. We have considered the case of genes whose effect on both the trait measured and on fitness shows complete dominance. Thus recessive and dominant favourable and unfavourable mutants were considered, and their expected contribution to variance computed during their lifetime to fixation or loss, using transition matrix methods. Results are given in _{A}/_{G} but even here it is 0.44 and these cases also show the lowest total variance. Consequently, in a trait affected by a mix of genes with varying types of gene action, _{A}/_{G} is likely to be well above 0.5.

Model | E(_{G}) |
E(_{A})/E(_{G}) |
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Neutral dominant | 0 | 0 | 1 | 1 | 0.388 | 0.86 |

Neutral recessive | 0 | 0 | 1 | −1 | 0.166 | 0.66 |

Neutral random |
0 | 0 | 1 | 1 or −1 | 0.277 | 0.80 |

Deleterious dominant | −0.05 | −0.05 | 1 | 1 | 0.145 | 0.97 |

Deleterious recessive | 0 | −0.05 | 1 | −1 | 0.052 | 0.44 |

Advantageous dominant | 0.05 | 0.05 | 1 | 1 | 0.375 | 0.74 |

Advantageous recessive | 0 | 0.05 | 1 | −1 | 0.151 | 0.71 |

e.g., if the mutant gene is completely recessive for the trait and for fitness,

Equally likely to be completely dominant or recessive mutants, hence values as in

Thus if the highest and lowest genotypic values correspond to multiple homozygous classes, it is clear that a high proportion of the variance is expected to be additive genetic even with selection. The potential exceptions occur when there is a maximum at intermediate frequencies, such as with an overdominant locus or some of the cases shown in

The theoretical analysis has been undertaken for large populations but much of the experimental data comes from livestock, laboratory animals and humans, all of which have experienced bottlenecks of reduced effective population size. As has been much explored, bottlenecks of population size are likely to change the proportion of variation that is additive, and for example to increase levels of _{A} for recessives at low frequency _{A}/_{G}. For example, for the additive × additive two locus model, the ratio of variances at inbreeding level _{A}(_{G}(_{A}+4_{AA})/(_{A}+_{AA}+3_{AA}) for any gene frequency (using results of _{A}(_{G}(_{A}/_{G}, whereas if frequencies initially follow the ‘U’ distribution, there is little _{AA} initially, total variance falls and the level of dispersion and _{A}/_{G} do not increase appreciably. Indeed, for a population that starts with the gene frequency distribution U-shaped, the loss of heterozygosity is due to fixation. Among the genes that remain segregating the distribution of gene frequencies flattens considerably, and in the absence of new mutation approaches the uniform distribution which has a lower ratio of _{A}/_{G} than the ‘U’ distribution. However, despite this, _{AA} declines faster than _{A} because, as loci become fixed, the number of pairs of segregating loci declines faster than the number of segregating loci. Thus it is not obvious what effect the bottlenecks in livestock, laboratory or human populations have had on the ratio _{A}/_{G}. We suspect it has not been large because, if a large reduction in heterozygosity had occurred, these populations would show low genetic variance and there is no indication that this is the case. In any case, the results show that the conclusion that most genetic variance is additive is fairly robust to assumptions about the distribution of gene frequencies, for instance the ‘U’ and uniform distributions both lead to qualitatively the same conclusion.

A test of the hypothesis that the lack of non-additive variance observed in populations of humans or animals is because gene frequencies near 0.5 are much less common than those more extreme, not because non-additive effects are absent, is to compare variance components among populations with different gene frequency profiles. For crops such as maize and for laboratory animals, estimates can be got both from outbreds and from populations with gene frequencies of one-half derived from crosses of inbred lines. There are a limited number of possible contrasts and linkage confounds comparisons of variation in F_{2} and later

The most extensive data are on yield traits in maize. The magnitudes of heritability and of dominance relative to additive variance estimated for different kinds of populations in a substantial number of studies (including 24 on F_{2} and 27 on open-pollinated, i.e. outbreds) have been summarised ^{2} were 0.19 for open-pollinated populations, 0.23 for synthetics from recombination of many lines, 0.24 for F_{2} populations, 0.13 for variety crosses and 0.14 for composites. Estimates of _{A}/_{G} (from tabulated values of _{D}/_{A} _{2} populations of maize, one found substantial epistasis _{2} and triple test crosses _{D}/_{A} in the range 0.3 to 0.5, essentially no significant additive × additive epistatic effects, but several cases of epistasis involving dominance

Although there does appear to be more dominance variance in populations with gene frequencies of one-half than with dispersed frequencies, from these results we cannot reject or accept the hypothesis that there is relatively much more epistatic variance in such populations. One explanation is indeed that there is not a vast amount of epistatic variance in populations at whatever frequency, although another is that maize has unusually small amounts of epistasis. Many additive QTL were identified in an analysis of a line derived from the F_{2} of highly divergent high and low oil content lines from the long term Illinois maize selection experiment, but with almost no evidence of epistasis or indeed dominance effects _{2} of divergent lines of long-term selected poultry and an F_{2} from inbred lines of mice showed evidence of highly epistatic QTL effects for body weight

We have summarised empirical evidence for the existence of non-additive genetic variation across a range of species, including that presented here from twin data in humans, and shown that most genetic variance appears to be additive genetic. There are two primary explanations, first that there is indeed little real dominant or epistatic gene action, or second that it is mainly because allele frequencies are distributed towards extreme values, as for example in the neutral mutation model. Complete or partial dominance of genes is common, at least for those of large effect; and epistatic gene action has been reported in some QTL experiments

The theoretical models we have investigated predict high proportions of additive genetic variance even in the presence of non-additive gene action, basically because most alleles are likely to be at extreme frequencies. If the spectrum of allele frequencies is independent of which are the dominant or epistatic alleles, _{A}/_{G} is large for almost any pattern of dominance and epistasis because _{A}/_{G} is low only at allele frequencies where _{G} is low, and so contributes little to the total _{G}_{A}/_{G} depending on whether it is dominant (low _{A}) or recessive (high _{A}). The equivalent case for epistasis is that all genotype combinations except one is favourable (low _{A}) vs. only one genotype combination is favourable (high _{A}).

If genetic variation in traits associated with fitness is due almost entirely to low frequency, deleterious recessive genes which are unresponsive to natural selection, these traits would show low _{A}/_{G}. However, neither the empirical evidence nor the theory supports this expectation. There seems to be substantial additive genetic variance for fitness associated traits _{A}/_{G} is one-half or more. In agreement with this, when the life history of deleterious, recessive mutants was modelled, _{A}/_{G} was found to be 0.44 (_{D}, in non-inbred populations.

We believe we have a plausible gene frequency model to explain the minimal amounts of non-additive genetic and particularly epistatic variance. What consequences do our findings have? For animal and plant breeding, maintaining emphasis on utilising additive variation by straightforward selection remains the best strategy. For gene mapping, our results imply that _{A} is important so we should be able to detect and identify alleles with a significant gene substitution effect within a population. Such variants have been reported from genome-wide association studies in human population

We thank Bernardo Ordas for helpful information and Nick Martin, Naomi Wray, Nick Barton, and referees for comments or discussion on previous versions of the manuscript.