heritability

Huang W, Lyman RF, Lyman RA, Carbone MA, Harbison ST, Magwire MM, Mackay TFC 2016 Spontaneous mutations and the origin and maintenance of quantitative genetic variation. eLife 5:e14625.

• we inferred strong stabilizing natural selection on quantitative traits
• genetic variation among wild-derived inbred lines was much lower than predicted from a neutral model
• the mutational effects were much larger than allelic effects of standing polymorphisms
• our data are not consistent with simple models of mutation-stabilizing selection balance

• the overall spontaneous mutation rate for all types of mutations combined was 6.25 × 10−9 on autosomes and 6.96 × 10−9 on the X chromosome (Figure 7c), similar to recent mutation rate estimates from MA studies using high throughput sequencing
• there was substantial variation in spontaneous mutation rates among MA lines
• the mutation rate in MA19 was nearly a magnitude greater than the lines with the smallest mutation rates
• such a large difference cannot be solely explained by variability in 2Ne among the MA lines
• varying 2Ne from 10 to 40 can only account for a 28% difference in mutation rate

• strong stabilizing selection on quantitative trait variation
• the magnitude of standing genetic variation in the DGRP was much smaller than that predicted under the assumption of neutrality
• there must be strong stabilizing selection
• to understand the consequence of the strong apparent stabilizing selection, we estimated the expectation of allelic effects based on the observed sequence and quantitative trait variation among the MA and DGRP lines
• the amount of genetic variation is proportional to sequence variation by a factor of E(a²)
• a is the allelic effect of a mutation on quantitative traits
• for the majority of traits, the ratio of mutational to standing genetic variance, V_m/V_g, far exceeded the expectation given the observed sequence variation
• the allelic effects of spontaneous mutations, E(a_m²), were several orders of magnitude larger than that of standing DNA variation, E(a_g²)
• the apparent stabilizing selection, directly for fitness and indirectly for traits correlated with fitness, had either eliminated mutations with large effects on quantitative traits or modified their effects
• the former appears to be at least partly true given the obvious difference in functional categorization of spontaneous mutations and standing DNA variation

• our estimates of h_m² for gene expression traits were higher than observed in previous studies (Rifkin et al., 2005), possibly due to smaller technical variation and thus smaller V_e in this study

• gene expression traits often form co-expression modules
• mutations that directly influence expression of a small number of loci can cause secondary trans effects at a much larger number of genes
• taking this networked view of gene expression traits, any selection will not act on individual traits, but rather on the combined effects of all traits
• consistent with this notion, we found stronger selection on genes that would cause trans pleiotropic effects such as transcription factors

• there is limited evidence for genuine genetic variation for mutation rate
• this is primarily due to technical limitations
• mutation rate is sensitive to environmental and physiological factors that cannot be easily controlled
• it is prohibitive to collect genetic data on mutation rates in natural populations

• we inferred that a form of stabilizing selection on a large fraction of gene expression as well as organismal traits constrains naturally occurring genetic variation, consistent with earlier studies using a similar analysis in C. elegans

• the house-of-cards approximation holds when mutation rates are low, mutational effects are large, and selection is strong (Turelli, 1984)
• the Gaussian approximation holds under conditions of weak stabilizing selection, high mutation rates and small mutational effects (Lande, 1975)
• our observations of low mutation rates and mutational effects that are much larger than standing DNA polymorphisms favor the former parameterization
• under this model, V_g = 4nμV_s
• n is the number of loci potentially affecting the trait
• μ is the mutation rate
• V_s represents the strength of stabilizing selection
• assuming strong direct stabilizing selection (e.g. V_s = 20V_e), high heritabilities (e.g. V_g = V_e) and our estimated mutation rate (μ = 6.60 × 10⁻⁹), then n = 1.9 × 10⁶, which seems implausibly large given the total size of the D. melanogaster euchromatic genome of approximately 1.2 × 10⁸

• the equilibrium genetic variance is V_g = V_m/s
• s = V_m/V_g
• our estimate of V_m/V_g had a median 1.94 × 10⁻³ for organismal traits and 1.82 × 10⁻³ for gene expression traits
• we detect apparent stabilizing selection on quantitative traits
• it is too weak by an order of magnitude for the majority of genes and quantitative traits to be consistent with observed selection against heterozygous effects of new mutations (Mukai et al., 1972; Mackay et al., 1992)

• simple mutation – stabilizing selection models for either direct or apparent stabilizing selection cannot maintain the observed amounts of segregating genetic variation with the observed mutational input and strong selection
• the mutational variance is too low and/or the standing genetic variance is too high