... The preceding discussion is not intended to convey an overly simplistic view of genetics or systems biology. Complex nonlinear genetic systems certainly exist and are realized in every organism. However, quantitative differences between individuals within a species may be largely due to independent linear effects of specific genetic variants. As noted, linear effects are the most readily evolvable in response to selection, whereas nonlinear gadgets are more likely to be fragile to small changes. (Evolutionary adaptations requiring significant changes to nonlinear gadgets are improbable and therefore require exponentially more time than simple adjustment of frequencies of alleles of linear effect.) One might say that to first approximation, Biology = linear combinations of nonlinear gadgets, and most of the variation between individuals is in the (linear) way gadgets are combined, rather than in the realization of different gadgets in different individuals.
Linear models works well in practice, allowing, for example, SNP-based prediction of quantitative traits (milk yield, fat and protein content, productive life, etc.) in dairy cattle. ...
The question of additivity of genetic effects is discussed in more detail in reference [1] above (sections 3.1 and also 4): http://arxiv.org/pdf/1408.3421v2.pdf
In plant and animal genetics it is well established that the majority of phenotype variance in complex traits which is under genetic control is additive. (Linear models work well in species ranging from corn to cows; cattle breeding is now done using SNP genotypes and linear models to estimate phenotypes.) There are also direct estimates of the additive / non-additive components of variance for human height and IQ, from twin and sibling studies. Again, the conclusion is the majority of variance is due to additive effects.
There is a deep evolutionary reason behind additivity: nonlinear mechanisms are fragile and often "break" due to DNA recombination in sexual reproduction. Effects which are only controlled by a single locus are more robustly passed on to offspring. Fisher's fundamental theorem of natural selection says that the rate of change of fitness is controlled by additive variance in sexually reproducing species under relatively weak selection.
Many people confuse the following statements:
"The brain is complex and nonlinear and many genes interact in its construction and operation."
"Differences in brain performance between two individuals of the same species must be due to nonlinear effects of genes."
The first statement is true, but the second does not appear to be true across a range of species and quantitative traits.
Final technical comment: even the nonlinear part of the genetic architecture can be deduced using advanced methods in high dimensional statistics (see section 4.2 in [1] and also http://arxiv.org/abs/1408.6583).
... The preceding discussion is not intended to convey an overly simplistic view of genetics or systems biology. Complex nonlinear genetic systems certainly exist and are realized in every organism. However, quantitative differences between individuals within a species may be largely due to independent linear effects of specific genetic variants. As noted, linear effects are the most readily evolvable in response to selection, whereas nonlinear gadgets are more likely to be fragile to small changes. (Evolutionary adaptations requiring significant changes to nonlinear gadgets are improbable and therefore require exponentially more time than simple adjustment of frequencies of alleles of linear effect.) One might say that to first approximation, Biology = linear combinations of nonlinear gadgets, and most of the variation between individuals is in the (linear) way gadgets are combined, rather than in the realization of different gadgets in different individuals.
Linear models works well in practice, allowing, for example, SNP-based prediction of quantitative traits (milk yield, fat and protein content, productive life, etc.) in dairy cattle. ...