GIFT: new method for the genetic analysis of small gene effects involving small sample sizes.

Small gene effects involved in complex/omnigenic traits remain costly to analyse using current genome-wide association studies (GWAS) because of the number of individuals required to return meaningful association(s), a.k.a. study power. Inspired by field theory in physics, we provide a different method called genomic informational field theory (GIFT). In contrast to GWAS, GIFT assumes that the phenotype is measured precisely enough and/or the number of individuals in the population is too small to permit the creation of categories. To extract information, GIFT uses the information contained in the cumulative sums difference of gene microstates between two configurations: (i) when the individuals are taken at random without information on phenotype values, and (ii) when individuals are ranked as a function of their phenotypic value. The difference in the cumulative sum is then attributed to the emergence of phenotypic fields. We demonstrate that GIFT recovers GWAS, that is, Fisher's theory, when the phenotypic fields are linear (first order). However, unlike GWAS, GIFT demonstrates how the variance of microstate distribution density functions can also be involved in genotype-phenotype associations when the phenotypic fields are quadratic (second order). Using genotype-phenotype simulations based on Fisher's theory as a toy model, we illustrate the application of the method with a small sample size of 1000 individuals.