  Based on the normal distribution and its properties, i.e., average and
variance, Fisher works have provided a conceptual framework to identify
genotype-phenotype associations. While Fisher intuition has proved fruitful
over the past century, the current demands for higher mapping precisions have
led to the formulation of a new genotype-phenotype association method a.k.a.
GIFT (Genomic Informational Field Theory). Not only is the method more powerful
in extracting information from genotype and phenotype datasets, GIFT can also
deal with any phenotype distribution density function. Here we apply GIFT to a
hypothetical Cauchy-distributed phenotype. As opposed to the normal
distribution that restricts fluctuations to a finite variance defined by the
bulk of the distribution, Cauchy distribution embraces large phenotypic
fluctuations and as a result, averages and variances from Cauchy-distributed
phenotypes cannot be defined mathematically. While classic genotype-phenotype
association methods (GWAS) are unable to function without proper average and
variance, it is demonstrated here that GIFT can associate genotype to phenotype
in this case. As phenotypic plasticity, i.e., phenotypic fluctuation, is
central to surviving sudden environmental changes, by applying GIFT the unique
characteristic of the genotype permitting evolution of biallelic organisms to
take place is determined in this case.
