Here is a simple metabolic phenotype.  The trait is flux through a sequential 3-enzyme pathway.  Suppose the Vmax of two of the enzymes can vary (due to mutations in the coding region that alter the efficacy of the enzymes, or mutations in the regulatory region that alter their level of expression). Such mutations will alter the flux through the pathway.

The figure is a graph of how the flux/phenotype (z axis) depends on the genotypes of the two genes/enzymes, using the equation of Kacser and Burns. 

So it’s a G-P map.




Here is the interesting problem. Take two genotypes X and Y.  They have the same phenotype (flux = z axis), but due to very different genotypes (activities of the 2 enzymes).  For an individual with genotype X small mutations  in Gene A would have little effect on the phenotype, but mutations in Gene B would have a big effect.  Thus Gene B would be called a big-effect gene and Gene A would be considered a modifier gene.

The exact opposite is true for an individual with genotype Y, even though they have teh identical genetci mechanism.

So we have  simple mechanism in which it is obvious that any phenotype (a contour on the surface) can be due to a virtually infinite number of genotypes. 

Three step pathways of this sort are ubiquitous: embedded in metabolic systems, synthesis pathways, signaling pathways, gene-regulatory networks, developmental and physiological systems.  So there is reason to suspect that these kinds of nonlinear phenotypic landscapes are the rule rather than the exception.

You can see that if you had a population with a mean genotype/phenotype clustered around X, you would deduce a completely different set of statistical G-P associations than if you had a population centered around Y, and neither would be informative about the other. But the underlying mechanism explains both.