## Polygenetic Trait Variation

This monogenetic example applies well to diseases like Huntington and PKU but is obviously wrong for blood pressure that is, in reality, influenced by a great many genes (Newton-Cheh et al, 2009). However, the core principles for a single gene can be readily expanded to a polyge-netic example (Mather and Jinks, 1971). Again, we use a thought experiment to illustrate this. Assume we cross double heterozygote parents for two additive SBP loci, in our SBP gene B and a second SBP gene C. The two heterozygous parents (both BbCc genotype), can segregate four different allele combinations to their offspring, listed in bold in Fig. 28.3. The combinatorial result of this mating yields 16 possible genotype combinations in the offspring. As extensively described by Punnett as early as 1905 (Punnett, 1905), a total of nine unique genotypes are actually observed (the general rule is 3n, where n is the number of genes) because some genotypes have the same genotypic value (e.g., bBcC = BbCc = bBcC = bBCc). If the effect of both decreaser alleles ("b" and "c") is to add 0 to the mean blood pressure and the effect of both increaser alleles ("B" and "C") is to add +2 to the mean blood pressure, these two loci will increase the SBP in the various genotypes as depicted in the middle part of Fig. 28.3 (genotypic effects). We now encounter up to five different levels of the trait in the offspring (the general rule is 2n +1, where n is the number of genes). A histogram of these genotypic effects is shown in the lower part of Fig. 28.3. For example, there are four genotypes that produce an increase in SBP of +2 mm Hg (bbcC, bBcc, bbCc, Bbcc) because they all have exactly one increaser (+2) allele.

This Punnett square illustrates two core principles in genetics: (1) Allelic variation is discrete

Father'sallele combinations i e u '

Father'sallele combinations i e u '

BC |
bC |
Bc |
bc | ||||||||||||||||||||||||||

BC |
BBCC |
BbCC |
BBCc |
BbCc | |||||||||||||||||||||||||

bC |
bBCC |
bbCC |
bBCc |
bbCc | |||||||||||||||||||||||||

Bc |
BBcC |
BbcC |
BBcc |
Bbcc | |||||||||||||||||||||||||

bc |
bBcC |
bbcC |
bBcc |
Genotypes b = decreaser allele (+0), B = increaser allele (+2) c = decreaser allele (+0), C = increaser allele (+2) Genotypic effects Distribution of the phenotypes b = decreaser allele (+0), B = increaser allele (+2) c = decreaser allele (+0), C = increaser allele (+2)
Note that we still make the (unreasonable) assumptions that the parents are heterozygote for all loci, that increasing alleles of all three genes have the same effect size, that all alleles contribute additively such that there is no interaction within (dominance) or between loci (epistasis). If we, more realistically, move to a polygenic trait of 1500 genes or more with random allelic effect sizes and varying frequencies, also allowing for dominance and epistatic non-additivity while adding numerous environmental effects on the trait, empirical observation still overwhelmingly suggests that the summed effects of all determinants converge to a normal distribution for many biological and behavioral traits. Fig. 28.3 Genotypes, genotypic effects, and distribution of phenotypes in a double heterozygous mating for two hypothetical SBP genes for all genes but when summed across multiple genes allelic effects lead to a (semi)continuous trait, (2) Segregation of parental allelic variation leads to resemblance within a family but at the same time allows children in the same family to differ substantially (one child may have m+0, whereas another may have m+8). Importantly, the Punnett square keeps working its magic at 3-genic, 4-genic, or 100-genic traits. As is already evident from the simple example in Fig. 28.3, adding more and more genes acts to create an increasingly normal-shaped distribution for the trait. This was the stroke of genius of Sir Ronald Fisher who invoked the central limit theorem to bring discontinuous Mendelian principles of heredity in line with the continuous trait variation observed for almost all traits (Fisher, 1918). |

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