Wednesday, December 6, 2017

Yet More DifferInt

More on genetic integration.

Some interesting quotes from this paper; emphasis added:
The elementary genic difference does not distinguish homologous from non-homologous genes. Hence, the homologous and non-homologous gene arrangements within the objects affect the elementary genic differences between them only through their sum. For example, in the case of diploid individuals scored at two gene loci A and B, say, the genotypes A1A1/B1B2 and A1A2/B1B3 represent three (A1, B1, B2) and four (A1, A2, B1, B3), respectively, of the total of five gene-types. A1 is represented by two copies in the first genotype and by one copy in the second, and the remaining four gene-types are represented by at most one copy in each of the two genotypes. The sum of copy number differences between the two genotypes thus equals four. After division by twice the number of individual genes in a genotype (i.e. 2·4), this yields 0.5 as the elementary genic difference. The same result is obtained for the two genotypes A1A2/B1B2 and A1A2/B3B3, even though all genic differences are now due to the alleles at a single locus (B). 
Proceeding from lower to higher levels of integration, one expects an increase in differentiation among populations simply because of the larger varietal potential inherent in more complex structures. Since differentiation is based on distances, the distance between two populations should therefore also increase, or at least not decrease, with integration level. 
…it appears that differentiation among populations with respect to their forms of gene association may be a normal occurrence. This insight questions the common practice of restricting the measurement of population differentiation to the allelic level (e.g. FST), thereby ignoring the considerable effects of gene association on population differentiation.

One major finding of the paper is that model data routinely give no increase in differentiation (measured including elementary genic differences) with increasing genetic integration, but real data does show increases.  One wonders if large scale human SNP data would demonstrate such differences, as opposed to the limited SNP data or model systems I have used, which demonstrate increased differentiation only when elementary genic differences are neglected.  On the other hand, as I’ve previously written, neglecting elementary genic differences is, I believe, more compatible with my idea of genetic structure.

That said, one can, if they choose allele structure carefully, produce models that do the exact opposite, have equality at the lower levels of genetic integration, but differentiation at the highest level.

Here is an interesting population model I devised and tested with DifferInt; the differences between the two populations are highlighted.  Note that total numbers of each allele are the same, and the total numbers of single locus genotypes are the same as well.  Thus, genepool differentiation is zero (0.000), as is single locus genotype differentiation, also zero (0.000).  The arrangement of the first and ninth single locus genotypes, together, were changed in six of ten individuals between the two populations, thus producing differentiation specifically at the level of multilocus genotypes. 
(A = 1, T = 2, C= 3, G = 4; first number = number of individuals) 

MLG with EGD: 0.0246
MLG w/o EGD: 0.6000 (6/10 individuals per population altered)

#Population1
1 1  2 2  2 3  3 3  1 1  1 4 1 1  2 2  3 3  3 3  1 1  1 4
1 1  2 2  2 3  3 3  1 1  1 4 1 1  2 2  3 3  3 3  1 1  1 4
1 1  2 2  2 3  3 3  1 1  1 4 1 1  2 2  3 3  3 3  1 1  1 4
1  1 1  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4
1  1 1  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4
1  1 2  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4
1  1 2  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4
1 2  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4
1 2  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4
1 2  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4


#Population2
1 2  2 2  2 3  3 3  1 1  1 4 1 1  2 2  3 3  3 3  1 1  1 4
1 2  2 2  2 3  3 3  1 1  1 4 1 1  2 2  3 3  3 3  1 1  1 4
1 2  2 2  2 3  3 3  1 1  1 4 1 1  2 2  3 3  3 3  1 1  1 4
1  1 1  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4
1  1 1  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4
1  1 2  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4
1  1 2  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4
1 1  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4
1 1 2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4
1 1  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4