Information-entropy approach to the analysis of genetic diversity of populations (analytical review)

Abstract

The application of information-entropy analysis on real data is shown: 84 bulls of Jersey (n = 10), Ayrshire (n = 10), red Danish (n = 10), red Swedish (n = 9) breeds and Holstein ecotypes of German (n = 13), Dutch (n = 17) and North American (n = 15) breeding genotyped by 11 microsatellite loci. The Shannon information index for the combined breed samples was 1.695, the weighted average for the samples was 1.325, the inter-sample component (SHAP) was 0.370 nits or 21.8 % (all calculations according to GenAlEx 6.502). The total absolute diversity of Shannon was 5.45, averaged by samples – 3.76 effective alleles per locus, between breeds – 1.45 effective samples. The relative estimate of the differentiation of breed samples (D'β) was 36.2 % and was close to the «traditional» estimates for Hedrick, Jost and Ciao. The influence of within samples heterozygosity on SHAP estimates has not been established, but a positive trend of D'β-estimates has been noted. The matrix of paired genetic distances by breeds (D'β) and its 2D projection had a high correspondence with those by GST(NEI)-, FST(W&C)-, G"ST(HED)-, F'ST(W&C)-, DJOST-, DCHAO-measures (RMantel ≥ 0,94). Fixation indices (GST(NEI) and FST(W&C)) should be used to study the evolutionary stories of subdivided populations. To analyze the current structure of the genetic diversity of (sub)populations with an emphasis on dominant allele measures based on heterozygosity (G'ST(HED), F'ST(W&C), DJOST and DCHAO), if necessary, take into account all alleles – the Shannon measure (D'β). In conclusion, a family of Hill power measures of order q = 0, 1, 2 is considered for constructing diversity profiles containing all information about the distribution of alleles in a population.

Keywords

• dairy cattle
• microsatellites
• differentiation
• genetic distance
• information
• entropy
• shannon exponent
• analysis of principal coordinates
• ordination