Entropy and Information Approaches to Genetic Diversity and its Expression: Genomic Geography

Abstract

This article highlights advantages of entropy-based genetic diversity measures, at levels from gene expression to landscapes. Shannon's entropy-based diversity is the standard for ecological communities. The exponentials of Shannon's and the related "mutual information" excel in their ability to express diversity intuitively, and provide a generalised method of considering microscopic behaviour to make macroscopic predictions, under given conditions. The hierarchical nature of entropy and information allows integrated modeling of diversity along one DNA sequence, and between different sequences within and among populations, species, etc. The aim is to identify the formal connections between genetic diversity and the flow of information to and from the environment.

Unexpected Patterns of Admixture in German Populations of Aedes japonicus japonicus (Diptera: Culicidae) Underscore the Importance of Human Intervention

“…Shannon’s information index is a diversity measure that takes into consideration the frequency of each allele in addition to the total number of alleles [43], [44]. We also assigned individuals to putative populations based on the expected frequencies of their genotypes in those populations using a “leave one out” option in GenAlEx 6.5 [45], [46].…”

Minimum Mutual Information and Non-Gaussianity through the Maximum Entropy Method: Estimation from Finite Samples

“…The seminal work of Shannon on Information Theory [1] gave rise to the concept of Mutual Information (MI) [2] as a measure of probabilistic dependence among random variables (RVs), with a broad range of applications, including neuroscience [3], communications and engineering [4], physics, statistics, economics [5], genetics [6], linguistics [7] and geosciences [8]. MI is the positive difference between two Shannon entropies of the RVs: the one assuming statistical independence ( ) , obtained after subtraction to the sum of fixed marginal entropies of the maximum joint entropy (ME) max H , compatible with imposed cross constraints.…”

“…The number of independent and cross moments of j T (13) is 2j and ( 1)/ 2 j j  respectively (e.g. (4,1), (8,6), (12,15) and (16,28), for j=2, 4,6,8). Other more efficient basis cross functions could be used as for example orthogonal polynomials.…”

Environmental Dynamics in Salinas Grandes, Catamarca, Argentina

“…This effect would be compensated in part through adaptation of the species, quantified as genetic information. Therefore, reduction of biomass in a sub-system is sometimes compensated with an increment of information present in the genes (Sherwin, 2010). The presence of soluble salts in soils generates adverse conditions for unadapted species, reducing the total amount of biomass in the sub-system and, therefore, its exergy.…”