Entropy and Biology

Biology and medicine, from molecules to landscapes, are ideally suited to entropy or information approaches, because biological systems are highly variable, with stochastic processes:

• Innovation (mutation, epigenetics, recombination, speciation)
• Transmission of information (transcription, translation, reproduction, learning)
• Adaptation (natural and sexual selection, behaviour)
• Movement (molecules, gametes, seeds, individuals)

Measurement: For single pools of biological variants (molecules, species, etc), entropy estimates include: counts of different types; Shannon entropy; and the measure called Gini–Simpson, heterozygosity or nucleotide diversity. These, or their transforms, are entropies of order q=0,1,2 respectively (q is the exponent of a power-mean). These local ‘alpha’ measures lead to many ‘beta’ measures of differentiation between components of the biological system, such as Jaccard/Sorensen (q=0), mutual information and relative entropy (q=1), and Wright’s F-statistics (q=2).

Surprisingly, many measures violate vital criteria, such as the need for independence of alpha and beta measures, and to always show an increase with increased variation. Problems are often solved by converting entropies to “number-equivalent” diversities, which importantly share a common scale—the number of equally-frequent types (of species, genetic variants, etc) that would provide the entropy of the real (skewed) distribution of types for that particular order (q=0,1,2).

Biological fields prioritize particular measures: Shannon (q=1) in-species assemblages and networks of molecular information; heterozygosity and nucleotide diversity (q=2) in other aspects of molecular biology. However, informativeness is maximised by plotting a profile of number-equivalent measures (eg. q=0,1,2).

Forecasting: Biological entropy/information measurements need to be tested against predictions, which require further development. Forecasts have been unnecessarily restricted to particular areas. For example, geneticists have many forecasts for q=2 measures such as heterozygosity, yet few of these are used to analyse species assemblages. It was only in 2006 that a theoretical basis was established for forecasting q =1 Shannon-based molecular diversity.

The explicitly hierarchical Shannon approaches are ideal for the integration of biological analyses with all aspects of the environment, such as the flux of energy, water and nutrients through cells or landscapes, plus the interaction between genetic and neural information. Information methods also assist in biomolecule sequence alignment, and phylogeny construction. Each of these approaches benefits from approaches such as maximum-entropy and maximum-entropy production.

Scope and Submissions:

The Entropy and Biology Section aims to publish:

• Articles that highlight how entropic approaches are addressing an impressive array of questions, from molecular biology to landscape ecology and biomedicine
• New entropic approaches in biology
• Reviews that guide the biological use of novel entropic approaches.

Appropriate submissions are encouraged from biologists, physical scientists and mathematicians. Submissions should include examples of current or potential applications of entropy in biology or medicine. We encourage authors to make their contribution accessible to a wide range of science graduates, without compromising scientific content or flow, for example via a table of symbols and jargon, containing definitions understandable to most science graduates. We also encourage the addition of a supplementary short (e.g., three minute) video, which explains in plain language the general significance of the major finding(s). Download Section Flyer