Entropy, or Information, Unifies Ecology and Evolution and Beyond

Abstract

This article discusses how entropy/information methods are well-suited to analyzing and forecasting the four processes of innovation, transmission, movement, and adaptation, which are the common basis to ecology and evolution. Macroecologists study assemblages of differing species, whereas micro-evolutionary biologists study variants of heritable information within species, such as DNA and epigenetic modifications. These two different modes of variation are both driven by the same four basic processes, but approaches to these processes sometimes differ considerably. For example, macroecology often documents patterns without modeling underlying processes, with some notable exceptions. On the other hand, evolutionary biologists have a long history of deriving and testing mathematical genetic forecasts, previously focusing on entropies such as heterozygosity. Macroecology calls this Gini-Simpson, and has borrowed the genetic predictions, but sometimes this measure has shortcomings. Therefore it is important to note that predictive equations have now been derived for molecular diversity based on Shannon entropy and mutual information. As a result, we can now forecast all major types of entropy/information, creating a general predictive approach for the four basic processes in ecology and evolution. Additionally, the use of these methods will allow seamless integration with other studies such as the physical environment, and may even extend to assisting with evolutionary algorithms.These alternatives or 'alleles' can be characterized by the probabilities P(T) and P(A) in the biological population (usually at any position in the DNA, called a 'SNP' or single nucleotide polymorphism, only two of the possible four nucleotides are found). These molecular variants are exactly analogous to alternative species in ecological assemblages, and in most cases, measures or forecasts made in one of these areas have been, or could be, transferred directly to the other.This article will discuss how entropy/information methods are well suited to analyzing and forecasting the four common processes of innovation, transmission, movement, and adaptation in ecology and evolution. Despite the focus on a few variant types, this will apply broadly to variants of all types: DNA, epigenetics, behavior, species, the physical environment, etc., as well as their interactions [2,3]. Background: Measuring Biological Entropy, Information and DiversityMeasurement of ecological or evolutionary variants uses various entropy or information measures (Table 1a). The measures are all part of a 'q-profile' derived from a general power-sum of variant proportions (0 ≤ q ≤ ∞) [4,5]), composed of q D measures on a common scale of the 'effective' number of variants, which means the number of equally-frequent variants that would give the same entropy ( q H) as the typically unequal array of variants in the sampled system. The use of the q D profile has been recommended because each q value emphasizes different aspects of the diversity [6,7]; for example, higher q ...

Shannon diversity index: a call to replace the original Shannon’s formula with unbiased estimator in the population genetics studies

“…It can be utilised to describe variation at multiple levels of genetic organisation from single nucleotide polymorphisms (SNP), through whole species or larger taxonomic units to ecosystems. Due to its additive properties (Jost, 2007), the Shannon index has recently been postulated as a unifying measure for the partitioning of diversity at those levels (Gaggiotti et al, 2018;Sherwin, 2018). Additionally, Sherwin et al (2017) showed its potential utility in genomic studies.…”

The evolutionary pattern of language in scientific writings: A case study of Philosophical Transactions of Royal Society (1665–1869)

“…Measures in the information theory, such as relative entropy, can be used to evaluate diachronic changes in language and to detect cognitive evolution (Sherwin 2018). The use of relative entropy as a measure of changes in the probability distribution over linguistic features has proven effective in many studies (Murdock et al 2017;Klingenstein et al 2014;Barron et al 2018).…”

The Introduction of Entropy and Information Methods to Ecology by Ramon Margalef

“…Entropy/information methods provide the added benefit that they can also be used to comprehensively characterize the physical world that interacts with biota [ 65 , 66 , 67 , 68 ].…”

“…Margalef’s championing of these methods in ecology also led to their uptake in the related field of evolution, where Shannon methods are regarded as one of the best ways of summarizing adaptive change [ 66 ]. A recent attempt at unifying the whole of ecology and evolutionary genetics minimized the mathematical basis [ 70 ], but it has recently been suggested that an entropy/information approach is ideal for this unification [ 5 , 65 , 66 , 67 , 68 ].…”