The Value of Information for Populations in Varying Environments

Abstract

The notion of information pervades informal descriptions of biological systems, but formal treatments face the problem of defining a quantitative measure of information rooted in a concept of fitness, which is itself an elusive notion. Here, we present a model of population dynamics where this problem is amenable to a mathematical analysis. In the limit where any information about future environmental variations is common to the members of the population, our model is equivalent to known models of financial investment. In this case, the population can be interpreted as a portfolio of financial assets and previous analyses have shown that a key quantity of Shannon's communication theory, the mutual information, sets a fundamental limit on the value of information. We show that this bound can be violated when accounting for features that are irrelevant in finance but inherent to biological systems, such as the stochasticity present at the individual level. This leads us to generalize the measures of uncertainty and information usually encountered in information theory.

The More You Know, the More You Can Grow: An Information Theoretic Approach to Growth in the Information Age

“…Since optimal growth implies that the population absorbs all the information between the environment and the cue during updating, the result is the special case of a Markov chain: I(G + ; E; C) = I(E; C). This links our results back to the well-established result from the literature of bet-hedging, which identified I(E; C) as the key variable in optimized growth (in line with [47,48,50,56]). …”

“…As early as 1956, the information theorist John Kelly suggested to optimize long term growth by endogenously adjusting the distribution of types in a population to an exogenously given environmental pattern [33] (for a clear review see [14]). This idea has grown several branches [34], and is known as portfolio theory [35][36][37][38][39][40], growth optimal investment [41][42][43], biological bet-hedging [44], mixed optimal strategies [45], or stochastic (phenotype) switching [46,47]. While Kelly originally worked with the limited case of a diagonal payoff matrix (one type per environmental [47][48][49][50].…”

“…This idea has grown several branches [34], and is known as portfolio theory [35][36][37][38][39][40], growth optimal investment [41][42][43], biological bet-hedging [44], mixed optimal strategies [45], or stochastic (phenotype) switching [46,47]. While Kelly originally worked with the limited case of a diagonal payoff matrix (one type per environmental [47][48][49][50]. The main result of this literature holds that fitness can be increased with information about the environment E through a signaling cue C. Such cues can for example consist of a fine-tuned environmental pattern detected by a machine learning algorithm of a big data company or an economic cycle detected by econometric analysis.…”

“…However, the noiseless channel sets the benchmark. Therefore, in most real-world cases, this first term of the noiseless channel is a hypothetical construct [45,47,49,50,56], which we note with d hyp W . The first term on the right hand side of Equation (2) refers to the benchmark of noiseless communication channel between the environment and the updated population.…”

Evolution of Robustness and Plasticity under Environmental Fluctuation: Formulation in Terms of Phenotypic Variances

“…The system loses plasticity against the One possible origin for the preservation of plasticity may be environmental fluctuation [51], as has also been studied in terms of statistical physics [52][53][54]. The plasticity of a biological system is relevant for coping with the environmental change that may alter phenotypic dynamics in order to achieve a higher fitness.…”