The Value of Information for Populations in Varying Environments

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

Distributing Defenses: How Resource Defendability Shapes the Optimal Response to Risk

Many organisms divide limited defenses among heterogeneous assets. Plants allocate defensive chemicals among tissues differing in value, cost of defense, and risk of herbivory. Some ant colonies allocate specialized defenders among multiple nests differing in volume, entrance size, and risk of attack. We develop a general mathematical model to determine the optimal strategy for dividing defenses among assets depending on their value, defendability, and risk of attack. We build on plant defense theory by focusing on defendability, which we define as the functional relationship between defensive investment and successful defense. We show that if hard-to-defend assets cost more to defend, as assumed in resource defense theory, the optimal strategy allocates more defenses to those assets, regardless of risk. Inspired by cavity-nesting ants, we also consider the possibility that hard-to-defend assets have a lower chance to be successfully defended, even when defensive investment is high. Under this assumption, the optimal response to elevated risk is to reduce defensive allocation to hard-to-defend assets, a conservative strategy previously observed in turtle ants (Cephalotes). This new perspective on defendability suggests that in systems where assets differ in the chance of successful defense, defensive strategies may evolve to be sensitive to risk in surprising ways. © 2022 The University of Chicago. All rights reserved.12 month embargo; published: 31 May 2022This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]