dorsal/arxiv
View SchemaThe fitness value of information
| Authors | Carl T. Bergstrom, Michael Lachmann |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0510007 |
| URL | https://arxiv.org/abs/q-bio/0510007 |
Abstract
Biologists measure information in different ways. Neurobiologists and researchers in bioinformatics often measure information using information-theoretic measures such as Shannon's entropy or mutual information. Behavioral biologists and evolutionary ecologists more commonly use decision-theoretic measures, such the value of information, which assess the worth of information to a decision maker. Here we show that these two kinds of measures are intimately related in the context of biological evolution. We present a simple model of evolution in an uncertain environment, and calculate the increase in Darwinian fitness that is made possible by information about the environmental state. This fitness increase -- the fitness value of information -- is a composite of both Shannon's mutual information and the decision-theoretic value of information. Furthermore, we show that in certain cases the fitness value of responding to a cue is exactly equal to the mutual information between the cue and the environment. In general the Shannon entropy of the environment, which seemingly fails to take anything about organismal fitness into account, nonetheless imposes an upper bound on the fitness value of information.
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"abstract": "Biologists measure information in different ways. Neurobiologists and\nresearchers in bioinformatics often measure information using\ninformation-theoretic measures such as Shannon\u0027s entropy or mutual information.\nBehavioral biologists and evolutionary ecologists more commonly use\ndecision-theoretic measures, such the value of information, which assess the\nworth of information to a decision maker. Here we show that these two kinds of\nmeasures are intimately related in the context of biological evolution. We\npresent a simple model of evolution in an uncertain environment, and calculate\nthe increase in Darwinian fitness that is made possible by information about\nthe environmental state. This fitness increase -- the fitness value of\ninformation -- is a composite of both Shannon\u0027s mutual information and the\ndecision-theoretic value of information. Furthermore, we show that in certain\ncases the fitness value of responding to a cue is exactly equal to the mutual\ninformation between the cue and the environment. In general the Shannon entropy\nof the environment, which seemingly fails to take anything about organismal\nfitness into account, nonetheless imposes an upper bound on the fitness value\nof information.",
"arxiv_id": "q-bio/0510007",
"authors": [
"Carl T. Bergstrom",
"Michael Lachmann"
],
"categories": [
"q-bio.PE",
"cs.IT",
"math.IT",
"q-bio.NC"
],
"title": "The fitness value of information",
"url": "https://arxiv.org/abs/q-bio/0510007"
},
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