### Darwinian Fitness and the evolution of biological diversity

20 January 2006

Lloyd Demetrius

OEB, Harvard and

Max-Planck Institute for Molecular Genetics, Berlin

#### Abstract

Darwinian fitness describes the capacity of a rare mutant to displace a resident population in competition for the available resources. This property is determined by population stability, that is, the rate at which a population returns to its steady state condition after a random perturbation in the individual birth and death rates. Population stability can be quantitatively described by the demographic parameter evolutionary entropy, a measure of the uncertainty in the age of the mother of a randomly chosen newborn. I will discuss the mathematical and empirical basis for these claims. I will also show how the concept evolutionary entropy can be invoked to construct an analytical theory of evolutionary dynamics which quantitatively explains species diversity in the following phenotypic properties: (i) life span, (ii) metabolic rate, (iii) body size.

#### References

K Dietz, *"Darwinian fitness, evolutionary entropy and directionality theory"*, Bioessays 27:1097-1101 2005. PubMed

A Kowald, L Demetrius, *"Directionality theory: a computational study of an entropic principle in evolutionary processes"*, Proc. Roy. Soc. B. 272:741-749 2005. PubMed

M Ziehe, L Demetrius, *"Directionality theory: an empirical study of an entropic principle in life-history evolution"*, Proc. Roy. Soc. B. 272:1185-94 2005. PubMed

L Demetrius, *"Directionality principles in thermodynamics and evolution"*, PNAS 94:3491-3498 1997. PubMed HTML

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