Closed form modeling of evolutionary rates by exponential Brownian functionals
- 172 Downloads
Accurate estimation of species divergence times from the analysis of genetic sequences relies on probabilistic models of evolution of the rate of molecular evolution. Importantly, while these models describe the sample paths of the substitution rates along a phylogenetic tree, only the (random) average rate can be estimated on each edge. For mathematical convenience, the stochastic nature of these averages is generally ignored. In this article we derive the probabilistic distribution of the average substitution rate assuming a geometric Brownian motion for the sample paths, and we investigate the corresponding error bounds via numerical simulations. In particular we confirm the validity of the gamma approximation proposed in Guindon (Syst Biol 62(1):22–34, 2013) for “small” values of the autocorrelation parameter.
KeywordsEvolutionary rates Exponential Brownian functionals Geometric Brownian bridge Molecular clocks Phylogenetics
Mathematics Subject Classification92D15 92D20 33C10 62J10 60J22 60J27 60J65 81S40 60H30 60H07
- Thompson EA (1975) Human evolutionary trees. CUP Archive, CambridgeGoogle Scholar
- Watson GN (1995) A treatise on the theory of Bessel functions. Cambridge University Press, Cambridge (reprint of the second (1944) edition)Google Scholar
- Zuckerkandl E, Pauling L (1962) Molecular disease, evolution, and genic heterogeneity. In: Kasha M, Pullman B (eds) Horizons in biochemistry. Elsevier, Amsterdam, pp 189–225Google Scholar