April 25, 2003 50th anniversary of DNA structure “educated guess” http://www.nature.com/nature/dna50/

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© National Health Museum © National Center for Biotechnology Information

EcoRV 5’-GAT|ATC-3’

A A B B C C long branch attraction true tree

= substitution rate t = time after red green blue yellow 1/16μt before Lewis, Paul 1996. pp. 132-163 in Molecular Systematics of Plants II.

= substitution rate t = time μt = expected # of substitutions / parking space over time t after red green blue yellow 1/16μt before 12/16 result in color changes d = 3/4μt = expected # of color changes Lewis, Paul 1996. pp. 132-163 in Molecular Systematics of Plants II.

= substitution rate t = time π = frequency of each car after red green blue yellow π2 μt ππ μt before d = (1- π2 - π2 - π2 - π2 ) μt unequal “color” frequencies

for nucleotide changes A G C T d = 3/4μt d = expected # of nucleotide-changing substitutions μt = 4/3 d # changes / site / time t P (t) probability of seeing at least one change / site P (t) = 1 - e-µt instantaneous rate of change p proportion of changed sites d = -3/4 ln (1- 4p / 3) “evolutionary distance”

http://lewis.eeb.uconn.edu/lewishome/applets/Bulbs/bulbs.html

P (t) = 1 - e-µt

d = -3/4 ln (1- 4p / 3) d = “evolutionary distance” p = proportion of changed sites e.g. if p = 10/100 -.144 d = .108   if p = 50/100 -1.10 d = .825 if p = 1/5 -.310 d = .2326

d = -3/4 ln (1- 4p / 3) .2326 = -3/4 ln (1- ((4*.2) / 3))

Reverend Thomas Bayes 1702-1761