Copyright © 1998 by Paul O. Lewis
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This applet begins with a matrix of 200 working light bulbs. The graph plots the proportion of bulbs burned out as a function of time. The instantaneous rate at which bulbs burn out remains constant, howver the proportion of bulbs burned out is not linear with time. This must be the case because time continues on forever whereas proportion cannot exceed 1.0.
The close correspondence between the curve present at the start of the run and the curve that develops during the run demonstrates that this failure process can be modeled quite well. The only parameter necessary to draw the expected curve is the instantaneous bulb failure rate.
The same sort of model is used in substitution models to predict the proportion of sites in a nucleotide sequence that will have incurred at least one substitution by time t. While it is true that nucleotide sites differ from light bulbs in many ways, the stochastic processes that govern substitution events can be modeled well using the same kind of model used here. A "failure" in a nucleotide site occurs when a mistake is made in DNA replication that not only remains uncorrected (by DNA repair mechanisms) but also becomes fixed in a lineage. Many mutations occur that never become fixed in a lineage, and thus the "failure" rate to which we are referring is the substitution rate rather than the mutation rate
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