Chapter 20 Testing the Molecular Clock Hypothesis

Chapter 20 Testing the Molecular Clock Hypothesis

In previous chapters we have learned the concept of the molecular clock and the fundamentals of phylogenetic reconstruction. We used the molecular clock without checking its validity, and we reconstructed phylogenetic trees without evaluating their statistical support relative to alternative trees. This chapter introduces a method for testing the validity of the molecular clock hypothesis. Evaluating relative statistical support for alternative phylogenetic hypotheses is treated in a later chapter. Evolutionary biologists often use a molecular clock to date speciation events, or infer when and where the common ancestor of a population has lived. For example, a few years ago, it has been claimed that the mitochondrial Eve lived somewhere in Africa about 200,000 years ago (Cann et al. 1987). This is based on the assumption that mitochondrial clock is constant in different human lineages. Is this a valid assumption? In the previous chapter on molecular phylogenetics, we have already mentioned several factors causing the molecular clock to tick at different rates in different lineages, i.e., the generation time effect (Ellsworth et al. 1993; Gu and Li 1992; Seino et al. 1992), the germ line effect (Miyata et al. 1987) and the effect of genetic context (see the chapter on molecular phylogenetics for more details). Will the molecular clock still works in spite of all these distorting factors? The molecular clock hypothesis is typically formulated as the null hypothesis of equal evolution rates along different lineages, which can be tested by using the likelihood ratio test implemented in DAMBE. A likelihood ratio test is a significance test. We will first refresh your memory of basic concepts of statistical significance tests by reviewing the simple ttest. The t-test is then cast in the framework of a likelihood ratio test. The only purpose of presenting this simple t-test is just to let you see the similarity between a simple t-test and a more involved likelihood ratio test so

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that you will be more courageous in future statistical endeavours. The last part of the chapter deals with how to use DAMBE to carry out a likelihood ratio test of the molecular clock hypothesis.

1.

THE T-TEST

Suppose we have a normally distributed variable x with sample values and we are interested in whether the mean value of x is significantly different from This is a typical situation for a t-test, with the null hypothesis being The test is done as follows:

We see that if

then t = 0. If

is very different from

then the

absolute value of t will be large and the likelihood of the null hypothesis being true becomes smaller. Thus, we can view the absolute value of the t

statistic as a measure of the difference between the observed value and the expected value under the null hypothesis. A large t means a great deviation of the observation from the expectation. If the absolute value of t is larger than a predetermined value (i.e., the critical value), then we reject the null hypothesis. The t statistic has a probability distribution called the t distribution, which is similar to the normal distribution except that it is flatter and with longer tails. If the sample size is infinitely large, then the t distribution converges to the normal distribution. The t-test is invented for small samples from which the estimated mean and variance have a small chance of being