a common ancestor 10 million years ago, then T2 when A and B diverged is about one-third of that time. Assumptions in these time estimates are that rates of substitution are constant over time, among lineages, and over loci. These assumptions will be explored critically later in the chapter.

The molecular clock has been widely used to date major evolutionary transitions, establish times when the ancestors of many different organisms first evolved, and test hypotheses related to divergence times. One example is testing the hypothesis that early mammal evolution was facilitated by ecological niches that opened up when the dinosaurs went extinct. The molecular clock suggests that the earliest mammal lineages had appeared well before the extinction of the dinosaurs was complete (Bromham et al. 1999; Bininda-Emonds et al. 2007). Thus, the estimated divergence time rejects the hypothesis that mammals first originated in habitats left empty as dinosaurs disappeared.

A second illustration is the classic question of when humans and their close ancestors diverged. Using calibration times of13 million years for the divergence between orangutans and humans and 90 million years between artiodactyls (hoofed mammals with an even number of digits, such as cattle, deer, and pigs) and primates, as well as numerous loci, Glazko and Nei (2003) estimated the divergence of humans and chimpanzees occurred 5-7 million years ago.

A third example is employment of the molecular clock to date the origin of the human immunodeficiency virus or HIV. The date that HIV was transmitted from primates to humans is a critical question. Identifying related viruses in primates and the genetic features that facilitated transmission and virulence in humans would facilitate the development of treatments for HIV. One highly controversial hypothesis for the origin of HIV was that it was first spread to humans through contaminated human polio vaccine made from cultured chimpanzee cells that was administered in the former Belgian Congo between 195 7 and 1960. This hypothesis is supported by indirect evidence, such as the timing and location of the earliest known cases of HIV/AIDS and that fact that the chimpanzee simian virus 40 (SV40) has been transmitted to humans. A molecular clock suggests that HIV was introduced to humans around 1920-30 and that HIV and the simian immunodeficiency virus (SIV) may have diverged as much as 300 years ago (Leitner & Albert 1999; Salemi et al. 2001). However, application of the molecular clock to HIV faces substantial challenges and interpretation remains controversial due to issues such as rate variation and recombination (see Korber et al. 1998; Schierup & Hein 2000).

The use of the molecular clock to estimate times of divergence is complicated by numerous issues in practice (see review by Arbogast et al. 2002), contributing to both statistical uncertainty as well as controversy over interpretation of date estimates. First, calibration times usually have considerable ranges, leading to uncertainty in any divergence time estimated from the molecular clock. Then, corrections to divergence estimates are required for multiple substitutions occurring at the same nucleotide site. In addition, the rate of substitution is assumed to be constant over time. However, variation in rates of substitution over time and among different loci is now considered the rule rather than the exception, complicating the methods needed to estimate divergence times (see Culter 2000b; Glazko & Nei 2003). Testing for and explaining variation in substitution rates is explored in the next section.

8.4 Testing the molecular clock hypothesis and explanations for rate variation in molecular evolution

• Rate heterogeneity in the molecular clock.

• The Poisson process model of the molecular clock.

• Ancestral polymorphism and the molecular clock.

• Relative rate tests of the molecular clock.

• Possible causes of rate heterogeneity.

The molecular clock predicts that selectively neutral homologous sequences (meaning sequences that were once identical by descent) with equal mutation rates should experience a similar number of substitutions per unit time as divergence increases. Therefore, the molecular clock hypothesis provides a null model to examine the processes that operate during molecular evolution. It is possible to directly test the molecular clock hypothesis and thereby test this null model. Rejecting the molecular clock hypothesis suggests that the sequences compared evolve at unequal rates, a situation referred to as rate heterogeneity. Rejecting the molecular clock hypothesis is a way to identify processes that influence the chance of substitution such that rates of fixation are either higher or lower than expected by genetic drift alone. For example, a previous section showed how natural selection changes the probability of fixation and therefore the rate of substitution. So, for example, one sequence taken from a population where most mutations are deleterious and selected against and another sequence taken from a population where most mutations are neutral would have different rates of substitution and show different numbers of substitutions over a fixed time interval (see Fig. 8.3). Thus, testing for equal rates of substitution, or rate homogeneity, is a useful step in identifying the processes that may be operating in molecular evolution.

Rate heterogeneity Variation in the rate of substitution over time or among different lineages for homologous genome regions.

The molecular clock and rate variation

Since the neutral theory leads to the molecular clock hypothesis, evidence for rate heterogeneity would appear to be evidence that genetic drift is not the main process leading to the ultimate substitution of most mutations. Rejecting the hypothesis of rate homogeneity would suggest that natural selection is operating on mutations such that their rates of substitution are either sped up or slowed down relative to substitution rates under genetic drift. The probability that a new mutation is fixed by natural selection depends on the selection coefficient, s, and the effective population size rather than just-as it

2Ne does for genetic drift. Natural selection is therefore very unlikely to produce a molecular clock because s, Ne, and p are not likely to be constant through time or among different lineages. Before reaching the conclusion that natural selection explains all rate heterogeneity, however, it is necessary to dig deeper into the molecular clock hypothesis. The molecular clock is potentially more complex than was revealed at the beginning of the chapter. Understanding these complications is a necessary prerequisite to understanding the range of alternative hypotheses that may explain heterogeneity in rates of molecular evolution.

The molecular clock was originally proposed by Zuckerkandl and Pauling (1962, 1965; Zuckerkandl 1987) to model amino acid substitutions. It was based on a simple statistical method used to describe events that happen at random times given some rate at which events occur (such models are called point processes). The simplest point process for a

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