12.3: The Molecular Clock
- Page ID
- 149283
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Let’s consider a protein’s amino acid sequence in an ancestral species and the same protein sequence in two derived species. (We say that these genes in these two species are “orthologues.”) Now let’s make two assumptions.
- Our first assumption is that this gene accumulates random mutations at a constant rate in both evolving species – for this example, let’s say that one change is fixed in this gene every 10 million years.
- The second assumption is that these mutations are selectively neutral – they confer neither a fitness advantage nor a fitness penalty. This means that for a mutation to be fixed in the population, it needs to happen to an individual – and then, by genetic drift, it needs to end up being present in the entire population.
If we make these two assumptions – that the rate of mutations is constant, and that these mutations are selectively neutral – then we can use the number of mutations in orthologous genes to estimate the length of time since the last common ancestor. We call this scenario a “molecular clock.” In our example, let’s assume that there are four amino acids that are different between these orthologous genes. That means the combined evolutionary “distance”, if you will, between these two genes is 40 million years. And unless we’ve got evidence otherwise, we assume that the mutations accumulated at the same rate for each species – so these two species are about 20 million years removed from their last common ancestor.
Now this is so simple that perhaps you’re wondering, “well, what’s the catch?” The catch is that the two assumptions we made were really strong. The idea that mutations occur at a constant rate is appealing, but we know that some portions of the genome are more prone to mutations than others, and that some species mutate faster than others. And the second assumption we made is even more problematic – especially when we’re discussing amino acid sequences in proteins, a change in an amino acid almost always has a phenotypic effect, even if it’s slight, and thus may be selectively advantageous or selectively neutral. And this is a problem for our molecular clock, too – because if a mutation is advantageous, it will be fixed in the population much more quickly than a neutral mutation. On the other hand, if the mutation is deleterious, it will be selected against and lost. Thus, proteins don’t make great molecular clocks – at least, not until we consider their DNA sequences, instead.
The numbers of substitutions in three proteins, corrected for multiple hits, between various pairs of groups plotted against the time these groups shared a common ancestor in the fossil record. Data from Dicker- son (1971). The lines give the linear regression through the origin for each protein. The slope of the regression is given next to the protein name. Code here. See (Robinson et al., 2016) who revisited this classic study and confirmed the conclusions.
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