Evolution, 4th Edition

PHylogENy: THE UNITy ANd dIvERSITy of lIfE 413

lutionary pattern as the first, and so it also lends statistical

support to tree A.But the third base is different: because

of parallel evolution from A to G in the recent ancestors of

species 2 and species 3, this base suggests that tree B is

the most likely.

After combining the data from all three sites, we find

that the likelihood is greatest for tree A, with t 1 = 3.4 million

years and t 2 = 0.6 million years (FIGURE 16.A3). Thus the

estimate for the age of the MRCA of species 1 and species

2 is t 2 = 0.6 Mya, and the MRCA of all three species (that is,

the root of the tree) is t 1 + t 2 = 4.0 Mya.

This example is, of course, tremendously simplified. In

practice, we would typically have data from many DNA

bases. We would also make more realistic (but complicat-

ed) assumptions about evolution (for example, that rates of

substitution differ among the four DNA bases, and among

different sites in the genome), and we would also use the

data to estimate those rates (rather than assuming their

values). Last, rather than assuming what the bases were

in the ancestor, we would account for uncertainty in their

states, for example by averaging over the probabilities that

the ancestor had any one of the four bases at each of the

three sites.

But even in those more complex settings, the basic

approach is the same: we make assumptions about how

evolution works, derive a function that gives the prob-

ability of our data given any specific phylogeny, and finally

determine which phylogeny is most likely. Comparing

these results with those we obtained from parsimony in

the main text, we see some of the advantages and disad-

vantages of the two approaches. Among them, likelihood

is able to estimate the ages of nodes in the phylogeny,

but it requires us to make explicit assumptions about the

evolutionary process and to carry out some moderately

complicated calculations.

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1 2

Maximum

Increasingly

likely

3 4

0

1

2

t 1

t 2

FIGURE 16.A2 Contour plot of the likelihood for different

branch lengths (t 1 and t 2 ) of tree A, based on Equation 16.A1

and using a substitution rate of λ = 0.3/million years. Com-

binations of t 1 and t 2 values in the darker regions of the plot

yield the lowest likelihoods; those in the lightest region yield

the highest likelihoods. The trees in the four corners show

the tree shapes for the corresponding values of t 1 and t 2. The

maximum value of the likelihood occurs when t 1 = 2.7 million

years and t 2 = 0 (indicated by the red circle).

FIGURE 16.A3 Using all the data in Figure 16.12, maximum

likelihood estimates that species 1 and species 2 are most

closely related, that their MRCA lived 0.6 Mya, and that the

MRCA of all three species lived 4 Mya.

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Evolution4e_Box16.A3.ai Date 02-13-2017

t 2

t 1

2 4 6 8

0

1.5

1

0.5

Sp 1

0.6 Mya

4.0 Mya

Sp 2 Sp 3

BOX 16A

Estimating Trees with Likelihood (continued)

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