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scientists have found that neutral mutations like those found in cytochrome c occur at a fairly steady rate throughout evolutionary history. for this reason, neutral mutations are used to measure the time that has passed since two species diverged through evolution. the rate of mutation must be calibrated with samples where the actual time of species divergence is known from fossil records. in other words, scientists have developed a molecular clock that can be used to estimate the divergence time between organisms.

1. plot the percentage sequence divergence on the y - axis and the known age of common ancestor on the x - axis for the following species pairs.

species - pair	percentage sequence divergence	known age of common ancestor (millions of years)
human - chimpanzee	9.8	5.5
human - gorilla	12	7.0
chimpanzee - gorilla	12.8	7.0
human - orangutan	16.65	11.0

sequence divergence of hominids

0	2	4	6	8	10	12
0	5	10	15	20

% sequence divergence
known age of common ancestor (millions of years)

1. draw the trend line for the points you have plotted. using the trend line, calculate the slope of the line that describes the relationship between sequence divergence and known age. give a value as % divergence/million years. this is the calibration value for this molecular clock.
2. at the same gene the sequence divergence between chimpanzees and bonobos is 4.2%. using the calibrated molecular clock estimate the time at which these species diverged.
3. the sequence divergence between humans and neanderthals at the same gene is 1.2%. using the calibrated molecular clock, estimate the time these species diverged.

Explanation:

Step1: Recall slope formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For the molecular - clock data, $y$ is the percentage sequence divergence and $x$ is the known age of the common ancestor. We can choose two points from the data. Let's take (Human - Chimpanzee: $(x_1,y_1)=(5.5,9.8)$) and (Human - Orangutan: $(x_2,y_2)=(11.0,16.65)$).

Step2: Calculate the slope

$m=\frac{16.65 - 9.8}{11.0 - 5.5}=\frac{6.85}{5.5}\approx1.25$ % divergence/million years.

Step3: Estimate divergence time for chimpanzees and bonobos

We know that the slope $m$ is the rate of divergence. Using the formula $t=\frac{d}{m}$, where $d$ is the sequence divergence and $t$ is the time of divergence. Given $d = 4.2$% and $m=1.25$ % divergence/million years. Then $t=\frac{4.2}{1.25}=3.36$ million years.

Step4: Estimate divergence time for humans and Neanderthals

Using the same formula $t=\frac{d}{m}$, with $d = 1.2$% and $m = 1.25$ % divergence/million years. Then $t=\frac{1.2}{1.25}=0.96$ million years.

Answer:

1. The slope (calibration value) is approximately 1.25 % divergence/million years.
2. The estimated divergence time between chimpanzees and bonobos is 3.36 million years.
3. The estimated divergence time between humans and Neanderthals is 0.96 million years.