## Rates of evolution - How do we measure the rate of evolution?

The rate of evolution

The rate of evolution is a measurement of the change in an evolutionary lineage over time.

The method for measuring the rate of evolution can be illustrated by work done by MacFadden on horse teeth: horse teeth are classic materials in the study of evolution.

The rate of evolution is measured as follows:

Suppose that a character has been measured at two times, t_{1} and t_{2} ; t_{1} and t_{2} are expressed as times before the present in millions of years.

The time interval between the two samples can be written as:Dt = t_{1} - t_{2},

which is 1 million years if t_{1} = 15.2 and t_{2} =14.2 The average value of the character is defined as x_{1} in the earlier sample and x_{2} in the later sample; we then take natural logarithms of x_{1} and x_{2} (the natural logarithm is the log to base e where e = 2.718, and it is symbolized by ln ).

The evolutionary rate (r) then is

r = (ln(x_{2}) - ln(x_{1})) / Dt

The rate of evolution is measured in 'darwins'.

Haldane (pictured opposite) defined a 'darwin' as a unit to measure evolutionary rates; one darwin is a change in the character by a factor of e in one million years.

The formula above for r gives the rate in darwins provided that the time interval is in millions of years.

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