Evolutionary Rates

Absolute dating of fossils

Various methods that use radioisotopes are employed to find out the age of fossils. For example U235 decays to Pb217 with a half-life of 713,000,000 years, that is, whatever amount you begin with will be halved every 713,000,000 years.

We need to know how much radioactive material was there in the rock to begin with which can be found out by assuming that ratios in fresh volcanic rock are the same in the past as now. Some of best methods require volcanic rocks, so you can only date sedimentary layers by dating surrounding volcanic layers. Different isotopes have different half-lives.

For example, U235 has a very long half-life, so it is useful for very distant dates, but not very short ones as the change is too little in the isotope ratios over short periods. C14 has a very short half-life (under 7000 years) so it is only useful over periods of tens of thousands of years since over longer periods, there is too little C14 left. The absolute dating methods have confirmed both each other, and the correctness of the relative dating methods.

Measurement of evolutionary rates

Out of several methods, the most common is to measure changes in units called darwins. One darwin is a change by a factor of 2.718 (the base of the natural logarithm) in 1 million years. To calculate from two means, X1 and X2, use logX2logX1/t, where t is the time separating the two measurements, expressed in millions of years. The logarithm transforms it so that changes are expressed as proportions of the current size, and that allows studies of different-sized traits to be compared.

Example. The house sparrow was introduced to North America a little over 100 years ago. It has spread across North America and diverged into local populations. For example, the tibiotarsus bone has changed by about 5% in 100 years. That doesn’t seem like much, but its almost 500 darwins.

Suppose the tibiotarsus changed at that rate for the geologically short time of the most recent geological epoch, the Pleistocene, about 1.8 million years. That would be enough for it to evolve up to the length of an ostrich tibiotarsus, and back down to sparrow size, 54 times. In general, the changes measured over short intervals are much greater than those in the fossil record.

 In the fossil record, we measure rates using pairs thought to be ancestor and descendant. If the change has been very extensive, we may not recognize the pair as ancestor and descendant, so the largest rates may not get measured.

In selection studies, we may ignore changes that are very small. Rates much smaller than 5% in 100 years (as in the above exam seems trivial and, for that matter, hard to statistically distinguish from zero change.

These are average rates, calculated using two endpoints, and the average rates over long periods are likely to average out many ups and downs. There may be little net change even if there is considerable overall change. Example from study of stickleback fish.

Punctuated equilibrium was introduced by Eldredge and Gould in 1972. They argued that the fossil record usually showed stasis (lack of change) for long periods of time, and that transitions between species were hard to find. This was traditionally explained by gaps in the fossil record which, if filled, would show rather gradual evolution. Punctuated equilibrium includes, Stasis with brief periods of change (usually missing from fossil record). Change mainly takes place during speciation events.

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 Mac Fadden 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, t1 and t2; t1and t2 are expressed as times before the present in millions of years.

The time interval between the two samples can be written as: Dt = t1 – t2, which is 1 million years if t1 = 15.2 and t2 =14.2.

The average value of the character is defined as x1 in the earlier sample and x2 in the later sample; we then take natural logarithms of x1and x2 (the natural logarithm is the log to base e where e = 2.718).

The evolutionary rate then is r

r = (log X2 – log X1) / dt

The rate of evolution is measured in ‘darwins’, which is 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. It has been observed that there is an inverse relation between the rate of evolution and the time interval over which it was measured.the observed cases of rapid evolution have tended to be for shorter intervals than the cases of slower evolution.

The measurement of evolutionary rates in darwins is appropriate for metrical changes, such as a character evolving to be longer or shorter; but for larger changes, such as from a leg to a wing, this method ceases to be useful. However, it is still possible to measure rates of evolution for larger changes. Evolutionary rates can be studied quantitatively in characters whose evolutionary changes are not simply metrical. The characters can be divided into discrete states; the states assigned arbitrary scores; and the changes in those scores measured through time. An example are lungfish.

The classic example of this method was Westoll’s investigation into lungfish, living fossils that have changed little from their fossil ancestors in the distant past. Westoll distinguished 21 different characters of fossil Dipnoi. For each of the 21characters, he distinguished a number of character states. The 21 characters were awarded scores between 0 and 4 with the highest score being the most primitive condition and the lowest the most derived, and therefore advanced state. For each fossil, Westoll calculated a total score, made up of its total for all 21 characters. The most advanced possible lungfish, with 21 characters in the most advanced state, would therefore have a total score of zero.