Evolution is a rather complex phenomenon and does not fit into a linear equation with time especially at the molecular level. The process of genetic drift results in changes in allele frequencies over generations. However the average rate of change remains fairly constant in a population. Hence most of the genetic variations are in effect neutral.

The rate of genetic drift can be modeled using statistical approaches in probability as a function of time. The effective population size can be designated as Ne. This constitutes the individuals in any population who can pass the genes to the next generation effectively. Ne is less than the total population size N.

The neutral theory of molecular evolution holds that alternative alleles at variable loci are neutral. In other words, the genetic variations are effectively neutral.

Number of substitutions/generation = (Number of mutations/generation) * (probability of fixation)
= μ0 * P0

The genes that are available to mutate in any population is thus twice the effective population size. NG = 2* Ne

The probability of allele fixation (P0) over the generations is 1/(2* Ne )

The number of alleles getting fixed over generations therefore becomes

μ0 = μ* 2* Ne where μ is the mutation rate.

Hence the Number of substitutions/generation becomes

μ*(2* Ne ) * 1/(2* Ne ) = μ

Thus, the allele fixation rate after a few generations is equal to the allele frequency of the original population. To summarize the substitution rate equals the mutation rate when the mutations are selectively neutral. This is the basis of molecular clocks.
The rate of production of neutral mutations can be estimated by

μ = D/2t
Where D - mutational differences between the two species
And't' - Number of generations from the common ancestor.

This can be used to establish the molecular clocks for each gene evolution. The applications range from predicting the rate of evolution to establishing the time of evolution. The first research in the field was done on amino acid sequences to conclude that the rates were roughly the same for various species with common ancestry as proved from fossil records.
The theory of molecular clock proposed by Zuckerkandl and Pauling explained the cause of such similarities and paved way for a new era of research in evolutionary genetics. Since then several researchers have used the tool to find the hominid ancestry and the time of origin of various species including humans.

The phenomenon received applauses as well as heavy blows about accuracy and applicability. The primary concern was how the molecular clocks could be so similar even in different species with varied life history and traits.

The early researchers used the relative rate of approach. In this, species within the same group were compared with an external reference species termed as out group species. This approach required no assumption about the time of species divergence. However it immediately raised the reliability factor. The inverse correlation between the time of species divergence and the sequence identity of proteins and nucleic acids were soon established from further experiments in the field.

There are a few drawbacks for this hypothesis.

1. Smaller differences between protein and/or nucleic acid sequences can occur by chance alone even if the rates are constant.
2. A single analysis of a gene or amino acid sequence will not be statistically significant to establish evolutionary correlation between species.
3. There are other factors which affect the constancy of molecular clocks like the length of amino acid sequence, rate of evolution and the duration from the evolutionary divergence.
4. Hominoid slowdown was reported in some cases in which the gene evolution rate was slower in humans when compared to similar gene sequences in other species. This was found to be erroneous since the approach used by the researchers involves assumption of a referral time of divergence. When similar research was conducted using the relative rate approach, the time of divergence was found to be inaccurate and hence the validity of the slow down became insignificant.
5. Proteome evolutionary rates were not consistent among species.

There have been a few instances in the evolutionary history when the diversification of the organisms was rapid and this was found to be on selected genes. Further the rates of mutations were found to be non uniform among different mammalian species. Hence including more genes in analysis would be beneficial. Evolutionary genetics is not as stochastic as it was thought to be and newer algorithms and models need to be developed. Further research need to be done in the field to unravel the statistical relationships between these 'stochastic' evolutionary processes and geologic time scales.

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