Molecular equidistance

From the early studies of protein homology across different species (Fitch and Margoliash, 1967; Margoliash, 1963; Zuckerkandl and Pauling, 1962), two equally valid sets of data were evident. The first is the widely known and publicized story of protein homology confirming common ancestry, where humans are more related to monkeys, less to rodents, still less to birds, still less to fishes, still less to yeasts, and least to bacteria. The second set of data is the molecular equidistance phenomenon where sister species are roughly equally distant to an outgroup. Species that originated from fishes are all equidistant to fishes. Species that originated from fungi are all equidistant to fungi. Humans, chimpanzees, monkeys, and birds are equally distant from frogs. This striking molecular equidistance phenomenon is in contrast to the obvious non-equidistance at morphological levels. The term molecular equidistance was first used by Michael Denton in his 1986 book Evolution: A Theory in Crisis (Denton, 1986).

The equidistance may not be exactly the same for any given gene of any specific individual organism, for example, the albumin gene of a specific bird individual is 47% identical to that of a specific human and 44% identical to that of a specific rat. So, are rat and human equidistant to bird or not? Some evolution biologists have viewed such small differences to be statistically significant that indicates non-equidistance or non-equal mutation rates, based on the assumption of a gradual mutation model (Nei and Kumar, 2000). They call such statistical calculation the Relative Rate Tests. But such analysis is usually based on single data point and does not consider sampling variations. Also, the calculation presupposes the validity of the gradual mutation hypothesis. But a proper evaluation of a fact should not be influenced by any hypothesis. Prior to knowing the facts to be true, one cannot know how to explain it or which model to use. The molecular equidistance phenomenon should be judged to be either true or false independent of any theories about how mutations accumulate.

A small difference in distance may be merely normal sampling variations around a mean and may not indicate a true and significant difference in distance. If large numbers of bird, human, and rat albumin sequences are available for analysis, the average distance between 10 randomly selected bird albumin sequences (of different sub-species of birds) and 10 randomly selected human albumin sequences may not be statistically different from the average distance between 10 randomly selected bird albumin sequences and 10 randomly selected rat albumin sequences, if the molecular equidistance phenomenon is real. Indeed, if the equidistance were not a real phenomenon, we should observe significant differences in distance between the ancestor lineage and its descendant lineages, which should easily manifest as a wide spectrum from small to huge differences. Thus, using the example of albumin, bird to human may be 47% identical, to rat 44%, to dog 20%, to cow 60%, and to goat 10%. But the fact shows that we only observe small but never huge differences. In the case of albumin, all different mammals are equidistant to birds in the range of 43-47% identity. Thus, the small differences of 4% may not be statistically significant. They are evidence of equidistance rather than non-equidistance. To consider such small differences as being significant also makes it impossible to reconcile it with other contradicting fact where a frog (Xenopus tropicalis) albumin gene is 38% identical to human and 40% to rat. It is self-contradicting for the rat lineage to have a faster mutation rate than humans when birds are the outgroup but a slower mutation rate than humans when frogs are the outgroup. If the faster mutation rate than humans with birds as the outgroup is real, the rate with frogs as the outgroup can only be faster and cannot possibly be slower or equal. Therefore, the facts can only be explained by considering such small differences as insignificant variations of the equidistance phenomenon. Rats and humans are equidistant to birds as well as to frogs. The reality of equidistance is compatible with small and insignificant variations in distance. Given the overwhelming reality of equidistance, any observation of minor deviations from an exact equidistance is almost certainly going to be statistically non-significant. No one has reported a statistically significant violation of the molecular equidistance phenomenon that is not based on calculations presupposing the validity of the gradual mutation hypothesis.

This striking phenomenon of molecular equidistance is so real that it has provoked a novel hypothesis termed the molecular clock hypothesis (Ayala, 1999; Bromham and Penny, 2003; Hedges, 2002; Kumar, 2005; Zuckerkandl and Pauling, 1962). The clock hypothesis was inspired by the early studies of protein homology across different species (Fitch and Margoliash, 1967; Margoliash, 1963; Zuckerkandl and Pauling, 1962), which shows two equally valid sets of data as explained above. These two data sets are deeply related and merely different expressions of the same fact of an apparently constant mutation rate. The first data set would not be possible without the reality of the second data set. The clock hypothesis was invented by emphasizing the first data set while ignoring the molecular equidistance phenomenon. Thus the clock hypothesis may not appear to be inspired by the molecular equidistance phenomenon but in fact was. However, because the molecular equidistance phenomenon was not emphasized by evolution biologists, the vast majority of biologists, except the evolution specialists, are not aware of the molecular equidistance phenomenon. While all of them know that human is more related to chimpanzees than to monkeys, few know that humans and chimpanzees are equally related to monkeys. Most of them would guess erroneously that monkey is more related to chimpanzees than to humans.