Some simple formulae were obtained which enable us to estimate evolutionary distances in terms of the number of nucleotide substitutions (and, also, the evolutionary rates when the divergence times are known). In comparing a pair of nucleotide sequences, we distinguish two types of differences; if homologous sites are occupied by different nucleotide bases but both are purines or both pyrimidines, the difference is called type I (or “transition” type), while, if one of the two is a purine and the other is a pyrimidine, the difference is called type II (or “transversion” type). Letting P and Q be respectively the fractions of nucleotide sites showing type I and type II differences between two sequences compared, then the evolutionary distance per site is K = — (1/2) ln {(1 — 2P — Q) }. The evolutionary rate per year is then given by k = K/(2T), where T is the time since the divergence of the two sequences. If only the third codon positions are compared, the synonymous component of the evolutionary base substitutions per site is estimated by K'S = — (1/2) ln (1 — 2P — Q). Also, formulae for standard errors were obtained. Some examples were worked out using reported globin sequences to show that synonymous substitutions occur at much higher rates than amino acid-altering substitutions in evolution.

A simple method for estimating evolutionary rates of base substitutions through comparative studies of nucleotide sequences.

A measure of genetic distance (D) based on the identity of genes between populations is formulated. It is defined as D = -logeI, where I is the normalized identity of genes between two populations. This genetic distance measures the accumulated allele differences per locus. If the rate of gene substitution per year is constant, it is linearly related to the divergence time between populations under sexual isolation. It is also linearly related to geographical distance or area in some migration models. Since D is a measure of the accumulated number of codon differences per locus, it can also be estimated from data on amino acid sequences in proteins even for a distantly related species. Thus, if enough data are available, genetic distance between any pair of organisms can be measured in terms of D. This measure is applicable to any kind of organism without regard to ploidy or mating scheme.

Genetic distance between populations

Fitch, W. M. (Dept. of Physiological Chemistry, Univ. of Wisconsin, Madison, Wisconsin, 53706), 1971. Toward defining the course of evolution: minimum change for a specific tree topology. Syst. Zool., 20:406-416.-A method is presented that is asserted to provide all hypothetical ancestral character states that are consistent with describing the descent of the present-day character states in a minimum number of changes of state using a predetermined phylogenetic relationship among the taxa represented. The character states used as examples are the four messenger RNA nucleotides encoding the amino acid sequences of proteins, but the method is general. [Evolution; parsimonious trees.] It has been a goal of those attempting to deduce phylogenetic relationships from information on biological characteristics to find the ancestral relationship(s) that would permit one to account for the descent of those characteristics in a manner requiring a minimum number of evolutionary steps or changes. The result could be called the most parsimonious evolutionary tree and might be expected to have a high degree of correspondence to the true phylogeny (Camin and Sokal, 1965). It's justification lies in the most efficient use of the information available and does not presuppose that evolution follows a most parsimonious course. There are no known algorithms for finding the most parsimonious tree(s) apart from the brute force method of examining nearly every possible tree.' This is impractical for trees involving a dozen or more taxonomic units. Most numerical taxonomic procedures (Sokal and Sneath, 1963; Farris, 1969, 1970; Fitch and Margoliash, 1967) provide dendrograms that would be among the more parsimonious solutions; one just cannot be sure that a more parsimonious tree structure does not exist. Farris (1970) has explicitly considered the parsimony principle as a part of 'An elegant beginning to an attack on the problem has recently been published by Farris (1969) who developed a method which estimates the reliability of various characters and then weights the characters on the basis of that reliability. his method which, like the present method, has its roots in the Wagner tree (Wagner,

https://www.jstor.org/stable/pdfplus/2412116.pdf

Toward Defining the Course of Evolution: Minimum Change for a Specific Tree Topology

IA. Cause and Effect . . . . . . . . . . . . . . 465 1.2. Prerequisites of Selforganization . . . . . . . 467 1.2.3. Evolut ion Must S ta r t f rom R andom Even ts 467 1.2.2. Ins t ruc t ion Requires In format ion . . . . 467 1.2.3. In format ion Originates or Gains Value by S e l e c t i o n . . . . . . . . . . . . . . . 469 1.2.4. Selection Occurs wi th Special Substances under Special Conditions . . . . . . . . 470

/pdf/selforganization-of-matter-and-the-evolution-of-biological-3ms9rkbxjp.pdf

Selforganization of matter and the evolution of biological macromolecules

IN 1966, I became interested in the amino acid sequences of cytochrome c molecules ([Jukes 1966][1]). I noted that these sequences differed in the cytochromes c of various species to an extent that seemed unnecessary from the standpoint of their function. I stated, “The changes produced in

https://www.genetics.org/content/genetics/154/3/956.full.pdf

The neutral theory of molecular evolution.

NonDarwinian evolution of protein and DNA, comparing expectations of evolution models for protein and amino acid changes

http://science.sciencemag.org/content/sci/164/3881/788.full.pdf

Non-Darwinian Evolution

With the increasing availability of analytical information on mRNA molecules, it is now possible to compare homologous nucleotide sequences from different organisms and to draw conclusions about their evolution. Such comparisons1,2 have shown that silent changes in codons occur more frequently than nucleotide replacements that produce changes in amino acid sequences (code-altering changes). Furthermore, there is an important difference between amino acid sequence comparisons and nucleotide sequence comparisons. The former show only differences in amino acid residues, but the latter show several types of differences when corresponding codons are compared3. Single-base replacements may be degenerate (silent) or expressed as amino acid replacements. Two-base codon changes may be degenerate, single-base changes, or be visible as such. Three-base codon changes may be degenerate (involving serine), simulate either single-base or two-base changes or be visible as such. All nine types of change are found in comparisons of genes from the viruses ΦX74 and G4. The relative numbers of these nine types as based on all possible interchanges between all 61 amino acid codons were listed by Holmquist et al.3 and are shown in Table 1. We discuss these results in the light of the significance of nucleotide changes in molecular evolution.

Jack Lester King

Papers

Non-Darwinian Evolution

Evolutionary nucleotide replacements in DNA.

Biology: The Science of Life

Biosphere: The Realm of Life

Response: Evolution or Not