Markers for genetic distance

Different biomolecular markers such DNA, RNA and amino acid sequences (protein) can be used for determining the genetic distance. ^[15][16]

The selection criteria^[17] of appropriate biomarker for genetic distance entails the following three steps:

1. choice of variability
2. choice of specific region of DNA or RNA
3. the use of technique

The choice of variability depends on the intended outcome. For example, very high level of variability is recommended for demographic studies and parentage analyses, medium to high variability for comparing distinct populations, and moderate to very low variability is recommended for phylogenetic studies.^[17] The genomic localization and ploidy of the marker is also an important factor. For example, the gene copy number is inversely proportional to the robustness with haploid genome (mitochondrial DNA) more prone to genetic drift than diploid genome (nuclear DNA).

The choice and examples of molecular markers for evolutionary biology studies.^[17]

Application of genetic distance

• Phylogenetics: Exploring the genetic distance among species can help in establishing evolutionary relationships among them, the time of divergence between them and creating a comprehensive phylogenetic tree that connect them to their common ancestors.
•  Accuracy of genomic prediction: Genetic distance can be used to predict unobserved phenotypes which has implication in medical diagnostics, and breeding of plants and animals. ^[18]
• Population Genetics: Genetic distance can help in studying population genetics, understanding intra and inter-population genetic diversity.
• Taxonomy and Species Delimitation: Determining genetic distance through DNA barcoding is an effective tool for delimiting species especially identifying cryptic species.^[19] An optimized percentage threshold genetic distance is recommended based on the data and species being studied to improve and enhance the reliability and applicability of delimitation^[20][21][22] that can delineate species boundaries and identify cryptic species that look similar but are genetically distinct.

Evolutionary forces affecting genetic distance

Evolutionary forces such as mutation, genetic drift, natural selection, and gene flow drive the process of evolution and genetic diversity. All these forces play significant role in genetic distance within and among species.^[23]

Jukes-Cantor Distance

One of the most basic and straight forward distance measures is Jukes-Cantor distance. This measure is constructed based on the assumption that no insertions or deletions occurred, all substitutions are independent, and that each nucleotide change is equally likely. With these axioms, we can obtain the following equation^[27]:

${\displaystyle d_{AB}=-{\frac {3}{4}}\ln(1-{\frac {4}{3}}f_{AB})}$

where ${\displaystyle d_{AB}}$ is the Jukes-Cantor distance between two sequences A, and B, and ${\displaystyle f_{AB}}$ being the dissimilarity between the two sequences.

Nei's standard genetic distance

In 1972, Masatoshi Nei published what came to be known as Nei's standard genetic distance. This distance has the nice property that if the rate of genetic change (amino acid substitution) is constant per year or generation then Nei's standard genetic distance (D) increases in proportion to divergence time. This measure assumes that genetic differences are caused by mutation and genetic drift.^[11]

${\displaystyle D=-\ln {\frac {\sum \limits _{\ell }\sum \limits _{u}X_{u}Y_{u}}{\sqrt {\left(\sum \limits _{u}X_{u}^{2}\right)\left(\sum \limits _{u}Y_{u}^{2}\right)}}}}$

This distance can also be expressed in terms of the arithmetic mean of gene identity. Let ${\displaystyle j_{X}}$ be the probability for the two members of population ${\displaystyle X}$ having the same allele at a particular locus and ${\displaystyle j_{Y}}$ be the corresponding probability in population ${\displaystyle Y}$. Also, let ${\displaystyle j_{XY}}$ be the probability for a member of ${\displaystyle X}$ and a member of ${\displaystyle Y}$ having the same allele. Now let ${\displaystyle J_{X}}$, ${\displaystyle J_{Y}}$ and ${\displaystyle J_{XY}}$ represent the arithmetic mean of ${\displaystyle j_{X}}$, ${\displaystyle j_{Y}}$ and ${\displaystyle j_{XY}}$ over all loci, respectively. In other words,

${\displaystyle J_{X}=\sum _{u}{\frac {{X_{u}}^{2}}{L}}}$

${\displaystyle J_{Y}=\sum _{u}{\frac {{Y_{u}}^{2}}{L}}}$

${\displaystyle J_{XY}=\sum _{\ell }\sum _{u}{\frac {X_{u}Y_{u}}{L}}}$

where ${\displaystyle L}$ is the total number of loci examined.^[28]

Nei's standard distance can then be written as^[11]

${\displaystyle D=-\ln {\frac {J_{XY}}{\sqrt {J_{X}J_{Y}}}}}$

Cavalli-Sforza chord distance

In 1967 Luigi Luca Cavalli-Sforza and A. W. F. Edwards published this measure. It assumes that genetic differences arise due to genetic drift only. One major advantage of this measure is that the populations are represented in a hypersphere, the scale of which is one unit per gene substitution. The chord distance in the hyperdimensional sphere is given by^[2][25]

${\displaystyle D_{\text{CH}}={\frac {2}{\pi }}{\sqrt {2\left(1-\sum _{\ell }\sum _{u}{\sqrt {X_{u}Y_{u}}}\right)}}}$

Some authors drop the factor ${\displaystyle {\frac {2}{\pi }}}$ to simplify the formula at the cost of losing the property that the scale is one unit per gene substitution.

Reynolds, Weir, and Cockerham's genetic distance

In 1983, this measure was published by John Reynolds, Bruce Weir and C. Clark Cockerham. This measure assumes that genetic differentiation occurs only by genetic drift without mutations. It estimates the coancestry coefficient ${\displaystyle \Theta }$ which provides a measure of the genetic divergence by:^[26]

${\displaystyle \Theta _{w}={\sqrt {\frac {\sum \limits _{\ell }\sum \limits _{u}(X_{u}-Y_{u})^{2}}{2\sum \limits _{\ell }\left(1-\sum \limits _{u}X_{u}Y_{u}\right)}}}}$

Other measures

Many other measures of genetic distance have been proposed with varying success.