# Nucleotide diversity

Nucleotide diversity is a concept in molecular genetics which is used to measure the degree of polymorphism within a population. [1]

One commonly used measure of nucleotide diversity was first introduced by Nei and Li in 1979. This measure is defined as the average number of nucleotide differences per site between two DNA sequences in all possible pairs in the sample population, and is denoted by ${\displaystyle \pi }$.

An estimator for ${\displaystyle \pi }$ is given by:

${\displaystyle {\hat {\pi }}={\frac {n}{n-1}}\sum _{ij}x_{i}x_{j}\pi _{ij}={\frac {n}{n-1}}\sum _{i=2}^{n}\sum _{j=1}^{i-1}2x_{i}x_{j}\pi _{ij}}$

where ${\displaystyle x_{i}}$ and ${\displaystyle x_{j}}$ are the respective frequencies of the ${\displaystyle i}$ th and ${\displaystyle j}$ th sequences, ${\displaystyle \pi _{ij}}$ is the number of nucleotide differences per nucleotide site between the ${\displaystyle i}$ th and ${\displaystyle j}$ th sequences, and ${\displaystyle n}$ is the number of sequences in the sample. The term in front of the sums guarantees an unbiased estimator, which does not depend on how many sequences you sample.[2]

Nucleotide diversity is a measure of genetic variation. It is usually associated with other statistical measures of population diversity, and is similar to expected heterozygosity. This statistic may be used to monitor diversity within or between ecological populations, to examine the genetic variation in crops and related species,[3] or to determine evolutionary relationships.[4]

Nucleotide diversity can be calculated by examining the DNA sequences directly, or may be estimated from molecular marker data, such as Random Amplified Polymorphic DNA (RAPD) data [5] and Amplified Fragment Length Polymorphism (AFLP) data.[6]

## Software

• DnaSP — DNA Sequence Polymorphism, is a software package for the analysis of nucleotide polymorphism from aligned DNA sequence data.
• MEGA, Molecular Evolutionary Genetics Analysis, is a software package used for estimating rates of molecular evolution, as well as generating phylogenetic trees, and aligning DNA sequences. Available for Windows, Linux and Mac OS X (since ver. 5.x).
• Arlequin3 software can be used for calculations of nucleotide diversity and a variety of other statistical tests for intra-population and inter-population analyses. Available for Windows.
• Variscan
• R package PopGenome
• pixy
• R package QSutils

## References

1. ^ Nei, M.; Masatoshi Nei; Wen-Hsiung Li (October 1, 1979). "Mathematical Model for Studying Genetic Variation in Terms of Restriction Endonucleases". PNAS. 76 (10): 5269–73. Bibcode:1979PNAS...76.5269N. doi:10.1073/pnas.76.10.5269. PMC 413122. PMID 291943.
2. ^ Nei, M; Tajima, F (January 1981). "DNA polymorphism detectable by restriction endonucleases". Genetics. 97 (1): 145–63. doi:10.1093/genetics/97.1.145. PMC 1214380. PMID 6266912.
3. ^ Kilian, B; Ozkan H; Walther A; Kohl J; Dagan T; Salamini F; Martin W (December 2007). "Molecular diversity at 18 loci in 321 wild and 92 domesticate lines reveal no reduction of nucleotide diversity during Triticum monococcum (Einkorn) domestication: implications for the origin of agriculture". Molecular Biology and Evolution. 24 (12): 2657–68. doi:10.1093/molbev/msm192. hdl:11858/00-001M-0000-0012-37D5-9. PMID 17898361.
4. ^ Yu, N.; Jensen-Seaman MI; Chemnick L; Ryder O; Li WH (March 2004). "Nucleotide diversity in gorillas". Genetics. 166 (3): 1375–83. doi:10.1534/genetics.166.3.1375. PMC 1470796. PMID 15082556.
5. ^ Borowsky, Richard L. (January 2001). "Estimating nucleotide diversity from random amplified polymorphic DNA and amplified fragment length polymorphism data". Molecular Phylogenetics and Evolution. 18 (1): 143–8. doi:10.1006/mpev.2000.0865. PMID 11161751.
6. ^ Innan, Hideki; Ryohei Terauchib Günter Kahlb; Fumio Tajima (March 1, 1999). "A method for estimating nucleotide diversity from AFLP data". Genetics. 151 (3): 1157–64. doi:10.1093/genetics/151.3.1157. PMC 1460529. PMID 10049931.