Kelly's ZnS
Kelly's [math]\displaystyle{ Z_{nS} }[/math] is a test statistic that can be used to test a genetic region for deviations from the neutral model, based on the squared correlation of allelic identity between loci.[1]
Details
Given loci [math]\displaystyle{ i }[/math] and [math]\displaystyle{ j }[/math], [math]\displaystyle{ D_{ij} }[/math] the Linkage Disequilibrium between these loci, is denoted as
[math]\displaystyle{ D_{ij} = p_{ij}-p_ip_j }[/math]
where [math]\displaystyle{ p_{ij} }[/math] is the frequency of the alternative allele at i and j co-occurring and [math]\displaystyle{ p_{i} }[/math] and [math]\displaystyle{ p_{j} }[/math] the frequency of the alternative allele at [math]\displaystyle{ i }[/math] and [math]\displaystyle{ j }[/math] respectively.
a standardised measure of this is [math]\displaystyle{ \delta_{ij} }[/math] the squared correlation of allelic identity between loci [math]\displaystyle{ i }[/math] and [math]\displaystyle{ j }[/math][2]
[math]\displaystyle{ \delta_{ij} = \frac{D_{ij}^2}{p_i(1 - p_i)p_j (1-p_j)} }[/math]
Where [math]\displaystyle{ Z_{nS} }[/math] averages [math]\displaystyle{ \delta_{ij} }[/math] over all pairwise combinations between S loci.
[math]\displaystyle{ Z_{nS} = \frac{2}{S(S-1)}\sum_{i=1}^{S-1} \sum_{j=i+1}^{S} \delta_{ij} }[/math]
Usage
Inflated [math]\displaystyle{ Z_{nS} }[/math] scores indicate a deviation from the neutral model and can be used as a potential signature of previous selection
References
- ↑ Kelly, J. K. (July 1997). "A test of neutrality based on interlocus associations". Genetics 146 (3): 1197–1206. doi:10.1093/genetics/146.3.1197. ISSN 0016-6731. PMID 9215920.
- ↑ Hartl, Daniel L. (1989). Principles of population genetics. Andrew G. Clark (2nd ed.). Sunderland, Mass.: Sinauer Associates. ISBN 0-87893-302-6. OCLC 18558351. https://www.worldcat.org/oclc/18558351.
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