Quartet site pattern frequency under Hybridization



A model phylogenetic network with a parameter set Tau 1, Tau 2, Tau 3, Tau 4 and gamma.
Tau 4 represents the speciation time from the root,
Tau 3 represents the speciation time from the first internal node from the root,
and Tau 1 and Tau 2 represents the speciation time from the internal nodes that are the ancestor species of the present day species/populations P1 and P2, respectively. It is that ancestral population at the time of Tau 1 and Tau 2 that hybridize and give rise to the hybrid species H.
Below range bars adjust
Tau 4:
Tau 3:
Tau 2:
Tau 1:
Gamma:
Theta:
Sequence Length:
Warning : y-axis maximum is set to the second largest number + 100. xxxx is the most likely to be the largest. So xxxx bar is not scaled with respect to the rest of the bars.

Estimate inheritance parameter using xxyy, xyxy, and xyyx; the computed gamma= when true gamma=

Detect Introgression using the D-statistic:

The D-statiscic (or also popularly referred to as the ABBA-BABA test) was originally developed to detect gene flow (or introgression) between Neanderthals and present day humans. Site pattern refers to the pattern of nucleotide assignment at the tips of a topology, and on a quartet (a tree with four tips), there are 256 possible site patterns that can be generalized into 15 patterns. These 15 patterns are shown on the bar graph below where x,y,z, and w can be any one of nucleotide states (A,C,T,G) as long as they are different from each other. Among these, the D-statistic utilizes the number of times patterns xyxy and xyyx appears throughout the genome of the four taxa in consideration, where we consider x as ancestral and y as derived.
If the four taxa did not experience gene flow or introgression, the patterns xyyx and xyxy should occur in similar frequency. However, if these taxa experienced those processes at some time during their evolutionary history, the two patterns should appear in significantly different frequency. We compute Z-score to assess the significance and we interpret Z-score > 3 or < -3 as significant. See Durant et al. (2011) for more information.
D-stat can detect introgression when 0< gamma< 0.5.
xyyx:
xyxy:
D-stat value:
Z-score value:

The D-statistic Calculator

xyyx:
xyxy:

D-stat value:
Z-score value: