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Measuring Haplotype Rarity

Taylor Ratio Index

We considered a modification of Casey’s concept, to attain greater comparability between marker sets and, hopefully, between haplogroups. -- using a ratio of an individual’s score to the modal score. The most common possible haplotypes (e.g., WAMH) will score exactly one (1) and less common haplotypes will have higher scores. However, a haplotype score of 5.0 is not five times as rare as one scoring 1.0.[43]

This metric is calculated by

  1. Determining, for each marker, the percentage of men who do not have the particular value.
  2. Determining the percentage of men who do have the modal value.
  3. Dividing A by B to obtain a ratio.
  4. Averaging scores across marker sets.


Figure 7: Taylor Ratio Index Scores

Figure 7 displays the distributions for the ratio indices. See Appendix C for distributions.

Distributions for -- respectively, 25, 37 & 67 markers -- are highly similar; their frequency peaks all occur at the same index value, showing the intent of this system. (The 12-marker distribution is irregular and bi-modal.) This metric is useful for distinguishing average, uncommon and rare haplotypes at all resolution levels.

However, also note steep slopes on left tails and peaks at low indices (<1.35); these aspects suggest the ratio index is imprecise in distinguishing very common from common haplotypes, especially at lower resolutions (<37 markers).

Summary statistics of the Ratio Index:

Table 6
Ratio Index Summary Statisitcs<
Statistic 12 mkr. 25 mkr. 37 mkr. 67 mkr.
Average 1.62 1.65 1.60 1.62
Standard Deviation 1.59 0.94 0.68 0.46
Minimum 1.00 1.00 1.00< 1.00
Maximum 78.3 40.0 27.9 9.9
Median 1.41 1.43 1.44 1.49
Mode # N/A< # N/A # N/A # N/A
n= 4,941 4,203 3,824 1,953

Interpretation of the Ratio Index:

Table 7
Ratio Index Interpretation
Category/th> 12 markers 25 markers 37 markers 67 markers
Very common =1.000 1.0-1.1 1.0-1.2 1.0-1.2
Common >1-1.1 1.1-1.3 1.2-1.3 1.2-1.3
Average 1.1-1.6 1.3-1.6 1.3-1.8 1.3-1.8
Uncommon 1.6-1.8 1.6-2.6 1.8-2.4  1.8-2.4 
Rare ≥1.8 ≥2.6 ≥2.4 ≥2.4

Advantages of this “Taylor ratio index” are

Disadvantages:

Comment:
Attempting to more clearly differentiate scores, we tried a modification – squaring the ratios and then taking the square roots of the sums. We also experimented with higher powers. These proved not worth the complications; only minor differentiation was seen.