Table 3.

Comparison of Kim-Sinha’s probability with ab initio probability for case (iv) local PWA

(∆L A, ∆L D)	Ratio (= ref/KS) a	Overlapping b
(1, 1)	1.667	0.167
(3, 1)	1.883	0.383
(3, 3)	2.449	0.949
(5, 5)	3.325	1.825
(10, 1)	2.165	0.665
(10, 10)	5.572	4.072
(25, 1)	2.355	0.855
(25, 4)	4.714	3.214
(30, 10)	8.300	6.800
(100, 1)	2.561	1.061
(100, 3)	4.896	3.396
(300, 1)	2.659	1.159

Each row gives values for a local PWA with ∆L ^A ancestral sites and ∆L ^D descendant sites in between a pair of PASs. See section M1 of Methods for the parameter setting. When λ _I = λ _D, the ratio for (ΔL ^A, ΔL ^D) = (L ₁, L ₂) is identical to that for (ΔL ^A, ΔL ^D) = (L ₂, L ₁). Thus, we only showed the results for ΔL ^A ≥ ΔL ^D. The ratios less than 2 are in boldface. This table is a modified version of Table 4 of [43]

^a The ratio of the ab initio probability to the corresponding probability given by the HMM of Kim and Sinha [36], in the limit where the time interval (or branch length) approaches zero

^b The portion of the ratio contributed by overlapping indels (such as those in panels d and e of Additional file 1: Figure S3)