Fig. 3From: General continuous-time Markov model of sequence evolution via insertions/deletions: local alignment probability computationPower-law behaviors of “exact” multiplication factors from case (iii) local PWAs. a Log-log plots of the “exact” multiplication factors (\( {\mu}_P^{\left\langle {N}_{ID}=200\right\rangle}\left[\varDelta L\right] \), ordinate) against the local PWA size (∆L, abscissa), showing nearly perfect power-law behaviors. Although this panel shows the results under λ I : λ D = 1 : 1 only, the power-law approximation is actually very good also under λ I : λ D = 1 : 3 and λ I : λ D = 3 : 1 (Additional file 1: Table S2). Panels b and c show the power-law exponent (γ) and the coefficient (A), respectively, as functions of the distance ((λ I + λ D )(t − t I ) indels/site, abscissa) and the rate ratio (λ I : λ D , different curves). Here, we assumed the approximate power-law relation, \( {\mu}_P^{\left\langle {N}_{ID}=200\right\rangle}\left[\varDelta L\right]\kern0.5em \approx \kern0.5em A{\left(\varDelta L\right)}^{-\gamma } \). (See Additional file 1: Table S2 also for the results of correlation and regression analyses.) Note that the results apply also to case (ii) local PWAs with due modificationsBack to article page