Table 4.

Log-likelihood ratio tests of nested models

Modela	log(P)b	2LLRc	dfd	Pe
ms>p = 0, mp>s = 0	−40.75	106.5	2	<0.0000
ms>d = 0, md>s = 0	12.49	0	2	1.0000
mp>d = 0, md>p = 0	9.265	6.448	2	0.0255
mp>sp = 0, msp>d = 0	9.333	6.313	2	0.0273

^aFour nested models with zero migration rates between (1) A. scirpaceus and A. palustris, (2) A. scirpaceus and A. dumetorum, (3) A. palustris and A. dumetorum, and (4) A. dumetorum and the common ancestor of A. scirpaceus and A. palustris were compared to the estimated full model

^bEstimates of the posterior density function under the full model

^cLog-likelihood ratio statistics calculated as the difference between the highest posterior probability for the full model and the highest posterior probability for the nested model

^dThe degrees of freedom. Models in which migration at least in one direction is equal to 0 have distributions of 2LLR that are a mixture and χ2 mixture distribution was thus used to calculate the P-value

^eThe probability of achieving the test statistics by chance under the null model (significant values in bold)