Model comparison and selection results.

NP: number of parameters. Branch numbers refer to the branches from the tree in Figure 3.P-value: P-values of likelihood ratio tests.ΔAIC: AIC (of the first model)- AIC (of the second model).Conclusion: Decisions of a better model are based on the likelihood ratio test result (when parameter numbers are different) or on the Akaike Information Criterion (AIC = 2k -2ln (L), where k is the number of parameters in the model, and L is the maximized value of the likelihood function for the estimated model).