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Using the available biological knowledge, several terms in the models were approximated by conventional kinetic terms with kinetic orders equal to one.

The posterior probabilities of trees and parameters in the substitution models were approximated with MCMC and Metropolis coupling using the program MrBayes 3.1 [ 30].

The posterior probabilities of trees and parameters in the substitution models were approximated with MCMC and Metropolis coupling using the program MrBayes [ 58].

Posterior probabilities of trees and parameters in the substitution models were approximated with MCMC and Metropolis coupling using the program MrBayes 3.1.1 [ 33].

The p-values for the fixed effects in the mixed models were approximated by a t distribution with degrees of freedom equal to the number of individuals minus the number of fixed effect parameters estimated in the model.

The unreliable link models are approximated for AWGN channels.

With non-Gaussian noise approximated by Gaussian mixtures, the non-Gaussian noise models are approximated by banks of Gaussian noise models.

The unreliable link models are approximated for AWGN and Rayleigh block fading channels, respectively, as follows (refer to [17] for more details): in AWGN channels, (11). in Rayleigh fast fading channels, (12).

In practice, such continuous mixture models are approximated via discretization (Yang 1994).

The crude costs for the CT treatments in the IM model were approximated to 365 € (3320 SEK).

The marginal likelihoods for each model were approximated by thermodynamic integration of the Markov chain Monte Carlo (MCMC) over four spaced heated chains (Metropolis coupled MCMC), as described by Beerli and Palczewski (2010).