The first 25% of generations were discarded as burnin, an approach verified through graphical analysis of the stabilization of likelihood values.
Assessment of likelihood values for multiple STRUCTURE runs indicates that the best supported hypothesis of true population structure occurs between K = 3 and K = 4.
We accept that the data is a plausible outcome of the model when its likelihood is within the range of likelihood values of typical model outcomes, as described below.
The burn-in period was determined by visual assessment of stationarity, the average standard deviation of bipartition probabilities among runs, convergence of likelihood values between runs, and apparent stationarity of model parameter estimates.
Bayesian posterior probabilities were calculated from the majority rule consensus of the tree sampled after the initial burnin period as determined by checking the convergence of likelihood values across MCMCMC generations (corresponding to 50,000 generations, depending on the analysis).
Prior to phylogenetic tree estimation, the codon position model was optimised using the model selection feature in the TOPALi v2 package [41] which produces improved estimates of Likelihood values and derived statistical quantities (AIC, BIC).
Proper mixing of chains, acceptance probabilities and convergence of likelihood values, tree topologies, branch lengths and model substitution parameters were checked in the four runs before the samples were pooled.
Phylogenetic hypotheses of the sister taxon of Stygiocaris in the Combined 16S/H3 dataset were investigated using the Shimodaira–Hasegawa (S H) test in PAUP (1000 replicates of resampling of estimated log-likelihood test distribution) and Bayes Factors [63] in MrBayes (constrained versus unconstrained harmonic means of likelihood values [64]).
We ran Structure for K ranging from 1 to 13 and we performed at least six repetitions to check for convergence of likelihood values for each value of K. Convergence of the MCMC could not be achieved for K values higher than 13.
From the estimates of likelihood values of the two models, the log likelihood ratio test was conducted.
