Correlated evolution between change in morphology and shift to exposed epiphytic or epilithic habitat.

Results from test of correlated evolution between change in morphology and shift to exposed epiphytic or epilithic habitat. Test result based on i) comparisons of harmonic means of likelihoods (lnL) from reversible-jump Markov Chain Monte Carlo (RJ MCMC) runs with an independent (I) and a dependent (D) model of character evolution; and ii) numbers of visits in I models during RJ MCMC runs (D1, D2, D3). For i) mean of harmonic means (mean lnL), standard deviations (st.dev. lnL), and maximum harmonic mean of likelihood (max lnL) for three I and D runs are given. Bayes Factor values (BF) are calculated using the maximum harmonic mean of likelihood obtained from the best I and D run, i.e. the run yielding the highest likelihood after 200 000 000 iterations (I max lnL and D max lnL in the table). For ii) chains were run three times (D1, D2, D3), and for the best run, number of visits to I models was compared with the prior odds (see 10). BFs >5 based on prior and posterior odds give support for unexpectedly high number of visits to D models, and thus strongly support the evolutionary model assuming correlated evolution between morphological character change and habitat shift. When the support for the D model is the strongest and visits to I models are absent, zero values in the divisor yield non-applicable (NA) BF. BF >5 are considered strong evidence for correlated evolution [46], [48] and are bolded.