APPENDIX 5
VARIATION IN EVOLUTIONARY RATES ESTIMATED BY DIFFERENT MODELS FIT TO DATA
SIMULATED WHILE VARYING RELATIVE OPTIMA AND RELATIVE RATES PARAMETERS
The convergence of different models in terms of their goodness of fit to data simulated using
different relative rate and relative optima parameters (see Results and Fig. 4) suggested that these
models may be also converging in terms of the estimated model parameters, actually providing
similar predicted covariance structures for the data. To verify if this was the case, we compared
the evolutionary rate parameters estimated by each model, for the subset of simulations and fit
models presented in Fig. 4.
In accordance with what was predicted, the three models fit to data simulated under an OU
process with two optima and a single evolutionary rate (OUM) provided very similar estimates
for the evolutionary rate parameter, which became more and more similar as the relative optima
parameter increased (Fig. A5A and A5B). Two aspects of the evolutionary rates estimated under
different models are of interest here for explaining how these models exhibit similar fits to the
data: first, the two separate evolutionary rates estimated for each group of taxa under the BMSG
and OUMV models (BMSG1 and BMSG2; OUMV1 and OUMV2 respectively, Fig. A5A) are
very similar to each other, such that the relative evolutionary rate parameter of both models was
close to σ22 / σ21 = 1 (Fig. A5B). Second, the (similar) evolutionary rates estimated by BMSG
and OUMV for the two groups of taxa are also very similar in absolute value to the single
evolutionary rate estimated under the OUM model, which is the “real” evolutionary model
underlying the data. This means that, when fit to data simulated under an OU process with a
single evolutionary rate, these models actually provide similar parameter estimates that
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essentially represent the same covariance structure at the tips of the phylogeny, resulting in
similar goodness of fit to the data (Fig. 4). This effect is more prominent with increasing values
of the relative optima parameter (β2 / β1), which also augments the conflation of the BMSG and
OU models (Fig. 4).
Figure A5: Standard boxplots of the estimated evolutionary rate parameters (A) and
relative rate (B) under the BMSG, OUM and OUMV models when fitted to data
simulated under an OU process with two optima and a single evolutionary rate (OUM).
See Fig. 4 for the corresponding ΔAICc values and Material and Methods for details on
the simulating parameters used.
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