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Table 5 Models implemented using a maximum-likelihood inference to test evolutionary models for changes in asymmetry

From: Wonky whales: the evolution of cranial asymmetry in cetaceans

Model name State Model type Description
‘OU-ancestral’ Ancestral state OU A classic Ornstein-Ulenbeck (OU) model
‘BM-ancestral’ Ancestral state BM A classic Brownian motion (BM) model
‘BMtr-ancestral’ Ancestral state BMtr A classic BM model with an independent trend
‘BMsm-ancestral’ Ancestral state BMsm A classic BM model with no selective regime and which estimates separate phylogenetic means
‘BMM-ancestral’, ‘BMM-regime’, ‘BMM-regime-split’, ‘BMM-echo’, BMM-echo-freq’ Ancestral state, regime, regime-split, echolocation, echolocation-frequency BMM A BM model with a selective regime
‘BMMtr-ancestral’, ‘BMMtr-regime’, ‘BMMtr-regime-split’, ‘BMMtr-echo’, BMMtr-echo-freq’ Ancestral state, regime, regime-split, echolocation, echolocation-frequency BMMtr A BM model with a selective regime and an independent trend
‘BMMsm-ancestral’, ‘BMMsm-regime’, ‘BMMsm-regime-split’, ‘BMMsm-echo’, BMMsm-echo-freq’ Ancestral state, regime, regime-split, echolocation, echolocation-frequency BMMsm A BM model with a selective regime which estimates separate phylogenetic means
‘OUM-ancestral’, ‘OUM-regime’, ‘OUM-regime-split’, ‘OUM-echo’, ‘OUM-echo-freq’ Ancestral state, regime, regime-split, echolocation, echolocation-frequency OUM An OU model with a selective regime
  1. Models test whether evolutionary changes in asymmetry (the studied trait) are associated with the states of another discrete trait. The model name is a combination of the model state and the model type and is used throughout the study for consistency. The state describes the model scenario. The model types are variations of an Ornstein-Uhlenbeck (OU) model of continuous trait evolution and a Brownian motion (BM) model of continuous trait evolution (see description). All models were run using an ‘equal-rates’ (ER) likelihood model (Additional file 1: Table S12—likelihood model results (AIC) for each potential scenario for asymmetry in the cetacean cranium). For details on the model assumptions, see Table 4—models testing whether changes in cetacean cranial asymmetry are associated with other discrete traits
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