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Table 1 Comparisons of different evolutionary model fits and parameters for the four phenotypic traits: PCa1, PCb1, body size, and HWI

From: Trophic niche shifts and phenotypic trait evolution are largely decoupled in Australasian parrots

Trait Model Loglik AICc \(\Delta\) AIC Parameter
PCa1 1.BM − 161.49 327.09 17.66  
  1.1.1 BMS nectar − 161.35 328.91 19.48  
  1.1.2 BMS diet − 156.56 325.88 16.45  
  1.2 delta − 159.31 324.83 15.40 \(\delta\) = 2.18
  1.3 kappa − 151.61 309.43 0 \(\kappa\)= 0.39
  2. OU − 158.97 324.15 14.72 \(\alpha\)= 0.026
  2.1.1 OU2 nectar − 158.96 326.28 16.85  
  2.1.2 OU5 diet − 157.75 330.53 21.10  
  3. FPK − 157.61 323.58 14.15  
  4. EB − 161.49 329.19 19.76  
  NIG* − 207.06 422.48   
  JN* − 215.06 438.48   
  JEM* − 147.95 303.99   λ = 0.012, α = 28.8
PCb1 1. BM − 223.62 451.35 24.09  
  1.1.1 BMS nectar − 220.77 447.75 20.49  
  1.2.1 BMS diet − 207.25 427.26 0  
  1.2 delta − 219.31 444.83 17.57 \(\delta\)= 2.99
  1.3 kappa − 218.56 443.33 16.07 \(\kappa\)= 0.47
  2. OU − 219.71 445.63 18.37 \(\alpha\)= 0.037
  2.1.1 OU2 nectar − 219.30 446.96 19.70  
  2.1.2 OU5 diet − 218.24 451.51 24.25  
  3. FPK − 213.83 436.02 8.76  
  4. EB − 223.62 453.45 26.19  
  NIG* − 207.06 422.48   
  JN* − 215.06 438.48   
  JEM* − 192.58 393.52   λ = 0.008, α = 100.0
Body size 1. BM 96.44 − 188.77 10.94  
  1.1.1 BMS nectar 97.33 − 188.45 11.26  
  1.1.2 BMS diet 100.94 − 189.12 10.59  
  1.2 delta 96.55 − 186.89 12.82 \(\delta\)= 1.18
  1.3 kappa 102.96 − 199.71 0 \(\kappa\)= 0.43
  2. OU 96.90 − 187.59 12.12 \(\alpha\)= 0.005
  2.1.1 OU2 nectar 97.11 − 185.86 13.85  
  2.1.2 OU5 diet 96.60 − 178.17 21.54  
  3. FPK 100.72 − 193.08 6.63  
  4. EB 96.44 − 186.67 13.04  
  NIG* 134.03 − 259.70   
  JN* 89.47 − 170.58   
  JEM* 101.71 − 195.06   λ = 0.004, α = 38.8
HWI 1.BM 198.43 − 392.88 6.29  
  1.1.1 BMS nectar 199.45 − 392.69 6.48  
  1.1.2 BMS diet 202.77 − 392.78 6.39  
  1.2 delta 199.46 − 392.71 6.46 \(\delta\) = 1.72
  1.3 kappa 202.69 − 399.17 0 \(\kappa\)= 0.60
  2. OU 199.69 − 393.17 6.00 \(\alpha\)= 0.017
  2.1.1 OU2 nectar 201.07 − 393.78 5.39  
  2.1.2 OU5 diet 204.19 − 393.35 5.82  
  3. FPK 201.88 − 395.40 3.77  
  4. EB 198.44 − 390.67 8.50  
  NIG* 195.20 − 382.04   
  JN* 198.01 − 387.66   
  JEM* 207.96 − 407.56   λ = 0.011, α = 26.8
  1. Bolded rows represent the best-fit model for each class
  2. We tested three main “classic” Gaussian models (Brownian Motion, BM; Ornstein–Uhlenbeck, OU; and Early-Burst, EB) and modifications of such models (BMS; OU2; OU5), Under these evolutionary models, the adaptive optimum of a lineage may wander gradually and freely (incremental change: BM), it may change gradually but remain stationary (incremental stationarity: OU), or it may change most rapidly following the initial diversification of a clade while decelerating over time (explosive change: EB). In addition, we tested a recently developed model (FPK), which assumes that characters evolve under both random diffusion and deterministic forces of any possible shape and strength. While in multi-OU model different peaks can only be discovered by certain lineages (which are inferred to be under the same regime), the FPK model does not impose such restriction. To test for pulsed evolution, three Lévy processes were fitted: a normally distributed jump process (JN) model, a variant of this model that implements an Expectation–Maximization approach (JEM), and a pure-normal inverse Gaussian process (NIG). Values are means from model fitting across 500 reconstructions of nectarivory/diet for models with multiple selective regimes (BMS nectar, BMS diet, OU2, and OU5). Mean Akaike information criterion (AICc) is the averaged AICc, and \(\Delta\) AICc is the model’s mean AICc minus the minimum AICc between models. Bolded rows represent the best-fit model for each class (Lévy and non-Lévy processes) as indicated by the lowest AICc score. The phylogenetic parameters kappa (\(\kappa\)) and delta (\(\delta\)) and its associated models were also assessed in order to determine different processes (gradual vs. punctuated evolution; early vs. late evolution). κ = 1 indicates gradual evolution and κ = 0 indicates punctuated evolution. δ < 1 indicate temporally early trait evolution or ‘early-burst’, indicative of adaptive radiation whereas δ > 1 indicate temporally latter trait evolution, indicative of species‐specific adaptation (see main text for more details). Asterisks indicate jump (pulsed) models