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Table 3 Comparison of models of (log) bill size with increasing complexity of random effects structure, to test for effects of phylogeny and of variance between species in the slope of their response to humidity; see Methods for details of models

From: Spatial variation in avian bill size is associated with humidity in summer among Australian passerines

Model Variance components LogL χ 2 d.f. p-value
1 Vregion + Vyear + Vspecies + Vres 5163.20  
2 Vregion + Vyear + Vsp.non-phylo + Vsp.phylo + Vres 5179.149 19.83 1 <0.001
3 V region + V year + V sp.non-phylo + V sp.phylo + (V sp.non-phylo x humidity) + V res 5183.95 23.36 2 <0.001
4 Vregion + Vyear + Vsp.non-phylo + Vsp.phylo + (Vsp.non-phylo x humidity) + (Vsp.phylo x humidity) + Vres 5183.95 0.00 2 1.00
  1. All models included fixed effects of wing length (to correct for body size), sex, season, year of capture, humidity, Tmax, and the interaction between humidity and Tmax. LogL gives the log-likelihood of each model; χ 2 is the likelihood ratio test for comparison with the previous model, with corresponding degrees of freedom (d.f.): models 3 and 4 each required an additional 2 d.f. because they estimated one additional parameter for variance in slopes and and one for covariance between intercept in slope (see Methods). The best model (Model 3) is shown in bold. Definitions of terms: V region IBRA region, V year year, V sp.non-phylo variance between species not associated with phylogeny, V sp.phylo variance between species associated with the phylogeny, V sp.non-phylo x humidity variance in humidity-slope not associated with phylogeny, V sp.phylo x humidity variance in humidity-slope associated with phylogeny, V res residual variance