Fig. 4: The links between cooperative breeding and female song in phylogenetic path analyses are robust to correcting for data availability biases.

a, Directed acyclic graph showing conditional-averaged path coefficients from phylogenetic path analysis of the relationships between female song presence, cooperative breeding, strength of territoriality and body mass (log-scaled and normalized). The arrow thickness indicates the magnitude of path coefficients, with all paths shown representing positive relationships. Only the four models considered statistically equivalent to the best model (ΔCICc < 2) were averaged. b, Forest plot showing the mean and 95% CI for the cooperative breeding → female song path coefficient across 500 iterations for each bias correction type, compared to the value from the full dataset (dashed line). c, Forest plot showing the mean and 95% CI for the female song → cooperative breeding path coefficient across 500 iterations for each bias correction type, compared to the value from the full dataset. d, Model consistency across bias corrections. Heatmap shows the proportion of iterations in which each phylogenetic path model was supported (had a ΔCICc < 2) across 500 iterations for each bias correction type. Cells for models that were found to be the best-supported model in at least 1% of downsampled simulation iterations are labeled with the proportion of iterations in which the model was the best-supported. The row underneath the heatmap contains the ΔCICc values for each model in the phylopath analysis performed using the full dataset, with the ΔCICc values of the four models that were statistically equivalent (ΔCICc < 2) in the full dataset in italics. Bottom, Dots indicate the presence or absence of each rate in the model. The models shown are all those that were in the top 20 models (of 47 models in total; Supplementary Fig. 1) according to the number of iterations with a ΔCICc < 2 for any of the bias correction types.