Supplementary Figure: Probability (P-value) curves for reproductive strategy factor in PGLS models from Table 1 with varying degrees of freedom

Probability (P-value) curves for reproductive strategy factor in PGLS models from Table 1 with varying degrees of freedom. As the true phylogeny is unknowable, all statistical estimates are best guesses. Because there are five clades with the benthic guarding reproductive strategy, the most conservative choice for degrees of freedom would be d.f. = 4, shown as a dotted vertical line; d.f. = 4 is certain to be an underestimate of the true degrees of freedom as benthic guarding is common among freshwater fishes suggesting many character state changes along the full acanthomorph tree. An upper bound to degrees of freedom might be set by adjusting for polytomies (following Purvis and Garland 1993; Garland and Díaz-Uriarte 1999) as shown as vertical dotted lines. Finally the phylogenetic degrees of freedom determined by GEE is shown as a solid vertical line. The true degrees of freedom for our PGLS analyses are likely to fall somewhere within this bounded range for degrees of freedom.