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Detecting trait-dependent diversification under diversification slowdowns

Antonin Machac

Simulations and analyses, as described in the main text, were conducted under two rates of trait evolution: σ2 = 0.2 (conservative trait) and σ2 = 2.2 (labile trait). Since the labile trait causes larger fluctuations in the speciation rate, its effects on diversification should be easier to detect. Effects of the conservative trait, in contrast, should be less pronounced and difficult to uncover. However, both rates of trait evolution yielded similar outcomes. Therefore, results for the labile trait (σ2= 2.2) are presented in the main text while results for the conservative trait (σ2=0.2) are presented here. In sum,the results suggest that CR estimators are sensitive to trait-driven shifts in diversification rate even under diversification slowdowns.

Table S1.Rates of Type I error calculated for CR estimators. Results of these simulations, where diversification was controlled by the conservative trait (σ2 =0.2), are highly consistent with results presented in the main text. Rates of Type I error are below or equal to the commonly used5 % threshold and do not increase even under decelerating diversification.

Strength of diversity / γ parameter / Type I error
dependence
γ0 / 0.000 / 0.050
γ1 / -0.001 / 0.048
γ2 / -0.002 / 0.047
γ3 / -0.004 / 0.044
γ4 / -0.008 / 0.038
γ5 / -0.020 / 0.050

Table S2. Comparison of CR estimators with QuaSSE.Rates of Type I and Type II error were calculated for both CR estimators and QuaSSE under constant diversification (γ0) and diversification slowdowns of increasing strengths (γ1 - γ5).These results for the conservative trait are highly consistent with the results for the labile trait presented in the main text.

Strength of diversity / γ parameter / Type I error / Type II error
dependence / CR estimators / QuaSSE / CR estimators / QuaSSE
γ0 / 0 / 0.05 / 0.01 / 0.60 / 0.04
γ1 / -0.001 / 0.04 / 0.02 / 0.70 / 0.02
γ2 / -0.002 / 0.04 / 0.03 / 0.77 / 0.11
γ3 / -0.004 / 0.03 / 0.15 / 0.70 / 0.31
γ4 / -0.008 / 0.05 / 0.14 / 0.80 / 0.54
γ5 / -0.020 / 0.04 / 0.15 / 0.79 / 0.59

Table S3.Kruskal-Wallis test did not detect any significant differences between the distributions of gamma, beta, and skewness across simulated and empirical phylogenies (see Fig.S3), suggesting that the simulated phylogenies may have similar architecture as empirical phylogenies.

Tree statistic / KW Chi-squared / df / p
gamma / 0.358 / 1 / 0.549
beta / 0.138 / 1 / 0.711
kurtosis / 8.581 / 1 / 0.030
skewness / 2.926 / 1 / 0.087

Figure S1.The detected correlations between inferred diversification rates and mean trait values. Under all the strengths of diversity dependence (γ0=0, γ1=-0.001, γ2=-0.002, γ3=-0.004, γ4=-0.008, γ5=-0.02), CR estimators successfully uncovered underlying correlations. These results, based on simulations where diversification was controlled by a conservatively evolving trait, are consistent with conclusions presented in the main text.

Figure S2.Type II error associated with CR inference tends to decline with the number of clades analyzed. Similar trends emerge under all the examined strengths of diversification slowdowns (γ0=0, γ1=-0.001, γ2=-0.002, γ3=-0.004, γ4=-0.008, γ5=-0.02). When the number of clades that enter CR analysis is small (< 20 clades), statistical power to detect present trait-diversification dependence may be limited. Under such circumstances, CR estimators can detect only strong relationships, thus yielding conservative tests.


Figure S3.Topologies and branch-length distributions of the herein analyzed phylogenies were described in terms of the gamma statistic, the beta parameter, skewness, and kurtosis.Distributions of these metrics across simulated and real phylogenies are highly congruent. For a more quantitative comparison of these distributions, see Table S3.