<p>Supplementary information to “Theory predicts a rapid transition from niche- structured to neutral biodiversity patterns across a speciation-rate gradient”</p><p>Here we present the results of sensitivity analyses on the parameters m and K (Fig. S1-S16). The results for m = 0.1 and K = 16 were presented in the main text (Fig. 1-2). We repeated the simulations described in the main text for all combinations of the immigration parameter m = 0.01, 0.1, 0.5 and the number of niches K = 4, 16, 64.</p><p>Figure S1. Species richness (S) in a local community at equilibrium as a function of 12 speciation rate for the neutral and hybrid models (m = 0.01, J = 20,000, JM = 10 , K = 4). Dashed lines show 95% confidence intervals. The dotted line corresponds to S = K = 4, which is the species richness in a system completed dominated by niche structure. Figure S2. Posterior probability that an observed species abundance distribution from the hybrid model comes from a neutral model, given an uninformative dichotomous prior that specifies equal probabilities for the neutral model and the pure (broken-stick) niche model (P(neutral) = P(broken stick) = 0.5), for different values of the speciation rate. Other 12 parameters are m = 0.01, J = 20,000, JM = 10 , K = 4. See text for model details. Dashed lines show 95% confidence intervals (estimated from 20 simulations). Figure S3. Species richness (S) in a local community at equilibrium as a function of 12 speciation rate for the neutral and hybrid models (m = 0.1, J = 20,000, JM = 10 , K = 4). Dashed lines show 95% confidence intervals. The dotted line corresponds to S = K = 4, which is the species richness in a system completed dominated by niche structure. Figure S4. Posterior probability that an observed species abundance distribution from the hybrid model comes from a neutral model, given an uninformative dichotomous prior that specifies equal probabilities for the neutral model and the pure (broken-stick) niche model (P(neutral) = P(broken stick) = 0.5), for different values of the speciation rate. Other 12 parameters are m = 0.1, J = 20,000, JM = 10 , K = 4. See text for model details. Dashed lines show 95% confidence intervals (estimated from 20 simulations). Figure S5. Species richness (S) in a local community at equilibrium as a function of 12 speciation rate for the neutral and hybrid models (m = 0.5, J = 20,000, JM = 10 , K = 4). Dashed lines show 95% confidence intervals. The dotted line corresponds to S = K = 4, which is the species richness in a system completed dominated by niche structure. Figure S6. Posterior probability that an observed species abundance distribution from the hybrid model comes from a neutral model, given an uninformative dichotomous prior that specifies equal probabilities for the neutral model and the pure (broken-stick) niche model (P(neutral) = P(broken stick) = 0.5), for different values of the speciation rate. Other 12 parameters are m = 0.5, J = 20,000, JM = 10 , K = 4. See text for model details. Dashed lines show 95% confidence intervals (estimated from 20 simulations). Figure S7. Species richness (S) in a local community at equilibrium as a function of 12 speciation rate for the neutral and hybrid models (m = 0.01, J = 20,000, JM = 10 , K = 16). Dashed lines show 95% confidence intervals. The dotted line corresponds to S = K = 16, which is the species richness in a system completed dominated by niche structure. Figure S8. Posterior probability that an observed species abundance distribution from the hybrid model comes from a neutral model, given an uninformative dichotomous prior that specifies equal probabilities for the neutral model and the pure (broken-stick) niche model (P(neutral) = P(broken stick) = 0.5), for different values of the speciation rate. Other 12 parameters are m = 0.01, J = 20,000, JM = 10 , K = 16. See text for model details. Dashed lines show 95% confidence intervals (estimated from 20 simulations). Figure S9. Species richness (S) in a local community at equilibrium as a function of 12 speciation rate for the neutral and hybrid models (m = 0.5, J = 20,000, JM = 10 , K = 16). Dashed lines show 95% confidence intervals. The dotted line corresponds to S = K = 16, which is the species richness in a system completed dominated by niche structure. Figure S10. Posterior probability that an observed species abundance distribution from the hybrid model comes from a neutral model, given an uninformative dichotomous prior that specifies equal probabilities for the neutral model and the pure (broken-stick) niche model (P(neutral) = P(broken stick) = 0.5), for different values of the speciation rate. Other 12 parameters are m = 0.5, J = 20,000, JM = 10 , K = 16. See text for model details. Dashed lines show 95% confidence intervals (estimated from 20 simulations). Figure S11. Species richness (S) in a local community at equilibrium as a function of 12 speciation rate for the neutral and hybrid models (m = 0.01, J = 20,000, JM = 10 , K = 64). Dashed lines show 95% confidence intervals. The dotted line corresponds to S = K = 64, which is the species richness in a system completed dominated by niche structure. Figure S12. Posterior probability that an observed species abundance distribution from the hybrid model comes from a neutral model, given an uninformative dichotomous prior that specifies equal probabilities for the neutral model and the pure (broken-stick) niche model (P(neutral) = P(broken stick) = 0.5), for different values of the speciation rate. Other 12 parameters are m = 0.01, J = 20,000, JM = 10 , K = 64. See text for model details. Dashed lines show 95% confidence intervals (estimated from 20 simulations). Figure S13. Species richness (S) in a local community at equilibrium as a function of 12 speciation rate for the neutral and hybrid models (m = 0.1, J = 20,000, JM = 10 , K = 64). Dashed lines show 95% confidence intervals. The dotted line corresponds to S = K = 64, which is the species richness in a system completed dominated by niche structure. Figure S14. Posterior probability that an observed species abundance distribution from the hybrid model comes from a neutral model, given an uninformative dichotomous prior that specifies equal probabilities for the neutral model and the pure (broken-stick) niche model (P(neutral) = P(broken stick) = 0.5), for different values of the speciation rate. Other 12 parameters are m = 0.1, J = 20,000, JM = 10 , K = 64. See text for model details. Dashed lines show 95% confidence intervals (estimated from 20 simulations). Figure S15. Species richness (S) in a local community at equilibrium as a function of 12 speciation rate for the neutral and hybrid models (m = 0.5, J = 20,000, JM = 10 , K = 64). Dashed lines show 95% confidence intervals. The dotted line corresponds to S = K = 64, which is the species richness in a system completed dominated by niche structure. Figure S16. Posterior probability that an observed species abundance distribution from the hybrid model comes from a neutral model, given an uninformative dichotomous prior that specifies equal probabilities for the neutral model and the pure (broken-stick) niche model (P(neutral) = P(broken stick) = 0.5), for different values of the speciation rate. Other 12 parameters are m = 0.5, J = 20,000, JM = 10 , K = 64. See text for model details. Dashed lines show 95% confidence intervals (estimated from 20 simulations).</p>