DOI: 10.5061/dryad.tg37f
title: Data from: How reliably can we infer diversity-dependent diversification from phylogenies?

description: Slowdowns in lineage accumulation in phylogenies suggest that speciation
 rates decline as diversity increases. Likelihood methods have been
 developed to detect such diversity dependence. However, a thorough test of
 whether such approaches correctly infer diversity dependence is lacking.
 Here, we simulate phylogenetic branching under linear negative
 diversity-dependent and diversity-independent models and estimate from the
 simulated phylogenies the maximum-likelihood parameters for three
 different conditionings – on survival of the birth–death process given the
 crown age, on tree size (N) and on tree size given the crown age. We
 report the accuracy of recovering the simulation parameters and the
 reliability of the model selection based on the χ2 likelihood ratio test.
 Parameter estimate accuracy: Conditioning on survival given the crown age
 yields a severe bias of the carrying capacity K towards N and an upward
 bias of the speciation rate, particularly in clades where
 diversity-dependent feedbacks are still weak (N « K). Conditioning on N
 yields an overestimate of K and an underestimate of speciation rate,
 particularly when saturation has been reached. Dual conditioning yields
 relatively unbiased parameter estimates on average, but the deviation from
 the true value for any single estimate may be large. Model selection
 reliability: The frequency of incorrectly rejecting a
 diversity-independent model when the simulation was diversity-independent
 (type I error) differs substantially from the significance level α used in
 the likelihood ratio test, rendering the likelihood ratio test
 inappropriate. The frequency of correctly rejecting the
 diversity-independent model when the simulation was diversity-dependent
 (power) is larger when the clade is closer to equilibrium and for
 conditioning on crown age. We conclude that conditioning on crown age has
 the best statistical properties overall, but caution that parameter
 estimates may be biased. To assess parameter uncertainty in future studies
 of diversity dependence on real data, we recommend parametric
 bootstrapping, examination of the likelihood surface and comparison of
 estimates across the types of conditioning. To assess model selection
 reliability, we discourage the use of the χ2 likelihood ratio test or AIC
 (which are equivalent in this case), but recommend a likelihood ratio test
 based on parametric bootstrap. We illustrate this method for the
 diversification of Dendroica warblers.
description: Simulations under CR and
 DD models - part 2Second batch of .RData
 files of the tree simulations under the CR and DD
 models.biastestCRDD_sims2.zipSimulations under CR and DD models - part 1First of two batches of .RData files of the trees simulation under the CR and DD models and the R-script that generated both batches.biastestCRDD_sims1.zipMaximum likelihood results under CR modelRData files with maximum likelihoods and corresponding parameter estimates under the constant-rate (CR) model, and the R-script that generated them.biastestCR_LL.zipMaximum likelihood results under DD model - 1RData files with maximum likelihoods and corresponding parameter estimates under the diversity-dependent model, and the R-script that generated them. The starting values of the optimization are the simulation values.biastestDD_LL1.zipMaximum likelihood results under DD model - 2RData files with maximum likelihoods and corresponding parameter estimates under the diversity-dependent model, and the R-script that generated them. The starting values of the optimization are the results from the CR models fits with a large but finite carrying capacity..biastestDD_LL2.zipR-script to make plots from resultsR-script to make plots from simulation resultsplot_params.RBootstrap likelihood ratio test results of the Dendroica case studyRData file of the bootstrap likelihood ratio test results of the Dendroica case study.DendroicaLRtestresults.RData