Bayesian model selection with BAMM: effects of the model prior on the inferred number of diversification shifts

1. Understanding variation in rates of speciation and extinction -- both among lineages and through time -- is critical to the testing of many hypotheses about macroevolutionary processes. BAMM is a flexible Bayesian framework for inferring the number and location of shifts in macroevolutionary rate across phylogenetic trees and has been widely used in empirical studies. BAMM requires that researchers specify a prior probability distribution on the number of diversification rate shifts before conducting an analysis. The consequences of this "model prior" for inference are poorly known but could potentially influence both the probability of accepting models that are more (high error rate) or less (low power) complex than the generating model.
2. The hierarchical Poisson process prior in BAMM reduces to a simple geometric distribution on number of rate shifts and we use this property to increase the efficiency of model selection with Bayes factors. Using BAMM v2.5, we analyzed phylogenies simulated with and without diversification heterogeneity across a broad range of prior parameterizations. We also assessed the impact of the model prior on MCMC convergence times and on diversification rate estimates.
3. For all simulation scenarios, model evidence (Bayes factor support) for the number of shifts is not sensitive to the choice of model prior over the wide range examined here. The best-supported model found using BAMM rarely includes spurious shifts (<2% of all runs) when diversification models are selected using Bayes factors. BAMM was reliably able to infer the true number of diversification rate shifts across prior expectations that varied by three orders of magnitude. However, we find a strong effect of model prior on MCMC convergence properties: a flatter prior distribution (larger expected number of shifts) can dramatically increase the efficiency of the MCMC simulation.
4. Our results support the use of a liberal model prior in BAMM, as it reduces computation time without distorting the evidence for rate heterogeneity.

1. 解析物种形成与灭绝速率的变异——无论是在不同支系间还是随时间推移的变异——对于检验诸多宏观进化过程相关假说至关重要。BAMM是一款灵活的贝叶斯框架，用于推断系统发育树（phylogenetic trees）跨宏观进化速率转变的数量与位置，已在实证研究中得到广泛应用。在开展分析前，BAMM要求研究者先指定多样化速率转变数量的先验概率分布。目前学界对该“模型先验”在推断过程中的影响尚不明晰，但它可能同时影响接受比生成模型更复杂（误差率更高）或更简单（统计效力更低）模型的概率。
2. BAMM中采用的分层泊松过程先验（hierarchical Poisson process prior）可简化为关于速率转变数量的简单几何分布，我们利用这一特性提升了基于贝叶斯因子（Bayes factors）的模型选择效率。本研究使用BAMM v2.5版本，针对多样化异质性存在与缺失两种模拟场景下的系统发育树，在宽泛的先验参数配置范围内开展了分析。同时我们还评估了模型先验对马尔可夫链蒙特卡洛（Markov Chain Monte Carlo, MCMC）收敛时长以及多样化速率估计结果的影响。
3. 在所有模拟场景中，本研究所考察的宽泛先验范围内，模型证据（贝叶斯因子支持度）与转变数量的相关性不受模型先验选择的影响。当通过贝叶斯因子筛选多样化模型时，BAMM所选出的最优支持模型极少包含虚假转变（仅占全部运行结果的<2%）。在先验期望跨越三个数量级的前提下，BAMM仍能可靠地推断出多样化速率转变的真实数量。不过我们发现，模型先验对MCMC收敛特性存在显著影响：更平缓的先验分布（对应更高的预期转变数量）可显著提升MCMC模拟的效率。
4. 本研究结果支持在BAMM中使用宽松的模型先验，因为它可在不扭曲速率异质性相关证据的前提下缩短计算时长。