Data from: Complex models of sequence evolution require accurate estimators as exemplified with the invariable site plus Gamma model

The invariable site plus Γ model is widely used to model rate heterogeneity among alignment sites in maximum likelihood and Bayesian phylogenetic analyses. The proof that the invariable site plus continuous Γ model is identifiable (model parameters can be inferred correctly given enough data) has increased the creditability of its application to phylogeny reconstruction. However, most phylogenetic software implement the invariable site plus discrete Γ model, whose identifiability is likely but unproven. How well the parameters of the invariable site plus discrete Γ model are estimated is still disputed. Especially the correlation of the fraction of invariable sites with the fractions of sites with a slow evolutionary rate is discussed as being problematic. We show that optimization heuristics as implemented in frequently used phylogenetic software cannot always reliably estimate the shape parameter, the proportion of invariable sites and the tree length. Here, we propose an improved optimization heuristic that accurately estimates the three parameters. While research efforts mainly focus on tree search methods, our results signify the equal importance of verifying and developing effective estimation methods for complex models of sequence evolution.不变位点加Γ模型（invariable site plus Γ model）被广泛应用于最大似然法与贝叶斯系统发育分析中，用于刻画序列比对位点间的进化速率异质性。不变位点加连续Γ模型（invariable site plus continuous Γ model）已被证明具备可识别性，即模型参数可在充足数据下被正确推断，这提升了其在系统发育重建中应用的可信度。然而，多数主流系统发育软件均实现了不变位点加离散Γ模型（invariable site plus discrete Γ model），但该模型的可识别性仅为合理推测，尚未得到严格证明。目前，关于不变位点加离散Γ模型的参数估计效果仍存在广泛争议，其中不变位点比例与低进化速率位点比例间的相关性被普遍认为存在问题。本研究表明，常用系统发育软件所搭载的优化启发式算法，无法始终可靠地估计形状参数、不变位点比例与树长三类核心参数。为此，本文提出一种改进的优化启发式算法，可精准估计上述三类参数。尽管当前系统发育领域的研究主要聚焦于树搜索方法，但本研究结果表明，验证与开发适用于复杂序列进化模型的有效参数估计算法，同样具备同等重要的研究价值。