图1 贝叶斯法时间树构建过程示意图(改自: Bromham et al, 2018)。进化模型的参数设置是贝叶斯法系统发育树构建的关键步骤, 由替换模型和树模型组成。替换模型包括了碱基替换模型(包括碱基转换速率rij和碱基频率πi参数)、速率的位点(sites)异质型(如Γ分布)以及不变位点的比例p(inv)。树模型可以解构为结构与支长两个组份。结构由树先验决定, 图中使用的是生灭过程模型, 包含物种生成率(λ)、物种灭绝率(μt)和取样频率(ρ)三个参数。在“两步法”中, 结构还可以来自于树文件的输入。支长由分支时长与速率分布共同决定。分支时长一方面受树先验的影响, 另一方面与节点年龄标记密切相关; 速率分布即分子钟模型, 决定了进化速率在不同支上的分布格局。数据集与进化模型共同计算得到各参数的后验及时间树。

Fig. 1 Schematic diagram of Bayesian time tree construction (modified from: Bromham et al, 2018). The parameter setting of evolutionary models is the key step of constructing phylogenetic tree based on Bayesian method, which is composed of substitution model and tree model. The substitution model includes base substitution model (including base conversion rate rij and base frequency πi as parameters), site heterogeneity of rate (such as Γ distribution) and proportion of invariant sites p(inv). The tree model can be decomposed into two components: structure and branch lengths. The structure is determined by tree priors (in this case the birth and death process model), which includes three parameters: species generation rate (λ), species extinction rate (μt) and sampling frequency (ρ). In the “two-step” method, the structure can also come from the input of the tree file. The branch length is determined by the branch duration and the rate distribution across branches. The branch duration is influenced by tree priors and node age calibration. The rate distribution is recognized as clock models, which determine the distribution pattern of evolution rate on different branches. The data set is applied to the evolutionary model to generate posteriors of each parameter and the time tree.

图2 不同的分子钟模型示意图(改自: Ho & Duchêne, 2014)。图中的6个时间树具有相同的结构, 但由于分子钟模型选择的不同, 支长有很大差异。(a)未添加分子钟模型的时间树, 比例尺显示了1个时间单位。(b)严格分子钟模型, 所有支的速率相等。(c)局部多速率分子钟, 允许一定量的速率存在, 并根据拓扑的聚类情况设置速率, 同一类群具有相同或相似的速率。(d)离散多速率分子钟, 允许一定量的速率存在, 不考虑拓扑聚类情况的模型。(e)自相关松弛分子钟, 允许最多等于支数的速率存在, 且邻近支的速率相关。(f)非自相关松弛分子钟, 没有任何对速率的数量、分布格局的限制, 是最宽松自由的模型设置。

Fig. 2 Schematic diagram of different molecular clock models (modified from Ho & Duchêne, 2014). The six time trees in this figure have the same structure, but the branch length varies greatly due to different selection of molecular clock models. (a) The time tree without applying molecular clock model. The scale bar indicates one time unit. (b) In strict molecular clock model, all branches have the same rate. (c) Local multi-rate molecular clock allows a certain amount of rate and sets the rate according to the clustering situation of topology. The related branches have the same or similar rate. (d) Discrete multi-rate molecular clock, which also allows a certain amount of rate, does not consider the topological clustering. (e) The autocorrelated relaxed molecular clock allows the existence of a rate at most equal to the number of branches, and the rate dependence of adjacent branches. (f) The uncorrelated relaxed molecular clock, without any restrictions on the number and distribution pattern of rates, is the most relaxed and free model setting.

图3 系统发育树中部分术语示意图。图中冠节点的年龄代表了类群A现存所有物种最近共同祖先的节点, 而干节点代表了该类群最近共同祖先与其最近缘类群共祖的节点。以衍征法为例, 图中的化石A与类群A现存物种存在共同衍征, 因此可以作为类群A干节点的最小年龄限制; 而要为类群A的冠节点添加年龄限制, 需要获得与类群A的亚类群具有共同衍征的化石记录, 如图中的物种Z、W和化石B所表示的关系。系统发育法同理。

Fig. 3 Schematic diagram of some terms in phylogenetic tree. The age of the crown node in the figure represents the node of the nearest common ancestor of all species in group A, while the stem node represents the node of the nearest common ancestor of the group A and its nearest related group. Taking the apomorphy-based method as an example, fossil A in the figure has synapomorphies with the extant species of group A, so it can be used as the minimum age constraint for the stem node of group A. To apply age constraint to the crown node of group A, it is necessary to obtain fossil records sharing synapomorphies with subgroups of group A, as indicated by the relationship of species Z, W and fossil B in the figure. The same is true of phylogenetic method.

图4 化石年龄不确定性的3种情形。(a)“年轻但可靠”和“古老但有风险”的两种化石在化石年龄和可靠性两个维度上的分布, 其他大多数化石分布于两虚线围成的区域中。(b)某个类群已知最古老化石的年龄随着古生物学发掘过程不断扩展补充、逐步接近类群真实分化时间的趋势。(c)随着化石定年技术的发展, 化石年龄的精确度不断提升。

Fig. 4 Three cases of fossil age uncertainty. (a) The present of “young but safe” and “old but risky” fossils in two dimensions: age of fossils and reliability. Most of the other fossils are distributed in the area surrounded by the two dotted lines. (b) The age of the oldest known fossil of a certain group tends to be close to the real divergence time of the group as the paleobiological excavation continues to expand. (c) With the development of fossil dating technology, the accuracy of fossil age has been improved.

图5 节点年龄的概率分布。在不同节点设置最大或最小年龄限制, 可以采用不同的概率分布。其中(a)图表示系统发育树上设置最小和最大年龄限制的两个节点, (b)-(f)强调均匀、正态、伽马、对数正态和指数分布中的最小年龄限制, 而(g)和(h)则分别表示了均匀分布中的严格和宽松最大年龄限制(虚线及虚线框)。另外, (c)-(f)中虚线框强调的部分等同于宽松最大年龄限制。图中的soft maximum/minimum constraint又称软边界(soft bound)。

Fig. 5 Probability distribution of node age. The maximum or minimum age constraint can be set on different nodes, and different probability distribution can be adopted. Where (a) shows two nodes with minimum and maximum age constraint, respectively, in phylogenetic tree; (b)-(f) emphasize the minimum age constraints in uniform, normal, gamma, lognormal and exponential distribution, while (g) and (h) represent strict and relaxed maximum age constraints on uniform distribution, respectively. In addition, the part highlighted by the dotted box in (c)-(f) is equivalent to the relaxed maximum age constraint. The soft maximum/minimum constraint in the figure is also called soft bound.