Data from: Measuring rates of phenotypic evolution and the inseparability of tempo and mode

Rates of phenotypic evolution are central to many issues in paleontology, but traditional rate metrics such as darwins or haldanes are seldom used because of their strong dependence on interval length. In this paper, I argue that rates are usefully thought of as model parameters that relate magnitudes of evolutionary divergence to elapsed time. Starting with models of directional evolution, random walks, and stasis, I derive for each a reasonable rate metric. These metrics can be linked to existing approaches in evolutionary biology, and simulations show that they can be estimated accurately at any temporal resolution via maximum likelihood, but only when that metric's underlying model is true. The estimation of generational rates of a random walk under realistic paleontological conditions is compared with simulations to that of a prominent alternative approach, Gingerich's LRI (log-rate, log-interval) method. Generational rates are estimated poorly by LRI; they often reflect sampling error more than the actual pace of change. Further simulations show that under some realistic conditions, it is simply not possible to infer generational rates from coarsely sampled populations. These modeling results indicate a complex dependence between evolutionary mode and the measurement of evolutionary rates, and that there is unlikely to be a rate metric that works well for all traits and time scales. Compilations of paleontological and phylogenetic data indicate that all of the three rate metrics derived here show some relationship with interval length. Although there is no perfect rate metric, at present the most practical choices derive from the parameters of the stasis and random walk models. The latter, called the step variance, is particularly promising as a rate metric in paleontology and comparative biology.

表型进化速率是古生物学诸多核心议题的关键所在，但诸如达尔文单位（darwins）与霍尔丹单位（haldanes）这类传统速率指标却极少被采用，究其原因在于其对时间间隔长度存在极强的依赖性。本文主张，可将进化速率合理地视为将进化分歧幅度与流逝时间相关联的模型参数。本文从定向进化、随机游走以及停滞三种进化模型出发，分别推导得到了合理的速率指标。这些指标可与进化生物学领域现有方法建立关联，模拟实验表明，仅当指标所依托的进化模型成立时，方可通过最大似然法在任意时间分辨率下对其进行精准估算。本文将真实古生物条件下随机游走的世代速率估算结果，与模拟实验中采用的主流替代方法——吉恩格里奇LRI（对数速率-对数间隔，log-rate, log-interval）法——的估算结果进行了对比。LRI法对世代速率的估算效果欠佳，其结果往往更多反映的是抽样误差，而非实际的进化变化速率。进一步的模拟实验表明，在部分真实场景下，仅通过低分辨率抽样的种群根本无法推断世代进化速率。上述建模结果揭示，进化模式与进化速率的测算之间存在复杂的关联依赖关系，且并不存在能够适用于所有性状与时间尺度的通用速率指标。对古生物学与系统发育数据的汇编分析表明，本文推导得到的三类速率指标均与时间间隔长度存在一定关联。尽管不存在完美的速率指标，但当前最为实用的选择源自停滞模型与随机游走模型的参数。其中后者被称为步长方差（step variance），作为古生物学与比较生物学领域的速率指标极具应用前景。