We present an algebraic approach to evolutionary accumulation modelling (EvAM). EvAM is concerned with learning and predicting the order in which evolutionary features accumulate over time. Our approach is complementary to the more common optimisation-based inference methods used in this field. Namely, we first use the natural underlying polynomial structure of the evolutionary process to define a semi-algebraic set of candidate parameters consistent with a given data set before maximising the likelihood function. We consider explicit examples and show that this approach is compatible with the solutions given by various statistical evolutionary accumulation models. Furthermore, we discuss the additional information of our algebraic model relative to these models.

翻译：本文提出了一种用于进化累积建模（EvAM）的代数方法。EvAM关注于学习和预测进化特征随时间累积的顺序。我们的方法是对该领域中更常见的基于优化的推断方法的补充。具体而言，我们首先利用进化过程固有的多项式结构，定义一个与给定数据集一致的候选参数半代数集，然后最大化似然函数。我们考虑了具体示例，并证明该方法与多种统计进化累积模型给出的解是兼容的。此外，我们讨论了代数模型相对于这些模型的附加信息。