An Algebraic Approach to Evolutionary Accumulation Models

TL;DR

This paper introduces an algebraic method for modeling evolutionary feature accumulation, leveraging polynomial structures to improve parameter inference and compatibility with existing models.

Contribution

It presents a novel algebraic framework for evolutionary accumulation models that complements traditional optimization approaches.

Findings

Algebraic approach defines a semi-algebraic set of candidate parameters.

Method is compatible with existing statistical evolutionary models.

Provides additional algebraic insights into evolutionary accumulation processes.

Abstract

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.