paper.md

title	tags	authors	affiliations	date	bibliography
FEArS: a python package for simulating evolution on arbitrary fitness seascapes	Python evolution fitness landscape fitness seascape	name orcid affiliation Eshan S. King 0000-0002-0345-3780 1 name orcid affiliation Davis T. Weaver 0000-0003-3086-497X 1 name corresponding affiliation orcid Jacob G. Scott true 2 0000-0003-2971-7673	name index Systems Biology and Bioinformatics Program, Case Western Reserve University School of Medicine, USA 1 name index Translational Hematology Oncology Research, Cleveland Clinic Lerner Research Institute, USA 2	03 November 2022	paper.bib

Summary

The evolution of drug resistance across kingdoms, including in cancer and infectious disease, is governed by the same fundamental laws. Modeling evolution with genotype-specific dose response curves, collectively forming a 'fitness seascape', enables simulations that include realistic pharmacokinetic constraints, more closely resembling the environmental conditions within a patient [@Merrell:1994;@Mustonen:2009;@King:2022;@Agarwala:2019]. FEArS (Fast Evolution on Arbitrary Seascapes) is a python package that enables simulating evolution with fitness seascapes. FEArS can simulate a wide variety of experimental conditions with many arbitrary biological parameters. FEArS remains computationally efficient despite being an agent-based model, even for very large population sizes. FEArS also contains powerful and flexible utilities for data analysis, plotting, and experimental fitness seascape estimation.

The two core classes for simulating populations and running experiments are Population and Experiment, respectively. The Population class includes all biological parameters relevant for the evolving population under study in addition to methods for simulating evolution. The Experiment class includes parameters for running an experiment with multiple populations, including varying pharmacokinetic parameters, number of simulations, and results saving methods.

A hybrid agent-based algorithm

FEArS achieves fast runtimes while simulating large populations of evolving agents by employing what we term a 'hybrid agent-based' approach. When possible, populations are stored as vectors of cell numbers $\hat n$, where each position in the vector corresponds to a genotype and the number at that position gives the number of cells of that type in the population. Then, stochastic events such as cell division and cell death are simply drawn from poission distributions:

\begin{equation}\label{eq:cell_death} \hat n_{d} \sim poisson(r_{d}*\hat n), \end{equation}

where $\hat n_{d}$ refers to the vector of dead cells of each type, for example. However, in the mutation step, FEArS switches to a strictly agent-based process. Here, every mutating agent is enumerated in a vector, where each entry in the vector represents the genotype of the agent. Then, mutating agents are randomly allocated to adjacent genotypes (\autoref{fig:flowchart}). Since the number of mutating cells is much smaller than the total population size (i.e., with a mutation rate on the order of $10^{-6}$ to $10^{-9}$ per base pair), this agent-based step does not compromise computational efficiency.

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By modeling realistic population sizes, FEArS enables investigation of population extinction and stochastic evolutionary rescue.

A suite of useful utilies

In addition to the core population and experiment classes, FEArS includes utilities to assist with computational experiments, empirical data analysis, and results visualization.

• plotter: a broad and flexible plotting utility, including functions for plotting evolutionary dynamics timetraces, Kaplan-Meier curves, and fitness landscapes.

• pharm: functions for pharmacokinetics, including generating arbitrary pharmacokinetic curves and simulating patient nonadherence.

• fitness: functions for pharmacodynamics, including computing fitness landscapes and fitness seascapes.

• AutoRate: classes and methods for estimating fitness seascapes from experimental data.

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Statement of need

FEArS enables stochastic simulations of clonally evolving systems subject to arbitrary drug concentrations over time. By using an agent-based algorithm, we are able to model mutation and selection, with evolution arising as an emergent phenomena. Furthermore, by nature of being an agent-based algorithm and allowing for arbitrary population sizes, FEArS can model population extinction. Arbitrary population sizes also allows us to simulate how a disease population within a patient may respond to therapy. In addition, FEArS models genotype-sprecific dose-response curves, allowing for more fine-grained prediction of evolution. Modeling genotpye-specific dose-response curves will likely be critical for the translation of adaptive drug therapy [@Iram:2021]

Other common evolutionary simulation approaches are Moran processes [@Moran:1958] and Wright-Fisher models [@Wright:1931; @Fisher:1930]. However, both approaches have limitations that preclude modeling evolutionary dynamics in a wide variety of settings, including with varying population size and varying drug concentration. Other software for simulating evolution with fitness landcsapes utilize Markov chains, which achieve extremely high computational efficiency but cannot model arbitrary population sizes and time-varying selection [@Maltas:2021;@Nichol:2015;Nichol:2019]. In addition, there exists a suite of software packages for simulating tumor evolution [@McDonald:2017;@Irurzun-Arana:2020;@Roney:2020;@Angaroni:2022]. However, these packages either do not model drug pharmacokinetics and pharmacodynamics, do not model genotype-specific dose-response curves, or are simply more suited for studying spatial tumor evolution (in contrast to well-mixed pathogen populations that FEArS is suited for). To our knowledge, there is no open-source software that permits stochastic evolutionary simulations with empirical genotype-specific dose-response curves and arbitrary drug pharmacokinetics. To date, FEArS has been used extensively in two manuscripts, @King:2022 and @King:2023.

References