AUTHOR=Kurpas Monika K. , Kimmel Marek 

TITLE=Modes of Selection in Tumors as Reflected by Two Mathematical Models and Site Frequency Spectra

JOURNAL=Frontiers in Ecology and Evolution

VOLUME=Volume 10 - 2022

YEAR=2022

URL=https://www.frontiersin.org/journals/ecology-and-evolution/articles/10.3389/fevo.2022.889438

DOI=10.3389/fevo.2022.889438

ISSN=2296-701X

ABSTRACT=The Tug-of-War model was developed in a series of papers of McFarland and co-authors to account for existence of mutually counteracting rare advantageous driver mutations and more frequent slightly deleterious passenger mutations in cancer. In its original version, it was a state-dependent branching process. Because of its formulation, the Tug-of-War model is of importance for tackling the problem as to whether evolution of cancerous tumors is "Darwinian" or "non-Darwinian".
We define two Time-Continuous Markov Chain versions of the model, including identical mutation processes but adopting different drift and selection components. In Model A, drift and selection process preserves expected fitness whereas in Model B it leads to non-decreasing expected fitness.
We investigate these properties using mathematical analysis and extensive simulations, which detect the effect of the so-called drift barrier in Model B but not in Model A. These effects are reflected in different structure of clone genealogies in the two models. In addition, we verify how neutrality tests, based on the overall allele count and singleton count, fail more frequently under Model B. Our work is related to the past theoretical work in the field of evolutionary genetics, concern the interplay among mutation, drift and selection, in absence of recombination (asexual reproduction), where epistasis plays a major role. 
Finally, we use the statistics of mutation frequencies known as the Site Frequency Spectra, to compare the variant frequencies in DNA of sequenced HER2+ breast cancers, to those based on Model A and B simulations. The tumor-based SFS are better reproduced by Model A, pointing out a possible selection pattern of HER2+ tumor evolution.