Trait trajectories in evolving populations: insights from mathematical models
Promoting extinction or minimizing growth? The impact of treatment on trait trajectories in evolving populations
Recommendation: posted 04 January 2023, validated 05 January 2023
Wodarz, D. (2023) Trait trajectories in evolving populations: insights from mathematical models. Peer Community in Evolutionary Biology, 100555. https://doi.org/10.24072/pci.evolbiol.100555
The evolution of cells within organisms can be an important determinant of disease. This is especially clear in the emergence of tumors and cancers from the underlying healthy tissue. In the healthy state, homeostasis is maintained through complex regulatory processes that ensure a relatively constant population size of cells, which is required for tissue function. Tumor cells escape this homeostasis, resulting in uncontrolled growth and consequent disease. Disease progression is driven by further evolutionary processes within the tumor, and so is the response of tumors to therapies. Therefore, evolutionary biology is an important component required for a better understanding of carcinogenesis and the treatment of cancers. In particular, evolutionary theory helps define the principles of mutant evolution and thus to obtain a clearer picture of the determinants of tumor emergence and therapy responses.
The study by Raatz and Traulsen  makes an important contribution in this respect. They use mathematical and computational models to investigate trait evolution in the context of evolutionary rescue, motivated by the dynamics of cancer, and also bacterial infections. This study views the establishment of tumors as cell dynamics in harsh environments, where the population is prone to extinction unless mutants emerge that increase evolutionary fitness, allowing them to expand (evolutionary rescue). The core processes of the model include growth, death, and mutations. Random mutations are assumed to give rise to cell lineages with different trait combinations, where the birth and death rates of cells can change. The resulting evolutionary trajectories are investigated in the models, and interesting new results were obtained. For example, the turnover of the population was identified as an important determinant of trait evolution. Turnover is defined as the balance between birth and death, with large rates corresponding to fast turnover and small rates to slow turnover. It was found that for fast cell turnover, a given adaptive step in the trait space results in a smaller increase in survival probability than for cell populations with slower turnover. In other words, evolutionary rescue is more difficult to achieve for fast compared to slow turnover populations. While more mutants can be produced for faster cell turnover rates, the analysis showed that this is not sufficient to overcome the barrier to the evolutionary rescue. This result implies that aggressive tumors with fast cell birth and death rates are less likely to persist and progress than tumors with lower turnover rates. This work emphasizes the importance of measuring the turnover rate in different tumors to advance our understanding of the determinants of tumor initiation and progression. The authors discuss that the well-documented heterogeneity in tumors likely also applies to cellular turnover. If a tumor consists of sub-populations with faster and slower turnover, it is possible that a slower turnover cell clone (e.g. characterized by a degree of dormancy) would enjoy a selective advantage. Another source of heterogeneity in turnover could be given by the hierarchical organization of tumors. Similar to the underlying healthy tissue, many tumors are thought to be maintained by a population of cancer stem cells, while the tumor bulk is made up of more differentiated cells. Tissue stem cells tend to be characterized by a lower turnover than progenitor or transit-amplifying cells. Depending on the assumptions about the self-renewal capacity of these different cell populations, the potential for evolutionary rescue could be different depending on the cell compartment in which the mutant emerges. This might be interesting to explore in the future.
There are also implications for treatment. Two types of treatment were investigated: density-affecting treatments in which the density of cells is reduced without altering their trait parameters, and trait-affecting treatments in which the birth and/or death rates are altered. Both types of treatment were found to change the trajectories of trait adaptation, which has potentially important practical implications. Interestingly, it was found that competitive release during treatment can result in situations where after treatment cessation, the non-extinct populations recover to reach sizes that were higher than in the absence of treatment. This points towards the potential of adaptive therapy approaches, where sensitive cells are maintained to some extent to suppress resistant clones  competitively. In this context, it is interesting that the success of such approaches might also depend on the turnover of the tumor cell population, as shown by a recent mathematical modeling study . In particular, it was found that adaptive therapy is less likely to work for slow compared to fast turnover tumors. Yet, the current study by Raatz and Traulsen  suggests that tumors are more likely to evolve in a slow turnover setting.
While there is strong relevance of this analysis for tumor evolution, the results generated in this study have more general relevance. Besides tumors, the paper discusses applications to bacterial disease dynamics in some detail, which is also interesting to compare and contrast to evolutionary processes in cancer. Overall, this study provides insights into the dynamics of evolutionary rescue that represent valuable additions to evolutionary theory.
 Raatz M, Traulsen A (2023) Promoting extinction or minimizing growth? The impact of treatment on trait trajectories in evolving populations. bioRxiv, 2022.06.17.496570, ver. 2 peer-reviewed and recommended by Peer Community in Evolutionary Biology. https://doi.org/10.1101/2022.06.17.496570
 Gatenby RA, Silva AS, Gillies RJ, Frieden BR (2009) Adaptive Therapy. Cancer Research, 69, 4894–4903. https://doi.org/10.1158/0008-5472.CAN-08-3658
 Strobl MAR, West J, Viossat Y, Damaghi M, Robertson-Tessi M, Brown JS, Gatenby RA, Maini PK, Anderson ARA (2021) Turnover Modulates the Need for a Cost of Resistance in Adaptive Therapy. Cancer Research, 81, 1135–1147. https://doi.org/10.1158/0008-5472.CAN-20-0806
The recommender in charge of the evaluation of the article and the reviewers declared that they have no conflict of interest (as defined in the code of conduct of PCI) with the authors or with the content of the article. The authors declared that they comply with the PCI rule of having no financial conflicts of interest in relation to the content of the article.
Evaluation round #1
DOI or URL of the preprint: https://doi.org/10.1101/2022.06.17.496570
Version of the preprint: 1
Author's Reply, 20 Dec 2022
Decision by Dominik Wodarz, posted 08 Oct 2022
The paper seems very interesting, and in general is viewed positively by the reviewers. The reviewers make a number of useful suggestions and have some questions, which should be straightforward to address in a revision; this might benefit the paper.