Preventing evolutionary rescue in cancer

First-line cancer treatment frequently fails due to initially rare therapeutic resistance. An important clinical question is then how to schedule subsequent treatments to maximize the probability of tumour eradication. Here, we provide a theoretical solution to this problem by using mathematical analysis and extensive stochastic simulations within the framework of evolutionary rescue theory to determine how best to exploit the vulnerability of small tumours to stochastic extinction. Whereas standard clinical practice is to wait for evidence of relapse, we confirm a recent hypothesis that the optimal time to switch to a second treatment is when the tumour is close to its minimum size before relapse, when it is likely undetectable. This optimum can lie slightly before or slightly after the nadir, depending on tumour parameters. Given that this exact time point may be difficult to determine in practice, we study windows of high extinction probability that lie around the optimal switching point, showing that switching after the relapse has begun is typically better than switching too early. We further reveal how treatment dose and tumour demographic and evolutionary parameters influence the predicted clinical outcome, and we determine how best to schedule drugs of unequal efficacy. Our work establishes a foundation for further experimental and clinical investigation of this evolutionarily-informed "extinction therapy" strategy.

Stackelberg evolutionary game theory: how to manage evolving systems

Stackelberg evolutionary game (SEG) theory combines classical and evolutionary game theory to frame interactions between a rational leader and evolving followers. In some of these interactions, the leader wants to preserve the evolving system (e.g. fisheries management), while in others, they try to drive the system to extinction (e.g. pest control). Often the worst strategy for the leader is to adopt a constant aggressive strategy (e.g. overfishing in fisheries management or maximum tolerable dose in cancer treatment). Taking into account the ecological dynamics typically leads to better outcomes for the leader and corresponds to the Nash equilibria in game-theoretic terms. However, the leader's most profitable strategy is to anticipate and steer the eco-evolutionary dynamics, leading to the Stackelberg equilibrium of the game. We show how our results have the potential to help in fields where humans try to bring an evolutionary system into the desired outcome, such as, among others, fisheries management, pest management and cancer treatment. Finally, we discuss limitations and opportunities for applying SEGs to improve the management of evolving biological systems. This article is part of the theme issue 'Half a century of evolutionary games: a synthesis of theory, application and future directions'.

A survey of open questions in adaptive therapy: Bridging mathematics and clinical translation

Adaptive therapy is a dynamic cancer treatment protocol that updates (or 'adapts') treatment decisions in anticipation of evolving tumor dynamics. This broad term encompasses many possible dynamic treatment protocols of patient-specific dose modulation or dose timing. Adaptive therapy maintains high levels of tumor burden to benefit from the competitive suppression of treatment-sensitive subpopulations on treatment-resistant subpopulations. This evolution-based approach to cancer treatment has been integrated into several ongoing or planned clinical trials, including treatment of metastatic castrate resistant prostate cancer, ovarian cancer, and BRAF-mutant melanoma. In the previous few decades, experimental and clinical investigation of adaptive therapy has progressed synergistically with mathematical and computational modeling. In this work, we discuss 11 open questions in cancer adaptive therapy mathematical modeling. The questions are split into three sections: (1) integrating the appropriate components into mathematical models (2) design and validation of dosing protocols, and (3) challenges and opportunities in clinical translation.

Different costs of therapeutic resistance in cancer: Short- and long-term impact of population heterogeneity

Therapeutic resistance continues to undercut long-term success of many promising cancer treatments. At times, development of therapeutic resistance can come at a fitness cost for the cancer cell population, which could potentially be leveraged to the patient's advantage. A mathematical formulation of such a situation was proposed by Pressley et al. (2020), who discussed two scenarios, namely, when developing therapeutic resistance can come at a cost to proliferative capacity (such as when a drug targets a growth receptor), or to the total tumor carrying capacity (such as when a drug targets neovascularization). Here we expand the analysis of the two models and evaluate both short- and long-term dynamics of a population heterogeneous with respect to resistance. We analyze the four initial distributions with respect to resistance at the time of treatment initiation: uniform, bell-shaped, exponential, and U-shaped. We show that final population composition is invariant to the initial distribution, with a single clone eventually dominating within the population; the value of the resistance parameter of the final clone depends on other system parameters but not on the initial distribution. Transitional behaviors, however, which may have more significant implications for immediate treatment decisions, depend critically on the initial distribution. Furthermore, we show that depending on the mechanism for the cost of resistance (i.e., proliferation vs carrying capacity), increase in natural cell death rate has opposite effects, with higher natural death rate selecting for less resistant cell clones in the long term for proliferation-dependent model, and selecting for more resistant cell clones for carrying capacity-dependent model, a prediction that may have implications for combination therapy with cytotoxic agents. We conclude with a discussion of strengths and limitations of using modeling for understanding treatment trajectory, as well as the promise of model-informed evolutionary steering for improved long-term therapeutic outcomes.

The role of evolutionary game theory in spatial and non-spatial models of the survival of cooperation in cancer: a review

Evolutionary game theory (EGT) is a branch of mathematics which considers populations of individuals interacting with each other to receive pay-offs. An individual’s pay-off is dependent on the strategy of its opponent(s) as well as on its own, and the higher its pay-off, the higher its reproductive fitness. Its offspring generally inherit its interaction strategy, subject to random mutation. Over time, the composition of the population shifts as different strategies spread or are driven extinct. In the last 25 years there has been a flood of interest in applying EGT to cancer modelling, with the aim of explaining how cancerous mutations spread through healthy tissue and how intercellular cooperation persists in tumour-cell populations. This review traces this body of work from theoretical analyses of well-mixed infinite populations through to more realistic spatial models of the development of cooperation between epithelial cells. We also consider work in which EGT has been used to make experimental predictions about the evolution of cancer, and discuss work that remains to be done before EGT can make large-scale contributions to clinical treatment and patient outcomes.

Ecology of Human Medical Enterprises: From Disease Ecology of Zoonoses, Cancer Ecology Through to Medical Ecology of Human Microbiomes

In nature, the interaction between pathogens and their hosts is only one of a handful of interaction relationships between species, including parasitism, predation, competition, symbiosis, commensalism, and among others. From a non-anthropocentric view, parasitism has relatively fewer essential differences from the other relationships; but from an anthropocentric view, parasitism and predation against humans and their well-beings and belongings are frequently related to heinous diseases. Specifically, treating (managing) diseases of humans, crops and forests, pets, livestock, and wildlife constitute the so-termed medical enterprises (sciences and technologies) humans endeavor in biomedicine and clinical medicine, veterinary, plant protection, and wildlife conservation. In recent years, the significance of ecological science to medicines has received rising attentions, and the emergence and pandemic of COVID-19 appear accelerating the trend. The facts that diseases are simply one of the fundamental ecological relationships in nature, and the study of the relationships between species and their environment is a core mission of ecology highlight the critical importance of ecological science. Nevertheless, current studies on the ecology of medical enterprises are highly fragmented. Here, we (i) conceptually overview the fields of disease ecology of wildlife, cancer ecology and evolution, medical ecology of human microbiome-associated diseases and infectious diseases, and integrated pest management of crops and forests, across major medical enterprises. (ii) Explore the necessity and feasibility for a unified medical ecology that spans biomedicine, clinical medicine, veterinary, crop (forest and wildlife) protection, and biodiversity conservation. (iii) Suggest that a unified medical ecology of human diseases is both necessary and feasible, but laissez-faire terminologies in other human medical enterprises may be preferred. (iv) Suggest that the evo-eco paradigm for cancer research can play a similar role of evo-devo in evolutionary developmental biology. (v) Summarized 40 key ecological principles/theories in current disease-, cancer-, and medical-ecology literatures. (vi) Identified key cross-disciplinary discovery fields for medical/disease ecology in coming decade including bioinformatics and computational ecology, single cell ecology, theoretical ecology, complexity science, and the integrated studies of ecology and evolution. Finally, deep understanding of medical ecology is of obvious importance for the safety of human beings and perhaps for all living things on the planet.

The Genomic Processes of Biological Invasions: From Invasive Species to Cancer Metastases and Back Again

The concept of invasion is useful across a broad range of contexts, spanning from the fine scale landscape of cancer tumors up to the broader landscape of ecosystems. Invasion biology provides extraordinary opportunities for studying the mechanistic basis of contemporary evolution at the molecular level. Although the field of invasion genetics was established in ecology and evolution more than 50 years ago, there is still a limited understanding of how genomic level processes translate into invasive phenotypes across different taxa in response to complex environmental conditions. This is largely because the study of most invasive species is limited by information about complex genome level processes. We lack good reference genomes for most species. Rigorous studies to examine genomic processes are generally too costly. On the contrary, cancer studies are fortified with extensive resources for studying genome level dynamics and the interactions among genetic and non-genetic mechanisms. Extensive analysis of primary tumors and metastatic samples have revealed the importance of several genomic mechanisms including higher mutation rates, specific types of mutations, aneuploidy or whole genome doubling and non-genetic effects. Metastatic sites can be directly compared to primary tumor cell counterparts. At the same time, clonal dynamics shape the genomics and evolution of metastatic cancers. Clonal diversity varies by cancer type, and the tumors’ donor and recipient tissues. Still, the cancer research community has been unable to identify any common events that provide a universal predictor of “metastatic potential” which parallels findings in evolutionary ecology. Instead, invasion in cancer studies depends strongly on context, including order of events and clonal composition. The detailed studies of the behavior of a variety of human cancers promises to inform our understanding of genome level dynamics in the diversity of invasive species and provide novel insights for management.

The Contribution of Evolutionary Game Theory to Understanding and Treating Cancer

Evolutionary game theory mathematically conceptualizes and analyzes biological interactions where one's fitness not only depends on one's own traits, but also on the traits of others. Typically, the individuals are not overtly rational and do not select, but rather inherit their traits. Cancer can be framed as such an evolutionary game, as it is composed of cells of heterogeneous types undergoing frequency-dependent selection. In this article, we first summarize existing works where evolutionary game theory has been employed in modeling cancer and improving its treatment. Some of these game-theoretic models suggest how one could anticipate and steer cancer's eco-evolutionary dynamics into states more desirable for the patient via evolutionary therapies. Such therapies offer great promise for increasing patient survival and decreasing drug toxicity, as demonstrated by some recent studies and clinical trials. We discuss clinical relevance of the existing game-theoretic models of cancer and its treatment, and opportunities for future applications. Moreover, we discuss the developments in cancer biology that are needed to better utilize the full potential of game-theoretic models. Ultimately, we demonstrate that viewing tumors with evolutionary game theory has medically useful implications that can inform and create a lockstep between empirical findings and mathematical modeling. We suggest that cancer progression is an evolutionary competition between different cell types and therefore needs to be viewed as an evolutionary game.