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To maintain optimal fitness, a cell must balance the risk of inadequate energy reserve for response to a potentially fatal perturbation against the long-term cost of maintaining high concentrations of ATP to meet occasional spikes in demand. Here we apply a game theoretic approach to address the dynamics of energy production and expenditure in eukaryotic cells. Conventionally, glucose metabolism is viewed as a function of oxygen concentrations in which the more efficient oxidation of glucose to CO2 and H2O produces all or nearly all ATP except under hypoxic conditions when less efficient (2 ATP/ glucose vs. about 36ATP/glucose) anaerobic metabolism of glucose to lactic acid provides an emergency backup. We propose an alternative in which energy production is governed by the complex temporal and spatial dynamics of intracellular ATP demand. In the short term, a cell must provide energy for constant baseline needs but also maintain capacity to rapidly respond to fluxes in demand particularly due to external perturbations on the cell membrane. Similarly, longer-term dynamics require a trade-off between the cost of maintaining high metabolic capacity to meet uncommon spikes in demand versus the risk of unsuccessfully responding to threats or opportunities. Here we develop a model and computationally explore the cell's optimal mix of glycolytic and oxidative capacity. We find the Warburg effect, high glycolytic metabolism even under normoxic conditions, is represents a metabolic strategy that allow cancer cells to optimally meet energy demands posed by stochastic or fluctuating tumor environments.

Many effective drugs for metastatic and/or advanced-stage cancers have been developed over the past decade, although the evolution of resistance remains the major barrier to disease control or cure. In large, diverse populations such as the cells that compose metastatic cancers, the emergence of cells that are resistant or that can quickly develop resistance is virtually inevitable and most likely cannot be prevented. However, clinically significant resistance occurs only when the pre-existing resistant phenotypes are able to proliferate extensively, a process governed by eco-evolutionary dynamics. Attempts to disrupt the molecular mechanisms of resistance have generally been unsuccessful in clinical practice. In this Review, we focus on the Darwinian processes driving the eco-evolutionary dynamics of treatment-resistant cancer populations. We describe a variety of evolutionarily informed strategies designed to increase the probability of disease control or cure by anticipating and steering the evolutionary dynamics of acquired resistance.Most systemic cancer therapies are administered at doses at or close to the maximum tolerated dose until disease progression. However, this approach usually leads to treatment resistance and fails to take into account several potentially relevant evolutionary principles. In this Review, the authors describe how existing approaches to cancer therapy might be optimized by incorporating an understanding of evolutionary dynamics into cancer therapy.

Abiraterone treats metastatic castrate-resistant prostate cancer by inhibiting CYP17A, an enzyme for testosterone auto-production. With standard dosing, evolution of resistance with treatment failure (radiographic progression) occurs at a median of ~16.5 months. We hypothesize time to progression (TTP) could be increased by integrating evolutionary dynamics into therapy. We developed an evolutionary game theory model using Lotka–Volterra equations with three competing cancer “species”: androgen dependent, androgen producing, and androgen independent. Simulations with standard abiraterone dosing demonstrate strong selection for androgen-independent cells and rapid treatment failure. Adaptive therapy, using patient-specific tumor dynamics to inform on/off treatment cycles, suppresses proliferation of androgen-independent cells and lowers cumulative drug dose. In a pilot clinical trial, 10 of 11 patients maintained stable oscillations of tumor burdens; median TTP is at least 27 months with reduced cumulative drug use of 47% of standard dosing. The outcomes show significant improvement over published studies and a contemporaneous population. Evolution of resistance is a common cause of cancer treatment failure and tumor progression. Here, the authors present a method for integrating evolutionary principles based on adaptive therapy into abiraterone therapy for metastatic castrate-resistant prostate cancer and show the positive results of an interim analysis of a trial cohort.

Humans have marvelled at the fit of form and function, the way organisms' traits seem remarkably suited to their lifestyles and ecologies. While natural selection provides the scientific basis for the fit of form and function, Darwin found certain adaptations vexing or particularly intriguing: sex ratios, sexual selection and altruism. The logic behind these adaptations resides in frequency-dependent selection where the value of a given heritable phenotype (i.e. strategy) to an individual depends upon the strategies of others. Game theory is a branch of mathematics that is uniquely suited to solving such puzzles. While game theoretic thinking enters into Darwin's arguments and those of evolutionists through much of the twentieth century, the tools of evolutionary game theory were not available to Darwin or most evolutionists until the 1970s, and its full scope has only unfolded in the last three decades. As a consequence, game theory is applied and appreciated rather spottily. Game theory not only applies to matrix games and social games, it also applies to speciation, macroevolution and perhaps even to cancer. I assert that life and natural selection are a game, and that game theory is the appropriate logic for framing and understanding adaptations. Its scope can include behaviours within species, state-dependent strategies (such as male, female and so much more), speciation and coevolution, and expands beyond microevolution to macroevolution. Game theory clarifies aspects of ecological and evolutionary stability in ways useful to understanding eco-evolutionary dynamics, niche construction and ecosystem engineering. In short, I would like to think that Darwin would have found game theory uniquely useful for his theory of natural selection. Let us see why this is so.

Abiraterone acetate is an effective treatment for metastatic castrate-resistant prostate cancer (mCRPC), but evolution of resistance inevitably leads to progression. We present a pilot study in which abiraterone dosing is guided by evolution-informed mathematical models to delay onset of resistance. In the study cohort, abiraterone was stopped when PSA was <50% of pretreatment value and resumed when PSA returned to baseline. Results are compared to a contemporaneous cohort who had >50% PSA decline after initial abiraterone administration and met trial eligibility requirements but chose standard of care (SOC) dosing. 17 subjects were enrolled in the adaptive therapy group and 16 in the SOC group. All SOC subjects have progressed, but four patients in the study cohort remain stably cycling (range 53-70 months). The study cohort had significantly improved median time to progression (TTP; 33.5 months; p<0.001) and median overall survival (OS; 58.5 months; hazard ratio, 0.41, 95% confidence interval (CI), 0.20-0.83, p<0.001) compared to 14.3 and 31.3 months in the SOC cohort. On average, study subjects received no abiraterone during 46% of time on trial. Longitudinal trial data demonstrated the competition coefficient ratio ( ) of sensitive and resistant populations, a critical factor in intratumoral evolution, was two- to threefold higher than pre-trial estimates. Computer simulations of intratumoral evolutionary dynamics in the four long-term survivors found that, due to the larger value for cycled therapy significantly decreased the resistant population. Simulations in subjects who progressed predicted further increases in OS could be achieved with prompt abiraterone withdrawal after achieving 50% PSA reduction. Incorporation of evolution-based mathematical models into abiraterone monotherapy for mCRPC significantly increases TTP and OS. Computer simulations with updated parameters from longitudinal trial data can estimate intratumoral evolutionary dynamics in each subject and identify strategies to improve outcomes. Moffitt internal grants and NIH/NCI U54CA143970-05 (Physical Science Oncology Network).

Fish populations subject to heavy exploitation are expected to evolve over time smaller average body sizes. We introduce Stackelberg evolutionary game theory to show how fisheries management should be adjusted to mitigate the potential negative effects of such evolutionary changes. We present the game of a fisheries manager versus a fish population, where the former adjusts the harvesting rate and the net size to maximize profit, while the latter responds by evolving the size at maturation to maximize the fitness. We analyze three strategies: i) ecologically enlightened (leading to a Nash equilibrium in game-theoretic terms); ii) evolutionarily enlightened (leading to a Stackelberg equilibrium) and iii) domestication (leading to team optimum) and the corresponding outcomes for both the fisheries manager and the fish. Domestication results in the largest size for the fish and the highest profit for the manager. With the Nash approach the manager tends to adopt a high harvesting rate and a small net size that eventually leads to smaller fish. With the Stackelberg approach the manager selects a bigger net size and scales back the harvesting rate, which lead to a bigger fish size and a higher profit. Overall, our results encourage managers to take the fish evolutionary dynamics into account. Moreover, we advocate for the use of Stackelberg evolutionary game theory as a tool for providing insights into the eco-evolutionary consequences of exploiting evolving resources.

Tumors are not static masses of cells but dynamic ecosystems where cancer cells experience constant turnover and evolve fitness-enhancing phenotypes. Selection for different phenotypes may vary with (1) the tumor niche (edge or core), (2) cell turnover rates, (3) the nature of the tradeoff between traits, and (4) whether deaths occur in response to demographic or environmental stochasticity. Using a spatially-explicit agent-based model, we observe how two traits (proliferation rate and migration speed) evolve under different tradeoff conditions with different turnover rates. Migration rate is favored over proliferation at the tumor ’ s edge and vice-versa for the interior. Increasing cell turnover rates slightly slows tumor growth but accelerates the rate of evolution for both proliferation and migration. The absence of a tradeoff favors ever higher values for proliferation and migration, while a convex tradeoff tends to favor proliferation, often promoting the coexistence of a generalist and specialist phenotype. A concave tradeoff favors migration at low death rates, but switches to proliferation at higher death rates. Mortality via demographic stochasticity favors proliferation, and environmental stochasticity favors migration. While all of these diverse factors contribute to the ecology, heterogeneity, and evolution of a tumor, their effects may be predictable and empirically accessible.

Convergence between species and entire clades can occur due to shared environmental conditions and shared resource use. Comparisons of biogeography between convergent clades and taxa may reveal some of these properties unique to each taxon. We sought to characterize and compare the global scale biogeography of hummingbirds (family Trochilidae), which possess unique adaptations for nectar feeding, with sunbirds (family Nectariniidae), which also feed on nectar but are more generalist in their feeding ecology. We collected the latitudinal and elevational range of all species in both clades to create species distributions along those gradients by way of empirical cumulative distribution functions. We compared those distributions to see 1) if they differed, by way of minimum difference estimation and 2) how they differed, by way of non-linear regression. Hummingbirds are shown to extend into higher elevations and latitudes compared to sunbirds, and better maintain their species number in these more extreme environments. We provide possible reasons for these patterns including dispersal limitation, land area, diversity of resources, and climatic conditions. In one particularly interesting hypothesis, we propose that hummingbirds’ unique adaptations for nectar feeding allow them to exploit resources more efficiently, gain higher intrinsic fitness, and therefore speciate and spread into more extreme climates than less efficient nectar feeding sunbirds.

Based on a consensus conference of experts in the evolution and ecology of cancer, this article proposes a framework for classifying tumours that includes four evolutionary and ecological processes: neoplastic cell diversity and changes over time in that diversity, hazards to cell survival and available resources. Neoplasms change over time through a process of cell-level evolution, driven by genetic and epigenetic alterations. However, the ecology of the microenvironment of a neoplastic cell determines which changes provide adaptive benefits. There is widespread recognition of the importance of these evolutionary and ecological processes in cancer, but to date, no system has been proposed for drawing clinically relevant distinctions between how different tumours are evolving. On the basis of a consensus conference of experts in the fields of cancer evolution and cancer ecology, we propose a framework for classifying tumours that is based on four relevant components. These are the diversity of neoplastic cells (intratumoural heterogeneity) and changes over time in that diversity, which make up an evolutionary index (Evo-index), as well as the hazards to neoplastic cell survival and the resources available to neoplastic cells, which make up an ecological index (Eco-index). We review evidence demonstrating the importance of each of these factors and describe multiple methods that can be used to measure them. Development of this classification system holds promise for enabling clinicians to personalize optimal interventions based on the evolvability of the patient's tumour. The Evo- and Eco-indices provide a common lexicon for communicating about how neoplasms change in response to interventions, with potential implications for clinical trials, personalized medicine and basic cancer research.

State‐structured populations are ubiquitous in biology, from the age‐structure of animal societies to the life cycles of parasitic species. Understanding how this structure contributes to eco‐evolutionary dynamics is critical not only for fundamental understanding but also for conservation and treatment purposes. Although some methods have been developed in the literature for modelling eco‐evolutionary dynamics in structured population, such methods are wholly lacking in the G function evolutionary game theoretic framework. In this paper, we integrate standard matrix population modelling into the G function framework to create a theoretical framework to probe eco‐evolutionary dynamics in structured populations. This framework encompasses age‐ and stage‐structured matrix models with basic density‐ and frequency‐dependent transition rates and probabilities. For both discrete and continuous time models, we define and characterize asymptotic properties of the system such as eco‐evolutionary equilibria (including ESSs) and the convergence stability of these equilibria. For multistate structured populations, we introduce an ergodic flow preserving folding method for analysing such models. The methods developed in this paper for state‐structured populations and their extensions to multistate‐structured populations provide a simple way to create, analyse and simulate eco‐evolutionary dynamics in structured populations. Furthermore, their generality allows these techniques to be applied to a variety of problems in ecology and evolution.