Evolutionary Game Dynamics Driven By Mutations Under Frequency Dependent Selection

Evolutionary game theory and theoretical population genetics are two different fields sharing many common properties. In both fields, theoretical models are built to explore evolutionary dynamics; various evolutionary forces, such as selection, mutation, and random genetic drift, are involved in the modeling. However, in terms of concrete models, evolutionary game theory is often considered to deal with phenotypes, while theoretical population genetics describes genotypes. Is it possible and worth to combine approaches from both fields? We address this question by analyzing the evolutionary dynamics driven by random mutations in the framework of evolutionary game theory. Mutations provide a continuous input of new variability into a population, which is exposed to natural selection. In evolutionary game theory, mutations are often assumed to occur among predefined types. This assumption initially made in the study of behavioral phenotypes (i.e. human behaviors), might be less reasonable in studies at the level of genes or genotypes. An alternative assumption is made in the infinite allele model in theoretical population genetics, where every mutation brings a new allele to the population. However, the resulting evolutionary dynamics based on the infinite allele model has only been studied in the context of neutral and constant selection. In this thesis, we propose an evolutionary game theoretic model, which combines the assumption of infinite alleles and frequency dependent fitness. We investigate the evolutionary dynamics in finite and infinite populations based on this model. The fixation probability of a single mutant, the diversity of a population, and the changes of the average population fitness are strikingly different under constant selection and frequency dependent selection scenarios. These results imply that connecting evolutionary game theory and theoretical population genetics approaches can bring a different and insightful view in understanding evolutionary dynamics

Single-cell mutational burden distributions in birth-death processes

Genetic mutations are footprints of cancer evolution and reveal critical dynamic parameters of tumour growth, which otherwise are hard to measure in vivo. The mutation accumulation in tumour cell populations has been described by various statistics, such as site frequency spectra (SFS) from bulk or single-cell data, as well as single-cell division distributions (DD) and mutational burden distributions (MBD). An integrated understanding of these distributions obtained from different sequencing information is important to illuminate the ecological and evolutionary dynamics of tumours, and requires novel mathematical and computational tools. We introduce dynamical matrices to analyse and unite the SFS, DD and MBD based on a birth-death process. Using the Markov nature of the model, we derive recurrence relations for the expectations of these three distributions. While recovering classic exact results in pure-birth cases for the SFS and the DD through our new framework, we also derive a new expression for the MBD as well as approximations for all three distributions when death is introduced, confirming our results with stochastic simulations. Moreover, we demonstrate a natural link between the SFS and the single-cell MBD, and show that the MBD can be regenerated through the DD. Surprisingly, the single-cell MBD is mainly driven by the stochasticity arising in the DD, rather than the extra stochasticity in the number of mutations at each cell division.Comment: 27 pages, 6 figure

Stochastic game dynamics under demographic fluctuations.

Frequency-dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency-dependent selection, the average fitness of the population may increase or decrease based on interactions between individuals within the population. This should be reflected in fluctuations of the population size even in constant environments. Here, we propose a stochastic model that naturally combines these two evolutionary ingredients by assuming frequency-dependent competition between different types in an individual-based model. In contrast to previous game theoretic models, the carrying capacity of the population, and thus the population size, is determined by pairwise competition of individuals mediated by evolutionary games and demographic stochasticity. In the limit of infinite population size, the averaged stochastic dynamics is captured by deterministic competitive Lotka-Volterra equations. In small populations, demographic stochasticity may instead lead to the extinction of the entire population. Because the population size is driven by fitness in evolutionary games, a population of cooperators is less prone to go extinct than a population of defectors, whereas in the usual systems of fixed size the population would thrive regardless of its average payoff.This work was supported by the Natural Sciences and Engineering Research Council of Canada (C.H.) and Foundational Questions in Evolutionary Biology Fund Grant RFP-12-10 (to C.H.) and the Max Planck Society (W.H. and A.T.)

Dynamical trade-offs arise from antagonistic coevolution and decrease intraspecific diversity

Trade-offs play an important role in evolution. Without trade-offs, evolution would maximize fitness of all traits leading to a "master of all traits". The shape of trade-offs has been shown to determine evolutionary trajectories and is often assumed to be static and independent of the actual evolutionary process. Here we propose that coevolution leads to a dynamical trade-off. We test this hypothesis in a microbial predator-prey system and show that the bacterial growth-defense trade-off changes from concave to convex, i.e., defense is effective and cheap initially, but gets costly when predators coevolve. We further explore the impact of such dynamical trade-offs by a novel mathematical model incorporating de novo mutations for both species. Predator and prey populations diversify rapidly leading to higher prey diversity when the trade-off is concave (cheap). Coevolution results in more convex (costly) trade-offs and lower prey diversity compared to the scenario where only the prey evolves.Peer reviewe

Measuring single cell divisions in human tissues from multi-region sequencing data

Both normal tissue development and cancer growth are driven by a branching process of cell division and mutation accumulation that leads to intra-tissue genetic heterogeneity. However, quantifying somatic evolution in humans remains challenging. Here, we show that multi-sample genomic data from a single time point of normal and cancer tissues contains information on single-cell divisions. We present a new theoretical framework that, applied to whole-genome sequencing data of healthy tissue and cancer, allows inferring the mutation rate and the cell survival/death rate per division. On average, we found that cells accumulate 1.14 mutations per cell division in healthy haematopoiesis and 1.37 mutations per division in brain development. In both tissues, cell survival was maximal during early development. Analysis of 131 biopsies from 16 tumours showed 4 to 100 times increased mutation rates compared to healthy development and substantial inter-patient variation of cell survival/death rates

Hepatocytes undergo punctuated expansion dynamics from a periportal stem cell niche in normal human liver

Background & Aims: While normal human liver is thought to be generally quiescent, clonal hepatocyte expansions have been observed, though neither their cellular source nor their expansion dynamics have been determined. Knowing the hepatocyte cell of origin, and their subsequent dynamics and trajectory within the human liver will provide an important basis to understand disease-associated dysregulation. Methods: Herein, we use in vivo lineage tracing and methylation sequence analysis to demonstrate normal human hepatocyte ancestry. We exploit next-generation mitochondrial sequencing to determine hepatocyte clonal expansion dynamics across spatially distinct areas of laser-captured, microdissected, clones, in tandem with computational modelling in morphologically normal human liver. Results: Hepatocyte clones and rare SOX9+ hepatocyte progenitors commonly associate with portal tracts and we present evidence that clones can lineage-trace with cholangiocytes, indicating the presence of a bipotential common ancestor at this niche. Within clones, we demonstrate methylation CpG sequence diversity patterns indicative of periportal not pericentral ancestral origins, indicating a portal to central vein expansion trajectory. Using spatial analysis of mitochondrial DNA variants by next-generation sequencing coupled with mathematical modelling and Bayesian inference across the portal-central axis, we demonstrate that patterns of mitochondrial DNA variants reveal large numbers of spatially restricted mutations in conjunction with limited numbers of clonal mutations. Conclusions: These datasets support the existence of a periportal progenitor niche and indicate that clonal patches exhibit punctuated but slow growth, then quiesce, likely due to acute environmental stimuli. These findings crucially contribute to our understanding of hepatocyte dynamics in the normal human liver. Impact and implications: The liver is mainly composed of hepatocytes, but we know little regarding the source of these cells or how they multiply over time within the disease-free human liver. In this study, we determine a source of new hepatocytes by combining many different lab-based methods and computational predictions to show that hepatocytes share a common cell of origin with bile ducts. Both our experimental and computational data also demonstrate hepatocyte clones are likely to expand in slow waves across the liver in a specific trajectory, but often lie dormant for many years. These data show for the first time the expansion dynamics of hepatocytes in normal liver and their cell of origin enabling the accurate measurment of changes to their dynamics that may lead to liver disease. These findings are important for researchers determining cancer risk in human liver

Clonal transitions and phenotypic evolution in Barrett esophagus

BACKGROUND & AIMS: Barrett's esophagus (BE) is a risk factor for esophageal adenocarcinoma but our understanding of how it evolves is poorly understood. We investigated BE gland phenotype distribution, the clonal nature of phenotypic change, and how phenotypic diversity plays a role in progression. METHODS: Using immunohistochemistry and histology, we analyzed the distribution and the diversity of gland phenotype between and within biopsy specimens from patients with nondysplastic BE and those who had progressed to dysplasia or had developed postesophagectomy BE. Clonal relationships were determined by the presence of shared mutations between distinct gland types using laser capture microdissection sequencing of the mitochondrial genome. RESULTS: We identified 5 different gland phenotypes in a cohort of 51 nondysplastic patients where biopsy specimens were taken at the same anatomic site (1.0-2.0 cm superior to the gastroesophageal junction. Here, we observed the same number of glands with 1 and 2 phenotypes, but 3 phenotypes were rare. We showed a common ancestor between parietal cell-containing, mature gastric (oxyntocardiac) and goblet cell-containing, intestinal (specialized) gland phenotypes. Similarly, we have shown a clonal relationship between cardiac-type glands and specialized and mature intestinal glands. Using the Shannon diversity index as a marker of gland diversity, we observed significantly increased phenotypic diversity in patients with BE adjacent to dysplasia and predysplasia compared to nondysplastic BE and postesophagectomy BE, suggesting that diversity develops over time. CONCLUSIONS: We showed that the range of BE phenotypes represents an evolutionary process and that changes in gland diversity may play a role in progression. Furthermore, we showed a common ancestry between gastric and intestinal-type glands in BE

A Novel, Simple, and Low-Cost Approach for Machine Learning Screening of Kidney Cancer: An Eight-Indicator Blood Test Panel with Predictive Value for Early Diagnosis

Clear cell renal cell carcinoma (ccRCC) accounts for more than 90% of all renal cancers. The five-year survival rate of early-stage (TNM 1) ccRCC reaches 96%, while the advanced-stage (TNM 4) is only 23%. Therefore, early screening of patients with renal cancer is essential for the treatment of renal cancer and the long-term survival of patients. In this study, blood samples of patients were collected and a pre-defined set of blood indicators were measured. A random forest (RF) model was established to predict based on each indicator in the blood, and was trained with all relevant indicators for comprehensive predictions. In our study, we found that there was a high statistical significance (p < 0.001) for all indicators of healthy individuals and early cancer patients, except for uric acid (UA). At the same time, ccRCC also presented great differences in most blood indicators between males and females. In addition, patients with ccRCC had a higher probability of developing a low ratio of albumin (ALB) to globulin (GLB) (AGR < 1.2). Eight key indicators were used to classify and predict renal cell carcinoma. The area under the receiver operating characteristic (ROC) curve (AUC) of the eight-indicator model was as high as 0.932, the sensitivity was 88.2%, and the specificity was 86.3%, which are acceptable in many applications, thus realising early screening for renal cancer by blood indicators in a simple blood-draw physical examination. Furthermore, the composite indicator prediction method described in our study can be applied to other clinical conditions or diseases, where multiple blood indicators may be key to enhancing the diagnostic potential of screening strategies