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 LotkaVolterra 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.evolutionary games | stochastic dynamics | changing population size A ll natural populations are composed of a finite number of individuals. These individuals can reproduce, interact, die, or migrate, which leads to changes in the population size over time. In many theoretical models, it is convenient and possible to neglect the effect of demographic fluctuations by assuming infinite populations when population sizes are sufficiently large
Quantification of the effect of spatial tumour sampling on the patterns of mutations detected in next-generation sequencing data is largely lacking. Here we use a spatial stochastic cellular automaton model of tumour growth that accounts for somatic mutations, selection, drift and spatial constraints, to simulate multi-region sequencing data derived from spatial sampling of a neoplasm. We show that the spatial structure of a solid cancer has a major impact on the detection of clonal selection and genetic drift from both bulk and single-cell sequencing data. Our results indicate that spatial constrains can introduce significant sampling biases when performing multi-region bulk sampling and that such bias becomes a major confounding factor for the measurement of the evolutionary dynamics of human tumours. We also propose a statistical inference framework that incorporates spatial effects within a growing tumour and so represents a further step forwards in the inference of evolutionary dynamics from genomic data. Our analysis shows that measuring cancer evolution using next-generation sequencing while accounting for the numerous confounding factors remains challenging. However, mechanistic model-based approaches have the potential to capture the sources of noise and better interpret the 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 multisample 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.
Intra-tumor heterogeneity (ITH) is a major underlying cause of therapy resistance and disease recurrence, and is a read-out of tumor growth. Current genetic ITH analysis methods do not preserve spatial context and may not detect rare subclones. Here, we address these shortfalls by developing and validating BaseScope—a novel mutation-specific RNA in situ hybridization assay. We target common point mutations in the BRAF, KRAS and PIK3CA oncogenes in archival colorectal cancer samples to precisely map the spatial and morphological context of mutant subclones. Computational modeling suggests that subclones must arise sufficiently early, or carry a considerable fitness advantage, to form large or spatially disparate subclones. Examples of putative treatment-resistant cells isolated in small topographical areas are observed. The BaseScope assay represents a significant technical advance for in situ mutation detection that provides new insight into tumor evolution, and could have ramifications for selecting patients for treatment.
Under neutrality, polymorphisms are maintained through the balance between mutation and drift. Under selection, a variety of mechanisms may be involved in the maintenance of polymorphisms, for example, sexual selection or host-parasite coevolution on the population level or heterozygote advantage in diploid individuals. Here we address the emergence of polymorphisms in a population of interacting haploid individuals. In our model, each mutation generates a new evolutionary game characterized by a payoff matrix with an additional row and an additional column. Hence, in general, the fitness of new mutations is frequency-dependent rather than constant. This dynamical process is distinct from the sequential fixation of advantageous traits and naturally leads to the emergence of polymorphisms under selection. It causes substantially higher diversity than observed under the established models of neutral or frequency-independent selection. Our framework allows for the coexistence of an arbitrary number of types, but predicts an intermediate average 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.
Oncogene amplification on extrachromosomal DNA (ecDNA) is a common event, driving aggressive tumor growth, drug resistance and shorter survival. Currently, the impact of nonchromosomal oncogene inheritance—random identity by descent—is poorly understood. Also unclear is the impact of ecDNA on somatic variation and selection. Here integrating theoretical models of random segregation, unbiased image analysis, CRISPR-based ecDNA tagging with live-cell imaging and CRISPR-C, we demonstrate that random ecDNA inheritance results in extensive intratumoral ecDNA copy number heterogeneity and rapid adaptation to metabolic stress and targeted treatment. Observed ecDNAs benefit host cell survival or growth and can change within a single cell cycle. ecDNA inheritance can predict, a priori, some of the aggressive features of ecDNA-containing cancers. These properties are facilitated by the ability of ecDNA to rapidly adapt genomes in a way that is not possible through chromosomal oncogene amplification. These results show how the nonchromosomal random inheritance pattern of ecDNA contributes to poor outcomes for patients with cancer.
Species interactions and coevolution are integral to ecological communities, but we lack empirical information on when and how these interactions generate and purge genetic diversity. Using genomic time series data from host-virus experiments, we found that coevolution occurs through consecutive selective sweeps in both species, with temporal consistency across replicates. Sweeps were accompanied by phenotypic change (resistance or infectivity increases) and expansions in population size. In the host, population expansion enabled rapid generation of genetic diversity in accordance with neutral processes. Viral molecular evolution was, in contrast, confined to few genes, all putative targets of selection. This study demonstrates that molecular evolution during species interactions is shaped by both eco-evolutionary feedback dynamics and interspecific differences in how genetic diversity is generated and maintained.
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