The Birth-Death-Mutation process: a new paradigm for fat tailed distributions

Fat tailed statistics and power-laws are ubiquitous in many complex systems. Usually the appearance of of a few anomalously successful individuals (bio-species, investors, websites) is interpreted as reflecting some inherent "quality" (fitness, talent, giftedness) as in Darwin's theory of natural selection. Here we adopt the opposite, "neutral", outlook, suggesting that the main factor explaining success is merely luck. The statistics emerging from the neutral birth-death-mutation (BDM) process is shown to fit marvelously many empirical distributions. While previous neutral theories have focused on the power-law tail, our theory economically and accurately explains the entire distribution. We thus suggest the BDM distribution as a standard neutral model: effects of fitness and selection are to be identified by substantial deviations from it

On the Validity of Using Increases in 5-Year Survival Rates to Measure Success in the Fight against Cancer

Background: The 5-year survival rate of cancer patients is the most commonly used statistic to reflect improvements in the war against cancer. This idea, however, was refuted based on an analysis showing that changes in 5-year survival over time bear no relationship with changes in cancer mortality. Methods: Here we show that progress in the fight against cancer can be evaluated by analyzing the association between 5-year survival rates and mortality rates normalized by the incidence (mortality over incidence, MOI). Changes in mortality rates are caused by improved clinical management as well as changing incidence rates, and since the latter can mask the effects of the former, it can also mask the correlation between survival and mortality rates. However, MOI is a more robust quantity and reflects improvements in cancer outcomes by overcoming the masking effect of changing incidence rates. Using population-based statistics for the US and the European Nordic countries, we determined the association of changes in 5-year survival rates and MOI. Results: We observed a strong correlation between changes in 5-year survival rates of cancer patients and changes in the MOI for all the countries tested. This finding demonstrates that there is no reason to assume that the improvements in 5-year survival rates are artificial. We obtained consistent results when examining the subset of cancer types whose incidence did not increase, suggesting that over-diagnosis does not obscure the results. Conclusions: We have demonstrated, via the negative correlation between changes in 5-year survival rates and changes in MOI, that increases in 5-year survival rates reflect real improvements over time made in the clinical management of cancer. Furthermore, we found that increases in 5-year survival rates are not predominantly artificial byproducts of lead-time bias, as implied in the literature. The survival measure alone can therefore be used for a rough approximation of the amount of progress in the clinical management of cancer, but should ideally be used with other measures

Stochastic Tunneling of Two Mutations in a Population of Cancer Cells

Cancer initiation, progression, and the emergence of drug resistance are driven by specific genetic and/or epigenetic alterations such as point mutations, structural alterations, DNA methylation and histone modification changes. These alterations may confer advantageous, deleterious or neutral effects to mutated cells. Previous studies showed that cells harboring two particular alterations may arise in a fixed-size population even in the absence of an intermediate state in which cells harboring only the first alteration take over the population; this phenomenon is called stochastic tunneling. Here, we investigated a stochastic Moran model in which two alterations emerge in a cell population of fixed size. We developed a novel approach to comprehensively describe the evolutionary dynamics of stochastic tunneling of two mutations. We considered the scenarios of large mutation rates and various fitness values and validated the accuracy of the mathematical predictions with exact stochastic computer simulations. Our theory is applicable to situations in which two alterations are accumulated in a fixed-size population of binary dividing cells

Nonlocal competition and logistic growth: patterns, defects and fronts

Logistic growth of diffusing reactants on spatial domains with long range competition is studied. The bifurcations cascade involved in the transition from the homogenous state to a spatially modulated stable solution is presented, and a distinction is made between a modulated phase, dominated by single or few wavenumbers, and the spiky phase, where localized colonies are separated by depleted region. The characteristic defects in the periodic structure are presented for each phase, together with the invasion dynamics in case of local initiation. It is shown that the basic length scale that controls the bifurcation is the width of the Fisher front, and that the total population grows as this width decreases. A mix of analytic results and extensive numerical simulations yields a comprehensive examination of the possible phases for logistic growth in the presence of nonlocal competition

Polyploidy can drive rapid adaptation in yeast

Polyploidy is observed across the tree of life, yet its influence on evolution remains incompletely understood1–4. Polyploidy, usually whole genome duplication (WGD), is proposed to alter the rate of evolutionary adaptation. This could occur through complex effects on the frequency or fitness of beneficial mutations 2,5–7. For example, in diverse cell types and organisms, immediately after a WGD, newly formed polyploids missegregate chromosomes and undergo genetic instability8–13. The instability following WGDs is thought to provide adaptive mutations in microorganisms13,14 and can promote tumorigenesis in mammalian cells11,15. Polyploidy may also affect adaptation independent of beneficial mutations through ploidy-specific changes in cell physiology16. Here, we performed in vitro evolution experiments to directly test whether polyploidy can accelerate evolutionary adaptation. Compared to haploids and diploids, tetraploids underwent significantly faster adaptation. Mathematical modeling suggested that rapid adaptation of tetraploids was driven by higher rates of beneficial mutations with stronger fitness effects, which was supported by whole-genome sequencing and phenotypic analyses of evolved clones. Chromosome aneuploidy, concerted chromosome loss, and point mutations all provided large fitness gains. We identified several mutations whose beneficial effects were manifest specifically in the tetraploid strains. Together, these results provide direct quantitative evidence that in some environments polyploidy can accelerate evolutionary adaptation

Polymorphism Data Can Reveal the Origin of Species Abundance Statistics

What is the underlying mechanism behind the fat-tailed statistics observed for species abundance distributions? The two main hypotheses in the field are the adaptive (niche) theories, where species abundance reflects its fitness, and the neutral theory that assumes demographic stochasticity as the main factor determining community structure. Both explanations suggest quite similar species-abundance distributions, but very different histories: niche scenarios assume that a species population in the past was similar to the observed one, while neutral scenarios are characterized by strongly fluctuating populations. Since the genetic variations within a population depend on its abundance in the past, we present here a way to discriminate between the theories using the genetic diversity of noncoding DNA. A statistical test, based on the Fu-Li method, has been developed and enables such a differentiation. We have analyzed the results gathered from individual-based simulation of both types of histories and obtained clear distinction between the Fu-Li statistics of the neutral scenario and that of the niche scenario. Our results suggest that data for 10–50 species, with approximately 30 sequenced individuals for each species, may allow one to distinguish between these two theories

Genome-wide data from medieval German Jews show that the Ashkenazi founder event pre-dated the 14th century

We report genome-wide data from 33 Ashkenazi Jews (AJ), dated to the 14th century, obtained following a salvage excavation at the medieval Jewish cemetery of Erfurt, Germany. The Erfurt individuals are genet-ically similar to modern AJ, but they show more variability in Eastern European-related ancestry than mod-ern AJ. A third of the Erfurt individuals carried a mitochondrial lineage common in modern AJ and eight carried pathogenic variants known to affect AJ today. These observations, together with high levels of runs of homozygosity, suggest that the Erfurt community had already experienced the major reduction in size that affected modern AJ. The Erfurt bottleneck was more severe, implying substructure in medieval AJ. Overall, our results suggest that the AJ founder event and the acquisition of the main sources of ancestry pre-dated the 14th century and highlight late medieval genetic heterogeneity no longer present in modern AJ.The study was funded by the Israel Science Foundation grant 407/17 and the United States-Israel Binational Science Foundation grant 2017024 to S.C., by the National Science Foundation (USA) grants 1912776 and 0922374 to V.R., by the MCIN/AEI/10.13039/501100011033 and by "ESF Investing in your future" grant "Ayudas para contratos Ramon y Cajal" to I.O., and by the following grants to D.R.: NIH grants GM100233 and HG012287; the Allen Discovery Center program, a Paul G. Allen Frontiers Group advised program of the Paul G. Allen Family Foundation; John Templeton Foundation grant 61220; a private gift from Jean-Francois Clin; and the Howard Hughes Medical Institute

Cell Lineage Analysis of the Mammalian Female Germline

Fundamental aspects of embryonic and post-natal development, including maintenance of the mammalian female germline, are largely unknown. Here we employ a retrospective, phylogenetic-based method for reconstructing cell lineage trees utilizing somatic mutations accumulated in microsatellites, to study female germline dynamics in mice. Reconstructed cell lineage trees can be used to estimate lineage relationships between different cell types, as well as cell depth (number of cell divisions since the zygote). We show that, in the reconstructed mouse cell lineage trees, oocytes form clusters that are separate from hematopoietic and mesenchymal stem cells, both in young and old mice, indicating that these populations belong to distinct lineages. Furthermore, while cumulus cells sampled from different ovarian follicles are distinctly clustered on the reconstructed trees, oocytes from the left and right ovaries are not, suggesting a mixing of their progenitor pools. We also observed an increase in oocyte depth with mouse age, which can be explained either by depth-guided selection of oocytes for ovulation or by post-natal renewal. Overall, our study sheds light on substantial novel aspects of female germline preservation and development