Statistical Physics of Evolutionary Trajectories on Fitness Landscapes

Random walks on multidimensional nonlinear landscapes are of interest in many areas of science and engineering. In particular, properties of adaptive trajectories on fitness landscapes determine population fates and thus play a central role in evolutionary theory. The topography of fitness landscapes and its effect on evolutionary dynamics have been extensively studied in the literature. We will survey the current research knowledge in this field, focusing on a recently developed systematic approach to characterizing path lengths, mean first-passage times, and other statistics of the path ensemble. This approach, based on general techniques from statistical physics, is applicable to landscapes of arbitrary complexity and structure. It is especially well-suited to quantifying the diversity of stochastic trajectories and repeatability of evolutionary events. We demonstrate this methodology using a biophysical model of protein evolution that describes how proteins maintain stability while evolving new functions

BAYESIAN NONPARAMETRIC CROSS-STUDY VALIDATION OF PREDICTION METHODS

We consider comparisons of statistical learning algorithms using multiple data sets, via leave-one-in cross-study validation: each of the algorithms is trained on one data set; the resulting model is then validated on each remaining data set. This poses two statistical challenges that need to be addressed simultaneously. The first is the assessment of study heterogeneity, with the aim of identifying a subset of studies within which algorithm comparisons can be reliably carried out. The second is the comparison of algorithms using the ensemble of data sets. We address both problems by integrating clustering and model comparison. We formulate a Bayesian model for the array of cross-study validation statistics, which defines clusters of studies with similar properties and provides the basis for meaningful algorithm comparison in the presence of study heterogeneity. We illustrate our approach through simulations involving studies with varying severity of systematic errors, and in the context of medical prognosis for patients diagnosed with cancer, using high-throughput measurements of the transcriptional activity of the tumor’s genes

Machine and deep learning meet genome-scale metabolic modeling

Omic data analysis is steadily growing as a driver of basic and applied molecular biology research. Core to the interpretation of complex and heterogeneous biological phenotypes are computational approaches in the fields of statistics and machine learning. In parallel, constraint-based metabolic modeling has established itself as the main tool to investigate large-scale relationships between genotype, phenotype, and environment. The development and application of these methodological frameworks have occurred independently for the most part, whereas the potential of their integration for biological, biomedical, and biotechnological research is less known. Here, we describe how machine learning and constraint-based modeling can be combined, reviewing recent works at the intersection of both domains and discussing the mathematical and practical aspects involved. We overlap systematic classifications from both frameworks, making them accessible to nonexperts. Finally, we delineate potential future scenarios, propose new joint theoretical frameworks, and suggest concrete points of investigation for this joint subfield. A multiview approach merging experimental and knowledge-driven omic data through machine learning methods can incorporate key mechanistic information in an otherwise biologically-agnostic learning process

Methods and practice of detecting selection in human cancers

Cancer development and progression is an evolutionary process, understanding these evolutionary dynamics is important for treatment and diagnosis as how a cancer evolves determines its future prognosis. This thesis focuses on elucidating selective evolutionary pressures in cancers and somatic tissues using population genetics models and cancer genomics data. First a model for the expected diversity in the absence of selection was developed. This neutral model of evolution predicts that under neutrality the frequency of subclonal mutations is expected to follow a power law distribution. Surprisingly more than 30% of cancer across multiple cohorts fitted this model. The next part of the thesis develops models to explore the effects of selection given these should be observable as deviations from the neutral prediction. For this I developed two approaches. The first approach investigated selection at the level of individual samples and showed that a characteristic pattern of clusters of mutations is observed in deep sequencing experiments. Using a mathematical model, information encoded within these clusters can be used to measure the relative fitness of subclones and the time they emerge during tumour evolution. With this I observed strikingly high fitness advantages for subclones of above 20%. The second approach enables measuring recurrent patterns of selection in cohorts of sequenced cancers using dN/dS, the ratio of non-synonymous to synonymous mutations, a method originally developed for molecular species evolution. This approach demonstrates how selection coefficients can be extracted by combining measurements of dN/dS with the size of mutational lineages. With this approach selection coefficients were again observed to be strikingly high. Finally I looked at population dynamics in normal colonic tissue given that many mutations accumulate in physiologically normal tissue. I found that the current view of stem cell dynamics was unable to explain sequencing data from individual colonic crypts. Some new models were proposed that introduce a longer time scale evolution that suppresses the accumulation of mutations which appear consistent with the data

Inference of single-cell phylogenies from lineage tracing data using Cassiopeia.

The pairing of CRISPR/Cas9-based gene editing with massively parallel single-cell readouts now enables large-scale lineage tracing. However, the rapid growth in complexity of data from these assays has outpaced our ability to accurately infer phylogenetic relationships. First, we introduce Cassiopeia-a suite of scalable maximum parsimony approaches for tree reconstruction. Second, we provide a simulation framework for evaluating algorithms and exploring lineage tracer design principles. Finally, we generate the most complex experimental lineage tracing dataset to date, 34,557 human cells continuously traced over 15 generations, and use it for benchmarking phylogenetic inference approaches. We show that Cassiopeia outperforms traditional methods by several metrics and under a wide variety of parameter regimes, and provide insight into the principles for the design of improved Cas9-enabled recorders. Together, these should broadly enable large-scale mammalian lineage tracing efforts. Cassiopeia and its benchmarking resources are publicly available at www.github.com/YosefLab/Cassiopeia

OPENMENDEL: A Cooperative Programming Project for Statistical Genetics

Statistical methods for genomewide association studies (GWAS) continue to improve. However, the increasing volume and variety of genetic and genomic data make computational speed and ease of data manipulation mandatory in future software. In our view, a collaborative effort of statistical geneticists is required to develop open source software targeted to genetic epidemiology. Our attempt to meet this need is called the OPENMENDELproject (https://openmendel.github.io). It aims to (1) enable interactive and reproducible analyses with informative intermediate results, (2) scale to big data analytics, (3) embrace parallel and distributed computing, (4) adapt to rapid hardware evolution, (5) allow cloud computing, (6) allow integration of varied genetic data types, and (7) foster easy communication between clinicians, geneticists, statisticians, and computer scientists. This article reviews and makes recommendations to the genetic epidemiology community in the context of the OPENMENDEL project.Comment: 16 pages, 2 figures, 2 table

Unsupervised Machine Learning Algorithms to Characterize Single-Cell Heterogeneity and Perturbation Response

Recent advances in microfluidic technologies facilitate the measurement of gene expression, DNA accessibility, protein content, or genomic mutations at unprecedented scale. The challenges imposed by the scale of these datasets are further exacerbated by non-linearity in molecular effects, complex interdependencies between features, and a lack of understanding of both data generating processes and sources of technical and biological noise. As a result, analysis of modern single-cell data requires the development of specialized computational tools. One solution to these problems is the use of manifold learning, a sub-field of unsupervised machine learning that seeks to model data geometry using a simplifying assumption that the underlying system is continuous and locally Euclidean. In this dissertation, I show how manifold learning is naturally suited for single-cell analysis and introduce three related algorithms for characterization of single-cell heterogeneity and perturbation response. I first describe Vertex Frequency Clustering, an algorithm that identifies groups of cells with similar responses to an experiment perturbation by analyzing the spectral representation of condition labels expressed as signals over a cell similarity graph. Next, I introduce MELD, an algorithm that expands on these ideas to estimate the density of each experimental sample over the graph to quantify the effect of an experimental perturbation at single cell resolution. Finally, I describe a neural network for archetypal analysis that represents the data as continuously distributed between a set of extrema. Each of these algorithms are demonstrated on a combination of real and synthetic datasets and are benchmarked against state-of-the-art algorithms

IST Austria Thesis

Hybrid zones represent evolutionary laboratories, where recombination brings together alleles in combinations which have not previously been tested by selection. This provides an excellent opportunity to test the effect of molecular variation on fitness, and how this variation is able to spread through populations in a natural context. The snapdragon Antirrhinum majus is polymorphic in the wild for two loci controlling the distribution of yellow and magenta floral pigments. Where the yellow A. m. striatum and the magenta A. m. pseudomajus meet along a valley in the Spanish Pyrenees they form a stable hybrid zone Alleles at these loci recombine to give striking transgressive variation for flower colour. The sharp transition in phenotype over ~1km implies strong selection maintaining the hybrid zone. An indirect assay of pollinator visitation in the field found that pollinators forage in a positive-frequency dependent manner on Antirrhinum, matching previous data on fruit set. Experimental arrays and paternity analysis of wild-pollinated seeds demonstrated assortative mating for pigmentation alleles, and that pollinator behaviour alone is sufficient to explain this pattern. Selection by pollinators should be sufficiently strong to maintain the hybrid zone, although other mechanisms may be at work. At a broader scale I examined evolutionary transitions between yellow and anthocyanin pigmentation in the tribe Antirrhinae, and found that selection has acted strate that pollinators are a major determinant of reproductive success and mating patterns in wild Antirrhinum