Self-organized pattern behavior is ubiquitous throughout nature, from fish schooling to collective cell dynamics during organism development. Qualitatively these patterns display impressive consistency, yet variability inevitably exists within pattern-forming systems on both microscopic and macroscopic scales. Quantifying variability and measuring pattern features can inform the underlying agent interactions and allow for predictive analyses. Nevertheless, current methods for analyzing patterns that arise from collective behavior capture only macroscopic features or rely on either manual inspection or smoothing algorithms that lose the underlying agent-based nature of the data. Here we introduce methods based on topological data analysis and interpretable machine learning for quantifying both agent-level features and global pattern attributes on a large scale. Because the zebrafish is a model organism for skin pattern formation, we focus specifically on analyzing its skin patterns as a means of illustrating our approach. Using a recent agent-based model, we simulate thousands of wild-type and mutant zebrafish patterns and apply our methodology to better understand pattern variability in zebrafish. Our methodology is able to quantify the differential impact of stochasticity in cell interactions on wild-type and mutant patterns, and we use our methods to predict stripe and spot statistics as a function of varying cellular communication. Our work provides an approach to automatically quantifying biological patterns and analyzing agent-based dynamics so that we can now answer critical questions in pattern formation at a much larger scale.

Accurate estimation of recombination rates is critical for studying the origins and maintenance of genetic diversity. Because the inference of recombination rates under a full evolutionary model is computationally expensive, an alternative approach using topological data analysis (TDA) on genome sequences has been developed. We find that this method can analyze datasets larger than what can be handled by any existing recombination inference software, and has accuracy comparable to commonly used model-based methods with significantly less processing time. Previous TDA methods used information contained solely in the first Betti number (β₁) of a set of genomes, which aims to capture the number of loops that can be detected within a genealogy. These explorations have proven difficult to connect to the theory of the underlying biological process of recombination, and consequently have unpredictable behavior under perturbations of the data. We introduce a new topological feature with a natural connection to coalescent models, which we call ψ, and present novel arguments relating β₁ to population genetic models. Using simulations, we show that ψ and β₁ are differentially affected by missing data, and package our approach as TREE (Topological Recombination Estimator). TREE9s efficiency and accuracy make it well suited as a first-pass estimator of recombination rate heterogeneity or hotspots throughout the genome. Our work empirically and theoretically justifies the use of topological statistics as summaries of genome sequences and describes a new, unintuitive relationship between topological features of the distribution of sequence data and the footprint of recombination on genomes.

McGuirl et al. present a new method, Ward clustering to identify Internal Node branch length outliers using Gene Scores (WINGS), for identifying shared genetic architecture among multiple phenotypes. Past research... Emerging large-scale biobanks pairing genotype data with phenotype data present new opportunities to prioritize shared genetic associations across multiple phenotypes for molecular validation. Past research, by our group and others, has shown gene-level tests of association produce biologically interpretable characterization of the genetic architecture of a given phenotype. Here, we present a new method, Ward clustering to identify Internal Node branch length outliers using Gene Scores (WINGS), for identifying shared genetic architecture among multiple phenotypes. The objective of WINGS is to identify groups of phenotypes, or “clusters,” sharing a core set of genes enriched for mutations in cases. We validate WINGS using extensive simulation studies and then combine gene-level association tests with WINGS to identify shared genetic architecture among 81 case-control and seven quantitative phenotypes in 349,468 European-ancestry individuals from the UK Biobank. We identify eight prioritized phenotype clusters and recover multiple published gene-level associations within prioritized clusters.

Single-photon emission computed tomography images of murine tumors are interpreted as the values of functions on a three-dimensional domain. Motivated by Morse theory, the local maxima of the tumor image functions are analyzed. This analysis captures tumor heterogeneity that cannot be identified with standard measures. Utilizing decreasing sequences of uptake values to filter the images, a modified form of the standard persistence diagrams for 0-dimensional persistent homology as well as novel childhood diagrams are constructed. Applying statistical methods to time series of persistence and childhood diagrams detects heterogeneous uptake of radioactive antibody within tumors over time and distinguishes uptake in two groups of mice injected with different labeled antibodies.

Accurate estimation of recombination rates is critical for studying the origins and maintenance of genetic diversity. Because the inference of recombination rates under a full evolutionary model is computationally expensive, an alternative approach using topological data analysis (TDA) has been proposed. Previous TDA methods used information contained solely in the first Betti number ( β ₁ )of the cloud of genomes, which relates to the number of loops that can be detected within a genealogy. While these methods are considerably less computationally intensive than current biological model-based methods, these explorations have proven difficult to connect to the theory of the underlying biological process of recombination, and consequently have unpredictable behavior under different perturbations of the data. We introduce a new topological feature with a natural connection to coalescent models, which we call ψ . We show that ψ and β ₁ are differentially affected by changes to the structure of the data and use them in conjunction to provide a robust, efficient, and accurate estimator of recombination rates, TREE. Compared to previous TDA methods, TREE more closely approximates of the results of commonly used model-based methods. These characteristics make TREE well suited as a first-pass estimator of recombination rate heterogeneity or hotspots throughout the genome. In addition, we present novel arguments relating β ₁ to population genetic models; our work justifies the use of topological statistics as summaries of distributions of genome sequences and describes a new, unintuitive relationship between topological summaries of distance and the footprint of recombination on genome sequences.