Shape is data and data is shape. Biologists are accustomed to thinking about how the shape of biomolecules, cells, tissues, and organisms arise from the effects of genetics, development, and the environment. Less often do we consider that data itself has shape and structure, or that it is possible to measure the shape of data and analyze it. Here, we review applications of topological data analysis (TDA) to biology in a way accessible to biologists and applied mathematicians alike. TDA uses principles from algebraic topology to comprehensively measure shape in data sets. Using a function that relates the similarity of data points to each other, we can monitor the evolution of topological features—connected components, loops, and voids. This evolution, a topological signature, concisely summarizes large, complex data sets. We first provide a TDA primer for biologists before exploring the use of TDA across biological sub‐disciplines, spanning structural biology, molecular biology, evolution, and development. We end by comparing and contrasting different TDA approaches and the potential for their use in biology. The vision of TDA, that data are shape and shape is data, will be relevant as biology transitions into a data‐driven era where the meaningful interpretation of large data sets is a limiting factor.

The field of plant science has grown dramatically in the past two decades, but global disparities and systemic inequalities persist. Here, we analyzed ~300,000 papers published over the past two decades to quantify disparities across nations, genders, and taxonomy in the plant science literature. Our analyses reveal striking geographical biases—affluent nations dominate the publishing landscape and vast areas of the globe have virtually no footprint in the literature. Authors in Northern America are cited nearly twice as many times as authors based in Sub-Saharan Africa and Latin America, despite publishing in journals with similar impact factors. Gender imbalances are similarly stark and show remarkably little improvement over time. Some of the most affluent nations have extremely male biased publication records, despite supposed improvements in gender equality. In addition, we find that most studies focus on economically important crop and model species, and a wealth of biodiversity is underrepresented in the literature. Taken together, our analyses reveal a problematic system of publication, with persistent imbalances that poorly capture the global wealth of scientific knowledge and biological diversity. We conclude by highlighting disparities that can be addressed immediately and offer suggestions for long-term solutions to improve equity in the plant sciences.

Shape plays a fundamental role in biology. Traditional phenotypic analysis methods measure some features but fail to measure the information embedded in shape comprehensively. To extract, compare, and analyze this information embedded in a robust and concise way, we turn to Topological Data Analysis (TDA), specifically the Euler Characteristic Transform. TDA measures shape comprehensively using mathematical representations based on algebraic topology features. To study its use, we compute both traditional and topological shape descriptors to quantify the morphology of 3121 barley seeds scanned with X-ray Computed Tomography (CT) technology at 127 micron resolution. The Euler Characteristic Transform measures shape by analyzing topological features of an object at thresholds across a number of directional axes. A Kruskal-Wallis analysis of the information encoded by the topological signature reveals that the Euler Characteristic Transform picks up successfully the shape of the crease and bottom of the seeds. Moreover, while traditional shape descriptors can cluster the seeds based on their accession, topological shape descriptors can cluster them further based on their panicle. We then successfully train a support vector machine (SVM) to classify 28 different accessions of barley based exclusively on the shape of their grains. We observe that combining both traditional and topological descriptors classifies barley seeds better than using just traditional descriptors alone. This improvement suggests that TDA is thus a powerful complement to traditional morphometrics to comprehensively describe a multitude of “hidden” shape nuances which are otherwise not detected.

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The field of plant science has grown dramatically in the past two decades, but global disparities and systemic inequalities persist. Here, we analyzed ~300,000 papers published over the past two decades to quantify disparities across nations, genders, and taxonomy in the plant science literature. Our analyses reveal striking geographical biases, where affluent nations dominate the publishing landscape and vast areas of the globe have virtually no footprint in the literature. Authors in Northern America are cited nearly twice as many times as authors based in Sub-Saharan Africa and Latin America, despite publishing in journals with similar impact factors. Gender imbalances show remarkably little improvement over time, and some of the most affluent nations have extremely male biased publication records, despite supposed improvements in gender equality. In addition we find that most studies focus on economically important crop and model species and a wealth of biodiversity is under-represented in the literature. Taken together, our analyses reveal a problematic system of publication, with persistent bias that poorly captures the global wealth of scientific knowledge and biological diversity. We conclude by highlighting immediately addressable disparities and suggestions for long-term solutions to improve equity in the plant sciences.