Analyzing Collective Motion with Machine Learning and Topology

We use topological data analysis and machine learning to study a seminal model of collective motion in biology [D'Orsogna et al., Phys. Rev. Lett. 96 (2006)]. This model describes agents interacting nonlinearly via attractive-repulsive social forces and gives rise to collective behaviors such as flocking and milling. To classify the emergent collective motion in a large library of numerical simulations and to recover model parameters from the simulation data, we apply machine learning techniques to two different types of input. First, we input time series of order parameters traditionally used in studies of collective motion. Second, we input measures based in topology that summarize the time-varying persistent homology of simulation data over multiple scales. This topological approach does not require prior knowledge of the expected patterns. For both unsupervised and supervised machine learning methods, the topological approach outperforms the one that is based on traditional order parameters.Comment: Published in Chaos 29, 123125 (2019), DOI: 10.1063/1.512549

Edaphic adaptation maintains the coexistence of two cryptic species on serpentine soil

• Premise of the study: Divergent edaphic adaptation can contribute to reproductive isolation and coexistence between closely related species, yet we know little about how small-scale continuous edaphic gradients contribute to this phenomenon. We investigated edaphic adaptation between two cryptic species of California wildflower, Lasthenia californica and L. gracilis (Asteraceae), which grow in close parapatry on serpentine soil. • Methods: We reciprocally transplanted both species into the center of each species’ habitat and the transition zone between species. We quantified multiple components of fitness and used aster models to predict fitness based on environmental variables. We sampled soil across the ridge throughout the growing season to document edaphic changes through time. We sampled naturally germinating seedlings to determine whether there was dispersal into the adjacent habitat and to help pinpoint the timing of any selection against migrants. • Key results: We documented within-serpentine adaptation contributing to habitat isolation between close relatives. Both species were adapted to the edaphic conditions in their native region and suffered fitness trade-offs when moved outside that region. However, observed fitness values did not perfectly match those predicted by edaphic variables alone, indicating that other factors, such as competition, also contributed to plant fitness. Soil water content and concentrations of calcium, magnesium, sodium, and potassium were likely drivers of differential fitness. Plants either had limited dispersal ability or migrants experienced early-season mortality outside their native region. • Conclusions: Demonstrating that continuous habitats can support differently adapted, yet closely related, taxa is important to a broader understanding of how species are generated and maintained in nature