Charting a New Frontier Integrating Mathematical Modeling in Complex Biological Systems from Molecules to Ecosystems.

Advances in quantitative biology data collection and analysis across scales (molecular, cellular, organismal, and ecological) have transformed how we understand, categorize, and predict complex biological systems. This surge of quantitative data creates an opportunity to apply, develop, and evaluate mathematical models of biological systems and explore novel methods of analysis. Simultaneously, thanks to increased computational power, mathematicians, engineers and physical scientists have developed sophisticated models of biological systems at different scales. Novel modeling schemes can offer deeper understanding of principles in biology, but there is still a disconnect between modeling and experimental biology that limits our ability to fully realize the integration of mathematical modeling and biology. In this work, we explore the urgent need to expand the use of existing mathematical models across biological scales, develop models that are robust to biological heterogeneity, harness feedback loops within the iterative modeling process, and nurture a cultural shift towards interdisciplinary and cross-field interactions. Better integration of biological experimentation and robust mathematical modeling will transform our ability to understand and predict complex biological systems.

Understanding Drivers of Variation and Predicting Variability Across Levels of Biological Organization.

Differences within a biological system are ubiquitous, creating variation in nature. Variation underlies all evolutionary processes and allows persistence and resilience in changing environments; thus, uncovering the drivers of variation is critical. The growing recognition that variation is central to biology presents a timely opportunity for determining unifying principles that drive variation across biological levels of organization. Currently, most studies that consider variation are focused at a single biological level and not integrated into a broader perspective. Here we explain what variation is and how it can be measured. We then discuss the importance of variation in natural systems, and briefly describe the biological research that has focused on variation. We outline some of the barriers and solutions to studying variation and its drivers in biological systems. Finally, we detail the challenges and opportunities that may arise when studying the drivers of variation due to the multi-level nature of biological systems. Examining the drivers of variation will lead to a reintegration of biology. It will further forge interdisciplinary collaborations and open opportunities for training diverse quantitative biologists. We anticipate that these insights will inspire new questions and new analytic tools to study the fundamental questions of what drives variation in biological systems and how variation has shaped life.

Movement, demographics, and occupancy dynamics of a federally-threatened salamander: evaluating the adequacy of critical habitat.

Critical habitat for many species is often limited to occupied localities. For rare and cryptic species, or those lacking sufficient data, occupied habitats may go unrecognized, potentially hindering species recovery. Proposed critical habitat for the aquatic Jollyville Plateau salamander (Eurycea tonkawae) and two sister species were delineated based on the assumption that surface habitat is restricted to springs and excludes intervening stream reaches. To test this assumption, we performed two studies to understand aspects of individual, population, and metapopulation ecology of E. tonkawae. First, we examined movement and population demographics using capture-recapture along a spring-influenced stream reach. We then extended our investigation of stream habitat use with a study of occupancy and habitat dynamics in multiple headwater streams. Indications of extensive stream channel use based on capture-recapture results included frequent movements of >15 m, and high juvenile abundance downstream of the spring. Initial occupancy of E. tonkawae was associated with shallow depths, maidenhair fern presence and low temperature variation (indicative of groundwater influence), although many occupied sites were far from known springs. Additionally, previously dry sites were three times more likely to be colonized than wet sites. Our results indicate extensive use of stream habitats, including intermittent ones, by E. tonkawae. These areas may be important for maintaining population connectivity or even as primary habitat patches. Restricting critical habitat to occupied sites will result in a mismatch with actual habitat use, particularly when assumptions of habitat use are untested, thus limiting the potential for recovery.