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Both mathematical models and biological model systems stand as tractable representations of complex biological systems or behaviors. They facilitate research and provide insights, and they can describe general rules. Models that represent biological processes or formalize general hypotheses are essential to any broad understanding. Mathematical or biological models necessarily omit details of the natural systems and thus may ultimately be "incorrect" representations. A key challenge is that tractability requires relatively simple models but simplification can result in models that are incorrect in their qualitative, broad implications if the abstracted details matter. Our paper discusses this tension, and how we can improve our inferences from models. We advocate for further efforts dedicated to model development, improvement, and acceptance by the scientific community, all of which may necessitate a more explicit discussion of the purpose and power of models. We argue that models should play a central role in reintegrating biology as a way to test our integrated understanding of how molecules, cells, organs, organisms, populations, and ecosystems function. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]