Beyond networks: Toward adaptive models of biological complexity.

Network science models have transformed our understanding of complex systems across biology, technology, and society, proving valuable in neuroscience. However, modeling biological complexity poses specific challenges, calling for expansions of traditional network frameworks. This paper explores constructive ways to enhance models, highlighting opportunities such as incorporating time-varying connections, adaptive topologies, and multilayer structures to better represent the temporal dynamics and multilevel interactions characteristic of biological systems. Additionally, it addresses deeper conceptual challenges, notably the substantial context dependence, open-endedness, and history sensitivity often observed in biology. By reviewing concepts such as Kauffman's "adjacent possible," the discussion emphasizes how biological state spaces themselves may dynamically evolve, suggesting the need for modeling strategies beyond static or pre-specified assumptions. Rather than undermining network science, these considerations highlight areas where traditional formalisms can fruitfully adapt and grow, ultimately deepening their explanatory power. The paper advocates integrating data-driven approaches that dynamically infer system properties from empirical observations, balancing modeling generality with biological specificity. Overall, this synthesis provides an assessment of both the strengths of network science and the challenges it faces, proposing constructive avenues for methodological and conceptual innovation that advance our ability to capture the nuanced complexity inherent in biological phenomena.