Richard A. Watson,  Michael Levin,  Tim Lewens`

Interface Focus (2025) 15 (6): 20250025 .

It is conventionally assumed that all evolutionary adaptation is produced, and could only possibly be produced, by natural selection. Natural induction is a different mechanism of adaptation. It occurs in dynamical systems described by a network of interactions, where connections give way slightly under stress and the system is subject to occasional perturbations. This differential adjustment of connections causes reorganization of the system’s internal structure in a manner equivalent to associative learning familiar in neural networks. This is sufficient for storage and recall of multiple patterns, learning with generalization and solving difficult constraint problems (without any natural selection involved). Various biological systems (from gene-regulation networks to metabolic networks to ecosystems) meet these basic conditions and therefore have potential to exhibit adaptation by natural induction. Here (and in a follow-on paper), we consider various ways that natural induction and natural selection might interact in biological evolution. For example, in some cases, natural selection may act not as a source of adaptations but as a memory of adaptations discovered by natural induction. We conclude that evolution by natural induction is a viable process that expands our understanding of evolutionary adaptation.

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Amahury J. López-Díaz, Pedro Juan Rivera Torres, Gerardo L. Febres, Carlos Gershenson

Discrete dynamical models underpin systems biology, but we still lack substrate-agnostic diagnostics for when such models can sustain genuinely open-ended evolution (OEE): the continual production of novel phenotypes rather than eventual settling. We introduce a simple, model-independent metric, {\Omega}, that quantifies OEE as the residence-time-weighted contribution of each attractor’s cycle length across the sequence of attractors realized over time. {\Omega} is zero for single-attractor dynamics and grows with the number and persistence of distinct cyclic phenotypes, separating enduring innovation from transient noise. Using Random Boolean Networks (RBNs) as a unifying testbed, we compare classical Boolean dynamics with biologically motivated non-classical mechanisms (probabilistic context switching, annealed rule mutation, paraconsistent logic, modal necessary/possible gating, and quantum-inspired superposition/entanglement) under homogeneous and heterogeneous updating schemes. Our results support the view that undecidability-adjacent, state-dependent mechanisms — implemented as contextual switching, conditional necessity/possibility, controlled contradictions, or correlated branching — are enabling conditions for sustained novelty. At the end of our manuscript we outline a practical extension of {\Omega} to continuous/hybrid state spaces, positioning {\Omega} as a portable benchmark for OEE in discrete biological modeling and a guide for engineering evolvable synthetic circuits.

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Alberto Aleta, Andreia Sofia Teixeira, Guilherme Ferraz de Arruda, Andrea Baronchelli, Alain Barrat, János Kertész, Albert Díaz-Guilera, Oriol Artime, Michele Starnini, Giovanni Petri, Márton Karsai, Siddharth Patwardhan, Alessandro Vespignani, Yamir Moreno, Santo Fortunato

Multilayer network science has emerged as a central framework for analysing interconnected and interdependent complex systems. Its relevance has grown substantially with the increasing availability of rich, heterogeneous data, which makes it possible to uncover and exploit the inherently multilayered organisation of many real-world networks. In this review, we summarise recent developments in the field. On the theoretical and methodological front, we outline core concepts and survey advances in community detection, dynamical processes, temporal networks, higher-order interactions, and machine-learning-based approaches. On the application side, we discuss progress across diverse domains, including interdependent infrastructures, spreading dynamics, computational social science, economic and financial systems, ecological and climate networks, science-of-science studies, network medicine, and network neuroscience. We conclude with a forward-looking perspective, emphasizing the need for standardized datasets and software, deeper integration of temporal and higher-order structures, and a transition toward genuinely predictive models of complex systems.

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