arXiv subjects

Tim Rogers

Publications and source records attributed to Tim Rogers.

At least 19 recordsLinked to original sources

arXiv2026

Extinction drives emergent metastability in complex ecosystems

Extinction is inevitable; every species eventually dies out, impacting the ecosystem it is part of. Over the past few decades, extensive research stemming from the stability-diversity debate has addressed how species diversity contributes to the stability of large ecosystems. However, conventional stability criteria often rely on deterministic frameworks, overlooking the intrinsic population fluctuations that allow any species to go extinct by chance. In this paper, we incorporate demographic stochasticity into large complex ecosystems with a rule-based model. We demonstrate that such demographic fluctuations rapidly prune the low-abundance species from the ecological community, thereby securing higher systemic stability. By developing a bottom-up theory to characterise the statistics of extinction dynamics, we discover that the fraction of surviving species exhibits an anomalous heavy-tailed decay over time, revealing the emergence of remnant communities with robust metastability. Our results highlight that when demographic fluctuations are accounted for, ecosystems self-stabilise by reducing their diversity even when they are predicted to be chaotic in the deterministic limit.

q-bio.PE↗

arXiv2026

Evolutionary path dependence of semantic complexity

Attempts to quantify biological complexity often consider intrinsic structural properties at a chosen hierarchical level and resolution, such as counts of body parts and their degree of differentiation. These measures are inherently \emph{syntactic}, being concerned with the information needed to specify an arrangement rather than the biological functions performed. Syntactic complexity alone is therefore not sophisticated enough of a measure to fully address the role of complexity as either a driver or consequence of evolution. We propose to study the counterpart, \emph{semantic} complexity: the subset of structural features whose variation has a measurable effect on organismal fitness. We illustrate this distinction in a simple mathematical model of tagmosis with functional constraints, symmetry breaking, and specialisation. We find that the total syntactic complexity evolved as selection drives lineages toward globally optimal fitness is path-dependent, revealing two evolutionary modes: a driven mode, in which semantic and syntactic complexity rise together, and an entropic mode, in which syntactic complexity drifts upward under a near-neutral evolution. Historical contingencies in early specialisation, combined with multi-optima fitness landscapes, govern how long lineages stay in each mode. Those on paths that do not lead directly to the highest-fitness states remain in the driven mode for longer and can eventually reach comparable fitness, but only by evolving morphologies with greater syntactic complexity.

q-bio.PE↗

arXiv2026

Emergence of polymorphism in stochastic evolutionary games

Deterministic evolutionary game theory makes no distinction between a monomorphic population of individuals all of whom share a mixed evolutionarily stable strategy and a polymorphic population of players of pure strategies present in a ratio that reproduces the mixed strategy on average. The so-called trembling hand hypothesis posits that in finite populations demographic noise selects for monomorphism, however, simulation studies have found contradictory results in some situations. Here we resolve this discrepancy by conducting a theoretical analysis of the paradigmatic Hawk-Dove game using timescale separation. We characterise the emergence of polymorphism driven by stochastic effects, finding long-lasting polymorphic states in certain conditions.

q-bio.PE↗

arXiv2026

Balancing innovation and assimilation in research communities

It has been statistically observed that the speed at which a corpus of knowledge advances does not scale linearly with quantities like the number of active researchers or number of research papers published in a given field. Furthermore, as a body of knowledge grows, individual researchers must somehow strike the right balance between generating new knowledge through innovation and assimilating knowledge generated by others. Here, we propose and analyse a pair of interacting particle system models representing some stylised features of the advancement of knowledge in a research community, captured as a stochastic travelling wave in knowledge space. Both particle systems exhibit a diminishing return in the knowledge advancement speed as research communities grow larger, and suggest that researchers should spend more time on assimilation of knowledge than innovation as their research community grows.

physics.soc-ph↗

arXiv2026

Fundamental Limits of Stability Inference in High-Dimensional Complex Systems

Many complex systems, including ecosystems, neural circuits, and financial markets, are inferred to operate close to a threshold of instability, at which a small perturbation can propagate across the entire system. This proximity is often interpreted as functionally advantageous, yet it poses a question common to all these fields: from a finite, noisy recording, how precisely can the distance of a system from that threshold be estimated? Using the multivariate Ornstein-Uhlenbeck process as the canonical linear model of relaxation near a stable fixed point, we show that the attainable precision is governed by three factors: an effective measurement budget, set by the number of samples relative to the system dimension and the sampling interval; the signal-to-noise ratio, given by the magnitude of deterministic interactions relative to stochastic forcing; and the distance to criticality, which simultaneously sets the system's correlation times and degrades both of the preceding factors. As the slowest dynamical mode softens near the threshold, the curvature of the log-likelihood flattens along the direction that determines stability, so that the relative uncertainty on the estimated distance diverges as that distance vanishes. Critically, temporal correlations near instability reduce the effective number of independent observations far below the nominal sample count, and inference breaks down when this effective count falls below the system dimension, even when the raw data volume appears sufficient. A direct consequence is the existence of an optimal sampling interval that diverges as the system approaches criticality, with practical implications for experimental design.

cond-mat.dis-nn↗

arXiv2026

Local density of states distribution and multifractal eigenvectors of weighted random networks via the cavity approach

We study the local density of states (LDoS) distribution of a general class of weighted Erd\H{o}s-R\'enyi graphs. Using the cavity method, we obtain a good approximation to the full LDoS distribution and compact expressions for its power-law tails, which we show to have exponent $3$ in the extended phase. We deduce that the eigenvectors in the continuous part of the spectrum are extended but (weakly) multifractal, and we extract expressions for the associated fractal dimensions and the singularity spectrum. We also demonstrate that the inverse participation ratio in this multifractal phase exhibits an unusual logarithmic scaling with system size, which is neither fully-extended nor localised by the usual definitions. Finally, we verify that some symmetry properties (derived from the non-linear sigma model), which have been shown to hold for many systems exhibiting multifractality, also hold in our case, both for the LDoS distribution and the singularity spectrum.

cond-mat.dis-nn↗

arXiv2026

Slow evolution towards generalism in a model of variable dietary range

Species sharing a habitat will co-evolve to make use of the available resources, as consumption is modulated by competition and negative feedback loops between consumers and resources. The dietary range of a given species determines the resources it has access to and thus the other species with which it competes. A narrow dietary range avoids competition at the cost of over-reliance on a small selection of resources; conversely a wide dietary range provides more alternatives but also more chance of competition with other species. Here, we investigate the evolution of dietary range within a mathematical model of niche formation. We find highly path dependent co-evolution dynamics characterised by long-lived quasi-stable states. Ultimately, stochastic effects drive the evolution of generalist diets, as we uncover in our analysis and simulations.

q-bio.PE↗

arXiv2026

Predicting oscillations in complex networks with delayed feedback

Oscillatory dynamics are common features of complex networks, often playing essential roles in regulating function. Across scales from gene regulatory networks to ecosystems, delayed feedback mechanisms are key drivers of system-scale oscillations. The analysis and prediction of such dynamics are highly challenging, however, due to the combination of high-dimensionality, non-linearity and delay. Here, we systematically investigate how structural complexity and delayed feedback jointly induce oscillatory dynamics in complex systems, and introduce an analytic framework comprising theoretical dimension reduction and data-driven prediction. We reveal that oscillations emerge from the interplay of structural complexity and delay, with reduced models uncovering their critical thresholds and showing that greater connectivity lowers the delay required for their onset. Our theory is empirically tested in an experiment on a programmable electronic circuit, where oscillations are observed once structural complexity and feedback delay exceeded the critical thresholds predicted by our theory. Finally, we deploy a reservoir computing pipeline to accurately predict the onset of oscillations directly from timeseries data. Our findings deepen understanding of oscillatory regulation and offer new avenues for predicting dynamics in complex networks.

cond-mat.dis-nn↗

arXiv2025

Origins of Instability in Dynamical Systems on Undirected Networks

Robustness to perturbation is a key topic in the study of complex systems occurring across a wide variety of applications from epidemiology to biochemistry. Here we analyze the eigenspectrum of the Jacobian matrices associated to a general class of networked dynamical systems, which contains information on how perturbations to a stationary state develop over time. We find that stability is always determined by a spectral outlier, but with pronounced differences to the corresponding eigenvector in different regimes. We show that, depending on model details, instability may originate in nodes of anomalously low or high degree, or may occur everywhere in the network at once. Importantly, the dependence on extremal degrees results in considerable finite-size effects with different scaling depending on the ensemble degree distribution. Our results have potentially useful applications in network monitoring to predict or prevent catastrophic failures, and we validate our analytical findings through applications to epidemic dynamics and gene regulatory systems.

nlin.AO↗

arXiv2025

Misaligned from Within: Large Language Models Reproduce Our Double-Loop Learning Blindness

This paper examines a critical yet unexplored dimension of the AI alignment problem: the potential for Large Language Models (LLMs) to inherit and amplify existing misalignments between human espoused theories and theories-in-use. Drawing on action science research, we argue that LLMs trained on human-generated text likely absorb and reproduce Model 1 theories-in-use - a defensive reasoning pattern that both inhibits learning and creates ongoing anti-learning dynamics at the dyad, group, and organisational levels. Through a detailed case study of an LLM acting as an HR consultant, we show how its advice, while superficially professional, systematically reinforces unproductive problem-solving approaches and blocks pathways to deeper organisational learning. This represents a specific instance of the alignment problem where the AI system successfully mirrors human behaviour but inherits our cognitive blind spots. This poses particular risks if LLMs are integrated into organisational decision-making processes, potentially entrenching anti-learning practices while lending authority to them. The paper concludes by exploring the possibility of developing LLMs capable of facilitating Model 2 learning - a more productive theory-in-use - and suggests this effort could advance both AI alignment research and action science practice. This analysis reveals an unexpected symmetry in the alignment challenge: the process of developing AI systems properly aligned with human values could yield tools that help humans themselves better embody those same values.

cs.HC↗

arXiv2025

The Brownian marble

Let $R:(0,\infty) \to [0,\infty)$ be a measurable function. Consider coalescing Brownian motions started from every point in the subset $\{ (0,x) : x \in \mathbb{R} \}$ of $[0,\infty) \times \mathbb{R}$ (with $[0,\infty)$ denoting time and $\mathbb{R}$ denoting space) and proceeding according to the following rule: the interval $\{t\} \times [L_t,U_t]$ between two consecutive Brownian motions instantaneously fragments' at rate $R(U_t - L_t)$. At a fragmentation event at a time $t$, we initiate new coalescing Brownian motions from each of the points $\{ (t,x) : x \in [L_t,U_t]\}$. The resulting process, which we call the $R$-marble, is easily constructed when $R$ is bounded, and may be considered a random subset of the Brownian web. Under mild conditions, we show that it is possible to construct the $R$-marble when $R$ is unbounded as a limit as $n \to \infty$ of $R_n$-marbles where $R_n(g) = R(g) \wedge n$. The behaviour of this limiting process is mainly determined by the shape of $R$ near zero. The most interesting case occurs when the limit $\lim_{g \downarrow 0} g^2 R(g) = \lambda$ exists in $(0,\infty)$, in which case we find a phase transition. For $\lambda \geq 6$, the limiting object is indistinguishable from the Brownian web, whereas if $\lambda < 6$, then the limiting object is a nontrivial stochastic process with large gaps. When $R(g) = \lambda/g^2$, the $R$-marble is a self-similar stochastic process which we refer to as the \emph{Brownian marble with parameter $\lambda > 0$}. We give an explicit description of the spacetime correlations of the Brownian marble, which can be described in terms of an object we call the Brownian vein; a spatial version of a recurrent extension of a killed Bessel-$3$ process.

math.PR↗

arXiv2025

Percolation and localisation: Sub-leading eigenvalues of the nonbacktracking matrix

The spectrum of the nonbacktracking matrix associated to a network is known to contain fundamental information regarding percolation properties of the network. Indeed, the inverse of its leading eigenvalue is often used as an estimate for the percolation threshold. However, for many networks with nonbacktracking centrality localised on a few nodes, such as networks with a core-periphery structure, this spectral approach badly underestimates the threshold. In this work, we study networks that exhibit this localisation effect by looking beyond the leading eigenvalue and searching deeper into the spectrum of the nonbacktracking matrix. We identify that, when localisation is present, the threshold often more closely aligns with the inverse of one of the sub-leading real eigenvalues: the largest real eigenvalue with a "delocalised" corresponding eigenvector. We investigate a core-periphery network model and determine, both theoretically and experimentally, a regime of parameters for which our approach closely approximates the threshold, while the estimate derived using the leading eigenvalue does not. We further present experimental results on large scale real-world networks that showcase the usefulness of our approach.

physics.soc-ph↗

arXiv2025

An iterative spectral algorithm for digraph clustering

Graph clustering is a fundamental technique in data analysis with applications in many different fields. While there is a large body of work on clustering undirected graphs, the problem of clustering directed graphs is much less understood. The analysis is more complex in the directed graph case for two reasons: the clustering must preserve directional information in the relationships between clusters, and directed graphs have non-Hermitian adjacency matrices whose properties are less conducive to traditional spectral methods. Here we consider the problem of partitioning the vertex set of a directed graph into $k\ge 2$ clusters so that edges between different clusters tend to follow the same direction. We present an iterative algorithm based on spectral methods applied to new Hermitian representations of directed graphs. Our algorithm performs favourably against the state-of-the-art, both on synthetic and real-world data sets. Additionally, it is able to identify a "meta-graph" of $k$ vertices that represents the higher-order relations between clusters in a directed graph. We showcase this capability on data sets pertaining food webs, biological neural networks, and the online card game Hearthstone.

physics.soc-ph↗

arXiv2024

Speed and shape of population fronts with density-dependent diffusion

We investigate travelling wave solutions in reaction-diffusion models of animal range expansion in the case that population diffusion is density-dependent. We find that the speed of the selected wave depends critically on the strength of diffusion at low density. For sufficiently large low-density diffusion, the wave propagates at a speed predicted by a simple linear analysis. For small or zero low-density diffusion, the linear analysis is not sufficient, but a variational approach yields exact or approximate expressions for the speed and shape of population fronts.

q-bio.PE↗

arXiv2023

Stay in your lane: Density fluctuations in multi-lane traffic

When a new vehicle joins a lane, those behind may have to temporarily slow to accommodate them. Changing lane can be forced due to lane drops or junctions, but may also take place spontaneously at discretion of drivers, and recent studies have found that traffic jams and traffic oscillations can form even without such bottlenecks. Understanding how lane changing behaviour affects traffic flow is important for learning how to design roads and control traffic more effectively. Here, we present a stochastic model of spontaneous lane changing which exhibits a reduction in the overall flow of traffic. By examining the average flow rate both analytically and through simulations we find a definitive slow down of vehicles due to random switching between lanes. By extending the model to three lane traffic we find a larger impact on the flow of the middle lane compared to the side lanes.

physics.soc-ph↗

arXiv2023

Binary synchronization of noise-coupled oscillators

After decades of study, there are only two known mechanisms to induce global synchronization in a population of oscillators: deterministic coupling and common forcing. The inclusion of independent random forcing in these models typically serves to drive disorder, increasing the stability of the incoherent state. Here we show that the reverse is also possible. We propose and analyse a simple model of purely noise coupled oscillators whose linear response around incoherence is identical to that of the paradigmatic Kuramoto model, but which exhibits binary phase locking instead of full coherence. We characterise the phase diagram, stationary states and approximate low dimensional dynamics for the model, revealing the curious behaviour of this new mechanism of synchronization.

nlin.AO↗

arXiv2023

Assisted percolation of slow-spreading mutants in heterogeneous environments

Environmental heterogeneity can drive genetic heterogeneity in expanding populations; mutant strains may emerge that trade overall growth rate for an improved ability to survive in patches that are hostile to the wild type. This evolutionary dynamic is of practical importance when seeking to prevent the emergence of damaging traits. We show that a sub-critical slow-spreading mutant can attain dominance even when the density of patches is below their percolation threshold and predict this transition using geometrical arguments. This work demonstrates a phenomenon of ''assisted percolation'', where one sub-critical process assists another to achieve super-criticality.

q-bio.PE↗

arXiv2022

Stochastic drift in discrete waves of non-locally interacting-particles

In this paper, we investigate a generalised model of $N$ particles undergoing second-order non-local interactions on a lattice. Our results have applications across many research areas, including the modelling of migration, information dynamics and Muller's ratchet -- the irreversible accumulation of deleterious mutations in an evolving population. Strikingly, numerical simulations of the model are observed to deviate significantly from its mean-field approximation even for large population sizes. We show that the disagreement between deterministic and stochastic solutions stems from finite-size effects that change the propagation speed and cause the position of the wave to fluctuate. These effects are shown to decay anomalously as $(\log N)^{-2}$ and $(\log N)^{-3}$, respectively -- much slower than the usual $N^{-1/2}$ factor. Our results suggest that the accumulation of deleterious mutations in a Muller's ratchet and the loss of awareness in a population may occur much faster than predicted by the corresponding deterministic models. The general applicability of our model suggests that this unexpected scaling could be important in a wide range of real-world applications.

q-bio.QM↗