When minor issues matter: symmetries, pluralism, and polarization in similarity-based opinion dynamics

ArXiv.org · 2026-03-05

Polarization is a problem in modern society. Understanding how opinions evolve through social interactions is crucial for addressing conditions that lead to polarization, consensus, or opinion diversity. Classical opinion dynamics models have explored bounded confidence and homophily, but most assume equal issue importance and purely attractive forces. We extend these frameworks by developing a stochastic agent-based model where individuals hold binary opinions on multiple issues of heterogeneous weights and interact through both attraction (with similar others) and repulsion (from dissimilar others). Our model reveals that the similarity threshold determining friend-or-foe interactions fundamentally shapes outcomes, which in this model can be of three types: consensus, polarization, and persistent pluralism, where each opinion combination occurs in the population. Low thresholds promote consensus, while high thresholds lead to polarization or persistent pluralism. Surprisingly, introducing even a single issue of arbitrarily small weight can destabilize stable states, thus changing the solution type and increasing convergence times by orders of magnitude. To explain these phenomena, we derive a deterministic system of ordinary differential equations and analyze equilibrium symmetries. For up to five-issue systems, we provide a complete characterization: all weight configurations fall into a number of cases, each exhibiting distinct symmetry cascades as the threshold varies. Our analysis shows polarization risk increases when importance concentrates on few issues. This suggests mitigation strategies: fostering cross-cutting social ties, broadening discourse beyond core issues, and introducing new topics to disrupt polarization. The symmetry-based framework reveals how issue salience and social tolerance jointly shape collective opinion evolution.

When minor issues matter: symmetries, pluralism, and polarization in similarity-based opinion dynamics

Open MIND · 2026-03-05

Polarization is a problem in modern society. Understanding how opinions evolve through social interactions is crucial for addressing conditions that lead to polarization, consensus, or opinion diversity. Classical opinion dynamics models have explored bounded confidence and homophily, but most assume equal issue importance and purely attractive forces. We extend these frameworks by developing a stochastic agent-based model where individuals hold binary opinions on multiple issues of heterogeneous weights and interact through both attraction (with similar others) and repulsion (from dissimilar others). Our model reveals that the similarity threshold determining friend-or-foe interactions fundamentally shapes outcomes, which in this model can be of three types: consensus, polarization, and persistent pluralism, where each opinion combination occurs in the population. Low thresholds promote consensus, while high thresholds lead to polarization or persistent pluralism. Surprisingly, introducing even a single issue of arbitrarily small weight can destabilize stable states, thus changing the solution type and increasing convergence times by orders of magnitude. To explain these phenomena, we derive a deterministic system of ordinary differential equations and analyze equilibrium symmetries. For up to five-issue systems, we provide a complete characterization: all weight configurations fall into a number of cases, each exhibiting distinct symmetry cascades as the threshold varies. Our analysis shows polarization risk increases when importance concentrates on few issues. This suggests mitigation strategies: fostering cross-cutting social ties, broadening discourse beyond core issues, and introducing new topics to disrupt polarization. The symmetry-based framework reveals how issue salience and social tolerance jointly shape collective opinion evolution.

Population structure reverses selection of variants with proportionally scaled birth and death rates

bioRxiv (Cold Spring Harbor Laboratory) · 2025-02-02

Abstract A frequently observed phenomenon across the kingdom of life is that a higher reproduction rate can be accompanied by higher mortality. During tumor progression, variants emerge that both reproduce and die faster; faster replicating viruses can be characterized by a faster decay rate; and more frequent pregnancy can be accompanied by a higher chance to die due to predation in ecological systems. Variants with proportionally scaled birth and death rates have been called quasi-neutral mutants. Although life-time reproductive success is not changed, such variants are characterized by fixation probabilities that are somewhat lower (higher) than expected for neutral mutants if birth and death rates are proportionally larger (smaller). Studies were performed in the context of well-mixed populations, and despite the deviation from neutrality, quasi-neutral mutants do not have characteristics of disadvantageous or advantageous mutants, as their fixation probabilities still scale with their initial fractions. Here, we report that in deme-or spatially structured populations, variants with proportionally increased (decreased) birth and death rates become truly disadvantageous (advantageous), and calculate their effective fitness. Furthermore, if mutants have a higher life-time reproductive output than the wild-types and are thus advantageous, a proportional increase of birth and death rates can render them strongly disadvantageous, and vice versa. This changes our understanding of how life-time reproductive success correlates with selection, and has implications for evolutionary dynamics across a range of biological systems.

Cellular turnover can increase or decrease the mutant burden in expanding cell population

bioRxiv (Cold Spring Harbor Laboratory) · 2025-11-17

Abstract Expanding cell populations, such as bacterial and tumor colonies, continuously accumulate mutations as they grow. However, how mutational burden depends on cell turnover, i.e. the ratio of birth and death rates, remains poorly understood. Elucidating this relationship is crucial for predicting how populations adapt to changing environments, including during evolutionary rescue and resistance evolution. Previous theory suggested that higher turnover increases mutant abundance at a given population size, since more cell divisions are required to reach that size. Using well-mixed and spatial stochastic models, we find the relationship is more nuanced. For advantageous mutants, higher turnover does increase mutant numbers. For disadvantageous mutants, however, mutant abundance can actually decreases with turnover or exhibit non-monotonic behavior, with these somewhat counterintuitive patterns being more pronounced in spatially expanding populations. We derive explicit analytical boundaries separating different regimes and quantify the contribution of stochastic “jackpot” events to mutant burden. In spatial models, we show that the interplay between two timescales is critical: the time to reach the target population size versus the time for wild-type cells to erode disadvantageous mutant clusters. Our results reveal how basic demographic parameters influence the ability of cell populations to overcome selective barriers during growth, with implications for understanding both evolution in natural settings and disease progression.

Compartmental structure in the secondary lymphoid tissue can slow down <i>in vivo</i> HIV-1 evolution in the presence of strong CTL responses

Journal of The Royal Society Interface · 2025-02-01

Human immunodeficiency virus (HIV-1) replicates in the secondary lymphoid tissues, which are characterized by complex compartmental structures. While cytotoxic T lymphocytes (CTL) readily access infected cells in the extrafollicular compartments, they do not home to follicular compartments, which thus represent an immune-privileged site. Using mathematical models, previous work has shown that this compartmental tissue structure can delay the emergence of CTL escape mutants. Here, we show computationally that the compartmental structure can have an impact on the evolution of advantageous mutants that are not related to CTL recognition: (i) compartmental structure can influence the fixation probability of an advantageous mutant, with weakened selection occurring if CTL responses are of intermediate strength; (ii) compartmental structure is predicted to reduce the rate of mutant generation, which becomes more pronounced for stronger CTL responses; and (iii) compartmental structure is predicted to slow down the overall rate of mutant invasion, with the effect becoming more pronounced for stronger CTL responses. Altogether, this work shows that in vivo virus evolution proceeds slower in models with compartmental structure compared with models that assume equivalent virus load in the absence of compartmental structure, especially for strong CTL-mediated virus control. This has implications for understanding the rate of disease progression.

Author Correction: Barcoded HIV-1 reveals viral persistence driven by clonal proliferation and distinct epigenetic patterns

Nature Communications · 2025-10-27 · 1 citations

Efficient mathematical methodology to determine multistep mutant burden in spatially growing cell populations

PNAS Nexus · 2025-08-30 · 1 citations

The accurate computational prediction of mutant burden in spatially structured growing cell populations is a major goal both for basic evolutionary science, such as interpreting bacterial evolution studies, and for clinical applications, such as predicting the timing of drug resistance-induced cancer relapse for individual patients. Yet, this is currently not feasible for biologically realistic parameters, due to the inefficiency of computationally simulating stochastic mutant dynamics in large populations. Here, we fill this gap by deriving universal scaling laws that allow the straightforward prediction of the number of single-hit, double-hit, and multihit mutants as a function of wild-type population size in spatially expanding populations, in different spatial geometries, without the need to perform lengthy computer simulations. We demonstrate the applicability of this approach by reconciling different results from experimental evolution studies in bacteria that examine the role of gene amplifications for the rate of evolution.

Population structure reverses selection of variants with proportionally scaled birth and death rates

Nature Communications · 2025-12-27

A widespread biological phenomenon is that higher reproduction rates are often accompanied by higher mortality. During tumor progression, variants can both reproduce and die faster; rapidly replicating viruses decay more quickly; arthropods with faster reproduction have shorter lifespans; and in ecological systems, more frequent reproduction can increase predation risk. Variants with proportionally scaled birth and death rates are termed quasi-neutral mutants. Although their lifetime reproductive success is unchanged, such mutants have fixation probabilities slightly lower (or higher) than neutral mutants if birth and death rates are proportionally larger (or smaller). Previous studies, limited to well-mixed populations, showed that quasi-neutral mutants deviate from neutrality but still exhibit fixation probabilities scaling with their initial frequencies. Here, we show that in deme- or spatially structured populations, variants with proportionally increased (decreased) birth and death rates become genuinely disadvantageous (advantageous). We calculate their effective fitness and further demonstrate that even when mutants have higher lifetime reproductive output, proportional increases in both birth and death rates can render them strongly disadvantageous-and vice versa. This effect intensifies in larger populations. These findings revise the relationship between lifetime reproductive success and selection, with implications for evolutionary dynamics across biological systems.

Post-transfusion activation of coagulation pathways during severe COVID-19 correlates with COVID-19 convalescent plasma antibody profiles

Journal of Clinical Investigation · 2025-03-16

Early antibody therapy can prevent severe SARS-CoV-2 infection (COVID-19). However, the effectiveness of COVID-19 convalescent plasma (CCP) therapy in treating severe COVID-19 remains inconclusive. To test a hypothesis that some CCP units are associated with a coagulopathy hazard in severe disease that offsets its benefits, we tracked 304 CCP units administered to 414 hospitalized COVID-19 patients to assess their association with the onset of unfavorable post-transfusion D-dimer trends. CCP recipients with increasing or persistently elevated D-dimer trajectories after transfusion experienced higher mortality than those whose D-dimer levels were persistently low or decreasing after transfusion. Within the CCP donor-recipient network, recipients with increasing or persistently high D-dimer trajectories were skewed toward association with a minority of CCP units. In in vitro assays, CCP from "higher-risk" units had higher cross-reactivity with the spike protein of human seasonal betacoronavirus OC43. "Higher-risk" CCP units also mediated greater Fcγ receptor IIa signaling against cells expressing SARS-CoV-2 spike compared with "lower-risk" units. This study finds that post-transfusion activation of coagulation pathways during severe COVID-19 is associated with specific CCP antibody profiles and supports a potential mechanism of immune complex-activated coagulopathy.