449 papers
Competition at the front of expanding populations
When competing species grow into new territory, the population is dominated by descendants of successful ancestors at the expansion front. Successful ancestry depends on both the reproductive advantage (fitness), as well as ability and opportunity to colonize new domains. We present a model that integrates both elements by coupling the classic description of one-dimensional competition (Fisher equation) to the minimal model of front shape (KPZ equation). Macroscopic manifestations of these equations are distinct growth morphologies controlled by expansion rates, competitive abilities, or spatial anisotropy. In some cases the ability to expand in space may overcome reproductive advantage in colonizing new territory. When new traits appear with accumulating mutations, we find that variations in fitness in range expansion may be described by the Tracy--Widom distribution.
2604.01187Apr 2026
View
How to Forage for a Mate?
Foraging is a central decision-making behavior performed by all animals, essential to garnishing enough energy for an organism to survive. Similarly, mating is crucial for evolutionary continuity and offspring production. Mate choice is one of the central tenets of sexual selection, driving major evolutionary processes, and can be regarded as a decision-making process between potential mating partners. Often researchers have used coarse-grained models to describe macroscopic phenomenology pertaining to mate choice without detailed quantitative mechanisms of how animals use individual and environmental signals to guide their mating decisions. In this letter, we show that mate choice can be cast as a foraging problem, and we present an analytically tractable optimal foraging-inspired mechanistic theory of decision-making underlying mate choice. We begin from the premise that deciding upon which partner with which to mate is at its core a stochastic decision-making process. Agents adopt a variety of decision strategies, tuned by decision thresholds for leaving or committing to a mate. We find that sensitive leaving thresholds are favored independently of signal availability in the population. By contrast, optimal thresholds for committing to a mate depend upon signal availability in the population, with signal-rich populations generally favoring less eager strategies compared to signal-poor populations.
2604.00393Apr 2026
View
Macroscopic Signatures of Gauge-Mediated Contagion: Deriving Behavioral Shielding from Stochastic Field Theory
We present a unified theoretical model relating stochastic microscopic epidemic dynamics with macroscopic non-linear population behavior. Utilizing the Doi-Peliti formalism, we model the pathogen as a gauge mediator field coupled to susceptible and infected host populations, and introduce a Reactive Immunity Field capable of spontaneous symmetry breaking. We demonstrate that the naive epidemic vacuum is destabilized by radiative loop corrections via the Coleman-Weinberg mechanism, generating a dynamic herd immunity threshold. By extracting the classical saddle-point limit of the Effective Action, we derive the macroscopic reaction-diffusion equations governing the host population. We show that integrating out the gauge mediator inherently generates a thermodynamic Free Energy dependent on the square of the susceptible density. This non-linearity produces a macroscopic spatial ``Fear Drift'' proportional to the magnitude of the immunity field, and a cubic shielding penalty in the effective reproductive number ($R_{eff}$). In this work, we establish a mapping between fundamental field-theoretic mechanisms and specific terms in the macroscopic behavioral equations. We demonstrate that Debye screening is physically executed by the spatial cross-diffusion fluxes driving host evacuation. Simultaneously, vacuum polarization manifests as a non-linear cubic penalty ($-S^3 I$) in the dressed reaction rate that dynamically suppresses the effective reproductive number. As a validation of our model, we apply the formalism to high-resolution spatiotemporal COVID-19 data from Germany.
2604.00153Mar 2026
View
Pathogen diversity emerging from coevolutionary dynamics in interconnected systems
The spread of infectious disease and the evolution of antigenically distinct strains are often modeled separately, despite strong feedbacks mediated by host immune memory and heterogeneous contacts. To tackle this challenging problem, we introduce a coevolutionary framework in which transmission occurs on a metapopulation network while mutational exploration of strain space follows a mutation network. In this multiscale model, cross-immunity is encoded by similarity in the latent diffusion geometry of the strain network, so that nearby strains confer partial immune protection. We first identify an effective critical region that controls the transition between extinction, recurrent outbreak episodes, and long-lived endemic persistence, thus characterizing the resulting strain-turnover dynamics. We then derive a replicator-mutator-like equation for strain composition and an explicit dynamical evolutionary landscape induced by the coupling of mutation and transmission. Finally, allowing host heterogeneity to modulate the local mutation structure, we show that spreading across demes can effectively connect otherwise disconnected components of strain space, increasing long-term endemic diversity while producing a non-monotonic change in overall prevalence. Together, our results isolate minimal mechanisms by which immune-mediated competition and network structure can shape antigenic diversification.
2603.29398Mar 2026
View
Disentangling the interactive effects of anthropogenic disturbances on biodiversity
Anthropogenic activity threatens biodiversity through climate change, habitat fragmentation, and increasing frequency and scale of disturbance. Various theoretical studies have sought to shed light on how these factors could promote or hinder the coexistence of species. However, our understanding of the relative importance of, and interactions between, these factors remains limited. In this study, we employ a theoretical approach integrating three commonly cited coexistence mechanisms -- the competition-colonisation trade-off, the intermediate disturbance hypothesis, and spatial heterogeneity -- into a unified model. We implement a novel method to integrate habitat autocorrelation into a system of differential equations, to create a simple and flexible model that can be used to investigate coexistence of multiple species arranged in a competitive hierarchy under different disturbance and habitat structure scenarios. Using this model, we find that considering interactions between different mechanisms is crucial for explaining the coexistence of species. Biodiversity patterns alternative to the uni-peak curve predicted by the intermediate disturbance hypothesis (e.g., bimodal) emerge along disturbance gradients as habitat fragmentation increases. Furthermore, habitat loss outweighs habitat autocorrelation effects in highly disturbed scenarios, yet autocorrelation can shape species coexistence under low disturbance. These findings underscore the need to integrate spatial and temporal mechanisms in biodiversity management.
2603.29116Mar 2026
View
When can fitness epistasis be ignored in a polygenic trait at equilibrium?
Although many phenotypic traits are determined by a large number of genetic variants, the behavior of allele frequencies in a polygenic trait is not completely understood. The problem is especially challenging when the quantitative trait of interest is under epistatic selection as the allele frequency at a locus is affected by those at other loci. Here, we consider a panmictic, diploid finite population evolving under stabilizing selection and symmetric mutations when the population is in linkage equilibrium. In the stationary state, using a diffusion theory, we calculate the marginal distribution of allele frequency, and find parameter regimes where fitness epistasis can not be ignored for an accurate description of the frequency distribution. For such parameters, the mean deviation in the phenotypic optimum and genic variance are, however, found to be well captured even when epistatic interactions are neglected. Thus, while the presence of epistasis may not be evident in phenotypic quantities, it can strongly affect the allele frequency distribution.We also find that the allele frequency distribution at a locus is unimodal if its effect size is below a threshold effect and bimodal otherwise; these results are the stochastic analog of the deterministic ones where the stable allele frequency becomes bistable when the effect size exceeds a threshold. Our analytical results are verified against Monte Carlo simulations and numerical integration of a Langevin equation.
2603.27255Mar 2026
View
Evaluating Phylogenetic Comparative Methods under Reticulate Evolutionary Scenarios
Phylogenetic comparative methods (PCMs) are widely used to study trait evolution. However, many evolutionary histories involve reticulate evolutionary scenarios, such as hybridization, that violate core assumptions of these methods. In this study, we evaluate how such violations affect the performance of PCMs. In particular, we focus on the ancestral character estimation, evolutionary rate estimation, and model selection. We simulate continuous trait evolution on various phylogenetic network topologies and assess the performance of PCMs that assume a bifurcating tree (i.e., major tree of the network) as the underlying model of evolution. We found that the performance of the tested PCMs was suboptimal. Using random forest, generalized linear models, and model-based clustering, we identified key factors contributing to these inaccuracies. Our results show that frequent and/or recent hybridization accompanied by one ore more transgressive events and rapidly evolving traits (i.e., high evolutionary rate) lead to significant estimation error, especially with respect to rate estimation and model choice. These factors substantially shift trait values away from tree-based model expectations, leading to overall increased error in parameter estimates. Our study demonstrates cases in which PCMs that rely on trees are likely to misinterpret biological histories and offers recommendations for researchers studying systems with complex evolutionary histories.
2603.25986Mar 2026
View
2603.25628Modeling the mutational dynamics of very short tandem repeats
Short tandem repeats (STRs) are low-entropy regions in the genome, consisting of a short (1-6 bp) unit that is consecutively repeated multiple times. They are known for high mutational instability, due to so-called stutter-mutations, in which the number of units in the run increases or descreases. In particular, STRs with repeat unit length of 1-2 bp are prone to mutate even within several cell divisions. The extremely rapid accumulation of variation makes them interesting phylogenetic markers for retrospective single-cell lineage reconstruction. Here we model their mutational dynamics at the level of individual repeat unit type and then aggregate length variations over many STR loci with the aim of obtaining a very fast ``molecular clock''. We calibrate our model based on several datasets with known lineage structure prepared from cultured cells. We find that the mutational dynamics of STRs are reasonably consistent for a given cell line, but vary among different ones. This suggests that the dynamics are not entirely explained by mutations in caretaker genes, rather, various other factors play a role -- possibly tissue origin and differentiation state. Further data and research is necessary to asses their relative effects.
2603.25628Mar 2026
View
The Self-Replication Phase Diagram: Mapping Where Life Becomes Possible in Cellular Automata Rule Space
What substrate features allow life? We exhaustively classify all 262,144 outer-totalistic binary cellular automata rules with Moore neighbourhood for self-replication and produce phase diagrams in the $(λ, F)$ plane, where $λ$ is Langton's rule density and $F$ is a background-stability parameter. Of these rules, 20,152 (7.69%) support pattern proliferation, concentrated at low rule density ($λ\approx 0.15$--$0.25$) and low-to-moderate background stability ($F \approx 0.2$--$0.3$), in the weakly supercritical regime (Derrida coefficient $μ= 1.81$ for replicators vs. $1.39$ for non-replicators). Self-replicating rules are more approximately mass-conserving (mass-balance 0.21 vs. 0.34), and this generalises to $k{=}3$ Moore rules. A three-tier detection hierarchy (pattern proliferation, extended-length confirmation, and causal perturbation) yields an estimated 1.56% causal self-replication rate. Self-replication rate increases monotonically with neighbourhood size under equalised detection: von Neumann 4.79%, Moore 7.69%, extended Moore 16.69%. These results identify background stability and approximate mass conservation as the primary axes of the self-replication phase boundary.
2603.25239Mar 2026
View
Balancing training load, rest and musculoskeletal injury risk: a mathematical modelling study in Thoroughbred racehorses
Musculoskeletal injuries (MSI) in Thoroughbred racehorses are a leading cause of death and premature retirement in racehorses and are heavily influenced by training practices. Greater distances of high-speed galloping accumulated during racing campaigns are associated with MSI. Bone injury is the most common MSI, and understanding how training practices influence bone damage accumulation is critical for improving both horse welfare and racing outcomes. This study builds on an existing mathematical model of bone adaptation and damage to investigate the impact of different training programs on bone injury risk. Several training programs (three progressive, four race-fit, six rest programs and two with rest replaced by low-intensity training) were constructed to reflect representative practices undertaken by professional trainers in Victoria, Australia. Training programs varied in training volume, rest frequency and program duration. Lower volume training programs that included high-speed training, achieved sufficient bone adaptation with less accumulation of bone damage, and subsequently lower risk of bone failure. In addition, incorporating more frequent rests (at least 2 per year) and/or longer rest periods (at least 6 weeks) reduced bone damage due to the extended opportunity to remove and repair bone damage. These results provide an in-silico mathematical model of the bone response to training, demonstrating the effects of training programs on bone adaptation, damage formation and repair. The findings can guide the design of training programs that balance both bone adaptation and bone health throughout horses racing career.
2603.22680Mar 2026
View
Modelling SARS-CoV-2 epidemics via compartmental and cellular automaton SEIRS model with temporal immunity and vaccination
We consider the SEIRS epidemiology model with such features of the COVID-19 outbreak as: abundance of unidentified infected individuals, limited time of immunity and a possibility of vaccination. The control of the pandemic dynamics is possible by restricting the transmission rate, increasing identification and isolation rate of infected individuals, and via vaccination. For the compartmental version of this model, we found stable disease-free and endemic stationary states. The basic reproductive number is analysed with respect to balancing quarantine and vaccination measures. The positions and heights of the first peak of outbreak are obtained numerically and fitted to simple in usage algebraic forms. Lattice-based realization of this model is studied by means of the asynchronous cellular automaton algorithm. This permitted to study the effect of social distancing by varying the neighbourhood size of the model. The attempt is made to match the quarantine and vaccination effects.
2603.22498Mar 2026
View
Epidemic reproduction numbers in spatial networks
The basic and effective reproduction numbers are widely used metrics for characterizing the dynamics of infectious disease epidemics. However, the interpretation of these numbers is based on the assumption of homogeneous mixing and may not hold in real-world populations where the contact patterns deviate from that assumption. In this paper, we present a network-based framework to compare reproduction numbers in populations with and without spatial structure, while other parameters of the disease remain fixed. Using this framework, we show that in homogeneously mixed populations, in the absence of external interventions, the effective reproduction number decreases exponentially as the susceptible population declines. In contrast, in spatially structured populations, the basic reproduction number is smaller, and the effective reproduction number initially decreases faster but eventually converges to unity. We show that the reproduction number is determined by the level of competition between infectious nodes, which is governed by the network structure. Our results suggest that without knowledge of the network structure, reproduction numbers may not be informative for parameterizing the contagiousness of the disease or predicting the behavior of epidemic spreading.
2603.22150Mar 2026
View
Pattern Formation in a Spatial Public Goods Dilemma due to Diffusive or Directed Motion
The costly provision of public goods serves as a model problem for the evolution of cooperative behavior, presenting a social dilemma between the collective benefits of shared resources and the individual incentive to free-ride in resource production. The spatial structure of populations can also impact cooperation over public goods, as diffusion of public goods and intentional motion of individuals towards regions with greater resources can interact with population and public goods dynamics to produce heterogeneous patterns in the spatial distribution of strategies and resources. In this paper, we build off a model introduced by Young and Belmonte for the reaction dynamics of interacting individuals and explicit public good, deriving a system of PDEs that describes the spatial profiles of strategies and the public good in the presence of both diffusive motion of individuals and resources and chemotaxis-like directed motion of individuals in response to gradients in the concentration of public goods. Through linear stability analysis, we show that spatial patterns in strategic and public goods profiles can emerge due to either Turing instability with high defector diffusivity or a directed-motion instability through strong sensitivity of cooperators towards increasing resource concentration. We further explore the emergent spatial patterns with a mix of weakly nonlinear stability analysis and numerical simulation, showing that diffusion-driven instability appears to increase cooperation and public goods across the spatial domain, while directed motion of cooperators towards regions with great public goods provision tends to decrease cooperation and environmental quality across the environment.
2603.21025Mar 2026
View
Spectral Geometry and Heat Kernels on Phylogenetic Trees
We develop a unified spectral framework for finite ultrametric phylogenetic trees, grounding the analysis of phylogenetic structure in operator theory and stochastic dynamics in the finite setting. For a given finite ultrametric measure space $(X,d,m)$, we introduce the ultrametric Laplacian $L_X$ as the generator of a continuous time Markov chain with transition rate $q(x,y)=k(d(x,y))m(y)$. We establish its complete spectral theory, obtaining explicit closed-form eigenvalues and an eigenbasis supported on the clades of the tree. For phylogenetic applications, we associate to any ultrametric phylogenetic tree $\mathcal{T}$ a canonical operator $L_{\mathcal{T}}$, the ultrametric phylogenetic Laplacian, whose jump rates encode the temporal structure of evolutionary divergence. We show that the geometry and topology of the tree are explicitly encoded in the spectrum and eigenvectors of $L_{\mathcal{T}}$: eigenvalues aggregate branch lengths weighted by clade mass along ancestral paths, while eigenvectors are supported on the clades, with one eigenspace attached to each internal node. From this we derive three main contributions: a spectral reconstruction theorem with linear complexity $O(|X|)$; a rigorous geometric interpretation of the spectral gaps of $L_{\mathcal{T}}$ as detectors of distinct evolutionary modes, validated on an empirical primate phylogeny; an eigenmode decomposition of biological traits that resolves trait variance into contributions from individual splits of the phylogeny; and a closed-form centrality index for continuous-time Markov chains on ultrametric spaces, which we propose as a mathematically grounded measure of evolutionary distinctiveness. All results are exact and biologically interpretable, and are supported by numerical experiments on empirical primate data.
2603.20922Mar 2026
View
Coexistence coalitions in propagule disperser quasi-communities
Many natural ecosystems harbor large numbers of coexisting species competing for far fewer distinct resources, in apparent defiance of the competitive exclusion principle. Various mechanisms have been proposed to explain this apparent paradox, among the most prominent being competition--colonization trade-offs, environmental heterogeneity, and ecological neutrality. We develop a unified stochastic model class that combines all three coexistence narratives in the context of propagule disperser communities and show that this setting encompasses several important classical models. We then prove a general theorem on coexistence at macroscopic equilibria and provide an algorithm that determines equilibrium coalitions solely from readily available matrix spectra, thereby bypassing the costly computation of exact equilibrium states. Using illustrative examples, we demonstrate the potential of this approach for quantifying the relative merits of different coexistence narratives and for studying their synergistic effects.
2603.20707Mar 2026
View
Interplay between evolutionary and epidemic time scales challenges the outcome of control policies
The SIR model is the cornerstone model for mathematical epidemiology, explaining key epidemic features such as the second-order transition between disease-free and epidemic states, the initial exponential growth of outbreaks or the short-term benefits of control measures. Nonetheless, the classical SIR model assumes that pathogen traits remain fixed, thus neglecting viral evolution. Here we propose a minimal extension of the SIR model, allowing infectiousness to evolve. We show that such evolution can cause superexponential early growth of outbreaks, create abrupt epidemic transitions, and undermine the effectiveness of control policies, as lifting interventions too early can lead to worse epidemic scenarios than no action. We derive analytical expressions for the critical mutation rate and intervention time governing this behavior, and identify a strong asymmetry between control strategies: while shortening the infectious period hinders transmission without suppressing viral evolution, lowering transmission both reduces cases and slows down viral evolution.
2603.18801Mar 2026
View
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.
2603.17754Mar 2026
View
Sympatric speciation by symmetry-breaking: The three-clade case
In this paper we expand the concept of biological speciation by symmetry breaking of Golubitsky and Stewart to the case of three clades in which N populations following the same dynamical laws can separate. The underlying differential equation is based on a fifth order polynomial of a trait variable with first or second order coupling. We present some general strategies to find all possible steady states and their stabilities. Numerical data are given for a specific system. We show the locations of three-clade distributions in dependence on the coupling and an environmental parameter. The results show a decrease of the number of stable states with higher coupling and a higher probability of ending in a three-clade state for larger N. Limits and potentials of the approach if zero roots for the trait variable occur are discussed.
2603.17026Mar 2026
View
A multiscale discrete-to-continuum framework for structured population models
Mathematical models of biological populations commonly use discrete structure classes to capture trait variation among individuals (e.g. age, size, phenotype, intracellular state). Upscaling these discrete models into continuum descriptions can improve analytical tractability and scalability of numerical solutions. Common upscaling approaches based solely on Taylor expansions may, however, introduce ambiguities in truncation order, uniform validity and boundary conditions. To address this, here we introduce a discrete multiscale framework to systematically derive continuum approximations of structured population models. Using the method of multiple scales and matched asymptotic expansions applied to discrete systems, we identify regions of structure space for which a continuum representation is appropriate and derive the corresponding partial differential equations. The leading-order dynamics are given by a nonlinear advection equation in the bulk domain and advection-diffusion processes in small inner layers about the leading wavefronts and stagnation point. We further derive discrete boundary layer descriptions for regions where a continuum representation is fundamentally inappropriate. Finally, we demonstrate the method on a simple lipid-structured model for early atherosclerosis and verify consistency between the discrete and continuum descriptions. The multiscale framework we present can be applied to other heterogeneous systems with discrete structure in order to obtain appropriate upscaled dynamics with asymptotically consistent boundary conditions.
2603.15217Mar 2026
View2603.15198Geometric framework for biological evolution
We develop a generally covariant description of evolutionary dynamics that operates consistently in both genotype and phenotype spaces. We show that the maximum entropy principle yields a fundamental identification between the inverse metric tensor and the covariance matrix, revealing the Lande equation as a covariant gradient ascent equation. This demonstrates that evolution can be modeled as a learning process on the fitness landscape, with the specific learning algorithm determined by the functional relation between the metric tensor and the noise covariance arising from microscopic dynamics. While the metric (or the inverse genotypic covariance matrix) has been extensively characterized empirically, the noise covariance and its associated observable (the covariance of evolutionary changes) have never been directly measured. This poses the experimental challenge of determining the functional form relating metric to noise covariance.
2603.15198Mar 2026
ViewPage 1 of 23
