Journal of Theoretical Biology

Demographic shifts are reshaping population age structures worldwide, with implications for infectious disease dynamics. Since contact patterns, susceptibility and infectiousness often vary by age, the risk that pathogen introductions initiate a substantial outbreak depends on the populations age distribution and associated behavioural characteristics. We develop an age-structured mathematical model to estimate the risk that a single pathogen introduction leads to sustained transmission (the probability of a major outbreak) under long-term demographic transitions, incorporating changes in age-specific contact patterns and behavioural adaptation. Using the Republic of Korea (projected to become the worlds oldest population by 2050) as a case study, we show that population ageing generally reduces the probability of a major outbreak due to older individuals lower contact rates. However, this effect is attenuated for pathogens with increasing susceptibility or infectiousness with age, and if future older cohorts have higher contact levels than at present (e.g. through extended workforce participation in an ageing society). These findings demonstrate that, while outbreak risks are affected by demographic changes, they are further modified by associated behavioural responses, highlighting the importance of accounting for demographic and socio-behavioural context when assessing future infectious disease outbreak risks. Author SummaryIn the early stages of an infectious disease outbreak, the risk that initial cases lead to a substantial outbreak is shaped by a range of factors including the characteristics of the host population. Demographic changes, such as population ageing, are transforming societies worldwide, yet their implications for infectious disease emergence remain unclear. Here, we show that ageing populations reduce the likelihood that imported infections trigger major infectious disease outbreaks due to lower contact rates between individuals of older ages. However, this effect depends on how susceptibility, infectiousness and host behaviour vary with age. For example, increased social and economic activity among future older adults (due to a higher retirement age) could offset the decrease in the outbreak risk. These findings underscore the need to account for demographic and socio-behavioural factors, in addition to biological factors, when assessing future outbreak risks and designing robust public health strategies, particularly in societies undergoing rapid demographic change.

The ecological and evolutionary dynamics of populations, including viral populations, are known to be jointly shaped by deterministic and stochastic processes. While the impact of stochastic processes has been rigorously explored for viral dynamics at the level of the host population, most dynamic models for acutely-infecting respiratory viral pathogens at the within-host scale remain deterministic in their formulation. While this may be reasonable for identifying key processes shaping their within-host viral population dynamics, recent studies indicate that stochastic processes need to be invoked for understanding patterns of within-host viral evolution. Specifically, several studies have shown that viral allele frequencies can change dramatically over the time course of days in acute infections. Here, we use stochastic dynamic models to explore the role of environmental noise in shaping observed patterns of virus evolution in acute respiratory virus infections. We summarize ways in which environmental stochasticity can be biologically realized in these acute viral infections and describe within-host models that can be implemented to jointly yield viral population dynamics and evolutionary dynamics. We further develop a statistical approach to estimate the extent of environmental noise from observed within-host allele frequency changes. We test this approach on simulated data and apply it to existing influenza A virus and SARS-CoV-2 within-host data. With these applications, we show that environmental stochasticity can parsimoniously reproduce key features of empirically observed allele frequency changes without needing to invoke demographic stochasticity or to adopt Wright-Fisher model formulations with a constant effective population size. Finally, we show that purifying selection and positive selection can both still contribute to within-host viral evolution in the context of a noisy environment, providing theoretical support for studies that have found purifying and positive selection in acutely-infecting respiratory virus populations.

In the dynamic interplay between hosts and pathogens, hosts may produce a defense compound that acts as a toxin to deter pathogen attack. Conversely, pathogens may evolve to produce a counter-defense enzyme, neutralizing the hosts toxin. This evolutionary arms race incurs costs for both parties, prompting adaptations and strategic shifts. We conceptualize this interaction as an asymmetric game, with hosts and pathogens as players, and their potential responses - defense, counter-defense, or inaction - as their strategic options. In this scenario, if the pathogens counter-defense enzyme is entirely effective, then the hosts toxin is rendered obsolete. However, should the host cease toxin production, the pathogens enzyme becomes redundant, ironically reinstating the toxins utility. This interaction leads to potential red-queen cycles in defense and counter-defense strategies under certain conditions, or a balanced, optimal production of toxin and enzymes by hosts and parasites, respectively. To explore this, we introduce a game-theoretical model incorporating replicator dynamics to examine temporal shifts in strategy from active (counter-)defense to non-(counter-)defense and back. In addition, we analyze compromise strategies and interpret them as bet-hedging-like. We provide a deterministic illustration of how partial defense and counter-defense generate a fitness-buffering structure in unpredictable environments and increase the geometric mean fitness of the population. In conclusion, our analysis supports the notion of continuous periodic adjustments in strategies, notably in the levels of defensive and counter-defensive measures.

Minimum viable populations (MVPs) are population levels large enough to surmount risk from demographic, environmental, and genetic stochasticity. MVPs are estimated by biologists to guide conservation practices. However, MVPs are generally estimated for a target population without regard for how they interact with intra- and inter-species population dynamics in the broader ecological community. Thus, how and why population dynamics interact with MVPs imposed by conservation biologists remain unclear. When MVPs are imposed on a continuous population model, traditional analyses fail to capture the range of possible outcomes those MVPs create. Here, we describe viability space decomposition (VSD) as a mathematical tool to systematically analyze the potential crossing of MVPs during population dynamics. We demonstrate that different extinction and survival outcomes can be recovered from a model with imposed MVPs using three VSD concepts in junction with a traditional phase portrait: mortality manifolds which separate conditions that lead to different existential outcomes, ordering manifolds which determine the order of extinction events for multiple populations, and collapse manifolds which determine the survival or extinction of one species given the loss of another. We employ these methods with a standard consumer-resource model, and the methods can be scaled to systems with more species. VSD is a useful tool for conservation biologists and community ecologists concerned with boundary crossing problems in any dynamical system.

Hippocampal adult neurogenesis (HANG) is a highly regulated process where neural stem cells progress through distinct stages--from Type 1 radial glia-like cells to mature neurons--via a complex series of proliferative and differentiative divisions. While recent in vivo imaging has provided valuable insights to cellular processes, the exact relationship between individual cell-fate decisions and long-term population stability remains difficult to quantify empirically. In this study, we utilized an agent-based (AB) model to simulate the stochastic dynamics of the hippocampal neurogenic niche. Our results demonstrate that while individual progenitor lineages exhibit high variability and probabilistic division symmetries (proliferative symmetric, asymmetric, and differentiative symmetric), the system achieves deterministic stability as the initial progenitor density increases. We found that the T1 progenitor pool follows a negative exponential decay profile, with its longevity primarily dictated by the differentiation rate (d,0). Critically, the terminal output of immature neurons (CIN,t) was non-linearly coupled to the proliferative capacity of transit-amplifying cells (pp,0); even marginal increases in symmetric proliferative divisions resulted in an exponential expansion of the neuronal pool. These findings suggest that the homeostatic maintenance of the hippocampal niche is governed by a kinetic tuning of division probabilities, providing a theoretical bridge between single-cell stochasticity and robust tissue-level output.

Predicting the outcome of species or pathogen strain competition is a fundamental aim in both community ecology and infectious disease dynamics. Recent work revealed major challenges in predicting strain co-circulation from ecological coexistence theory due to overcompensatory competition among pathogens for susceptible resources, which can prevent the re-invasion of other competing strains. This resource overcompensation is ubiquitous across host-pathogen systems, but not apparent in simple Lotka-Volterra competition system, highlighting fundamental differences between pathogen strain and species competition. To address this gap, we begin by deriving classical models of pathogen strain and species competition from a resource-consumer model. This generalization illustrates that the relative time scale between resource and consumer dynamics limits the degree of resource overcompensation and therefore dictates the outcome of stochastic competition. Moreover, by introducing a mathematical framework for quantifying pairwise and higher-order terms from general competition systems, we show that a simple, ecological competition model can accurately predict the equilibrium dynamics of strain competition. A case study of rotavirus strain competition reveals that the ability to predict the outcome of strain competition from ecological theory depends on the underlying cross immunity structure. This work synthesizes coexistence theory across two fields by providing a unifying framework for predicting the outcome of complex ecological competition.

Multicellular organisms regularly encounter microbes, which are, however, only rarely pathogenic. Our understanding of this phenomenon is currently restricted due to lacking theory on evolutionary transitions between non-pathogenic and pathogenic microbial lifestyles. Here we addressed this gap by investigating a mathematical model of host-microbe interactions that is based on the danger theory of immunology, which states that danger signals related to host tissue damage play a key role in activating immune responses. We formally implemented this idea by assuming that immune activation increases with costs that microbes cause to their host, and we compared this to scenarios in which immune activation depends only on the presence or load of infecting microbes. Our model analysis revealed that cost-based - but not presence or load-based - immune activation favours the evolution of avirulence and associated non-pathogenic microbial lifestyles. Based on our results, we propose the danger hypothesis of virulence evolution which states that evolution towards avirulence and intermediate virulence are both possible - depending on whether hosts can accurately assess costs generated by microbes. The idea that basic host immune responses can select for avirulence offers a new explanation for why most microbes are not pathogenic to a given host.

The c-MYC proto-oncogene regulates cellular proliferation, and its aberrant expression drives a range of human cancers. It also has a bidirectional regulatory relationship with the mammalian core circadian clock, with emerging evidence suggesting that MYC overexpression leads to clock disruption and loss of rhythms. While prior studies have probed MYCs role in clock disruption by overexpressing or mutating the c-MYC gene, our understanding of the endogenous nature of c-MYC is limited. A major gap in knowledge is whether MYC itself is expressed rhythmically and if so, how its timing relates to that of core clock components. To address these shortcomings, we generated a c-MYC reporter and assessed its circadian nature, comparing it to BMAL1 and PER2, and developed a computational model based on these and previous findings to evaluate its role(s). We developed lentiviral constructs for and established a U2OS (common circadian model) reporter cell line expressing luciferase (luc) driven by a human-derived c-MYC promoter sequence. To facilitate comparisons, as part of this work, we also developed a human-sequence derived BMAL1 promoter reporter to more readily recapitulate its behaviors. Using luminometry studies and subsequent data analyses, we demonstrated that the c-MYC promoter oscillated rhythmically in U2OS cells, which possess inherently low levels of c-MYC. Furthermore, we found that c-MYC oscillates out-of-phase relative to BMAL1 and PER2. Using this information, we built a mathematical model to better understand how c-MYCs oscillations at both basal and over-expressed levels affect the clock and vice versa. The model reproduced expected alterations to the core clock resulting from c-MYC overexpression and showed that MYCs role is as a disruptor, although the timing of MYC regulation can minimize its negative impact(s) on circadian timekeeping. This work is the first to assess c-MYCs phase relationships relative to the core clock and to provide evidence for its circadian nature. Author summaryc-MYC is a transcription factor that is highly regulated and plays an important role in cellular proliferation. In cancers, deregulation of c-MYC causes its overexpression, resulting in tumorigenesis. There have been multiple connections demonstrated between MYC and the circadian clock, including the clocks role in MYC expression and that its overexpression can lead to disruptions to the core circadian clock. However, knowledge of the expression patterns of MYC are limited, including whether they occur in a circadian manner. To address this, we developed a c-MYC-luciferase reporter in a human circadian cell model (U2OS). For the first time, we were able to directly assess the rhythmic nature of c-MYC using this tool. Subsequently, we developed a mathematical model to gain insights into the disruptive role of MYC in clock regulation under disease-like conditions and, in turn, the effects of the circadian clock on MYC. We found that c-MYC oscillated in a circadian manner in U2OS cells and that the MYC proteins role is as a disruptor, but its timing can minimize its negative impact(s) on circadian rhythms.

This work focuses on the global and partial identification problem for fractional differential equations. We provide a general numerical procedure based on global and local optimization algorithms with two refinements for biological systems that ensure solution positivity and homogeneous parameter units. The method is applied to a new fractional model of Dengue outbreak called the Fractional Homogeneous Nishiura (FHN) model, calibrated using data of newly infected people in Cape Verde. We show that our identification method yields a better fit between data and model solutions than previous approaches and that our FHN model captures the dynamics of Dengue more closely than existing systems.

Infectious disease time series often show signs of epidemic transitions, such as the peaks and troughs of the time series. In these time series, key system parameters can lead to catastrophic changes in the dynamical system behaviour (often called critical transitions). Modellers have increasingly shown that early warning signals can anticipate these transitions, both critical and non-critical, in infectious disease time series. Existing methods, however, generally focus on univariate time series data, or ignore spatiotemporal patterns that may be present as a disease spreads through a population. Recent ecological literature developments expand existing temporal and spatial methods to consider the covariance matrix of multiple, related time series. However, many of these proposed signals still make an assumption of stationary time series/system equilibrium. Whilst often true in ecological modelling, disease systems are seldom at equilibrium. In this paper, we propose the usage of the eigendecomposition of the non-stationary covariance matrix as a more suitable early warning signal for epidemiological data. We first analyse the expected trends in the eigenvalues and eigenbasis of the covariance matrix on approach to a transition. Next we apply these methods to a spatially-structured susceptible-infectious-recovered model to explore how the eigenbasis may provide extra information to modellers. Finally, we test these methods on SARS-CoV-2 case data during the 2020-2021 pandemic period in England.

Glucosinolates are an important group of specialized metabolites in the Brassicaceae family, playing a role as defensive compounds against biotic attackers. In response to biotic stress, plants upregulate glucosinolate biosynthesis in part by increasing the abundance of enzymes in the glucosinolate biosynthetic pathway. As an increase in enzyme abundance is often preceded by an increase in the corresponding mRNA levels, the dynamic changes in mRNA levels should capture the information required to infer how metabolite levels change over time. In order to test this hypothesis, a time series of experimental glucosinolate content data collected from Arabidopsis thaliana, exposed to either a mock or methyl jasmonate (MeJA) treatment, as a proxy for biotic stress, was combined with existing mRNA abundance data over time at the same developmental stage and treatment. We propose the GEEM model, a multilevel mechanistic ordinary differential equation (ODE) model, which goes from Gene expression to an enzyme level model, followed by a Michaelis Menten kinetics metabolite model, to simulate the dynamics of a segment of the indolic glucosinolate pathway. In order to constrain the GEEM model, three models were fit to experimental de novo specialized metabolite data, using different degrees of freedom by utilizing both a Gradient Boosted Tree model with a tested architecture to predict the kinetic constants, and augmenting these predictions with a literature review of the known Michaelis Menten kinetic constants from the glucosinolate pathway. Using Sequential Monte Carlo - Approximate Bayesian Computing to fit the GEEM model to the experimental data, we showed that given the mRNA levels and initial concentrations of metabolites, the changes in specialized metabolites over time and treatment can be modeled. Author SummaryWe study how plants adjust their natural chemical defenses over time when they are under attack from living organisms. In the mustard family, including the subject of our experiment Arabidopsis, one important group of defense chemicals is called glucosinolates. When Arabidopsis is under attack, certain gene pathways can be activated or deactivated, allowing the plant to modulate the amount of enzymes they produce, which in turn modulates the levels of these defensive chemicals. In this work, we combine measurements of gene activity and glucosinolate levels from Arabidopsis treated with a compound used in stress signal that mimics insect or pathogen attack. We then constructed a mathematical model that goes from gene activity, to amount of enzyme present, and ends with the amounts of specific glucosinolates over time. By fitting this model to experimental data, we show that it is possible to predict how glucosinolate levels change over time from the gene activity and initial glucosinolate levels. Our approach offers a way to connect gene expression datasets to real changes in plant defense chemistry, with potential applications in plant breeding and insight into how these pathways change due to stress.

Coexistence of multiple predators in ecological communities and their combined effects on the abundance and diversity of shared prey are often difficult to predict. In some theoretical models, predator coexistence is limited by antagonistic interactions, especially in the form of intraguild predation (IGP) that typically leads to out-competition between predators and high prey densities. However, empirical studies show that predator coexistence is common even in the presence of IGP. This discrepancy between theoretical expectations and empirical observations can be highly relevant for practical applications like using multiple natural enemies for pest suppression in agriculture. It is proposed that greater functional differences between natural enemies (i.e. predators) could reduce competition and overcome the negative effects of IGP, thereby promoting their coexistence and enhancing herbivore (i.e. prey) suppression. In this study, we theoretically explore this proposition. We develop a theoretical model based on the types of natural enemies of aphids to identify how functional differences between predators in IGP modules affect predator coexistence and herbivore suppression. We show that pairwise combinations of four functional predator types (ladybird, predatory bug, hoverfly, and parasitoid) can increase the coexistence range for different intraguild predation and competition strengths between predators (IGP symmetry), along a productivity gradient. This outcome depends on the external food input rate for the predatory bug and hoverfly types, and on their position as IG predator or IG prey. Herbivore suppression was primarily driven by IGP symmetry (i.e. the relative intraguild predation and exploitative competition strength between predators) and was especially pronounced in competitive-like modules where the IG predator was excluded for most scenarios. However, for some competitive-like IGP modules with predatory bug and hoverfly types, both predators can persist and provide a high herbivore suppression across increasing productivity. Our results can help explain experimental findings in conservation biocontrol, where coexistence between natural enemies is joined with effective herbivore suppression, and offer additional support for the role of functional diversity in reconciling theoretical predictions with experimental observations in multiple-predator communities.

Multiple global-change forces, from habitat alterations to warming, are altering food webs and trophic interaction strengths. Such changes in trophic interactions have important implications, as it is a tenet of ecology that trophic interactions are linked to the functioning and stability of ecosystems. For example, changes in the presence or strength of intraguild predation (IGP), the consumption of a predator by another predator that competes for shared prey, can have cascading effects on the biomasses of species and trophic levels. For this reason, IGP can affect key ecosystem functions at the base of the food web and is of special interest to practitioners of biological pest control. However, the relationship between IGP and ecosystem stability is not yet well understood, especially whether and how IGP might affect the stability of non-adjacent lower trophic levels including primary producers. In this study we simulate the dynamics of a six-species, four-trophic-level food web plus a limiting nutrient to explore the relationship between IGP strength and the temporal variability of species- and trophic group-biomass. By varying the IGP rate given the abundance of the eaten predator, we find that the model food web abruptly shifts between equilibria in which all species maintain either constant biomass or stable limit cycles where all trophic levels exhibit sustained and significant oscillations. While complex feedback in the model creates a divergence between the IGP functional response and the resulting realized IGP strength, both stronger IGP functional responses and stronger realized IGP are associated with a higher likelihood of oscillations. Furthermore, analyses indicate that the strongest consumptive interaction induces the oscillating behavior in an indirect effect initiated by the change in IGP. Overall, these results suggest that as food web structure changes in ecosystems worldwide, strengthening IGP runs the risk of inducing destabilizing effects that extend to the base of food webs, while weakening IGP could confer stability to ecosystem functions such as primary production. Finally, we discuss relevance to management, including the implication that IGP among biological control agents should be minimized to maintain stable crop production.

With the increasing availability of large scale empirical fitness landscape data, there is a need for simple yet informative null models that can be used to interpret metrics of landscape ruggedness and navigability. A natural choice of a null model that maximizes ruggedness in a statistical sense assigns independent and identically distributed fitness values to the genotypes, a setting often referred to as the House-of-Cards (HoC) or mutational landscape model. In this work we examine the navigability of these landscapes, as quantified by the mean size of the adaptive basins of local fitness peaks. The adaptive basin is the set of genotypes from which a peak can be reached via selectively accessible, i.e., strictly fitnessincreasing mutational paths. Building on recent rigorous results on the statistics of accessible paths, we show that the adaptive basins in the HoC landscape encompass a positive fraction of all genotypes that is an analytically computable, increasing function of the number of alleles per site. For the four letter nucleotide alphabet, an average peak basin contains 52.8 % of all genotypes. When conditioned on peak fitness, the expected basin size increases linearly with fitness rank. The exact results on adaptive basins are complemented by an approximate analysis of gradient basins formed by greedy adaptive paths which maximize the fitness increase in each step. We argue that recent reports of large adaptive basins in empirical fitness landscapes should be reinterpreted in the light of our findings.

In the respiratory epithelium, interferon (IFN)-induced antiviral resistance acts as a defense against infection. Influenza A viruses (IAVs) have evolved multiple strategies to counteract these defenses, including expression of the viral protein NS1, which inhibits both IFN production and the IFN-mediated transcription of Interferon Stimulated Genes (ISG) in infected cells. However, experiments show that this inhibition is imperfect, especially at a low multiplicity of infection (MOI). One hypothesis to describe this phenomenon relies on the presence of Semi-infectious Particles (SIPs) that fail to express NS1. In this scenario, the IFN response is incompletely suppressed at low MOI, while it is successfully inhibited at high MOI because most cells are infected by multiple virions, allowing complementation to rescue NS1 expression. To test this hypothesis, we developed a computer simulation that models viral gene defects and complementation. We compared the model outputs with in vitro experiments at different MOIs. To assess inter-host reproducibility and calibrate the model parameters, we measured IFN levels and viral load over time in bronchial epithelial cell cultures from five human donors. We observed no statistically significant heterogeneity in IFN response or virus production between donors, and the calibrated simulation fits the experimental time series for IFN and viral load. Consistent with literature (1,2), the model predicted higher IFN levels at low MOI than at high MOI. Finally, simulations of IFN treatment applied before and during infection showed reduced viral load, in agreement with our experiments. Increasing the viral genome defect rate above the experimentally estimated rate increased IFN levels and reduced viral load. High MOI simulations showed lower cumulative IFN levels, while NS1 knockout recovered high IFN levels. These results demonstrate the ability of mechanistic models of viral dynamics to predict the innate immune response of epithelial cells during viral infection. Author SummaryRespiratory viruses such as influenza A are highly infectious and pose significant challenges for the human immune system. Through laboratory experiments and computer simulations, we investigated how cells in the respiratory epithelium defend themselves and their neighbors against infection. Using cells collected from different donors, we generated 3-dimensional cell cultures that mimic human airways and measured how they respond to IAV. When a tissue was initially exposed to a small amount of virus, cells could successfully slow or stop the spread of the infection. This phenomenon is hypothesized to be due in part to the high error rate in IAV replication, resulting in many viral particles that are not fully functional. We recapitulated this experimental result with our computational model, validating the model design and parameter estimates. We then simulated a scenario in which cells were pre-treated with interferon, a protective cytokine important to early immune response, and showed that this pre-treatment could successfully limit infection. Laboratory experiments subsequently confirmed this predicted behavior. The computational model reproduced key observations across infection conditions and identified nonfunctional viral particles as important drivers of the early immune response.

The Hajj is an annual pilgrimage made by millions of Muslims to Mecca in the Kingdom of Saudi Arabia (KSA). The large number of international attendees at the Hajj increases the risk of global infectious disease spread. However, we know very little about the benefits, costs, and cost-effectiveness of testing and quarantining strategies to contain epidemic spread during mass gathering events. In this work we developed a stochastic discrete-time compartmental metapopulation model to simulate international epidemics of infectious pathogens and their potential importation into KSA during the Hajj. We used the model and an epidemic simulation study to evaluate the impact and cost-effectiveness of three testing and quarantining strategies for arriving pilgrims: randomly testing 99% of pilgrims, 80% of pilgrims, or using a symptom-based screening strategy. The simulations lasted 100 days, covering the 30 days before the Hajj and 65 days after the Hajj. Under the conditions assumed in our simulation study, there was strong evidence that testing and quarantining strategies are cost-effective measures for controlling epidemic threats at the Hajj. The median net monetary benefits of intervention strategies ranged from Intl$-41.89M [95% quantile range Intl$-42.37M to Intl$3.18B] to Intl$12.68B [Intl$-8.70B to Intl$13.82B] across scenarios with different pathogen characteristics (based on the natural histories of SARS-CoV-2 and H1N1 Influenza) and epidemic seed locations. Our results were sensitive to the data sources that were used to estimate the number of pilgrims travelling to KSA by origin country, with flight passenger statistics providing biased estimates of pilgrim numbers. Our work provides an adaptable tool to inform infectious disease risk assessments and evaluate the cost-effectiveness of possible disease control measures for the Hajj, and could be extended to other mass gathering events.

Perceptual systems in humans and many other animals are able to segment scenes into regions that are likely to be physically meaningful. This ability depends on having low-level mechanisms that can accurately categorize whether local image patches are samples from the same or different kinds of texture. We find that using spatial proximity as a proxy for same-different ground truth makes it possible to train accurate decision variables and bounds directly from arbitrary natural images with no feedback. We also find that performance can be further improved by using proximity as a ground truth for adjusting the final decision variables and bounds for the current image/scene. These surprising findings result from the simple fact that under a wide range of conditions proximity discrimination (near vs. far) and texture discrimination (same vs. different) have mathematically identical decision bounds if the same image features are used for both tasks. We used the decision variables and bounds trained on natural images as the initial steps in a hierarchical Bayesian observer (HBO) model of texture discrimination [9]. Given the relative simplicity of this HBO model, it did an excellent job of segmenting images having randomly shaped regions containing arbitrary natural textures. We suggest that the proximity proxy is something that natural selection could discover and exploit for any same-different task where the task-relevant stimulus features also vary systematically with distance in space and/or time. For example, natural selection could have created developmental learning/plasticity mechanisms that exploit the proximity proxy.

Cooperative and competitive interactions among individuals harvesting resources can shape environmental states, such as prey abundance. In turn, environmental conditions feed back to influence strategic interactions. Eco-evolutionary game theory studies how these feedbacks shape the co-evolution of behavior and environment. Existing models typically assume deterministic, noise-free environmental dynamics. However, real environments are inherently stochastic, for example due to finite resources, and noise can qualitatively alter social outcomes. Here, we incorporate stochastic environmental dynamics into eco-evolutionary game theory. When environmental change is slow relative to strategy updates, we show that behavior reflects a mixture of the games associated with low and high environmental states, often yielding outcomes qualitatively distinct from deterministic predictions. In particular, environmental stochasticity can eliminate bistability and enforce dominance of a single behavior. When environmental dynamics are faster, populations have less opportunity to track fluctuations, and behavior converges toward strategies that are optimal on average. Stochasticity can even causes persistent oscillations in the tragedy of commons, in regimes where classical models predict stability. Our framework provides a tractable approach for analyzing social behavior linked to environmental dynamics how noise shapes long-term eco-evolutionary outcomes.

Mechanical properties of epithelial tissues play essential roles in morphogenesis and physiological function. In this study, we analytically derived the in-plane bulk modulus, shear modulus, and Poissons ratio of a three-dimensional cell vertex model of epithelial monolayers. We showed that the model can robustly reproduce a near-zero in-plane Poissons ratio, a mechanical feature reported in cultured epithelial tissues. Numerical simulations further confirmed that the theoretically predicted Poissons ratio accurately describes the response of the model under finite, biologically relevant strains. In addition, the model exhibits not only morphological bistability between squamous-like and columnar-like states, but also mechanical bistability characterized by distinct elastic responses. Together, these results provide a minimal three-dimensional framework that links cell-scale mechanical interactions and epithelial morphology to tissue-scale elastic properties.

A phylogenetic network represents evolutionary relationships involving hybridization, gene flow, or admixture. While the full network may not be identifiable from genomic data under common coalescent models, its tree of blobs, depicting only the tree-like portions of the network structure, is. We introduce ECToBlob (Edge Contraction for Tree of Blobs), a new statistically-consistent algorithm to estimate the tree of blobs from quartet concordance factors. Starting from a resolved tree, ECToBlob successively contracts edges which statistical tests indicate do not belong in the tree of blobs, due to reticulate or polytomous signal. We show that ASTRAL provides a valid starting tree under common assumptions, in that, asymptotically in the number of loci, trees optimizing ASTRALs criterion refine the tree of blobs. We describe several algorithm variants, differing in how evidence from multiple tests are combined to determine if the edge should be contracted, and provide software implementations. Relevance to Life SciencesHybridization, gene flow, or admixture are now recognized as important aspects of evolutionary history, but their genomic signal is confounded with that from a coalescent process, creating substantial challenges for inferring phylogenetic networks. The networks tree of blobs identifies areas where reticulation occurred, separated by tree-like branching. ECToBlob quickly estimates the tree of blobs using quartet concordance factors from gene trees, and provides a measure of statistical support for its result. Performance is illustrated through simulation and on empirical data, using an implementation in the R package MSCquartets. While the presence of a blob may be all that can be inferred in some cases, in others ECToBlob offers a robust and principled way to focus further analyses on more local reticulate structure. Mathematical ContentThis work makes contributions to mathematical phylogenetics in optimization, combinatorics, and statistics. We show that any tree maximizing quartet support (the criterion underlying ASTRAL) is a refinement of the networks tree of blobs under the coalescent model. Second, we give a concise proof that whether a network has a cut-edge corresponding to a given split is determined by information in certain subcollections of its 4-taxon subnetworks (quarnets). Finally, we propose valid statistical approaches for combining p-values across multiple quarnet hypothesis tests, proving that their use with specific decreasing test levels leads to statistically consistent inference as the number of loci grows. MSC codes05C90, 60J95, 62-04, 62F07, 92D15