Intratumor phenotypic heterogeneity plays a pivotal role in shaping the evolutionary dynamics of tumor growth and drug responses. Nonlocal reaction-diffusion equations have been developed to model the spatio-temporal dynamics of tumor cells with heterogeneous phenotypes. However, rigorous mathematical analysis of such nonlocal reaction-diffusion equations with high spatial and phenotypic dimensions remains challenging. Additionally, previous studies have seldom explored key determinants of phenotypic heterogeneity by integrating models with realistic spatial data. To address these challenges and gaps, we present a rigorous mathematical framework for dissecting phenotypic heterogeneity and evolution within vascularized tumors, utilizing a nonlocal reaction-diffusion model coupled with spatial gene expression data. First, we establish the mathematical foundation of the model by proving the well-posedness, boundedness, and nonnegativity of solutions, as well as the existence of stationary positive solutions. Subsequently, we develop a stable and convergent alternating direction explicit-implicit scheme to numerically solve the nonlocal partial differential equations. Furthermore, we investigate the impact of key parameters on the evolution of tumor phenotypic heterogeneity, revealing that the epimutation rate governs the concentrated distribution of tumor cell phenotypes. Additionally, we leverage spatially resolved transcriptomics data to quantify tumor cell spatial density, phenotypic states, and vessel distribution within the model. Our integrative analysis uncovers significant associations between spatial transcriptomics features and the long-term progression of intratumor heterogeneity. This study provides a rigorous mathematical analysis of intratumor phenotypic heterogeneity evolution using a nonlocal reaction-diffusion model and identifies pivotal determinants of phenotypic heterogeneity through the integration of novel spatial data.
For this Special Collection we invited experts in the area of mathematical and computational biology to share their views on the major problems in their areas of interest and their recent research results - focusing on the development of state-of-the-art modeling approaches and computational techniques applied to problems in the life sciences - and to present their vision of the new directions needed for addressing unsolved problems. Papers in this Special Collection address mathematical and computational problems in several areas of the life sciences, including theoretical neuroscience, cancer modeling, and cell and developmental systems. With respect to methodologies, these papers cover dynamical systems, differential equations, stochastic processes, and modern computational techniques, all with an emphasis on techniques in modern modeling and computational methodologies. This Special Collection is jointly hosted by the Bulletin of Mathematical Biology and the Journal of Mathematical Biology.
This study presents a mathematical model that describes the unsteady interstitial fluid percolation through a solid tumour and its surrounding healthy tissue, as well as the deformation of the cellular phase of the solid tumour and healthy tissue. The tumour and its healthy host are assumed to be connected via a smooth, fixed interface. Each of these tissue regions comprises interstitial fluid and solid constituents (i.e., tumour cells and extracellular matrix). The general mixture theory equations are adopted to represent conservation of mass and momentum in each tissue region. The fluid phase is modelled as an incompressible Newtonian fluid, and the solid phase as an isotropic deformable porous material. The governing equations are of mixed parabolic-hyperbolic type. We assume continuity of the interface fluid velocity (IFV), the solid-phase displacement (SPD), and the normal stress at the host-tumour interface, along with the Beavers-Joseph-Saffman condition. We establish well-posedness in a weak sense for the unsteady governing system using a Galerkin method and weak convergence. We then focus on calculating the system energy using the velocity fields of the fluid and solid components of the tumour and its host. The energy estimates in the context of well-posedness yield the maximum system energy (MASE), and the minimum system energy (MISE) is computed from the definitions of the L 2 and H 1 norms using the 1D solution of the governing equations. The system energy assists in ranking the viability of five types of tumours associated with five distinct carcinomas.
Breast cancer is a leading cause of mortality and morbidity among females worldwide. As part of the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2023, we provided an updated comprehensive assessment of the epidemiological trends, disease burden, and risk factors associated with breast cancer globally, regionally, and nationally from 1990 to 2023. Breast cancer incidence, mortality, prevalence, years lived with disability (YLDs), years of life lost (YLLs), and disability-adjusted life-years (DALYs) were estimated by age and sex for 204 countries and territories from 1990 to 2023. Mortality estimates were generated using GBD Cause of Death Ensemble models, leveraging data from population-based cancer registration systems, vital registration systems, and verbal autopsies. Mortality-to-incidence ratios were calculated to derive both mortality and incidence estimates. Prevalence was calculated by combining incidence and modelled survival estimates. YLLs were established by multiplying age-specific deaths with the GBD standard life expectancy at the age of death. YLDs were estimated by applying disability weights to prevalence estimates. The sum of YLLs and YLDs equalled the number of DALYs. Breast cancer burden attributable to seven risk factors was examined through the comparative risk assessment framework. The GBD forecasting framework was used to forecast breast cancer incidence and mortality from 2024 to 2050. Age-standardised rates were calculated for each metric using the GBD 2023 world standard population. In 2023, there were an estimated 2·30 million (95% uncertainty interval [UI] 2·01 to 2·61) breast cancer incident cases, 764 000 deaths (672 000 to 854 000), and 24·1 million (21·3 to 27·5) DALYs among females globally. In the World Bank low-income group, where a low age-standardised incidence rate (ASIR) was estimated (44·2 per 100 000 person-years [31·2 to 58·4]), the age-standardised mortality rate (ASMR) was the highest (24·1 per 100 000 [16·8 to 31·9]). The highest ASIR was in the high-income group (75·7 per 100 000 [67·1 to 84·0]), and the lowest ASMR was in the upper-middle-income group (11·2 per 100 000 [10·2 to 12·3]). Between 1990 and 2023, the ASIR in the low-income group increased by 147·2% (38·1 to 271·7), compared with a 1·2% (-11·5 to 17·2) change in the high-income group. The ASMR decreased in the high-income group, changing by -29·9% (-33·6 to -25·9), but increased by 99·3% (12·5 to 202·9) in the low-income group. The increase in age-standardised DALY rates followed that of ASMRs. Risk factors such as dietary risks, tobacco use, and high fasting plasma glucose contributed to 28·3% (16·6 to 38·9) of breast cancer DALYs in 2023. The risk factors with a decrease in attributable DALYs between 1990 and 2023 were high alcohol use and tobacco. By 2050, the global incident cases of breast cancer among females were forecast to reach 3·56 million (2·29 to 4·83), with 1·37 million (0·841 to 2·02) deaths. The stable incidence and declining mortality rates of female breast cancer in high-income nations reflect success in screening, diagnosis, and treatment. In contrast, the concurrent rise in incidence and mortality in other regions signals health system deficits. Without effective interventions, many countries will fall short of the WHO Global Breast Cancer Initiative's ambitious target of achieving an annual reduction of 2·5% in age-standardised mortality rates by 2040. The mounting breast cancer burden, disproportionately affecting some of the world's most vulnerable populations, will further exacerbate health inequalities across the globe without decisive immediate action. Gates Foundation, St Jude Children's Research Hospital.
In recent years, the application of fractional derivatives in mathematical models has gained significant popularity. In the case of time-fractional derivatives, one of the main reasons for their use lies in their nonlocal property, which can overcome the limitations of ordinary differential equation models that are purely local and might fail to describe memory-dependent processes. The most common approach, often called fractionalisation, is based on the direct replacement of the classical derivatives in the ODE models, with fractional ones. When they are compared to real data, fractionalised models are often shown to provide better fitting results. The most common interpretation of this is that fractionalised models keep track of the history, while local models do not. However, while the physical meaning of a classical derivative is clear, the same cannot be said for fractional derivatives. Therefore, the relationship between modelling assumptions and mathematical equations remains unclear. Here, we introduce and critically discuss the fractionalisation approach by considering two representative examples of fractionalised biomathematical models. In our discussion, we address several properties of fractional operators that may impose significant limitations in their applications. However, the key question on which we would like to reflect is: is a fractionalised model still a model?
Transmission of tuberculosis (TB) among human population depends on an individual's infectiousness, which is further determined by the concentration of Mycobacterium tuberculosis (Mtb) in the body. Additionally, Mtb is resistant to dryness, cold, acidic, and alkaline environments and can survive in acidic and alkaline environments for 4-5 years. Mtb in the environment plays a significant role in TB transmission and should not be overlooked. To investigate the epidemiologic relationships among pathogens, hosts, and the environment, we first develop a multiscale TB model that includes multiple transmission routes (human-to-human and environment-to-human) and links Mtb-immune response interactions to TB transmission in population. We comprehensively analyze the dynamic properties of the fast system, slow system, and full system. Analysis results reveal that coupling bacterial processes within-host with transmission mechanisms between-host can trigger diverse complex behaviors, including both forward and backward bifurcation phenomena. This implies that thresholds routinely used to control TB infection or eliminate Mtb from an epidemiological or immunological perspective may fail under specific conditions; that is, even if the basic reproduction number R 0 is less than 1, endemic equilibria may still exist in the system. Second, from a microtherapeutic point of view, we establish an impulsive time-delayed differential equation to characterize the actual medication regimen for TB. The basic reproduction number R 0 ' is defined as the spectral radius of a linear integral operator. Then, we show that R 0 ' is a critical parameter that determines the persistence of the model. More precisely, if R 0 ' < 1 , the disease-free periodic solution is globally attractive; if R 0 ' > 1 , the disease is uniformly persistent. Finally, we employ numerical methods to elucidate the interactions between population transmission dynamics and pathogen dynamics. Specifically, the basic reproduction number R 0 of the full system increases rapidly with the rise in Mtb release rate, while its change is relatively slower with an increase in the immune rate. These results highlight the dominant role of chemotherapy, with immunotherapy playing only a supporting role.
The brain, as a reservoir of human immunodeficiency virus (HIV), has received tremendous attention due to the association with the brain's infection with HIV-associated neurocognitive disorders (HAND). Along with the blood-brain barrier (BBB), heterogeneity across the various regions inside the brain makes HIV infection particularly complex to identify the ideal treatment for controlling HIV in the brain. In this study, we developed a mathematical model to describe the spatiotemporal dynamics of HIV infection in three essential regions of the brain: the prefrontal cortex (PF), the choroid plexus (CP), and the primary visual cortex (V1). We use our model to study the impact of drug pharmacodynamics and the CPE score (a permeability index for drugs into the brain) on viral control in the brain. The infection invasion threshold, which we theoretically established as the determinant of infection avoidance or virus persistence, enables us to select drugs for treatment protocols with pharmacodynamic properties (dose-response curve slope, dose, half-life, dose interval, CPE score) that prevent and control HIV infection in the brain. Our novel model and related theoretical and numerical results provide further insights into the impact of antiretroviral therapy on the spatiotemporal dynamics of HIV infection in the brain.
Population genetic processes, such as the adaptation of a quantitative trait to directional selection, may occur on longer time scales than the sweep of a single advantageous mutation. To study such processes in finite populations, approximations for the time course of the distribution of a beneficial mutation were derived previously by branching process methods. The application to the evolution of a quantitative trait requires bounds for the probability of survival S ( n ) up to generation n of a single beneficial mutation. Here, we present a method to obtain a simple, analytically explicit, either upper or lower, bound for S ( n ) in a supercritical Galton-Watson process. We prove the existence of an upper bound for offspring distributions including Poisson, binomial, and negative binomial. They are constructed by bounding the given generating function, φ , by a fractional linear one that has the same survival probability S ∞ and yields the same rate of convergence of S ( n ) to S ∞ as φ . For distributions with at most three offspring, we characterize when this method yields an upper bound, a lower bound, or only an approximation. Because for many distributions it is difficult to get a handle on S ∞ , we derive an approximation by series expansion in s, where s is the selective advantage of the mutant. We briefly review well-known asymptotic results that generalize Haldane's approximation 2s for S ∞ , as well as less well-known results on sharp bounds for S ∞ . We apply them to explore when bounds for S ( n ) exist for a family of generalized Poisson distributions. Numerical results demonstrate the accuracy of our and of previously derived bounds for S ∞ and S ( n ) . Finally, we treat an application of these results to determine the response of a quantitative trait to prolonged directional selection.
We study a minimal stochastic individual-based model for a microbial population challenged by a persistent (lytic) virus epidemic. We focus on the situation in which the resident microbial host population and the virus population are in stable coexistence upon arrival of a single new "mutant" host individual. We assume that this mutant is capable of switching to a reversible state of dormancy upon contact with virions as a means of avoiding infection by the virus. At the same time, we assume that this new dormancy trait comes with a cost, namely a reduced individual reproduction rate. We prove that there is a non-trivial range of parameters where the mutants can nevertheless invade the resident population with strictly positive probability (bounded away from 0) in the large population limit. Given the reduced reproductive rate, such an invasion would be impossible in the absence of either the dormancy trait or the virus epidemic. We explicitly characterize the parameter regime where this emergence of a host dormancy trait is possible, determine the success probability of a single invader and the typical amount of time it takes the successful mutants to reach a macroscopic population size. We conclude this study by an investigation of the fate of the population after the successful emergence of a dormancy trait. Heuristic arguments and simulations suggest that after successful invasion, either both host types and the virus will reach coexistence, or the mutants will drive the resident hosts to extinction while the virus will stay in the system.
Neurodegenerative diseases (NDs), such as Alzheimer's, Parkinson's, and prion diseases, are characterized by the dynamical spread of toxic proteins through the brain. In prion diseases, cellular prion protein ( PrP C ), produced by neurons, misfolds into a toxic form, known as scrapie prion protein ( PrP Sc ). PrP Sc induces neuronal stress which ultimately leads to cell death. In this paper, we develop mathematical models for the progression of prion diseases, incorporating a cellular defense mechanism that introduces a delay term affecting protein translation and a volatility term accounting for unaccounted biological factors influencing the system. We also extend the model to capture the spatial spread of toxic proteins over the brain connectome. Our first objective is to establish the existence and uniqueness of a global positive solution to the prion disease models. Afterwards, we analyze the asymptotic behavior of the models by identifying regimes of persistence and extinction of toxic proteins. For the deterministic delayed systems, we perform a stability analysis for the persistence and demonstrate that the system undergoes a Hopf bifurcation. We also study the intensity of fluctuations of the equilibrium state of the stochastic model. Additionally, we present numerical simulations to illustrate the model dynamics using biologically relevant parameters.
Information on childhood cancer burden is crucial for effective cancer policy planning. Unfortunately, observed paediatric cancer data are not available in every country, and previous global burden estimates have not discretely reported several common cancers of childhood. We aimed to inform efforts to address childhood cancer burden globally by analysing results from the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2023, which now include nine additional cancer causes compared with previous GBD analyses. GBD 2023 data sources for cancer estimation included population-based cancer registries, vital registration systems, and verbal autopsies. For childhood cancers (defined as those occurring at ages 0-19 years), mortality was estimated using cancer-specific ensemble models and incidence was estimated using mortality estimates and modelled mortality-to-incidence ratios (MIRs). Years of life lost (YLLs) were estimated by multiplying age-specific cancer deaths by the standard life expectancy at the age of death. Prevalence was estimated using survival estimates modelled from MIRs and multiplied by sequelae-specific disability weights to estimate years lived with disability (YLDs). Disability-adjusted life-years (DALYs) were estimated as the sum of YLLs and YLDs. Estimates are presented globally and by geographical and resource groupings, and all estimates are presented with 95% uncertainty intervals (UIs). Globally, in 2023, there were an estimated 377 000 incident childhood cancer cases (95% UI 288 000-489 000), 144 000 deaths (131 000-162 000), and 11·7 million (10·7-13·2) DALYs due to childhood cancer. Deaths due to childhood cancer decreased by 27·0% (15·5-36·1) globally, from 197 000 (173 000-218 000) in 1990, but increased in the WHO African region by 55·6% (25·5-92·4), from 31 500 (24 900-38 500) to 49 000 (42 600-58 200) between 1990 and 2023. In 2023, age-standardised YLLs due to childhood cancer were inversely correlated with country-level Socio-demographic Index. Childhood cancer was the eighth-leading cause of childhood deaths and the ninth-leading cause of DALYs among all cancers in 2023. The percentage of DALYs due to uncategorised childhood cancers was reduced from 26·5% (26·5-26·5) in GBD 2017 to 10·5% (8·1-13·1) with the addition of the nine new cancer causes. Target cancers for the WHO Global Initiative for Childhood Cancer (GICC) comprised 47·3% (42·2-52·0) of global childhood cancer deaths in 2023. Global childhood cancer burden remains a substantial contributor to global childhood disease and cancer burden and is disproportionately weighted towards resource-limited settings. The estimation of additional cancer types relevant in childhood provides a step towards alignment with WHO GICC targets. Efforts to decrease global childhood cancer burden should focus on addressing the inequities in burden worldwide and support comprehensive improvements along the childhood cancer diagnosis and care continuum. St Jude Children's Research Hospital, Gates Foundation, and St Baldrick's Foundation.
Pressure-volume (PV) loop analysis remains the gold standard for assessing the intrinsic global diastolic properties of the left ventricle (LV). Traditional fitting techniques rely on local, phase-constrained fittings and are limited due to their sensitivity to noise, landmark selection, violation of assumptions, and nonconvergence. We aimed to develop and validate DIA-, a physics-informed neural network (PINN) framework capable of calculating intrinsic diastolic properties of the LV from measured instantaneous PV data, combining mechanistic interpretability with machine learning flexibility. Instantaneous LV diastolic pressure was modeled as the sum of 1) time-dependent relaxation-related pressure and 2) volume-dependent recoil and stiffness-related pressures. DIA-PINN was trained using time, LV pressure, and LV volume as inputs, enforcing data fidelity, model consistency, and physiological plausibility within the loss function. Performance was evaluated in 4,000 Monte Carlo simulations of LV PV-loops, and in clinical data from 59 patients who underwent catheterization (39 with heart failure and normal ejection fraction and 20 controls). DIA-PINN-derived indices were compared with those obtained from a previously validated global optimization method (GOM). On the simulation data, DIA-PINN accurately recovered all constitutive indices (intraclass correlation coefficients near unity) and improved GOM performance. On the clinical data, diastolic indices derived using DIA-PINN strongly correlated with GOM estimates (R > 0.90, P < 0.001) but were insensitive to initialization. DIA-PINN performed best under vena cava occlusion, as varying preload improved parameter identifiability. When applied to instantaneous pressure-volume data, a generalizable PINN framework, DIA-PINN, provides an improved method for assessing global intrinsic diastolic properties of cardiac chambers.NEW & NOTEWORTHY Our work introduces DIA-PINN, a physics-informed neural network framework to process instantaneous ventricular pressure-volume data, solving a mechanistic model of diastole with machine learning techniques. Compared with current conventional or optimization-based approaches, the PINN provides the most reliable estimates of diastolic stiffness, relaxation, and elastic recoil, insensitive to initialization. By embedding physiological constraints into network training, this approach achieves robust, interpretable, and clinically applicable quantification of gold-standard metrics of intrinsic global diastolic chamber properties.
This paper investigates the conditions for the stability and emergence of patterns in a new three-component reaction-diffusion system. The system describes the coexistence and interaction of water reservoirs, vegetation, and bushfire activity in a given ecosystem. We perform a detailed stability analysis to determine the parameter space where an unstable homogeneous equilibrium becomes stable with respect to spatially nonuniform perturbations. We also use diffusion to generate traveling trains in the form of periodic orbits of the linearized system. These orbits are remnants of an unstable equilibrium in the absence of diffusion and arise from a nonsingular eigenvalue crossing of the imaginary axis, while a third eigenvalue remains real and negative, thereby ensuring linear stability for monocromatic waves. These phenomena differ from "classical" Turing and Hopf bifurcations, as the model does not involve distinct "activators" and "inhibitors", and the effects observed are not the byproduct of diffusion with necessarily differing speeds. Also, differently from the classical Turing pattern, the role of diffusion in this context is to stabilize, rather than destabilize, homogeneous equilibria. We also consider the case of plant competition, showing a suitable form of Turing instability for slow-frequency oscillations in a small rainfall regime.
We propose a predator-prey model with an age-structured predator population that exhibits a functional role reversal. The structure of the predator population in our model embodies the ecological concept of an "ontogenetic niche shift," in which a species' functional role changes as it grows. This structure adds complexity to our model but increases its biological relevance. The time evolution of the age-structured predator population is motivated by the Kermack-McKendrick Renewal Equation (KMRE). Unlike KMRE, the predator population's birth and death rate functions depend on the prey population's size. We establish the existence, uniqueness, and positivity of the solutions to the proposed model's initial value problem. The dynamical properties of the proposed model are investigated via Latin Hypercube Sampling in the 15-dimensional space of its parameters. Our Linear Discriminant Analysis suggests that the most influential parameters are the maturation age of the predator and the rate of consumption of juvenile predators by the prey. We carry out a detailed study of the long-term behavior of the proposed model as a function of these two parameters. In addition, we reduce the proposed age-structured model to ordinary and delayed differential equation (ODE and DDE) models. The comparison of the long-term behavior of the ODE, DDE, and the age-structured models with matching parameter settings shows that the age structure promotes the instability of the Coexistence Equilibrium and the emergence of the Coexistence Periodic Attractor.
We study the mechanisms of pattern formation for vegetation dynamics in water-limited regions. Our analysis is based on a set of two partial differential equations (PDEs) of reaction-diffusion type for the biomass and water, and one ordinary differential equation (ODE) describing the dependence of the toxicity on the biomass. We perform a linear stability analysis in the one-dimensional finite space, we derive analytically the conditions for the appearance of Turing instability that gives rise to spatio-temporal patterns emanating from the homogeneous solution, and provide its dependence with respect to the size of the domain. Furthermore, we perform a numerical bifurcation analysis in order to study the pattern formation of the inhomogeneous solution, with respect to the precipitation rate, thus analyzing the stability and symmetry properties of the emanating patterns. Based on the numerical bifurcation analysis, we have found new patterns, which form due to the onset of secondary bifurcations from the primary Turing instability, thus giving rise to a multistability of asymmetric solutions.
A core challenge for modern biology is how to infer the trajectories of individual cells from population-level time courses of high-dimensional gene expression data. Birth and death of cells present a particular difficulty: existing trajectory inference methods cannot distinguish variability in net proliferation from cell differentiation dynamics, and hence require accurate prior knowledge of the proliferation rate. Building on Global Waddington-OT (gWOT), which performs trajectory inference with rigorous theoretical guarantees when birth and death can be neglected, we show how to use lineage trees available with recently developed CRISPR-based measurement technologies to disentangle proliferation and differentiation. In particular, when there is neither death nor subsampling of cells, we show that we extend gWOT to the case with proliferation with similar theoretical guarantees and computational cost, without requiring any prior information. In the case of death and/or subsampling, our method introduces a bias, that we describe explicitly and argue to be inherent to these lineage tracing data. We demonstrate in both cases the ability of this method to reliably reconstruct the landscape of a branching SDE from time-courses of simulated datasets with lineage tracing, outperforming even a benchmark using the experimentally unavailable true branching rates.
We consider a metapopulation made up of K demes, each containing N individuals bearing a heritable quantitative trait. Demes are connected by migration and undergo independent Moran processes with mutation and selection based on trait values. Mutation and migration rates are tuned so that each deme receives a migrant or a mutant in the same slow timescale and is thus essentially monomorphic at all times for the trait value (adaptive dynamics). In the timescale of mutation/migration, the metapopulation can then be seen as a giant spatial Moran model with size K that we characterize. As K → ∞ and physical space becomes continuous, the empirical distribution of the trait value (over the physical and trait spaces) evolves deterministically according to an integro-differential evolution equation. In this limit, the trait value of every migrant is drawn from this global distribution, so that conditional on its initial state, trait values from finitely many demes evolve independently (propagation of chaos). Under mean-field dispersal, the value X t of the trait at time t and at any given location has a law denoted μ t and a jump kernel with two terms: a mutation-fixation term and a migration-fixation term involving μ t - (McKean-Vlasov equation). In the limit where mutations have small effects and migration is further slowed down accordingly, we obtain the convergence of X, in the new migration timescale, to the solution of a stochastic differential equation which can be referred to as a new, canonical jump-diffusion of adaptive dynamics. This equation includes an advection term representing selection, a diffusive term due to genetic drift, and a jump term, representing the effect of migration, to a state distributed according to its own law.
Cognitive control mechanisms ensure goal-directedness in behaviour. Difficulties in cognitive control are well-established in conditions such as attention-deficit/hyperactivity disorder (ADHD) and autism. On the neural level, midfrontal theta (4-8 Hz) activity has emerged as a reliable correlate of cognitive control processes. Previous findings showed alterations in theta-based signals in both ADHD and autism, most notably an increase in the variability of theta phases across trials in cognitive control tasks, which was predictive of increased response time variability (RTV) as well. Crucially, recent work on twin studies has provided strong evidence for the genetic underpinning of these associations. Here, for the first time, we investigated whether polygenic scores (PGS) for ADHD and autism can predict RTV and EEG-derived theta-based measures of cognitive control in 454 participants. We found that PGS for ADHD, but not autism, accounted for a significant proportion of the variance in theta phase variability, captured via inter-trial coherence (ITC), in the well-standardised arrow-flanker task (2.5% of total variance, corresponding to 3.3% of the reliable variance). Furthermore, theta-ITC showed excellent test-retest reliability in our sample, indicating psychometric robustness, which in turn, further strengthens our findings. These results provide robust evidence linking genetic risk to neural measures and suggest that core dysregulation of the temporal coordination of control processes in ADHD is under genetic influence.
Habitat fragmentation is one of the most immediate and substantial threats to biodiversity, generating isolated populations with reduced genetic diversity. Genetic monitoring has become essential for detecting fragmentation and tracking its progress. However, the coherent interpretation of genetic monitoring data and understanding the genetic consequences of fragmentation require frameworks that accurately represent real-world complexity. Existing theoretical frameworks typically rely on simplified spatial structures and do not adequately capture the heterogeneous migration patterns of natural populations. Here, we integrate network theory and mathematical population genetics to develop a framework for studying the genetic consequences of fragmentation processes, explicitly accounting for heterogeneous connectivity and temporal dynamics. We apply this framework to examine how different fragmentation processes affect genetic measures commonly used in genetic monitoring. Through analysis of simulated and empirical networks, we find that different fragmentation scenarios produce substantially distinct trajectories in key genetic measures, sometimes exhibiting rapid transitional dynamics. Furthermore, fragmentation can cause deviations from classical theoretical expectations, such as the expected correlation between genetic and geographic distance (isolation-by-distance) or between genetic diversity and connectivity. Finally, we propose and demonstrate detectable early warning signals in genetic monitoring data that precede rapid transitional phases. Our framework thus provides a practical interpretation of genetic monitoring data, and a proof-of-concept that bridges the gap between idealized theoretical models and real-world connectivity dynamics.
Most theoretical work on the origin of heredity has focused on how genetic information can be maintained without mutational degradation in the absence of error-proofing systems. A simple and parsimonious solution assumes the first gene sequences evolved inside dividing protocells, which enables selection for functional sets. But this model of information maintenance does not consider how protocells acquired their genetic information in the first place. Clues to this transition are suggested by patterns in the genetic code, which indicate a strong link to autotrophic metabolism, with early translation based on direct physical interactions between amino acids and short RNA polymers, grounded in their hydrophobicity. Here, we develop a mathematical model to investigate how random RNA polymers inside autotrophically growing protocells could evolve better coding sequences for discrete functions. The model tracks a population of protocells that evolve towards two essential functions: CO2 fixation (which drives monomer synthesis and cell growth) and copying (which amplifies replication and translation of sequences inside protocells). The model shows that distinct coding sequences can emerge from random RNA sequences driving increased protocell division. The analysis reveals an important restriction: growth-supporting functions such as CO2 fixation must be more easily attained than informational processes such as RNA copying and translation. This uncovers a fundamental constraint on the emergence of genetic heredity: growth precedes information at the origin of life.