Journal of Theoretical Biology

Global populations are ageing at an unprecedented rate. For many diseases, age is a strong indicator of susceptibility, morbidity, or mortality. Principles of evolutionary biology can be leveraged to understand how pathogens may optimally exploit new populations, and the impact of this on the global burden of infectious-disease-induced mortality. We parameterised an age-specific R0 model with 2017 epidemiological data on Measles, Tuberculosis, Meningitis, and Ebola, and age-specific demographic estimates for 2017 and 2050, for the seven Global Burden of Disease super-regions. We explored the theoretical trade-offs between pathogen virulence & transmission, and virulence & host recovery, parameterising trade-off parameters using Latin Hypercube Sampling. Population ageing between 2017-2050 saw an increase in virulence induced mortality in four settings: 1) Ebola in sub-Saharan Africa, 2) Measles in central/eastern Europe & central Asia region, 3) Measles in North Africa & the Middle East and 4) Tuberculosis in the central/eastern Europe & central Asia region. The decrease in infection duration due to an increase of elderly people drives pathogen virulence down for diseases in the remaining settings. Understanding the mechanisms that shape pathogen dynamics and leveraging this to predict future challenges is key to endemic disease management in a rapidly changing world. Author SummaryKey aspects of disease transmission including susceptibility to infection, the severity of infection, and the probability of dying from that infection, are affected by host age. Global populations are rapidly ageing, so that the mean age of most populations is generally higher than it used to be and is set to continue on this trajectory. This suggests that the dynamics of infectious diseases are also likely to change, although infectious disease dynamics tend to be non-linear as these key parameters interact. We have developed a dynamic modelling framework to explore how changes in population age structure might impact the optimal level of pathogen virulence in a population. We have chosen four infectious diseases as case studies, that differentially impact certain age classes to illustrate these dynamics. We have parameterised this framework with open access data for each of the seven Global Burden of Disease super-regions and show that population ageing can increase virulence for several diseases in differing global regions, whilst increased background rates of mortality can drive virulence down in others.

Trees accumulate somatic mutations throughout their long lifespan, resulting in genetic mosaicism among branches. While recent genomic studies quantified these mutations, they were largely limited to describing static patterns of variation. In this study, we developed a mathematical model to infer the dynamic processes of somatic mutation accumulation from snapshot genomic data obtained from four tropical trees (Dipterocarpaceae), which dominate tropical rain forests in Southeast Asia. Our model focus on genetic differences between shoot apical meristems (SAMs) at branch tips and explicitly incorporate stem cell dynamics within SAMs during shoot elongation and branching, enabling us to quantify somatic genetic drift arising from stem cell lineage replacement. By comparing model predictions with empirical data from Dipterocarpaceae trees, we estimated key parameters governing stem cell dynamics and somatic mutation rates. Our results indicate that both shoot elongation and branching involve replacement of stem cell lineages, leading to a moderate degree of somatic genetic drift. Accounting for stem cell dynamics resulted in slightly lower mutation rate estimates than previous approaches that ignored these processes. Using the estimated parameters, we further performed stochastic simulations to predict patterns of somatic mutations, including features not directly observed in the sampled trees, such as occasional deviations of somatic mutation phylogenies from physical architecture. Together, our modeling framework provides insights into how genetic mosaicism is shaped within tropical trees and reveals the stem cell dynamics underlying their long-term growth and accumulation of somatic mutations. (236 words) Highlights- We built mathematical models to predict the genetic differences between branch tips by somatic mutations. - The model considers the varying dynamics of stem cells in shoot meristem during shoot elongation and branching. - We compared the model prediction with empirical data from tropical trees, Dipterocarpaceae, and estimated the dynamics of stem cells and mutation rate. - Somatic mutation dynamics were shaped by somatic genetic drift arising from stem cell lineage replacement during shoot elongation and branching. - Accounting for stem cell dynamics led to slightly smaller estimates of mutation rates compared with previous estimates that ignored the dynamics. - Our models offer insights into how genetic variability is shaped in the tropical trees and the stem cell dynamics underlying their long-term growth.

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.

Alzheimers disease (AD) is characterized by the accumulation of amyloid-{beta} (A{beta}), yet the specific link between plaque burden and cognitive decline remains a subject of intense investigation. This paper presents a mathematical model that simulates the coupled dynamics of A{beta} monomers, soluble oligomers, and fibrillar species in the brain tissue. By modifying existing moment equations to include a dedicated conservation equation for A{beta} monomers, the model explores how various microscopic processes, such as primary nucleation, surface-catalyzed secondary nucleation, fibril elongation, and fragmentation, contribute to macroscopic disease progression. Central to this study is the concept of "accumulated neurotoxicity" as a surrogate marker of biological age, defined as the time-integrated concentration of soluble A{beta} oligomers. Unlike plaque burden, accumulated neurotoxicity cannot be reversed, and the harm it causes depends critically on the sequence of events that produced it. Numerical results demonstrate that while plaque burden and neurotoxicity both increase over time, their relationship is non-linear and highly sensitive to the efficiency of protein degradation machinery. Specifically, impaired degradation leads to a rapid advancement of biological age relative to calendar age. The model further identifies oligomer dissociation and fibril fragmentation as potential protective mechanisms that can counterintuitively reduce neurotoxic burden by diverting monomers away from the soluble oligomer pool. These findings provide a quantitative framework for understanding why individuals with similar plaque burdens may experience vastly different cognitive outcomes, underscoring the importance of targeting soluble oligomers early in therapeutic interventions.

Price equation and genotype dynamics are two methods for studying the fixation of one allele by natural selection in a diploid population. There are two strict monotonicity conditions that imply the fixation of one allele. The genotype dynamics is called Haldane monotone if the relative frequency of one allele strictly increases along all solutions of the genotype dynamics, so this allele is fixed. In this paper, we show that the genotype dynamics is Haldane monotone if and only if the right-hand side of the Price equation is always strictly positive. The other strict monotonicity condition requires that the relative frequency of a homozygote strictly increase according to the genotype dynamics. For example, in a model where the genotype dynamics is governed by interactions between individuals, the cost-accepting homozygote is fixed by natural selection if the other genotypes always receive a smaller average gain from all interactions than the cost-accepting homozygote. Both monotonicity conditions require that the interaction is not well-mixed in the population. These two conditions are not equivalent. In addition, we give a non-monotonicity condition, which also implies the fixation of a homozygote. The fixation of a homozygote depends on the phenotypic payoff of the interaction, the genotype-phenotype mapping, and the interaction scheme. In a sexual population, the interaction scheme of siblings depends on the mating system, and so do the conditions of fixation of the cost-accepting homozygote. We present examples showing that if we only change the monogamous mating system, assuming panmixing or mating assortativity, then the condition for the fixation of the cooperator homozygote is b > 2c and b > c, respectively.

Studies of appendage regeneration in vertebrates have shown that the fundamental building block of any regenerative tissue is a blastema. The blastema is a cone-shaped accumulation that forms at the site of amputation post wound-healing and is the result of a highly coordinated process involving a cluster of cells capable of growth, migration, and differentiation. Although several key signaling pathways involved in regeneration have been identified, which cellular processes they control and how these processes are coordinated across space and time are not yet fully understood. This study introduces a computational tool to examine how the outgrowth results from the interaction of two tissue layers: the bulk (mesenchyme) and the overlying epithelium. We developed a novel hybrid agent-based modeling framework and an accompanying parameter inference pipeline to uncover the cellular properties in the epithelium and the mesenchyme driving the formation of a normal regenerative blastema with a morphology similar to that observed in experiments. Using our model, we report two conditions for blastema formation: retained local softening of the epithelial layer at the site of injury, which was confirmed experimentally with atomic force microscopy (AFM) measurements, and the involvement of the Wnt signaling pathway in the directed migration of mesenchyme cells towards the distal tip. Taken together, this combined experimental-theoretical approach provides a framework for understanding how the Wnt signaling pathway influences the formation of the early blastema at multiple levels of organization and how key cellular behaviors contribute to its formation. Author SummaryA small number of tetrapods have retained the ancestral ability to regenerate tissues and even limbs. Indifferent of species or tissue, the decisive initial stage of limb regeneration is the formation of a specialized structure called the blastema, a heterogeneous mass of mesenchymal cells, in a relatively short timescale of 2-14 days post injury or amputation. To study the mechanical and cellular conditions for limb blastema formation in the axolotl model organism, we developed a novel hybrid agent-based modeling framework and accompanying kinetic parameter inference pipeline. By recapitulating blastema morphometrics of healthy and stalled regenerative states, our model finds two conditions for blastema formation: retained local softening of the epithelial layer at the injury site post wound-healing, which we confirmed with atomic force microscopy measurements, and that the Wnt signaling pathway plays a role in the migration of mesenchyme cells to the distal tip in order to produce the blastema.

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.

Patterns in the vegetation across arid and semiarid regions may be explained as a form of self-organization driven by water scarcity, and are often modeled through reaction-diffusion dynamics. Recent work has shown that similar mathematical models generate patterns on networks. However, these studies have focused on idealized topologies with no reference to natural pattern-forming systems. Our study aims at bridging these two fields: we employ a physical reaction-diffusion vegetation model, and gradually modify the topology of the diffusion network by adding random shortcuts over a 2-dimensional grid, interpolating between a regular lattice and a random network. We found that network topology strongly shapes both the resulting vegetation patterns and the precipitation range that supports them. Three behavioral regimes emerge. On a regular lattice, high-regularity patterns develop reflecting local diffusion processes. On a random network, the system is dominated by global pressure towards homogenization yielding either a uniform state or a single patch. In the intermediate shortcut density range, as the network topology resembles a small world network, the interaction between the two scales of diffusion generates two kinds of disordered patterns: low-regularity patterns with a well-defined characteristic wavelength, and irregular patterns characterized by a broad patch size distribution. These disordered patterns resemble real-world observations and, in our model, they show different responses to changing precipitation. Although we focused on dryland vegetation, we suggest that network-mediated diffusion could lead to similar mechanisms in a wide variety of pattern-forming systems. HighlightsO_LIWe study vegetation pattern formation over different diffusion network topologies. C_LIO_LITwo kinds of stable disordered patterns states develop over small world topologies. C_LIO_LILow-regularity patterns with a well-defined characteristic wavelength. C_LIO_LIIrregular patterns characterized by a broad patch size distribution. C_LIO_LIThese different kinds of disordered states show different relations to precipitation. C_LI

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.

Melanoma is a cancer of the melanocyte, known to have an ability to readily switch between different transcriptional cell states that convey different phenotypic properties (e.g. hyper-differentiated, neural crest-like). This ability is believed to underpin intratumour heterogeneity and plastic adaptation, which contributes to resistance to therapy and immune evasion of the tumour. Therefore, understanding the mechanisms underlying acquisition of transcriptional cell states and cell-state switching is crucial for the development of therapies. We model a minimal gene regulatory network comprising three key transcription factors, whose varying gene expression encodes different melanoma cell states, and use deterministic spatiotemporal differential-equation models to study gene-expression dynamics. We exploit an approximation, based on cooperative binding of transcription factors, in which the models are piecewise-linear. We classify stable states of the local model in a biologically relevant manner and, using a naive model of intercellular communication, we explore how a population of cells can take on a shared characteristic through travelling waves of gene expression. We derive a condition determining which characteristic will become dominant, under sufficiently strong cell-cell signalling, which creates a partition of parameter space.

Infectious disease surveillance systems in tropical countries show that respiratory disease incidence generally manifests as year-round activity with weak fluctuations and irregular seasonality. Previously, using a ten-year time series of influenza-like illness (ILI) collected from outpatient clinics in Ho Chi Minh City (HCMC), Vietnam, we found a combination of nonannual and annual signals driving these dynamics, but with unknown mechanisms. In this study, we use seven stochastic dynamical models incorporating humidity, temperature, and school term to investigate plausible mechanisms behind these annual and nonannual incidence trends. We use iterated filtering to fit the models and evaluate the models by comparing how well they replicate the combination of annual and nonannual signals. We find that a model including specific humidity, temperature, and school term best fits our observed data from HCMC and partially reproduces the irregular seasonality. The estimated effects from specific humidity and temperature on transmission are nonlinearly negative but weak. School dismissal is associated with decreased transmission, but also with low magnitude. Under these weak external drivers, we hypothesize that stochasticity makes a strong sub-annual cycle more likely to be observed in ILI disease dynamics. Our study shows a possible mechanism for respiratory disease dynamics in the tropics. When the external drivers are weak, the seasonality of respiratory disease dynamics is prone to the influence of stochasticity. Author SummaryAlthough the mechanisms driving seasonality of respiratory disease dynamics have been well-studied in temperate regions, they are unknown in the tropics. In this study, we used a 10-year influenza-like-illness (ILI) daily-reporting data set collected from outpatient clinics in Ho Chi Minh City (HCMC) in Vietnam to investigate the mechanisms associated with annual and nonannual ([~]215 days) periodic patterns in the data. By comparing seven mechanistic models against the data, we showed that the mechanism that best explains respiratory disease dynamics in HCMC is a stochastic susceptible-infected-recovered-susceptible (SIRS) model weakly driven by external drivers including specific humidity, temperature, and school term. The nonannual cycles duration is consistent with the inferred duration of immunity of the model. By showing the nonannual cycle as strong as in the data is only observed in stochastic model, we showed that the observed respiratory disease dynamics in HCMC is under the influence of stochasticity when external drivers are weak.

Hepatocyte transplantation is a promising alternative to liver transplantation; however, it currently serves only as a temporary treatment until a donor organ becomes available. In contrast, animal studies have demonstrated "liver repopulation", a phenomenon in which transplanted hepatocytes progressively replace host hepatocytes. Despite extensive documentation, the mechanisms driving this process remain poorly understood. More fundamentally, it remains unclear whether liver repopulation is driven by active cell-cell interactions between host and transplanted hepatocytes that induce host cell death, or whether it can be explained solely by intrinsic differences in proliferation and survival between these populations. To address this, we performed computational simulations using an agent-based model constrained by experimental data from repopulation in uninjured rat livers. Our analysis reveals that host hepatocyte death rate is the dominant determinant of repopulation kinetics, whereas variations in proliferation rate have only a limited impact. Notably, experimentally observed repopulation dynamics were only reproduced when cell- cell interactions were incorporated, or alternatively when host hepatocyte lifespan was set to unrealistically short values (approximately 25 days). These findings support a model in which cell- cell interactions play a critical role in efficient liver repopulation. More broadly, this study establishes a conceptual and computational framework for evaluating the requirement for cell-cell interactions in tissue replacement, even in the absence of a defined molecular mechanism.

Mass-conserved reaction-diffusion systems are used as mathematical models for various phenomena such as cell polarity. Numerical simulations of this system present transient dynamics in which multiple stripe patterns converge to spatially monotonic patterns. Previous studies indicated that the transient dynamics are driven by a mass conservation law and by variations in the amount of substance contained in each pattern, which we refer to as "pattern flux". However, it is challenging to mathematically investigate these pattern dynamics. In this study, we introduce a reaction-diffusion compartment model to investigate the pattern dynamics in view of the conservation law and the pattern flux. This model is defined on multiple intervals (compartments), and diffusive couplings are imposed on each boundary of the compartments. Corresponding to the transient dynamics in the original system, we consider the dynamics around stripe patterns in the compartment model. We derive ordinary differential equations describing the pattern dynamics of the compartment model and analyze the existence and stability of equilibria for the reduced ODE with respect to the boundary parameters. For a specific parameter setting, we obtained results consistent with previous studies. Moreover, we present that the stripe patterns in the compartment model are potentially stabilized by changing the parameter, which is not observed in the original system. We expect that the methodology developed in this paper is extendable to various directions, such as membrane-induced pattern control.

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.

The influence of arbitrary randomness in cell division times on the variability of protein copy numbers within a lineage ensemble has been recently studied, going beyond the contributions of noisy gene expression and partitioning error. However, variability of protein concentrations need separate study, since cell size growth between cell divisions dilute protein concentrations at the same rate as size growth, which also determines mean division times. Here for a model of bursty protein production, we present exact moments (of all orders) of protein concentrations in the cyclo-stationary state, comparing: (i) population and lineage cell ensembles, and (ii) statistics at different cell ages. Two interesting results emerge. While the variance of protein concentration changes with the degree of division time heterogeneity at any cell age, the age-averaged variance is independent of it within lineage ensemble but stays dependent within population ensemble. The skewness within population ensemble is higher in younger cells than within lineage ensemble, and this behavior reverses at older ages. Such a feature vanishes for the age-averaged distribution, with population based skewness always dominating over that of lineage. We also show that mother-daughter correlations in generation times, do not add any significant difference to the results.

Human walking is intrinsically variable. For example, there is considerable stride to stride variability even when walking speed is constant. This variability is due to uncertainty in the sensorimotor system and the environment, and is shaped by both musculoskeletal dynamics (e.g. joint stiffness and damping originating from muscles) and the control strategy used to mitigate the effects of uncertainty. Yet, insight into how sensorimotor noise shapes walking variability is limited due to a lack of experimental methods to assess sensorimotor noise and control strategies during walking. Simulations that account for uncertainty can elucidate how sensorimotor noise affects movement variability but due to numerical challenges, accounting for sensorimotor noise is not common in simulations of walking. Existing simulations have hugely simplified musculoskeletal dynamics (e.g. no muscles), the control policy (e.g. pre-defined feedback loops), or sensorimotor noise sources (e.g. only motor noise). Here, we performed stochastic optimal control simulations of walking based on a model with 9 degrees of freedom and 18 muscles to study how the level of sensory and motor noise influences walking. We solved for feedforward muscle excitations and full-state time-varying feedback gains that minimised expected effort while generating periodic, and hence stable, gait patterns. To enable these simulations, we approximated the state distribution with a Gaussian and used an unscented transform to propagate the state covariance. Resulting optimisation problems were solved with direct collocation. Sensorimotor noise level had a small effect on the mean kinematics but shaped kinematic and muscle activity variability as well as expected effort. Although simulations underestimated the magnitude of experimental positional variability, they captured its structure. In agreement with experimental results, the control policy prioritised limiting variability of centre of mass kinematics and minimal swing foot clearance over limiting joint angle variability. Hence, our simulations suggest that effort minimisation underlies these observations. Author summaryWhen performing a movement multiple times, each repetition will be slightly different due to random disturbances in the neural signals used to control movement, i.e. sensorimotor noise. Because it is difficult to measure inside the nervous system of a moving person, computer simulations are used to study movement control. They found that both sensorimotor noise and musculoskeletal mechanics determine how people control arm movements and standing. However, there are no simulations of walking that systematically evaluated how sensorimotor noise level influences walking kinematics because they pose computational challenges. Here, we proposed and used an approach for minimal effort simulations of walking in the presence of uncertainty. We imposed forward speed and stability but not kinematics. We found that the level of sensorimotor noise had little effect on the mean movement but a strong effect on the variability and the expected effort. The control strategy prioritised reducing the variability of the centre of mass position and swing foot clearance over reducing the variability of individual joint angles, which is also observed in experiments. Interestingly, strict control of centre of mass position and foot clearance in our simulations emerged from minimising effort.

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.

Evolving populations, especially in the strong-selection-weak-mutation limit, can be modelled as adaptive walks on fitness landscapes, moving in fitness-increasing mutational steps until reaching a fitness peak--a local optimum. Simulations of such adaptive walks--on a multi-peaked empirical landscape of the folA gene and on landscapes generated by the Rough Mount Fuji (RMF) model-- have shown that some landscapes are highly navigable, meaning that the highest x% of peaks are reached by >> x% of adaptive walks. This prompts the question of how adaptive walks can be so successful despite the local, myopic rules behind each adaptive step. Here, we investigate this question using simulations and mathematical approximations of random adaptive walks on a simplified RMF landscape. The landscape has a low-to-intermediate fitness region, whose size reconciles a low peak density with a high peak number. Despite the high number of peaks, walkers are likely to exit this region without terminating at a peak because the probability of a peak transition at each step is low and a fitness gradient guides walkers to the high-fitness region in few steps. Thus, three features are sufficient to explain why adaptive walks in the simplified RMF landscape are likely to reach a small fraction of top-ranking peaks: a low-to-intermediate fitness region with a high number of peaks, a low peak-transition probability, and which is crossed in few steps. We find that these three features are also present in the empirical folA landscape, suggesting that similar principles may apply.

The practical utility of many modern phylogenetic comparative methods can depend on how accurately mathematical models capture the evolutionary process of traits. Boucher and Demery (2016) described a new quantitative trait model, Brownian motion with reflective limits, that they anticipated might be of use in testing hypotheses about a particular sort of constraint on phenotypic character evolution. Since their analytic solution for the probability function under this bounded evolutionary scenario was not practical to evaluate for reasonably-sized trees, Boucher and Demery (2016) also identified a creative technique for computing the likelihood of their model. The basis of this methodology derives from the convergence of an equal-rates, symmetric, ordered Markov chain and continuous stochastic diffusion in the limit as the number of steps in our chain goes to {infty} (or, alternatively, as their widths decrease towards zero). We refer to this convergence in the limit as the discretized diffusion approximation or (more compactly) the discrete approximation. We realized that this discrete approximation of Boucher and Demery (2016) unlocked a number of additional models for the phylogenetic comparative analysis of discrete and continuous trait data, and we explore several of these in the present article. Specifically, we examine application of this discretized diffusion approximation to the threshold model from evolutionary quantitative genetics, to a new "semi-threshold" trait evolution model, to a joint model of discrete and continuous traits in which the discrete trait influences the rate of evolution of our continuous character, as well as a model where precisely the converse is true, and to a discrete character dependent multi-trend trended continuous trait evolution model. We conclude with some context for the origins of our article and discussion of other possible applications of this powerful approach.