An immune memory-structured SIS epidemiological model for hyperdiverse pathogens.

A hyperdiverse class of pathogens of humans and wildlife, including the malaria parasite Plasmodium falciparum, relies on multigene families to encode antigenic variation. As a result, high (asymptomatic) prevalence is observed despite high immunity in local populations under high-transmission settings. The vast diversity of "strains" and genes encoding this variation challenges the application of established models for the population dynamics of such infectious diseases. Agent-based models have been formulated to address theory on strain coexistence and structure, but their complexity can limit application to gain insights into population dynamics. Motivated by P. falciparum malaria, we develop an alternative formulation in the form of a structured susceptible-infected-susceptible population model in continuous time, where individuals are classified not only by age, as is standard, but also by the diversity of parasites they have been exposed to and retain in their specific immune memory. We analyze the population dynamics and bifurcation structure of this system of partial-differential equations, showing the existence of alternative steady states and an associated tipping point with transmission intensity. We attribute the critical transition to the positive feedback between parasite genetic diversity and force of infection. Basins of attraction show that intervention must drastically reduce diversity to prevent a rebound to high infection levels. Results emphasize the importance of explicitly considering pathogen diversity and associated specific immune memory in the population dynamics of hyperdiverse epidemiological systems. This statement is discussed in a more general context for ecological competition systems with hyperdiverse trait spaces.

Blood Lipoproteins Shape the Phenotype and Lipid Content of Early Atherosclerotic Lesion Macrophages: A Dual-Structured Mathematical Model.

Macrophages in atherosclerotic lesions exhibit a spectrum of behaviours or phenotypes. The phenotypic distribution of monocyte-derived macrophages (MDMs), its correlation with MDM lipid content, and relation to blood lipoprotein densities are not well understood. Of particular interest is the balance between low density lipoproteins (LDL) and high density lipoproteins (HDL), which carry bad and good cholesterol respectively. To address these issues, we have developed a mathematical model for early atherosclerosis in which the MDM population is structured by phenotype and lipid content. The model admits a simpler, closed subsystem whose analysis shows how lesion composition becomes more pathological as the blood density of LDL increases relative to the HDL capacity. We use asymptotic analysis to derive a power-law relationship between MDM phenotype and lipid content at steady-state. This relationship enables us to understand why, for example, lipid-laden MDMs have a more inflammatory phenotype than lipid-poor MDMs when blood LDL lipid density greatly exceeds HDL capacity. We show further that the MDM phenotype distribution always attains a local maximum, while the lipid content distribution may be unimodal, adopt a quasi-uniform profile or decrease monotonically. Pathological lesions exhibit a local maximum in both the phenotype and lipid content MDM distributions, with the maximum at an inflammatory phenotype and near the lipid content capacity respectively. These results illustrate how macrophage heterogeneity arises in early atherosclerosis and provide a framework for future model validation through comparison with single-cell RNA sequencing data.

Impacts of estuarine habitat degradation on the modeled life history of marine estuarine-dependent and resident fish species.

Shallow coastal and estuarine habitats play an essential role in the life cycles of many fish species, providing spawning, nursery, feeding, and migration areas. However, these ecologically valuable habitats are increasingly threatened by anthropogenic activities, causing substantial changes in both habitat availability and quality. Fish species use these shallow coastal habitats and estuaries during various life stages, leading to their categorization into guilds based on how and when they rely on these areas. This differential functional use of estuaries means that changes to these habitats may affect each guild differently. To understand the impact of estuarine habitat degradation on fish populations, it is therefore necessary to consider the full life cycle of fish and when they rely on these coastal habitats. Here, we use conceptual size-structured population models to study how estuarine habitat degradation affects two functionally different guilds. We use these models to predict how reduced food productivity in the estuary affects the demographic rates and population dynamics of these groups. Specifically, we model estuarine residents, which complete their entire life cycle in estuaries, and marine estuarine-dependent species, which inhabit estuaries during early life before transitioning offshore. We find that total fish biomass for both guilds decreases with decreasing food productivity. However, the density of juveniles of the marine estuarine-dependent guild can, under certain conditions, increase in the estuary. This occurs due to a shift in the population biomass distribution over different life stages and a simultaneous shift in which life stage is most limited by food. At the individual level, somatic growth of juveniles belonging to the estuarine-dependent guild decreased with lower food supply in the estuary, due to increased competition for food. The somatic growth rates of fish belonging to the resident guild were largely unaffected by low food supply, as the total fish density decreased at the same time and therefore the per-capita food availability was similar. These outcomes challenge the assumption that responses to habitat degradation are similar between fish guilds. Our study highlights the need to assess not only fish biomass but also size distributions, survival, and somatic growth rates for a comprehensive understanding of the effects of habitat degradation on fish populations. This understanding is crucial not only for estuary fish communities but also for successful conservation and management of commercially harvested offshore population components.

A Cost-Benefit Analysis of Alternative Management Strategies for Red Deer in Denmark.

In this paper, we conduct a cost-benefit analysis (CBA) of five alternative management strategies for red deer in Denmark: free harvest, trophy hunting, maximum harvest and two cases for natural demographic population compositions. To capture the outcome under each strategy we use a biological sex- and age-structured population model. The net benefit function includes meat values, recreational values, browsing damage costs and traffic damage costs and these values and costs are assumed to differ for the various sex and age classes of red deer. We show that the maximum harvest strategy leads to a reasonably high positive total net benefit, while the free harvest strategy yields a small positive net benefit. On the other hand, the trophy hunting strategy generates a high negative net benefit, while small negative net benefits are obtained under the two strategies for natural demographic population compositions.

Evaluating the importance of individual heterogeneity in reproduction to Weddell seal population dynamics using integral projection models.

Identifying and accounting for unobserved individual heterogeneity in vital rates in demographic models is important for estimating population-level vital rates and identifying diverse life-history strategies, but much less is known about how this individual heterogeneity influences population dynamics. We aimed to understand how the distribution of individual heterogeneity in reproductive and survival rates influenced population dynamics using vital rates from a Weddell seal population by altering the distribution of individual heterogeneity in reproduction, which also altered the distribution of individual survival rates through the incorporation of our estimate of the correlation between the two rates and assessing resulting changes in population growth. We constructed an integral projection model (IPM) structured by age and reproductive state using estimates of vital rates for a long-lived mammal that has recently been shown to exhibit large individual heterogeneity in reproduction. Using output from the IPM, we evaluated how population dynamics changed with different underlying distributions of unobserved individual heterogeneity in reproduction. Results indicate that the changes to the underlying distribution of individual heterogeneity in reproduction cause very small changes in the population growth rate and other population metrics. The largest difference in the estimated population growth rate resulting from changes to the underlying distribution of individual heterogeneity was less than 1%. Our work highlights the differing importance of individual heterogeneity at the population level compared to the individual level. Although individual heterogeneity in reproduction may result in large differences in the lifetime fitness of individuals, changing the proportion of above- or below-average breeders in the population results in much smaller differences in annual population growth rate. For a long-lived mammal with stable and high adult-survival that gives birth to a single offspring, individual heterogeneity in reproduction has a limited effect on population dynamics. We posit that the limited effect of individual heterogeneity on population dynamics may be due to canalization of life-history traits.

A Lipid-Structured Model of Atherosclerotic Plaque Macrophages with Lipid-Dependent Kinetics.

Atherosclerotic plaques are fatty growths in artery walls that cause heart attacks and strokes. Plaque formation is driven by macrophages that are recruited to the artery wall. These cells consume and remove blood-derived lipids, such as modified low-density lipoprotein. Ineffective lipid removal, due to macrophage death and other factors, leads to the accumulation of lipid-loaded macrophages and formation of a necrotic lipid core. Experimental observations suggest that macrophage functionality varies with the extent of lipid loading. However, little is known about the influence of macrophage lipid loads on plaque fate. Extending work by Ford et al. (J Theor Biol 479:48-63, 2019) and Chambers et al. (A lipid-structured model of atherosclerosis with macrophage proliferation, 2022), we develop a plaque model where macrophages are structured by their ingested lipid load and behave in a lipid-dependent manner. The model considers several macrophage behaviours, including recruitment to and emigration from the artery wall; proliferation and apotosis; ingestion of plaque lipids; and secondary necrosis of apoptotic cells. We consider apoptosis, emigration and proliferation to be lipid-dependent and we model these effects using experimentally informed functions of the internalised lipid load. Our results demonstrate that lipid-dependent macrophage behaviour can substantially alter plaque fate by changing both the total quantity of lipid in the plaque and the distribution of lipid between the live cells, dead cells and necrotic core. The consequences of macrophage lipid-dependence are often unpredictable because lipid-dependent effects introduce subtle, nonlinear interactions between the modelled cell behaviours. These observations highlight the importance of mathematical modelling in unravelling the complexities of macrophage lipid accumulation during atherosclerotic plaque formation.

Pulse disturbances in age-structured populations: Life history predicts initial impact and recovery time.

Understanding population responses to discrete 'pulsed' environmental disturbances is essential to conservation and adaptive management. Populations of concern can be driven to low levels by disturbance, and understanding interspecific differences in recovery trajectories is necessary for evaluating management options. We analysed single-species models to investigate the demographic and management factors determining the two components of population 'resilience': the magnitude of initial impact on population abundance, and duration of the recovery time. We simulated age-structured populations with density-dependent recruitment, subjected to a pulse disturbance consisting of a period of increased mortality of either the juvenile age class or all age classes, and calculated both impact and return time. For illustration, we used demographic parameters from a suite of 16 fish species. We formulated the model as a renewal equation, allowing us to describe disturbance impacts mathematically as a convolution. We also included nonlinear dynamics, representing populations that recover to a steady state; this is more realistic (in most cases) than prior analyses of resilience in linear models without density-dependence. When the disturbance affected only one or a few young age-classes, longevity was the major life-history determinant of impact and recovery time. Shorter-lived species endured greater impacts when disturbed because each age class is a greater proportion of the population. However, shorter-lived species also had faster recovery times, for the same reason. When disturbance affected adult age-classes, the impact was more immediate and no longer affected by species' longevity, though the effect of longevity on recovery time remained. These results improve our understanding of interspecific differences in resilience and increase our ability to make predictions for adaptive management. Additionally, formulating the problem as a renewal equation and using mathematical convolutions allows us to quantify how disturbances with different time courses (not just an immediate, constant level of disturbance but gradually increasing or decreasing levels of disturbance) would have different effects on population resilience: delayed responses for species in which biomass is concentrated in older age classes, and for disturbances that become progressively more severe.

Entender las respuestas de la población a perturbaciones ambientales, específicamente a pulsadas individuales, es esencial para la conservación y la gestión adaptativa. Las poblaciones de interés pueden reducirse a niveles bajas debido a la perturbación, y es necesario entender las diferencias interespecíficas en las trayectorias de recuperación para evaluar las opciones de gestión. Analizamos modelos para especies individuales para investigar los factores demográficos y de gestión que determinan los dos componentes de la 'resiliencia' de la población: la magnitud del impacto inicial sobre la abundancia de la población y la duración del tiempo de recuperación. Simulamos poblaciones estructuradas por edad con reclutamiento que depende de la densidad, las sometimos a una perturbación pulsada que consiste en un período de mayor mortalidad del grupo etário juvenil o de todos los grupos etários, y calculamos tanto el impacto como el tiempo de retorno. A modo de ilustración, utilizamos parámetros demográficos de un conjunto de 16 especies de peces. Formulamos el modelo como una ecuación de renovación, lo que nos permite describir matemáticamente los impactos de las perturbaciones como una convolución. También incluimos dinámicas no lineales que representan poblaciones que se recuperan hacia un estado estable; esto es más realista (en la mayoría de los casos) que los análisis previos de resiliencia en modelos lineales sin la dependencia de la densidad. Cuando la perturbación ha afectado a uno o a algunos pocos grupos etários jóvenes, la longevidad fue el principal determinante de la historia de vida del impacto y el tiempo de recuperación. Las especies de vida más corta sufrieron mayores impactos cuando fueron perturbadas porque cada grupo etáreo representa una mayor proporción de la población. Sin embargo, las especies con vidas más cortas también tuvieron tiempos de recuperación más rápidos, por la misma razón. Cuando la perturbación afectó a los grupos etários adultos, el impacto fue más inmediato y ya no se vio afectado por la longevidad de las especies, aunque se mantuvo el efecto de la longevidad sobre el tiempo de recuperación. Estos resultados mejoran nuestra comprensión de las diferencias interespecíficas de la resiliencia y aumentan nuestra capacidad para hacer predicciones con fin a la gestión adaptativa. Además, formular el problema como una ecuación de renovación y usar convoluciones matemáticas nos permite cuantificar cómo las perturbaciones con distintos lapsos de tiempo (no solo un nivel de perturbación constante e inmediato, sino niveles de perturbación que aumentan o disminuyen gradualmente) tendrían diferentes efectos sobre la resiliencia de la población: respuestas tardías para especies en las que la biomasa se concentra en grupos etários de mayor edad y para perturbaciones que se vuelven progresivamente más severas.

Transmission Dynamics of Tuberculosis with Age-specific Disease Progression.

Demographic structure and latent phenomenon are two essential factors determining the rate of tuberculosis transmission. However, only a few mathematical models considered age structure coupling with disease stages of infectious individuals. This paper develops a system of delay partial differential equations to model tuberculosis transmission in a heterogeneous population. The system considers demographic structure coupling with the continuous development of disease stage, which is crucial for studying how aging affects tuberculosis dynamics and disease progression. Here, we determine the basic reproduction number, and several numerical simulations are used to investigate the influence of various progression rates on tuberculosis dynamics. Our results support that the aging effect on the disease progression rate contributes to tuberculosis permanence.

DEVELOPING INTEGRAL PROJECTION MODELS FOR ECOTOXICOLOGY.

In many ecosystems, especially aquatic ecosystems, size plays a critical role in the factors that determine an individual's ability to survive and reproduce. In aquatic ecotoxicology, size informs both realized and potential acute and chronic effects of chemical exposure. This paper demonstrates how chemical and nonchemical effects on growth, survival, and reproduction can be linked to population-level dynamics using size-structured integral projection models (IPM). The modeling approach was developed with the goals and constraints of ecological risk assessors in mind, who are tasked with estimating the effects of chemical exposures to wildlife populations in a data-limited environment. The included case study is a collection of daily time-step IPMs parameterized for the life history and annual cycle of fathead minnows (Pimephales promelas), which motivated the development of modeling techniques for seasonal, iteroparous reproduction, density dependent growth effects, and size-dependent over-winter survival. The effects of a time-variable annual chemical exposure were interpreted using a toxicokinetic-toxicodynamic model for acute survival and sub-lethal growth effects model for chronic effects and incorporated into the IPMs. This paper presents a first application of integral projection models to ecotoxicology. Our research demonstrates that size-structured IPMs provide a promising, flexible, framework for synthesizing ecotoxicologically relevant data and theory to explore the effects of chemical and nonchemical stressors and the resulting impacts on exposed populations.

Age-Structured SIR Model for the Spread of Infectious Diseases Through Indirect Contacts.

In this article, we discuss an age-structured SIR model in which disease spread not only through direct person-to-person contacts, but also spread through indirect contacts. It is evident that age also plays a crucial role in SARS virus infection including COVID-19 infection. We formulate our model as an abstract semilinear Cauchy problem in an appropriate Banach space to show the existence of solution and also show the existence of steady states. In this study, it is assumed that the population is in a demographic stationary state and we show that there is no disease-free equilibrium point as long as there is a transmission of infection due to the indirect contacts in the environment. We also solved our model numerically to study the effect of indirect contacts on the density of infected individuals.

Synchrony erodes spatial portfolios of an anadromous fish and alters availability for resource users.

Environmental forces can create spatially synchronous dynamics among nearby populations. However, increased climate variability, driven by anthropogenic climate change, will likely enhance synchrony among spatially disparate populations. Population synchrony may lead to greater fluctuations in abundance, but the consequences of population synchrony across multiple scales of biological organization, including impacts to putative competitors, dependent predators or human communities, are rarely considered in this context. Chinook salmon Oncorhynchus tshawytscha stocks distribute across the Northeast Pacific, creating spatially variable portfolios that support large ocean fisheries and marine mammal predators, such as killer whales Orcinus orca. We rely on a multi-population model that simulates Chinook salmon ocean distribution and abundance to understand spatial portfolios, or variability in abundance within and among ocean distribution regions, of Chinook salmon stocks across 17 ocean regions from Southeast Alaska to California. We found the expected positive correlation between the number of stocks in an ocean region and spatial portfolio strength; however, increased demographic synchrony eroded Chinook salmon spatial portfolios in the ocean. Moreover, we observed decreased resource availability within ocean fishery management jurisdictions but not within killer whale summer habitat. We found a strong portfolio effect across both Southern Resident and Northern Resident killer whale habitats that was relatively unaffected by increased demographic synchrony, likely a result of the large spatial area included in these habitats. However, within the areas of smaller fishing management jurisdictions we found a weakening of Chinook salmon portfolios and increased but inconsistent likelihood of low abundance years as demographic synchrony increased. We suggest that management and conservation actions that reduce spatial synchrony can enhance short-term ecosystem resilience by promoting the stabilizing effect multiple stocks have on aggregate Chinook salmon populations and overall resource availability.

Predicting phenological shifts in a changing climate.

Phenological shifts constitute one of the clearest manifestations of climate warming. Advanced emergence is widely reported in high-latitude ectotherms, but a significant number of species exhibit delayed, or no change in, emergence. Here we present a mechanistic theoretical framework that reconciles these disparate observations and predicts population-level phenological patterns based solely on data on temperature responses of the underlying life history traits. Our model, parameterized with data from insects at different latitudes, shows that peak abundance occurs earlier in the year when warming increases the mean environmental temperature, but is delayed when warming increases the amplitude of seasonal fluctuations. We find that warming does not necessarily lead to a longer activity period in high-latitude species because it elevates summer temperatures above the upper limit for reproduction and development. Our findings both confirm and confound expectations for ectotherm species affected by climate warming: an increase in the mean temperature is more detrimental to low-latitude species adapted to high mean temperatures and low-amplitude seasonal fluctuations; an increase in seasonal fluctuations is more detrimental to high-latitude species adapted to low mean temperatures and high-amplitude fluctuations.

Persistence and spread of stage-structured populations in heterogeneous landscapes.

Conditions for population persistence in heterogeneous landscapes and formulas for population spread rates are important tools for conservation ecology and invasion biology. To date, these tools have been developed for unstructured populations, yet many, if not all, species show two or more distinct phases in their life cycle. We formulate and analyze a stage-structured model for a population in a heterogeneous habitat. We divide the population into pre-reproductive and reproductive stages. We consider an environment consisting of two types of patches, one where population growth is positive, one where it is negative. Individuals move randomly within patches but can show preference towards one patch type at the interface between patches. We use linear stability analysis to determine persistence conditions, and we derive a dispersion relation to find spatial spread rates. We illustrate our results by comparing the structured population model with an appropriately scaled unstructured model. We find that a long pre-reproductive state typically increases habitat requirements for persistence and decreases spatial spread rates, but we also identify scenarios in which a population with intermediate maturation rate spreads fastest.

Noise-driven growth rate gain in clonal cellular populations.

Cellular populations in both nature and the laboratory are composed of phenotypically heterogeneous individuals that compete with each other resulting in complex population dynamics. Predicting population growth characteristics based on knowledge of heterogeneous single-cell dynamics remains challenging. By observing groups of cells for hundreds of generations at single-cell resolution, we reveal that growth noise causes clonal populations of Escherichia coli to double faster than the mean doubling time of their constituent single cells across a broad set of balanced-growth conditions. We show that the population-level growth rate gain as well as age structures of populations and of cell lineages in competition are predictable. Furthermore, we theoretically reveal that the growth rate gain can be linked with the relative entropy of lineage generation time distributions. Unexpectedly, we find an empirical linear relation between the means and the variances of generation times across conditions, which provides a general constraint on maximal growth rates. Together, these results demonstrate a fundamental benefit of noise for population growth, and identify a growth law that sets a "speed limit" for proliferation.

Forecasting and Uncertainty Quantification Using a Hybrid of Mechanistic and Non-mechanistic Models for an Age-Structured Population Model.

In this paper, we present a new method for the prediction and uncertainty quantification of data-driven multivariate systems. Traditionally, either mechanistic or non-mechanistic modeling methodologies have been used for prediction; however, it is uncommon for the two to be incorporated together. We compare the forecast accuracy of mechanistic modeling, using Bayesian inference, a non-mechanistic modeling approach based on state space reconstruction, and a novel hybrid methodology composed of the two for an age-structured population data set. The data come from cannibalistic flour beetles, in which it is observed that the adults preying on the eggs and pupae result in non-equilibrium population dynamics. Uncertainty quantification methods for the hybrid models are outlined and illustrated for these data. We perform an analysis of the results from Bayesian inference for the mechanistic model and hybrid models to suggest reasons why hybrid modeling methodology may enable more accurate forecasts of multivariate systems than traditional approaches.

A structured population model with diffusion in structure space.

A structured population model is described and analyzed, in which individual dynamics is stochastic. The model consists of a PDE of advection-diffusion type in the structure variable. The population may represent, for example, the density of infected individuals structured by pathogen density x, [Formula: see text]. The individuals with density [Formula: see text] are not infected, but rather susceptible or recovered. Their dynamics is described by an ODE with a source term that is the exact flux from the diffusion and advection as [Formula: see text]. Infection/reinfection is then modeled moving a fraction of these individuals into the infected class by distributing them in the structure variable through a probability density function. Existence of a global-in-time solution is proven, as well as a classical bifurcation result about equilibrium solutions: a net reproduction number [Formula: see text] is defined that separates the case of only the trivial equilibrium existing when [Formula: see text] from the existence of another-nontrivial-equilibrium when [Formula: see text]. Numerical simulation results are provided to show the stabilization towards the positive equilibrium when [Formula: see text] and towards the trivial one when [Formula: see text], result that is not proven analytically. Simulations are also provided to show the Allee effect that helps boost population sizes at low densities.

Using global sensitivity analysis of demographic models for ecological impact assessment.

Population viability analysis (PVA) is widely used to assess population-level impacts of environmental changes on species. When combined with sensitivity analysis, PVA yields insights into the effects of parameter and model structure uncertainty. This helps researchers prioritize efforts for further data collection so that model improvements are efficient and helps managers prioritize conservation and management actions. Usually, sensitivity is analyzed by varying one input parameter at a time and observing the influence that variation has over model outcomes. This approach does not account for interactions among parameters. Global sensitivity analysis (GSA) overcomes this limitation by varying several model inputs simultaneously. Then, regression techniques allow measuring the importance of input-parameter uncertainties. In many conservation applications, the goal of demographic modeling is to assess how different scenarios of impact or management cause changes in a population. This is challenging because the uncertainty of input-parameter values can be confounded with the effect of impacts and management actions. We developed a GSA method that separates model outcome uncertainty resulting from parameter uncertainty from that resulting from projected ecological impacts or simulated management actions, effectively separating the 2 main questions that sensitivity analysis asks. We applied this method to assess the effects of predicted sea-level rise on Snowy Plover (Charadrius nivosus). A relatively small number of replicate models (approximately 100) resulted in consistent measures of variable importance when not trying to separate the effects of ecological impacts from parameter uncertainty. However, many more replicate models (approximately 500) were required to separate these effects. These differences are important to consider when using demographic models to estimate ecological impacts of management actions.

Crop Fertilization Impacts Epidemics and Optimal Latent Period of Biotrophic Fungal Pathogens.

Crop pathogens are known to rapidly adapt to agricultural practices. Although cultivar resistance breakdown and resistance to pesticides have been broadly studied, little is known about the adaptation of crop pathogens to fertilization regimes and no epidemiological model has addressed that question. However, this is a critical issue for developing sustainable low-input agriculture. In this article, we use a model of life history evolution of biotrophic wheat fungal pathogens in order to understand how they could adapt to changes in fertilization practices. We focus on a single pathogen life history trait, the latent period, which directly determines the amount of resources allocated to growth and reproduction along with the speed of canopy colonization. We implemented three fertilization scenarios, corresponding to major effects of increased nitrogen fertilization on crops: (i) increase in nutrient concentration in leaves, (ii) increase of leaf lifespan, and (iii) increase of leaf number (tillering) and size that leads to a bigger canopy size. For every scenario, we used two different fitness measures to identify putative evolutionary responses of latent period to changes in fertilization level. We observed that annual spore production increases with fertilization, because it results in more resources available to the pathogens. Thus, diminishing the use of fertilizers could reduce biotrophic fungal epidemics. We found a positive relationship between the optimal latent period and fertilization when maximizing total spore production over an entire season. In contrast, we found a negative relationship between the optimal latent period and fertilization when maximizing the within-season exponential growth rate of the pathogen. These contrasting results were consistent over the three tested fertilization scenarios. They suggest that between-strain diversity in the latent period, as has been observed in the field, may be due to diversifying selection in different cultural environments.

Structured models of cell migration incorporating molecular binding processes.

The dynamic interplay between collective cell movement and the various molecules involved in the accompanying cell signalling mechanisms plays a crucial role in many biological processes including normal tissue development and pathological scenarios such as wound healing and cancer. Information about the various structures embedded within these processes allows a detailed exploration of the binding of molecular species to cell-surface receptors within the evolving cell population. In this paper we establish a general spatio-temporal-structural framework that enables the description of molecular binding to cell membranes coupled with the cell population dynamics. We first provide a general theoretical description for this approach and then illustrate it with three examples arising from cancer invasion.

How to quantify the temporal storage effect using simulations instead of math.

The storage effect has become a core concept in community ecology, explaining how environmental fluctuations can promote coexistence and maintain biodiversity. However, limitations of existing theory have hindered empirical applications: the need for detailed mathematical analysis whenever the study system requires a new model, and restricted theory for structured populations. We present a new approach that overcomes both these limitations. We show how temporal storage effect can be quantified by Monte Carlo simulations in a wide range of models for competing species. We use the lottery model and a generic integral projection model (IPM) to introduce ideas, and present two empirical applications: (1) algal species in a chemostat with variable temperature, showing that the storage effect can operate without a long-lived life stage and (2) a sagebrush steppe community IPM. Our results highlight the need for careful modelling of nonlinearities so that conclusions are not driven by unrecognised model constraints.