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Evolutionary graph theory has considerably advanced the process of modelling the evolution of structured populations, which models the interactions between individuals as pairwise contests. In recent years, these classical evolution models have been extended to incorporate more realistic features, e.g. multiplayer games. A recent series of papers have developed a new evolutionary framework including structure, multiplayer interactions, evolutionary dynamics, and movement. However, so far, the developed models have mainly considered independent movement without coordinated behaviour. Although the theory underlying the framework has been developed and explored in various directions, several movement mechanisms have been produced which characterise coordinated movement, for example, herding. By embedding these newly constructed movement distributions, within the evolutionary setting of the framework, we demonstrate that certain levels of aggregation and dispersal benefit specific types of individuals. Moreover, by extending existing parameters within the framework, we are not only able to develop a general process of embedding any of the considered movement distributions into the evolutionary setting on complete graphs but also analytically produce the probability of fixation of a mutant on a complete N-sized network, for the multiplayer Public Goods and Hawk–Dove games. Also, by applying weak selection methods, we extended existing previous analyses on the pairwise Hawk–Dove Game to encompass the multiplayer version considered in this paper. By producing neutrality and equilibrium conditions, we show that hawks generally do worse in our models due to the multiplayer nature of the interactions. [ABSTRACT FROM AUTHOR]

In this paper a kinetic modeling approach for an ecological system is proposed, based on the prey–predator structure in terms of individuals experience. Specifically, a system of nonlinear kinetic equations is formulated using standard tools. Both conservative and nonconservative events are considered since proliferative/destructive rates and an external force field occur. These results are compared to the ones of the classical theory of dynamical system to show their consistency. In addition to a first local analytical result, some numerical simulations are performed. The results thus obtained ensure that the kinetic model behaves in a way consistent with other similar ecological models formulated by dynamical systems, involving ordinary differential equations with lumped dependent variables. For each simulation, stationary solutions are shown. Moreover, oscillations appear for some values of the parameters of the ecological system, and this suggests that bifurcations may appear. [ABSTRACT FROM AUTHOR]

Abstract State‐structured populations are ubiquitous in biology, from the age‐structure of animal societies to the life cycles of parasitic species. Understanding how this structure contributes to eco‐evolutionary dynamics is critical not only for fundamental understanding but also for conservation and treatment purposes. Although some methods have been developed in the literature for modelling eco‐evolutionary dynamics in structured population, such methods are wholly lacking in the G function evolutionary game theoretic framework. In this paper, we integrate standard matrix population modelling into the G function framework to create a theoretical framework to probe eco‐evolutionary dynamics in structured populations. This framework encompasses age‐ and stage‐structured matrix models with basic density‐ and frequency‐dependent transition rates and probabilities. For both discrete and continuous time models, we define and characterize asymptotic properties of the system such as eco‐evolutionary equilibria (including ESSs) and the convergence stability of these equilibria. For multistate structured populations, we introduce an ergodic flow preserving folding method for analysing such models. The methods developed in this paper for state‐structured populations and their extensions to multistate‐structured populations provide a simple way to create, analyse and simulate eco‐evolutionary dynamics in structured populations. Furthermore, their generality allows these techniques to be applied to a variety of problems in ecology and evolution.

We study the limit of many small mutations for a model of population dynamics. The population is structured by phenological traits and is spatially inhomogeneous. The various sub-populations compete for the same nutrient which diffuses through the spatial environment, with the possibility of creating fast time oscillations in the dynamics. We control those oscillations by the stability of an auxiliary system (without mutations) which guides the dynamics over fast time scales. [ABSTRACT FROM AUTHOR]

State‐structured populations are ubiquitous in biology, from the age‐structure of animal societies to the life cycles of parasitic species. Understanding how this structure contributes to eco‐evolutionary dynamics is critical not only for fundamental understanding but also for conservation and treatment purposes. Although some methods have been developed in the literature for modelling eco‐evolutionary dynamics in structured population, such methods are wholly lacking in the G function evolutionary game theoretic framework.In this paper, we integrate standard matrix population modelling into the G function framework to create a theoretical framework to probe eco‐evolutionary dynamics in structured populations. This framework encompasses age‐ and stage‐structured matrix models with basic density‐ and frequency‐dependent transition rates and probabilities.For both discrete and continuous time models, we define and characterize asymptotic properties of the system such as eco‐evolutionary equilibria (including ESSs) and the convergence stability of these equilibria. For multistate structured populations, we introduce an ergodic flow preserving folding method for analysing such models.The methods developed in this paper for state‐structured populations and their extensions to multistate‐structured populations provide a simple way to create, analyse and simulate eco‐evolutionary dynamics in structured populations. Furthermore, their generality allows these techniques to be applied to a variety of problems in ecology and evolution. [ABSTRACT FROM AUTHOR]

Cell division is a process that involves many biochemical steps and complex biophysical mechanisms. To simplify the understanding of what triggers cell division, three basic models that subsume more microscopic cellular processes associated with cell division have been proposed. Cells can divide based on the time elapsed since their birth, their size, and/or the volume added since their birth-the timer, sizer, and adder models, respectively. Here, we propose unified adder-sizer models and investigate some of the properties of different adder processes arising in cellular proliferation. Although the adder-sizer model provides a direct way to model cell population structure, we illustrate how it is mathematically related to the well-known model in which cell division depends on age and size. Existence and uniqueness of weak solutions to our 2+1-dimensional PDE model are proved, leading to the convergence of the discretized numerical solutions and allowing us to numerically compute the dynamics of cell population densities. We then generalize our PDE model to incorporate recent experimental findings of a system exhibiting mother-daughter correlations in cellular growth rates. Numerical experiments illustrating possible average cell volume blowup and the dynamical behavior of cell populations with mother-daughter correlated growth rates are carried out. Finally, motivated by new experimental findings, we extend our adder model cases where the controlling variable is the added size between DNA replication initiation points in the cell cycle.

Evolutionary game theory and the adaptive dynamics approach have made invaluable contributions to understanding how gradual evolution leads to adaptation when individuals interact. Here, we review some of the basic tools that have come out of these contributions to model the evolution of quantitative traits in complex populations. We collect together mathematical expressions that describe directional and disruptive selection in class- and group-structured populations in terms of individual fitness, with the aims of bridging different models and interpreting selection. In particular, our review of disruptive selection suggests there are two main paths that can lead to diversity: (i) when individual fitness increases more than linearly with trait expression; (ii) when trait expression simultaneously increases the probability that an individual is in a certain context (e.g. a given age, sex, habitat, size or social environment) and fitness in that context. We provide various examples of these and more broadly argue that population structure lays the ground for the emergence of polymorphism with unique characteristics. Beyond this, we hope that the descriptions of selection we present here help see the tight links among fundamental branches of evolutionary biology, from life history to social evolution through evolutionary ecology, and thus favour further their integration. This article is part of the theme issue 'Half a century of evolutionary games: a synthesis of theory, application and future directions'. [ABSTRACT FROM AUTHOR]

The first part of this works deals with an integro-differential operator with boundary condition related to the interior solution. We prove that the model is governed by a strongly continuous semigroup and we precise its growth inequality. In the second part of this works, we model the proliferationquiescence phases through a system of first order equations. We also prove that the proliferation-quiescence model is governed by a strongly continuous semigroup and we precise its growth inequality. In the last part, we give some applications in Demography and Biology. [ABSTRACT FROM AUTHOR]

Species experience both internal feedbacks with endogenous factors such as trait evolution and external feedbacks with exogenous factors such as weather. These feedbacks can play an important role in determining whether populations persist or communities of species coexist. To provide a general mathematical framework for studying these effects, we develop a theorem for coexistence for ecological models accounting for internal and external feedbacks. Specifically, we use average Lyapunov functions and Morse decompositions to develop sufficient and necessary conditions for robust permanence, a form of coexistence robust to large perturbations of the population densities and small structural perturbations of the models. We illustrate how our results can be applied to verify permanence in non-autonomous models, structured population models, including those with frequency-dependent feedbacks, and models of eco-evolutionary dynamics. In these applications, we discuss how our results relate to previous results for models with particular types of feedbacks.

The structured coalescent allows inferring migration patterns between viral subpopulations from genetic sequence data. However, these analyses typically assume that no genetic recombination process impacted the sequence evolution of pathogens. For segmented viruses, such as influenza, that can undergo reassortment this assumption is broken. Reassortment reshuffles the segments of different parent lineages upon a coinfection event, which means that the shared history of viruses has to be represented by a network instead of a tree. Therefore, full genome analyses of such viruses are complex or even impossible. Although this problem has been addressed for unstructured populations, it is still impossible to account for population structure, such as induced by different host populations, whereas also accounting for reassortment. We address this by extending the structured coalescent to account for reassortment and present a framework for investigating possible ties between reassortment and migration (host jump) events. This method can accurately estimate subpopulation dependent effective populations sizes, reassortment, and migration rates from simulated data. Additionally, we apply the new model to avian influenza A/H5N1 sequences, sampled from two avian host types, Anseriformes and Galliformes. We contrast our results with a structured coalescent without reassortment inference, which assumes independently evolving segments. This reveals that taking into account segment reassortment and using sequencing data from several viral segments for joint phylodynamic inference leads to different estimates for effective population sizes, migration, and clock rates. This new model is implemented as the Structured Coalescent with Reassortment package for BEAST 2.5 and is available at https://github.com/jugne/SCORE. [ABSTRACT FROM AUTHOR]

We analyze the evolution of a multidimensional quantitative trait in a class-structured focal species interacting with other species in a wider metacommunity. The evolutionary dynamics in the focal species as well as the ecological dynamics of the whole metacommunity is described as a continuous-time process with birth, physiological development, dispersal, and death given as rates that can depend on the state of the whole metacommunity. This can accommodate complex local community and global metacommunity environmental feedbacks owing to inter- and intra-specific interactions, as well as local environmental stochastic fluctuations. For the focal species, we derive a fitness measure for a mutant allele affecting class-specific trait expression. Using classical results from geometric singular perturbation theory, we provide a detailed proof that if the effect of the mutation on phenotypic expression is small ("weak selection"), the large system of dynamical equations needed to describe selection on the mutant allele in the metacommunity can be reduced to a single ordinary differential equation on the arithmetic mean mutant allele frequency that is of constant sign. This invariance on allele frequency entails the mutant either dies out or will out-compete the ancestral resident (or wild) type. Moreover, the directional selection coefficient driving arithmetic mean allele frequency can be expressed as an inclusive fitness effect calculated from the resident metacommunity alone, and depends, as expected, on individual fitness differentials, relatedness, and reproductive values. This formalizes the Darwinian process of gradual evolution driven by random mutation and natural selection in spatially and physiologically class-structured metacommunities. [ABSTRACT FROM AUTHOR]

The familial structure of a population and the relatedness of its individuals are determined by its demography. There is, however, no general method to infer kinship directly from the life cycle of a structured population. Yet, this question is central to fields such as ecology, evolution and conservation, especially in contexts where there is a strong interdependence between familial structure and population dynamics. Here, we give a general formula to compute, from any matrix population model, the expected number of arbitrary kin (sisters, nieces, cousins, etc) of a focal individual ego, structured by the class of ego and of its kin. Central to our approach are classic but little‐used tools known as genealogical matrices. Our method can be used to obtain both individual‐based and population‐wide metrics of kinship, as we illustrate. It also makes it possible to analyse the sensitivity of the kinship structure to the traits implemented in the model. [ABSTRACT FROM AUTHOR]

Pediculus humanus capitis are human ectoparasites which cause infestations, mostly in children, worldwide. Understanding the life cycle of head lice is an important step in knowing how to treat lice infestations, as the parasite behavior depends considerably on its age and gender. In this work we propose a mathematical model for head lice population dynamics in hosts who could be or not quarantined and treated. Considering a lice population structured by age and gender we formulate the model as a system of hyperbolic PDEs, which can be reduced to compartmental systems of delay or ordinary differential equations. Besides studying fundamental properties of the model, such as existence, uniqueness and nonnegativity of solutions, we show the existence of (in certain cases multiple) equilibria at which the infestation persists on the host’s head. Aiming to assess the performance of treatments against head lice infestations, by mean of computer experiments and numerical simulations we investigate four possible treatment strategies. Our main results can be summarized as follows: (i) early detection is crucial for quick and efficient eradication of lice infestations; (ii) dimeticone-based products applied every 4 days effectively remove lice in at most three applications even in case of severe infestations and (iii) minimization of the reinfection risk, e.g. by mean of synchronized treatments in families/classrooms is recommended.

We present two finite-difference methods for approximating solutions to a structured population model in the space of non-negative Radon Measures. The first method is a first-order upwind-based scheme and the second is high-resolution method of second-order. We prove that the two schemes converge to the solution in the Bounded-Lipschitz norm. Several numerical examples demonstrating the order of convergence and behavior of the schemes around singularities are provided. In particular, these numerical results show that for smooth solutions the upwind and high-resolution methods provide a first-order and a second-order approximation, respectively. Furthermore, for singular solutions the second-order high-resolution method is superior to the first-order method.

In mutualistic associations, two species cooperate by exchanging goods or services with members of another species for their mutual benefit. At the same time, competition for reproduction primarily continues with members of their own species. In intra -species interactions, the prisoner's dilemma is the leading mathematical metaphor to study the evolution of cooperation. Here we consider inter -species interactions in the spatial prisoner's dilemma, where members of each species reside on one lattice layer. Cooperators provide benefits to neighbouring members of the other species at a cost to themselves. Hence, interactions occur across layers but competition remains within layers. We show that rich and complex dynamics unfold when varying the cost-to-benefit ratio of cooperation, r . Four distinct dynamical domains emerge that are separated by critical phase transitions, each characterized by diverging fluctuations in the frequency of cooperation: (i) for large r cooperation is too costly and defection dominates; (ii) for lower r cooperators survive at equal frequencies in both species; (iii) lowering r further results in an intriguing, spontaneous symmetry breaking of cooperation between species with increasing asymmetry for decreasing r ; (iv) finally, for small r , bursts of mutual defection appear that increase in size with decreasing r and eventually drive the populations into absorbing states. Typically, one species is cooperating and the other defecting and hence establish perfect asymmetry. Intriguingly and despite the symmetrical model set-up, natural selection can nevertheless favour the spontaneous emergence of asymmetric evolutionary outcomes where, on average, one species exploits the other in a dynamical equilibrium., (© The Author(s) 2024. Published by Oxford University Press on behalf of National Academy of Sciences.)

Cooperative investments in social dilemmas can spontaneously diversify into stably coexisting high and low contributors in well-mixed populations. Here we extend the analysis to emerging diversity in (spatially) structured populations. Using pair approximation, we derive analytical expressions for the invasion fitness of rare mutants in structured populations, which then yields a spatial adaptive dynamics framework. This allows us to predict changes arising from population structures in terms of existence and location of singular strategies, as well as their convergence and evolutionary stability as compared to well-mixed populations. Based on spatial adaptive dynamics and extensive individual-based simulations, we find that spatial structure has significant and varied impacts on evolutionary diversification in continuous social dilemmas. More specifically, spatial adaptive dynamics suggests that spontaneous diversification through evolutionary branching is suppressed, but simulations show that spatial dimensions offer new modes of diversification that are driven by an interplay of finite-size mutations and population structures. Even though spatial adaptive dynamics is unable to capture these new modes, they can still be understood based on an invasion analysis. In particular, population structures alter invasion fitness and can open up new regions in trait space where mutants can invade, but that may not be accessible to small mutational steps. Instead, stochastically appearing larger mutations or sequences of smaller mutations in a particular direction are required to bridge regions of unfavorable traits. The net effect is that spatial structure tends to promote diversification, especially when selection is strong. [ABSTRACT FROM AUTHOR]

Integral projection models (IPMs) are an important tool for studying the dynamics of populations structured by one or more continuous traits (e.g. size, height, body mass). Researchers use IPMs to investigate questions ranging from linking drivers to population dynamics, planning conservation and management strategies, and quantifying selective pressures in natural populations. The popularity of stage‐structured population models has been supported by R scripts and packages (e.g. IPMpack, popbio, popdemo, lefko3) aimed at ecologists, which have introduced a broad repertoire of functionality and outputs. However, pressing ecological, evolutionary and conservation biology topics require developing more complex IPMs, and considerably more expertise to implement them. Here, we introduce ipmr, a flexible R package for building, analysing and interpreting IPMs.The ipmr framework relies on the mathematical notation of the models to express them in code format. Additionally, this package decouples the model parameterization step from the model implementation step. The latter point substantially increases ipmr's flexibility to model complex life cycles and demographic processes.ipmr can handle a wide variety of models, including those that incorporate density dependence, discretely and continuously varying stochastic environments, and multiple continuous and/or discrete traits. ipmr can accommodate models with individuals cross‐classified by age and size. Furthermore, the package provides methods for demographic analyses (e.g. asymptotic and stochastic growth rates) and visualization (e.g. kernel plotting).ipmr is a flexible R package for integral projection models. The package substantially reduces the amount of time required to implement general IPMs. We also provide extensive documentation with six vignettes and help files, accessible from an R session and online. [ABSTRACT FROM AUTHOR]

We present a structured coagulation-fragmentation model which describes the population dynamics of oceanic phytoplankton. This model is formulated on the space of Radon measures equipped with the bounded Lipschitz norm and unifies the study of the discrete and continuous coagulation-fragmentation models. We prove that the model is well-posed and show it can reduce down to the classic discrete and continuous coagulation-fragmentation models. To understand the interplay between the physical processes of coagulation and fragmentation and the biological processes of growth, reproduction, and death, we establish a regularity result for the solutions and use it to show that stationary solutions are absolutely continuous under some conditions on model parameters. We develop a semi-discrete approximation scheme which conserves mass and prove its convergence to the unique weak solution. We then use the scheme to perform numerical simulations for the model. [ABSTRACT FROM AUTHOR]

The evolution of cooperation in network-structured populations has been a major focus of theoretical work in recent years. When players are embedded in fixed networks, cooperators are more likely to interact with, and benefit from, other cooperators. In theory, this clustering can foster cooperation on fixed networks under certain circumstances. Laboratory experiments with humans, however, have thus far found no evidence that fixed network structure actually promotes cooperation. Here, we provide such evidence and help to explain why others failed to find it. First, we show that static networks can lead to a stable high level of cooperation, outperforming well-mixed populations. We then systematically vary the benefit that cooperating provides to one's neighbors relative to the cost required to cooperate (b/c), as well as the average number of neighbors in the network (k). When b/c > k, we observe high and stable levels of cooperation. Conversely, when b/c ≤ k or players are randomly shuffled, cooperation decays. Our results are consistent with a quantitative evolutionary game theoretic prediction for when cooperation should succeed on networks and, for the first time to our knowledge, provide an experimental demonstration of the power of static network structure for stabilizing human cooperation.

We consider models of evolution in structured populations involving multiplayer games. Whilst also discussing other models, we focus on the modelling framework developed by Broom and Rychtář (J Theor Biol 302:70–80, 2012) onwards. This includes key progress so far, the main gaps and limitations, the relationship and synergies with other models and a discussion of the direction of future work. In this regard as well as discussing existing work, there is some new research on the applicability and robustness of current models with respect to using them to model real populations. This is an important potential advance, as previously all of the work has been entirely theoretical. In particular, the most complex models will have many parameters, and we concentrate on considering simpler versions with a small number of parameters which still possess the key features which would make them applicable. We find that these models are generally robust, in particular issues that can arise related to small payoff changes at critical values and removal of pivotal vertices would have similar effects on other modelling system including evolutionary graph theory. These often occur where it can be argued that there is a lack of robustness in the real system that the model faithfully picks up, and so is not a problematic feature. [ABSTRACT FROM AUTHOR]

This paper provides two different extensions of a previous joint work "Time asymptotics of structured populations with diffusion and dynamic boundary conditions; Discrete Cont Dyn Syst, Series B, 23 (10) (2018)" devoted to asynchronous exponential asymptotics for bounded and weakly compact reproduction operators. The first extension considers bounded non weakly compact reproduction operators while the second extension deals with unbounded kernel reproduction operators and needs, as a preliminary step, a new generation result. [ABSTRACT FROM AUTHOR]

Recently, many realistic models of structured populations are described through delay equations which involve quantities defined by the solutions of external problems. For instance, the size or survival probability of individuals may be described by ordinary differential equations, and their maturation age may be determined by a nonlinear condition. When treating these complex models with existing continuation approaches in view of analyzing stability and bifurcations, the external quantities are computed from scratch at every continuation step. As a result, the requirements from the computational point of view are often demanding. In this work we propose to improve the overall performance by investigating a suitable numerical treatment of the external problems in order to include the relevant variables into the continuation framework, thus exploiting their values computed at each previous step. We explore and test this internal continuation with prototype problems first. Then we apply it to a representative class of realistic models, demonstrating the superiority of the new approach in terms of computational time for a given accuracy threshold. [ABSTRACT FROM AUTHOR]

Nei's decomposition of total expected heterozygosity in subdivided populations into within‐ and between‐subpopulation components, HS and DST, respectively, is a classical tool in the conservation and management of genetic resources. Reviewing why this is not a decomposition into independent terms of within‐ and between‐subpopulation gene diversity, we illustrate how this approach can be misleading because it overemphasizes the within‐subpopulation component compared to Jost's nonadditive decomposition based on gene diversity indices. Using probabilistic partitioning of the total expected heterozygosity into independent within‐ and between‐subpopulation contributions, we show that the contribution of the within‐subpopulation expected heterozygosity to the total expected heterozygosity is not HS, as suggested by Nei's decomposition, but HS/s, with s being the number of subpopulations. Finally, we compare three possible approaches of decomposing total heterozygosity in subdivided populations (i.e., Nei's decomposition, Jost's approach, and probabilistic partitioning) with regard to independence between terms and sensitivity to unequal subpopulation sizes. For the conservation and management of genetic resources, we recommend using probabilistic partitioning and Jost's differentiation parameter rather than Nei's decomposition. [ABSTRACT FROM AUTHOR]

Long-term evolution of quantitative traits is classically and usefully described as the directional change in phenotype due to the recurrent fixation of new mutations. A formal justification for such continual evolution ultimately relies on the "invasion implies substitution"-principle. Here, whenever a mutant allele causing a small phenotypic change can successfully invade a population, the ancestral (or wild-type) allele will be replaced, whereby fostering gradual phenotypic change if the process is repeated. It has been argued that this principle holds in a broad range of situations, including spatially and demographically structured populations experiencing frequency- and density-dependent selection under demographic and environmental fluctuations. However, prior studies have not been able to account for all aspects of population structure, leaving unsettled the conditions under which the "invasion implies substitution"-principle really holds. In this paper, we start by laying out a program to explore and clarify the generality of the "invasion implies substitution"-principle. Particular focus is given on finding an explicit and functionally constant representation of the selection gradient on a quantitative trait. Using geometric singular perturbation methods, we then show that the "invasion implies substitution"-principle generalizes to well-mixed and scalar-valued polymorphic multispecies ecological communities that are structured into finitely many demographic (or physiological) classes. The selection gradient is shown to be constant over the evolutionary timescale and that it depends only on the resident phenotype, individual growth-rates, population steady states and reproductive values, all of which are calculated from the resident dynamics. Our work contributes to the theoretical foundations of evolutionary ecology. [ABSTRACT FROM AUTHOR]

This work provides a general spectral analysis of size-structured two-phase population models. Systematic functional analytic results are given. We deal first with the case of finite maximal size. We characterize the irreducibility of the corresponding L1 semigroup in terms of properties of the different parameters of the system. We characterize also the spectral gap property of the semigroup. It turns out that the irreducibility of the semigroup implies the existence of the spectral gap. In particular, we provide a general criterion for asynchronous exponential growth. We show also how to deal with time asymptotics in case of lack of irreducibility. Finally, we extend the theory to the case of infinite maximal size. [ABSTRACT FROM AUTHOR]

Cell division is a process that involves many biochemical steps and complex biophysical mechanisms. To simplify the understanding of what triggers cell division, three basic models that subsume more microscopic cellular processes associated with cell division have been proposed. Cells can divide based on the time elapsed since their birth, their size, and/or the volume added since their birth|the timer, sizer, and adder models, respectively. Here, we propose unified addersizer models and investigate some of the properties of different adder processes arising in cellular proliferation. Although the adder-sizer model provides a direct way to model cell population structure, we illustrate how it is mathematically related to the well-known model in which cell division depends on age and size. Existence and uniqueness of weak solutions to our 2+1-dimensional PDE model are proved, leading to the convergence of the discretized numerical solutions and allowing us to numerically compute the dynamics of cell population densities. We then generalize our PDE model to incorporate recent experimental findings of a system exhibiting mother-daughter correlations in cellular growth rates. Numerical experiments illustrating possible average cell volume blowup and the dynamical behavior of cell populations with mother-daughter correlated growth rates are carried out. Finally, motivated by new experimental findings, we extend our adder model cases where the controlling variable is the added size between DNA replication initiation points in the cell cycle. [ABSTRACT FROM AUTHOR]

Temporal fluctuations in growth rates can arise from both variation in age‐specific vital rates and temporal fluctuations in age structure (i.e. the relative abundance of individuals in each age‐class). However, empirical assessments of temporal fluctuations in age structure and their effects on population growth rate are relatively rare. Most research has focused on understanding the contribution of changing vital rates to population growth rates and these analyses routinely assume that: (a) populations have stable age distributions, (b) environmental influences on vital rates and age structure are stationary (i.e. the mean and/or variance of these processes does not change over time), and (c) dynamics are independent of density.Here we quantified fluctuations in age structure and assessed whether they were stationary for four populations of free‐ranging vertebrates: moose (observed for 48 years), elk (15 years), tawny owls (15 years) and grey wolves (17 years). We also assessed the extent that fluctuations in age structure were useful for predicting annual population growth rates using models which account for density dependence.Fluctuations in age structure were of a similar magnitude to fluctuations in abundance. For three populations (moose, elk, owls), the mean and the skew of the age distribution fluctuated without stabilizing over the observed time periods. More precisely, the sample variance (interannual variance) of age structure indices increased with the length of the study period, which suggests that fluctuations in age structure were non‐stationary for these populations – at least over the 15‐ to 48‐year periods analysed.Fluctuations in age structure were associated with population growth rate for two populations. In particular, population growth varied from positive to negative for moose and from near zero to negative for elk as the average age of adults increased over its observed range.Non‐stationarity in age structure may represent an important mechanism by which abundance becomes non‐stationary – and therefore difficult to forecast – over time‐scales of concern to wildlife managers. Overall, our results emphasize the need for vertebrate populations to be modelled using approaches that consider transient dynamics and density dependence and that do not rely on the assumption that environmental processes are stationary. A free Plain Language Summary can be found within the Supporting Information of this article. [ABSTRACT FROM AUTHOR]

Modelling evolution of virulence in host-parasite systems is an actively developing area of research with ever-growing literature. However, most of the existing studies overlook the fact that individuals within an infected population may have a variable infection load, i.e. infected populations are naturally structured with respect to the parasite burden. Empirical data suggests that the mortality and infectiousness of individuals can strongly depend on their infection load; moreover, the shape of distribution of infection load may vary on ecological and evolutionary time scales. Here we show that distributed infection load may have important consequences for the eventual evolution of virulence as compared to a similar model without structuring. Mathematically, we consider an SI model, where the dynamics of the infected subpopulation is described by a von Förster-type equation, in which the infection load plays the role of age. We implement the adaptive dynamics framework to predict evolutionary outcomes in this model. We demonstrate that for simple trade-off functions between virulence, disease transmission and parasite growth rates, multiple evolutionary attractors are possible. Interestingly, unlike in the case of unstructured models, achieving an evolutionary stable strategy becomes possible even for a variation of a single ecological parameter (the parasite growth rate) and keeping the other parameters constant. We conclude that evolution in disease-structured populations is strongly mediated by alterations in the overall shape of the parasite load distribution. [ABSTRACT FROM AUTHOR]

The environment has a strong influence on a population's evolutionary dynamics. Driven by both intrinsic and external factors, the environment is subject to continual change in nature. To capture an ever-changing environment, we consider a model of evolutionary dynamics with game transitions, where individuals' behaviors together with the games that they play in one time step influence the games to be played in the next time step. Within this model, we study the evolution of cooperation in structured populations and find a simple rule: Weak selection favors cooperation over defection if the ratio of the benefit provided by an altruistic behavior, b, to the corresponding cost, c, exceeds k-k', where k is the average number of neighbors of an individual and k' captures the effects of the game transitions. Even if cooperation cannot be favored in each individual game, allowing for a transition to a relatively valuable game after mutual cooperation and to a less valuable game after defection can result in a favorable outcome for cooperation. In particular, small variations in different games being played can promote cooperation markedly. Our results suggest that simple game transitions can serve as a mechanism for supporting prosocial behaviors in highly connected populations. [ABSTRACT FROM AUTHOR]

BackgroundGene expression patterns in the brain are strongly influenced by the severity and duration of physiological stress at the time of death. This agonal effect, if not well controlled, can lead to spurious findings and diminished statistical power in case-control comparisons. While some recent studies match samples by tissue pH and clinically recorded agonal conditions, we found that these indicators were sometimes at odds with observed stress-related gene expression patterns, and that matching by these criteria still sometimes results in identifying case-control differences that are primarily driven by residual agonal effects. This problem is analogous to the one encountered in genetic association studies, where self-reported race and ethnicity are often imprecise proxies for an individual's actual genetic ancestry.ResultsWe developed an Agonal Stress Rating (ASR) system that evaluates each sample's degree of stress based on gene expression data, and used ASRs in post hoc sample matching or covariate analysis. While gene expression patterns are generally correlated across different brain regions, we found strong region-region differences in empirical ASRs in many subjects that likely reflect inter-individual variabilities in local structure or function, resulting in region-specific vulnerability to agonal stress.ConclusionVariation of agonal stress across different brain regions differs between individuals, revealing a new level of complexity for gene expression studies of brain tissues. The Agonal Stress Ratings quantitatively assess each sample's extent of regulatory response to agonal stress, and allow a strong control of this important confounder.

Cooperative behavior, the costly provision of benefits to others, is common across all domains of life. This review article discusses cooperative behavior in the microbial world, mediated by the exchange of extracellular products called public goods. We focus on model species for which the production of a public good and the related growth disadvantage for the producing cells are well described. To unveil the biological and ecological factors promoting the emergence and stability of cooperative traits we take an interdisciplinary perspective and review insights gained from both mathematical models and well-controlled experimental model systems. Ecologically, we include crucial aspects of the microbial life cycle into our analysis and particularly consider population structures where ensembles of local communities (subpopulations) continuously emerge, grow, and disappear again. Biologically, we explicitly consider the synthesis and regulation of public good production. The discussion of the theoretical approaches includes general evolutionary concepts, population dynamics, and evolutionary game theory. As a specific but generic biological example, we consider populations of Pseudomonas putida and its regulation and use of pyoverdines, iron scavenging molecules, as public goods. The review closes with an overview on cooperation in spatially extended systems and also provides a critical assessment of the insights gained from the experimental and theoretical studies discussed. Current challenges and important new research opportunities are discussed, including the biochemical regulation of public goods, more realistic ecological scenarios resembling native environments, cell-to-cell signaling, and multispecies communities. Image 1 • Cooperation and public good production of microbial communities. • Evolutionary stability of cooperation in structured microbial population. • Theoretical concepts and models to analyze evolutionary dynamics in structured populations. • Pyoverdine – a public good of Pseudomonas populations: regulation and benefits. • The public good dilemma in spatially extended systems. [ABSTRACT FROM AUTHOR]

In this work we study the coupling of a nonlinear renewal equation to an ordinary differential equation. We start with existence and uniqueness issues for the coupled equations and, in particular cases, we study the long-time behaviour. The novelty here is the nonlinearity in the renewal equation. This model arises in the context of atherosclerosis. The renewal part accounts for the inflammatory process: leucocyte recruitment in the arterial wall, differentiation when internalizing low-density lipoprotein (LDL) and death. The ordinary differential equation describes the LDL dynamics in the arterial wall, leucocyte absorption and release in the blood. [ABSTRACT FROM AUTHOR]

Understanding the mechanisms of evolution of cooperation and its sustenance has gathered momentum since the last few decades of the twentieth century. However, the complete picture is yet to emerge. Evolutionary game theory aims to model evolutionary dynamics in a population by drawing on the principles of game theory. Spatially restricted interactions, such as in ecological systems, are rather common in nature. When interactions among the individuals in a population are structured, the outcome of the game is significantly different from that of a well-mixed population. In this mini-review, targeted towards a very broad audience of all backgrounds, we summarise some of the critical research by evolutionary biologists, computer scientists, mathematicians and physicists on evolutionary games in structured populations. We also discuss the influence of structure on evolutionary games in diverse scenarios ranging from laboratory environments to multiplex networks. Along the way, we also try to harmonise a few conflicting results in the literature. [ABSTRACT FROM AUTHOR]

Abstract We a propose an adaptive population model, which is structured in groups, to investigate the appearance of division of labor. In the model, the individuals respond to a given set of stimuli according to their propensities for producing the action. In this study, the individuals' response thresholds can evolve due to mutation and selection at the colony level. Two alternative formulations are presented: in the former, the colonies are subject to strict conditions and need to fulfill a certain level of productivity, η cr , across all tasks in order to ensure their expansion and thence its propagation. In the second formulation, tasks determining the group's growth rate and the group's viability are uncoupled. We observe the emergence of division of labor over a broad range of parameter values. The two models display distinct behavior concerning the resulting levels of functional specialization in terms of η cr mainly due to the strength of between-group selection. On the other hand, the dependence of the level of specialization on colony size is strikingly similar, and unlike found in previous approaches, a positive correlation between division of labor and colony size is not always verified. Highlights • We propose a structured population model and a variant of this model to investigate the emergence of division of labor. • The models rely on the existence of selection at the colony level. • The models succeed in finding high levels of division of labor. • Our simulation results demonstrate that the size-complexity hypothesis does not hold in the whole range of colony sizes. • If tasks related to reproduction and groupś viability are uncoupled, functional specialization first assures reproduction. [ABSTRACT FROM AUTHOR]

We study the mathematical properties of a model of cell division structured by two variables – the size and the size increment – in the case of a linear growth rate and a self-similar fragmentation kernel. We first show that one can construct a solution to the related two dimensional eigenproblem associated to the eigenvalue 1 from a solution of a certain one dimensional fixed point problem. Then we prove the existence and uniqueness of this fixed point in the appropriate L1 weighted space under general hypotheses on the division rate. Knowing such an eigenfunction proves useful as a first step in studying the long time asymptotic behaviour of the Cauchy problem. [ABSTRACT FROM AUTHOR]

This work revisits and extends in various directions a work by J.Z. Farkas and P. Hinow (Math. Biosc and Eng, 8 (2011) 503-513) on structured populations models (with bounded sizes) with diffusion and generalized Wentzell boundary conditions. In particular, we provide first a self-contained L1 generation theory making explicit the domain of the generator. By using Hopf maximum principle, we show that the semigroup is always irreducible regardless of the reproduction function. By using weak compactness arguments, we show first a stability result of the essential type and then deduce that the semigroup has a spectral gap and consequently the asynchronous exponential growth property. Finally, we show how to extend this theory to models with arbitrary sizes and point out an open problem pertaining to this extension. [ABSTRACT FROM AUTHOR]

We show, by way of an example, that numerical bifurcation tools for ODE yield reliable bifurcation diagrams when applied to the pseudospectral approximation of a one-parameter family of nonlinear renewal equations. The example resembles logistic- and Ricker-type population equations and exhibits transcritical, Hopf and period doubling bifurcations. The reliability is demonstrated by comparing the results to those obtained by a reduction to a Hamiltonian Kaplan-Yorke system and to those obtained by direct application of collocation methods (the latter also yield estimates for positive Lyapunov exponents in the chaotic regime). We conclude that the methodology described here works well for a class of delay equations for which currently no tailor-made tools exist (and for which it is doubtful that these will ever be constructed).

Understanding the basis of the genetic variations responsible for the complex traits found in Eucalyptus cladocalyx under arid environmental conditions is crucial for designing genetic architecture studies. Forty-five half-sib families from Australia were used to identify inter-simple sequence repeat (ISSR) markers that are associated with growth (height, diameter at breast height, and stem straightness), flowering traits (flowering intensity, flowering precocity, reproductive capacity, and late flowering) and tree survival under arid conditions in southern Atacama Desert, Chile. Each DNA pellet consisted of a pool of five trees from each family. ISSR markers were associated with all the traits studied and accounted for 9.8 to 23.4 % of the phenotypic variation. Several loci were associated with more than one trait. For example, UBC810(450-500 bp), ISO1(600-610 bp), and TGT9(780-800 bp) were associated with three of the traits studied. These identified genomic regions may contribute to the increase of the efficiency of the conventional tree breeding program for E. cladocalyx.

Embryos of annual killifish diapause in soil egg banks while ponds are dry. Their rates of development and survival in different developmental stages determine the numbers and stages of embryos at rewetting. In the Argentinean pearlfish Austrolebias bellottii, we investigated plasticity for desiccation in such embryonal life history components across phases of mild desiccation and rewetting and also effects of life history on hatching. In comparison with nonannuals, our data suggest that incidences of diapause have become relatively independent of the occurrence of desiccation, as if they have become genetically assimilated. We found limited survival effects of desiccation, limited developmental delays, and an acceleration of development into the prehatching stage. This response can be adaptive when desiccation informs that an opportunity to hatch approaches. Embryos arrest development in the prehatching stage (diapause DIII) or in the dispersed‐cell phase (diapause DI). Parental pair variation in rates of development and survival in the earliest developmental stages affects the fraction of embryos that are in DI at rewetting and the number surviving. Given such effects on life history fitness components, rates during embryonal development seem "visible" to selection and the developmental system can thus adapt when pair variation contains a heritable component. In agreement with expectations for the presence of diversified bet‐hedging, some embryos hatched and others not in over half of the clutches with several developed embryos at the moment of rewetting. Hatching probabilities increased for eggs produced later in the experiment, and they increased when embryos were rewetted a second time after two months. This response is opposite of what is expected when age‐dependent hatching would be adapted to exploit opportunities for completing another generation before the dry season. Embryos of annual killifish diapause in soil egg banks while ponds are dry. Their numbers at pond rewetting depend on rates of development and survival. We investigated plasticity for desiccation in the embryonal life histories of the Argentinean pearlfish Austrolebias bellottii across phases of mild desiccation and rewetting. [ABSTRACT FROM AUTHOR]

We study the influence of a mortality trade-off in a nonlocal reaction-diffusion-mutation equation that we introduce to model the invasion of cane toads in Australia. This model is built off of one that has attracted attention recently, in which the population of toads is structured by a phenotypical trait that governs the spatial diffusion. We are concerned with the case when the diffusivity can take unbounded values and the mortality trade-off depends only on the trait variable. Depending on the rate of increase of the penalization term, we obtain the rate of spreading of the population. We identify two regimes, an acceleration regime when the penalization is weak and a linear spreading regime when the penalization is strong. While the development of the model comes from biological principles, the bulk of the article is dedicated to the mathematical analysis of the model, which is very technical. The upper and lower bounds are proved via the Li-Yau estimates of the fundamental solution of the heat equation with potential on Riemannian manifolds and a moving ball technique, respectively, and the traveling waves by a Leray-Schauder fixed point argument. We also present a simple method for a priori bounds. [ABSTRACT FROM AUTHOR]

The behaviour of populations consisting of animals that interact with each other for their survival and reproduction is usually investigated assuming homogeneity amongst the animals. However, real populations are non-homogeneous. We focus on an established model of kleptoparasitism and investigate whether and how much population heterogeneities can affect the behaviour of kleptoparasitic populations. We consider a situation where animals can either discover food items by themselves or attempt to steal the food already discovered by other animals through aggressive interactions. Representing the likely interactions between animals by a network, we develop pairwise and individual-based models to describe heterogeneities in both the population structure and other individual characteristics, including searching and fighting abilities. For each of the models developed we derive analytic solutions at the steady state. The high accuracy of the solutions is shown in various examples of populations with different degrees of heterogeneity. We observe that highly heterogeneous structures can significantly affect the food intake rate and therefore the fitness of animals. In particular, the more highly connected animals engage in more conflicts, and have a reduced food consumption rate compared to poorly connected animals. Further, for equivalent average level of connectedness, the average consumption rate of a population with heterogeneous structure can be higher. [ABSTRACT FROM AUTHOR]

The important biological problem of how groups of animals should allocate themselves between different habitats has been modelled extensively. Such habitat selection models have usually involved infinite well-mixed populations. In particular, the model of allocation over a number of food patches when movement is not costly, the ideal free distribution (IFD) model, is well developed. Here we generalize (and solve) a habitat selection game for a finite structured population. We show that habitat selection in such a structured population can have multiple stable solutions (in contrast to the equivalent IFD model where the solution is unique). We also define and study a “predator dilution game” where unlike in the habitat selection game, individuals prefer to aggregate (to avoid being caught by predators due to the dilution effect) and show that this model has a unique solution when movement is unrestricted. [ABSTRACT FROM AUTHOR]