Global models of growth and competition

Interconnection between density-regulation and stability in competitive ecological network

In natural ecosystems, species can be characterized by the nonlinear density-dependent self-regulation of their growth profile. Species of many taxa show a substantial density-dependent reduction for low population size. Nevertheless, many show the opposite trend; density regulation is minimal for small populations and increases significantly when the population size is near the carrying capacity. The theta-logistic growth equation can portray the intraspecific density regulation in the growth profile, theta being the density regulation parameter. In this study, we examine the role of these different growth profiles on the stability of a competitive ecological community with the help of a mathematical model of competitive species interactions. This manuscript deals with the random matrix theory to understand the stability of the classical theta-logistic models of competitive interactions. Our results suggest that having more species with strong density dependence, which self-regulate at low densities, leads to more stable communities. With this, stability also depends on the complexity of the ecological network. Species network connectance (link density) shows a consistent trend of increasing stability, whereas community size (species richness) shows a context-dependent effect. We also interpret our results from the aspect of two different life history strategies: r and K-selection. Our results show that the stability of a competitive network increases with the fraction of r-selected species in the community. Our result is robust, irrespective of different network architectures.

Diversity begets stability: Sublinear growth and competitive coexistence across ecosystems

The worldwide loss of species diversity brings urgency to understanding how diverse ecosystems maintain stability. Whereas early ecological ideas and classic observations suggested that stability increases with diversity, ecological theory makes the opposite prediction, leading to the long-standing "diversity-stability debate." Here, we show that this puzzle can be resolved if growth scales as a sublinear power law with biomass (exponent <1), exhibiting a form of population self-regulation analogous to models of individual ontogeny. We show that competitive interactions among populations with sublinear growth do not lead to exclusion, as occurs with logistic growth, but instead promote stability at higher diversity. Our model realigns theory with classic observations and predicts large-scale macroecological patterns. However, it makes an unsettling prediction: Biodiversity loss may accelerate the destabilization of ecosystems.

Modeling interactions of Clostridium cadaveris and Clostridium sporogenes in anaerobic acidogenesis of glucose and peptone

This study focuses on developing a mathematical model to assess interaction among acidogenic bacteria during the anaerobic degradation of two substrates. Clostridium cadaveris and Clostridium sporogenes were cultured in various combinations with glucose and peptone. Parameter estimates are given for both conventional Monod parameters from single substrate-single species cultures and sum kinetics with interaction parameters obtained from dual substrate-single species cultures. The presence of multiple substrates led to both inhibitory and enhancing effects on biodegradation rates for dual substrates compared to single substrate cultures. A new model of interspecies interaction was developed within the framework of Lotka-Volterra incorporating substrate interaction parameters, with a focus on accuracy, realism, simplicity, and biological significance. The model demonstrated competitive interaction for resource sharing and the additional non-linearity parameter eliminated the constraint of the linear relationship between growth rate and population density.

Modularized Design and Construction of Tunable Microbial Consortia with Flexible Topologies

Complex and fluid bacterial community compositions are critical to diversity, stability, and function. However, quantitative and mechanistic descriptions of the dynamics of such compositions are still lacking. Here, we develop a modularized design framework that allows for bottom-up construction and the study of synthetic bacterial consortia with different topologies. We showcase the microbial consortia design and building process by constructing amensalism and competition consortia using only genetic circuit modules to engineer different strains to form the community. Functions of modules and hosting strains are validated and quantified to calibrate dynamic parameters, which are then directly fed into a full mechanistic model to accurately predict consortia composition dynamics for both amensalism and competition without further fitting. More importantly, such quantitative understanding successfully identifies the experimental conditions to achieve coexistence composition dynamics. These results illustrate the process of both computationally and experimentally building up bacteria consortia complexity and hence achieve robust control of such fluid systems.

Coexistence in two-species competition with delayed maturation

Inter- and intraspecific competition is most important during the immature life stage for many species of interest, such as multiple coexisting mosquito species that act as vectors of diseases. Mortality caused by competition that occurs during maturation is explicitly modelled in some alternative formulations of the Lotka-Volterra competition model. We generalise this approach by using a distributed delay for maturation time. The kernel of the distributed delay is represented by a truncated Erlang distribution. The shape and rate of the distribution, as well as the position of the truncation, are found to determine the solution at equilibrium. The resulting system of delay differential equations is transformed into a system of ordinary differential equations using the linear chain approximation. Numerical solutions are provided to demonstrate cases where competitive exclusion and coexistence occur. Stability conditions are determined using the nullclines method and local stability analysis. The introduction of a distributed delay promotes coexistence and survival of the species compared to the limiting case of a discrete delay, potentially affecting management of relevant pests and threatened species.

The existence and strength of higher order interactions is sensitive to environmental context

One strategy for understanding the dynamics of any complex system, such as a community of competing species, is to study the dynamics of parts of the system in isolation. Ecological communities can be decomposed into single species, and pairs of interacting species. This reductionist strategy assumes that whole-community dynamics are predictable and explainable from knowledge of the dynamics of single species and pairs of species. This assumption will be violated if higher order interactions (HOIs) are strong. Theory predicts that HOIs should be common. But it is difficult to detect HOIs, and to infer their long-term consequences for species coexistence, solely from short-term data. I conducted a protist microcosm experiment to test for HOIs among competing bacterivorous ciliates, and test the sensitivity of HOIs to environmental context. I grew three competing ciliate species in all possible combinations at each of two resource enrichment levels, and used the population dynamic data from the one- and two-species treatments to parameterize a competition model at each enrichment level. I then compared the predictions of the parameterized model to the dynamics of the whole community (three-species treatment). I found that the existence, and thus strength, of HOIs was environment dependent. I found a strong HOI at low enrichment, which enabled the persistence of a species that would otherwise have been competitively excluded. At high enrichment, three-species dynamics could be predicted from a parameterized model of one- and two-species dynamics, provided that the model accounted for nonlinear intraspecific density dependence. The results provide one of the first rigorous demonstrations of the long-term consequences of HOIs for species coexistence, and demonstrate the context dependence of HOIs. HOIs create difficult challenges for predicting and explaining species coexistence in nature.

Formulation of Chemically Defined Media and Growth Evaluation of Ligilactobacillus salivarius ZJ614 and Limosilactobacillus reuteri ZJ625

Lactic acid bacteria are increasingly becoming important dietary supplements due to their health benefits when consumed in adequate quantity. The increasing attention on these important microbes has necessitated an in-depth understanding of their physiological processes, such as nutritional requirements and growth patterns, to better harness their probiotic potentials. This study was carried out to determine the nutritional requirements for the growth of L. salivarius ZJ614 and L. reuteri ZJ625 from a chemically defined medium and evaluate growth kinetics by fitting different sigmoidal growth models. The complete CDM contains 49 nutritional ingredients such as glucose, Tween 80^®, mineral salts, buffers, amino acids, vitamins, and nucleotides at defined concentrations. In addition, the minimal nutritional requirements of the isolates were determined in a series of single-omission experiments (SOEs) to compose the MDM. Growth curve data were generated by culturing in an automated 96-well micro-plate reader at 37°C for 36 h, and photometric readings (optical density: OD₆₀₀) were taken. The data were summarized in tables and charts using Microsoft Excel, while growth evaluation was carried out using open-source software (Curveball) on Python. The results revealed that omission of the amino acids, vitamins, and nucleotides groups resulted in 2.0, 20.17, and 60.24% (for L. salivarius ZJ614) and 0.95, 42.7, and 70.5% (for L. reuteri ZJ625) relative growths, respectively. Elimination of the individual CDM components also indicates varying levels of growth by the strains. The growth curve data revealed LogisticLag2 and Baranyi–Roberts models as the best fits for L. reuteri ZJ625 and L. salivarius ZJ614, respectively. All the strains showed appreciable growth on the CDM and MDM as observed in de Man–Rogosa–Sharpe (MRS) broth. We also described the growth kinetics of L. reuteri ZJ625 and L. salivarius ZJ614 in the CDM, and the best models revealed the estimated growth parameters.

Dynamics of an autonomous Gilpin–Ayala competition model with random perturbation

This paper discusses the dynamics of a Gilpin–Ayala competition model of two interacting species perturbed by white noise. We obtain the existence of a unique global positive solution of the system and the solution is bounded in [Formula: see text]th moment. Then, we establish sufficient and necessary conditions for persistence and the existence of an ergodic stationary distribution of the model. We also establish sufficient conditions for extinction of the model. Moreover, numerical simulations are carried out for further support of present research.

Modeling herbivore functional responses causing boom-bust dynamics following predator removal

Native biodiversity is threatened by invasive species in many terrestrial and marine systems, and conservation managers have demonstrated successes by responding with eradication or control programs. Although invasive species are often the direct cause of threat to native species, ecosystems can react in unexpected ways to their removal or reduction. Here, we use theoretical models to predict boom-bust dynamics, where the removal of predatory or competitive pressure from a native herbivore results in oscillatory population dynamics (boom-bust), which can endanger the native species' population in the short term. We simulate control activities, applied to multiple theoretical three-species Lotka-Volterra ecosystem models consisting of vegetation, a native herbivore, and an invasive predator. Based on these communities, we then develop a predictive tool that-based on relative parameter values-predicts whether control efforts directed at the invasive predator will lead to herbivore release followed by a crash. Further, by investigating the different functional responses, we show that model structure, as well as model parameters, are important determinants of conservation outcomes. Finally, control strategies that can mitigate these negative consequences are identified. Managers working in similar data-poor ecosystems can use the predictive tool to assess the probability that their system will exhibit boom-bust dynamics, without knowing exact community parameter values.

Habitat selection patterns are density dependent under the ideal free distribution

Despite being widely used, habitat selection models are rarely reliable and informative when applied across different ecosystems or over time. One possible explanation is that habitat selection is context-dependent due to variation in consumer density and/or resource availability. The goal of this paper is to provide a general theoretical perspective on the contributory mechanisms of consumer and resource density-dependent habitat selection, as well as on our capacity to account for their effects. Towards this goal we revisit the ideal free distribution (IFD), where consumers are assumed to be omniscient, equally competitive and freely moving, and are hence expected to instantaneously distribute themselves across a heterogeneous landscape such that fitness is equalised across the population. Although these assumptions are clearly unrealistic to some degree, the simplicity of the structure in IFD provides a useful theoretical vantage point to help clarify our understanding of more complex spatial processes. Of equal importance, IFD assumptions are compatible with the assumptions underlying common habitat selection models. Here we show how a fitness-maximising space use model, based on IFD, gives rise to resource and consumer density-dependent shifts in consumer distribution, providing a mechanistic explanation for the context-dependent outcomes often reported in habitat selection analysis. Our model suggests that adaptive shifts in consumer distribution patterns would be expected to lead to nonlinear and often non-monotonic patterns of habitat selection. These results indicate that even under the simplest of assumptions about adaptive organismal behaviour, habitat selection strength should critically depend on system-wide characteristics. Clarifying the impact of adaptive behavioural responses may be pivotal in making meaningful ecological inferences about observed patterns of habitat selection and allow reliable transferability of habitat selection predictions across time and space.

Competition delays multi-drug resistance evolution during combination therapy

Combination therapies have shown remarkable success in preventing the evolution of resistance to multiple drugs, including HIV, tuberculosis, and cancer. Nevertheless, the rise in drug resistance still remains an important challenge. The capability to accurately predict the emergence of resistance, either to one or multiple drugs, may help to improve treatment options. Existing theoretical approaches often focus on exponential growth laws, which may not be realistic when scarce resources and competition limit growth. In this work, we study the emergence of single and double drug resistance in a model of combination therapy of two drugs. The model describes a sensitive strain, two types of single-resistant strains, and a double-resistant strain. We compare the probability that resistance emerges for three growth laws: exponential growth, logistic growth without competition between strains, and logistic growth with competition between strains. Using mathematical estimates and numerical simulations, we show that between-strain competition only affects the emergence of single resistance when resources are scarce. In contrast, the probability of double resistance is affected by between-strain competition over a wider space of resource availability. This indicates that competition between different resistant strains may be pertinent to identifying strategies for suppressing drug resistance, and that exponential models may overestimate the emergence of resistance to multiple drugs. A by-product of our work is an efficient strategy to evaluate probabilities of single and double resistance in models with multiple sequential mutations. This may be useful for a range of other problems in which the probability of resistance is of interest.

Temperature Shapes Ecological Dynamics in Mixed Culture Fermentations Driven by Two Species of the Saccharomyces Genus

Mixed culture wine fermentations combining species within the Saccharomyces genus have the potential to produce new market tailored wines. They may also contribute to alleviating the effects of climate change in winemaking. Species, such as S. kudriavzevii, show good fermentative properties at low temperatures and produce wines with lower alcohol content, higher glycerol amounts and good aroma. However, the design of mixed culture fermentations combining S. cerevisiae and S. kudriavzevii species requires investigating their ecological interactions under cold temperature regimes. Here, we derived the first ecological model to predict individual and mixed yeast dynamics in cold fermentations. The optimal model combines the Gilpin-Ayala modification to the Lotka-Volterra competitive model with saturable competition and secondary models that account for the role of temperature. The nullcline analysis of the proposed model revealed how temperature shapes ecological dynamics in mixed co-inoculated cold fermentations. For this particular medium and species, successful mixed cultures can be achieved only at specific temperature ranges or by sequential inoculation. The proposed ecological model can be calibrated for different species and provide valuable insights into the functioning of alternative mixed wine fermentations.

Permanence and extinction of a single species model in polluted environment

Under the assumption that the growth of the population satisfies the generalized logistic equation, a new single species model in polluted environment is proposed in this work. Sufficient conditions for permanence and extinction of the species in the model are given respectively. It is shown that our model and the results are improvements of those in He and Wang [Appl. Math. Model. 31 (2007) 2227–2238].

Population dynamics of foxes during restricted-area culling in Britain: Advancing understanding through state-space modelling of culling records

Lethal control is widely employed to suppress the numbers of target wildlife species within restricted management areas. The success of such measures is expected to vary with local circumstances affecting rates of removal and replacement. There is a need both to evaluate success in individual cases and to understand variability and its causes. In Britain, red fox (Vulpes vulpes) populations are culled within the confines of shooting estates to benefit game and wildlife prey species. We developed a Bayesian state-space model for within-year fox population dynamics within such restricted areas and fitted it to data on culling effort and success obtained from gamekeepers on 22 shooting estates of 2 to 36 km². We used informative priors for key population processes—immigration, cub recruitment and non-culling mortality–that could not be quantified in the field. Using simulated datasets we showed that the model reliably estimated fox density and demographic parameters, and we showed that conclusions drawn from real data were robust to alternative model assumptions. All estates achieved suppression of the fox population, with pre-breeding fox density on average 47% (range 20%–90%) of estimated carrying capacity. As expected, the number of foxes killed was a poor indicator of effectiveness. Estimated rates of immigration were variable among estates, but in most cases indicated rapid replacement of culled foxes so that intensive culling efforts were required to maintain low fox densities. Due to this short-term impact, control effort focussed on the spring and summer period may be essential to achieve management goals for prey species. During the critical March-July breeding period, mean fox densities on all estates were suppressed below carrying capacity, and some maintained consistently low fox densities throughout this period. A similar model will be useful in other situations to quantify the effectiveness of lethal control on restricted areas.

Infection in patchy populations: Contrasting pathogen invasion success and dispersal at varying times since host colonization

Repeated extinction and recolonization events generate a landscape of host populations that vary in their time since colonization. Within this dynamic landscape, pathogens that excel at invading recently colonized host populations are not necessarily those that perform best in host populations at or near their carrying capacity, potentially giving rise to divergent selection for pathogen traits that mediate the invasion process. Rarely, however, has this contention been empirically tested. Using Daphnia magna, we explored how differences in the colonization history of a host population influence the invasion success of different genotypes of the pathogen Pasteuria ramosa. By partitioning the pathogen invasion process into a series of individual steps, we show that each pathogen optimizes invasion differently when encountering host populations that vary in their time since colonization. All pathogen genotypes were more likely to establish successfully in recently colonized host populations, but the production of transmission spores was typically maximized in either the subsequent growth or stationary phase of host colonization. Integrating across the first three pathogen invasion steps (initial establishment, proliferation, and secondary infection) revealed that overall pathogen invasion success (and its variance) was, nonetheless, highest in recently colonized host populations. However, only pathogens that were slow to kill their host were able to maximize host‐facilitated dispersal. This suggests that only a subset of pathogen genotypes—the less virulent and more dispersive—are more likely to encounter newly colonized host populations at the front of a range expansion or in metapopulations with high extinction rates. Our results suggest a fundamental trade‐off for a pathogen between dispersal and virulence, and evidence for higher invasion success in younger host populations, a finding with clear implications for pathogen evolution in spatiotemporally dynamic settings.

Predicting microbial growth in a mixed culture from growth curve data

We present a model-based approach for prediction of microbial growth in a mixed culture and relative fitness using data solely from growth curve experiments, which are easier to perform than competition experiments. Our approach combines growth and competition models and utilizes the total densities of mixed cultures. We implemented our approach in an open-source software package, validated it using experiments with bacteria, and demonstrated its application for estimation of relative fitness. Our approach establishes that growth in a mixed culture can be predicted using growth and competition models. It provides a way to infer relative strain or species frequencies even when competition experiments are not feasible, and to determine how differences in growth affect differences in fitness.

Determining the fitness of specific microbial genotypes has extensive application in microbial genetics, evolution, and biotechnology. While estimates from growth curves are simple and allow high throughput, they are inaccurate and do not account for interactions between costs and benefits accruing over different parts of a growth cycle. For this reason, pairwise competition experiments are the current “gold standard” for accurate estimation of fitness. However, competition experiments require distinct markers, making them difficult to perform between isolates derived from a common ancestor or between isolates of nonmodel organisms. In addition, competition experiments require that competing strains be grown in the same environment, so they cannot be used to infer the fitness consequence of different environmental perturbations on the same genotype. Finally, competition experiments typically consider only the end-points of a period of competition so that they do not readily provide information on the growth differences that underlie competitive ability. Here, we describe a computational approach for predicting density-dependent microbial growth in a mixed culture utilizing data from monoculture and mixed-culture growth curves. We validate this approach using 2 different experiments with Escherichia coli and demonstrate its application for estimating relative fitness. Our approach provides an effective way to predict growth and infer relative fitness in mixed cultures.

How Does the Evolution of Universal Ecological Traits Affect Population Size? Lessons from Simple Models

This article argues that adaptive evolutionary change in a consumer species should frequently decrease (and maladaptive change should increase) population size, producing adaptive decline. This conclusion is based on analysis of multiple consumer-resource models that examine evolutionary change in consumer traits affecting the universal ecological parameters of attack rate, conversion efficiency, and mortality. Two scenarios are investigated. In one, evolutionary equilibrium is initially maintained by opposing effects on the attack rate and other growth rate parameters; the environment or trait is perturbed, and the trait then evolves to a new (or back to a previous) equilibrium. Here evolution exhibits adaptive decline in up to one-half of all cases. The other scenario assumes a genetic perturbation having purely fitness-increasing effects. Here adaptive decline in the consumer requires that the resource be self-reproducing and overexploited and requires a sufficient increase in the attack rate. However, if the resource exhibits adaptive defense via behavior or evolution, adaptive decline may characterize consumer traits affecting all parameters. Favorable environmental change producing parameter shifts similar to those produced by adaptive evolution has similar counterintuitive effects on consumer population size. Many different food web models have already been shown to exhibit such counterintuitive changes in some species.

Global exponential stability of positive periodic solution of the n-species impulsive Gilpin-Ayala competition model with discrete and distributed time delays

In this paper, we study the n-species impulsive Gilpin-Ayala competition model with discrete and distributed time delays. The existence of positive periodic solution is proved by employing the fixed point theorem on cones. By constructing appropriate Lyapunov functional, we also obtain the global exponential stability of the positive periodic solution of this system. As an application, an interesting example is provided to illustrate the validity of our main results.

The effect of harvesting on the spatial synchrony of population fluctuations

Harvesting in space affects, in general, the spatial scale of the synchrony in the population fluctuations, which determines the size of the areas subjected to simultaneous quasi-extinction risk. Here we show that harvesting reduces the population synchrony scale if it depends more strongly on population fluctuations than the density dependence of the growth rate in the absence of harvesting. We show that constant and proportional harvesting always increases the spatial scale, using a theta-logistic model for density regulation. We also provide exact scaling results under harvesting for the Beverton-Holt and the Ricker stock-recruitment models that are commonly applied, e.g. in fisheries. Our results indicate that harvest in areas with large abundances should be encouraged to avoid increase of the spatial scale of synchrony in the population fluctuations that can lead to unexpected quasi-extinction of populations over large areas. Our results quantify this harvesting impact giving the resulting scales of spatial synchrony of population fluctuations. This emphasizes the importance of estimating the form of density dependence as well as the dependency of harvest upon population density of exploited populations, in order to get reliable predictions of the size of areas that can undergo simultaneous quasi-extinction.

Making do with less: must sparse data preclude informed harvest strategies for European waterbirds?

The demography of many European waterbirds is not well understood because most countries have conducted little monitoring and assessment, and coordination among countries on waterbird management has little precedent. Yet intergovernmental treaties now mandate the use of sustainable, adaptive harvest strategies, whose development is challenged by a paucity of demographic information. In this study, we explore how a combination of allometric relationships, fragmentary monitoring and research information, and expert judgment can be used to estimate the parameters of a theta-logistic population model, which in turn can be used in a Markov decision process to derive optimal harvesting strategies. We show how to account for considerable parametric uncertainty, as well as for different management objectives. We illustrate our methodology with a poorly understood population of Taiga Bean Geese (Anser fabalis fabalis), which is a popular game bird in Fennoscandia. Our results for Taiga Bean Geese suggest that they may have demographic rates similar to other, well-studied species of geese, and our model-based predictions of population size are consistent with the limited monitoring information available. Importantly, we found that by using a Markov decision process, a simple scalar population model may be sufficient to guide harvest management of this species, even if its demography is age structured. Finally, we demonstrated how two different management objectives can lead to very different optimal harvesting strategies, and how conflicting objectives may be traded off with each other. This approach will have broad application for European waterbirds by providing preliminary estimates of key demographic parameters, by providing insights into the monitoring and research activities needed to corroborate those estimates, and by producing harvest management strategies that are optimal with respect to the managers' objectives, options, and available demographic information.

Critical thresholds for eventual extinction in randomly disturbed population growth models

This paper considers several single species growth models featuring a carrying capacity, which are subject to random disturbances that lead to instantaneous population reduction at the disturbance times. This is motivated in part by growing concerns about the impacts of climate change. Our main goal is to understand whether or not the species can persist in the long run. We consider the discrete-time stochastic process obtained by sampling the system immediately after the disturbances, and find various thresholds for several modes of convergence of this discrete process, including thresholds for the absence or existence of a positively supported invariant distribution. These thresholds are given explicitly in terms of the intensity and frequency of the disturbances on the one hand, and the population's growth characteristics on the other. We also perform a similar threshold analysis for the original continuous-time stochastic process, and obtain a formula that allows us to express the invariant distribution for this continuous-time process in terms of the invariant distribution of the discrete-time process, and vice versa. Examples illustrate that these distributions can differ, and this sends a cautionary message to practitioners who wish to parameterize these and related models using field data. Our analysis relies heavily on a particular feature shared by all the deterministic growth models considered here, namely that their solutions exhibit an exponentially weighted averaging property between a function of the initial condition, and the same function applied to the carrying capacity. This property is due to the fact that these systems can be transformed into affine systems.

Evolution of model specific relative growth rate: Its genesis and performance over Fisher's growth rates

Growth curve models play an instrumental role to quantify the growth of biological processes and have immense practical applications across disciplines. In the modelling approach, the absolute growth rate and relative growth rate (RGR) are two most commonly used measures of growth rates. RGR is empirically estimated by Fisher (1921) assuming exponential growth between two consecutive time points and remains invariant under any choice of the underlying growth model. In this article, we propose a new measure of RGR, called modified RGR, which is sensitive to the choice of underlying growth law. The mathematical form of the growth equations are utilized to develop the formula for model dependent growth rates and can be easily computed for commonly used growth models. We compare the efficiency of Fisher's measure of RGR and modified RGR to infer the true growth profile. To achieve this, we develop a goodness of fit testing procedure using Gompertz model as a test bed. The relative efficiency of the two rate measures is compared by generating power curves of the goodness of fit testing procedure. The asymptotic distributions of the associated test statistics are elaborately studied under Gompertz set up. The simulation experiment shows that the proposed formula has better discriminatory power than the existing one in identifying the true profile. The claim is also verified using existing real data set on fish growth. An algorithm for the model selection mechanism is also proposed based on the modified RGR and is generalized for some commonly used other growth models. The proposed methodology may serve as a valuable tool in growth studies in different research areas.

Stochastic Evolutionary Demography under a Fluctuating Optimum Phenotype

Many natural populations exhibit temporal fluctuations in abundance that are consistent with external forcing by a randomly changing environment. As fitness emerges from an interaction between the phenotype and the environment, such demographic fluctuations probably include a substantial contribution from fluctuating phenotypic selection. We study the stochastic population dynamics of a population exposed to random (plus possibly directional) changes in the optimum phenotype for a quantitative trait that evolves in response to this moving optimum. We derive simple analytical predictions for the distribution of log population size over time both transiently and at stationarity under Gompertz density regulation. These predictions are well matched by population- and individual-based simulations. The log population size is approximately reverse gamma distributed, with a negative skew causing an excess of low relative to high population sizes, thus increasing extinction risk relative to a symmetric (e.g., normal) distribution with the same mean and variance. Our analysis reveals how the mean and variance of log population size change with the variance and autocorrelation of deviations of the evolving mean phenotype from the optimum. We apply our results to the analysis of evolutionary rescue in a stochastic environment and show that random fluctuations in the optimum can substantially increase extinction risk by both reducing the expected growth rate and increasing the variance of population size by several orders of magnitude.

Dynamical system modeling to simulate donor T cell response to whole exome sequencing-derived recipient peptides: Understanding randomness in alloreactivity incidence following stem cell transplantation

Quantitative relationship between the magnitude of variation in minor histocompatibility antigens (mHA) and graft versus host disease (GVHD) pathophysiology in stem cell transplant (SCT) donor-recipient pairs (DRP) is not established. In order to elucidate this relationship, whole exome sequencing (WES) was performed on 27 HLA matched related (MRD), & 50 unrelated donors (URD), to identify nonsynonymous single nucleotide polymorphisms (SNPs). An average 2,463 SNPs were identified in MRD, and 4,287 in URD DRP (p<0.01); resulting peptide antigens that may be presented on HLA class I molecules in each DRP were derived in silico (NetMHCpan ver2.0) and the tissue expression of proteins these were derived from determined (GTex). MRD DRP had an average 3,670 HLA-binding-alloreactive peptides, putative mHA (pmHA) with an IC50 of <500 nM, and URD, had 5,386 (p<0.01). To simulate an alloreactive donor cytotoxic T cell response, the array of pmHA in each patient was considered as an operator matrix modifying a hypothetical cytotoxic T cell clonal vector matrix; each responding T cell clone’s proliferation was determined by the logistic equation of growth, accounting for HLA binding affinity and tissue expression of each alloreactive peptide. The resulting simulated organ-specific alloreactive T cell clonal growth revealed marked variability, with the T cell count differences spanning orders of magnitude between different DRP. Despite an estimated, uniform set of constants used in the model for all DRP, and a heterogeneously treated group of patients, higher total and organ-specific T cell counts were associated with cumulative incidence of moderate to severe GVHD in recipients. In conclusion, exome wide sequence differences and the variable alloreactive peptide binding to HLA in each DRP yields a large range of possible alloreactive donor T cell responses. Our findings also help understand the apparent randomness observed in the development of alloimmune responses.

Spatial memory shapes density dependence in population dynamics

Most population dynamics studies assume that individuals use space uniformly, and thus mix well spatially. In numerous species, however, individuals do not move randomly, but use spatial memory to visit renewable resource patches repeatedly. To understand the extent to which memory-based foraging movement may affect density-dependent population dynamics through its impact on competition, we developed a spatially explicit, individual-based movement model where reproduction and death are functions of foraging efficiency. We compared the dynamics of populations of with- and without-memory individuals. We showed that memory-based movement leads to a higher population size at equilibrium, to a higher depletion of the environment, to a marked discrepancy between the global (i.e. measured at the population level) and local (i.e. measured at the individual level) intensities of competition, and to a nonlinear density dependence. These results call for a deeper investigation of the impact of individual movement strategies and cognitive abilities on population dynamics.

Evolution of stochastic demography with life history tradeoffs in density-dependent age-structured populations

We analyze the stochastic demography and evolution of a density-dependent age- (or stage-) structured population in a fluctuating environment. A positive linear combination of age classes (e.g., weighted by body mass) is assumed to act as the single variable of population size, [Formula: see text], exerting density dependence on age-specific vital rates through an increasing function of population size. The environment fluctuates in a stationary distribution with no autocorrelation. We show by analysis and simulation of age structure, under assumptions often met by vertebrate populations, that the stochastic dynamics of population size can be accurately approximated by a univariate model governed by three key demographic parameters: the intrinsic rate of increase and carrying capacity in the average environment, [Formula: see text] and [Formula: see text], and the environmental variance in population growth rate, [Formula: see text] Allowing these parameters to be genetically variable and to evolve, but assuming that a fourth parameter, [Formula: see text], measuring the nonlinearity of density dependence, remains constant, the expected evolution maximizes [Formula: see text] This shows that the magnitude of environmental stochasticity governs the classical trade-off between selection for higher [Formula: see text] versus higher [Formula: see text] However, selection also acts to decrease [Formula: see text], so the simple life-history trade-off between [Formula: see text]- and [Formula: see text]-selection may be obscured by additional trade-offs between them and [Formula: see text] Under the classical logistic model of population growth with linear density dependence ([Formula: see text]), life-history evolution in a fluctuating environment tends to maximize the average population size.

Stochastic foundations in nonlinear density-regulation growth

In this work we construct individual-based models that give rise to the generalized logistic model at the mean-field deterministic level and that allow us to interpret the parameters of these models in terms of individual interactions. We also study the effect of internal fluctuations on the long-time dynamics for the different models that have been widely used in the literature, such as the theta-logistic and Savageau models. In particular, we determine the conditions for population extinction and calculate the mean time to extinction. If the population does not become extinct, we obtain analytical expressions for the population abundance distribution. Our theoretical results are based on WKB theory and the probability generating function formalism and are verified by numerical simulations.

Emergence of coupling-induced oscillations and broken symmetries in heterogeneously driven nonlinear reaction networks

Many natural systems including the brain comprise coupled elements that are stimulated non-uniformly. In this paper we show that heterogeneously driven networks of excitatory-inhibitory units exhibit a diverse range of collective phenomena, including the appearance of spontaneous oscillations upon coupling quiescent elements. On varying the coupling strength a previously unreported transition is seen wherein the symmetries of the synchronization patterns in the stimulated and unstimulated groups undergo mutual exchange. The system also exhibits coexisting chaotic and non-chaotic attractors - a result that may be of interest in connection to earlier reports of varying degrees of chaoticity in the brain.

Stability and ergodicity of a stochastic Gilpin–Ayala model under regime switching on patches

The purpose of this work is to investigate the asymptotic properties of a stochastic Gilpin–Ayala population system under regime switching on patches. We establish the global stability and the extinction of the trivial equilibrium state of the model. Furthermore, we show the existence of the stationary distribution for our system model. The analytical results are illustrated by computer simulations.

r- and K-selection in fluctuating populations is determined by the evolutionary trade-off between two fitness measures: Growth rate and lifetime reproductive success

In a stable environment, evolution maximizes growth rates in populations that are not density regulated and the carrying capacity in the case of density regulation. In a fluctuating environment, evolution maximizes a function of growth rate, carrying capacity and environmental variance, tending to r-selection and K-selection under large and small environmental noise, respectively. Here we analyze a model in which birth and death rates depend on density through the same function but with independent strength of density dependence. As a special case, both functions may be linear, corresponding to logistic dynamics. It is shown that evolution maximizes a function of the deterministic growth rate r₀ and the lifetime reproductive success (LRS) R₀ , both defined at small densities, as well as the environmental variance. Under large noise this function is dominated by r₀ and average lifetimes are small, whereas R₀ dominates and lifetimes are larger under small noise. Thus, K-selection is closely linked to selection for large R₀ so that evolution tends to maximize LRS in a stable environment. Consequently, different quantities (r₀ and R₀ ) tend to be maximized at low and high densities, respectively, favoring density-dependent changes in the optimal life history.

Chemical antipredator defence is linked to higher extinction risk

Many attributes of species may be linked to contemporary extinction risk, though some such traits remain untested despite suggestions that they may be important. Here, I test whether a trait associated with higher background extinction rates, chemical antipredator defence, is also associated with current extinction risk, using amphibians as a model system-a group facing global population declines. I find that chemically defended species are approximately 60% more likely to be threatened than species without chemical defence, although the severity of the contemporary extinction risk may not relate to chemical defence. The results confirm that background and contemporary extinction rates can be predicted from the same traits, at least in certain cases. This suggests that associations between extinction risk and phenotypic traits can be temporally stable over long periods. The results also provide novel insights into the relevance of antipredator defences for species subject to conservation concerns.

Dynamical System Modeling to Simulate Donor T Cell Response to Whole Exome Sequencing-Derived Recipient Peptides Demonstrates Different Alloreactivity Potential in HLA-Matched and -Mismatched Donor-Recipient Pairs

Immune reconstitution kinetics and subsequent clinical outcomes in HLA-matched recipients of allogeneic stem cell transplantation (SCT) are variable and difficult to predict. Considering SCT as a dynamical system may allow sequence differences across the exomes of the transplant donors and recipients to be used to simulate an alloreactive T cell response, which may allow better clinical outcome prediction. To accomplish this, whole exome sequencing was performed on 34 HLA-matched SCT donor-recipient pairs (DRPs) and the nucleotide sequence differences translated to peptides. The binding affinity of the peptides to the relevant HLA in each DRP was determined. The resulting array of peptide-HLA binding affinity values in each patient was considered as an operator modifying a hypothetical T cell repertoire vector, in which each T cell clone proliferates in accordance with the logistic equation of growth. Using an iterating system of matrices, each simulated T cell clone's growth was calculated with the steady-state population being proportional to the magnitude of the binding affinity of the driving HLA-peptide complex. Incorporating competition between T cell clones responding to different HLA-peptide complexes reproduces a number of features of clinically observed T cell clonal repertoire in the simulated repertoire, including sigmoidal growth kinetics of individual T cell clones and overall repertoire, Power Law clonal frequency distribution, increase in repertoire complexity over time with increasing clonal diversity, and alteration of clonal dominance when a different antigen array is encountered, such as in SCT. The simulated, alloreactive T cell repertoire was markedly different in HLA-matched DRPs. The patterns were differentiated by rate of growth and steady-state magnitude of the simulated T cell repertoire and demonstrate a possible correlation with survival. In conclusion, exome wide sequence differences in DRPs may allow simulation of donor alloreactive T cell response to recipient antigens and may provide a quantitative basis for refining donor selection and titration of immunosuppression after SCT.

A simple approximation of moments of the quasi-equilibrium distribution of an extended stochastic theta-logistic model with non-integer powers

The stochastic versions of the logistic and extended logistic growth models are applied successfully to explain many real-life population dynamics and share a central body of literature in stochastic modeling of ecological systems. To understand the randomness in the population dynamics of the underlying processes completely, it is important to have a clear idea about the quasi-equilibrium distribution and its moments. Bartlett et al. (1960) took a pioneering attempt for estimating the moments of the quasi-equilibrium distribution of the stochastic logistic model. Matis and Kiffe (1996) obtain a set of more accurate and elegant approximations for the mean, variance and skewness of the quasi-equilibrium distribution of the same model using cumulant truncation method. The method is extended for stochastic power law logistic family by the same and several other authors (Nasell, 2003; Singh and Hespanha, 2007). Cumulant truncation and some alternative methods e.g. saddle point approximation, derivative matching approach can be applied if the powers involved in the extended logistic set up are integers, although plenty of evidence is available for non-integer powers in many practical situations (Sibly et al., 2005). In this paper, we develop a set of new approximations for mean, variance and skewness of the quasi-equilibrium distribution under more general family of growth curves, which is applicable for both integer and non-integer powers. The deterministic counterpart of this family of models captures both monotonic and non-monotonic behavior of the per capita growth rate, of which theta-logistic is a special case. The approximations accurately estimate the first three order moments of the quasi-equilibrium distribution. The proposed method is illustrated with simulated data and real data from global population dynamics database.