Dynamic modeling of cooperative protein secretion in microorganism populations

Interactions between microorganisms can have a crucial effect on their population dynamics. Typically, interactions are mediated through the environment by molecules and proteins that are products of cell metabolism and physiology; they therefore reflect the internal dynamics of the single cell. In this work we aim to integrate single-cell properties of gene expression that affect indirect interactions between microorganisms under challenging conditions, into a quantitative model of population dynamics. Specifically we address the problem of a microbial population secreting a protein that can actively extract a growth-limiting resource, such as a simple sugar or iron, from the environment. The genes coding for the protein can undergo random epigenetic transitions between active and silenced states, and can be repressed by the product of their reaction. We model cooperative and competitive interactions between protein producing and non-producing phenotypes by nonlinear dynamical systems and analyze them both in terms of asymptotic states and of transient dynamics. Our model shows that phenotypic transitions allow a stable coexistence of the two phenotypes, and enables us to make predictions regarding the conditions required for such coexistence and the typical timescales of transient dynamics. It also shows how repression by the reaction product induces a feedback at the population-environment level that can result in limit cycle dynamics. The relation of these results to experiments are discussed.     

昆虫种群动态模拟模型

昆虫是动物界中最大的类群,与人类有着密切的利害关系。对昆虫的数量预测与符合经济和生态规律的管理,一直都被国内外列入重点研究课题。种群动态模拟是害虫管理中重要的基础工作。近十年来,关于昆虫种群动态模型的理论和实验研究进展迅速。现分别从单种种群和多种种群两个方面对国内外近些年来昆虫种群动态模拟模型的研究进展进行了概括和总结。单种种群从两个方面阐述:一是最基本的种群动态模拟模型Log istic方程的研究成果,包括方程的修正、参数的拟合与最优捕获策略等;另一个方面是对种群动态模拟常用的矩阵模型的概述,主要介绍不等期年龄组、矩阵维数的变化、矩阵维数与历期的关系、个体之间的发育差异以及发育速率差异等等对昆虫种群动态模型的影响。多种群主要从建模和模型应用两个部分对国内外研究成果进行综述。最后,对种群动态模拟模型研究的发展方向做了深入地讨论,即在原有的数据采集工作的基础上,使用面向对象程序设计语言,把各种要素包括各种物种及各种环境条件抽象成类,用消息传递来表示昆虫种群内个体与个体、昆虫种群与环境之间的相互作用,再结合先进的数学算法,建立一个直观的、操作简单的昆虫种群动态模型库,使模型结构与现实世界有最大的相似性。这样就可以实现昆虫种群动态的可视化、立体化、实时化和精确化的监测及预测。     

Birth, growth and death as structuring operators in bacterial population dynamics

A new model is presented that describes microbial population dynamics that emerge from complex interactions among birth, growth and death as oriented, discrete events. Specifically, birth and death act as structuring operators for individual organisms within the population, which become synchronised as age clusters (called cell generations that are structured in age classes) that are born at the same time and die in concert; a pattern very consistent with recent experimental data that show bacterial group death correlates with temporal population dynamics in chemostats operating at carrying capacity. Although the model only assumes “natural death” (i.e., no death from predation or antimicrobial exposure), it indicates that short-term non-linear dynamic behaviour can exist in a bacterial population growing under longer term pseudo-steady-state conditions (a confined dynamic equilibrium). After summarizing traditional assumptions about bacterial aging, simulations of batch, continuous-flow, and bioreactors with recycle are used to show how population dynamics vary as function of hydraulic retention time, microbial kinetics, substrate level, and other factors that cause differential changes in the distribution of living and dead cells within the system. In summary, we show that population structures induced by birth and death (as discrete and delayed events) intrinsically create a non-linear dynamic system, implying that a true steady state can never exist in growing bacterial populations. This conclusion is discussed within the context of process stability in biotechnology.     

The role of density-dependent individual growth in the persistence of freshwater salmonid populations

Theoretical and empirical models of populations dynamics have paid little attention to the implications of density-dependent individual growth on the persistence and regulation of small freshwater salmonid populations. We have therefore designed a study aimed at testing our hypothesis that density-dependent individual growth is a process that enhances population recovery and reduces extinction risk in salmonid populations in a variable environment subject to disturbance events. This hypothesis was tested in two newly introduced marble trout (Salmo marmoratus) populations living in Slovenian streams (Zakojska and Gorska) subject to severe autumn floods. We developed a discrete-time stochastic individual-based model of population dynamics for each population with demographic parameters and compensatory responses tightly calibrated on data from individually tagged marble trout. The occurrence of severe flood events causing population collapses was explicitly accounted for in the model. We used the model in a population viability analysis setting to estimate the quasi-extinction risk and demographic indexes of the two marble trout populations when individual growth was density-dependent. We ran a set of simulations in which the effect of floods on population abundance was explicitly accounted for and another set of simulations in which flood events were not included in the model. These simulation results were compared with those of scenarios in which individual growth was modelled with density-independent Von Bertalanffy growth curves. Our results show how density-dependent individual growth may confer remarkable resilience to marble trout populations in case of major flood events. The resilience to flood events shown by the simulation results can be explained by the increase in size-dependent fecundity as a consequence of the drop in population size after a severe flood, which allows the population to quickly recover to the pre-event conditions. Our results suggest that density-dependent individual growth plays a potentially powerful role in the persistence of freshwater salmonids living in streams subject to recurrent yet unpredictable flood events. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

The impact of non-lethal synergists on the population and evolutionary dynamics of host-pathogen interactions

Multiple pathogenic infections can influence disease transmission and virulence, and have important consequences for understanding the community ecology and epidemiology of host-pathogen interactions. Here the population and evolutionary dynamics of a host-pathogen interaction with free-living stages are explored in the presence of a non-lethal synergist that hosts must tolerate. Through the coupled effects on pathogen transmission, host mass gain and allometry it is shown how investing in tolerance to a non-lethal synergist can lead to a broad range of different population dynamics. The effects of the synergist on pathogen fitness are explored through a series of life-history trait trade-offs. Coupling trade-offs between pathogen yield and pathogen speed of kill and the presence of a synergist favour parasites that have faster speeds of kill. This evolutionary change in pathogen characteristics is predicted to lead to stable population dynamics. Evolutionary analysis of tolerance of the synergist (strength of synergy) and lethal pathogen yield show that decreasing tolerance allows alternative pathogen strategies to invade and replace extant strategies. This evolutionary change is likely to destabilise the host-pathogen interaction leading to population cycles. Correlated trait effects between speed of kill and tolerance (strength of synergy) show how these traits can interact to affect the potential for the coexistence of multiple pathogen strategies. Understanding the consequences of these evolutionary relationships is important for the both the evolutionary and population dynamics of host-pathogen interactions.     

Propriospinal neurones as a relay system for transmission of cortico-spinal influences.

1. Synaptic organization and transmission have been studied in the lateral group of short propriospinal neurones of the lumbar and cervical regions of the cat spinal cord. Special attention was paid to their role in the transmission of cortico-spinal volleys. 2. The majority of these neurones are mono- or oligosynaptically excited after pyramidal tract stimulation. Convergence of excitatory actions from rubrospinal and lateral reticulospinal tracts was typical for these cells. Neurones with relatively low-level and delayed effects from segmental afferents are frequent in this population. 3. Temporal summation is important for the transmission of descending vlleys through these neurones. Mutual excitatory and recurrent inhibitory connections are supposed to play a substantial role in their function. 4. Possible participation of the short lateral propriospinal system in the transmission, transformation and re-distribution of corticofugal signals to the segmental spinal mechanisms is discussed.     

The interaction between plant competition and disease

It is well documented that pathogens can affect the survival, reproduction, and growth of individual plants. Drawing together insights from diverse studies in ecology and agriculture, we evaluate the evidence for pathogens affecting competitive interactions between plants of both the same and different species. Our objective is to explore the potential ecological and evolutionary consequences of such interactions. First, we address how disease interacts with intraspecific competition and present a simple graphical model suggesting that diverse outcomes should be expected. We conclude that the presence of pathogens may have either large or minimal effects on population dynamics depending on many factors including the density-dependent compensatory ability of healthy plants and spatial patterns of infection. Second, we consider how disease can alter competitive abilities of genotypes, and thus may affect the genetic composition of populations. These genetic processes feed back on population dynamics given trade-offs between disease resistance and other fitness components. Third, we examine how the effect of disease on interspecific plant interactions may have potentially far-reaching effects on community composition. A host-specific pathogen, for example, may alter a competitive hierarchy that exists between host and non-host species. Generalist pathogens can also induce indirect competitive interactions between host species. We conclude by highlighting lacunae in our current understanding and suggest that future studies should (1) examine a broader taxonomic range of pathogens since work to date has largely focused on fungal pathogens; (2) increase the use of field competition studies; (3) follow interactions for multiple generations; (4) characterize density-dependent processes; and (5) quantify pathogen, as well as plant, population and community dynamics.     

Frequency-dependent community dynamics driven by sexual interactions

Research in community ecology has tended to focus on trophic interactions (e.g., predation, resource competition) as driving forces of community dynamics, and sexual interactions have often been overlooked. Here we discuss how sexual interactions can affect community dynamics, especially focusing on frequency-dependent dynamics of horizontal communities (i.e., communities of competing species in a single ecological guild). By combining mechanistic and phenomenological models of competition, we place sexual reproduction into the framework of modern coexistence theory. First, we review how population dynamics of two species competing for two resources can be represented by the Lotka–Volterra competition model as well as frequency dynamics, and how niche differentiation and overlap produce negative and positive frequency-dependence (i.e., stable coexistence and priority effect), respectively. Then, we explore two situations where sexual interactions change the frequency-dependence in community dynamics: (1) reproductive interference, that is, negative interspecific interactions due to incomplete species recognition in mating trials, can promote positive frequency-dependence and (2) density-dependent intraspecific adaptation load, that is, reduced population growth rates due to adaptation to intraspecific sexual (or social) interactions, produces negative frequency-dependence. We show how reproductive interference and density-dependent intraspecific adaptation load can decrease and increase niche differences in the framework of modern coexistence theory, respectively. Finally, we discuss future empirical and theoretical approaches for studying how sexual interactions and related phenomena (e.g., reproductive interference, intraspecific adaptation load, and sexual dimorphism) driven by sexual selection and conflict can affect community dynamics.     

昆虫种群动态非线性建模理论与应用

本文以非线性动力学为基础,对自然界中昆虫种群动态的复杂性、不确定性进行了建模方法的探讨,在讨论了昆虫种群动态的混沌与非线性时间序列预测方法的前提下,以山东省玉米螟等种群动态资料进行了实例分析。     

Simple discrete-time metapopulation models of patch occupancy

Simple models in theoretical ecology have a long-standing history of being used to understand how specific processes influence population dynamics as well as providing a foundation for future endeavors. The Levins model is the seminal example of this for continuous-time metapopulation dynamics. However, many natural populations have a distinct separation between processes and data is not collected continuously leading to the need for using a discrete-time model. Our goal is to develop a simple discrete-time metapopulation model of patch occupancy using difference equations. In our formulation, we consider the two fundamental processes of colonization and extinction that will be treated as sequential events and will only consider patch occupancy. To achieve this, we use a composition of two functions where one will reflect the extinction process and the other for the colonization process. Under some mild assumptions, we are able determine the dynamic behavior of the metapopulation. In addition, we provide numerous examples for the functions used to emulate the colonization and extinction processes. Our results illustrate that the dynamics of the model are tied to properties such as convexity and monotonicity of the colonization and extinction functions. In particular, if the model is non-monotone, then complex dynamics can arise such as cyclic and even chaotic behavior. Overall, our approach shows how certain properties of the colonization and extinction functions can influence metapopulation dynamics.     

Scaling from optimal behavior to population dynamics and ecosystem function

While behavioral responses of individual organisms can be predicted with optimal foraging theory, the theory of how individual behavior feeds back to population and ecosystem dynamics has not been fully explored. Ecological models of trophic interactions incorporating behavior of entire populations commonly assume either that populations act as one when making decisions, that behavior is slowly varying or that non-linear effects are negligible in behavioral choices at the population scale. Here, we scale from individual optimal behavior to ecosystem structure in a classic tri-trophic chain where both prey and predators adapt their behavior in response to food availability and predation risk. Behavior is modeled as playing the field, with both consumers and predators behaving optimally at every instant basing their choices on the average population behavior. We establish uniqueness of the Nash equilibrium, and find it numerically. By modeling the interactions as playing the field, we can perform instantaneous optimization at the individual level while taking the entire population into account. We find that optimal behavior essentially removes the effect of top-down forcing at the population level, while drastically changing the behavior. Bottom-up forcing is found to increase populations at all trophic levels. These phenomena both appear to be driven by an emerging constant consumption rate, corresponding to a partial satiation. In addition, we find that a Type III functional response arises from a Type II response for both predators and consumers when their behavior follows the Nash equilibrium, showing that this is a general phenomenon. Our approach is general and computationally efficient and can be used to account for behavior in population dynamics with fast behavioral responses.     

Adaptive foraging behaviour of individual pollinators and the coexistence of co-flowering plants

Although pollinators can play a central role in determining the structure and stability of plant communities, little is known about how their adaptive foraging behaviours at the individual level, e.g. flower constancy, structure these interactions. Here, we construct a mathematical model that integrates individual adaptive foraging behaviour and population dynamics of a community consisting of two plant species and a pollinator species. We find that adaptive foraging at the individual level, as a complementary mechanism to adaptive foraging at the species level, can further enhance the coexistence of plant species through niche partitioning between conspecific pollinators. The stabilizing effect is stronger than that of unbiased generalists when there is also strong competition between plant species over other resources, but less so than that of multiple specialist species. This suggests that adaptive foraging in mutualistic interactions can have a very different impact on the plant community structure from that in predator–prey interactions. In addition, the adaptive behaviour of individual pollinators may cause a sharp regime shift for invading plant species. These results indicate the importance of integrating individual adaptive behaviour and population dynamics for the conservation of native plant communities.     

Food webs in space: On the interplay of dynamic instability and spatial processes

Ecologists increasingly recognize that a consideration of spatial dynamics is essential for resolving many classical problems in community ecology. In the present paper, I argue that understanding how trophic interactions influence population stability can have important implications for the expression of spatial processes. I use two examples to illustrate this point. The first example has to do with spatial determinants of food chain length. Prior theoretical and empirical work has suggested that colonization–extinction dynamics can influence food chain length, at least for specialist consumers. I briefly review evidence and prior theory that food chain length is sensitive to area. A metacommunity scenario, in which each of various patches can have a food chain varying in length (but in which a consumer is not present on a patch unless its required resource is also present), shows that alternative landscape states are possible. This possibility arises if top predators moderate unstable interactions between intermediate predators and basal resources. The second example has to do with the impact of recurrent immigration on the stability of persistent populations. Immigration can either stabilize or destabilize local population dynamics. Moreover, an increase in immigration can decrease average population size for unstable populations with direct density-dependence, or in predator–prey systems with saturating functional responses. These theoretical models suggest that the interplay of temporal variation and spatial fluxes can lead to novel qualitative phenomena.     

Co‐adaptation impacts the robustness of predator–prey dynamics against perturbations

Global change threatens the maintenance of ecosystem functions that are shaped by the persistence and dynamics of populations. It has been shown that the persistence of species increases if they possess larger trait adaptability. Here, we investigate whether trait adaptability also affects the robustness of population dynamics of interacting species and thereby shapes the reliability of ecosystem functions that are driven by these dynamics. We model co‐adaptation in a predator–prey system as changes to predator offense and prey defense due to evolution or phenotypic plasticity. We investigate how trait adaptation affects the robustness of population dynamics against press perturbations to environmental parameters and against pulse perturbations targeting species abundances and their trait values. Robustness of population dynamics is characterized by resilience, elasticity, and resistance. In addition to employing established measures for resilience and elasticity against pulse perturbations (extinction probability and return time), we propose the warping distance as a new measure for resistance against press perturbations, which compares the shapes and amplitudes of pre‐ and post‐perturbation population dynamics. As expected, we find that the robustness of population dynamics depends on the speed of adaptation, but in nontrivial ways. Elasticity increases with speed of adaptation as the system returns more rapidly to the pre‐perturbation state. Resilience, in turn, is enhanced by intermediate speeds of adaptation, as here trait adaptation dampens biomass oscillations. The resistance of population dynamics strongly depends on the target of the press perturbation, preventing a simple relationship with the adaptation speed. In general, we find that low robustness often coincides with high amplitudes of population dynamics. Hence, amplitudes may indicate the robustness against perturbations also in other natural systems with similar dynamics. Our findings show that besides counteracting extinctions, trait adaptation indeed strongly affects the robustness of population dynamics against press and pulse perturbations.     

Dynamics of populations with individual variation in dispersal on bounded domains

Most classical models for the movement of organisms assume that all individuals have the same patterns and rates of movement (for example, diffusion with a fixed diffusion coefficient) but there is empirical evidence that movement rates and patterns may vary among different individuals. A simple way to capture variation in dispersal that has been suggested in the ecological literature is to allow individuals to switch between two distinct dispersal modes. We study models for populations whose members can switch between two different nonzero rates of diffusion and whose local population dynamics are subject to density dependence of logistic type. The resulting models are reaction–diffusion systems that can be cooperative at some population densities and competitive at others. We assume that the focal population inhabits a bounded region and study how its overall dynamics depend on the parameters describing switching rates and local population dynamics. (Traveling waves and spread rates have been studied for similar models in the context of biological invasions.) The analytic methods include ideas and results from reaction–diffusion theory, semi-dynamical systems, and bifurcation/continuation theory.     

The dynamics of hierarchical age-structured populations

An age-structured population is considered in which the birth and death rates of an individual of age a is a function of the density of individuals older and/or younger than a. An existence/uniqueness theorem is proved for the McKendrick equation that governs the dynamics of the age distribution function. This proof shows how a decoupled ordinary differential equation for the total population size can be derived. This result makes a study of the population's asymptotic dynamics (indeed, often its global asymptotic dynamics) mathematically tractable. Several applications to models for intra-specific competition and predation are given.     

The ideal free distribution: a review and synthesis of the game-theoretic perspective

The Ideal Free Distribution (IFD), introduced by Fretwell and Lucas in [Fretwell, D.S., Lucas, H.L., 1970. On territorial behavior and other factors influencing habitat distribution in birds. Acta Biotheoretica 19, 16-32] to predict how a single species will distribute itself among several patches, is often cited as an example of an evolutionarily stable strategy (ESS). By defining the strategies and payoffs for habitat selection, this article puts the IFD concept in a more general game-theoretic setting of the “habitat selection game”. Within this game-theoretic framework, the article focuses on recent progress in the following directions: (1) studying evolutionarily stable dispersal rates and corresponding dispersal dynamics; (2) extending the concept when population numbers are not fixed but undergo population dynamics; (3) generalizing the IFD to multiple species.For a single species, the article briefly reviews existing results. It also develops a new perspective for Parker’s matching principle, showing that this can be viewed as the IFD of the habitat selection game that models consumer behavior in several resource patches and analyzing complications involved when the model includes resource dynamics as well. For two species, the article first demonstrates that the connection between IFD and ESS is now more delicate by pointing out pitfalls that arise when applying several existing game-theoretic approaches to these habitat selection games. However, by providing a new detailed analysis of dispersal dynamics for predator-prey or competitive interactions in two habitats, it also pinpoints one approach that shows much promise in this general setting, the so-called “two-species ESS”. The consequences of this concept are shown to be related to recent studies of population dynamics combined with individual dispersal and are explored for more species or more patches.     

Climatic conditions during migration affect population size and arrival dates in an Afro-Palaearctic migrant

Long-distance migrants are particularly susceptible to climate change because of their multi-stage life-cycle, but understanding how climatic conditions at each of these stages influence population dynamics remains a key challenge. Here, we use long-term data from a UK population of Sand Martins Riparia riparia, a declining Afro-Palaearctic migrant, to investigate how weather on the wintering grounds and at passage sites impacts population size and arrival date. General linear models revealed that population size increased and arrival date advanced over the study period, and both were predicted by regional climatic variables in the previous winter and on passage. These results add to a growing body of evidence showing that population change in migrant birds is influenced by climatic conditions at all stages of the life cycle.