Evolution of complex dynamics in spatially structured populations

Dynamics of populations depend on demographic parameters which may change during evolution. In simple ecological models given by one-dimensional difference equations, the evolution of demographic parameters generally leads to equilibrium population dynamics. Here we show that this is not true in spatially structured ecological models. Using a multi-patch metapopulation model, we study the evolutionary dynamics of phenotypes that differ both in their response to local crowding, i.e. in their competitive behaviour within a habitat, and in their rate of dispersal between habitats. Our simulation results show that evolution can favour phenotypes that have the intrinsic potential for very complex dynamics provided that the environment is spatially structured and temporally variable. These phenotypes owe their evolutionary persistence to their large dispersal rates. They typically coexist with phenotypes that have low dispersal rates and that exhibit equilibrium dynamics when alone. This coexistence is brought about through the phenomenon of evolutionary branching, during which an initially uniform population splits into the two phenotypic classes.     

Metapopulation dynamics with quasi-local competition

Stepping-stone models for the ecological dynamics of metapopulations are often used to address general questions about the effects of spatial structure on the nature and complexity of population fluctuations. Such models describe an ensemble of local and spatially isolated habitat patches that are connected through dispersal. Reproduction and hence the dynamics in a given local population depend on the density of that local population, and a fraction of every local population disperses to neighboring patches. In such models, interesting dynamic phenomena, e.g. the persistence of locally unstable predator-prey interactions, are only observed if the local dynamics in an isolated patch exhibit non-equilibrium behavior. Therefore, the scope of these models is limited. Here we extend these models by making the biologically plausible assumption that reproductive success in a given local habitat not only depends on the density of the local population living in that habitat, but also on the densities of neighboring local populations. This would occur if competition for resources occurs between neighboring populations, e.g. due to foraging in neighboring habitats. With this assumption of quasi-local competition the dynamics of the model change completely. The main difference is that even if the dynamics of the local populations have a stable equilibrium in isolation, the spatially uniform equilibrium in which all local populations are at their carrying capacity becomes unstable if the strength of quasi-local competition reaches a critical level, which can be calculated analytically. In this case the metapopulation reaches a new stable state, which is, however, not spatially uniform anymore and instead results in an irregular spatial pattern of local population abundance. For large metapopulations, a huge number of different, spatially non-uniform equilibrium states coexist as attractors of the metapopulation dynamics, so that the final state of the system depends critically on the initial conditions. The existence of a large number of attractors has important consequences when environmental noise is introduced into the model. Then the metapopulation performs a random walk in the space of all attractors. This leads to large and complicated population fluctuations whose power spectrum obeys a red-shifted power law. Our theory reiterates the potential importance of spatial structure for ecological processes and proposes new mechanisms for the emergence of non-uniform spatial patterns of abundance and for the persistence of complicated temporal population fluctuations.     

具有年龄结构的食蚜蝇-蚜虫捕食模型

现有的具有年龄结构的捕食-食饵模型总是假设只有成年捕食者捕食猎物,这与实际情况不符。建立了一个幼年捕食者捕食食饵的具有年龄结构的食蚜蝇-蚜虫模型,应用微分方程定性理论,讨论了系统平衡点及其稳定性:其中平衡点E1(0,0,0)为不稳定的;满足一定条件时,边界平衡点E2(K,0,0)及正平衡点E3(x*,y1*,y2*)为局部渐近稳定的;且应用一致持续生存理论得到了系统永久持续生存的条件,为有害生物综合治理提供了理论依据。     

科尔沁沙地不同生境植被凋落物年际及年内动态

凋落物是植被土壤系统之间重要的物质和能量通道之一,在生态脆弱区植被和土壤修复过程中发挥着特殊的功能和作用.以科尔沁沙地流动沙丘、固定沙丘和草地为对象,通过连续测定9个生长季凋落物量,并结合气温与降水量数据,研究沙地生态系统不同生境的凋落物年际和年内动态及其调控因子.结果表明:不同生境植被年凋落物大小依次为:流动沙丘(9.01 g·m^-2)<固定沙丘(67.46 g·m^-2)<草地(119.55 g·m^-2).凋落物总量年际动态波动明显,固定沙丘年际变化呈“双峰”曲线,草地年际变化呈“W”型曲线.凋落物量年内变化均表现为“U”型曲线,在4和9月出现高峰值.降水量和气温对固定沙丘和草地凋落物量月际动态影响显著,而对不同生境条件下凋落物量年际变化影响均不显著.气温是影响该沙地生态系统生长季(4—9月)凋落物量月动态的主要因素.     

Ideal free distributions, evolutionary games, and population dynamics in multiple-species environments

In this article, we develop population game theory, a theory that combines the dynamics of animal behavior with population dynamics. In particular, we study interaction and distribution of two species in a two-patch environment assuming that individuals behave adaptively (i.e., they maximize Darwinian fitness). Either the two species are competing for resources or they are in a predator-prey relationship. Using some recent advances in evolutionary game theory, we extend the classical ideal free distribution (IFD) concept for single species to two interacting species. We study population dynamical consequences of two-species IFD by comparing two systems: one where individuals cannot migrate between habitats and one where migration is possible. For single species, predator-prey interactions, and competing species, we show that these two types of behavior lead to the same population equilibria and corresponding species spatial distributions, provided interspecific competition is patch independent. However, if differences between patches are such that competition is patch dependent, then our predictions strongly depend on whether animals can migrate or not. In particular, we show that when species are settled at their equilibrium population densities in both habitats in the environment where migration between habitats is blocked, then the corresponding species spatial distribution need not be an IFD. Thus, when species are given the opportunity to migrate, they will redistribute to reach an IFD (e.g., under which the two species can completely segregate), and this redistribution will also influence species population equilibrial densities. Alternatively, we also show that when two species are distributed according to the IFD, the corresponding population equilibrium can be unstable.     

Interplay of Darwinian and frequency-dependent selection in the host-associated microbial populations

In order to analyze the microevolutionary processes in host-associated microorganisms, we simulated the dynamics of rhizobia populations composed of a parental strain and its mutants possessing the altered fitness within "plant-soil" system. The population dynamics was presented as a series of cycles (each one involves "soil-->rhizosphere-->nodules-->soil" succession) described using recurrent equations. For representing the selection and mutation pressures, we used a universal approach based on calculating the shifts in the genetic ratios of competing bacterial genotypes within the particular habitats and across several habitats. Analysis of the model demonstrated that a balanced polymorphism may be established in rhizobia population: mutants with an improved fitness do not supplant completely the parental strain while mutants with a decreased fitness may be maintained stably. This polymorphism is caused by a rescue of low-fitted genotypes via negative frequency-dependent selection (FDS) that is implemented during inoculation of nodules and balances the Darwinian selection that occurs during multiplication or extinction of bacteria at different habitats. The most diverse populations are formed if the rhizobia are equally successful in soil and nodules, while a marked preference for any of these habitats results in the decrease of diversity. Our simulation suggests that FDS can maintain the mutualistic rhizobia-legume interactions under the stress conditions deleterious for surviving the bacterial strains capable for intensive N2 fixation. Genetic consequences of releasing the modified rhizobia strains may be addressed using the presented model.     

Transmission dynamics of an emerging infectious disease in wildlife through host reproductive cycles

Emerging infectious diseases are major threats to wildlife populations. To enhance our understanding of the dynamics of these diseases, we investigated how host reproductive behavior and seasonal temperature variation drive transmission of infections among wild hosts, using the model system of cyprinid herpesvirus 3 (CyHV-3) disease in common carp. Our main findings were as follows: (1) a seroprevalence survey showed that CyHV-3 infection occurred mostly in adult hosts, (2) a quantitative assay for CyHV-3 in a host population demonstrated that CyHV-3 was most abundant in the spring when host reproduction occurred and water temperature increased simultaneously and (3) an analysis of the dynamics of CyHV-3 in water revealed that CyHV-3 concentration increased markedly in breeding habitats during host group mating. These results indicate that breeding habitats can become hot spots for transmission of infectious diseases if hosts aggregate for mating and the activation of pathogens occurs during the host breeding season.     

Evolutionary dynamics and highly optimized tolerance

We develop a numerical model of a lattice community based on Highly Optimized Tolerance (HOT), which relates the evolution of complexity to robustness tradeoffs in an uncertain environment. With the model, we explore scenarios for evolution and extinction which are abstractions of processes which are commonly discussed in biological and ecological case studies. These include the effects of different habitats on the phenotypic traits of the organisms, the effects of different mutation rates on adaptation, fitness, and diversity, and competition between generalists and specialists. The model exhibits a wide variety of microevolutionary and macroevolutionary phenomena which can arise in organisms which are subject to random mutation, and selection based on fitness evaluated in a specific environment. Generalists arise in uniform habitats, where different disturbances occur with equal frequency, while specialists arise when the relative frequency of different disturbances is skewed. Fast mutators are seen to play a primary role in adaptation, while slow mutators preserve well-adapted configurations. When uniform and skewed habitats are coupled through migration of the organisms, we observe a primitive form of punctuated equilibrium. Rare events in the skewed habitat lead to extinction of the specialists, whereupon generalists invade from the uniform habitat, adapt to their new surroundings, ultimately leading their progeny to become vulnerable to extinction in a subsequent rare disturbance.     

Violation of the fluctuation-dissipation theorem in a protein system

We report the results of molecular dynamics simulations of the protein myosin carried out with an elastic network model. Quenching the system, we observe glassy behavior of a density correlation function and a density response function that are often investigated in structure glasses and spin glasses. In the equilibrium, the fluctuation-response relation, a representative relation of the fluctuation-dissipation theorem, holds that the ratio of the density correlation function to the density response function is equal to the temperature of the environment. We show that, in the quenched system that we study, this relation can be violated. In the case that this relation does not hold, this ratio can be regarded as an effective temperature. We find that this effective temperature of myosin is higher than the temperature of the environment. We discuss the relation between this effective temperature and energy transduction that occurs after ATP hydrolysis in the myosin molecule.     

Population dynamics with a stable efficient equilibrium

We propose a game-theoretic dynamics of a population of replicating individuals. It consists of two parts: the standard replicator one and a migration between two different habitats. We consider symmetric two-player games with two evolutionarily stable strategies: the efficient one in which the population is in a state with a maximal payoff and the risk-dominant one where players are averse to risk. We show that for a large range of parameters of our dynamics, even if the initial conditions in both habitats are in the basin of attraction of the risk-dominant equilibrium (with respect to the standard replication dynamics without migration), in the long run most individuals play the efficient strategy.     

Transmission Dynamics of an SIS Model with Age Structure on Heterogeneous Networks

Infection age is often an important factor in epidemic dynamics. In order to realistically analyze the spreading mechanism and dynamical behavior of epidemic diseases, in this paper, a generalized disease transmission model of SIS type with age-dependent infection and birth and death on a heterogeneous network is discussed. The model allows the infection and recovery rates to vary and depend on the age of infection, the time since an individual becomes infected. We address uniform persistence and find that the model has the sharp threshold property, that is, for the basic reproduction number less than one, the disease-free equilibrium is globally asymptotically stable, while for the basic reproduction number is above one, a Lyapunov functional is used to show that the endemic equilibrium is globally stable. Finally, some numerical simulations are carried out to illustrate and complement the main results. The disease dynamics rely not only on the network structure, but also on an age-dependent factor (for some key functions concerned in the model).     

The effect of evolution on host-parasitoid systems

It is well known that a simple first-order difference equation can exhibit complex population dynamics, such as sustained oscillations and chaos. An interesting problem is whether such oscillatory dynamics are expected to occur in real populations. This paper assumes that the resident system is composed of 1-host and 1-parasitoid and that only the host is allowed to evolve, but not the parasitoid. Based on the invasibility of a host to host-parasitoid systems, we investigate the dynamics of the host-parasitoid system favored by natural selection. We consider two cases. In the first case, the host's evolution involving both the intrinsic growth rate and the sensitivity to density is considered. In the second case, the host's evolution involving both the intrinsic growth rate and the vulnerability to the parasitoid is considered. In both cases, we see that the dynamics with a stable equilibrium will not be favored by natural selection without the trade-off between the host's traits which are allowed to evolve. The host-parasitoid system with a stable equilibrium will be eventually invaded by a host type that develops an unstable equilibrium with the parasitoid. If there is a trade-off between the host's traits which are allowed to evolve, a host-parasitoid system with a stable equilibrium can be favored by natural selection.     

Seasonal subsidy stabilizes food web dynamics: Balance in a heterogeneous landscape

Resource subsidies from external habitats can substantially affect the food web dynamics of local habitats. In this paper, we explore a mathematical model that is tailored for a stream food web, studied by Nakano and colleagues, in which consumers, in situ prey and subsidies all show seasonal fluctuation. The model reveals that the food web dynamics are stabilized if subsidies increase in summer when in situ productivity is low. Consumer dynamics are stabilized because subsidies complement seasonal resource deficiency. In situ prey dynamics are stabilized because subsidies indirectly balance the predation pressure by consumers, with seasonal change in prey carrying capacity. In summer when prey carrying capacity is low, seasonally abundant subsidies indirectly decrease predation pressure, whereas in winter, with high prey carrying capacity, scarce subsidies increase the predation pressure. Our results suggest that temporal productivity differences between spatially linked habitats are important to promote the stability of food web dynamics in a landscape context.     

长江口潮沟大型底栖动物群落的初步研究

通过对长江口崇明东滩潮沟系统与大型底栖无脊椎动物进行取样调查 ,研究了潮沟不同生境的底栖动物群落及其多样性 ,分析了潮沟生境异质性与底栖动物群落的关系。研究发现 :①潮沟剖面中出现明显的动物群落分带现象 ,从潮沟底、潮沟边滩到草滩 ,底栖动物种类、生活型组成和生活类群比例反映了河口潮滩潮沟底栖动物生态系列 ;②密度和生物量的分布皆为潮沟边滩 >草滩 >潮沟底 ,但密度与生物量的面上群 /面下群值格局却有不同 ,说明了密度和生物量的优势生活型和生活类群随潮沟生境的差异而变化 ;③潮沟系统 3种生境的多样性指数D ,H′和J值均为草滩 >潮沟边滩 >潮沟底 ,是潮沟系统生境结构分化的结果。潮沟底和潮沟边滩等特殊生境的存在 ,提高了淤泥质河口潮滩的生境异质性 ,说明了潮沟系统在维持河口生态系统底栖动物物种多样性中的重要作用。     

Identifying Environmental Determinants of Diurnal Distribution in Marine Birds and Mammals

Marine birds and mammals move between various habitats during the day as they engage in behaviors related to resting, sleeping, preening, feeding, and breeding. The per capita rates of movement between these habitats, and hence the habitat occupancy dynamics, often are functions of environmental variables such as tide height, solar elevation, wind speed, and temperature. If the system recovers rapidly after disturbance, differential equation models of occupancy dynamics can be reduced to algebraic equations on two time scales. Identification of environmental factors that influence movement between habitats requires time series census data collected in both the absence and presence of disturbance.     

Habitat requirements of weasels <Emphasis Type="Italic">Mustela nivalis</Emphasis> constrain their impact on prey populations in complex ecosystems of the temperate zone

Differences in habitat use by prey and predator may lead to a shift of occupied niches and affect dynamics of their populations. The weasel Mustela nivalis specializes in hunting rodents, therefore habitat preferences of this predator may have important consequences for the population dynamics of its prey. We investigated habitat selection by weasels in the Bia?owie?a Forest in different seasons at the landscape and local scales, and evaluated possible consequences for the population dynamics of their prey. At the landscape scale, weasels preferred open habitats (both dry and wet) and avoided forest. In open areas they selected habitats with higher prey abundance, except during the low-density phase of the vole cycle, when the distribution of these predators was more uniform. Also in winter, the distribution of weasels at the landscape scale was proportional to available resources. In summer, within open dry and wet habitats, weasels preferred areas characterised by dense vegetation, but avoided poor plant cover. In winter, weasels used wet open areas proportionally to availability of habitats when hunting, but in contrast to summer, they rested only in habitats characterized by a lower water level, which offered better thermal conditions. At the local scale, the abundance of voles was a less important factor affecting the distribution of these predators. Although we were not able to provide direct evidence for the existence of refuges for voles, our results show that they may be located within habitat patches, where availability of dense plant cover and physiological constraints limit the activity of weasels. Our results indicate that in complex ecosystems of the temperate zone, characterized by a mosaic pattern of vegetation types and habitat specific dynamics of rodents, impact of weasels on prey populations might be limited.     

Landscape- and time-dependent benefits of wildflower areas to ground-dwelling arthropods

Wildflower areas are a popular agri-environment scheme to counteract agro-biodiversity loss. Yet, their benefits are controversially discussed. Since inconsistent benefits may be owed to landscape context and temporal dynamics, we applied a multi-year study to unravel effects of permanent and transient habitats on ground-dwelling arthropods in wildflower areas and cereal fields.Across three consecutive years, we studied activity density, species richness and community composition of rove beetles, carabid beetles and spiders in ten pairs of wildflower areas and cereal fields along independent gradients of proportions of permanent semi-natural habitats or transient wildflower areas.Arthropod responses to the proportions of permanent semi-natural habitats often followed a hump-shaped pattern, whereas transient wildflower areas seemed to drive linear responses. An interactive effect on rove beetle richness in wildflower areas implies that benefits were highest either at intermediate proportions of permanent semi-natural habitats or at lower proportions, but with additional availability of transient wildflower areas or in landscapes with low proportions of permanent semi-natural habitats, but high proportions of wildflower areas. However, ground-dwelling arthropod activity density or species richness did not systematically increase over the three study years.Our results suggest that both permanent and transient habitats differ in how they affect biodiversity, possibly due to different temporal continuity and resource diversity. Benefits of permanent semi-natural habitats seemed highest at an equilibrium between an increasing resource-related species pool and an increasing diversity dilution, whereas benefits of transient wildflower areas seemed to increase with resource complementarity and connectivity at the landscape scale. Nevertheless, both habitats seem to complement each other and considered in concert, seem to be most effective in promoting benefits of wildflower areas to ground-dwelling arthropods at intermediate landscape complexity. The substantial variation in diversity patterns among years with weather extremes, suggests that optimizing benefits of wildflower areas requires further multi-year studies.     

Biomass and biodiversity in species-rich tritrophic communities

We consider a tritrophic system with one basal and one top species and a large number of primary consumers, and derive upper and lower bounds for the total biomass of the middle trophic level. These estimates do not depend on dynamical regime, holding for fixed point, periodic, or chaotic dynamics. We have two kinds of estimates, depending on whether the predator abundance is zero. All these results are uniform in a self-limitation parameter, which regulates prey diversity in the system. For strong self-limitation, diversity is large; for weak self-limitation, it is small. Diversity depends on the variance of species’ parameter values. The larger this variance, the lower the diversity, and vice versa. Moreover, variation in the parameters of the Holling type II functional response changes the bifurcation character, with the equilibrium state with nonzero predator abundance losing stability. If that variation is small then the bifurcation can lead to oscillations (the Hopf bifurcation). Under certain conditions, there exists a supercritical Hopf bifurcation. We then find a connection between diversity and Hopf bifurcations. We also show that the system exhibits top-down regulation and a hump-shaped diversity-productivity curve.We then extend the model by allowing species to experience self-regulation. For this extended model, explicit estimates of prey diversity are obtained. We study the dynamics of this system and find the following. First, diversity and system dynamics crucially depend on variation in species parameters. We show that under certain conditions, the system undergoes a supercritical Hopf bifurcation. We also establish a connection between diversity and Hopf bifurcations. For strong self-limitation, diversity is large and complex dynamics are absent. For weak self-limitation, diversity is small and the equilibrium with non-zero predator abundance is unstable.     

Parametric dependence on shear viscosity of SPC/E water from equilibrium and non-equilibrium molecular dynamics simulations

A parametric dependent study is crucial for the accurate determination of transport coefficients such as shear viscosity. In this study, we calculate the shear viscosity of extended simple point charge water using a transverse current auto-correlation function (TCAF) from equilibrium molecular dynamics (EMD) and the periodic perturbation method from non-equilibrium molecular dynamics (NEMD) simulations for varying coupling time and system sizes. Results show that the shear viscosity calculated using EMD simulations with different thermostats varies significantly with coupling times and system size. The use of Berendsen and velocity-rescale thermostats in NEMD simulations generates a significant drift from the target temperature and results in an inconsistent shear viscosity with coupling time and system size. The use of Nosé–Hoover thermostat in NEMD simulations offers thermodynamic stability which results in a consistent shear viscosity for various coupling times and system sizes.