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.     

Vibrational frequency shifts and relaxation rates for a selected vibrational mode in cytochrome C

The vibrational energy relaxation of a selected vibrational mode in cytochrome c--a C-D stretch in the terminal methyl group of Met80--has been studied using equilibrium molecular dynamics simulation and normal mode analysis methods. As demonstrated in the pioneering work of Romesberg and co-workers, isotopic labeling of the C-H (to C-D) stretch in alkyl side chains shifts the stretching frequency to the transparent region of the protein's density of states, making it an effective and versatile probe of protein structure and dynamics. Molecular dynamics trajectories of solvated cytochrome c were run at 300 K, and vibrational population relaxation times were estimated using the classical Landau-Teller-Zwanzig model and a number of semiclassical theories of resonant and two-phonon vibrational relaxation processes. The C-D stretch vibrational population relaxation time is estimated to be T(1) = 14-40 ps; the relatively close agreement between various semiclassical estimates of T(1) lends support to the applicability of those expressions. Normal mode calculations were used to identify the dominant coupling between the protein and C-D oscillator. All bath modes strongly coupled to the C-D stretch are in close proximity. Angle bending modes in the terminal methyl group of Met80 appear to be the most likely acceptor modes defining the mechanism of population relaxation of the C-D vibration.     

Genetic dynamics of population systems represented by small subpopulations: analytical modeling and numeric results

Genetic dynamics of population systems consisting of a finite number of small (Ne < 10(2)) semiisolated subpopulations was studied. A method of quantitative estimation of statistical parameters was developed for different types of population systems and different directions or intensities of selection. The following regularities were established: (1) optimal numbers of subpopulations, their effective size and rates of gene migration promoting continuous maintenance of genetic diversity can be chosen; (2) the genetic process in a population system is stationary only in the case of a specific structure of gene migrations corresponding to Wright's island model; (3) cyclic dynamics can stabilize the population system at high levels of gene diversity in a heterogeneous environment if gene migration and subpopulation size change in time. Similarities and differences between the concept of population system and the concept of metapopulation, which have been simultaneously proposed in Russia and abroad, are discussed in the final section.     

不同放牧模式下高原鼠兔洞口的空间分布格局变化

2019年4-11月,在四川省若尔盖县选取全年禁牧、冬季放牧、全年放牧3种放牧模式样地,对高原鼠兔(Ochotona curzoniae)洞口的数量、空间分布格局变化及影响因子进行了研究.计算平均最近邻指数和S2/m比值来分析样方(10m×10m)和样地水平下的空间分布格局,通过非参数检验评估空间分布格局在不同放牧模式...     

Stochastic theory of early viral infection: continuous versus burst production of virions

Viral production from infected cells can occur continuously or in a burst that generally kills the cell. For HIV infection, both modes of production have been suggested. Standard viral dynamic models formulated as sets of ordinary differential equations can not distinguish between these two modes of viral production, as the predicted dynamics is identical as long as infected cells produce the same total number of virions over their lifespan. Here we show that in stochastic models of viral infection the two modes of viral production yield different early term dynamics. Further, we analytically determine the probability that infections initiated with any number of virions and infected cells reach extinction, the state when both the population of virions and infected cells vanish, and show this too has different solutions for continuous and burst production. We also compute the distributions of times to establish infection as well as the distribution of times to extinction starting from both a single virion as well as from a single infected cell for both modes of virion production.     

Maternal effect on seed survival and emergence in Cytisus scoparius: an experimental approach

The role of the individual origin of seeds in the variability of demographic parameters within a seed-bank has been little studied despite the recognition of its important contribution to species adaptation strategies to environmental constraints. This study analyzed the seed-bank dynamics of Cytisus scoparius, a small woody species with a high aptitude for colonization and dominance. Our experimental setup made it possible to monitor seed emergence dynamics in situ for maternal individuals within the study population. In addition to the characteristic traits of the species (maximum seed life span between 4 and 5 years in 75 % of the cases), there was a high variability of the emergence dynamics between individuals, distinguished both by their total emergence rate and profile. The total emergence rate of seeds was correlated with their quality (seed weight and number of seeds per pod), but was unrelated to either maternal age or fecundity. Different emergence profiles can be recognized between two distinct patterns: on one hand, a strategy that concentrates on emergence in the second year and, on the other, a regular decrease of the germinant number over time. The coexistence of different seed-bank strategies between individuals results in the ability for the population to face to disturbances and environmental variability.     

Conspecific brood parasitism and population dynamics

Conspecific brood parasitism (CBP), defined as parasitic laying of eggs in a conspecific nest without providing parental care, occurs in insects, fishes, amphibians, and many birds. Numerous factors have been proposed to influence the evolution of CBP, including nest site limitation; effects of brood size, laying order, or parasitic status on offspring survival; randomness of parasitic egg distribution; adult life-history trade-offs; and variation in parental female quality or risk of nest predation. However, few theoretical studies consider multiple possible types of parasitism or the interplay between evolution of parasitism and population dynamics. We review existing theory of CBP and develop a synthetic modeling approach to ask how best-of-a-bad job parasitism, separate-strategies parasitism (in which females either nest or parasitize), and joint-strategies parasitism (in which females can both nest and parasitize) differ in their evolutionary conditions and impacts on population dynamics using an adaptive dynamics framework including multivariate traits. CBP can either stabilize or destabilize population dynamics in different scenarios, and the role of comparable parameters on evolutionarily stable strategy parasitism rate, equilibrium population size, and population stability can differ for the different modes of parasitism.     

Dynamics of a feline virus with two transmission modes within exponentially growing host populations.

Feline panleucopenia virus (FPLV) was introduced in 1977 on Marion Island (in the southern Indian Ocean) with the aim of eradicating the cat population and provoked a huge decrease in the host population within six years. The virus can be transmitted either directly through contacts between infected and healthy cats or indirectly between a healthy cat and the contaminated environment: a specific feature of the virus is its high rate of survival outside the host. In this paper, a model was designed in order to take these two modes of transmission into account. The results showed that a mass-action incidence assumption was more appropriate than a proportionate mixing one in describing the dynamics of direct transmission. Under certain conditions the virus was able to control the host population at a low density. The indirect transmission acted as a reservoir supplying the host population with a low but sufficient density of infected individuals which allowed the virus to persist. The dynamics of the infection were more affected by the demographic parameters of the healthy hosts than by the epidemiological ones. Thus, demographic parameters should be precisely measured in field studies in order to obtain accurate predictions. The predicted results of our model were in good agreement with observations.     

The direction of selection of genetically heterogeneous cell populations ofDioscorea deltoidea Wall

The initial strain ofDioscorea cell culture is characterized by a double-peak curve of mitotic activity, by dominance in the population of meristematic cells, by a great variety in the number of chromosomes and also by polyploidization in the process of cultivation. After treatment with different doses of N-nitroso-N-methylurea (NMU) physiological parameters of the cell populations were found to change (dynamics of mitotic activity, ratio between types of cells). On passaging, physiological differences between the strains are levelled up. The studied strains are characterized by different directions of cell selections,i.e. the control strain — towards polyploidization, and in NMU treated strains are stabilized on di- and triploid levels.     

What life cycle graphs can tell about the evolution of life histories

We analyze long-term evolutionary dynamics in a large class of life history models. The model family is characterized by discrete-time population dynamics and a finite number of individual states such that the life cycle can be described in terms of a population projection matrix. We allow an arbitrary number of demographic parameters to be subject to density-dependent population regulation and two or more demographic parameters to be subject to evolutionary change. Our aim is to identify structural features of life cycles and modes of population regulation that correspond to specific evolutionary dynamics. Our derivations are based on a fitness proxy that is an algebraically simple function of loops within the life cycle. This allows us to phrase the results in terms of properties of such loops which are readily interpreted biologically. The following results could be obtained. First, we give sufficient conditions for the existence of optimisation principles in models with an arbitrary number of evolving traits. These models are then classified with respect to their appropriate optimisation principle. Second, under the assumption of just two evolving traits we identify structural features of the life cycle that determine whether equilibria of the monomorphic adaptive dynamics (evolutionarily singular points) correspond to fitness minima or maxima. Third, for one class of frequency-dependent models, where optimisation is not possible, we present sufficient conditions that allow classifying singular points in terms of the curvature of the trade-off curve. Throughout the article we illustrate the utility of our framework with a variety of examples.     

Successful invasion of a food web in a chemostat

A food web in a chemostat is considered in which an arbitrary number of competitor populations compete for a single, essential, nonreproducing, growth-limiting substrate, and an arbitrary number of predator populations prey on some or all of the competitor populations. Although any number of predator populations may prey on the same competitor population, each predator population preys on only one competitor population. The dynamics of substrate uptake is modeled by Lotka-Volterra or Michaelis-Menten (Holling type I or II), but the dynamics of competitor uptake is restricted to Lotka-Volterra. Based on certain parameters, the model predicts the asymptotic survival or extinction of each of the different populations and suggests how competitor and/or predator populations could successfully invade the chemostat with or without causing a diverse ecosystem to crash. Similarly, it suggests how the elimination of certain populations could result in a more diverse or less diverse system.     

Population Genetics and Molecular Evolution of DNA Sequences in Transposable Elements. I. A Simulation Framework

A population genetic simulation framework is developed to understand the behavior and molecular evolution of DNA sequences of transposable elements. Our model incorporates random transposition and excision of transposable element (TE) copies, two modes of selection against TEs, and degeneration of transpositional activity by point mutations. We first investigated the relationships between the behavior of the copy number of TEs and these parameters. Our results show that when selection is weak, the genome can maintain a relatively large number of TEs, but most of them are less active. In contrast, with strong selection, the genome can maintain only a limited number of TEs but the proportion of active copies is large. In such a case, there could be substantial fluctuations of the copy number over generations. We also explored how DNA sequences of TEs evolve through the simulations. In general, active copies form clusters around the original sequence, while less active copies have long branches specific to themselves, exhibiting a star-shaped phylogeny. It is demonstrated that the phylogeny of TE sequences could be informative to understand the dynamics of TE evolution.     

PPARγ non-covalent antagonists exhibit mutable binding modes with a similar free energy of binding: a case study

The structural and dynamical properties of PPARγ receptor in a complex with either partial or full agonists have been intensively studied but little is known about the receptor antagonistic conformation. A composition of microsecond accelerated molecular dynamics (aMD) simulation show that like partial agonists a non-covalent PPARγ full antagonist can bind in different modes of similar population size and free energies of binding. Four different and periodically exchanging ligand conformations are detected and described. The studied antagonist interacts with different receptor substructures and affects both the co-activator and the Cdk5 phosphorylation sites and, presumably, the natural complex with the DNA. However, no significant changes in the conformational states of the activation helix 12, and in particular an antagonist orientation, have been recorded. Finally, our results show also that the aMD approach can be successfully used in recovering the possible binding modes, considering fully the receptor flexibility, and is not dependent on the starting conformation.     

Genetic analysis of complex demographic scenarios: spatially expanding populations of the cane toad, Bufo marinus

Inferring the spatial expansion dynamics of invading species from molecular data is notoriously difficult due to the complexity of the processes involved. For these demographic scenarios, genetic data obtained from highly variable markers may be profitably combined with specific sampling schemes and information from other sources using a Bayesian approach. The geographic range of the introduced toad Bufo marinus is still expanding in eastern and northern Australia, in each case from isolates established around 1960. A large amount of demographic and historical information is available on both expansion areas. In each area, samples were collected along a transect representing populations of different ages and genotyped at 10 microsatellite loci. Five demographic models of expansion, differing in the dispersal pattern for migrants and founders and in the number of founders, were considered. Because the demographic history is complex, we used an approximate Bayesian method, based on a rejection-regression algorithm, to formally test the relative likelihoods of the five models of expansion and to infer demographic parameters. A stepwise migration-foundation model with founder events was statistically better supported than other four models in both expansion areas. Posterior distributions supported different dynamics of expansion in the studied areas. Populations in the eastern expansion area have a lower stable effective population size and have been founded by a smaller number of individuals than those in the northern expansion area. Once demographically stabilized, populations exchange a substantial number of effective migrants per generation in both expansion areas, and such exchanges are larger in northern than in eastern Australia. The effective number of migrants appears to be considerably lower than that of founders in both expansion areas. We found our inferences to be relatively robust to various assumptions on marker, demographic, and historical features. The method presented here is the only robust, model-based method available so far, which allows inferring complex population dynamics over a short time scale. It also provides the basis for investigating the interplay between population dynamics, drift, and selection in invasive species.     

Dominant ionic mechanisms explored in spiking and bursting using local low-dimensional reductions of a biophysically realistic model neuron

The large number of variables involved in many biophysical models can conceal potentially simple dynamical mechanisms governing the properties of its solutions and the transitions between them as parameters are varied. To address this issue, we extend a novel model reduction method, based on “scales of dominance,” to multi-compartment models. We use this method to systematically reduce the dimension of a two-compartment conductance-based model of a crustacean pyloric dilator (PD) neuron that exhibits distinct modes of oscillation—tonic spiking, intermediate bursting and strong bursting. We divide trajectories into intervals dominated by a smaller number of variables, resulting in a locally reduced hybrid model whose dimension varies between two and six in different temporal regimes. The reduced model exhibits the same modes of oscillation as the 16 dimensional model over a comparable parameter range, and requires fewer ad hoc simplifications than a more traditional reduction to a single, globally valid model. The hybrid model highlights low-dimensional organizing structure in the dynamics of the PD neuron, and the dependence of its oscillations on parameters such as the maximal conductances of calcium currents. Our technique could be used to build hybrid low-dimensional models from any large multi-compartment conductance-based model in order to analyze the interactions between different modes of activity.     

Dynamics of proliferating cell populations during exposure to periodic phase-specific factors

Dynamics of the numbers of population of proliferating cells under periodic phase-specific cytotoxic effect with and without blocking action was studied on the basis of a mathematical model. It has been shown that at real values of the model parameters after the beginning of the effects the population number exponentially depends of time. Dependence of the population number dynamics on integral parameters of the cell cycle and the exposure regime was studied. It has been shown that at certain periods a resonance decrease of the damage of the population cells must be observed. The values of the periods corresponding to the resonance decrease of the damage are determined mainly by the mean duration of the cell cycle and the time of blocking action, at small duration of the blocking action they are approximately multiple to the average time of the cell cycle. The theoretical predictions are proved experimentally in the experiments on determining the relationship between the damage of small intestine epithelium and mouse survival and the period of repeated periodic injections of S-phase-specific cytotoxic agent hydroxyurea. A distinct resonance increase of mouse survival and decreased damage of the epithelium were observed under the injections of oxyurea with the periods near to the mean and doubled mean time of the cell cycle of crypt enterocytes. The results obtained not only support the correctness of theoretical predictions, but make it possible to estimate the parameters of the stem cell cycle of mouse small intestine epithelium. They also show that this approach can be used for reducing aftereffects of chemotherapy by means of phase-specific agents.     

基因工程菌在活性污泥中的衰减及其影响因素

在间歇实验和连续运行的反应器中,考察了基因工程菌细胞密度在活性污泥中的衰减,进行了动力学模型拟合,求得模型参数,并分析了影响衰减的因素.结果表明,在间歇实验和连续运行反应器中,细胞密度在活性污泥中均呈现初期快速衰减而后趋于稳定的趋势.其衰减动力学可以用Logistic模型和Gompertz模型拟合,两个模型的拟合都有很好的相关性和显著性,拟合优度没有差异.在不同的条件下,间歇实验拟合得到的参数取值范围是：Logistic模型衰减系数r′=0.5～0.6 h^-1,稳定细胞密度K′=10⁴～10⁵ cfu·ml^-1;Gompertz模型初始衰减系数b=0.6～1.2 h^-1,比衰减系数a=0.02～0.09 h^-1.初始投加密度对衰减速率影响不大,但是显著影响稳定细胞密度.污泥浓度和温度对衰减速率和稳定密度均有显著影响. 污泥浓度越大,衰减越快,稳定密度越大;而温度越低,衰减越快,稳定密度也会越低.营养条件和微型动物捕食也是影响衰减的重要因素.基因工程菌在连续运行的膜生物反应器和活性污泥反应器中的细胞密度衰减,也可以用Logistic模型拟合,其参数在间歇实验的取值范围内.     

Finding the Missing Link between Landscape Structure and Population Dynamics: A Spatially Explicit Perspective

We construct and explore a general modeling framework that allows for a systematic investigation of the impact of changes in landscape structure on population dynamics. The essential parts of the framework are a landscape generator with independent control over landscape composition and physiognomy, an individual-based spatially explicit population model that simulates population dynamics within heterogeneous landscapes, and scale-dependent landscape indices that depict the essential aspects of landscape that interact with dispersal and demographic processes. Landscape maps are represented by a grid of 50x50 cells and consist of good-quality, poor-quality, or uninhabitable matrix habitat cells. The population model was shaped in accordance to the biology of European brown bears (Ursus arctos), and demographic parameters were adjusted to yield a source-sink configuration. Results obtained with the spatially explicit model do not confirm results of earlier nonspatial source-sink models where addition of sink habitat resulted in a decrease of total population size because of dilution of high-quality habitat. Our landscape indices, which describe scale-dependent correlation between and within habitat types, were able to explain variations in variables of population dynamics (mean number of females with sink home ranges, mean number of females with source home ranges, and mean dispersal distance) caused by different landscape structure. When landscape structure changed, changes in these variables generally followed the corresponding change of an appropriate landscape index in a linear way. Our general approach incorporates source-sink dynamics as well as metapopulation dynamics, and the population model can easily be modified for other species groups.     

Cell cycle analysis of plasmid-containing Escherichia coli HB101 populations with flow cytometry

The relationship between cell mass and cell number dynamics for bacteria such as Escherichia coli depends on the cell cycle parameters C and D. Effects of plasmid copy number on these cell cycle parameters have been studied for Escherichia coli HB101 containing pMB1 plasmids propagated at different copy numbers ranging from 12 to 122. Determination of cell cycle and cell size parameters was accomplished using flow cytometry data on single-cell light scattering and DNA content frequency functions in conjunction with a mathematical model of cell population statistics. Two independent methods for estimating C and D intervals based on flow cytometry were developed and applied with essentially identical results. The presence of plasmids decreases the C and D periods, mean cell sizes, and initiation masses for chromosome replication by 14, 24, 38, and 18%, respectively, relative to corresponding values for plasmid-free host cells. Plasmid copy number has a negligible influence on these parameters, suggesting that host-plasmid inter actions which determine these properties are centered on the single plasmid selected for replication according to the random selection model established for ColE1-type plasmids.     

Comparative demography of two co‐occurring Linum species with different distribution patterns

Understanding similarities and differences in population dynamics of closely related species is a key prerequisite in attempts to apply knowledge obtained in one species to another species, e.g., for the purpose of predicting future fate of populations of various rare species. It can be expected that species will have similar population dynamics if they are closely related and share similar habitats. Contrasting population sizes and distribution patterns may, however, indicate that the population dynamics will be different. To understand similarities and differences in population dynamics of closely related species, I studied demography of two congeneric endangered species, Linum flavum and L. tenuifolium co‐occurring in dry grasslands. Linum flavum occurs with a lower number of large populations, while L. tenuifolium occurs as a large number of small populations. The results showed that L. flavum had higher population growth rates, relied more on survival and growth and its populations were more persistent. In contrast, populations of L. tenuifolium were more prone to extinction and frequent recolonisation was necessary for their survival in the landscape. This was in accordance with observed population sizes of the two species and their frequency in the landscape. The results indicate that despite being closely related and occurring in the same habitat types, the two Linum species have different growth strategies. The strong differences in population dynamics between the two species suggest that similarity in population sizes and frequency of the species in the landscape may be more important when attempting to transfer knowledge between species than is taxonomic relatedness.