The rate of convergence of a generalized stable population

In an age-structured population that grows exponentially, each age groupP _i(t) at periodt is asymptotically equivalent tox ₀ ^t for some positive number x₀. In this paper we show that the speed at which the ith age group reaches its exponential state of equilibrium can be measured by the rate at which the ratio v_i(t)=P_i(t)/p_i(t–1) converges tox ₀. The age specific rate of convergence is determined by considering a quantityr satisfyingv _i(t)-x ₀ ¦ r ^t whent is large;R _i=Infr (over all initial populations,r satisfying the above inequality) is the R-factor used in numerical analysis to measure the rate at which the sequencev _i (t) converges tox ₀;S _i =- In R_i is then defined as the rate of convergence to stability of the ith age group. The case of constant net maternity rates is studied in detail; in this contextS ₀ is compared to the population entropyH, which was proposed by Tuljapurkar (1982) as a measure of the rate of convergence to stability.     

Asymptotic properties of infinite Leslie matrices

The stable population theory is classically applicable to populations in which there is a maximum age after which individuals die. Demetrius [1972. On an infinite population matrix. Math. Biosci. 13, 133-137] extended this theory to infinite Leslie matrices, in which the longevity of individuals is potentially infinite. However, Demetrius had to assume that the survival probability per time step tends to 0 with age. We generalise here the conditions of application of the stable population theory to infinite Leslie matrix models and apply these results to two examples, including or not senescence.     

Coalescent theory for a completely random mating monoecious population

Consider a large random mating monoecious diploid population that has N individuals in each generation. Let us assume that at time 0 a random sample of ninfinity. It is then possible to obtain a generalization of coalescent theory for haploid populations if the distribution of G1 has a finite second moment and E[G(1)(3)]/N-->0 as N-->infinity.     

斑苦竹(Pleioblastus maculata)无性系种群的数量和年龄结构动态

依据Ｈａｒｐｅｒ（１９７７）提出的构件生物种群理论,将源于同一地下根茎的每一竹子个构件。把斑苦竹竹子构件无性系种各的生活史小循环划分为８个阶段,用Ｌｅｓｌｉｅ矩阵表 预测了四川晋云山该种群的数量和年龄结构变化趋势。结果表明,用Ｌｅｓｌｉｅ矩阵来预测靠无性繁殖来扩大种群数量的竹类植物的年龄结构和数量动态,具有较高的可靠性。     

Linear discrete population models with two time scales in fast changing environments II: non-autonomous case

As the result of the complexity inherent in nature, mathematical models employed in ecology are often governed by a large number of variables. For instance, in the study of population dynamics we often deal with models for structured populations in which individuals are classified regarding their age, size, activity or location, and this structuring of the population leads to high dimensional systems. In many instances, the dynamics of the system is controlled by processes whose time scales are very different from each other. Aggregation techniques take advantage of this situation to build a low dimensional reduced system from which behavior we can approximate the dynamics of the complex original system.In this work we extend aggregation techniques to the case of time dependent discrete population models with two time scales where both the fast and the slow processes are allowed to change at their own characteristic time scale, generalizing the results of previous studies. We propose a non-autonomous model with two time scales, construct an aggregated model and give relationship between the variables governing the original and the reduced systems. We also explore how the properties of strong and weak ergodicity, regarding the capacity of the system to forget initial conditions, of the original system can be studied in terms of the reduced system.     

基于稳定同位素技术的增殖放流牙鲆群体鉴别

牙鲆是我国黄渤海重要的增殖放流鱼类,野生群体和放流群体的鉴别是评估牙鲆增殖效果的前提.为了研究稳定同位素技术在增殖放流牙鲆群体鉴别中的应用,本研究以秦皇岛近海增殖放流区捕捞牙鲆幼鱼为对象,先使用项目组前期开发的形态学和分子标记相结合的方法区分野生群体和放流群体,再分别测定肌肉碳、氮稳定同位素值和耳石(全耳石和耳石核心区...     

Effects of climate change on an emperor penguin population: analysis of coupled demographic and climate models

Sea ice conditions in the Antarctic affect the life cycle of the emperor penguin (Aptenodytes forsteri). We present a population projection for the emperor penguin population of Terre Adélie, Antarctica, by linking demographic models (stage‐structured, seasonal, nonlinear, two‐sex matrix population models) to sea ice forecasts from an ensemble of IPCC climate models. Based on maximum likelihood capture‐mark‐recapture analysis, we find that seasonal sea ice concentration anomalies (SIC_a) affect adult survival and breeding success. Demographic models show that both deterministic and stochastic population growth rates are maximized at intermediate values of annual SIC_a, because neither the complete absence of sea ice, nor heavy and persistent sea ice, would provide satisfactory conditions for the emperor penguin. We show that under some conditions the stochastic growth rate is positively affected by the variance in SIC_a. We identify an ensemble of five general circulation climate models whose output closely matches the historical record of sea ice concentration in Terre Adélie. The output of this ensemble is used to produce stochastic forecasts of SIC_a, which in turn drive the population model. Uncertainty is included by incorporating multiple climate models and by a parametric bootstrap procedure that includes parameter uncertainty due to both model selection and estimation error. The median of these simulations predicts a decline of the Terre Adélie emperor penguin population of 81% by the year 2100. We find a 43% chance of an even greater decline, of 90% or more. The uncertainty in population projections reflects large differences among climate models in their forecasts of future sea ice conditions. One such model predicts population increases over much of the century, but overall, the ensemble of models predicts that population declines are far more likely than population increases. We conclude that climate change is a significant risk for the emperor penguin. Our analytical approach, in which demographic models are linked to IPCC climate models, is powerful and generally applicable to other species and systems.     

High genetic variation in leopards indicates large and long-term stable effective population size

In this paper we employ recently developed statistical and molecular tools to analyse the population history of the Tanzanian leopard (Panthera pardus), a large solitary felid. Because of their solitary lifestyle little is known of their past or present population dynamics. Eighty-one individuals were scored at 18 microsatellite loci. Overall, levels of heterozygosity were high (0.77 +/- 0.03), with a small heterozygote deficiency (0.06 +/- 0.03). Effective population size (Ne) was calculated to be 38 000-48 000. A Ne:N ratio of 0.42 (average from four cat studies) gives a present population size of about 100 000 leopards in Tanzania. Four different bottleneck tests indicated that this population has been large and stable for a minimum of several thousand years. FST values were low and no significant genetic structuring of the population could be detected. This concurs well with the large migration values (Nm) obtained (>3.3 individuals/generation). Our analysis reveals that ecological factors (e.g. disease), which are known to have had major impact on other carnivore populations, are unlikely to have impacted strongly on the population dynamics of Tanzanian leopards. The explanation may be found in their solitary life-style, their often nonconfrontational behaviour toward interspecific competitors, or that any bottlenecks have been of limited size, localized, or too short to have affected genetic variation to any measurable degree. Since the genetic structuring is weak, gene flow is not restricted to within protected areas. Local loss of genetic variation is therefore not of immediate concern.     

Asymptotic behavior of some stochastic difference equation population models

We consider a general class of Markov population models formulated as stochastic difference equations. The population density is shown to converge either to 0, to +, or to a unique stationary distribution concentrated on (0, +), depending on the signs of the mean log growth rates near 0 and +. These results are applied to the Watkinson-MacDonald bottleneck model of annual plants with a seedbank, extended to allow for random environmental fluctuations and competition among co-occurring species. We obtain criteria for long-term persistence of single-species populations, and for coexistence of two competing species, and the biological significance of the criteria is discussed. The lamentably few applications to the problem at hand of classical limit-theory for Markov chains are surveyed.     

An eigenvalue ratio approach to inferring population structure from whole genome sequencing data

Inference of population structure from genetic data plays an important role in population and medical genetics studies. With the advancement and decreasing cost of sequencing technology, the increasingly available whole genome sequencing data provide much richer information about the underlying population structure. The traditional method originally developed for array-based genotype data for computing and selecting top principal components (PCs) that capture population structure may not perform well on sequencing data for two reasons. First, the number of genetic variants p is much larger than the sample size n in sequencing data such that the sample-to-marker ratio $n/p$ is nearly zero, violating the assumption of the Tracy-Widom test used in their method. Second, their method might not be able to handle the linkage disequilibrium well in sequencing data. To resolve those two practical issues, we propose a new method called ERStruct to determine the number of top informative PCs based on sequencing data. More specifically, we propose to use the ratio of consecutive eigenvalues as a more robust test statistic, and then we approximate its null distribution using modern random matrix theory. Both simulation studies and applications to two public data sets from the HapMap 3 and the 1000 Genomes Projects demonstrate the empirical performance of our ERStruct method.     

陕西榆林地区农田灯诱地下害虫种类组成及优势种群发生动态

为了明确陕西榆林地区农田地下害虫种类组成及优势种群发生动态,于2016年4月1日至2019年9月28日,在陕西省榆林市现代农业示范园,设置太阳能自动虫情测报箱对地下害虫进行收集,在室内对标本进行鉴定和数据分析。在榆林市农田一共灯诱到地下害虫12种,隶属3目5科。地下害虫混合种群发生期为4月中旬至9月上旬,盛发期为4月下旬至8月上旬。小地老虎Agrotis ypsilon、东方绢金龟Maladera orientalis、阔胫绢金龟Maladera verticalis和黄褐丽金龟Anomala exoleta是榆林农田地下害虫主要优势种群。小地老虎灯诱高峰期为4月上旬至5月中旬以及6月上旬至7月下旬,东方绢金龟的灯诱高峰期为4月中旬至6月中旬,阔胫绢金龟灯诱高峰期为6月上旬至8月上旬,黄褐丽金龟灯诱高峰期为6月中旬至7月上旬。本研究为榆林地区农田地下害虫的监测和综合治理提供了基础资料。     

Regime shifts in exploited marine food webs: detecting mechanisms underlying alternative stable states using size-structured community dynamics theory

Many marine ecosystems have undergone ‘regime shifts’, i.e. abrupt reorganizations across trophic levels. Establishing whether these constitute shifts between alternative stable states is of key importance for the prospects of ecosystem recovery and for management. We show how mechanisms underlying alternative stable states caused by predator–prey interactions can be revealed in field data, using analyses guided by theory on size-structured community dynamics. This is done by combining data on individual performance (such as growth and fecundity) with information on population size and prey availability. We use Atlantic cod (Gadus morhua) and their prey in the Baltic Sea as an example to discuss and distinguish two types of mechanisms, ‘cultivation-depensation’ and ‘overcompensation’, that can cause alternative stable states preventing the recovery of overexploited piscivorous fish populations. Importantly, the type of mechanism can be inferred already from changes in the predators'' body growth in different life stages. Our approach can thus be readily applied to monitored stocks of piscivorous fish species, for which this information often can be assembled. Using this tool can help resolve the causes of catastrophic collapses in marine predatory–prey systems and guide fisheries managers on how to successfully restore collapsed piscivorous fish stocks.     

Demography_Lab,an educational application to evaluate population growth: Unstructured and matrix models

Training in Population Ecology asks for scalable applications capable of embarking students on a trip from basic concepts to the projection of populations under the various effects of density dependence and stochasticity. Demography_Lab is an educational tool for teaching Population Ecology aspiring to cover such a wide range of objectives. The application uses stochastic models to evaluate the future of populations. Demography_Lab may accommodate a wide range of life cycles and can construct models for populations with and without an age or stage structure. Difference equations are used for unstructured populations and matrix models for structured populations. Both types of models operate in discrete time. Models can be very simple, constructed with very limited demographic information or parameter‐rich, with a complex density‐dependence structure and detailed effects of the different sources of stochasticity. Demography_Lab allows for deterministic projections, asymptotic analysis, the extraction of confidence intervals for demographic parameters, and stochastic projections. Stochastic population growth is evaluated using up to three sources of stochasticity: environmental and demographic stochasticity and sampling error in obtaining the projection matrix. The user has full control on the effect of stochasticity on vital rates. The effect of the three sources of stochasticity may be evaluated independently for each vital rate. The user has also full control on density dependence. It may be included as a ceiling population size controlling the number of individuals in the population or it may be evaluated independently for each vital rate. Sensitivity analysis can be done for the asymptotic population growth rate or for the probability of extinction. Elasticity of the probability of extinction may be evaluated in response to changes in vital rates, and in response to changes in the intensity of density dependence and environmental stochasticity.     

Modelling population dynamics in a unicellular social organism community using a minimal model and evolutionary game theory

Most unicellular organisms live in communities and express different phenotypes. Many efforts have been made to study the population dynamics of such complex communities of cells, coexisting as well-coordinated units. Minimal models based on ordinary differential equations are powerful tools that can help us understand complex phenomena. They represent an appropriate compromise between complexity and tractability; they allow a profound and comprehensive analysis, which is still easy to understand. Evolutionary game theory is another powerful tool that can help us understand the costs and benefits of the decision a particular cell of a unicellular social organism takes when faced with the challenges of the biotic and abiotic environment. This work is a binocular view at the population dynamics of such a community through the objectives of minimal modelling and evolutionary game theory. We test the behaviour of the community of a unicellular social organism at three levels of antibiotic stress. Even in the absence of the antibiotic, spikes in the fraction of resistant cells can be observed indicating the importance of bet hedging. At moderate level of antibiotic stress, we witness cyclic dynamics reminiscent of the renowned rock–paper–scissors game. At a very high level, the resistant type of strategy is the most favourable.     

A population model to simulate northern bobwhite population dynamics in southern Texas

Models are important tools that can help managers and researchers understand the population dynamics of a species and how different habitat or population management scenarios impact that species. We used radio-telemetry data from northern bobwhites (Colinus virginianus) in southern Texas from 2000 to 2005 to develop a stochastic simulation model for bobwhite populations. Our model is based on difference equations, with stochastic variables drawn from normal and Weibull distributions. We simulated bobwhite populations to 100 yr and evaluated our model by comparing results with independent estimates of 4 population parameters (spring and fall density, finite rate of increase in the fall population [λ], and winter juv:ad age ratios). Using a quasi-extinction criterion of ≤40 birds (density = ≤0.05 birds/ha), probability of persistence to 100 yr was 88.3% (106 of 120 simulations) for the spring population and 96.7% (116 of 120 simulations) for the fall population. Using a less restrictive quasi-extinction criteria (≤14 birds), probability of persistence was 93.3% (112 of 120 simulations) for the spring population and 98.3% (118 of 120 simulations) for the fall population. Simulated population parameters were similar to independent estimates for 4 of 4 population parameters. Winter age ratios differed between our model ( juv:ad, n = 120, SE = 0.32) and empirical age ratios from harvested bobwhites on our study area ( juv:ad, n = 25, SE = 0.24). However, when we corrected harvest age ratios for bias in juvenile harvest ( juv:ad, n = 25, SE = 0.32) simulated and empirical estimates were similar. Our model appears to be a reliable predictor of bobwhite populations in the southern Texas. Our simulation results indicate that bobwhite hunters and managers can expect excellent bobwhite hunting (fall populations ≥2.2 birds per ha) in about one of 10 yr. © 2011 The Wildlife Society     

害虫种群动态模型的燕尾突变分析

在农田生态系统中,以作物状况、气象因素及天敌分别为3种控制变量,以害虫种群数量动态为状态变量,建立了燕尾突变模型,并用燕尾突变模型的性质分析害虫种群数量动态中产生的突变现象.具体对燕尾突变的分歧点集所分各个控制区域的系统势函数形式和平衡点情况进行了分析,说明了害虫种群数量发生突变的条件和机理,为实际应用提供理论依据.同时利用燕尾突变的性质直观描述了害虫种群数量变化中的突跳和滞后等现象.