Nonlinear stochastic modeling of aphid population growth

This paper develops a stochastic population size model for the black-margined pecan aphid. Prajneshu [Prajneshu, A nonlinear statistical model for aphid population growth. J. Indian Soc. Agric. Statist. 51 (1998), p. 73] proposes a novel nonlinear deterministic model for aphid abundance. The per capita death rate in his model is proportional to the cumulative population size, and the solution is a symmetric analytical function. This paper fits Prajneshu's deterministic model to data. An analogous stochastic model, in which both the current and the cumulative aphid counts are state variables, is then proposed. The bivariate solution of the model, with parameter values suggested by the data, is obtained by solving a large system of Kolmogorov equations. Differential equations are derived for the first and second order cumulants, and moment closure approximations are obtained for the means and variances by solving the set of only five equations. These approximations, which are simple for ecologists to calculate, are shown to give accurate predictions of the two endpoints of applied interest, namely (1) the peak aphid count and (2) the final cumulative aphid count.     

On stochastic logistic population growth models with immigration and multiple births

This paper develops a stochastic logistic population growth model with immigration and multiple births. The differential equations for the low-order cumulant functions (i.e., mean, variance, and skewness) of the single birth model are reviewed, and the corresponding equations for the multiple birth model are derived. Accurate approximate solutions for the cumulant functions are obtained using moment closure methods for two families of model parameterizations, one for badger and the other for fox population growth. For both model families, the equilibrium size distribution may be approximated well using the Normal approximation, and even more accurately using the saddlepoint approximation. It is shown that in comparison with the corresponding single birth model, the multiple birth mechanism increases the skewness and the variance of the equilibrium distribution, but slightly reduces its mean. Moreover, the type of density-dependent population control is shown to influence the sign of the skewness and the size of the variance.     

Analytical methods for predicting the behaviour of population models with general spatial interactions

Many biologists use population models that are spatial, stochastic and individual based. Analytical methods that describe the behaviour of these models approximately are attracting increasing interest as an alternative to expensive computer simulation. The methods can be employed for both prediction and fitting models to data. Recent work has extended existing (mean field) methods with the aim of accounting for the development of spatial correlations. A common feature is the use of closure approximations for truncating the set of evolution equations for summary statistics. We investigate an analytical approach for spatial and stochastic models where individuals interact according to a generic function of their distance; this extends previous methods for lattice models with interactions between close neighbours, such as the pair approximation. Our study also complements work by Bolker and Pacala (BP) [Theor. Pop. Biol. 52 (1997) 179; Am. Naturalist 153 (1999) 575]: it treats individuals as being spatially discrete (defined on a lattice) rather than as a continuous mass distribution; it tests the accuracy of different closure approximations over parameter space, including the additive moment closure (MC) used by BP and the Kirkwood approximation. The study is done in the context of an susceptible-infected-susceptible epidemic model with primary infection and with secondary infection represented by power-law interactions. MC is numerically unstable or inaccurate in parameter regions with low primary infection (or density-independent birth rates). A modified Kirkwood approximation gives stable and generally accurate transient and long-term solutions; we argue it can be applied to lattice and to continuous-space models as a substitute for MC. We derive a generalisation of the basic reproduction ratio, R(0), for spatial models.     

Assessment of the relative impact of different natural enemies on population dynamics of the grain aphid Sitobion avenae in the field

1. A detailed population dynamics model was devised to provide a tool for integrated pest management against the cereal aphid Sitobion avenae on winter wheat. 2. This model allowed investigation of the relative impact of different natural enemies on aphid population dynamics. 3. The output of the model was compared with a set of data collected in the western part of France from 1976 to 1986. 4. Fungal diseases accounted for 75% of the reduction in peak aphid density and were the key factor acting on aphid dynamics in this region. 5. This study highlights the importance of detailed population dynamics modelling of keystone species, like aphids, for elucidation of the relations between the keystone species and other species associated in the ecosystem.     

The effect of reducing growth in winter wheat on the population dynamics of the grain aphid Sitobion avenae (F.)

1 The effect of reducing the growth of winter wheat on population size and development of the grain aphid Sitobion avenae was studied. 2 Automatic, mobile, crop shading devices, which reduced radiation comparable to levels found on a cloudy day, whilst minimizing other climatic changes, were used to reduce crop growth. Shading was applied between either GS 31 and 39 (1st node detectable → flag leaf ligule just visible) or GS 39 and 55 (flag leaf just visible → 50% of inflorescence emerged). 3 Sitobion avenae populations were initiated at GS 55 and highest populations were subsequently observed on plants shaded between GS 31 and 39. 4 Individual aphids confined within clip cages were observed to measure development from birth to adult moult, adult lifespan and fecundity. Results indicated that adult lifespan was shortest on plants shaded between GS31 and 39, whilst there were no differences in development time or fecundity. 5 Possible explanations for these observations are discussed.     

The evolution of juvenile-adult interactions in populations structured in age and space

We study the evolution of a spatially structured population with two age classes using spatial moment equations. In the model, adults can either help juveniles by increasing their survival, or adopt a cannibalistic behaviour and consume juveniles. While cannibalism is the sole evolutionary outcome when the population is well-mixed, both cannibalism and parental care can be evolutionarily stable if the population is viscous. Our analysis allows us to make two main technical points. First, we present a method to define invasion fitness in class-structured viscous populations, which allows us to apply adaptive dynamics methodology. Second, we show that ordinary pair approximation introduces an important quantitative bias in the evolutionary model, even on random networks. We propose a correction to the ordinary pair approximation that yields quantitative accuracy, and discuss how the bias associated with this approach is precisely what allows us to identify subtle aspects associated with the evolutionary dynamics of spatially structured populations.     

An approach to the nonlinear dynamics of Russian wheat aphid population growth with the cusp catastrophe model

Many insect field populations, especially aphids, often exhibit irregular and even catastrophic fluctuations. The objective of the present study is to explore whether or not the population intrinsic rates of growth ( r _m) obtained under laboratory conditions can shed some light on the irregular changes of insect field populations. We propose to use the catastrophe theory, one of the earliest nonlinear dynamics theories, to answer the question. To collect the necessary data, we conducted a laboratory experiment to investigate population growth of the Russian wheat aphid (RWA), Diuraphis noxia (Mordvilko), in growth chambers. The experiment was designed as the factorial combinations of five temperatures and five host plant-growth stages (25 treatments in total): 1800 newly born RWA nymphs arranged in the 25 treatments (each treatment with 72 repetitions) were observed for their development, reproduction and survival through their entire lifetimes. After obtaining the population intrinsic rates of growth ( r _m) from the experimental data under various environmental conditions, we built a cusp catastrophe model for RWA population growth by utilizing r _m as the system state variable, and temperature and host plant-growth stage as control variables. The cusp catastrophe model suggests that RWA population growth is intrinsically catastrophic , and dramatic jumps from one state to another might occur even if the temperature and plant-growth stage change smoothly . Other basic behaviors of the cusp catastrophe model, such as catastrophic jumps , hystersis and divergence , are also expected in RWA populations. These results suggest that the answer to the previously proposed question should be "yes".     

Generalized aphid population growth models with immigration and cumulative-size dependent dynamics

Mechanistic models in which the per-capita death rate of a population is proportional to cumulative past size have been shown to describe adequately the population size curves for a number of aphid species. Such previous cumulative-sized based models have not included immigration. The inclusion of immigration is suggested biologically as local aphid populations are initiated by migration of winged aphids and as reproduction is temperature-dependent. This paper investigates two models with constant immigration, one with continuous immigration and the other with restricted immigration. Cases of the latter are relatively simple to fit to data. The results from these two immigration models are compared for data sets on the mustard aphid in India.     

Asymmetric effects of a leaf‐chewing herbivore on aphid population growth

1. Plant responses to herbivory are often specific to the feeding guild of the attacking herbivore. These phytochemical responses to herbivore damage can affect herbivore performance and activity. Comprehensive studies on the ecological consequences of multi‐herbivore plant interactions are key to understanding plant–herbivore community dynamics. 2. This study examined how feeding damage by co‐occurring herbivores from separate feeding guilds, Myzus persicae (Sulzer), a sucking herbivore, and Leptinotarsa decemlineata (Say), a chewing herbivore, alter plant chemistry and indirectly affect herbivore performance. Performance was measured when each insect fed on plants individually, sequentially, or simultaneously in laboratory and field experiments. Phytohormone and glycoalkaloid content were measured for each feeding sequence to evaluate plant responses to herbivory by each guild. Mid‐season and end‐of‐season tuber yield were evaluated in the field study. 3. Damage by L. decemlineata negatively impacted M. persicae performance in both laboratory and field settings. Damage by M. persicae did not affect L. decemlineata performance in laboratory assays. However, L. decemlineata performance was positively affected by M. persicae herbivory in the field, but this effect was temporary. Although phytohormones and plant defences varied across treatments, they provide little resolution on interaction outcomes. 4. These results confirm that the presence of multiple feeding guilds on a single plant can affect these chewing and sucking herbivores differentially, but given the variability in our phytochemical analyses compared with other studies, the mechanism remains unclear. The study's findings show that aphids are negatively affected by chewing herbivores across systems, while aphids temporarily affected beetles positively.     

A model of physiologically structured population dynamics with a nonlinear individual growth rate

In this article we consider a size structured population model with a nonlinear growth rate depending on the individual's size and on the total population. Our purpose is to take into account the competition for a resource (as it can be light or nutrients in a forest) in the growth of the individuals and study the influence of this nonlinear growth in the population dynamics. We study the existence and uniqueness of solutions for the model equations, and also prove the existence of a (compact) global attractor for the trajectories of the dynamical system defined by the solutions of the model. Finally, we obtain sufficient conditions for the convergence to a stationary size distribution when the total population tends to a constant value, and consider some simple examples that allow us to know something about their global dynamics.This work was partially supported by DGICYT PB90-0730-C02-01 and PB91-0497.     

转Cry1Ac+Cry2Ab基因棉对棉蚜生命表参数及种群动态的影响

为研究新型转Cry1Ac+Cry2Ab基因棉对棉蚜Aphis gossypii Glover生命表参数及种群动态的影响。2010—2011年以常规棉中棉所49为对照,对新型转Cry1Ac+Cry2Ab基因棉在室内进行了生物测定和田间进行了系统的调查。结果表明,和常规棉相比,转Cry1Ac+Cry2Ab基因棉花上棉蚜的净增值率降低81.69%,差异达显著水平;内禀增长率和周限增长率分别降低65.00%和13.01%,但差异不显著;平均世代周期和种群加倍时间分别增加5.54%和154.19%,后者差异达显著水平。和常规棉相比,2010年转Cry1Ac+Cry2Ab基因棉花百株苗蚜、伏蚜和秋蚜的数量分别降低10.79%、37.18%和17.49%,差异均未达显著水平;2011年转Cry1Ac+Cry2Ab基因棉花百株苗蚜的数量增加2.03%,伏蚜和秋蚜的数量分别降低37.41%和64.03%,差异均未达显著水平。     

Determination the population trends of cereal aphids and associated parasitoids by yellow sticky traps with reference to aphid management on wheat

Population trends of cereal aphids and their associated parasitoids inhabiting wheat plantations were monitored by yellow sticky traps. The identified aphids exhibited one seasonal peak for each and were found to be active during the first half of March. Data revealed that, Rhopalosiphum padi L peak occurred one week later than both of Schizaphis graminum (Rondani) and Rhopalosiphum maidis (Fitch). The numbers of aphid complex was recorded more at 90 than at 30 and 60 cm height. Hymenopterous parasitoids activity is synchronised with aphid species, whereas they appeared in small numbers at early and late wheat season and showed their peak on March, with a positive correlation coefficient with aphid populations. The tested compounds (Karate, Biscaya, Match 5% EC, Tracer 24% SC and Neem Azal T/S) showed 100% reduction in aphid numbers after 24 h post application. However, the general reduction percentages indicated 99.31 > 98.32 > 97.97 > 97.06 > 95.66%, by using the abovementioned compounds, respectively.     

The population dynamics of the large pine aphid,Cinara pinea (Mordv.)

The large pine aphid, Cinara pinea lives exclusively on Pinus species, where it feeds on the foliated shoots of the current and previous year. The paper describes the development of a computer model designed to simulate the aphid's population dynamics on saplings in the controlled environment of the laboratory, i.e. in the absence of natural enemies. The model was able to account for about 80% of the variation in aphid numbers within and between trees over a three month period. Sensitivity analysis revealed that the number of pine aphids is limited primarily by nymphal emigration, the operation of which is sensitive both to density and to plant quality as reflected in aphid growth rates. Of secondary importance are changes in reproduction acting through increased reproductive delay, again a result of altered growth rates and adult size. Development, too, has an important secondary influence. Contrary to expectation and conventional belief, however, alate production proved to be of negligible importance, either in limiting or regulating population numbers. Alatae are produced in too few numbers and for too short a period to significantly alter the pattern of population change.     

General methodology for nonlinear modeling of neural systems with Poisson point-process inputs

This paper presents a general methodological framework for the practical modeling of neural systems with point-process inputs (sequences of action potentials or, more broadly, identical events) based on the Volterra and Wiener theories of functional expansions and system identification. The paper clarifies the distinctions between Volterra and Wiener kernels obtained from Poisson point-process inputs. It shows that only the Wiener kernels can be estimated via cross-correlation, but must be defined as zero along the diagonals. The Volterra kernels can be estimated far more accurately (and from shorter data-records) by use of the Laguerre expansion technique adapted to point-process inputs, and they are independent of the mean rate of stimulation (unlike their P-W counterparts that depend on it). The Volterra kernels can also be estimated for broadband point-process inputs that are not Poisson. Useful applications of this modeling approach include cases where we seek to determine (model) the transfer characteristics between one neuronal axon (a point-process 'input') and another axon (a point-process 'output') or some other measure of neuronal activity (a continuous 'output', such as population activity) with which a causal link exists.     

Semiclassical approximations of stochastic epidemiological processes towards parameter estimation using as prime example the SIS system with import

In this paper we investigate several schemes to approximate the stationary distribution of the stochastic SIS system with import. We begin by presenting the model and analytically computing its stationary distribution. We then approximate this distribution using Kramers–Moyal approximation, van Kampen's system size expansion, and a semiclassical scheme, also called WKB or eikonal approximation depending on its different applications in physics. For the semiclassical scheme, done in the context of the Hamilton–Jacobi formalism, two approaches are taken. In the first approach we assume a semiclassical ansatz for the generating function, while in the second the solution of the master equation is approximated directly. The different schemes are compared and the semiclassical approximation, which performs better, is then used to analyse the time dependent solution of stochastic systems for which no analytical expression is known. Stochastic epidemiological models are studied in order to investigate how far such semiclassical approximations can be used for parameter estimation.     

A nonlinear structured population model of tumor growth with quiescence

A nonlinear structured cell population model of tumor growth is considered. The model distinguishes between two types of cells within the tumor: proliferating and quiescent. Within each class the behavior of individual cells depends on cell size, whereas the probabilities of becoming quiescent and returning to the proliferative cycle are in addition controlled by total tumor size. The asymptotic behavior of solutions of the full nonlinear model, as well as some linear special cases, is investigated using spectral theory of positive simigroup of operators. Supported in part by the National Science Foundation under Grant No. DMS-8722947     

Stochastic population dynamics of clonal plants: Numerical experiments with ramet and genet models

Dynamics of ramer and genet populations were analyzed by use of stochastic matrix models. Based on field data, population development and extinction rates during 50 simulated years were estimated for ramet populations of three speciesPotentilla anserina, Rubus saxatilis andLinnaea borealis. Only small initial populations (below 125–250 ramets), experienced a detectable risk of extinction within this time interval. ForP. anserina andR. saxatilis, population increase occurred in some simulations despite negative average growth rates. A model for stochastic genet dynamics was constructed by combining field data and hypothesized parameter values. Growth rate and population structure were insensitive to variation in disturbance intensity and frequency, whereas variation in recruitment affected population structure but only to a minor extent growth rate. Decreasing recruitment causes extinction of genet populations, but the time-scale for the decline is in the magnitude of centuries for initial genet populations of about 1000 individuals. Dynamics of genets in clonal plants thus incorporate processes occurring on widely different scales. Some implications of the results for models of population dynamics in long-lived clonal plants are discussed.     

增强的UV-B辐射对麦田生态系统中种群数量动态的影响

研究了大田栽培和自然光条件下,模拟UV-B辐射(UV-B,280～315nm)增强对麦田生态系统杂草、大型土壤动物和麦蚜种群数量动态的影响。在UV-B辐射下,杂草和大型土壤动物的种类和数量降低,物种多样性改变,杂草总生物量也降低。UV-B辐射降低麦蚜复合种群数量,并与麦叶粗纤维、可溶性蛋白、可溶性糖、Mg和Zn含量有显著的相关性。UV-B辐射还导致麦蚜与麦叶Mg、Fe和Zn含量均显著增加。     

大豆蚜自然天敌种群动态及其控蚜作用研究

2008-2010年间,分别在辽东山区和辽西半干旱丘陵地区设置试验田,采用系统调查的方法,对大豆蚜Aphis glycines Matsumura自然天敌种群动态及控蚜作用进行研究。共鉴定辽宁地区大豆蚜天敌7目、16科、44种,其中优势天敌异色瓢虫Leis axyridis(Pallas)居首位。田间试验结果表明,大豆蚜天敌田间消长表现连续6个阶段,即初见期、波动期、上升期、盛期、下降期和消退期;田间3年平均大豆蚜数量与天敌(天敌单位)总体呈极显著的相关关系,各年度百株蚜量与天敌单位也均呈极显著相关关系。辽东地区天敌跟随紧密并随蚜虫数量变化波动,具有明显的自然控蚜作用。其中,7月11-21日天敌发生盛期与蚜虫高峰期吻合,蚜虫急剧下降;7月下旬后,受高温、多雨、蚜霉菌作用、植株老化等影响,蚜虫种群逐步下降、消退,天敌也陆续迁出豆田。辽西地区天敌迁入豆田比蚜虫晚10～15d,对前期蚜虫控制弱,且天敌峰期滞后蚜虫5d左右,一般年份蚜虫发生较重。