Allee threshold and extinction threshold for spatially explicit metapopulation dynamics with Allee effects

In this paper, we investigate a spatially explicit metapopulation model with Allee effects. We refer to the patch occupancy model introduced by Levins (Bull Entomol Soc Am 15:237–240, 1969) as a spatially implicit metapopulation model, i.e., each local patch is either occupied or vacant and a vacant patch can be recolonized by a randomly chosen occupied patch from anywhere in the metapopulation. When we transform the model into a spatially explicit one by using a lattice model, the obtained model becomes theoretically equivalent to a “lattice logistic model” or a “basic contact process”. One of the most popular or standard metapopulation models with Allee effects, developed by Amarasekare (Am Nat 152:298–302, 1998), supposes that those effects are introduced formally by means of a logistic equation. However, it is easier to understand the ecological meaning of associating Allee effects with this model if we suppose that only the logistic colonization term directly suffers from Allee effects. The resulting model is also well defined, and therefore we can naturally examine it by Monte Carlo simulation and by doublet and triplet decoupling approximation. We then obtain the following specific features of one-dimensional lattice space: (1) the metapopulation as a whole does not have an Allee threshold for initial population size even when each local population follows the Allee effects; and (2) a metapopulation goes extinct when the extinction rate of a local population is lower than that in the spatially implicit model. The real ecological metapopulation lies between two extremes: completely mixing interactions between patches on the one hand and, on the other, nearest neighboring interactions with only two nearest neighbors. Thus, it is important to identify the metapopulation structure when we consider the problems of invasion species such as establishment or the speed of expansion.     

Modelling Allee effects in a transgenic mosquito population during range expansion

ABSTRACT

Mosquitoes are vectors for many diseases that cause significant mortality and morbidity. As mosquito populations expand their range, they may undergo mate-finding Allee effects such that their ability to successfully reproduce becomes difficult at low population density. With new technology, creating target specific gene modification may be a viable method for mosquito population control. We develop a mathematical model to investigate the effects of releasing transgenic mosquitoes into newly established, low-density mosquito populations. Our model consists of two life stages (aquatic and adults), which are divided into three genetically distinct groups: heterogeneous and homogeneous transgenic that cause female infertility and a homogeneous wild type. We perform analytical and numerical analyses on the equilibria to determine the level of saturation needed to eliminate mosquitoes in a given area. This model demonstrates the potential for a gene drive system to reduce the spread of invading mosquito populations.     

Modelling the effects of population aggregation on the efficiency of insect pest control

A methodology is developed to assess the effects of spatial distribution on the efficiency of insect pest control. This methodology is especially applicable to pest control methods whose efficiency of action depends either positively or negatively on pest density It is applied here to the sterile insect technique and pheromone trapping for male annihilation, which both depend negatively on density. This methodology relies on quantifying clumps of various size and then relating this to efficiency of control and predicting the total pest production given the information on clump sizes and efficiency of control for each clump size. It is found that control is about four times as difficult for a population that is highly clumped (k of the negative binomial distribution=0.25) as for a regularly dispersed population.     

Backward bifurcations and strong Allee effects in matrix models for the dynamics of structured populations

In nonlinear matrix models, strong Allee effects typically arise when the fundamental bifurcation of positive equilibria from the extinction equilibrium at r=1 (or R₀=1) is backward. This occurs when positive feedback (component Allee) effects are dominant at low densities and negative feedback effects are dominant at high densities. This scenario allows population survival when r (or equivalently R₀) is less than 1, provided population densities are sufficiently high. For r>1 (or equivalently R₀>1) the extinction equilibrium is unstable and a strong Allee effect cannot occur. We give criteria sufficient for a strong Allee effect to occur in a general nonlinear matrix model. A juvenile–adult example model illustrates the criteria as well as some other possible phenomena concerning strong Allee effects (such as positive cycles instead of equilibria).     

A reappraisal of the population dynamics of the pine beauty moth, Panolis flammea, on lodgepole pine, Pinus contorta, in Scotland

The pine beauty moth, Panolis flammea, is a defoliating pest of lodgepole pine (Pinus contorta) forests in Scotland. This article reviews early and recent research on the population ecology of Panolis flammea and presents an analysis of pupal survey data collected between 1977 and 1993. Research in the 1980s suggested that natural enemies, although effective in preventing P. flammea outbreaks on Scots pine (Pinus sylvestris), played an insignificant role in the population dynamics of P. flammea on lodgepole pine. However, analysis of pupal survey data showed that delayed density-dependent action of natural enemies, probably parasitoids, was overlooked during the 1970s and 1980s. Recent research suggests that fungal pathogens are responsible for a decline in the frequency and severity of outbreaks of P. flammea on lodgepole pine. This suggestion, together with the overlooked importance of other natural enemies, indicates that the population ecology of P. flammea in Scotland has changed during the past 20 years and requires a full reappraisal. Received: May 31, 1999 / Accepted: August 18, 1999     

桃园害虫及天敌群落动态研究

通过对桃园害虫天敌群落的系统调查,应用主分量分析法、最优分割法和模糊聚类分析方法进行分析．结果表明,群落具有明显的主导因素和时间格局;对桃园节肢动物群落55种节肢动物的数量变化进行模糊聚类分析,选置信水平λ＝0．47,将其分为4个时期,利用最优分割法,将害虫天敌的发生量分为3段,利用主分量分析法,明确了主要害虫及其天敌种类．     

Allee effects, mating systems and the extinction risk in populations with two sexes

The Allee effect is one of the population consequences of sexual reproduction that has received increased attention in recent years. Due to its impact on small population dynamics, it is commonly accepted that Allee effects should render populations more extinction prone. In particular, monogamous species are considered more susceptible to the Allee effect and hence, more extinction prone, than polygamous species. Although this hypothesis has received theoretical support, there is little empirical evidence. In this study, we investigate (1) how variation in tertiary sex ratio affects the presence and intensity of the Allee effect induced by mating system, as well as (2) how this effect contributes to extinction risk. In contrast with previous predictions, we show that all mating systems are likely to experience a strong Allee effect when the operational sex ratio (OSR) is balanced. This strong Allee effect does not imply being exceptionally extinction prone because it is associated with an OSR that result in a relatively small extinction risk. As a consequence, the impact of Allee effects on overall extinction risk is buffered. Moreover, the OSR of natural populations appears to be often male biased, thus making it unlikely that they will suffer from an Allee effect induced by mating system.     

Natural enemy diversity and pest control: patterns of pest emergence with agricultural intensification

Concern over declining biodiversity and the implications for continued provision of ecosystem services has led, recently, to intense research effort to describe relationships between biodiversity and ecosystem functioning. Here we extend this effort to the relationship between natural enemy species diversity and natural pest control. From simple modelled food‐webs and simulations of natural enemy species loss we derive specific predictions concerning the effect of herbivore life‐history traits, such as life‐cycle type and concealment, on the shape (reflecting diversity effects) and variance (reflecting species composition effects) of the relationship between natural enemy diversity and pest‐control. We show that these predictions are consistent with the emergence of different pest types following intensification of rice production in Asia. We suggest that basic biological insights can help define the structure of ecological processes and allow more accurate predictions of the effect of species loss on the delivery of ecosystem services.     

A network approach to modeling population aggregation and genetic control of pest insects

Historically, models of the invasion and biological control of insect pests have omitted heterogeneities in the spatial structure of the targeted populations. In this study, we use stochastic network simulations to examine explicitly population heterogeneity as a function of landscape structure and insect behavior. We show that when insects are distributed non-randomly across a heterogeneous landscape, control can be significantly hindered. However, when insect populations are clustered as a result of limited dispersal, genetic control efficiency can be enhanced. In developing the model, we relax a key assumption of previous theoretical studies of genetic control: that released genetic control insects remain homogenously distributed irrespective of the spatial structure of the wild type populations. Here, this behavior (termed the ‘coverage proportion’) is parameterized and its properties are explored. We show that landscape heterogeneity and limited dispersal have little effect on the critical coverage proportion necessary for control.     

Synchrony's double edge: transient dynamics and the Allee effect in stage structured populations

In populations subject to positive density dependence, individuals can increase their fitness by synchronizing the timing of key life history events. However, phenological synchrony represents a perturbation from a population's stable stage structure and the ensuing transient dynamics create troughs of low abundance that can promote extinction. Using an ecophysiological model of a mass-attacking pest insect, we show that the effect of synchrony on local population persistence depends on population size and adult lifespan. Results are consistent with a strong empirical pattern of increased extinction risk with decreasing initial population size. Mortality factors such as predation on adults can also affect transient dynamics. Throughout the species range, the seasonal niche for persistence increases with the asynchrony of oviposition. Exposure to the Allee effect after establishment may be most likely at northern range limits, where cold winters tend to synchronize spring colonization, suggesting a role for transient dynamics in the determination of species distributions.     

大豆、玉米与水稻配置对稻田寄生蜂的影响

本文研究了稻田生境和非稻田生境间寄生性天敌的迁移扩散规律及其对水稻主要害虫的控制作用.结果表明,寄生蜂从大豆生境扩散到稻田生境的数量显著高于其从玉米生境扩散到稻田生境,而田埂种植玉米的寄生蜂扩散数量与不种植玉米相比无显著性差异.田埂配置大豆的有机稻田内二化螟Chilo suppressalis、三化螟Tryporyza incertulas、稻纵卷叶螟Cnaphalocrocis medinalis cnienee和褐飞虱Nilaparvata lugens的卵寄生率分别为17.8％,20.3％,10.2％和12.4％,与未配置大豆的对照相比分别增加了4.3％,7.5％,2.1％,和3.4％;它们的幼虫寄生率分别为14.7％,31.7％,21.3％,7.3％,与对照相比分别增加了5.3％,9.8％,5.7％和2.8％.而田埂配置玉米的有机稻田的二化螟,三化螟,稻纵卷叶螟和褐飞虱的卵寄生率分别为10.3％,14.4％,8.6％和9.3％;与未配置玉米的对照相比分别降低了3.2％,增加1.6％,0.5％和0.3％;它们的幼虫寄生率分别为10.3％,19.4％,17.5％和2.6％,与对照相比分别增加了0.9％,降低了2.5％,增加了1.9％和降低了1.9％.研究结果可为通过建立合理的水稻邻作模式进行害虫生物防治提供重要科学依据.     

Modelling selection for resistance to methods of insect pest control in combination

The development of resistance to insecticides is now widespread among insects. Other methods of pest control are also potentially at risk of encountering resistance. A modelling approach is presented here to evaluate the effects of combining methods of insect pest control on the selection for resistance to the control methods. This analysis is based on partitioning the total mortality acting on a population into its constituent components from all known sources, and these are related to selection for resistance. When two control methods are used in combination, selection for resistance against the two is a linear function if the two don't interact, otherwise it may be sublinear or supralinear. A specific example is presented using a model of the Olive fruit fly (Dacus oleae Gmel.) and employing food-baited and pheromone-baited traps for control. The control methods that appear least likely to encounter resistance are natural enemies and the use of pheromone traps for male annihilation. These should be integrated into a control program where possible to minimize the development of resistance to other control methods being used.     

Tea: Biological control of insect and mite pests in China

Tea is one of the most economically important crops in China. To secure its production and quality, biological control measures within the context of integrated pest management (IPM) has been widely popularized in China. IMP programs also provide better control of arthropod pests on tea with less chemical insecticide usage and minimal impact on the environment. More than 1100 species of natural enemies including about 80 species of viruses, 40 species of fungi, 240 species of parasitoids and 600 species of predators, as well as several species of bacteria have been recorded in tea ecosystems in China. Biological and ecological characteristics of some dominant natural enemies have been well documented. Several viral, bacterial, and fungal insecticides have been commercially utilized at large scale in China. Progress in biological control methods in conjunction with other pest control approaches for tea insect pest management is reviewed in this article. Knowledge gaps and future directions for tea pest management are also discussed.     

Dispersion in time and space affect mating success and Allee effects in invading gypsy moth populations

1. Understanding why invading populations sometimes fail to establish is of considerable relevance to the development of strategies for managing biological invasions. 2. Newly arriving populations tend to be sparse and are often influenced by Allee effects. Mating failure is a typical cause of Allee effects in low-density insect populations, and dispersion of individuals in space and time can exacerbate mate-location failure in invading populations. 3. Here we evaluate the relative importance of dispersal and sexual asynchrony as contributors to Allee effects in invading populations by adopting as a case study the gypsy moth (Lymantria dispar L.), an important insect defoliator for which considerable demographic information is available. 4. We used release-recapture experiments to parameterize a model that describes probabilities that males locate females along various spatial and temporal offsets between male and female adult emergence. 5. Based on these experimental results, we developed a generalized model of mating success that demonstrates the existence of an Allee threshold, below which introduced gypsy moth populations are likely to go extinct without any management intervention.     

Forest bolsters bird abundance,pest control and coffee yield

Efforts to maximise crop yields are fuelling agricultural intensification, exacerbating the biodiversity crisis. Low‐intensity agricultural practices, however, may not sacrifice yields if they support biodiversity‐driven ecosystem services. We quantified the value native predators provide to farmers by consuming coffee's most damaging insect pest, the coffee berry borer beetle (Hypothenemus hampei). Our experiments in Costa Rica showed birds reduced infestation by ~ 50%, bats played a marginal role, and farmland forest cover increased pest removal. We identified borer‐consuming bird species by assaying faeces for borer DNA and found higher borer‐predator abundances on more forested plantations. Our coarse estimate is that forest patches doubled pest control over 230 km² by providing habitat for ~ 55 000 borer‐consuming birds. These pest‐control services prevented US$75–US$310 ha‐year⁻¹ in damage, a benefit per plantation on par with the average annual income of a Costa Rican citizen. Retaining forest and accounting for pest control demonstrates a win–win for biodiversity and coffee farmers.     

The impact of weed diversity on insect population dynamics and crop yield in collards, Brassica oleraceae (Brassicaceae)

Vegetational diversity within agricultural fields is often suggested as a means to reduce insect herbivore populations and to increase their natural enemies. In this paper we compare population densities of herbivores, predators, and parasitoids on collards in monocultures and on collards interplanted with two different groups of weeds, one with weed species from the same plant family as the collards (Brassicaceae) and one with weed species from unrelated plant families (non-Brassicaceae). The collards in the Brassicaceae weed polyculture had higher densities (number of herbivores/mean leaf area (cm²) per plant) of specialist herbivores than collards in the non-Brassicaceae weed polyculture and in collard monoculture. The “resource concentration” hypothesis is supported by the observation of higher populations of Phyllotreta spp., acting as facultative polyphages, in the Brassicaceae weed polyculture than in the non-Brassicaceae weed polyculture where Phyllotreta spp. are facultative monophages. Population densities of natural enemies (mostly coccinellids, carabids, and staphylinids) were higher in the polycultures than in the monoculture: carabid and staphylinid predators may be responsible for larval mortality in the imported cabbage worm, Pieris␣rapae, and in the diamondback larvae, Plutella xylostella. In spite of differences in densities of specialist herbivores across treatments, crop yield, leaf area (cm²), the proportion of leaf area damaged, and the number of leaves undamaged did not differ. These findings suggest that plant competition may interfere with attempts to reduce herbivore damage. We conclude that the use of weedy cultures can provide effective means of reducing herbivores if the crop and weed species are not related and plant competition is prevented. Received: 25 December 1995 / Accepted: 24 February 1997     

Overcoming Allee effects through evolutionary,genetic, and demographic rescue

Despite the amplified threats of extinction facing small founder populations, successful colonization sometimes occurs, bringing devastating ecological and economic consequences. One explanation may be rapid evolution, which can increase mean fitness in populations declining towards extinction, permitting persistence and subsequent expansion. Such evolutionary rescue may be particularly important, given Allee effects. When a population is introduced at low density, individuals often experience a reduction in one or more components of fitness due to novel selection pressures that arise from diminished intraspecific interactions and positive density dependence (i.e. component Allee effects). A population can avoid extinction if it can adapt and recover on its own (i.e. evolutionary rescue), or if additional immigration sustains the population (i.e. demographic rescue) or boosts its genetic variation that facilitates adaptation (i.e. genetic rescue). These various forms of rescue have often been invoked as possible mechanisms for specific invasions, but their relative importance to invasion is not generally understood. Within a spatially explicit modelling framework, we consider the relative impact of each type of rescue on the probability of successful colonization, when there is evolution of a multi-locus quantitative trait that influences the strength of component Allee effects. We demonstrate that when Allee effects are important, the effect of demographic rescue via recurrent immigration overall provides the greatest opportunity for success. While highlighting the role of evolution in the invasion process, we underscore the importance of the ecological context influencing the persistence of small founder populations.     

边缘效应对棉田害虫和天敌种群的影响

比较了棉田中间棉株与边缘棉株上害虫、天敌的种群动态,分析了边缘效应对棉株-害虫-天敌能量动态的影响。结果表明,棉田边缘棉株上第2代棉铃虫幼虫发生量比其中间棉株高出1．94倍;第3代棉铃虫发生量比棉田中间要低62．12％;第4代棉铃虫比中间棉株高12．5％。棉田边缘棉株上苗蚜发生量比棉田中间要高出1．09倍,伏蚜和秋蚜的数量比棉田中间分别低97．73％和37．70％。棉田边缘棉株上捕食性瓢虫、蝽类、蜘蛛和寄生性天敌的种群数量低于棉田中间的数量,分别为棉田中间的73．81％、35．79％、52．90％和39．11％;棉田边缘棉株上害虫群落多样性高于棉田中间,而天敌群落的多样性低于棉田中间;棉田边缘的光能利用率和生产力比棉田中间的值要高。     

播种时间对棉田害虫和天敌种群的影响

通过对3种不同时间播种的棉田内害虫、天敌系统调查,分析和比较了播种时间对棉田害虫、天敌种群和群落的影响。结果表明,播种期推后,可减轻或避免第二代棉铃虫的为害,加重第三代和第四代棉铃虫的为害;但不同播种日期对不同时期的棉蚜影响不同,苗蚜以迟播棉田内种群数量最高,伏蚜则以夏播棉田内种群数量最高。播种期的推后,不利于棉田捕食性瓢虫、蝽类、蜘蛛和寄生性天敌种群增长。棉田害虫和天敌群落多样性指数也随播种期的推后而下降．因此．应针对不同时间播种的棉田开展相应的害虫生态管理。     

Ecological balance in the native population dynamics may cause the paradox of pest control with harvesting

We analyze a time-discrete mathematical model of host-parasite population dynamics with harvesting, in which the host can be regarded as a pest. We harvest a portion of the host population at a moment in each parasitism season. The principal target of the harvesting is the host; however, the parasite population may also be affected and reduced by a portion. Our model involves the Beverton-Holt type density effect on the host population. We investigate the condition in which the harvesting of the host results in an eventual increase of its equilibrium population size, analytically proving that the paradoxical increase could occur even when the harvesting does not directly affect the parasite population at all. We show that the paradox of pest control could be caused essentially by the interspecific relationship and the intraspecific density effect.