A Review of the Mathematical Models for the Impact of Seasonal Weather Variation and Infections on Prey Predator Interactions in Serengeti Ecosystem

Interaction between prey and predator species is a complex and non-linear process. Understanding various phenomena in the dynamics of prey-predator systems is vital to both mathematical ecology and conservation biology. Mathematical models on prey-predator systems have been the hot sport providing important information regarding the interactions of prey and predator species in various ecosystems. In this paper, a review of the available mathematical models on prey-predator systems was done. Our aim was to assess their structure, behaviour, available control strategies, population involved and their ability in predicting the future behaviour of the ecosystems. We observed diversities in the reviewed mathematical models, some model incorporated factors such as drought, harvesting and prey refuge as the factors that affect ecosystems, some ignored the contribution of environmental variations while others considered the variable carrying capacity. Most of the models reviewed have not considered the contribution of diseases and seasonal weather variation in the dynamics of prey predator systems. Some of the reviewed models do not match the real situation in most modelled ecosystems. Thus, to avoid unreliable results, this review reveals the need to incorporate seasonal weather variations and diseases in the dynamics of prey predator systems of Serengeti ecosystem.

一类食饵具有阶段结构的时滞Predator-Prey系统的周期解(英文)

研究了一类时滞Predator-Prey系统,其中Prey种群是具有两个生命阶段的种群,即幼年阶段和成年阶段。Predator种群只能捕食Prey幼年种群。通过应用Gaines和Mawhin重合度理论的连续函数定理,给出了系统正周期解存在的充分条件。

NONLINEAR SINGULARLY PERTURBED PREDATOR-PREY REACTION DIFFUSION SYSTEMS

A class of nonlinear predator prey reaction diffusion systems for singularly pe rturbed problems are considered.Under suitable conditions, by using theory of di fferential inequalities the existence and asymptotic behavior of solution for in itial boundary value problems are studied.

一类含扩散与时滞的Prey-Predator模型的周期解

利用上下解方法以及比较原理研究了一类含扩散与时滞的Prey-Predator模型,证明在一定条件下该模型的零平衡态及半平凡周期解的全局稳定性,并获得了这个系统具有一对周期拟解的充分条件.对任意的非负初值函数,这一对周期拟解构成的区间是此系统的一个吸引子.

Periodic Solutions of Periodic Delay Predator-Prey System with Nonmonotonic Functional Response

By using the continuation theorem of coincidence degree theory, sufficient conditions are obtained for the existence of positive periodic solutions of a delayed predator prey system with nonmonotonic functional response in a periodic environment.

Experimental clearance rate and intraguild predation of jellyfish Cyanea nozakii

Cyanea nozakii,a common jellyfish distributed in offshore China,has a complex trophic relationship with other zooplankton groups.However,few studies have reported the predation rates and prey selection patterns of C.nozakii medusae on different prey items.Research is also lacking on the intraguild predation of Aurelia coerulea(another common bloom jellyfish in offshore China)by C.nozakii.To address the knowledge gaps,the clearance rates of C.nozakii for different prey items,including copepods(small<1000μm and large>1000μm),fish larvae,and gelatinous prey(hydromedusae,A.coerulea ephyrae,and chaetognaths),were measured.The influence of predator size on the clearance rate was also determined.Additionally,we examined the intraguild predation of C.nozakii on A.coerulea medusae.The clearance rates of C.nozakii varied widely with prey organisms,being independent of prey concentrations.Gelatinous organisms,except for chaetognaths,were captured with considerably high efficiency,followed by fish larvae and copepods,indicating the preferential prey selection of gelatinous organisms by C.nozakii.The clearance rate increased linearly with the cross-sectional area of C.nozakii.Body size in medusae may,to some extents,underpin their capacity to capture more prey by increasing the encounter rate and capture success through ontogeny.C.nozakii preyed voraciously on A.coerulea in high feeding efficiency,but the clearance rate decreased with increasing A.coerulea(as prey)size.This phenomenon of intraguild predation suggests a speculative hypothesis of potential population regulation of A.coerulea by C.nozakii.The information regarding the feeding ecology of C.nozakii reported in this study is important for understanding plankton dynamics in marine ecosystems with extensive occurrences of this jellyfish.

Stability of the Bifurcation Solutions for a Predator-Prey Model

The bifurcation solution of the nonnegative steady state of a reaction diffusion system was investigated. The combination of the sturm type eigenvalue and the theorem of bifurcation was used to study the local coexistence solutions, and obtain the stability of bifurcation solutions. The system model describes predator prey interaction in an unstirred chemostat.

Can an Invasive Prey Species Induce Morphological and Behavioral Changes in an Endemic Predator? Evidence from a South Korean Snake(Oocatochus rufodorsatus)

Introduction of an invasive prey species into an ecosystem may affect an endemic predator＇s fitness by altering the prey-predator system. Successful adaptation may allow the endemic predator to eat and control the invasive species, while unsuccessful adaptation may result in extinction of the predator. We examine the possible effects of the invasive North American bullfrog （Rana [Lithobates] catesbeiana） on the endemic Red-backed rat snake （Oocatochus rufodorsatus） in South Korea. We do so by comparing the morphology and behavior of adult and hatchling snakes from bullfrog-exposed （Taean） and bullfrog-unexposed （Hongcheon） populations. Among the seven morphological characteristics investigated, relative tail length （tail length/snout-vent length） of both adults and hatchlings from Taean was significantly greater than that of adults and hatchlings from Hongcheon. Also, adult snakes from Taean had a signiifcantly shorter latency of ifrst tongue lfick in response to prey compared to adults from Hongcheon. This difference was not observed in hatchlings. In other snake species, a longer relative tail length and shorter latency of ifrst tongue lfick are known to improve foraging efifciency, and these characters may be adaptations ofO. rufodorsatus to prey on bullfrogs. This study provides preliminary evidence that the presence of an invasive prey species may cause morphological and behavioral changes in an endemic predator.

A CONDITION OF THE EXISTENCE OF STABLE POSITIVE STEADY-STATE SOLUTIONS FOR A ONE PREDATOR TWO PREY SYSTEM

One predator two prey system is a research topic which has both the theoretical and practical values. This paper provides a natural condition of the existence of stable positive steady-state solutions for the one predator two prey system. Under this condition we study the existence of the positive steady-state solutions at vicinity of the triple eigenvalue by implicit function theorem, discuss the positive stable solution problem bifurcated from the semi-trivial solutions containing two positive components with the help of bifurcation and perturbation methods.

Turing Instability of Diffusive Predator⁃Prey System with Gompertz Growth

This paper mainly focus on the research of a predator⁃prey system with Gompertz growth of prey.When the system does not contain diffusion,the stability conditions of positive equilibrium and the occurring condition of the Hopf bifurcation are obtained.When the diffusion term of the system appears,the stable conditions of positive equilibrium and the Turing instability condition are also obtained.Turing instability is induced by the diffusion term through theoretical analysis.Thus,the region of parameters in which Turing instability occurs is presented.Then the amplitude equations are derived by the multiple scale method.The results will enrich the pattern dynamics in predator⁃prey systems.

Prey Predator Fishery Model with Stage Structure in Two Patchy Marine Aquatic Environment

In this paper, we propose and analyze a mathematical model to study the dynamics of a fishery resource system with stage structure in an aquatic environment that consists of two zones namely unreserved zone (fishing permitted) and reserved zone (fishing is strictly prohibited). In this model we introduce a stage structure in which predators are split into two kinds as immature predators and mature predators. It is assumed that immature predators cannot catch the prey and their foods are given by their parents (mature predators). It is also assumed that the fishing of immature predators prohibited in the unreserved zone and predator species are not allowed to enter inside the reserved zone. The local and global stability analysis has been specified. Biological and Bionomical equilibriums of the system are derived. Mathematical formulation of the optimal harvesting policy is given and its solution is derived in the equilibrium case by using Pontryagin’s maximum principle.

Predator Population Dynamics Involving Exponential Integral Function When Prey Follows Gompertz Model

The current study investigates the predator-prey problem with assumptions that interaction of predation has a little or no effect on prey population growth and the prey’s grow rate is time dependent. The prey is assumed to follow the Gompertz growth model and the respective predator growth function is constructed by solving ordinary differential equations. The results show that the predator population model is found to be a function of the well known exponential integral function. The solution is also given in Taylor’s series. Simulation study shows that the predator population size eventually converges either to a finite positive limit or zero or diverges to positive infinity. Under certain conditions, the predator population converges to the asymptotic limit of the prey model. More results are included in the paper.

A Leslie-Gower Holling Type-II Predator-Prey Mathematical Model with Disease in Prey Population Incorporating a Prey Refuge

We formulate and analyze a predator-prey model followed by Leslie-Gower model in which the prey population is infected by disease. We assume that the disease can only spread over prey population. As a result prey population has been classified into two categories, namely susceptible prey, infected prey where as the predator population remains free from infection. To investigate the behaviour of prey population we incorporate prey refuge in this model. Since the prey refuge decreases the predation rate then it has an important effect in our predator-prey interaction model. We have discussed the existence of various equilibrium points and local stability analysis at those equilibrium points. We investigate the Hopf-bifurcation analysis about the interior equilibrium point by taking the rate of infection parameter and the prey refuge parameter as bifurcation parameters. The numerical analysis is carried out to support the analytical results and to discuss some interesting results that our model exhibits.

ON A PERIODIC PREY-PREDATOR SYSTEM WITH INFINITE DELAYS

Based on the theory of coincidence degree,the existence of positive periodic solutions is established for a periodic prey predator system with infinite delays (t)=x(t)[α(t)-γ(t)y(t)-γ(t)∫ ∞ 0K 1(t,s)y(t-s) d s- ∫ ∞ 0∫ ∞ 0R 1(t,s,θ)y(t-s)y(t-θ) d θ d s], (t)=y(t)[-β(t)+μ(t)x(t)+μ(t)∫ ∞ 0K 2(t,s)x(t-s) d s+ ∫ ∞ 0∫ ∞ 0R 2(t,s,θ)x(t-θ)x(t-s) d θ d s],where α,γ,β,μ are positive continuous ω periodic functions, K i∈C (R×[0,∞),(0,∞))( i =1,2) are ω periodic with respect to their first arguments,.respectively, R i∈C (R×[0,∞)×[0,∞),(0,∞))( i =1,2) are ω periodic with respect to their first arguments,respectively.

Effect of random movement and cooperative hunting in the prey-predator system:A dynamical approach

Self-diffusion prerequisite is obtained as the spreading approach of biological populations.Cooperative hunting is a common behavior in predator populations that promotes predation and the coexistence of the prey-predator system.On the other side,the Allee effect among prey may cause the system to become unstable.In this paper,a difusive prey predator system with cooperative hunting and the weak Allee effect in prey populations is discussed.The linear stability and Hopf-bifurcation analysis had been used to examine the system's stability.From the spatial stability of the system,the conditions for Turing instability have been derived.The multiple-scale analysis has been used to derive the amplitude equations of the system.The stability analysis of these amplitude equations leads to the formation of Turing patterns.Finally,numerical simulations are used to analyze spatial patterns forming in 1-D and 2-D.The studies indicate that the model can generate a complex pattern structure and that self-diffusion has a drastic impacton species distribution.

Field and Laboratory Observations on Predation and Prey Selectivity of the Scyphomedusa Chrysaora cf.caliparea in Southeast Indian Waters

Chrysaora cf.caliparea,one of the most abundant medusae species in India,seems to be an important predator in the coastal waters of Bay of Bengal.The ability of Chrysaora cf.caliparea to feed at maximum rate in high prey concentrations implies that this jellyfish can efficiently exploit dense prey patches,at least for a short period.This study presents preliminary information regarding digestion and feeding rate upon copepods in a warm water environment.The ingestion rate of the average-sized medusae Chrysaora cf.caliparea is well balanced in nature,which in turn implies that this jellyfish is tuned for optimal utilization of available prey resources.Comparison with earlier research indicates that prey escape speed is one important factor governing which prey will be captured.A full understanding of predation mechanics awaits further investigation of both predator and prey behavior.However,because of the scarcity of long-term quantitative population data most insights have to be made indirectly.Nevertheless,low abun-dance of Chrysaora cf.caliparea in the water column during summer (May 2007) and the overall annual abundance seem not to con-siderably affect the zooplankton population,especially copepods.The present work contributes to the knowledge of prey-predator relationship of the forgotten fauna in Indian waters,which is especially crucial for understanding the process of ecological recovery of coastal water environment.

The Predatory Function of Three Spiders to Two Insect Pests in Rice Within a Multi-species Co-existence System

The prey-seeking behavior of three spiders (X1-Pirata subpiraticus, X2-Clubiona japonicola and X3-Tetragnatha japonica) for brown plant hopper (X4-Nilaparvata lugens) and rice spittle bug (X5-Cal-litettix versicolor) was investigated, as well as how interference between and within species occurred, by using a quadratic regression rotational composite design. Six predation models derived from the analysis of interactions among and within predators and preys were developed. The total predatory capacity of spiders on rice insect pests after coexistence for one day can be expressed as follows: Y3 = 32.795 + 2.25X1 + 1.083X2 + 0.5X3 + 10.167X4 + 3.167X5 - 1.67X12 - 2.42X22 - 3.295X32 - 0.045X42 + 0.455X52 - 3.125X1X2 + 0.375X1X3 -0.625X1X4 - 0.375X1X5 + 0.375X2X3 - 0.875X2X4 + 0.125X2X5 + 0.375X3X4 - 0.375X3X5 + 0.125X4X5. The principal efficiency analysis using this model indicated that increases in insect pest density significantly increased predation by predators; this was much greater than the effect of any single predator. X4 had a greater effect than X5; however, X4 and X5 demonstrated little interspecific interference and even promoted each other and increased predation rates as the densities of the two pests increased. Among the three predators, an increase in the density of X, had the greatest effect on the increase in predation, X3 had the second, X2 the third greatest effect. As predator density increased inter- and intra-species interference occurred, which were largely related to the size, activity, niche breadth, niche overlap and searching efficiency of the predators. X2 produced the greatest interference between different individuals and between any other predator species. X3 had the second greatest, which reduced predation levels at high predator densities. Because of these factors, the highest predation rate was obtained at a prey density of 120 per 4 rice-hills. The optimal proportion of the three predators in the multi-predator prey system was X1: X2: X3 = 5.6:1.3:4.1.

Rearing the Predator Brontocoris tabidus(Heteroptera:Pentatomidae)with Tenebrio molitor(Coleoptera:Tenebrionidae)Pupa on Eucalyptus grandis in the Field

The use of natural enemies represents an important strategy in programs of Integrated Pest Management (IPM). Asopinae predators are reared with alternative prey, but supplementary plant may enhance the fecundity and longevity of their females. The objective of this research was to evaluate the development and reproduction of the predator Brontocoris tabidus Signoret, 1852 (Heteroptera: Pentatomidae) fed with Tenebrio molitor L., 1785 (Coleoptera: Tenebrionidae) pupae in a Eucalyptus grandis Hill ex Maiden (Myrtaceae) plant in the field. The duration and survival of the nymphal stage of B. tabidus were 32.07 ± 8.95 days and 77.00 ± 0.42%, respectively with 15.55 ± 8.19 egg masses, 603.00 ± 379.20 eggs and 387.45 ± 291.40 nymphs per female of this predator while longevity of its males and females was 119.80 ± 32.80 and 160.20 ± 42.13 days, respectively. Better results with E. grandis plant in the field and the fact that B. tabidus will be adapted at release time show that this predator should be reared in these conditions.

基于定性网络模型评价生态调控情景对海洋牧场生态系统的影响——以獐子岛海洋牧场为例

在海洋牧场建设过程中,生态调控方式实施后对海洋牧场生态系统的影响通常难以预测,这对海洋牧场的生态安全和高质量发展提出了严峻挑战。为此,建立了一种基于定性网络模型(Qualitative network model,QNM)的海洋牧场生态系统模拟评价方法,并以獐子岛海洋牧场近岸增殖海域作为研究区域,构建以增殖目标种为核心的定性网络模型,模拟评估海洋牧场3种不同类型的生态调控情景(增殖目标种、移除捕食者、海藻场修复)及其复合条件下,牧场群落范围内的响应,分析海洋牧场生态调控策略与生物功能群变化之间潜在关系。结果显示:目标种增殖(仿刺参和虾夷扇贝)产生的上行效应导致其捕食者呈现积极响应,产生的下行效应导致其它底栖动物、浮游植物和有机碎屑等功能群呈现消极响应,移除捕食者海星产生的下行效应导致虾夷扇贝呈现积极响应,表明在增殖区清除敌害生物的重要性,海藻场修复对整个群落有明显的积极影响,体现了海藻场在养护近岸生态系统的重要生态意义。研究表明:QNM可有效识别生态系统潜在的营养级联效应,评估生物功能群的响应,基于QNM的海洋牧场生态调控模拟评价方法,突破了定量食物网模型在数据有限系统中使用的局限性,可为海洋牧场建设的生态调控策略制定提供科学参考。

赤水桫椤自然保护区小灵猫及其潜在啮齿类猎物活动节律的季节适应格局

动物的日活动节律具有内源性且受外界生态因素(光周期、气候和食物等)影响,是动物生态适应性特征之一。阐明活动节律与气候和捕食者−猎物的关系,对于理解动物的生存策略、指导保护等至关重要。目前通过红外相机技术探究野生动物日活动节律日益受到学者们的关注。灵猫科动物是热带和亚热带生境中的重要次级消费者之一,但其野外相关研究甚少。本研究基于2016年12月至2022年7月在贵州赤水桫椤国家级自然保护区及其周边区域设置的60个红外相机位点监测影像资料,筛选小灵猫(Viverricula indica)及其相应监测位点的潜在啮齿类猎物数据。通过核密度函数比较分析了保护区内、外的小灵猫及其潜在啮齿类猎物在雨季、旱季的日活动节律特征。结果显示,小灵猫有明显的晨昏两个活动高峰,时间分别是03:00—06:00和19:00—24:00。季节比对发现,小灵猫雨季凌晨活动高峰(03:00—05:00)早于旱季(04:00—06:00),活动强度较旱季高且集中;黄昏后的活动较旱季有所延长。进一步分析其活动与潜在的啮齿类猎物的重叠度,结果发现小灵猫与赤腹松鼠(Callosciurus erythraeus)的重叠度整体较低(雨季,Δ=0.18;旱季,Δ=0.16);与夜行性鼠类的活动节律重叠度高达90%以上,其中旱季的重叠系数(Δ=0.93)高于雨季(Δ=0.90)。此外,在保护区内的小灵猫凌晨活动高峰结束较保护区外延迟约1 h;黄昏后高峰阶段的活动强度(核密度)峰值明显高于保护区外。少许日间活动也主要出现在保护区内。上述结果表明,小灵猫的昼夜节律既有保守性,也具有一定的季节可塑性。这些特征型表现与季节性猎物分布和环境变化关联,并受人类活动的影响。本研究结果对充分认识小灵猫生活史特征以及实现物种有效保护提供数据支持。