一类捕食者-食铒系统正周期解的存在性

利用重合度理论中的延拓定理研究了一类具有HollingⅡ型功能性反应的捕食者-食铒系统非平凡周期解的存在性,其中食饵种群服从Smith增长,捕食者种群具有密度制约效应。得到了存在正周期解的充分性判据,推广并改进了已知的相关结果。     

具避难所和Rosenzweig功能性反应的非自治两种群捕食者-食饵系统持久性与绝灭性研究

研究具有避难所和Rosenzweig功能性反应的非自治两种群捕食者-食饵系统的动力学行为,借助微分方程比较原理获得了保证系统持久性与绝灭性的一组充分性条件.我们的研究表明避难所的大小是影响捕食者种群绝灭的一个关键性因素.     

被捕食动物对捕食者的识别研究及在放归中的应用

对捕食者的认知能力是当前生态学研究的一个热点。一些物种具有对捕食者先天的识别能力,而一些物种必须通过后天学习才能获得对捕食者的认知能力,还有许多动物通过社会学习和文化传播获得对捕食者的识别能力。本文就国外被捕食动物对捕食者的识别的研究进展进行综述,并讨论了该项研究对野外放归工作提供的重要理论意义和应用价值。     

捕食者——食饵系统持久的充要条件及其分枝

本文研究了具无限时滞的捕食者-食系统的持续生存问题,得到了保证系统持续生存的充要条件,以此为基础,讨论了系统的持久性分枝问题．     

具性别偏食的二种群捕食者-食饵系统模型

本文根据生态学实验现象研究了一类二种群捕食者－食饵系统,其中捕食者对食饵有性别偏食情形。建立了相应的数学模型,并对该模型的有关性状进行了分析。     

捕食者-猎物关系的理论和应用研究

捕食者和猎物相互关系的研究,长期以来一直是动物生态学研究的中心课题之一。这种研究可区分为3种类型:第一是理论研究,即组建各种数学模型以便模拟捕食者和猎物间的相互关系;第二是实验种群研究,通常是在实验室内选用原生动物和节肢动物实验种群对捕食一猎物间的动态关系进行观察,并将观察结果与理论模型进行比较;第三是在田间对自然种群中的捕食者-猎物关系进行研究,并利用从理论研究和实验种群研究中所总结出来的各种基本原理对观察资料进行分析。在应用生态学领域中,常常靠引进新的更加有效的天敌来控制各种害虫。这些实际工作有些已获得成功,也有不少未取得预期效果,不管成功与否,它们都可被看作是对捕食者-猎物关系所进行的田间实验.     

一类捕食者与被捕食者模型的持久性与稳定性

研究了一类捕食者与被捕食者模型,该生态系统是一个食饵种群被一个捕食种群捕食.当给定参数满足一定条件下,利用比较原理和构造Lyapunov函数的方法,证明了系统的持久性和全局渐近稳定性,并讨论了正平衡点的渐近稳定性.     

用ELISA方法检测稻田捕食者对摇蚊的捕食作用

应用酶联免疫吸附（ELISA）双抗体夹心法,研究了稻田19种常见捕食性天敌对中性昆虫摇蚊的捕食作用。用摇蚊作抗原免疫雄性大白兔获得抗血清,用中和法、双向琼脂扩散实验及交叉反应对所制备的抗血清作特异性检测,抗体反应表明制备的抗血清对摇蚊抗原具有较高的特异性。测定了19种捕食者捕食摇蚊的临界吸收值。在检测的19种捕食者中,有13种捕食了摇蚊,占被检测捕食者种数的67.89％。ELISA阳性反应率最高的是在早稻前期采集的褶管巢蛛,阳性率高达50％,其次是晚稻中期采集的拟水狼蛛,其阳性率为40％。ELISA方法敏感,能快速检测捕食者对猎物的捕食作用及确定节肢类捕食者如蜘蛛对水稻害早控制作用大小,作为一种有效实验工具,可有助于发展水稻害虫综合管理理论。     

一类捕食者-食饵系统周期正解的全局存在性

利用Ｍａｗｈｉｎ重合度理论研究了一类具有偏差变元的捕食者－食饵系统周期正解的全局存在性问题,得到了一个新的存在性定理。     

Gause比率依赖型捕食者-食饵系统的周期解

考虑一类Gause比率依赖型捕食者-食饵系统,利用重合度理论中的延拓定理, 研究了全局周期解的存在性,得到保证周期解存在的充分条件．     

The stability of ecosystems: A brief overview of the paradox of enrichment

In theory, enrichment of resource in a predator-prey model leads to destabilization of the system,thereby collapsing the trophic interaction,a phenomenon referred to as "the paradox of enrichment". After it was first pro posed by Rosenzweig (1971), a number of subsequent studies were carried out on this dilemma over many decades. In this article, we review these theoretical and experimental works and give a brief overview of the proposed solutions to the paradox. The mechanisms that have been discussed are modifications of simple predator -prey models in the presence of prey that is inedible, invulnerable, unpalatable and toxic. Another class of mechanisms includes an incorporation of a ratio-dependent functional form,inducible defence of prey and density-dependent mortality of the predator. Moreover, we find a third set of explanations based on complex population dynamics including chaos in space and time. We conclude that,although any one of the various mechanisms proposed so far might potentially prevent destabilization of the predator-prey dynamics following enrichment, in nature different mechanisms may combine to cause stability, even when a system is enriched. The exact mechanisms,which may differ among systems,need to be disentangled through extensive field studies and laboratory experiments coupled with realistic theoretical models.     

Unpalatable prey resolves the paradox of enrichment

Enrichment is an increasingly serious trend in natural ecosystems. A theoretical model of a predator–prey system with a natural assumption of satiation in predation predicts that enrichment causes the populations to fluctuate to stochastic extinction. However, this ''paradox of enrichment'' does not always occur in experimental and natural communities. Here we present a theoretical model that describes a novel mechanism for resolving the paradox in the case of a predator with optimal selective feeding. Specifically, a less profitable but edible (thus `unpalatable'') prey species sharply reduces the amplitude of population oscillations and firmly prevents the minimum abundances of species from falling below certain values. The presence of such an unpalatable prey thus guarantees the robustness of the system against enrichment.     

A resolution of the paradox of enrichment

Theoretical studies have shown a paradoxical destabilizing response of predator-prey ecosystems to enrichment, but there is the gap between the intuitive view of nature and this theoretical prediction. We studied a minimal predator-prey system (a two predator-two prey system) in which the paradox of enrichment pattern can vanish; the destabilization with enrichment is reversed, leading to stabilization (a decrease in the amplitude of oscillation of population densities). For resolution of the paradox, two conditions must be met: (1) the same prey species must be preferred as a dietary item by both predator species, creating the potential for high exploitative competition between the predator species, and (2), while both predators are assumed to select their diet in accordance with optimal diet utilization theory, one predator must be a specialist and the other a generalist. In this system, the presence of a less profitable prey species can cause the increase in population oscillation amplitudes associated with increasing enrichment to be suppressed via the optimal diet utilization of the generalist predator. The resulting stabilization is explained by the mitigating effect of the less profitable prey showing better population growth with increasing enrichment on the destabilization underlying the specialist predator and prey relation, thus resolving the paradox of enrichment.     

Enrichment and stability: a phenomenological coupling of energy value and carrying capacity

Simple predator-prey models with a prey-dependent functional response predict that enrichment (increased carrying capacity) destabilizes community dynamics: this is the 'paradox of enrichment'. However, the energy value of prey is very important in this context. The intraspecific chemical composition of prey species determines its energy value as a food for the potential predator. Theoretical and experimental studies establish that variable chemical composition of prey affects the predator-prey dynamics. Recently, experimental and theoretical approaches have been made to incorporate explicitly the stoichiometric heterogeneity of simple predator-prey systems. Following the results of the previous experimental and theoretical advances, in this article we propose a simple phenomenological formulation of the variation of energy value at increased level of carrying capacity. Results of our study demonstrate that coupling the parameters representing the phenomenological energy value and carrying capacity in a realistic way, may avoid destabilization of community dynamics following enrichment. Additionally, under such coupling the producer-grazer system persists for only an intermediate zone of production--a result consistent with recent studies. We suggest that, while addressing the issue of enrichment in a general predator-prey model, the phenomenological relationship that we propose here might be applicable to avoid Rosenzweig's paradox.     

The effect of predator limitation on the dynamics of simple food chains

We investigate the influence of competition between predators on the dynamics of bitrophic predator–prey systems and of tritrophic food chains. Competition between predators is implemented either as interference competition, or as a density-dependent mortality rate. With interference competition, the paradox of enrichment is reduced or completely suppressed, but otherwise, the dynamical behavior of the systems is not fundamentally different from that of the Rosenzweig–MacArthur model, which contains no predator competition and shows only continuous transitions between fixed points or periodic oscillations. In contrast, with density-dependent predator mortality, the system shows a surprisingly rich dynamical behavior. In particular, decreasing the density regulation of the predator can induce catastrophic shifts from a stable fixed point to a large oscillation where the predator chases the prey through a cycle that brings both species close to the threshold of extinction. Other catastrophic bifurcations, such as subcritical Hopf bifurcations and saddle-node bifurcations of limit cycles, do also occur. In tritrophic food chains, we find again that fixed points in the model with predator interference become unstable only through Hopf bifurcations, which can also be subcritical, in contrast to the bitrophic situation. The model with a density limitation shows again catastrophic destabilization of fixed points and various nonlocal bifurcations. In addition, chaos occurs for both models in appropriate parameter ranges.     

Yield and dynamics of tritrophic food chains

Strong relationships between yield and dynamic behavior of tritrophic food chains are pointed out by analyzing the classical Rosenzweig-MacArthur model. On the one hand, food chains are subdivided into undersupplied and oversupplied categories, the first being those in which a marginal increase of nutrient supply to the bottom produces a marginal increase of mean yield at the top. On the other hand, a detailed bifurcation analysis proves that dynamic complexity first increases with nutrient supply (from stationary to a low-frequency cyclic regime and, finally, to chaos) and then decreases (from chaos to a high-frequency cyclic regime). A careful comparison of the two analyses supports the conclusion that food chains cycling at high frequency are oversupplied, while all others are undersupplied. A straightforward consequence of this result is that maximization of food yield requires a chaotic regime. This regime turns out to be very often on the edge of a potential catastrophic collapse of the top component of the food chain. In other words, optimality implies very complex and dangerous dynamics, as intuitively understood long ago for ditrophic food chains by Rosenzweig in his famous article on the paradox of enrichment.     

The paradox of enrichment in an adaptive world

Paradoxically, enrichment can destabilize a predator-prey food web. While adaptive dynamics can greatly influence the stability of interaction systems, few theoretical studies have examined the effect of the adaptive dynamics of interaction-related traits on the possibility of resolution of the paradox of enrichment. We consider the evolution of attack and defence traits of a predator and two prey species in a one predator-two prey system in which the predator practises optimal diet use. The results showed that optimal foraging alone cannot eliminate a pattern of destabilization with enrichment, but trait evolution of the predator or prey can change the pattern to one of stabilization, implying a possible resolution of the paradox of enrichment. Furthermore, trait evolution in all species can broaden the parameter range of stabilization. Importantly, rapid evolution can stabilize this system, but weaken its stability in the face of enrichment.     

Cross-ecosystem differences in stability and the principle of energy flux

Here, we review consumer-resource (C-R) theory to show that the paradox of enrichment is a special case of a more general theoretical result. That is, we show that increased energy flux, relative to the consumer loss rate, makes C-R interactions top heavy (i.e., greater C:R biomass ratio) and less stable. We then review the literature on the attributes of aquatic and terrestrial ecosystems to argue that empirical estimates of parameters governing energy flux find that aquatic ecosystems have higher rates of relative energy flux than terrestrial ecosystems. Consistent with theory, we then review empirical work that shows aquatic ecosystems have greater herbivore:plant biomass ratios while we produce novel data to show that aquatic ecosystems have greater variability in population dynamics than their terrestrial counterparts. We end by arguing that theory, allometric relationships and a significant, negative correlation between body size and population variability suggest that these results may be driven by the smaller average body sizes of aquatic organisms relative to terrestrial organisms.     

Enrichment can damp population cycles: a balance of inflexible and flexible interactions

Destabilization of one predator–one prey systems with an increase in nutrient input has been viewed as a paradox. We report that enrichment can damp population cycles by a food‐web structure that balances inflexible and flexible interaction links (i.e. specialist and generalist predators). We modeled six predator–prey systems involving three or four species in which the predators practice optimal foraging based on prey profitability determined by handling time. In all models, the balance of interaction links simultaneously decreased the amplitude of population oscillations and increased the minimum density with increasing enrichment, leading to a potential theoretical resolution of the paradox of enrichment in non‐equilibrium dynamics. The stabilization mechanism was common to all of the models. Important previous studies on the stability of food webs have also demonstrated that a balance of interaction strengths stabilizes systems, suggesting a general rule of ecosystem stability.     

Homage to the red queen. II. Coevolutionary response to enrichment of exploitation ecosystems

The model of predator-victim coevolution developed in the preceding paper (Schaffer and Rosenzweig, 1978) is used to analyze the coevolutionary response to ecosystem enrichment. It is shown that coevolution tends to oppose the destabilization that results from the enrichment itself. In the circumstance that the victims' r and K are proportional, gradual enrichment followed by coevolutionary adjustment actually enhances ecosystem stability.