Functional responses and scaling in predator-prey interactions of marine fishes: contemporary issues and emerging concepts

Predator-prey interactions are a primary structuring force vital to the resilience of marine communities and sustainability of the world's oceans. Human influences on marine ecosystems mediate changes in species interactions. This generality is evinced by the cascading effects of overharvesting top predators on the structure and function of marine ecosystems. It follows that ecological forecasting, ecosystem management, and marine spatial planning require a better understanding of food web relationships. Characterising and scaling predator-prey interactions for use in tactical and strategic tools (i.e. multi-species management and ecosystem models) are paramount in this effort. Here, we explore what issues are involved and must be considered to advance the use of predator-prey theory in the context of marine fisheries science. We address pertinent contemporary ecological issues including (1) the approaches and complexities of evaluating predator responses in marine systems; (2) the 'scaling up' of predator-prey interactions to the population, community, and ecosystem level; (3) the role of predator-prey theory in contemporary fisheries and ecosystem modelling approaches; and (4) directions for the future. Our intent is to point out needed research directions that will improve our understanding of predator-prey interactions in the context of the sustainable marine fisheries and ecosystem management.     

Effects of crop species richness on pest-natural enemy systems based on an experimental model system using a microlandscape

The relationship between crop richness and predator-prey interactions as they relate to pest-natural enemy systems is a very important topic in ecology and greatly affects biological control services. The effects of crop arrangement on predator-prey interactions have received much attention as the basis for pest population management. To explore the internal mechanisms and factors driving the relationship between crop richness and pest population management, we designed an experimental model system of a microlandscape that included 50 plots and five treatments. Each treatment had 10 repetitions in each year from 2007 to 2010. The results showed that the biomass of pests and their natural enemies increased with increasing crop biomass and decreased with decreasing crop biomass; however, the effects of plant biomass on the pest and natural enemy biomass were not significant. The relationship between adjacent trophic levels was significant (such as pests and their natural enemies or crops and pests), whereas non-adjacent trophic levels (crops and natural enemies) did not significantly interact with each other. The ratio of natural enemy/pest biomass was the highest in the areas of four crop species that had the best biological control service. Having either low or high crop species richness did not enhance the pest population management service and lead to loss of biological control. Although the resource concentration hypothesis was not well supported by our results, high crop species richness could suppress the pest population, indicating that crop species richness could enhance biological control services. These results could be applied in habitat management aimed at biological control, provide the theoretical basis for agricultural landscape design, and also suggest new methods for integrated pest management.     

Critical slowing down as an indicator of transitions in two-species models

Transitions in ecological systems often occur without apparent warning, and may represent shifts between alternative persistent states. Decreasing ecological resilience (the size of the basin of attraction around a stable state) can signal an impending transition, but this effect is difficult to measure in practice. Recent research has suggested that a decreasing rate of recovery from small perturbations (critical slowing down) is a good indicator of ecological resilience. Here we use analytical techniques to draw general conclusions about the conditions under which critical slowing down provides an early indicator of transitions in two-species predator-prey and competition models. The models exhibit three types of transition: the predator-prey model has a Hopf bifurcation and a transcritical bifurcation, and the competition model has two saddle-node bifurcations (in which case the system exhibits hysteresis) or two transcritical bifurcations, depending on the parameterisation. We find that critical slowing down is an earlier indicator of the Hopf bifurcation in predator-prey models in which prey are regulated by predation rather than by intrinsic density-dependent effects and an earlier indicator of transitions in competition models in which the dynamics of the rare species operate on slower timescales than the dynamics of the common species. These results lead directly to predictions for more complex multi-species systems, which can be tested using simulation models or real ecosystems.     

Disease-induced stabilization of predator-prey oscillations

Parasites are an integral part of virtually all food webs and species communities. Here we consider the invasion of a resident predator-prey system by an infectious disease with frequency-dependent transmission spreading within the predator population. We derive biologically plausible and insightful quantities (demographic and epizootiological reproduction numbers) that allow us to completely determine community composition. Successful disease invasion can have two contrary effects in driving its host population to extinction or in stabilizing predator-prey cycles. Our findings contradict predictions from previous models suggesting a destabilizing effect of parasites. We show that predator infection counteracts the paradox of enrichment. In turn, parasite removal from food webs can have catastrophic effects. We discuss the implications for biological control and resource management on more than one trophic level.     

Machine learning based control rights analysis of critical resources and the optimal ownership for management integration

The paper first divides control rights of critical resources into government macroeconomic regulation power and insider control power for the management. After the discussion of the current status of Chinese coal industry integration, the paper mathematically and empirically analyzes influences of the government and state owned enterprises’ management to ownership’s boundary, and suggests the optimal ownership in different cases. The contributions of the paper are as follows: (1) Based on incomplete contract theory, the paper builds two mathematical models -the model of management’s investment level of relationship-specific human capital and ownership boundary model demonstrating the government utility under different ownership cases; (2) With the application of numerical simulation and empirical test, the paper analyzes impacts on coal resource integration from the aspects of government regulation and insider control, and discusses the optimal option of ownerships. By the analysis of the control power and ownership boundary based on the models, the paper eventually raises the optimal option of ownership allocation.     

A ratio-dependent food chain model and its applications to biological control

While biological controls have been successfully and frequently implemented by nature and human, plausible mathematical models are yet to be found to explain the often observed deterministic extinctions of both pest and control agent in such processes. In this paper we study a three trophic level food chain model with ratio-dependent Michaelis-Menten type functional responses. We shall show that this model is rich in boundary dynamics and is capable of generating such extinction dynamics. Two trophic level Michaelis-Menten type ratio-dependent predator-prey system was globally and systematically analyzed in details recently. A distinct and realistic feature of ratio-dependence is its capability of producing the extinction of prey species, and hence the collapse of the system. Another distinctive feature of this model is that its dynamical outcomes may depend on initial populations levels. Theses features, if preserved in a three trophic food chain model, make it appealing for modelling certain biological control processes (where prey is a plant species, middle predator as a pest, and top predator as a biological control agent) where the simultaneous extinctions of pest and control agent is the hallmark of their successes and are usually dependent on the amount of control agent. Our results indicate that this extinction dynamics and sensitivity to initial population levels are not only preserved, but also enriched in the three trophic level food chain model. Specifically, we provide partial answers to questions such as: under what scenarios a potential biological control may be successful, and when it may fail. We also study the questions such as what conditions ensure the coexistence of all the three species in the forms of a stable steady state and limit cycle, respectively. A multiple attractor scenario is found.     

Biological control through provision of additional food to predators: a theoretical study

In this paper we analyze a variation of a standard predator-prey model with type II functional response which represents predator-prey dynamics in the presence of some additional food to the predator. The aim is to study the consequences of providing additional food on the system dynamics. We conclude that handling times for the available foods play a key role in determining the eventual state of the ecosystem. It is interesting to observe that by varying the quality and quantity of additional food we can not only control and limit the prey, but also limit and eradicate the predators. In the context of biological pest control, the results caution the manager on the choice of quality and quantity of the additional food used for this purpose. An arbitrary choice may have opposite effects leading to increase in pest concentration and eradication of the predator. This study offers insight into the possible management strategies that involve manipulation of quality and supply level of additional food to predators, for the benefit of biological control. The theoretical conclusions agree with results of some practical biological control experiments.     

Predator-prey interactions in natural communities.

The familiar concepts of harvest and yield are developed for the purpose of describing predator-prey interactions in a community context. In this regard the functional response (appropriate for one predator-one prey systems) is replaced by a community harvest function. Conditions for the stability of an ecological community are obtained. Exploring the dynamics of predator-prey interactions within this framework leads to new interpretations of other dynamical models such as the Lotka-Volterra model. The concept of a community moving attractor point is introduced in order to describe the changes in all populations over time.     

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.     

一类具分段常数变量的捕食-食饵系统的Neimark-Sacker分支

讨论了具时滞与分段常数变量的捕食-食饵生态模型的稳定性及Neimark-Sacker分支;通过计算得到连续模型对应的差分模型,基于特征值理论和Schur-Cohn判据得到正平衡态局部渐进稳定的充分条件;以食饵的内禀增长率为分支参数,运用分支理论和中心流形定理分析了Neimark-Sacker分支的存在性与稳定性条件;通过举例和数值模拟验证了理论的正确性。     

A universal bifurcation diagram for seasonally perturbed predator-prey models

The bifurcations of a periodically forced predator-prey model (the chemostat model), with a prey feeding on a limiting nutrient, are numerically detected with a continuation technique. Eight bifurcation diagrams are produced (one for each parameter in the model) and shown to be topologically equivalent. These diagrams are also equivalent to those of the most commonly used predator-prey model (the Rosenzweig-McArthur model). Thus, all basic modes of behavior of the two main predator-prey models can be explained by means of a single bifurcation diagram.     

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.     

Cannibalism in an age-structured predator-prey system

Recently, Kohlmeier and Ebenhöh showed that cannibalism can stabilize population cycles in a Lotka-Volterra type predator-prey model. Population cycles in their model are due to the interaction between logistic population growth of the prey and a hyperbolic functional response. In this paper, we consider a predator-prey system where cyclic population fluctuations are due to the age structure in the predator species. It is shown that cannibalism is also a stabilizing mechanism when population oscillations are due to this age structure. We conclude that in predator-prey systems, cannibalism by predators can stabilize both externally generated (consumer-resource) as well as internally generated (agestructure) fluctuations.     

Ecological Interactions Involving Feral Horses and Predators: Review with Implications for Biodiversity Conservation

For many ecosystems, feral horses are increasingly becoming an important if not dominant component of ungulate biomass and hence influence on community dynamics. Yet we still know little of how horses contribute to key ecological interactions including predator-prey and indirect competitive relationships at a community level. Notably, feral species like horses can exhibit life-history traits that differ from that of native (mainly artiodactyl) herbivore competitors. Artificial selection for traits like increased, early, or extended reproduction that have yet to be reversed by natural selection, coupled with naturally selected differences in anatomy and behavior, in addition to unique management objectives for horses compared to other species, means that the dynamics of feral horse populations are not likely to align with what might be expected of other large herbivores. Unexpected population dynamics and inherent biological asymmetries between native ungulates and feral horses may therefore influence the former via direct competition for shared resources and through enemy-mediated interactions like apparent competition. In several localities feral horses now co-exist with multiple native prey species, some of which are in decline or are species at risk. Compounding risks to native species from direct or indirect competitive exclusion by horses is the unique nature and socio-political context of feral horse management, which tends towards allowing horse populations to be limited largely by natural, density-dependent factors. We summarize the inherent asymmetries between feral horse biology and that of other ungulate prey species with consequences for conservation, focusing on predator-prey and emerging indirect interactions in multi-prey systems, and highlight future directions to address key knowledge gaps in our understanding of how feral horses may now be contributing to the (re)structuring of food webs. Observations of patterns of rapid growth and decline, and associated skews in sex ratios of feral horse populations, indicate a heightened potential for indirect interactions among large ungulate prey species, where there is a prevalence of feral horses as preferred prey, particularly where native prey are declining. In places like western North America, we expect predator-prey interactions involving feral horses to become an increasingly important factor in the conservation of wildlife. This applies not only to economically or culturally important game species but also at-risk species, both predators (e.g., wolves [Canis lupus], grizzly bears [Ursus arctos]) and prey (e.g., woodland caribou [Rangifer tarandus caribou]), necessitating an ecological understanding of the role of horses in natural environments that goes beyond that of population control. © 2021 The Wildlife Society.     

食饵庇护所对斑块环境下Leslie-Gower捕食系统的影响

建立了一个显式含有空间庇护所的两斑块Leslie-Gower捕食者-食饵系统。假设只有食饵种群在斑块间以常数迁移率迁移,且在每个斑块上食饵间的迁移比局部捕食者-食饵相互作用发生的时间尺度要快。利用两个时间尺度,可以构建用来描述所有斑块总的食饵和捕食者密度的综合系统。数学分析表明,在一定条件下,存在唯一的正平衡点,并且此平衡点全局稳定。进一步,捕食者的数量随着食饵庇护所数量增加而降低;在一定条件下,食饵的数量随着食饵庇护所数量增加先增加后降低,在足够强的庇护所强度下,两物种出现灭绝。对比以往研究,利用显式含有和隐含空间庇护所的数学模型所得结论不一致,这意味着在研究庇护所对捕食系统种群动态影响时,空间结构可能起着重要作用。     

Qualitative dynamics of three species predator-prey systems

Summary A qualitative analysis of some two and three species predator-prey models is achieved by application of the method of averaging in conjunction with a Lyapunov function constructed from the appropriate Volterra-Lotka model. We calculate the limit cycle solution for a two-species model with a Holling type functional response of the predator to its prey by means of a time-scaled transformation. The existence of a bifurcation of steady states for a community of three species is discussed and the periodic solution around one of the unstable steady states is calculated to the lowest approximation. Several comments are made regarding the behavior of these systems under changes of some control parameters.This work was supported in parts by USERDA, Contract number E(11-1)-3001.     

Invasive species management in two-patch environments: agricultural damage control in the raccoon (<Emphasis Type="Italic">Procyon lotor</Emphasis>) problem,Hokkaido, Japan

We develop discrete-time models for analyzing the long-run equilibrium outcomes on invasive species management in two-patch environments with migration. In particular, the focus is on a situation where removal operations for invasive species are implemented only in one patch (controlled patch). The new features of the model are that (1) asymmetry in density-dependent migration is considered, which may originate from impact of harvesting as well as heterogeneous habitat conditions, and (2) the effect of density-dependent catchability accounts for the fact that the required effort level to remove one individual may rise as the existing population decreases. The model is applied to agricultural damage control in the raccoon (Procyon lotor) problem that has occurred in Hokkaido, Japan. Numerical illustrations demonstrate that the long-run equilibrium outcomes largely depend on the degree of asymmetry in migration as well as the sensitivity of catchability in response to a change in the population size of the invasive species. Furthermore, we characterize the conditions under which the economically optimal effort levels are qualitatively affected by the above two factors, and conclude that aiming at local extermination of invasive species in the controlled patch is justified. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Stability analysis of a predator-prey system with mutual interference and density-dependent death rates

A two species predator-prey model is proposed incorporating the notions of mutual interference among predators as well as a density-dependent predator death rate. The latter leads to a curved predator isocline. Conditions for an interior equilibrium are given, and the stability of this equilibrium is analyzed. Certain critical cases, some of which cannot occur in the usual model are also discussed.