The responses of unstable food chains to enrichment

Summary This article investigates the mean abundances of trophic levels in simple models of two- and three-level food chains as a function of the rate of input of nutrients. The analysis concentrates on cases in which the equilibrium point with all species present is unstable. In most of the models, the instability arises because the consumer species become satiated when food density is high. In unstable two-level systems, bottom level abundance generally increases with increased nutrient input. The abundance of the second level may decrease with increased input. Changes in the intrinsic rate of increase and carrying capacity of the bottom level can have qualitatively opposite effects on trophic level abundances. Refuges for or immigration of the bottom level usually cause both levels to increase in mean abundance with an increased carrying capacity. A variety of different predator—prey models are discussed briefly and the results suggest that increased nutrient input will often increase the abundance of both levels; however, several circumstances can cause the top level to decrease. In three-level systems, an increased carrying capacity can cause extinction of the top level. Extinction may or may not be conditional on the initial densities of the three levels. These results may help explain the observed lack of correlation between productivity and the number of trophic levels in natural food webs, as well as the lack of very long food chains. The results suggest that patterns of abundances across productivity gradients cannot be used to assess the importance of top-down vs bottom-up effects.     

Trophic cascades and trophic trickles in pelagic food webs

Prey-dependent models, with the predation rate (per predator) a function of prey numbers alone, predict the existence of a trophic cascade. In a trophic cascade, the addition of a top predator to a two-level food chain to make a three-level food chain will lead to increases in the population size of the primary producers, and the addition of nutrients to three-level chains will lead to increases in the population numbers at only the first and third trophic levels. In contrast, ratio-dependent models, with the predation rate (per predator) dependent on the ratio of predator numbers to prey, predict that additions of top predators will not increase the population sizes of the primary producers, and that the addition of nutrients to a three-level food chain will lead to increases in population numbers at all trophic levels. Surprisingly, recent meta-analyses show that freshwater pelagic food web patterns match neither prey-dependent models (in pelagic webs, ''prey'' are phytoplankton, and ''predators'' are zooplankton), nor ratio-dependent models. In this paper we use a modification of the prey-dependent model, incorporating strong interference within the zooplankton trophic level, that does yield patterns matching those found in nature. This zooplankton interference model corresponds to a more reticulate food web than in the linear, prey-dependent model, which lacks zooplankton interference. We thus reconcile data with a new model, and make the testable prediction that the strength of trophic cascades will depend on the degree of heterogeneity in the zooplankton level of the food chain.     

Bottom-up trophic cascades and material transfer in terrestrial food webs

In contrast to top-down trophic cascades, few reviews have appeared of bottom-up trophic cascades. We review the recent development of research on bottom-up cascades in terrestrial food webs, focusing on tritrophic systems consisting of plants, herbivorous insects, and natural enemies, and attempt to integrate bottom-up cascade and material transfer among trophic levels. Bottom-up cascades are frequently reported in various tritrophic systems, and are important to determine community structure, population dynamics, and individual performance of higher trophic levels. In addition, we highlight several features of bottom-up cascades. Accumulation or dilution of plant nutritional and defensive materials by herbivorous insects provides a mechanistic base for several bottom-up cascades. Such a stoichiometric approach has the potential to improve our understanding of bottom-up cascading effects in terrestrial food webs. We suggest a future direction for research by integration of bottom-up cascades and material transfer among trophic levels.     

The relative importance of herbivory and carnivory on the distribution of energy in a stochastic tri-trophic food web

A three-state, discrete-time Markov chain is used to model the dynamics of energy flow in a tri-trophic food web. The distribution of energy in the three trophic levels is related to the rates of flow between the trophic levels and calculated for the entire range of possible flow values. These distributions are then analysed for stability and used to test the idea that plants are resource-limited and herbivores are predation-limited. Low rates of death and decomposition, when coupled with low rates of herbivory and carnivory, tend to destabilize this food web. Food webs with higher rates of death and decomposition are relatively more stable regardless of rates of herbivory and carnivory. Plants are more prone to resource-limitation and herbivores are, in general, limited by their predators, which supports Hairston et al. (Am. Nat. 94 (1960) 421). The rate of decomposition often mediates the roles of top-down and bottom-up control of energy flow in the food web.     

Modelling the role of highly unsaturated fatty acids in planktonic food web processes: Sensitivity analysis and examination of contemporary hypotheses

Aquatic food web models typically treat the constituent trophic levels as static elements interacting with one another and the environment. Dynamic biological stoichiometry has relaxed this assumption and considers evolutionary responses in said elements. The incorporation of organismal response in food web models holds promise for a more realistic portrayal of ecosystem dynamics. Recent advances in aquatic ecology pinpoint the importance of highly unsaturated fatty acids (HUFAs) on food web interactions and ecosystem resilience. In this study, we utilized a HUFA explicit submodel in conjunction with a limiting nutrient–phytoplankton–zooplankton–detritus (NPZD) mathematical system to incorporate elements of the physiology of individual animals into the context of plankton dynamics. Our HUFA-augmented plankton model provided a realistic platform to examine functional properties and physiological strategies that modulate resource procurement in different trophic environments and to effectively link variability at the organismal level with ecosystem-scale patterns. First, we were able to illustrate the implications of the filling-cup hypothesis, in which species’ fitness stems from dynamic HUFA turnover rates in response to bottom-up stresses. We then examined an evolutionary hypothesis of consumer fitness dependence on HUFA quota management strategies, whereby adaptive individuals with low HUFA minimum and optimum requirements gain competitive advantage. Several studies have reported higher HUFA concentrations in consumers than producers, and our results suggest that this pattern could be driven by a combination of conservative turnover and elevated bioconversion rates. Oligotrophic settings showed strong reliance upon exogenous phosphorus subsidies and frequently yielded inverted food web biomass distributions. With the prevalence of eutrophic conditions, consumer growth is primarily controlled by HUFA availability, and the associated biochemical limitation can ultimately result in patterns of algal accumulation. Finally, our study discusses directions to improve the representation of the producer–grazer interactions and thus advance our understanding of the factors that determine the flow of nutrients and energy to the higher trophic levels.     

Global patterns of aquatic food chain length

Food chain length is a fundamental ecosystem property, and plays a central role in determining ecosystem functioning. Recent advances in the field of stable isotope ecology allow the estimation of food chain length (FCL) from stable nitrogen isotope (δ¹⁵N) data. We conducted a global literature synthesis and estimated FCL for 219 lake, stream, and marine ecosystems. Streams had shorter food chains (∼3.5 trophic levels) than marine and lake ecosystems (∼4.0 trophic levels). In marine systems, inclusion of marine mammals increased FCL by 2/3 of a trophic level. For each ecosystem type, estimates of FCL were normally distributed and spanned two full trophic levels. Comparison with published connectance food webs revealed similar mean FCL values, though stable isotope-derived FCL estimates were less variable. At the global scale, FCL showed weak or no relationships with ecosystem size, mean annual air temperature, or latitude. Our study highlights the utility of stable isotopes for quantifying among-system food web variability, and the application of this approach for assessing global-scale patterns of food chain length.     

Trophic exploitation in grassland food chains: simple models and a field experiment

This study provides insight into the importance of top carnivores (top-down control) and nutrient inputs (bottom-up control) in structuring food chains in a terrestrial grassland system. Qualitative predictions about food chain structure are generated using 4 simple models, each differing in assumptions about some key component in the population dynamics of the herbivore trophic level. The four model systems can be classified broadly into two groups (1) those that assume plant resource intake by herbivores is limited by search rate and handling time as described by classic Lotka-Volterra models; and (2) those that assume plant resource intake by herbivores is limited externally by the supply rate of resources as described by alternatives to Lotka-Volterra formulations. The first class of models tends to ascribe greater importance to top-down control of food chain structure whereas the second class places greater weight on bottom-up control. I evaluated the model predictions using experimentally assembled grassland food chains in which I manipulated nutrient inputs and carnivore (wolf spider) abundance to determine the degree of top-down and bottom-up control of grassland plants and herbivores (grasshoppers). The experimental results were most consistent with predictions of the second class of models implying a predominance of bottom-up control of food chain structure.     

Ratio-dependent response of a temperate Australian estuarine system to sustained nitrogen loading

Classical resource- and the less studied ratio-dependent models of predator–prey relationships provide divergent predictions as to the sustained ecological effects of bottom-up forcing. While resource-dependent models, which consider only instantaneous prey density in modelling predator responses, predict community responses that are dependent on the number of trophic levels in a system, ratio-dependent models, which consider the number of prey per consumer, predict proportional increase in each level irrespective of chain length. The two models are only subtly different for systems with two or three trophic levels but in the case of four trophic levels, predict opposite effects of enrichment on primary producers. Despite the poor discriminatory power of tests of the models in systems with two or three trophic levels, field tests in estuarine and marine systems with four trophic levels have been notably absent. Sampling of phytoplankton, macroinvertebrates, invertebrate-feeding fishes, piscivorous fishes in Kooloonbung Creek, Hastings River estuary, eastern Australia, subject to over 20 years of sewage discharge, revealed increased abundances in all four trophic levels at the disturbed location relative to control sites. Increased abundance of phytoplankton at the disturbed site was counter to the predictions of resource-dependent models, which posit a reduction in the first trophic level in response to enrichment. By contrast, the increase in abundance of this first trophic level and the proportionality of increases in abundances of each of the four trophic groups to nitrogen loading provided strong support for ratio dependency. This first evidence of ratio dependence in an estuarine system with four trophic levels not only demonstrates the applicability of ecological theory which seeks to simplify the complexity of systems, but has implications for management. Although large nutrient inputs frequently induce mortality of invertebrates and fish, we have shown that smaller inputs may in fact enhance biomass of all trophic levels.     

Multiple attractors and boundary crises in a tri-trophic food chain

The asymptotic behaviour of a model of a tri-trophic food chain in the chemostat is analysed in detail. The Monod growth model is used for all trophic levels, yielding a non-linear dynamical system of four ordinary differential equations. Mass conservation makes it possible to reduce the dimension by 1 for the study of the asymptotic dynamic behaviour. The intersections of the orbits with a Poincaré plane, after the transient has died out, yield a two-dimensional Poincaré next-return map. When chaotic behaviour occurs, all image points of this next-return map appear to lie close to a single curve in the intersection plane. This motivated the study of a one-dimensional bi-modal, non-invertible map of which the graph resembles this curve. We will show that the bifurcation structure of the food chain model can be understood in terms of the local and global bifurcations of this one-dimensional map. Homoclinic and heteroclinic connecting orbits and their global bifurcations are discussed also by relating them to their counterparts for a two-dimensional map which is invertible like the next-return map. In the global bifurcations two homoclinic or two heteroclinic orbits collide and disappear. In the food chain model two attractors coexist; a stable limit cycle where the top-predator is absent and an interior attractor. In addition there is a saddle cycle. The stable manifold of this limit cycle forms the basin boundary of the interior attractor. We will show that this boundary has a complicated structure when there are heteroclinic orbits from a saddle equilibrium to this saddle limit cycle. A homoclinic bifurcation to a saddle limit cycle will be associated with a boundary crisis where the chaotic attractor disappears suddenly when a bifurcation parameter is varied. Thus, similar to a tangent local bifurcation for equilibria or limit cycles, this homoclinic global bifurcation marks a region in the parameter space where the top-predator goes extinct. The 'Paradox of Enrichment' says that increasing the concentration of nutrient input can cause destabilization of the otherwise stable interior equilibrium of a bi-trophic food chain. For a tri-trophic food chain enrichment of the environment can even lead to extinction of the highest trophic level.     

Return time and vulnerability for a food chain model

Simulation studies have shown that the time it takes for a system of interacting species in a food chain to return to equilibrium after a disturbance increases as the number of trophic levels increase. It has been argued that this effect is important in limiting the length of food chains subject to perturbations of the real world. We show that for an asymptotically stable system a lower bound on the return time is directly proportional to the number of trophic levels in agreement with simulation studies. In addition, the lower bound on the return time is shown to be inversely proportional to the sum of products of the intraspecific competition coefficient and equilibrium population of the species. A new method for directly computing the vulnerability of a system to external perturbations is presented. Using this method we demonstrate that for a food chain where the number of species is equal to the number of trophic levels, the return time alone is not a proper measure of system vulnerability. Indeed, adding an additional trophic level may make the system less vulnerable to disturbances. Interspecific coupling between the trophic levels is shown to be an important factor in determining system vulnerability.     

北部湾生态通道模型的构建

根据1997年～1999年在北部湾进行的渔业资源和生态环境调查数据,利用EwE软件构建北部湾生态系统的营养通道模型,模型由16个功能组构成,包括了哺乳动物和海鸟,每一组都代表在生态系统中具有相似地位的有机体,基本覆盖了北部湾生态系统能量流动的主要过程.模型分析表明,北部湾生态系统的能量流动主要以捕食食物链途径为主,其中无脊椎动物在能量从低级向高层次转换中起关键作用.各功能组的营养级范围为1.00～4.04,哺乳动物占据了最高营养层.生态网络分析表明,系统的能量流动主要有6级,来自初级生产者的能流效率为12.2%,来自碎屑的转换效率为12.3%,平均能量转换效率为12.2%.模型估算的可利用的生物量密度为8.7 t·km^-2,生态系统的生物生产量只占系统净初级生产力的1.81%.当前北部湾海洋生态系统处于不稳定状态.     

The dynamics of top-down and bottom-up effects in food webs of varying prey diversity, composition, and productivity

Prey diversity is thought to mediate the strength of top-down and bottom-up effects, but few experiments directly test this hypothesis. I assembled food webs of bacteria and bacterivorous protist prey in laboratory microcosms with all combinations of five productivity levels, two top predator treatments (present or absent), and three prey compositions. Depauperate food chains contained one of two edible prey species, while more diverse food webs contained both edible prey species plus two additional less-edible/inedible prey. Equilibrium theory predicts that prey diversity should weaken the top-down and bottom-up effects on trophic level biomasses, due to density compensation among prey species. Top-down effects should increase with productivity in food chains, but decrease with productivity in food webs. Results revealed highly dynamic top-down effects, the strength of which varied more over time than among treatments. Further, top-down effects did not merely vary in absolute strength over time, but also in relative strength across different prey compositions and productivity levels. It might be expected that equilibrium models would qualitatively reproduce time-averaged results. However, time-averaged data largely failed to support equilibrium predictions. This failure may reflect strong temporal variability in treatment effects combined with nonlinear density dependence of species' per-capita growth rates. Strong temporal variability in the strength of top-down effects has not previously been demonstrated, but likely is common in nature as well.     

互利关系和植物多样性对节肢动物群落不同营养级的影响路径和强度

食物网中的上行效应和下行效应对于群落的动态和生态系统功能有十分重要的影响,旨在探讨互利关系和植物多样性对节肢动物群落中食物网不同营养级之间的影响。通过随机裂区试验方法,分别设置了3种蚂蚁-紫胶虫互利关系处理(有互利关系、无互利关系和自然对照)以及3种植物多样性处理(单一种植、2树种混植和3树种混植),于2016年8月和9月分两次用手捡法、网扫法和震落法采集试验地寄主植物上所有的节肢动物,并按照不同营养级将其分类。利用结构方程模型分析方法对不同营养级之间的相互作用的路径和强度进行了比较,结果显示:1)互利关系对捕食者和消费者均有显著的下行作用,有互利关系处理下蚂蚁对捕食者的路径强度要强于自然对照组,互利关系对捕食者的影响要强于对消费者的影响。2)植物多样性会通过影响植物的生物量而对消费者和捕食者产生显著的上行效应影响,这种影响会随着营养级的升高而显著减小。3)消费者主要受植物多样性的上行效应影响,而捕食者主要受互利关系的下行效应影响。有互利关系的食物网结构更加复杂,营养级之间的相互作用更为显著。探讨了以蚂蚁-紫胶虫互利关系为核心作用的紫胶林生态系统中互利关系和植物多样性对节肢动物食物网中...     

Habitat structure alters top-down control in litter communities

The question whether top-down or bottom-up forces dominate trophic relationships, energy flow, and abundances within food webs has fuelled much ecological research with particular focus on soil litter ecosystems. Because litter simultaneously provides habitat structure and a basal resource, disentangling direct trophic and indirect non-trophic effects on different trophic levels remains challenging. Here, we focussed on short-term per capita interaction strengths of generalist predators (centipedes) on their microbi-detritivore prey (springtails) and addressed how the habitat structuring effects of the leaf litter modifies this interaction. We performed a series of laboratory functional response experiments where four levels of habitat structure were constructed by adding different amounts of leaf litter to the experimental arenas. We found that increased leaf litter reduced the consumption rate of the predator. We interpreted this as a dilution effect of the augmented habitat size provided by the increasing leaf litter surface available to the species. Dilution of the prey population decreased encounter rates, whereas the capture success was not affected. Interestingly, our results imply that top-down control by centipedes decreased with increasing resource supply for the microbi-detritivore prey (i.e. the leaf litter that simultaneously provides habitat structure). Therefore, effective top-down control of predators on microbi-detritvore populations seems unlikely in litter-rich ecosystems due to the non-trophic, habitat-structuring effect of the basal litter resource.     

Bottom-up effects may not reach the top: the influence of ant-aphid interactions on the spread of soil disturbances through trophic chains

Soil disturbances that increase nutrient availability may trigger bottom-up cascading effects along trophic chains. However, the strength and sign of these effects may depend on attributes of the interacting species. Here, we studied the effects of nutrient-rich refuse dumps of the leaf-cutting ant, Acromyrmex lobicornis, on the food chain composed of thistles, aphids, tending ants and aphid natural enemies. Using stable isotopes tracers, we show that the nitrogen accumulated in refuse dumps propagates upward through the studied food chain. Thistles growing on refuse dumps had greater biomass and higher aphid density than those growing in adjacent soil. These modifications did not affect the structure of the tending ant assemblage, but were associated with increased ant activity. In contrast to the expectations under the typical bottom-up cascade effect, the increase in aphid abundance did not positively impact on aphid natural enemies. This pattern may be explained by both an increased activity of tending ants, which defend aphids against their natural enemies, and the low capacity of aphid natural enemies to show numerical or functional responses to increased aphid density. Our results illustrate how biotic interactions and the response capacity of top predators could disrupt bottom-up cascades triggered by disturbances that increase resource availability.     

杭州湾北岸大型围隔海域人工生态系统的能量流动和网络分析

根据2006年在杭州湾北岸大型围隔海域进行的生态调查数据,利用EwE软件构建围隔海域人工生态系统的能量流动模型.模型由13个功能组构成,分别是肉食性鱼类、底栖捕食鱼类、浮游动物性鱼类、草食性鱼类、蟹类、虾类、软体动物、底栖动物、肉食性浮游动物、植食性浮游动物、大型藻类、浮游植物和有机碎屑,每一组都代表在生态系统中具有相似地位的有机体,基本覆盖了该人工生态系统能量流动的主要过程.能量流动分析表明,围隔海域人工生态系统中能量流动主要以碎屑食物链途径为主,其中植食性浮游动物在能量从低级向高层次转换中起关键作用.人工生态系统的营养级范围为1.00～3.90级,系统的能量流动主要有6级,来自初级生产者的能流效率为9.4%,来自碎屑的转换效率为9.8%,平均能量转换效率为9.6%.经生态网络分析,直接来源于碎屑的比例占总流量的57%,而直接来源于初级生产者的比例为43%,生态系统特征参数:总初级生产计算量/总呼吸量(TPP/TR)、系统物质和能量循环率(FCI)和系统聚合度(A)值分别为2.672、0.25、0.315,表明围隔海域人工生态系统目前正处于发育时期.该研究为首次利用Ecopath模型分析大型围隔海域人工生态系统的结构和能量流动,旨在为富营养化近岸海域的生态修复提供理论依据.     

Influence of consumer mutual interference on the stabilization of a three-level trophic system

In this paper, we present a three-level (food–prey–predator) trophic food chain which includes consumer mutual interference (MIF). In contrast with other analyses, we consider the effect of both prey and predator MIF on the dynamics of a three-level trophic system. MIF is generally considered to exert a stabilizing effect on population dynamics based on the predator–prey model. However, results from analytical and numerical simulations utilizing a simple three-species food chain model suggest that while the addition of prey MIF to the model provides a stabilizing influence, as the chaotic dynamics collapse to a stable steady state, adding only predator MIF to the model can only stabilize the system at intermediate MIF values. The three-species trophic food chain is also stabilized when combination of both prey and predator MIF is added to the model. Our work serves to provide insight into the effects of MIF in the real world.     

Decoupling of cascading trophic interactions in a freshwater,benthic food chain

Food chain theory provides explicit predictions for equilibrium biomasses among trophic levels in food chains of different lengths. Empirical studies on freshwater benthic food chains have typically been performed on chains with up to three levels and in field experiments with limited spatial and temporal scale. Here we use a natural snapshot experiment approach to study equilibrium biomass and abundance among trophic levels in natural ponds differing only with respect to fish assemblage structure. Forty-four ponds were surveyed for their densityand biomass of fish, snails and periphyton. Ponds were divided into three categories based on fish assemblage: ponds with no fish (two trophic levels), ponds with molluscivorous fish (three trophic levels) and ponds that also had piscivorous fish (four trophic levels). Ponds without fish had a high density and biomass of snails and a low biomass of periphyton, whereas snails were scarce and periphyton biomass was high in ponds with molluscivorous fish. In the presence of piscivores, molluscivore populations consisted of low numbers of large individuals. Snail assemblages in piscivore ponds were characterised by relativelyhigh densities of small-bodied detritivorous species and periphyton biomass was not significantlydifferent from ponds with three trophic levels. Thus, predictions from classic food chain theory were upheld in ponds with up to three trophic levels. In ponds with four trophic levels, however, there was a decoupling of the trophic cascade at the piscivore-molluscivore level. Gape-limited piscivory, predation on snails by molluscivores that have reached an absolute size refuge from predation, and changes in food preferences of the dominant snails are suggested to explain the observed patterns.     

Agricultural intensification and cereal aphid–parasitoid–hyperparasitoid food webs: network complexity, temporal variability and parasitism rates

Agricultural intensification (AI) is currently a major driver of biodiversity loss and related ecosystem functioning decline. However, spatio-temporal changes in community structure induced by AI, and their relation to ecosystem functioning, remain largely unexplored. Here, we analysed 16 quantitative cereal aphid–parasitoid and parasitoid–hyperparasitoid food webs, replicated four times during the season, under contrasting AI regimes (organic farming in complex landscapes vs. conventional farming in simple landscapes). High AI increased food web complexity but also temporal variability in aphid–parasitoid food webs and in the dominant parasitoid species identity. Enhanced complexity and variability appeared to be controlled bottom-up by changes in aphid dominance structure and evenness. Contrary to the common expectations of positive biodiversity–ecosystem functioning relationships, community complexity (food-web complexity, species richness and evenness) was negatively related to primary parasitism rates. However, this relationship was positive for secondary parasitoids. Despite differences in community structures among different trophic levels, ecosystem services (parasitism rates) and disservices (aphid abundances and hyperparasitism rates) were always higher in fields with low AI. Hence, community structure and ecosystem functioning appear to be differently influenced by AI, and change differently over time and among trophic levels. In conclusion, intensified agriculture can support diverse albeit highly variable parasitoid–host communities, but ecosystem functioning might not be easy to predict from observed changes in community structure and composition.