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.     

Energetics of microbial food webs

The energetic demand of microorganisms in natural waters and the flux of energy between microorganisms and metazoans has been evaluated by empirical measurements in nature, in microcosms and mesocosms, and by simulation models. Microorganisms in temperate and tropical waters often use half or more of the energy fixed by photosynthesis. Most simulations and some experimental results suggest significant energy transfer to metazoans, but empirical evidence is mixed. Considerations of the range of growth yields of microorganisms and the number of trophic transfers among them indicate major energy losses within microbial food webs. Our ability to verify and quantify these processes is limited by the variability of assimilation efficiency and uncertainty about the structure of microbial food webs. However, even a two-step microbial chain is a major energy sink. As an energetic link to metazoans, the detritus food web is inefficient, and its significance may have been overstated. There is not enough bacterial biomass associated with detritus to support metazoan detritivores. Much detritus is digestible by metazoans directly. Thus, metazoans and bacteria may to a considerable degree compete for a common resource. Microorganisms, together with metazoans, are important to the stability of planktonic communities through their roles as rapid mineralizers of organic matter, releasing inorganic nutrients. The competition for organic matter and the resultant rapid mineralization help maintain stable populations of phytoplankton in the absence of advective nutrient supply. At temperatures near O °C, bacterial metabolism is suppressed more than is the rate of photosynthesis. As a result, the products of the spring phytoplankton bloom in high-temperate latitudes are not utilized rapidly by bacteria. At temperatures below 0°C microbial food webs are neither energy sinks or links: they are suppressed. Because the underlying mechanism of low-temperature inhibition is not known, we cannot yet generalize about this as a control of food web processes. Microorganisms may operate on several trophic levels simultaneously. Therefore, the realism of the trophic level concept and the reality of the use of ecological efficiency calculations in ecosystem models is questionable.     

Effects of Extrinsic Mortality on the Evolution of Aging: A Stochastic Modeling Approach

The evolutionary theories of aging are useful for gaining insights into the complex mechanisms underlying senescence. Classical theories argue that high levels of extrinsic mortality should select for the evolution of shorter lifespans and earlier peak fertility. Non-classical theories, in contrast, posit that an increase in extrinsic mortality could select for the evolution of longer lifespans. Although numerous studies support the classical paradigm, recent data challenge classical predictions, finding that high extrinsic mortality can select for the evolution of longer lifespans. To further elucidate the role of extrinsic mortality in the evolution of aging, we implemented a stochastic, agent-based, computational model. We used a simulated annealing optimization approach to predict which model parameters predispose populations to evolve longer or shorter lifespans in response to increased levels of predation. We report that longer lifespans evolved in the presence of rising predation if the cost of mating is relatively high and if energy is available in excess. Conversely, we found that dramatically shorter lifespans evolved when mating costs were relatively low and food was relatively scarce. We also analyzed the effects of increased predation on various parameters related to density dependence and energy allocation. Longer and shorter lifespans were accompanied by increased and decreased investments of energy into somatic maintenance, respectively. Similarly, earlier and later maturation ages were accompanied by increased and decreased energetic investments into early fecundity, respectively. Higher predation significantly decreased the total population size, enlarged the shared resource pool, and redistributed energy reserves for mature individuals. These results both corroborate and refine classical predictions, demonstrating a population-level trade-off between longevity and fecundity and identifying conditions that produce both classical and non-classical lifespan effects.     

Dynamics of a Producer–Grazer Model Incorporating the Effects of Excess Food Nutrient Content on Grazer’s Growth

Modeling under the framework of ecological stoichiometric allows the investigation of the effects of food quality on food web population dynamics. Recent discoveries in ecological stoichiometry suggest that grazer dynamics are affected by insufficient food nutrient content (low phosphorus (P)/carbon (C) ratio) as well as excess food nutrient content (high P:C). This phenomenon is known as the “stoichiometric knife edge.” While previous models have captured this phenomenon, they do not explicitly track P in the producer or in the media that supports the producer, which brings questions to the validity of their predictions. Here, we extend a Lotka–Volterra-type stoichiometric model by mechanistically deriving and tracking P in the producer and free P in the environment in order to investigate the growth response of Daphnia to algae of varying P:C ratios. Bifurcation analysis and numerical simulations of the full model, that explicitly tracks phosphorus, lead to quantitative different predictions than previous models that neglect to track free nutrients. The full model shows that the fate of the grazer population can be very sensitive to excess nutrient concentrations. Dynamical free nutrient pool seems to induce extreme grazer population density changes when total nutrient is in an intermediate range.     

Bifurcation theory, adaptive dynamics and dynamic energy budget-structured populations of iteroparous species

In this paper, we describe a technique to evaluate the evolutionary dynamics of the timing of spawning for iteroparous species. The life cycle of the species consists of three life stages, embryonic, juvenile and adult whereby the transitions of life stages (gametogenesis, birth and maturation) occur at species-specific sizes. The dynamics of the population is studied in a semi-chemostat environment where the inflowing food concentration is periodic (annual). A dynamic energy budget-based continuous-time model is used to describe the uptake of the food, storage in reserves and allocation of the energy to growth, maintenance, development (embryos, juveniles) and reproduction (adults). A discrete-event process is used for modelling reproduction. At a fixed spawning date of the year, the reproduction buffer is emptied and a new cohort is formed by eggs with a fixed size and energy content. The population consists of cohorts: for each year one consisting of individuals with the same age which die after their last reproduction event. The resulting mathematical model is a finite-dimensional set of ordinary differential equations with fixed 1-year periodic boundary conditions yielding a stroboscopic map. We will study the evolutionary development of the population using the adaptive dynamics approach. The trait is the timing of spawning. Pairwise and mutual invasibility plots are calculated using bifurcation analysis of the stroboscopic map. The evolutionary singular strategy value belonging to the evolutionary endpoint for the trait allows for an interpretation of the reproduction strategy of the population. In a case study, parameter values from the literature for the bivalve Macoma balthica are used.     

Microbial food chains and food webs

Mathematical models for simple microbial food chains and food webs in continuous culture are developed and analyzed. A model for competition of two microbial species for a single scarce resource is also presented as a degenerate case of the food web model. Two models for food chains are developed. The first is based on a model of microbial growth (Monod's) that is widely mentioned and used at the present time. The second is based on a generalization of that model that recent experimental results on microbial food chains seem to require. Experimental data for microbial food webs are almost entirely lacking but a tentative model having what are felt to be the right properties is developed and analyzed. The results obtained from these models seem to be consistent in most circumstances with current ecological thinking on community dynamics.     

Intra-habitat heterogeneity of microbial food web structure under the regime of eutrophication and sediment resuspension in the large subtropical shallow Lake Taihu,China

Planktonic microbial community structure and classical food web were investigated in the large shallow eutrophic Lake Taihu (2338 km², mean depth 1.9 m) located in subtropical Southeast China. The water column of the lake was sampled biweekly at two sites located 22 km apart over a period of twelve month. Site 1 is under the regime of heavy eutrophication while Site 2 is governed by wind-driven sediment resuspension. Within-lake comparison indicates that phosphorus enrichment resulted in increased abundance of microbial components. However, the coupling between total phosphorus and abundance of microbial components was different between the two sites. Much stronger coupling was observed at Site 1 than at Site 2. The weak coupling at Site 2 was mainly caused by strong sediment resuspension, which limited growth of phytoplankton and, consequently, growth of bacterioplankton and other microbial components. High percentages of attached bacteria, which were strongly correlated with the biomass of phytoplankton, especially Microcystis spp., were found at Site 1 during summer and early autumn, but no such correlation was observed at Site 2. This potentially leads to differences in carbon flow through microbial food web at different locations. Overall, significant heterogeneity of microbial food web structure between the two sites was observed. Site-specific differences in nutrient enrichment (i.e. nitrogen and phosphorus) and sediment resuspension were identified as driving forces of the observed intra-habitat differences in food web structure.     

Consequences of symbiosis for food web dynamics

Basic Lotka-Volterra type models in which mutualism (a type of symbiosis where the two populations benefit both) is taken into account, may give unbounded solutions. We exclude such behaviour using explicit mass balances and study the consequences of symbiosis for the long-term dynamic behaviour of a three species system, two prey and one predator species in the chemostat. We compose a theoretical food web where a predator feeds on two prey species that have a symbiotic relationships. In addition to a species-specific resource, the two prey populations consume the products of the partner population as well. In turn, a common predator forages on these prey populations. The temporal change in the biomass and the nutrient densities in the reactor is described by ordinary differential equations (ODE). Since products are recycled, the dynamics of these abiotic materials must be taken into account as well, and they are described by odes in a similar way as the abiotic nutrients. We use numerical bifurcation analysis to assess the long-term dynamic behaviour for varying degrees of symbiosis. Attractors can be equilibria, limit cycles and chaotic attractors depending on the control parameters of the chemostat reactor. These control parameters that can be experimentally manipulated are the nutrient density of the inflow medium and the dilution rate. Bifurcation diagrams for the three species web with a facultative symbiotic association between the two prey populations, are similar to that of a bi-trophic food chain; nutrient enrichment leads to oscillatory behaviour. Predation combined with obligatory symbiotic prey-interactions has a stabilizing effect, that is, there is stable coexistence in a larger part of the parameter space than for a bi-trophic food chain. However, combined with a large growth rate of the predator, the food web can persist only in a relatively small region of the parameter space. Then, two zero-pair bifurcation points are the organizing centers. In each of these points, in addition to a tangent, transcritical and Hopf bifurcation a global heteroclinic bifurcation is emanating. This heteroclinic cycle connects two saddle equilibria where the predator is absent. Under parameter variation the period of the stable limit cycle goes to infinity and the cycle tends to the heteroclinic cycle. At this global bifurcation point this cycle breaks and the boundary of the basin of attraction disappears abruptly because the separatrix disappears together with the cycle. As a result, it becomes possible that a stable two-nutrient–two-prey population system becomes unstable by invasion of a predator and eventually the predator goes extinct together with the two prey populations, that is, the complete food web is destroyed. This is a form of over-exploitation by the predator population of the two symbiotic prey populations. When obligatory symbiotic prey-interactions are modelled with Liebigs minimum law, where growth is limited by the most limiting resource, more complicated types of bifurcations are found. This results from the fact that the Jacobian matrix changes discontinuously with respect to a varying parameter when another resource becomes most limiting.Revised version: 21 July 2003     

Omnivory and stability of food webs

The role and prevalence of omnivory, defined as feeding on more than one trophic level, are critical to understand food web structure and dynamics. Whether omnivory stabilizes or destabilizes food webs depends on the assumptions of theoretical models. Recently, Tanabe and Namba [Tanabe, K., Namba, T., 2005. Omivory creates chaos in simple food web models. Ecology 86, 3411–3414] found that omnivory can create chaos in a simple food web model with linear functional responses and 12 model parameters. In this paper, first we numerically examined bifurcation diagrams with all the parameters as bifurcation parameters, including self-limitation of the intermediate consumer and predator. Chaos spontaneously appears when the intraguild predator’s consumption rates are low for nutrient-rich intraguild prey and high for nutrient-poor basal resource and the intraguild prey reproduces efficiently feeding on the basal resource. Second, we investigated effects of the addition of a species into the basic model food web which exhibits chaos. The additional species is assumed to consume only one of the basal resource, intermediate consumer, or omnivorous predator. Consequences of the addition greatly depend on the trophic level on which the additional species feeds. While the increased diversity of predators feeding on the intermediate consumer stabilizes the web, the increased diversity of prey feeding on the basal resource induces collapse of the food web through exploitative competition for the basal resource. The food chain with the top predator feeding on the omnivorous predator is highly unstable unless the mortality of the top predator is extremely low. We discuss the possibility of real-world chaos and the reason why stability of food webs strongly depends on the topological structure of the webs. Finally, we consider the implications of our results for food web theory and resource management.     

Prokaryotes and the input of polyunsaturated fatty acids to the marine food web

The investigation of prokaryotes in aquatic ecology is often limited to their role in nutrient cycling and the degradation of organic matter. While this aspect of the microbial loop is undoubtedly important, further aspects of bacterial roles in marine food webs exist which have not been fully considered in light of recent research in related fields. The concept of bacteria providing essential nutrients may derive importance from two aspects of their role in the marine environment; firstly as a primary food source for omnivorous, sestonivorous and filtering benthic animals and secondly as components of the commensal microbial communities of marine animals. Many marine organisms lack the de novo ability to produce n-3 polyunsaturated fatty acids (PUFA) and hence rely on a dietary supply of PUFA. The issue of PUFA origin in the marine food web is particularly salient in light of recent research demonstrating the influence of PUFA levels on the efficiency of energy transfer between trophic levels. The assumption that microalgae provide the bulk of de novo PUFA production for all marine food webs must be actively reviewed with respect to particular microbial niches such as sea ice, marine animals and abyssal communities.     

Periodic response to periodic forcing of the Droop equations for phytoplankton growth

The dynamics of a phytoplankton population growing in a chemostat under a periodic supply of nutrients is investigated with the model proposed by Droop. This model differs from the well-known Monod equations by incorporating nutrient storage by the cells. In spite of its nonlinearity and the time delays introduced by an internal nutrient pool, the model predicts a simple response to a periodic nutrient supply. The population is shown to oscillate with the same frequency as the forcing. To prove the existence of a periodic solution local and global bifurcation results are used. This work establishes a basis on which to evaluate experimental data against the model as a representation of the nutrient-phytoplankton interaction when nutrients fluctuate.     

Above‐ and belowground linkages in Sphagnum peatland: climate warming affects plant‐microbial interactions

Peatlands contain approximately one third of all soil organic carbon (SOC). Warming can alter above‐ and belowground linkages that regulate soil organic carbon dynamics and C‐balance in peatlands. Here we examine the multiyear impact of in situ experimental warming on the microbial food web, vegetation, and their feedbacks with soil chemistry. We provide evidence of both positive and negative impacts of warming on specific microbial functional groups, leading to destabilization of the microbial food web. We observed a strong reduction (70%) in the biomass of top‐predators (testate amoebae) in warmed plots. Such a loss caused a shortening of microbial food chains, which in turn stimulated microbial activity, leading to slight increases in levels of nutrients and labile C in water. We further show that warming altered the regulatory role of Sphagnum‐polyphenols on microbial community structure with a potential inhibition of top predators. In addition, warming caused a decrease in Sphagnum cover and an increase in vascular plant cover. Using structural equation modelling, we show that changes in the microbial food web affected the relationships between plants, soil water chemistry, and microbial communities. These results suggest that warming will destabilize C and nutrient recycling of peatlands via changes in above‐ and belowground linkages, and therefore, the microbial food web associated with mosses will feedback positively to global warming by destabilizing the carbon cycle. This study confirms that microbial food webs thus constitute a key element in the functioning of peatland ecosystems. Their study can help understand how mosses, as ecosystem engineers, tightly regulate biogeochemical cycling and climate feedback in peatlands     

Dynamics of chemostat in which one microbial population grows on multiple complementary nutrients

The equations of a chemostat in which one microbial population grows on multiple rate-limiting nutrients are formulated. The dynamics of a chemostat involving growth on complementary nutrients is studied through stability analysis of the system of equations. Some conditions are derived that relate the dynamic behavior of the chemostat to its operating conditions and can be applied to any model for the specific growth rate of the population. It is shown that, if maintenance of the population is neglected, the system exhibits no sustained or damped oscillations. If maintenance of the population is considered, damped oscillations are observed for some operating conditions.     

Trophic coupling of the microbial and the classical food web in Lake Baikal,Siberia

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Current food web models cannot explain the overall topological structure of observed food webs

Topological food webs illustrating “who eats whom” in different systems exhibit similar, non‐random, structures suggesting that general rules govern food web structure. Current food web models correctly predict many measures of food web topology from knowledge of species richness and connectance (fraction of possible predator–prey links that actually occur), together with assumptions about the ecological rules governing “who eats whom”. However, current measures are relatively insensitive to small changes in topology. Improvement of, and discrimination among, current models requires development of new measures of food web structure. Here I examine whether current food web models (cascade, niche, and nested hierarchy models, plus a random null model) can predict a new measure of food web structure, structural stability. Structural stability complements other measures of food web topology because it is sensitive to changes in topology that other measures often miss. The cascade and null models respectively over‐ and underpredict structural stability for a set of 17 high‐quality food webs. While the niche and nested hierarchy models provide unbiased predictions on average, their 95% confidence intervals frequently fail to include the observed data. Observed structural stabilities for all models are overdispersed compared to model predictions, and predicted and observed structural stabilities are uncorrelated, indicating that important sources of variation in structural stability are not captured by the models. Crucially, poor model performance arises because observed variation in structural stability is unrelated to variation in species richness and connectance. In contrast, almost all other measures of food web topology vary with species richness and connectance in natural webs. No model that takes species richness and connectance as the only input parameters can reproduce observed variation in structural stability. Further progress in predicting and explaining food web topology will require fundamentally new models based on different input parameters.     

Successful strategies in size structured mixotrophic food webs

This study investigates how food web structures in aquatic microbial communities emerge based on different mixotrophic life strategies. Unicellular mixotrophic organisms that combine osmotrophy and primary production with phagotrophy account for significant amounts of primary production and bacterivory in marine environments, yet mixotrophs are still usually absent in large-scale biogeochemical models. We here present for the first time a thorough analysis of a food web model with a finely resolved structure in both cell size and foraging mode, where foraging mode is a strategy ranging from pure osmotrophy to pure phagotrophy. A trade-off for maximum uptake rates of mixotrophs is incorporated. We study how different factors determine the food web structure, here represented by the topology of the distribution of given amounts of total phosphorous over the cell size-foraging mode plane. We find that mixotrophs successfully coexist with foraging specialists (pure osmo- and phagotrophs) for a wide range of conditions, a result consistent with the observed prevalence of mixotrophs in recent oceanographic surveys. Mixotrophy trade-off and size-dependent parameters have a strong effect on the emerging community structure, stressing the importance of foraging mode and size considerations when working with microbial diversity and food web dynamics. The proposed model may be used to develop timely representations of mixotrophic strategies in larger biogeochemical ocean models.     

Impacts of Biotic Resource Enrichment on a Predator–Prey Population

The environmental carrying capacity is usually assumed to be fixed quantity in the classical predator–prey population growth models. However, this assumption is not realistic as the environment generally varies with time. In a bid for greater realism, functional forms of carrying capacities have been widely applied to describe varying environments. Modelling carrying capacity as a state variable serves as another approach to capture the dynamical behavior between population and its environment. The proposed modified predator–prey model is based on the ratio-dependent models that have been utilized in the study of food chains. Using a simple non-linear system, the proposed model can be linked to an intra-guild predation model in which predator and prey share the same resource. Distinct from other models, we formulate the carrying capacity proportional to a biotic resource and both predator and prey species can directly alter the amount of resource available by interacting with it. Bifurcation and numerical analyses are presented to illustrate the system’s dynamical behavior. Taking the enrichment parameter of the resource as the bifurcation parameter, a Hopf bifurcation is found for some parameter ranges, which generate solutions that posses limit cycle behavior.     

海洋浮游纤毛虫包囊的研究进展*

作为微型浮游动物的重要组成部分,海洋浮游纤毛虫是连接微食物环和经典食物链的重要中介。有些浮游纤毛虫在生活周期中会形成包囊,条件适宜时包囊会萌发,这对纤毛虫种群动态有重要的意义。目前国际上对于浮游纤毛虫生态学的研究主要集中在其营养期细胞,浮游纤毛虫包囊的研究尚少,中国还没有这方面的研究。本文对浮游纤毛虫包囊研究进展进行概述,包括包囊的形态、沉积物中包囊的丰度、包囊形成的环境因素、包囊萌发过程及环境因素对包囊萌发的影响等方面,希望对国内开展浮游纤毛虫包囊的研究有所裨益。     

Material recycling in a closed aquatic ecosystem. II. Bifurcation analysis of a simple food-chain model

The present paper deals with the bifurcation analysis of a simple food chain model consisting of components like detritus, nutrients, microorganisms, phytoplankton and zooplankton in an aquatic environment. The food chain model is described by a system of differential equations. If the length of the food chain (LFCH) is equal to 3 or 4, then an asymptotically stable equilibrium exists. For LFCH=5 or 6 the non-trivial equilibrium is unstable and the food-chain model has periodic orbits.