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.     

Individual base model of predator-prey system shows predator dominant dynamics

Individual base model of predator-prey system is constructed. Both predator and prey species have age structure and cohorts of early reproductive age have competitive advantage. The model has linear functional response in predation behavior and includes the effect of interference among predators and delay of population growth from resource intake, not by functional response but by calculation procedure. Each foraging action is calculated successively and surplus or scarce of acquired resources is interpreted into population size through individual birth and death. This model shows that biomass of prey killed by predator is dependent on demand of predator and that heterogeneity in predator population is essential in persistency and stability of predator-prey system. Heterogeneity of predator makes predator individuals of less competing ability die rapidly. Rapid death of weak individuals causes rapid decrease of total demand of predator and that makes enough room for survived predators. Therefore, the biomass of killed prey is dependent on predator's demand. As young or infant population of predator are the more vulnerable to shortage of prey, and when many of them cannot survive to reproductive age, they can stabilize the system by wasting excessive prey with only temporal numerical increase of predator population.     

Stoichiometry, herbivory and competition for nutrients: simple models based on planktonic ecosystems

Models are examined in which two prey species compete for two nutrient resources, and are preyed upon by a predator that recycles both nutrients. Two factors determine the effective relative supply of the nutrients, hence competitive outcomes: the external nutrient supply ratio, and the relative recycling of the two nutrients within the system. This second factor is governed by predator stoichiometry--its relative requirements for nutrients in its own biomass. A model with nutrient resources that are essential for the competing prey is detailed. Criteria are given to identify the limiting nutrient for a food chain of one competitor with the predator. Increased supply of this limiting nutrient increases predator density and concentration of this nutrient at equilibrium, while decreasing the concentration of a non-limiting nutrient. Changes in supply or recycling of a non-limiting nutrient affect only the concentration of that nutrient. Criteria for the invasion of a second prey competitor are presented. When different nutrients limit growth of the resident prey and the invader, increased supply or recycling of the invader's limiting nutrient assists invasion, while increased supply or recycling of the resident's limiting nutrient hinders invasion. If the same nutrient limits both resident and invader, then changes in supply and recycling have complex effects on invasion, depending on species properties. In a parameterized model of a planktonic ecosystem, green algae and cyanobacteria coexist over a wide range of nitrogen:phosphorus supply ratios, without predators. When the herbivore Daphnia is added, coexistence is eliminated or greatly restricted, and green algae dominate over a wide range of supply conditions, because the effective supply of P is greatly reduced as Daphnia rapidly recycles N.     

Prey Vulnerability Limits Top-Down Control and Alters Reciprocal Feedbacks in a Subsidized Model Food Web

Resource subsidies increase the productivity of recipient food webs and can affect ecosystem dynamics. Subsidies of prey often support elevated predator biomass which may intensify top-down control and reduce the flow of reciprocal subsidies into adjacent ecosystems. However, top-down control in subsidized food webs may be limited if primary consumers posses morphological or behavioral traits that limit vulnerability to predation. In forested streams, terrestrial prey support high predator biomass creating the potential for strong top-down control, however armored primary consumers often dominate the invertebrate assemblage. Using empirically based simulation models, we tested the response of stream food webs to variations in subsidy magnitude, prey vulnerability, and the presence of two top predators. While terrestrial prey inputs increased predator biomass (+12%), the presence of armored primary consumers inhibited top-down control, and diverted most aquatic energy (∼75%) into the riparian forest through aquatic insect emergence. Food webs without armored invertebrates experienced strong trophic cascades, resulting in higher algal (∼50%) and detrital (∼1600%) biomass, and reduced insect emergence (−90%). These results suggest prey vulnerability can mediate food web responses to subsidies, and that top-down control can be arrested even when predator-invulnerable consumers are uncommon (20%) regardless of the level of subsidy.     

Successful invasion of a food web in a chemostat

A food web in a chemostat is considered in which an arbitrary number of competitor populations compete for a single, essential, nonreproducing, growth-limiting substrate, and an arbitrary number of predator populations prey on some or all of the competitor populations. Although any number of predator populations may prey on the same competitor population, each predator population preys on only one competitor population. The dynamics of substrate uptake is modeled by Lotka-Volterra or Michaelis-Menten (Holling type I or II), but the dynamics of competitor uptake is restricted to Lotka-Volterra. Based on certain parameters, the model predicts the asymptotic survival or extinction of each of the different populations and suggests how competitor and/or predator populations could successfully invade the chemostat with or without causing a diverse ecosystem to crash. Similarly, it suggests how the elimination of certain populations could result in a more diverse or less diverse system.     

Obligate mutualism with a predator: Stability and persistence of three-species models

We present a general model for three interacting populations, where one population, called a mutualist, benefits a predator in its interaction with the prey. Biologically, there are four different ways in which the mutualist could benefit the predator: by enhancing prey growth rate, by enhancing the rate of prey capture, by providing an alternative food supply for the predator, and by enhancing the efficiency of utilization of prey, once they are ingested. We discuss examples of each type of interaction. We restrict our model to those situations in which the predator cannot survive on the prey in the absence of the mutualist. Therefore, if mutualism exists, it is obligate for the predator. Other conditions of the model include the dynamics of the prey and the mutualist alone and together in the absence of the predator. Given additional reasonable restrictions on the model, we determine the conditions for persistence, where persistence is defined as the continued existence of all three populations without any of them going extinct. There are two ways in which survival may arise in these models. Under one set of conditions, which is equivalent to the predator being able to invade a prey-mutualist system when rare, persistence will occur for any set of positive critical population sizes. Alternatively, survival will occur if there is an asymptotically stable interior equilibrium. However, the conditions for this are complex, and survival may occur only for initial populations in a limited region around the equilibrium.     

Predator kairomones change food web structure and function,regardless of cues from consumed prey

Predation risk in aquatic systems is often assessed by prey through chemical cues, either those released by prey or by the predator itself. Many studies on predation risk focus on simple pairwise interactions, with only a few studies examining community‐level and ecosystem responses to predation risk in species‐rich food webs. Further, of these few community‐level studies, most assume that prey primarily assess predation risk through chemical cues from consumed prey, even heterospecific prey, rather than just those released by the predator. Here, we compared the effects of different predation cues (predator presence with or without consumed prey) on the structure and functioning of a speciose aquatic food web housed in tropical bromeliads. We found that the mere presence of the top predator (a damselfly) had a strong cascading effect on the food web, propagating down to nutrient cycling. This predation risk cue had no effect on the identity of colonizing species, but strongly reduced the abundance and biomass of the macroinvertebrate colonists. As a result, bacterial biomass and nitrogen cycling doubled, with a concomitant decrease in bacterial production, but CO₂ flux was unaffected. These community and ecosystem effects of predator presence cues were not amplified by the addition of chemical cues from consumed prey. Our results show that some of the consequences of predation risk observed in controlled experiments with simplified food webs may be observed in a natural, species‐rich food web.     

Contribution of nematodes to the structure and function of the soil food web

As carbon and energy flow through the soil food web they are depleted by the metabolic and production functions of organisms. To be sustained, a "long" food web, with a large biomass at higher trophic levels, must receive a high rate of rhizodeposition or detrital subsidy, or be top-populated by organisms of slow growth and long life cycle. Disturbed soil food webs tend to be bottom heavy and recalcitrant to restoration due to the slow growth of upper predator populations, physical and chemical constraints of the soil matrix, biological imbalances, and the relatively low mobility and invasion potential of soil organisms. The functional roles of nematodes, determined by their metabolic and behavioral activities, may be categorized as ecosystem services, disservices or effect-neutral. Among the disservices attributable to nematodes are overgrazing, which diminishes services of prey organisms, and plant-damaging herbivory, which reduces carbon fixation and availability to other organisms in the food web. Unfortunately, management to ameliorate potential disservices of certain nematodes results in unintended but long-lasting diminution of the services of others. Beneficial roles of nematodes may be enhanced by environmental stewardship that fosters greater biodiversity and, consequently, complementarity and continuity of their services.     

Intraguild interactions among generalist predator functional groups drive impact on herbivore and decomposer prey

Different functional groups of generalist predators may complement each other in controlling prey populations; but intraguild interactions, common among generalist predators, may also reduce the strength of top–down control. In natural communities greater alterations to ecosystem function are expected if a whole functional group declines in abundance or is lost. Therefore studying functional group diversity is important for predicting effects of predator loss. We studied the top–down impact of web‐building spiders, hunting spiders and ants, which are highly abundant generalist predators in most terrestrial ecosystems, on prey from the herbivore and decomposer system of a grassland food web. The density of the three predator groups was manipulated by continuous removal in a three‐factorial designed field experiment, which was carried out for two years. We found no positive effect of increasing predator functional group richness on prey control. However there was evidence for strong composition effects between the functional groups. The presence of ants in predator assemblages reduced the prey suppression through mostly trait‐mediated intraguild interactions, while hunting and web‐building spiders contributed additively to prey suppression and reduced the density of herbivore and decomposer prey by 50–60%. A trophic cascade on plant biomass triggered by web‐builders and hunting spiders was diminished at levels of higher predator group diversity. In conclusion, our experiments showed that intraguild interactions strongly influence the strength of top–down control by generalist predators. Among spiders there was evidence for a positive relation between functional group richness and prey suppression but the overall outcome strongly depended on the occurrence of interference, driven by trait‐mediated indirect interactions.     

Warming up the system: higher predator feeding rates but lower energetic efficiencies

Predictions on the consequences of the rapidly increasing atmospheric CO₂ levels and associated climate warming for population dynamics, ecological community structure and ecosystem functioning depend on mechanistic energetic models of temperature effects on populations and their interactions. However, such mechanistic approaches combining warming effects on metabolic (energy loss of organisms) and feeding rates (energy gain by organisms) remain a key, yet elusive, goal. Aiming to fill this void, we studied the metabolic rates and functional responses of three differently sized, predatory ground beetles on one mobile and one more resident prey species across a temperature gradient (5, 10, 15, 20, 25 and 30 °C). Synthesizing metabolic and functional‐response theory, we develop novel mechanistic predictions how predator–prey interaction strengths (i.e., functional responses) should respond to warming. Corroborating prior theory, warming caused strong increases in metabolism and decreases in handling time. Consistent with our novel model, we found increases in predator attack rates on a mobile prey, whereas attack rates on a mostly resident prey remained constant across the temperature gradient. Together, these results provide critically important information that environmental warming generally increases the direct short‐term per capita interaction strengths between predators and their prey as described by functional‐response models. Nevertheless, the several fold stronger increase in metabolism with warming caused decreases in energetic efficiencies (ratio of per capita feeding rate to metabolic rate) for all predator–prey interactions. This implies that warming of natural ecosystems may dampen predator–prey oscillations thus stabilizing their dynamics. The severe long‐term implications; however, include predator starvation due to energetic inefficiency despite abundant resources.     

Bimodal trait distributions with large variances question the reliability of trait-based aggregate models

Functionally diverse communities can adjust their species composition to altered environmental conditions, which may influence food web dynamics. Trait-based aggregate models cope with this complexity by ignoring details about species identities and focusing on their functional characteristics (traits). They describe the temporal changes of the aggregate properties of entire communities, including their total biomasses, mean trait values, and trait variances. The applicability of aggregate models depends on the validity of their underlying assumptions that trait distributions are normal and exhibit small variances. We investigated to what extent this can be expected to work by comparing an innovative model that accounts for the full trait distributions of predator and prey communities to a corresponding aggregate model. We used a food web structure with well-established trade-offs among traits promoting mutual adjustments between prey edibility and predator selectivity in response to selection. We altered the shape of the trade-offs to compare the outcome of the two models under different selection regimes, leading to trait distributions increasingly deviating from normality. Their biomass and trait dynamics agreed very well for stabilizing selection and reasonably well for directional selection, under which different trait values are favored at different times. However, for disruptive selection, the results of the aggregate model strongly deviated from the full trait distribution model that showed bimodal trait distributions with large variances. Hence, the outcome of aggregate models is reliable under ideal conditions but has to be questioned when confronted with more complex selection regimes and trait distributions, which are commonly observed in nature.     

Effect of predator density dependent dispersal of prey on stability of a predator-prey system

This work presents a predator-prey Lotka-Volterra model in a two patch environment. The model is a set of four ordinary differential equations that govern the prey and predator population densities on each patch. Predators disperse with constant migration rates, while prey dispersal is predator density-dependent. When the predator density is large, the dispersal of prey is more likely to occur. We assume that prey and predator dispersal is faster than the local predator-prey interaction on each patch. Thus, we take advantage of two time scales in order to reduce the complete model to a system of two equations governing the total prey and predator densities. The stability analysis of the aggregated model shows that a unique strictly positive equilibrium exists. This equilibrium may be stable or unstable. A Hopf bifurcation may occur, leading the equilibrium to be a centre. If the two patches are similar, the predator density dependent dispersal of prey has a stabilizing effect on the predator-prey system.     

Transient dynamics limit the effectiveness of keystone predation in bringing about coexistence

We analyze the transient dynamics of simple models of keystone predation, in which a predator preferentially consumes the dominant of two (or more) competing prey species. We show that coexistence is unlikely in many systems characterized both by successful invasion of either prey species into the food web that lacks it and by a stable equilibrium with high densities of all species. Invasion of the predator-resistant consumer species often causes the resident, more vulnerable prey to crash to such low densities that extinction would occur for many realistic population sizes. Subsequent transient cycles may entail very low densities of the predator or of the initially successful invader, which may also preclude coexistence of finite populations. Factors causing particularly low minimum densities during the transient cycles include biotic limiting resources for the prey, limited resource partitioning between the prey, a highly efficient predator with relatively slow dynamics, and a vulnerable prey whose population dynamics are rapid relative to the less vulnerable prey. Under these conditions, coexistence of competing prey via keystone predation often requires that the prey's competitive or antipredator characteristics fall within very narrow ranges. Similar transient crashes are likely to occur in other food webs and food web models.     

A novel modeling approach for the “end-to-end” analysis of marine ecosystems

There is a growing demand for “end-to-end” models, which are modeling tools used to analyze and understand the fundamental complexities of marine ecosystems and processes emerging from the interaction of individuals from different trophic groups with respect to the physical environment and, even, human activity. These models are valuable quantitative tools for ecosystem-based management. To explore potential answers to complex questions regarding ecosystems using these models, it is necessary to incorporate classical ontogenic changes through the life cycle of target individuals, in addition to inherited behavioral strategies, as an additional differentiating aspect, particularly when the behavior has a direct impact on the ecosystem phenomena under study. However, it is difficult to combine different fine scale time and spatial granularities to infer animal behavior and ontogenic development. This complexity has kept these two levels of analysis separated, because most current tools do not have the required computational resources and advanced software architecture. To address this issue, we propose an individual-based modeling framework that is capable of handling and unifying the two experimental categories with a comprehensive biological and behavioral model that strictly adheres to the physiological functions of ingestion, growth, and metabolism of organisms. In addition, this model incorporates the exchange and transfer of mass and energy through local interactions at all trophic levels (lower to higher), the physical environment, and anthropogenic activity. For the framework to model short time events, such as classical predator–prey interactions, while also generating long-term ecosystem emergent properties, a special interleaving scheduling engine and physical space computer model was devised, which optimizes memory and processing resources. The framework was tested through several experiments with a three-population ecosystem containing up to 40 thousand organisms evolving inside a 200,000 m² simulation environment during 12,000 model-hours; yet, requiring only a few hours of program execution on a regular personal computer. The model included various environmental physical elements, such as several hundred shelters, the number of which can be easily modified in each experiment to simulate substrate degradation and its impact on populations. With the aid of the quantitative and qualitative tools provided by the model, it was possible to observe a coupling between prey and predator population dynamics. In conclusion, we confirmed that the end-to-end model developed here could successfully generate detailed specific hypotheses about fish behavior and quantify impacts on population dynamics.     

The ecology of fear and inverted biomass pyramids

In inverted biomass pyramids (IBPs) prey are outnumbered by their predators when measured by biomass. We investigate how prey should behave in the face of danger from higher predator biomass, and how anti-predator behavior (in the form of vigilance) can, in turn, affect the predator–prey system. In this study, we incorporate anti-predator behaviors into a Lotka–Volterra predator–prey model in the form of fixed and facultative vigilance. Facultative vigilance models behavior as a dynamic foraging game, allowing us to assess optimal behavioral responses in the context of IBPs using a dynamical fitness optimization approach. We model vigilance as a tradeoff between safety and either the prey's maximum growth rate or its carrying capacity. We assess the population dynamics of predators and prey with fear responses, and investigate the role fear plays on trophic structure. We found that the ecology of fear plays an important role in predator–prey systems, impacting trophic structure and the occurrence of IBPs. Fixed vigilance works against IBP structure by always reducing the predator–prey biomass ratio at equilibrium with increasing levels of vigilance. Facultative vigilance can actually promote IBPs, as prey can now adjust their vigilance levels to cope with increased predation and the costs associated with vigilance. This is especially true when the effectiveness of vigilance is low and predators are very lethal. In general, these trends are true whether the costs of vigilance are felt on the prey's maximum growth rate or its carrying capacity. Just as the ecology of fear, when first introduced, was used to explain why top carnivores are rare in terrestrial systems, it can also be used to understand how big fierce predators can be common in IBPs.     

A cross‐system meta‐analysis reveals coupled predation effects on prey biomass and diversity

Predator diversity and abundance are under strong human pressure in all types of ecosystems. Whereas predator potentially control standing biomass and species interactions in food webs, their effects on prey biomass and especially prey biodiversity have not yet been systematically quantified. Here, we test the effects of predation in a cross‐system meta‐analysis of prey diversity and biomass responses to local manipulation of predator presence. We found 291 predator removal experiments from 87 studies assessing both diversity and biomass responses. Across ecosystem types, predator presence significantly decreased both biomass and diversity of prey across ecosystems. Predation effects were highly similar between ecosystem types, whereas previous studies had shown that herbivory or decomposition effects differed fundamentally between terrestrial and aquatic systems based on different stoichiometry of plant material. Such stoichiometric differences between systems are unlikely for carnivorous predators, where effect sizes on species richness strongly correlated to effect sizes on biomass. However, the negative predation effect on prey biomass was ameliorated significantly with increasing prey richness and increasing species richness of the manipulated predator assemblage. Moreover, with increasing richness of the predator assemblage present, the overall negative effects of predation on prey richness switched to positive effects. Our meta‐analysis revealed strong general relationships between predator diversity, prey diversity and the interaction strength between trophic levels in terms of biomass. This study indicates that anthropogenic changes in predator abundance and diversity will potentially have strong effects on trophic interactions across ecosystems. Synthesis The past centuries we have experienced a dramatic loss of top–predator abundance and diversity in most types of ecosystems. To understand the direct consequences of predator loss on a global scale, we quantitatively summarized experiments testing predation effects on prey communities in a cross‐system meta‐analysis. Across ecosystem types, predator presence significantly decreased both biomass and diversity of prey, and predation effects were highly similar. However, with increasing predator richness, the overall negative effects of predation on prey richness switched to positive ones. Anthropogenic changes in predator communities will potentially have strong effects on prey diversity, biomass, and trophic interactions across ecosystems.     

Caught in the web: Spider web architecture affects prey specialization and spider–prey stoichiometric relationships

Quantitative approaches to predator–prey interactions are central to understanding the structure of food webs and their dynamics. Different predatory strategies may influence the occurrence and strength of trophic interactions likely affecting the rates and magnitudes of energy and nutrient transfer between trophic levels and stoichiometry of predator–prey interactions. Here, we used spider–prey interactions as a model system to investigate whether different spider web architectures—orb, tangle, and sheet‐tangle—affect the composition and diet breadth of spiders and whether these, in turn, influence stoichiometric relationships between spiders and their prey. Our results showed that web architecture partially affects the richness and composition of the prey captured by spiders. Tangle‐web spiders were specialists, capturing a restricted subset of the prey community (primarily Diptera), whereas orb and sheet‐tangle web spiders were generalists, capturing a broader range of prey types. We also observed elemental imbalances between spiders and their prey. In general, spiders had higher requirements for both nitrogen (N) and phosphorus (P) than those provided by their prey even after accounting for prey biomass. Larger P imbalances for tangle‐web spiders than for orb and sheet‐tangle web spiders suggest that trophic specialization may impose strong elemental constraints for these predators unless they display behavioral or physiological mechanisms to cope with nutrient limitation. Our findings suggest that integrating quantitative analysis of species interactions with elemental stoichiometry can help to better understand the occurrence of stoichiometric imbalances in predator–prey interactions.     

Subsidies to predators, apparent competition and the phylogenetic structure of prey communities

Ecosystems are fragmented by natural and anthropogenic processes that affect organism movement and ecosystem dynamics. When a fragmentation restricts predator but not prey movement, then the prey produced on one side of an ecosystem edge can subsidize predators on the other side. When prey flux is high, predator density on the receiving side increases above that possible by in situ prey productivity, and when low, the formerly subsidized predators can impose strong top-down control of in situ prey—in situ prey experience apparent competition from the subsidy. If predators feed on some evolutionary clades of in situ prey over others, then subsidy-derived apparent competition will induce phylogenetic structure in prey composition. Dams fragment the serial nature of river ecosystems by prohibiting movement of organisms and restricting flowing water. In the river tailwater just below a large central Mexican dam, fish density was high and fish gorged on reservoir-derived zooplankton. When the dam was closed, water flow and the zooplankton subsidy ceased, densely packed pools of fish formed, fish switched to feed on in situ prey, and the tailwater macroinvertebrate community was phylogenetic structured. We derived expectations of structure from trait-based community assembly models based on macroinvertebrate body size, tolerance to anthropogenic disturbance, and fish-diet selectivity. The diet-selectivity model best fit the observed tailwater phylogenetic structure. Thus, apparent competition from subsidies phylogenetically structures prey communities, and serial variation in phylogenetic community structure can be indicative of fragmentation in formerly continuous ecosystems.     

Bi-trophic food chain dynamics with multiple component populations

Food web models describe the patterns of material and energy flow in communities. In classical food web models the state of each population is described by a single variable which represents, for instance, the biomass or the number of individuals that make up the population. However, in a number of models proposed recently in the literature the individual organisms consist of two components. In addition to the structural component there is an internal pool of nutrients, lipids or reserves. Consequently the population model for each trophic level is described by two state variables instead of one. As a result the classical predator-prey interaction formalisms have to be revised. In our model time budgets with actions as searching and handling provide the formulation of the functional response for both components. In the model, assimilation of the ingested two prey components is done in parallel and the extracted energy is added to a predators reserve pool. The reserves are used for vital processes; growth, reproduction and maintenance. We will explore the top-down modelling approach where the perspective is from the community. We will demonstrate that this approach facilitates a check on the balance equations for mass and energy at this level of organization. Here it will be shown that, if the individual is allowed to shrink when the energy reserves are in short to pay the maintenance costs, the growth process has to be 100% effective. This is unrealistic and some alternative model formulations are discussed. The long-term dynamics of a microbial food chain in the chemostat are studied using bifurcation analysis. The dilution rate and the concentration of nutrients in the reservoir are the bifurcation parameters. The studied microbial bi-trophic food chain with two-component populations shows chaotic behaviour.