The responses of unstable food chains to enrichment

The Occurrence of Apparent Competition and Apparent Mutualism in a Modeled Greenhouse System with Two Non-competing Pests and a Shared Biocontrol Agent

This work puts forward a dynamical population model to qualitatively reproduce the phenomena of apparent competition and apparent mutualism found in an experiment with two arthropods being attacked by a predator in a context of pest biological control in greenhouse crops. The two agricultural pests consist of one species of thrips (Frankliniella occidentalis (Pergande 1895)) and one species of whiteflies (Trialeurodes vaporariorum Westwood, 1956), and the shared predator is a predatory mite (Amblyseius swirskii Athias-Herriot, 1962). The predatory mite is the biocontrol agent employed in order to achieve the biological control. The proposed model successfully reproduces this density mediated indirect interactions between pests when their carrying capacities are increased. Moreover, the pests' final population levels may depend on their initial densities and those of their predator. With these results, the proposed model may have the potential to assess whether these indirect pest interactions disrupt or enhance biological control. Additionally, it can also be used as an ancillary tool to theoretically assess the effects of pest biocontrol strategies in the referred experimental setup.

The interplay between fishery yield and top predator culling in a multispecies fishery context

In food webs, fishery can play the role of top predator, competing thus with other top predators for valuable food resources. In this view, it has been claimed in fisheries management that culling of top predators can be a means to improve fishery yield. To investigate this hypothesis, we use theoretical population models to assess in a multispecies context how fishery yield from target species harvest responds to top predator cull. Defying crisp summary, the four analysed food web models show that this response may be either positive or negative or both, indicating that in terms of multispecies fishery management the harvest yield may not accrue as a consequence of predator removal. In addition, this multitude of behaviours points also to the fact that the response of fishery yield to top predator cull may be difficult to assess.

Resource heterogeneity structures aquatic bacterial communities

Microorganisms are strongly influenced by the bottom-up effects of resource supply. While many species respond to fluctuations in the concentration of resources, microbial diversity may also be affected by the heterogeneity of the resource pool, which often reflects a mixture of distinct molecules. To test this hypothesis, we examined resource-diversity relationships for bacterioplankton in a set of north temperate lakes that varied in their concentration and composition of dissolved organic matter (DOM), which is an important resource for heterotrophic bacteria. Using 16S rRNA transcript sequencing and ecosystem metabolomics, we documented strong relationships between bacterial alpha-diversity (richness and evenness) and the bulk concentration and the number of molecules in the DOM pool. Similarly, bacterial community beta-diversity was related to both DOM concentration and composition. However, in some lakes the relative abundance of resource generalists, which was inversely related to the DOM concentration, may have reduced the effect of DOM heterogeneity on community composition. Together, our results demonstrate the potential metabolic interactions between bacteria and organic matter and suggest that changes in organic matter composition may alter the structure and function of bacterial communities.

PREY ADAPTATION AS A CAUSE OF PREDATOR-PREY CYCLES

We analyze simple models of predator-prey systems in which there is adaptive change in a trait of the prey that determines the rate at which it is captured by searching predators. Two models of adaptive change are explored: (1) change within a single reproducing prey population that has genetic variation for vulnerability to capture by the predator; and (2) direct competition between two independently reproducing prey populations that differ in their vulnerability. When an individual predator's consumption increases at a decreasing rate with prey availability, prey adaptation via either of these mechanisms may produce sustained cycles in both species' population densities and in the prey's mean trait value. Sufficiently rapid adaptive change (e.g., behavioral adaptation or evolution of traits with a large additive genetic variance), or sufficiently low predator birth and death rates will produce sustained cycles or chaos, even when the predator-prey dynamics with fixed prey capture rates would have been stable. Adaptive dynamics can also stabilize a system that would exhibit limit cycles if traits were fixed at their equilibrium values. When evolution fails to stabilize inherently unstable population interactions, selection decreases the prey's escape ability, which further destabilizes population dynamics. When the predator has a linear functional response, evolution of prey vulnerability always promotes stability. The relevance of these results to observed predator-prey cycles is discussed.

Allee effects in tritrophic food chains: some insights in pest biological control

Release of natural enemies to control pest populations is a common strategy in biological control. However, its effectiveness is supposed to be impaired, among other factors, by Allee effects in the biological control agent and by the fact that introduced pest natural enemies interact with some native species of the ecosystem. In this work, we devise a tritrophic food chain model where the assumptions previously raised are proved correct when a hyperpredator attacks the introduced pest natural enemy by a functional response type 2 or 3. Moreover, success of pest control is shown to be related to the release of large amounts (i.e., inundative releases) of natural enemies.

Integrated Pest Management in a Predator-Prey System with Allee Effects

A commonly used biocontrol strategy to control invasive pests with Allee effects consists of the deliberate introduction of natural enemies. To enhance the effectiveness of this strategy, several tactics of control of invasive species (e.g., mass-trapping, manual removal of individuals, and pesticide spraying) are combined so as to impair pest outbreaks. This combination of strategies to control pest species dynamics are usually named integrated pest management (IPM). In this work, we devise a predator-prey dynamical model in order to assess the influence of the intensity of chemical killing on the success of an IPM. The biological and mathematical framework presented in this study can also be analyzed in the light of species conservation and food web dynamics theory.

Is feedback control effective for ecosystem-based fisheries management?

We investigate the effects of species interactions on the robustness of feedback control of the harvesting of prey species. We consider the consequences of feedback control of fishing effort. If a prey species is exploited, increasing fishing effort decreases predator abundance more than it does the prey abundance. Feedback control of fishing effort may cause the extinction of the predator, even if the prey population is well controlled. Even when fishing effort is controlled by predator density, it is difficult for the fishery and the predator to coexist, and, if they do so, the system exhibits complex dynamic behaviors. If the predator and fishery coexist, feedback control of fishing effort converges to a stable equilibrium, a synchronous cycle, or an asynchronous cycle. In the last case, the system undergoes more complex cycling with a longer period than that when the fishing effort is kept constant. These analyses suggest that there is no effective strategy that is robust against measurement errors, process errors and complex interactions in ecosystem dynamics.

Carbon system measurements and potential climatic drivers at a site of rapidly declining ocean pH

We explored changes in ocean pH in coastal Washington state, USA, by extending a decadal-scale pH data series, by reporting independent measures of dissolved inorganic carbon (DIC), spectrophotometric pH, and total alkalinity (TA), by exploring pH patterns over larger spatial scales, and by probing for long-term trends in environmental variables reflecting potentially important drivers of pH. We found that pH continued to decline in this area at a rapid rate, that pH exhibited high natural variability within years, that our measurements of pH corresponded well to spectrophotometric pH measures and expected pH calculated from DIC/TA, and that TA estimates based on salinity predicted well actual alkalinity. Multiple datasets reflecting upwelling, including water temperature, nutrient levels, phytoplankton abundance, the NOAA upwelling index, and data on local wind patterns showed no consistent trends over the period of our study. Multiple datasets reflecting precipitation change and freshwater runoff, including precipitation records, local and regional river discharge, salinity, nitrate and sulfate in rainwater, and dissolved organic carbon (DOC) in rivers also showed no consistent trends over time. Dissolved oxygen did not decline over time, indicating that long-term changes did not result from shifts in contributions of respiration to pH levels. These tests of multiple potential drivers of the observed rapid rate of pH decline indicate a primary role for inorganic carbon and suggest that geochemical models of coastal ocean carbon fluxes need increased investigation.

ROLE OF PROTECTION IN A TRI-TROPHIC FOOD CHAIN DYNAMICS

In this paper, the role of protection in stabilizing the tri-trophic food chain dynamics has been explored. The density-dependent protection is provided to bottom prey or middle predator or both. It favors the oscillations damping and has the potential to control the chaotic fluctuations of population density. The bifurcation diagrams have been drawn with respect to protection parameter. They exhibit coexistence of all three species in the form of periodic solutions. The coexistence in the form of stable equilibrium is possible for higher values of protection parameters. Further increase in protection parameters may lead to extinction of one or two species. A two-parameter bifurcation diagram has also been drawn. The Poincaré Maps further confirm the role of protection in controlling the chaos.

Consumer-resource dynamics: quantity, quality, and allocation

BACKGROUND

The dominant paradigm for modeling the complexities of interacting populations and food webs is a system of coupled ordinary differential equations in which the state of each species, population, or functional trophic group is represented by an aggregated numbers-density or biomass-density variable. Here, using the metaphysiological approach to model consumer-resource interactions, we formulate a two-state paradigm that represents each population or group in a food web in terms of both its quantity and quality.

METHODOLOGY AND PRINCIPAL FINDINGS

The formulation includes an allocation function controlling the relative proportion of extracted resources to increasing quantity versus elevating quality. Since lower quality individuals senescence more rapidly than higher quality individuals, an optimal allocation proportion exists and we derive an expression for how this proportion depends on population parameters that determine the senescence rate, the per-capita mortality rate, and the effects of these rates on the dynamics of the quality variable. We demonstrate that oscillations do not arise in our model from quantity-quality interactions alone, but require consumer-resource interactions across trophic levels that can be stabilized through judicious resource allocation strategies. Analysis and simulations provide compelling arguments for the necessity of populations to evolve quality-related dynamics in the form of maternal effects, storage or other appropriate structures. They also indicate that resource allocation switching between investments in abundance versus quality provide a powerful mechanism for promoting the stability of consumer-resource interactions in seasonally forcing environments.

CONCLUSIONS/SIGNIFICANCE

Our simulations show that physiological inefficiencies associated with this switching can be favored by selection due to the diminished exposure of inefficient consumers to strong oscillations associated with the well-known paradox of enrichment. Also our results demonstrate how allocation switching can explain observed growth patterns in experimental microbial cultures and discuss how our formulation can address questions that cannot be answered using the quantity-only paradigms that currently predominate.

Adaptive changes in prey vulnerability shape the response of predator populations to mortality

Simple models are used to explore how adaptive changes in prey vulnerability alter the population response of their predator to increased mortality. If the mortality is an imposed harvest, the change in prey vulnerability also influences the relationship between harvest effort and yield of the predator. The models assume that different prey phenotypes share a single resource, but have different vulnerabilities to the predator. Decreased vulnerability is assumed to decrease resource consumption rate. Adaptive change may occur by phenotypic changes in the traits of a single species or by shifts in the abundances of a pair of coexisting species or morphs. The response of the predator population is influenced by the shape of the predator's functional response, the shape of resource density dependence, and the shape of the tradeoff between vulnerability and food intake in the prey. Given a linear predator functional response, adaptive prey defense tends to produce a decelerating decline in predator population size with increased mortality. Prey defense may also greatly increase the range of mortality rates that allow predator persistence. If the predator has a type-2 response with a significant handling time, adaptive prey defense may have a greater variety of effects on the predator's response to mortality, sometimes producing alternative attractors, population cycles, or increased mean predator density. Situations in which there is disruptive selection on prey defense often imply a bimodal change in yield as a function of harvesting effort, with a minimum at intermediate effort. These results argue against using single-species models of density dependent growth to manage predatory species, and illustrate the importance of incorporating anti-predator behavior into models in applied population ecology.

Will small population sizes warn us of impending extinctions?

Several models are used to show that population sizes are often relatively insensitive to deteriorating environmental conditions over most of the range of environments that allow population persistence. As conditions continue to worsen in these cases, equilibrium population sizes ultimately decline rapidly toward extinction from sizes similar to or larger than those before environmental decline began. Consumer-resource models predict that equilibrium or average population size can increase with deteriorating environmental conditions over a large part of the range of the environmental parameter that allows persistence. The initial insensitivity or increase in the population of the focal species occurs because changes in the populations of other components of the food web compensate for the decline in one or more fitness components of the focal population. However, the compensatory processes are generally nonlinear and often approach their limits abruptly rather than gradually. When there is steady directional change in the environment, populations lag behind the equilibrium population size specified by current environmental conditions. The environmental variable can then decline below the level required for population persistence while the population size is still close to or greater than its original value. Efficient consumers and self-reproducing resources are especially likely to produce this outcome. More complex models with adaptive behavior, additional consumers, or additional resources often exhibit similar trajectories of population size under environmental deterioration.

The interplay between predator's prey preference and environmental heterogeneity in food web long-term stability

Prey preference of a predator is commonly used in models to analyze the timely issue of the relation among food web structure, diversity and stability. Given the variety of these terms in ecological literature, this work shows that domains of stability and species coexistence in food webs can be significantly altered by the chosen structure of predator's prey preference and environmental heterogeneity. Such results may bear upon issues in applied ecology, e.g., species conservation, biological control. More generally, they may serve as a caution with respect to the robustness of some results of food web theory.

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.

Enrichment and ecosystem stability: effect of toxic food

Enrichment in resource availability theoretically destabilizes predator-prey dynamics (the paradox of enrichment). However, a minor change in the resource stoichiometry may make a prey toxic for the predator, and the presence of toxic prey affects the dynamics significantly. Here, theoretically we explore how, at increased carrying capacity, a toxic prey affects the oscillation or destabilization of predator-prey dynamics, and how its presence influences the growth of the predator as well as that of a palatable prey. Mathematical analysis determines the bounds on the food toxicity that allow the coexistence of a predator along with a palatable and a toxic prey. The overall results demonstrate that toxic food counteracts oscillation (destabilization) arising from enrichment of resource availability. Moreover, our results show that, at increased resource availability, toxic food that acts as a source of extra mortality may increase the abundance of the predator as well as that of the palatable prey.

Stoichiometry and food-chain dynamics

Traditional models of chemostat systems looking at interactions between predator, prey and nutrients have used only a single currency, such as energy or nitrogen. In reality, growth of autotrophs and heterotrophs may be limited by various elements, e.g. carbon, nitrogen, phosphorous or iron. In this study we develop a dynamic energy budget model chemostat which has both carbon and nitrogen as currencies, and examine how the dual availability of these elements affects the growth of phytoplankton, trophic transfer to zooplankton, and the resulting stability of the chemostat ecosystem. Both species have two reserve pools to obtain a larger metabolic flexibility with respect to changing external environments. Mineral nitrogen and carbon form the base of the food chain, and they are supplied at a constant rate. In addition, the biota in the chemostat recycle nutrients by means of respiration and excretion, and organic detritus is recycled at a fixed rate. We use numerical bifurcation analysis to assess the model's dynamic behavior. In the model, phytoplankton is nitrogen limited, and nitrogen enrichment can lead to oscillations and multiple stable states. Moreover, we found that recycling has a destabilizing effect on the food chain due to the increased repletion of mineral nutrients. We found that both carbon and nitrogen enrichment stimulate zooplankton growth. Therefore, we conclude that the concept of single-element limitation may not be applicable in an ecosystem context.

Indirect effects of contaminants in aquatic ecosystems

Contaminants such as petroleum hydrocarbons, heavy metals and pesticides can cause direct toxic effects when released into aquatic environments. Sensitive species may be impaired by sublethal effects or decimated by lethality, and this ecological alteration may initiate a trophic cascade or a release from competition that secondarily leads to responses in tolerant species. Contaminants may exert direct effects on keystone facilitator and foundation species, and contaminant-induced changes in nutrient and oxygen dynamics may alter ecosystem function. Thus, populations and communities in nature may be directly and/or indirectly affected by exposure to pollutants. While the direct effects of toxicants usually reduce organism abundance, indirect effects may lead to increased or decreased abundance. Here we review 150 papers that reference indirect toxicant effects in aquatic environments. Studies of accidental contaminant release, chronic contamination and experimental manipulations have identified indirect contaminant effects in pelagic and benthic communities caused by many types of pollutants. Contaminant-induced changes in behavior, competition and predation/grazing rate can alter species abundances or community composition, and enhance, mask or spuriously indicate direct contaminant effects. Trophic cascades were found in 60% of the manipulative studies and, most commonly, primary producers increased in abundance when grazers were selectively eliminated by contaminants. Competitive release may also be common, but is difficult to distinguish from trophic cascades because few experiments are designed to isolate the mechanism(s) causing indirect effects. Indirect contaminant effects may have profound implications in environments with strong trophic cascades such as the freshwater pelagic. In spite of their undesirable environmental influence, contaminants can be useful manipulative tools for the study of trophic and competitive interactions in natural communities.

The Effects of Enrichment on the Dynamics of Apparent Competitive Interactions in Stage‐Structured Systems

In the absence of other limiting factors, assemblages in which species share a common, effective natural enemy are not expected to persist. Although a variety of mechanisms have been postulated to explain the coexistence of species that share natural enemies, the role of productivity gradients has not been explored in detail. Here, we examine how enrichment can affect the outcome of apparent competition. We develop a structured resource/consumer/natural enemy model in which the prey are exposed to attacks during a vulnerable life phase, the length of which depends on resource availability. With a single prey species, the model exhibits the "paradox of enrichment," with unstable dynamics at high levels of resource productivity. We extend this model to consider two prey species linked by a shared predator, each with their own distinct resource base. We derive invasion and stability conditions and examine how enrichment influences prey species exclusion and coexistence. Contrary to expectations from simpler, prey-dependent models, apparent competition is not necessarily strong at high productivity, and prey species coexistence may thus be more likely in enriched environments. Further, the coexistence of apparent competitors may be facilitated by unstable dynamics. These results contrast with the standard theory that apparent competition in productive environments leads to nonpersistent interactions and that coexistence of multispecies interactions is more likely under equilibrial conditions.

Dynamics and responses to mortality rates of competing predators undergoing predator-prey cycles

Two or more competing predators can coexist using a single homogeneous prey species if the system containing all three undergoes internally generated fluctuations in density. However, the dynamics of species that coexist via this mechanism have not been extensively explored. Here, we examine both the nature of the dynamics and the responses of the mean densities of each predator to mortality imposed upon it or its competitor. The analysis of dynamics uncovers several previously undescribed behaviors for this model, including chaotic fluctuations, and long-term transients that differ significantly from the ultimate patterns of fluctuations. The limiting dynamics of the system can be loosely classified as synchronous cycles, asynchronous cycles, and chaotic dynamics. Synchronous cycles are simple limit cycles with highly positively correlated densities of the two predator species. Asynchronous cycles are limit cycles, frequently of complex form, including a significant period during which prey density is nearly constant while one predator gradually, monotonically replaces the other. Chaotic dynamics are aperiodic and generally have intermediate correlations between predator densities. Continuous changes in density-independent mortality rates often lead to abrupt transitions in mean population sizes, and increases in the mortality rate of one predator may decrease the population size of the competing predator. Similarly, increases in the immigration rate of one predator may decrease its own density and increase the density of the other predator. Proportional changes in one predator's birth and death rate functions can have significant effects on the dynamics and mean densities of both predator species. All of these responses to environmental change differ from those observed when competitors coexist stably as the result of resource (prey) partitioning. The patterns described here occur in many other competition models in which there are cycles and differences in the linearity of the responses of consumers to their resources.

The impact of consumer-resource cycles on the coexistence of competing consumers

This article seeks to determine the extent to which endogenous consumer-resource cycles can contribute to the coexistence of competing consumer species. It begins with a numerical analysis of a simple model proposed by Armstrong and McGehee. This model has a single resource and two consumers, one with a linear functional response and one with a saturating response. Coexistence of the two consumer species can occur when the species with a saturating response generates population cycles of the resource, and also has a lower resource requirement for zero population growth. Coexistence can be achieved over a wide range of relative efficiencies of the two consumers provided that the functional response of the saturating consumer reaches its half-saturation value when the resource population is a small fraction of its carrying capacity. In this case, the range of efficiencies allowing coexistence is comparable to that when two competitors have stable dynamics and a high degree of resource partitioning. A variety of modifications of this basic model are analyzed to investigate the consequences for coexistence of different resource growth equations, different functional and numerical response shapes, and other factors. Large differences in functional response shape appear to be the most important factor in producing robust coexistence via resource cycles. If the unstable species has a concave numerical response, this greatly expands the conditions allowing coexistence. If the stable consumer species has a convex (accelerating) functional and/or numerical response, the range of conditions allowing coexistence is also expanded. We argue that large between-species differences in functional response form can often be produced by between-consumer differences in the adaptive adjustments of foraging effort to food density. Consumer-resource cycles can also expand the conditions allowing coexistence when there is resource partitioning, but do so primarily when resource partitioning is relatively slight; this makes the ease of coexistence relatively independent of consumer similarity.