Enrichment in a stoichiometric model of two producers and one consumer

We consider a stoichiometric population model of two producers and one consumer. Stoichiometry can be thought of as the tracking of food quality in addition to food quantity. Our model assumes a reduced rate of conversion of biomass from producer to consumer when food quality is low. The model is open for carbon but closed for nutrient. The introduction of the second producer, which competes with the first, leads to new equilibria, new limit cycles, and new bifurcations. The focus of this paper is on the bifurcations which are the result of enrichment. The primary parameters we vary are the growth rates of both producers. Secondary variable parameters are the total nutrients in the system, and the producer nutrient uptake rates. The possible equilibria are: no-life, one-producer, coexistence of both producers, the consumer coexisting with either producer, and the consumer coexisting with both producers. We observe limit cycles in the latter three coexistence combinations. Bifurcation diagrams along with corresponding representative time series summarize the behaviours observed for this model.     

Complex food webs prevent competitive exclusion among producer species

Herbivorous top-down forces and bottom-up competition for nutrients determine the coexistence and relative biomass patterns of producer species. Combining models of predator-prey and producer-nutrient interactions with a structural model of complex food webs, I investigated these two aspects in a dynamic food-web model. While competitive exclusion leads to persistence of only one producer species in 99.7% of the simulated simple producer communities without consumers, embedding the same producer communities in complex food webs generally yields producer coexistence. In simple producer communities, the producers with the most efficient nutrient-intake rates increase in biomass until they competitively exclude inferior producers. In food webs, herbivory predominantly reduces the biomass density of those producers that dominated in producer communities, which yields a more even biomass distribution. In contrast to prior analyses of simple modules, this facilitation of producer coexistence by herbivory does not require a trade-off between the nutrient-intake efficiency and the resistance to herbivory. The local network structure of food webs (top-down effects of the number of herbivores and the herbivores' maximum consumption rates) and the nutrient supply (bottom-up effect) interactively determine the relative biomass densities of the producer species. A strong negative feedback loop emerges in food webs: factors that increase producer biomasses also increase herbivory, which reduces producer biomasses. This negative feedback loop regulates the coexistence and biomass patterns of the producers by balancing biomass increases of producers and biomass fluxes to herbivores, which prevents competitive exclusion.     

Herbivores, the Functional Diversity of Plants Species, and the Cycling of Nutrients in Ecosystems

Numerous investigators have suggested that herbivores almost always increase rates of nutrient and energy flow through terrestrial ecosystems by returning to the soil fecal material and urine with faster turnover rate than shed plant litter. These previous theories and models always treat the producer compartment as a homogenous pool. Essentially, they assume that consumers feed through a pureed cream of vegetable soup. However, many field observations and experiments have shown that consumers feed selectively (i.e., in a cafeteria) and that consumer choice is made on the same chemical basis that determines decomposition rates. Plants that are preferred food sources often have higher nutrient content, higher growth rates, and faster decomposition rates. As consumption reduces dominance of these species in favor of unpreferred species with slower decomposition, rates of nutrient cycling and energy flow should therefore decline. We analyze a model in which the consumer is given a choice among producers that vary in nutrient uptake rates, rates of nutrient return to decomposers, and consumer preference, and which is parameterized for plants and consumers characteristic of boreal regions. In this model, in an open, well-mixed system with one consumer and two such producers, the nutrient/energy flow will not exceed that of a system without the consumer. If the consumer has a choice between two such producers, it must choose one plant over the other at a greater ratio than that between the two plants in uptake and decay rates. In contrast, in a closed system the consumer must be less selective to coexist with the two plants. The system behavior is determined by the level of nutrient return through the consumer and the differences between the plants in nutrient uptake rates and consumer preference. Species richness affects properties of this model system to the extent that species are functionally distinct (i.e., have different rate constants) in a multivariate space of life history traits (i.e., nutrient uptake and palatability). We suggest that the biochemical variability of plant tissues that simultaneously determines both consumer preference and decomposition rates is an essential feature of food webs that cannot be ignored. Thus, ecosystem models should, at minimum, consider more than one producer type with consumer preference.     

Evolution of nutrient uptake reveals a trade-off in the ecological stoichiometry of plant-herbivore interactions

Nutrient limitation determines the primary production and species composition of many ecosystems. Here we apply an adaptive dynamics approach to investigate evolution of the ecological stoichiometry of primary producers and its implications for plant-herbivore interactions. The model predicts a trade-off between the competitive ability and grazing susceptibility of primary producers, driven by changes in their nutrient uptake rates. High nutrient uptake rates enhance the competitiveness of primary producers but also increase their nutritional quality for herbivores. This trade-off enables coexistence of nutrient exploiters and grazing avoiders. If herbivores are not selective, evolution favors runaway selection toward high nutrient uptake rates of the primary producers. However, if herbivores select nutritious food, the model predicts an evolutionarily stable strategy with lower nutrient uptake rates. When the model is parameterized for phytoplankton and zooplankton, the evolutionary dynamics result in plant-herbivore oscillations at ecological timescales, especially in environments with high nutrient availability and low selectivity of the herbivores. High herbivore selectivity stabilizes the community dynamics. These model predictions show that evolution permits nonequilibrium dynamics in plant-herbivore communities and shed new light on the evolutionary forces that shape the ecological stoichiometry of primary producers.     

A new class of non-linear stochastic population models with mass conservation

We study the effects of random feeding, growing and dying in a closed nutrient-limited producer/consumer system, in which nutrient is fully conserved, not only in the mean, but, most importantly, also across random events. More specifically, we relate these random effects to the closest deterministic models, and evaluate the importance of the various times scales that are involved. These stochastic models differ from deterministic ones not only in stochasticity, but they also have more details that involve shorter times scales. We tried to separate the effects of more detail from that of stochasticity. The producers have (nutrient) reserve and (body) structure, and so a variable chemical composition. The consumers have only structure, so a constant chemical composition. The conversion efficiency from producer to consumer, therefore, varies. The consumers use reserve and structure of the producers as complementary compounds, following the rules of Dynamic Energy Budget theory. Consumers die at constant specific rate and decompose instantaneously. Stochasticity is incorporated in the behaviour of the consumers, where the switches to handling and searching, as well as dying are Poissonian point events. We show that the stochastic model has one parameter more than the deterministic formulation without time scale separation for conversions between searching and handling consumers, which itself has one parameter more than the deterministic formulation with time scale separation for these conversions. These extra parameters are the contributions of a single individual producer and consumer to their densities, and the ratio of the two, respectively. The tendency to oscillate increases with the number of parameters. The focus bifurcation point has more relevance for the asymptotic behaviour of the stochastic model than the Hopf bifurcation point, since a randomly perturbed damped oscillation exhibits a behaviour similar to that of the stochastic limit cycle particularly near this bifurcation point. For total nutrient values below the focus bifurcation point, the system gradually becomes more confined to the direct neighbourhood of the isocline for which the producers do not change.     

Examination of the role of detritus food quality,phytoplankton intracellular storage capacity,and zooplankton stoichiometry on planktonic dynamics

Nutrient stoichiometric ratios are primary driving factors of planktonic food web dynamics. Ecological stoichiometry theory postulates the elemental ratios of consumer species to be homeostatic, while primary-producer stoichiometry may vary with ambient nutrient availability. The notion of phytoplankton intracellular storage is far from novel, but remains largely unexplored in modeling studies of population dynamics. We constructed a seasonally-unforced, zero-dimensional, nutrient–phytoplankton–zooplankton–detritus (NPZD) model that considers dynamic phytoplankton phosphorus reserves and quasi-dynamic zooplankton stoichiometry. A generic food quality term is used to express seston biochemical composition, ingestibility, and digestibility. We examined the sensitivity of the planktonic food web patterns to light and nutrient availability, zooplankton mortality, and detritus food quality as well as to phytoplankton intracellular storage and zooplankton stoichiometry. Our results reinforce earlier findings that high quality seston exerts a stabilizing effect on food web dynamics. However, we also found that the combination of low algal and high detritus food quality with high zooplankton mortality yielded limit cycles and multiple steady states, suggesting that the heterogeneity characterizing seston nutritional quality may have more complicated ecological ramifications. Our numerical experiments identify resource competition strategies related to nutrient transport rates and internal nutrient quotas that may be beneficial for phytoplankton to persevere in resource-limiting habitats. We also highlight the importance of the interplay between optimal stoichiometry and the factors controlling homeostatic rigidity in zooplankton. In particular, our predictions show that the predominance of phosphorus-rich and tightly-homeostatic herbivores in nutrient-enriched environments with low seston food quality can potentially result in high phytoplankton abundance, high phytoplankton-to-zooplankton ratios, and acceleration of oscillatory dynamics. Generally, our modeling study emphasizes the impact of both intracellular/somatic storage and food quality on prey–predator interactions, pinpointing an important aspect of food web dynamics usually neglected by the contemporary modeling studies.     

Linking limitation to species composition: importance of inter- and intra-specific variation in grazing resistance

Short-term responses of producers highlight that key nutrients (e.g., N, P)—or combinations of these nutrients—limit primary production in aquatic and terrestrial ecosystems. These discoveries continue to provide highly valuable insights, but it remains important to ask whether nutrients always predominantly limit producers despite wide variation in nutrient supply and herbivory among systems. After all, predictions from simple food chain models (derived here) readily predict that limitation by grazers can exceed that by nutrients, given sufficient enrichment. However, shifts in composition of producers and/or increasing dominance of invulnerable stages of a producer can, in theory, reduce grazer limitation and retain primacy of nutrient limitation along nutrient supply gradients. We observed both mechanisms (inter- and intra-species variation in vulnerability to herbivory) working in a two-part mesocosm experiment. We incubated diverse benthic algal assemblages for several months either in the presence or absence of benthic macro-grazers in mesocosms that spread a broad range of nutrient supply. We then conducted short-term assays of nutrient and grazer limitation on these communities. In the “historically grazed” assemblages, we found shifts from more edible, better competitors to more resistant producers over enrichment gradients (as anticipated by the food web model built with a tradeoff in resistance vs. competitive abilities). However, contrary to our expectations, “historically ungrazed” assemblages became dominated by producers with vulnerable juvenile forms but inedible adult forms (long filaments). Consequently, we observed higher resource limitation rather than grazer limitation over this nutrient supply gradient in both “historically grazed” (expected) and “historically ungrazed” (not initially expected). Thus, via multiple, general mechanisms involving resistance to grazing (changes in species composition or variation in stage-structured vulnerability), producer assemblages should remain more strongly or as strongly limited by nutrients than grazers, even over large enrichment gradients. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Bottom‐up control in the benthos of ocean‐exposed sandy beaches?

Bottom‐up control is a fundamental structuring force in food webs. Food webs of ocean‐exposed sandy beaches are predicted to be bottom‐up controlled systems, underpinned by imported organic matter rather than in situ primary production. This ecological model of resource‐based regulation of biological assemblages is juxtaposed against a prevailing paradigm built around a dominance of physical drivers in sandy beach ecosystems. Surprisingly, given the apparently ubiquitous energetic subsidies of beach food webs, the central premise of bottom‐up control has not been tested. Here we experimentally manipulated in situ nutrient levels on a sandy beach to test food web responses at the levels of primary producers (benthic microalgae) and their grazers (meiofauna). The meiofauna community as a whole appeared most strongly influenced by the local physical environment, particularly changes in sediment grain size – this supports the traditional ‘environmental control paradigm’. We also detected a significant, positive response of two consumer groups of the meiofauna (nematodes, ostracods) to nutrient enrichment that supports a model of biological, bottom‐up control. Although the predicted response of elevated producer biomass following nutrient enrichment was not detected, intense grazing pressure on new, stimulated production may have masked positive responses by the primary producers. Multichannel regulation of food webs is likely for many exposed sandy beaches, albeit an often lower importance of in situ bottom‐up forces compared with stronger environmental control.     

Food quantity and quality regulation of trophic transfer between primary producers and a keystone grazer (Daphnia) in pelagic freshwater food webs

The transfer of energy and nutrients from plants to animals is a key process in all ecosystems. In lakes, inefficient transfer of primary producer derived energy can result in low animal growth rates, accumulation of nuisance phytoplankton blooms and dissipation of energy from the ecosystem. Most research on carbon transfer efficiency in pelagic food webs has focused on either food quantity or food quality, with the latter considered separately as either elemental stoichiometry or biochemical composition. The natural occurrence and magnitude of these types of growth limitations and their combined effects on Daphnia , a keystone grazer in pelagic freshwater ecosystems, are largely unknown. Our empirical models predict that the strength and nature of food quantity and quality limitation varies greatly with lake trophic state (total phosphorus, TP) and that Daphnia growth rates and thus energy and nutrient transfer efficiency are highest in lakes with intermediate trophic status (TP 10–25 μg l⁻¹). We predict that food availability place the greatest constraint on Daphnia growth in nutrient poor lakes (TP≤4 μg l⁻¹). Phosphorus limitation of Daphnia growth increased with decreasing TP, but the overall effect was never predicted to be the dominant constraining factor. Eicosapentaenoic acid (EPA, 20:5ω3) limitation was predicted to occur in both nutrient poor and nutrient rich lakes and placed the primary constraint on food quality in the most productive lakes. Two contrasting EPA-models gave different results on the magnitude of EPA-limitation, implying that additional food quality factors decrease Daphnia growth at high TP. In conclusion, the model predicts that Daphnia growth should peak in mesotrophic lakes, food quantity will place the greatest constraint on growth in oligotrophic lakes and EPA will primarily limit growth in eutrophic lakes.     

High food quality of prey lowers its risk of extinction

The mineral and biochemical food quality of prey may limit predator production. This well‐studied direct bottom–up effect is especially prominent for herbivore–plant interactions. Low‐quality prey species, particularly when defended, are generally considered to be less prone to predator‐driven extinction. Undefended high‐quality prey species sustain high predator production thereby potentially increasing their own extinction risk. The food quality of primary producers is highly species‐specific. In communities of competing prey species, predators thus may supplement their diets of low‐quality prey with high‐quality prey, leading to indirect horizontal interactions between prey species of different food quality. We explore how these predator‐mediated indirect interactions affect species coexistence in a general predator–prey model that is parametrized for an experimental algae– rotifer system. To cover a broad range of three essential functional traits that shape many plant–herbivore interactions we consider differences in 1) the food quality of the prey species, 2) their competitive ability for nutrient uptake and 3) their defence against predation. As expected, low food quality of prey can, similarly to defence, provide protection against extinction by predation. Counterintuitively, our simulations demonstrate that being of high food quality also prevents extinction of that prey species and additionally promotes coexistence with a competing, low‐quality prey. The persistence of the high‐quality prey enables a high conversion efficiency and control of the low‐quality prey by the predator and allows for re‐allocation of nutrients to the high‐quality competitor. Our results show that high food quality is not necessarily detrimental for a prey species but instead can protect against extinction and promote species richness and functional biodiversity.     

Cachers, scavengers, and thieves: a novel mechanism for desert rodent coexistence

A biologically explicit simulation model of resource competition between two species of seed-eating heteromyid rodent indicates that stable coexistence is possible on a homogeneous resource if harvested food is stored and consumers steal each other's caches. Here we explore the coexistence mechanisms involved by analyzing how consumer phenotypes and presence of a noncaching consumer affect the competitive outcome. Without cache exchange, the winning consumer is better at harvesting seeds and produces more offspring per gram of stored food. With cache exchange, coexistence is promoted by interspecific trade-offs between harvest ability, metabolic efficiency, and ability to pilfer defended caches of heterospecifics or scavenge undefended caches of dead conspecifics or heterospecifics. Cache exchange via pilferage can equalize competitor fitnesses but has little stabilizing effect and leads to stable coexistence only in the presence of a noncaching consumer. In contrast, scavenging is both equalizing and stabilizing and promotes coexistence without a third consumer. Because body size affects a heteromyid rodent's metabolic rate, seed harvest rate, caching strategy, and ability to steal caches, interspecific differences in body size should produce the trade-offs necessary for coexistence. The observation that coexisting heteromyids differ in body size therefore indicates that cache exchange may promote diversity in heteromyid communities.     

Quasi-equilibrium reduction in a general class of stoichiometric producer–consumer models

This article compares a general closed nutrient, stoichiometric producer–consumer model to a two-dimensional ‘quasi-equilibrium’ approximation. We demonstrate that the quasi-equilibrium system can be rigorously analysed, resulting in nullcline-based criteria for the local stability of system equilibria and for the non-existence of periodic orbits. These results are applied to a study of the dependence of the reduced system on nutrient and energy enrichment. When energy and nutrient enrichment are considered together, the associated bifurcation structures of the two models are seen to share the same essential qualitative characteristics. However, numerical simulations of the three-dimensional parent model show highly complex domains of the persistence and extinction that by Poincare–Bendixson theory are not possible for the two-dimensional reduction. This complexity demonstrates a major difference between the two models, and suggests potential challenges in the use of either model for predicting the long-term behaviour of real-world systems at specific nutrient and energy levels.     

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.     

Nutrient Enrichment and Food Web Composition Affect Ecosystem Metabolism in an Experimental Seagrass Habitat

Background

Food web composition and resource levels can influence ecosystem properties such as productivity and elemental cycles. In particular, herbivores occupy a central place in food webs as the species richness and composition of this trophic level may simultaneously influence the transmission of resource and predator effects to higher and lower trophic levels, respectively. Yet, these interactions are poorly understood.

Methodology/Principal Findings

Using an experimental seagrass mesocosm system, we factorially manipulated water column nutrient concentrations, food chain length, and diversity of crustacean grazers to address two questions: (1) Does food web composition modulate the effects of nutrient enrichment on plant and grazer biomasses and stoichiometry? (2) Do ecosystem fluxes of dissolved oxygen and nutrients more closely reflect above-ground biomass and community structure or sediment processes? Nutrient enrichment and grazer presence generally had strong effects on biomass accumulation, stoichiometry, and ecosystem fluxes, whereas predator effects were weaker or absent. Nutrient enrichment had little effect on producer biomass or net ecosystem production but strongly increased seagrass nutrient content, ecosystem flux rates, and grazer secondary production, suggesting that enhanced production was efficiently transferred from producers to herbivores. Gross ecosystem production (oxygen evolution) correlated positively with above-ground plant biomass, whereas inorganic nutrient fluxes were unrelated to plant or grazer biomasses, suggesting dominance by sediment microbial processes. Finally, grazer richness significantly stabilized ecosystem processes, as predators decreased ecosystem production and respiration only in the zero- and one- species grazer treatments.

Conclusions/Significance

Overall, our results indicate that consumer presence and species composition strongly influence ecosystem responses to nutrient enrichment, and that increasing herbivore diversity can stabilize ecosystem flux rates in the face of perturbations.     

Computing the heteroclinic bifurcation curves in predator–prey systems with ratio-dependent functional response

Predator-prey models with Michaelis-Menten-Holling type ratio- dependent functional response exhibit very rich and complex dynamical behavior, such as the existence of degenerate equilibria, appearance of limit cycles and heteroclinic loops, and the coexistence of two attractive equilibria. In this paper, we study heteroclinic bifurcations of such a predator-prey model. We first calculate the higher order Melnikov functions by transforming the model into a Hamiltonian system and then provide an algorithm for computing higher order approximations of the heteroclinic bifurcation curves.     

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     

Interplay between the paradox of enrichment and nutrient cycling in food webs

Nutrient cycling is fundamental to ecosystem functioning. Despite recent major advances in the understanding of complex food web dynamics, food web models have so far generally ignored nutrient cycling. However, nutrient cycling is expected to strongly impact food web stability and functioning. To make up for this gap, we built an allometric and size structured food web model including nutrient cycling. By releasing mineral nutrients, recycling increases the availability of limiting resources for primary producers and links each trophic level to the bottom of food webs. We found that nutrient cycling can provide a significant part of the total nutrient supply of the food web, leading to a strong enrichment effect that promotes species persistence in nutrient poor ecosystems but leads to a paradox of enrichment at high nutrient inputs. The presence of recycling loops linking each trophic level to the basal resources weakly affects species biomass temporal variability in the food web. Recycling loops tend to slightly dampen the destabilising effect of nutrient enrichment on consumer temporal variability while they have opposite effects for primary producers. By considering nutrient cycling, this new model improves our understanding of the response of food webs to nutrient availability and opens perspectives to better link studies on food web dynamics and ecosystem functioning.     

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.     

Multiple limit cycles in the standard model of three species competition for three essential resources

We consider the dynamics of the standard model of 3 species competing for 3 essential (non-substitutable) resources in a chemostat using Liebig's law of the minimum functional response. A subset of these systems which possess cyclic symmetry such that its three single-population equilibria are part of a heteroclinic cycle bounding the two-dimensional carrying simplex is examined. We show that a subcritical Hopf bifurcation from the coexistence equilibrium together with a repelling heteroclinic cycle leads to the existence of at least two limit cycles enclosing the coexistence equilibrium on the carrying simplex- the ``inside' one is an unstable separatrix and the ``outside' one is at least semi-stable relative to the carrying simplex. Numerical simulations suggest that there are exactly two limit cycles and that almost every positive solution approaches either the stable limit cycle or the stable coexistence equilibrium, depending on initial conditions. Bifurcation diagrams confirm this picture and show additional features. In an alternative scenario, we show that the subcritical Hopf together with an attracting heteroclinic cycle leads to an unstable periodic orbit separatrix. This research was partially supported by NSF grant DMS 0211614. KY 40292, USA. This author's research was supported in part by NSF grant DMS 0107160     

Zooplankton eat what they need: copepod selective feeding and potential consequences for marine systems

Herbivores are generally faced with a plethora of resources which differ in quality. Therefore, they should be able to select foods which most closely match their metabolic needs. Here, we tested the hypothesis that copepods of the species Acartia tonsa select prey cells based on quality differences within prey species. We assessed age‐specific variation in feeding behaviour and evaluated the potential consequences of such variation for nutrient cycles. Nauplii (young) stages characterized by a low nitrogen to phosphorus (N:P) ratio in their body tissue selected for phosphorus‐rich food, while older copepodite stages with higher body N:P selected for nitrogen‐rich food. Further, the analysis of a 35‐year data set in the southern North Sea revealed a positive correlation between the abundance of nauplii and the ratio of dissolved inorganic N:P, thus suggesting that P‐availability for primary producers declines with the population densities of nauplii. Our findings demonstrate that a combination of stage‐specific selective feeding and body stoichiometry has the potential to affect cycling of limiting nutrients when consumer populations change in composition.