Stoichiometry and food-chain dynamics

Population dynamics of a stoichiometric aquatic tri-trophic level model with fear effect

In this paper, a stoichiometric aquatic tri-trophic level model is proposed and analyzed, which incorporates the effect of light and phosphorus, as well as the fear effect in predator-prey interactions. The analysis of the model includes the dissipativity and the existence and stability of equilibria. The influence of environmental factors and fear effect on the dynamics of the system is particularly investigated. The key findings reveal that the coexistence of populations is positively influenced by an appropriate level of light intensity and/or the dissolved phosphorus input concentration; however, excessive levels of phosphorus input can disrupt the system, leading to chaotic behaviors. Furthermore, it is found that the fear effect can stabilize the system and promote the chances of population coexistence.

Stoichiometric Ecotoxicology for a Multisubstance World

Nutritional and contaminant stressors influence organismal physiology, trophic interactions, community structure, and ecosystem-level processes; however, the interactions between toxicity and elemental imbalance in food resources have been examined in only a few ecotoxicity studies. Integrating well-developed ecological theories that cross all levels of biological organization can enhance our understanding of ecotoxicology. In the present article, we underline the opportunity to couple concepts and approaches used in the theory of ecological stoichiometry (ES) to ask ecotoxicological questions and introduce stoichiometric ecotoxicology, a subfield in ecology that examines how contaminant stress, nutrient supply, and elemental constraints interact throughout all levels of biological organization. This conceptual framework unifying ecotoxicology with ES offers potential for both empirical and theoretical studies to deepen our mechanistic understanding of the adverse outcomes of chemicals across ecological scales and improve the predictive powers of ecotoxicology.

What is the status of metabolic theory one century after Pütter invented the von Bertalanffy growth curve?

Metabolic theory aims to tackle ecological and evolutionary problems by explicitly including physical principles of energy and mass exchange, thereby increasing generality and deductive power. Individual growth models (IGMs) are the fundamental basis of metabolic theory because they represent the organisational level at which energy and mass exchange processes are most tightly integrated and from which scaling patterns emerge. Unfortunately, IGMs remain a topic of great confusion and controversy about the origins of the ideas, their domain and breadth of application, their logical consistency and whether they can sufficiently capture reality. It is now 100 years since the first theoretical model of individual growth was put forward by Pütter. His insights were deep, but his model ended up being attributed to von Bertalanffy and his ideas largely forgotten. Here I review Pütter's ideas and trace their influence on existing theoretical models for growth and other aspects of metabolism, including those of von Bertalanffy, the Dynamic Energy Budget (DEB) theory, the Gill-Oxygen Limitation Theory (GOLT) and the Ontogenetic Growth Model (OGM). I show that the von Bertalanffy and GOLT models are minor modifications of Pütter's original model. I then synthesise, compare and critique the ideas of the two most-developed theories, DEB theory and the OGM, in relation to Pütter's original ideas. I formulate the Pütter, DEB and OGM models in the same structure and with the same notation to illustrate the major similarities and differences among them. I trace the confusion and controversy regarding these theories to the notions of anabolism, catabolism, assimilation and maintenance, the connections to respiration rate, and the number of parameters and state variables their models require. The OGM model has significant inconsistencies that stem from the interpretation of growth as the difference between anabolism and maintenance, and these issues seriously challenge its ability to incorporate development, reproduction and assimilation. The DEB theory is a direct extension of Pütter's ideas but with growth being the difference between assimilation and maintenance rather than anabolism and catabolism. The DEB theory makes the dynamics of Pütter's 'nutritive material' explicit as well as extending the scheme to include reproduction and development. I discuss how these three major theories for individual growth have been used to explain 'macrometabolic' patterns including the scaling of respiration, the temperature-size rule (first modelled by Pütter), and the connection to life history. Future research on the connections between theory and data in these macrometabolic topics have the greatest potential to advance the status of metabolic theory and its value for pure and applied problems in ecology and evolution.

Predator-driven elemental cycling: the impact of predation and risk effects on ecosystem stoichiometry

Empirical evidence is beginning to show that predators can be important drivers of elemental cycling within ecosystems by propagating indirect effects that determine the distribution of elements among trophic levels as well as determine the chemical content of organic matter that becomes decomposed by microbes. These indirect effects can be propagated by predator consumptive effects on prey, nonconsumptive (risk) effects, or a combination of both. Currently, there is insufficient theory to predict how such predator effects should propagate throughout ecosystems. We present here a theoretical framework for exploring predator effects on ecosystem elemental cycling to encourage further empirical quantification. We use a classic ecosystem trophic compartment model as a basis for our analyses but infuse principles from ecological stoichiometry into the analyses of elemental cycling. Using a combined analytical-numerical approach, we compare how predators affect cycling through consumptive effects in which they control the flux of nutrients up trophic chains; through risk effects in which they change the homeostatic elemental balance of herbivore prey which accordingly changes the element ratio herbivores select from plants; and through a combination of both effects. Our analysis reveals that predators can have quantitatively important effects on elemental cycling, relative to a model formalism that excludes predator effects. Furthermore, the feedbacks due to predator nonconsumptive effects often have the quantitatively strongest impact on whole ecosystem elemental stocks, production and efficiency rates, and recycling fluxes by changing the stoichiometric balance of all trophic levels. Our modeling framework predictably shows how bottom-up control by microbes and top-down control by predators on ecosystems become interdependent when top predator effects permeate ecosystems.

Predation risk, stoichiometric plasticity and ecosystem elemental cycling

It is widely held that herbivore growth and production is limited by dietary nitrogen (N) that in turn constrains ecosystem elemental cycling. Yet, emerging evidence suggests that this conception of limitation may be incomplete, because chronic predation risk heightens herbivore metabolic rate and shifts demand from N-rich proteins to soluble carbohydrate-carbon (C). Because soluble C can be limiting, predation risk may cause ecosystem elemental cycling rates and stoichiometric balance to depend on herbivore physiological plasticity. We report on a stoichiometrically explicit ecosystem model that investigates this problem. The model tracks N, and soluble and recalcitrant C through ecosystem compartments. We evaluate how soluble plant C influences C and N stocks and flows in the presence and absence of predation risk. Without risk, herbivores are limited by N and respire excess C so that plant-soluble C has small effects only on elemental stocks and flows. With predation risk, herbivores are limited by soluble C and release excess N, so plant-soluble C critically influences ecosystem elemental stocks flows. Our results emphasize that expressing ecosystem stoichiometric balance using customary C:N ratios that do not distinguish between soluble and recalcitrant C may not adequately describe limitations on elemental cycling.

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.

Modelling the ecological niche from functional traits

The niche concept is central to ecology but is often depicted descriptively through observing associations between organisms and habitats. Here, we argue for the importance of mechanistically modelling niches based on functional traits of organisms and explore the possibilities for achieving this through the integration of three theoretical frameworks: biophysical ecology (BE), the geometric framework for nutrition (GF) and dynamic energy budget (DEB) models. These three frameworks are fundamentally based on the conservation laws of thermodynamics, describing energy and mass balance at the level of the individual and capturing the prodigious predictive power of the concepts of 'homeostasis' and 'evolutionary fitness'. BE and the GF provide mechanistic multi-dimensional depictions of climatic and nutritional niches, respectively, providing a foundation for linking organismal traits (morphology, physiology, behaviour) with habitat characteristics. In turn, they provide driving inputs and cost functions for mass/energy allocation within the individual as determined by DEB models. We show how integration of the three frameworks permits calculation of activity constraints, vital rates (survival, development, growth, reproduction) and ultimately population growth rates and species distributions. When integrated with contemporary niche theory, functional trait niche models hold great promise for tackling major questions in ecology and evolutionary biology.

From empirical patterns to theory: a formal metabolic theory of life

The diversity of life on Earth raises the question of whether it is possible to have a single theoretical description of the quantitative aspects of the organization of metabolism for all organisms. However, similarities between organisms, such as von Bertalanffy's growth curve and Kleiber's law on metabolic rate, suggest that mechanisms that control the uptake and use of metabolites are common to all organisms. These and other widespread empirical patterns in biology should be the ultimate test for any metabolic theory that hopes for generality. The present study (i) collects empirical evidence on growth, stoichiometry, feeding, respiration and energy dissipation and exhibits it as stylized biological facts; (ii) formalizes assumptions and propositions in a metabolic theory that is fully consistent with the Dynamic Energy Budget theory; and (iii) proves that these assumptions and propositions are consistent with the stylized facts.

Foraging behavior by Daphnia in stoichiometric gradients of food quality

Mismatches in the elemental composition of herbivores and their resources can impact herbivore growth and reproduction. In aquatic systems, the ratio of elements, such as C, P, and N, is used to characterize the food quality of algal prey. For example, large increases in the C:P ratio of edible algae can decrease rates of growth and reproduction in Daphnia. Current theory emphasizes that Daphnia utilize only assimilation and respiration processes to maintain an optimal elemental composition, yet studies of terrestrial herbivores implicate behavioral processes in coping with local variation in food quality. We tested the ability of juvenile and adult Daphnia to locate regions of high-quality food within a spatial gradient of algal prey differing in C:P ratio, while holding food density constant over space. Both juveniles and adults demonstrated similar behavior by quickly locating (i.e., <10 min) the region of high food quality. Foraging paths were centred on regions of high food quality and these differed significantly from paths of individuals exposed to a homogeneous environment of both food density and food quality. Ingestion rate experiments on algal prey of differing stoichiometric ratio show that individuals can adjust their intake rate over fast behavioral time-scales, and we use these data to examine how individuals choose foraging locations when presented with a spatial gradient that trades off food quality and food quantity. Daphnia reared under low food quality conditions chose to forage in regions of high food quality even though they could attain the same C ingestion rate elsewhere along a spatial gradient. We argue that these aspects of foraging behavior by Daphnia have important implications for how these herbivores manage their elemental composition and our understanding of the dynamics of these herbivore-plant systems in lakes and ponds where spatial variation in food quality is present.

Paradoxes of Enrichment: Effects of Increased Light versus Nutrient Supply on Pelagic Producer‐Grazer Systems

Energy-based plant-herbivore models produce the "paradox of enrichment," a destabilizing influence of enrichment on population dynamics. Because many plants change their carbon : nutrient stoichiometry in response to the light : nutrient supply ratio, enrichment with light can cause a mismatch between the elemental compositions of plants and their herbivores. Herbivore growth rates may then decrease with increased light supply, which is termed the "paradox of energy enrichment." I present a stoichiometric phytoplankton-grazer model that accounts for the dynamical vertical light gradient and explore how algal and grazer densities, mineral nutrient concentration, algal nutrient stoichiometry, and system stability respond to enrichment with light (through changes in irradiance, background turbidity, and water column depth) versus enrichment with nutrients. Parameterized for Daphnia, the model produces several "unusual" phenomena: multiple equilibria (with grazers extinct in spite of high algal biomass at one equilibrium), inconsistent light enrichment effects on stability (light enrichment first destabilizes and then stabilizes), and the paradox of energy enrichment. These phenomena are restricted to the low end of realistic nutrient supplies except in very shallow systems, where high sedimentation rates effectively deplete the water column of nutrients. At higher nutrient supplies, light enrichment produces the classical paradox of enrichment, leading first to an increase in grazers at a stable equilibrium and then to algae-grazer oscillations.

Biodiversity maintenance in food webs with regulatory environmental feedbacks

Although the food web is one of the most fundamental and oldest concepts in ecology, elucidating the strategies and structures by which natural communities of species persist remains a challenge to empirical and theoretical ecologists. We show that simple regulatory feedbacks between autotrophs and their environment when embedded within complex and realistic food-web models enhance biodiversity. The food webs are generated through the niche-model algorithm and coupled with predator-prey dynamics, with and without environmental feedbacks at the autotroph level. With high probability and especially at lower, more realistic connectance levels, regulatory environmental feedbacks result in fewer species extinctions, that is, in increased species persistence. These same feedback couplings, however, also sensitize food webs to environmental stresses leading to abrupt collapses in biodiversity with increased forcing. Feedback interactions between species and their material environments anchor food-web persistence, adding another dimension to biodiversity conservation. We suggest that the regulatory features of two natural systems, deep-sea tubeworms with their microbial consortia and a soil ecosystem manifesting adaptive homeostatic changes, can be embedded within niche-model food-web dynamics.