Global analysis of a stoichiometric producer–grazer model with Holling type functional responses

Cells, the basic units of organisms, consist of multiple essential elements such as carbon, nitrogen, and phosphorus. The scarcity of any of these elements can strongly restrict cellular and organismal growth. During recent years, ecological models incorporating multiple elements have been rapidly developed in many studies, which form a new research field of mathematical and theoretical biology. Among these models, the one proposed by Loladze et al. (Bull Math Biol 62:1137–1162, 2000) is prominent and has been highly cited. However, the global analysis of this nonsmooth model has never been done. The aim of this paper is to provide the complete global analysis for the model with Holling type I functional response and perform a bifurcation analysis for the model with Holling type II functional response.     

Towards a mechanistic understanding of the impacts of nitrogen deposition on producer–consumer interactions

Nitrogen (N) deposition has increased substantially since the second half of the 20th century due to human activities. This increase of reactive N into the biosphere has major implications for ecosystem functioning, including primary production, soil and water chemistry and producer community structure and diversity. Increased N deposition is also linked to the decline of insects observed over recent decades. However, we currently lack a mechanistic understanding of the effects of high N deposition on individual fitness, species richness and community structure of both invertebrate and vertebrate consumers. Here, we review the effects of N deposition on producer–consumer interactions, focusing on five existing ecological frameworks: C:N:P ecological stoichiometry, trace element ecological stoichiometry, nutritional geometry, essential micronutrients and allelochemicals. We link reported N deposition-mediated changes in producer quality to life-history strategies and traits of consumers, to gain a mechanistic understanding of the direction of response in consumers. We conclude that high N deposition influences producer quality via eutrophication and acidification pathways. This makes oligotrophic poorly buffered ecosystems most vulnerable to significant changes in producer quality. Changes in producer quality between the reviewed frameworks are often interlinked, complicating predictions of the effects of high N deposition on producer quality. The degree and direction of fitness responses of consumers to changes in producer quality varies among species but can be explained by differences in life-history traits and strategies, particularly those affecting species nutrient intake regulation, mobility, relative growth rate, host-plant specialisation, ontogeny and physiology. To increase our understanding of the effects of N deposition on these complex mechanisms, the inclusion of life-history traits of consumer species in future study designs is pivotal. Based on the reviewed literature, we formulate five hypotheses on the mechanisms underlying the effects of high N deposition on consumers, by linking effects of nutritional ecological frameworks to life-history strategies. Importantly, we expect that N-deposition-mediated changes in producer quality will result in a net decrease in consumer community as well as functional diversity. Moreover, we anticipate an increased risk of outbreak events of a small subset of generalist species, with concomitant declines in a multitude of specialist species. Overall, linking ecological frameworks with consumer life-history strategies provides a mechanistic understanding of the impacts of high N deposition on producer–consumer interactions, which can inform management towards more effective mitigation strategies.     

A mathematical model of the interactions in the mixed culture of invertebrates and algae in the “producer–consumer” aquatic biotic cycle

This paper presents a mathematical model of interactions between two herbivorous invertebrates (ciliate Paramecium caudatum and rotifer Brachionus plicatilis) and two planktonic algae (Chlorella vulgaris and Scenedesmus quadricauda) spatially segregated in two compartments of a chemostat–type experimental microcosm system. The model mimics a producer–consumer aquatic biotic cycle, describing the dynamics of the mixed culture of ciliates and rotifers, as consumer compartment, feeding on the mixed algal culture, as producer compartment, under N-limiting conditions. We experimentally found that metabolites of the alga Scenedesmus produce an adverse effect on the reproduction of ciliate Paramecium. Taking this effect into account improved the behavior of the model, the results of which came into qualitative agreement with the experimental results. Both our experimental and modeling approaches demonstrated that, even in conditions of a spatially–segregated producer-consumer biotic cycle, species coexistence is impossible either in the mixed algal culture or in the mixed invertebrate culture. Scenedesmus excluded Chlorella, whereas Brachionus excluded Paramecium.     

Coevolution of adaptive technology,maladaptive culture and population size in a producer–scrounger game

Technology (i.e. tools, methods of cultivation and domestication, systems of construction and appropriation, machines) has increased the vital rates of humans, and is one of the defining features of the transition from Malthusian ecological stagnation to a potentially perpetual rising population growth. Maladaptations, on the other hand, encompass behaviours, customs and practices that decrease the vital rates of individuals. Technology and maladaptations are part of the total stock of culture carried by the individuals in a population. Here, we develop a quantitative model for the coevolution of cumulative adaptive technology and maladaptive culture in a ‘producer–scrounger’ game, which can also usefully be interpreted as an ‘individual–social’ learner interaction. Producers (individual learners) are assumed to invent new adaptations and maladaptations by trial-and-error learning, insight or deduction, and they pay the cost of innovation. Scroungers (social learners) are assumed to copy or imitate (cultural transmission) both the adaptations and maladaptations generated by producers. We show that the coevolutionary dynamics of producers and scroungers in the presence of cultural transmission can have a variety of effects on population carrying capacity. From stable polymorphism, where scroungers bring an advantage to the population (increase in carrying capacity), to periodic cycling, where scroungers decrease carrying capacity, we find that selection-driven cultural innovation and transmission may send a population on the path of indefinite growth or to extinction.     

Bayesian latent class models for capture–recapture in the presence of missing data

We propose a method for estimating the size of a population in a multiple record system in the presence of missing data. The method is based on a latent class model where the parameters and the latent structure are estimated using a Gibbs sampler. The proposed approach is illustrated through the analysis of a data set already known in the literature, which consists of five registrations of neural tube defects.     

Patterns of patchy spread in multi-species reaction–diffusion models

Spread of populations in space often takes place via formation, interaction and propagation of separated patches of high species density, without formation of continuous fronts. This type of spread is called a ‘patchy spread’. In earlier models, this phenomenon was considered to be a result of a pronounced environmental or/and demographic stochasticity. Recently, it was found that a patchy spread can arise in a fully deterministic predator–prey system and in models of infectious diseases; in each case the process takes place in a homogeneous environment. It is well recognized that the observed patterns of patchy spread in nature are a result of interplay between stochastic and deterministic factors. However, the models considering deterministic mechanism of patchy spread are developed and studied much less compared to those based on stochastic mechanisms. A further progress in the understanding of the role of deterministic factors in the patchy spread would be extremely helpful. Here we apply multi-species reaction–diffusion models of two spatial dimensions in a homogeneous environment. We demonstrate that patterns of patchy spread are rather common for the considered approach, in particular, they arise both in mutualism and competition models influenced by predation. We show that this phenomenon can occur in a system without a strong Allee effect, contrary to what was assumed to be crucial in earlier models. We show, as well, a pattern of patchy spread having significantly different speeds in different spatial directions. We analyze basic features of spatiotemporal dynamics of patchy spread common for the reaction–diffusion approach. We discuss in which ecosystems we would observe patterns of deterministic patchy spread due to the considered mechanism.     

Malaria immunity in infants: a special case of a general phenomenon?

Newborn infants in endemic areas are markedly resistant to Plasmodium falciparum malaria. Consequently, severe disease is rare during the first few months of life, and infections tend to be low density and relatively asymptomatic during this period. Although this is generally ascribed to passively transferred immunity, attempts to identify the targets and mechanisms of this protection have been unsuccessful. The implications of the hypothesis that the progression from resistance through susceptibility and back to resistance during infancy and early childhood reflects the gradual acquisition of IgG to variant surface antigens (VSAs), while protection from maternal VSA-specific IgG steadily fades, are discussed here.     

A general reaction–diffusion model of acidity in cancer invasion

We model the metabolism and behaviour of a developing cancer tumour in the context of its microenvironment, with the aim of elucidating the consequences of altered energy metabolism. Of particular interest is the Warburg Effect, a widespread preference in tumours for cytosolic glycolysis rather than oxidative phosphorylation for glucose breakdown, as yet incompletely understood. We examine a candidate explanation for the prevalence of the Warburg Effect in tumours, the acid-mediated invasion hypothesis, by generalising a canonical non-linear reaction–diffusion model of acid-mediated tumour invasion to consider additional biological features of potential importance. We apply both numerical methods and a non-standard asymptotic analysis in a travelling wave framework to obtain an explicit understanding of the range of tumour behaviours produced by the model and how fundamental parameters govern the speed and shape of invading tumour waves. Comparison with conclusions drawn under the original system—a special case of our generalised system—allows us to comment on the structural stability and predictive power of the modelling framework.     

Monitoring in a predator–prey systems via a class of high order observer design

The goal of this work is the monitoring of the corresponding species in a class of predator–prey systems, this issue is important from the ecology point of view to analyze the population dynamics. The above is done via a nonlinear observer design which contains on its structure a high order polynomial form of the estimation error. A theoretical frame is provided in order to show the convergence characteristics of the proposed observer, where it can be concluded that the performance of the observer is improved as the order of the polynomial is high. The proposed methodology is applied to a class of Lotka–Volterra systems with two and three species. Finally, numerical simulations present the performance of the proposed observer.     

Statistical indicators and state–space population models predict extinction in a population of bobwhite quail

Early warning systems of extinction thresholds have been developed for and tested in microcosm experiments, but have not been applied to populations of wild animals. We used state–space population models and a statistical indicator to detect a transcritical bifurcation extinction threshold in a population of bobwhite quail (Colinus virginianus) located in an agricultural region experiencing habitat deterioration and loss. The extinction threshold was detectible using two independent data sets. We compared predictions from state–space population models to predictions from a statistical indicator and found that predictions were corroborated. Using state–space population models, we estimated that our study population crossed the extinction threshold in 2010 (2002–2036; 95 % confidence intervals [CI]) using the whistle count (WC) data set and in 2008 (1999–2064; 95 % CI) using the Breeding Bird Survey (BBS) data. With the statistical indicator, we estimated that the extinction threshold will be crossed in 2018 (2004–2031; 95 % CI) using the WC data and will be crossed in 2012 (2006–2018; 95 % CI) using the BBS data. We expect extinction in our study population soon after crossing the extinction threshold, but the time to extinction and potential reversibility of the threshold are unknown. Our results suggest that neither small nor decreasing population size will warn of the transcritical bifurcation extinction threshold. We suggest that managers of wildlife populations in regions experiencing land use change should try to predict extinction thresholds and make management decisions to ensure the persistence of the species.     

Effects of epibiosis on consumer–prey interactions

In many benthic communities predators play a crucialrole in the population dynamics of their prey. Surfacecharacteristics of the prey are important forrecognition and handling by the predator. Because theestablishment of an epibiotic assemblage on thesurface of a basibiont species creates a new interfacebetween the epibiotized organism and its environment,we hypothesised that epibiosis should have an impacton consumer–prey interactions. In separateinvestigations, we assessed how epibionts onmacroalgae affected the susceptibility of the latterto herbivory by the urchin Arbacia punctulataand how epibionts on the blue mussel Mytilusedulis affected its susceptibility to predation bythe shore crab Carcinus maenas.Some epibionts strongly affected consumer feedingbehavior. When epibionts were more attractive thantheir host, consumer pressure increased. Whenepibionts were less attractive than their host or whenthey were repellent, consumer pressure decreased. Insystems that are controlled from the top-down,epibiosis can strongly influence community dynamics.For the Carcinus/Mytilus system that westudied, the in situ distribution of epibiontson mussels reflected the epibiosis-determinedpreferences of the predator. Both direct and indirecteffects are involved in determining theseepibiont-prey–consumer interactions.     

Density estimation in a wolverine population using spatial capture–recapture models

Classical closed-population capture–recapture models do not accommodate the spatial information inherent in encounter history data obtained from camera-trapping studies. As a result, individual heterogeneity in encounter probability is induced, and it is not possible to estimate density objectively because trap arrays do not have a well-defined sample area. We applied newly-developed, capture–recapture models that accommodate the spatial attribute inherent in capture–recapture data to a population of wolverines (Gulo gulo) in Southeast Alaska in 2008. We used camera-trapping data collected from 37 cameras in a 2,140-km² area of forested and open habitats largely enclosed by ocean and glacial icefields. We detected 21 unique individuals 115 times. Wolverines exhibited a strong positive trap response, with an increased tendency to revisit previously visited traps. Under the trap-response model, we estimated wolverine density at 9.7 individuals/1,000 km² (95% Bayesian CI: 5.9–15.0). Our model provides a formal statistical framework for estimating density from wolverine camera-trapping studies that accounts for a behavioral response due to baited traps. Further, our model-based estimator does not have strict requirements about the spatial configuration of traps or length of trapping sessions, providing considerable operational flexibility in the development of field studies. © 2011 The Wildlife Society.     

Undamped oscillations in prey–predator models on a finite size lattice

Sustained oscillation is frequently observed in population dynamics of biospecies. The oscillation comes not only from deterministic but also from stochastic characteristics. In the present article, we deal with a finite size lattice which contains prey and predator. The interaction between a pair of lattice points is carried out by two different methods; local and global interactions. In the former, interaction occurs between adjacent sites, while in the latter interaction takes place between any pair of lattice sites. It is found that both systems exhibit undamped oscillations. The amplitude of oscillation decreases with the increase of the total lattice sites. In the case of global interaction, we can present a stochastic differential equation which is composed of two factors, i.e., the Lotka–Volterra equation with density dependence and noise term. The quantitative agreement between theory and simulation results of global interaction is almost perfect. The stochastic theory qualitatively expresses characteristics of sustainable oscillation for local interaction.     

Optimization of a diagnostic platform for oxidation–reduction potential (ORP) measurement in human plasma

Objectives: Oxidation–reduction potential (ORP) measurement can demonstrate the extent of oxidative stress in patients with severe illness and/or injury. A novel ORP diagnostic platform using disposable sensors (RedoxSYS) has been validated by comparison to mass spectrometry, but the optimal methods of sample handling for best performance of the device have not been described.

Methods: We sought to optimize ORP measurement in human plasma under controlled conditions. We hypothesized that the anticoagulant, freeze–thawing, and storage duration would influence measured ORP levels.

Results: The platform was sensitive to exogenous oxidation with hydrogen peroxide and reduction with ascorbic acid. Plasma anticoagulated with heparin was more sensitive to differences in ORP than plasma prepared in citrate. ORP measurements decreased slightly after a freeze–thaw cycle, but once frozen, ORP was stable for up to one month.

Discussion: We confirm that ORP detects oxidative stress in plasma samples. Optimal measurement of plasma ORP requires blood collection in heparin anticoagulant tubes and immediate analysis without a freeze–thaw cycle.     

SNA – a toolbox for the stoichiometric analysis of metabolic networks

Background  

Despite recent algorithmic and conceptual progress, the stoichiometric network analysis of large metabolic models remains a computationally challenging problem.     

Mobility unevenness in rock–paper–scissors models

We investigate a tritrophic system whose cyclic dominance is modelled by the rock–paper–scissors game. We consider that organisms of one or two species are affected by movement limitations, which unbalances the cyclic spatial game. Performing stochastic simulations, we show that mobility unevenness controls the population dynamics. In the case of one slow species, the predominant species depends on the level of mobility restriction, with the slow species being preponderant if the mobility limitations are substantial. If two species face mobility limitations, our outcomes show that being higher dispersive does not constitute an advantage in terms of population growth. On the contrary, if organisms move with higher mobility, they expose themselves to enemies more frequently, being more vulnerable to being eliminated. Finally, our findings show that biodiversity benefits in regions where species are slowed. Biodiversity loss for high mobility organisms, common to cyclic systems, may be avoided with coexistence probability being higher for robust mobility limitations. Our results may help biologists understand the dynamics of unbalanced spatial systems where organisms’ dispersal is fundamental to biodiversity conservation.     

Iodine concentration of milk in a dose–response study with dairy cows and implications for consumer iodine intake

Most feed is poor in iodine and iodine supplementation of cow's diets must guarantee milk iodine concentrations for humans that contribute to prevention of the deficiency and minimize the risk of exceeding an upper limit of iodine intake. Five Holstein cows were fed four iodine doses (via Ca(ΙO₃)₂·6H₂O). In four sequential 14-d periods, doses of 0.2 (basal diet), 1.3, 5.1, and 10.1 mg iodine kg^?1 diet dry matter (DM) were administered. Samples of milk were collected during each period; blood was also sampled from each cow for each iodine dosage. In an 18-d depletion period, a non-supplemented diet was provided. Iodine was determined by inductively coupled plasma-mass spectrometry. The iodine content of milk and serum reflected the iodine dosages in feed significantly. The levels for the four doses tested in milk were 101±32, 343±109, 1215±222, and 2762±852 μg iodine kg^?1. The total amount of iodine in milk per day was 30–40% of ingested supplemental iodine. Omitting additional iodine resulted in a short-term reduction of serum and milk iodine following an exponential decay function. The iodine supplementation of 0.5–1.5 mg kg^?1 diet DM represents the requirement of the cow, resulting in 100–300 μg iodine L^?1 milk, which optimally contributes to human supply. The maximum dietary levels of former and present EU legislations (10 and 5 mg iodine kg^?1 cow feed) increase the risk of iodine excess in humans.