Food Quality in Producer-Grazer Models: A Generalized Analysis

Stoichiometric constraints play a role in the dynamics of natural populations, but are not explicitly considered in most mathematical models. Recent theoretical works suggest that these constraints can have a significant impact and should not be neglected. However, it is not yet resolved how stoichiometry should be integrated in population dynamical models, as different modeling approaches are found to yield qualitatively different results. Here we investigate a unifying framework that reveals the differences and commonalities between previously proposed models for producer-grazer systems. Our analysis reveals that stoichiometric constraints affect the dynamics mainly by increasing the intraspecific competition between producers and by introducing a variable biomass conversion efficiency. The intraspecific competition has a strongly stabilizing effect on the system, whereas the variable conversion efficiency resulting from a variable food quality is the main determinant for the nature of the instability once destabilization occurs. Only if the food quality is high an oscillatory instability, as in the classical paradox of enrichment, can occur. While the generalized model reveals that the generic insights remain valid in a large class of models, we show that other details such as the specific sequence of bifurcations encountered in enrichment scenarios can depend sensitively on assumptions made in modeling stoichiometric constraints.Comment: Online appendixes include

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Abstract

Second intravenous immunoglobulin dose in patients with Guillain-Barre syndrome with poor prognosis (SID-GBS):a double-blind, randomised, placebo-controlled trial

Background Treatment with one standard dose (2 g/kg) of intravenous immunoglobulin is insufficient in a proportion of patients with severe Guillain-Barre syndrome. Worldwide, around 25% of patients severely affected with the syndrome are given a second intravenous immunoglobulin dose (SID), although it has not been proven effective. We aimed to investigate whether a SID is effective in patients with Guillain-Barre syndrome with a predicted poor outcome. Methods In this randomised, double-blind, placebo-controlled trial (SID-GBS), we included patients (>= 12 years) with Guillain-Barre syndrome admitted to one of 59 participating hospitals in the Netherlands. Patients were included on the first day of standard intravenous immunoglobulin treatment (2 g/kg over 5 days). Only patients with a poor prognosis (score of >= 6) according to the modified Erasmus Guillain-Barre syndrome Outcome Score were randomly assigned, via block randomisation stratified by centre, to SID (2 g/kg over 5 days) or to placebo, 7-9 days after inclusion. Patients, outcome adjudicators, monitors, and the steering committee were masked to treatment allocation. The primary outcome measure was the Guillain-Barre syndrome disability score 4 weeks after inclusion. All patients in whom allocated trial medication was started were included in the modified intention-to-treat analysis. Findings Between Feb 16, 2010, and June 5, 2018, 327 of 339 patients assessed for eligibility were included. 112 had a poor prognosis. Of those, 93 patients with a poor prognosis were included in the modified intention-to-treat analysis: 49 (53%) received SID and 44 (47%) received placebo. The adjusted common odds ratio for improvement on the Guillain-Barre syndrome disability score at 4 weeks was 1.4 (95% CI 0.6-3.3; p=0.45). Patients given SID had more serious adverse events (35% vs 16% in the first 30 days), including thromboembolic events, than those in the placebo group. Four patients died in the intervention group (13-24 weeks after randomisation). Interpretation Our study does not provide evidence that patients with Guillain-Barre syndrome with a poor prognosis benefit from a second intravenous immunoglobulin course; moreover, it entails a risk of serious adverse events. Therefore, a second intravenous immunoglobulin course should not be considered for treatment of Guillain-Barre syndrome because of a poor prognosis. The results indicate the need for treatment trials with other immune modulators in patients severely affected by Guillain-Barre syndrome. Funding Prinses Beatrix Spierfonds and Sanquin Plasma Products. Copyright (C) 2021 Elsevier Ltd. All rights reserved

Complexity of host-vector dynamics in a two-strain dengue model

We introduce a compartmental host-vector model for dengue with two viral strains, temporary cross-immunity for the hosts, and possible secondary infections. We study the conditions on existence of endemic equilibria where one strain displaces the other or the two virus strains co-exist. Since the host and vector epidemiology follow different time scales, the model is described as a slow-fast system. We use the geometric singular perturbation technique to reduce the model dimension. We compare the behaviour of the full model with that of the model with a quasi-steady approximation for the vector dynamics. We also perform numerical bifurcation analysis with parameter values from the literature and compare the bifurcation structure to that of previous two-strain host-only models

A safe harbor can protect an endangered species from its predators

The objective is the study of the dynamics of a prey–predator model where the prey species can migrate between two patches. The specialist predator is confined to the first patch, where it consumes the prey following the simple law of mass action. The prey is further “endangered” in that it suffers from the strong Allee effect, assumed to occur due to the lowering of successful matings. In the second patch the prey grows logistically. The model is formulated in a comprehensive way so as to include specialist as well as generalist predators, as a continuum of possible behaviors. This model described by a set of three ordinary differential equation is an extension of some previous models proposed and analysed in the literature on metapopulation models. The following analysis issues will be addressed: boundedness of the solution, equilibrium feasibility and stability, and dynamic behaviour dependency of the population and environmental parameters. Three types for both equilibria and limit cycles are possible: trivial, predator-free and coexistence. Classical analysis techniques are used and also theoretical and numerical bifurcation analysis. Besides the well-known local bifurcations, also a homoclinic connection as a global bifurcation is calculated. In view of the difficulty in the analysis, only the specialist case will be analysed. The obtained results indicate that the safe harbor can protect the endangered species under certain parametric restrictions