Allelochemicals determine competition and grazing control in Alexandrium catenella.

The production of allelochemicals by the toxigenic dinoflagellate Alexandrium catenella is one of the suggested mechanisms to facilitate its bloom formation and persistence by outcompeting other phototrophic protists and reducing grazing pressure. In Southern California, toxic events caused by A. catenella and paralytic shellfish toxins (PSTs) regularly impact coastal ecosystems; however, the trophic interactions and mechanisms promoting this species in a food web context are still not fully understood.

Prey group defense and hunting cooperation among generalist-predators induce complex dynamics: a mathematical study.

Group defense in prey and hunting cooperation in predators are two important ecological phenomena and can occur concurrently. In this article, we consider cooperative hunting in generalist predators and group defense in prey under a mathematical framework to comprehend the enormous diversity the model could capture. To do so, we consider a modified Holling-Tanner model where we implement Holling type IV functional response to characterize grazing pattern of predators where prey species exhibit group defense.

Bridging Theories for Ecosystem Stability Through Structural Sensitivity Analysis of Ecological Models in Equilibrium.

Ecologists are challenged by the need to bridge and synthesize different approaches and theories to obtain a coherent understanding of ecosystems in a changing world. Both food web theory and regime shift theory shine light on mechanisms that confer stability to ecosystems, but from different angles. Empirical food web models are developed to analyze how equilibria in real multi-trophic ecosystems are shaped by species interactions, and often include linear functional response terms for simple estimation of interaction strengths from observations.

Mathematical models for dengue fever epidemiology: A 10-year systematic review.

Mathematical models have a long history in epidemiological research, and as the COVID-19 pandemic progressed, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease spreading. Mathematical models describing dengue fever epidemiological dynamics are found back from 1970. Dengue fever is a viral mosquito-borne infection caused by four antigenically related but distinct serotypes (DENV-1 to DENV-4).

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.

On the role of vector modeling in a minimalistic epidemic model.

The motivation for the research reported in this paper comes from modeling the spread of vector-borne virus diseases. To study the role of the host versus vector dynamics and their interaction we use the susceptible-infected-removed (SIR) host model and the susceptible-infected (SI) vector model. When the vector dynamical processes occur at a faster scale than those in the host-epidemics dynamics, we can use a time-scale argument to reduce the dimension of the model.

Analysis of a predator-prey model with specific time scales: a geometrical approach proving the occurrence of canard solutions.

We study a predator-prey model with different characteristic time scales for the prey and predator populations, assuming that the predator dynamics is much slower than the prey one. Geometrical Singular Perturbation theory provides the mathematical framework for analyzing the dynamical properties of the model. This model exhibits a Hopf bifurcation and we prove that when this bifurcation occurs, a canard phenomenon arises.

The impact of a predator on the outcome of competition in the three-trophic food web.

We study the effects of predation on the competition of prey populations for two resources in a chemostat. We investigate a variety of small food web compositions: the bi-trophic food web (two resources-two competing prey) and the three-trophic food web (two resources-two prey-generalist predator) comparing different model formulations: substitutable resources and essential resources, namely Liebig's minimum law model (perfect essential resources) and complementary resources formulations. The prediction of the outcome of competition is solely based on bifurcation analysis in which the inflow of resources into the chemostat is used as the bifurcation parameter.

Ecoepidemic predator-prey model with feeding satiation, prey herd behavior and abandoned infected prey.

In this paper we analyse a predator-prey model where the prey population shows group defense and the prey individuals are affected by a transmissible disease. The resulting model is of the Rosenzweig-MacArthur predator-prey type with an SI (susceptible-infected) disease in the prey. Modeling prey group defense leads to a square root dependence in the Holling type II functional for the predator-prey interaction term.

Competition for light and nutrients in layered communities of aquatic plants.

Dominance of free-floating plants poses a threat to biodiversity in many freshwater ecosystems. Here we propose a theoretical framework to understand this dominance, by modeling the competition for light and nutrients in a layered community of floating and submerged plants. The model shows that at high supply of light and nutrients, floating plants always dominate due to their primacy for light, even when submerged plants have lower minimal resource requirements.

Analysis of an asymmetric two-strain dengue model.

In this paper we analyse a two-strain compartmental dengue fever model that allows us to study the behaviour of a Dengue fever epidemic. Dengue fever is the most common mosquito-borne viral disease of humans that in recent years has become a major international public health concern. The model is an extension of the classical compartmental susceptible-infected-recovered (SIR) model where the exchange between the compartments is described by ordinary differential equations (ode).

Describing dengue epidemics: Insights from simple mechanistic models.

We present a set of nested models to be applied to dengue fever epidemiology. We perform a qualitative study in order to show how much complexity we really need to add into epidemiological models to be able to describe the fluctuations observed in empirical dengue hemorrhagic fever incidence data offering a promising perspective on inference of parameter values from dengue case notifications.

Parameter Estimation in Epidemiology: from Simple to Complex Dynamics.

We revisit the parameter estimation framework for population biological dynamical systems, and apply it to calibrate various models in epidemiology with empirical time series, namely influenza and dengue fever. When it comes to more complex models like multi-strain dynamics to describe the virus-host interaction in dengue fever, even most recently developed parameter estimation techniques, like maximum likelihood iterated filtering, come to their computational limits. However, the first results of parameter estimation with data on dengue fever from Thailand indicate a subtle interplay between stochasticity and deterministic skeleton.

The role of seasonality and import in a minimalistic multi-strain dengue model capturing differences between primary and secondary infections: complex dynamics and its implications for data analysis.

In many countries in Asia and South-America dengue fever (DF) and dengue hemorrhagic fever (DHF) has become a substantial public health concern leading to serious social-economic costs. Mathematical models describing the transmission of dengue viruses have focussed on the so-called antibody-dependent enhancement (ADE) effect and temporary cross-immunity trying to explain the irregular behavior of dengue epidemics by analyzing available data. However, no systematic investigation of the possible dynamical structures has been performed so far.

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.

Ecological consequences of global bifurcations in some food chain models.

Food chain models of ordinary differential equations (ode's) are often used in ecology to gain insight in the dynamics of populations of species, and the interactions of these species with each other and their environment. One powerful analysis technique is bifurcation analysis, focusing on the changes in long-term (asymptotic) behaviour under parameter variation. For the detection of local bifurcations there exists standardised software, but until quite recently most software did not include any capabilities for the detection and continuation of global bifurcations.

Direct and indirect effects of pollutants on algae and algivorous ciliates in an aquatic indoor microcosm.

An aquatic indoor microcosm was used to study effects of the pesticides parathion-methyl and prometryn on phototrophic flagellates (Cryptomonas sp.) and predatory ciliates (Urotricha furcata). Parathion-methyl caused effects to flagellates and ciliates at the range of low mg L(-1), regardless of whether the organisms were exposed separately or combined in the multi-species test system.

Effects of density-dependent migrations on stability of a two-patch predator-prey model.

We consider a predator-prey model in a two-patch environment and assume that migration between patches is faster than prey growth, predator mortality and predator-prey interactions. Prey (resp. predator) migration rates are considered to be predator (resp.

Heteroclinic orbits indicate overexploitation in predator-prey systems with a strong Allee effect.

Species establishment in a model system in a homogeneous environment can be dependent not only on the parameter setting, but also on the initial conditions of the system. For instance, predator invasion into an established prey population can fail and lead to system collapse, an event referred to as overexploitation. This phenomenon occurs in models with bistability properties, such as strong Allee effects.

Ecological specialization of mixotrophic plankton in a mixed water column.

In recent years, the population dynamics of plankton in light- or nutrient-limited environments have been studied extensively. Their evolutionary dynamics, however, have received much less attention. Here, we used a modeling approach to study the evolutionary behavior of a population of plankton living in a mixed water column.

Bifurcation analysis of a predator-prey model with predators using hawk and dove tactics.

Most classical prey-predator models do not take into account the behavioural structure of the population. Usually, the predator and the prey populations are assumed to be homogeneous, i.e.

When do mixotrophs specialize? Adaptive dynamics theory applied to a dynamic energy budget model.

In evolutionary history, several events have occurred at which mixotrophs specialized into pure autotrophs and heterotrophs. We studied the conditions under which such events take place, using the Dynamic Energy Budget (DEB) theory for physiological rules of the organisms' metabolism and Adaptive Dynamics (AD) theory for evolutionary behavior of parameter values. We modeled a population of mixotrophs that can take up dissolved inorganic nutrients by autotrophic assimilation and detritus by heterotrophic assimilation.