Frank M. Hilker

Experimental demonstration of chaos in a microbial food web.

Discovering why natural population densities change over time and vary with location is a central goal of ecological and evolutional disciplines. The recognition that even simple ecological systems can undergo chaotic behaviour has made chaos a topic of considerable interest among theoretical ecologists. However, there is still a lack of experimental evidence that chaotic behaviour occurs in the real world of coexisting populations in multi-species systems. Here we study the dynamics of a defined predator–prey system consisting of a bacterivorous ciliate and two bacterial prey species. The bacterial species preferred by the ciliate was the superior competitor. Experimental conditions were kept constant with continuous cultivation in a one-stage chemostat. We show that the dynamic behaviour of such a two-prey, one-predator system includes chaotic behaviour, as well as stable limit cycles and coexistence at equilibrium. Changes in the population dynamics were triggered by changes in the dilution rates of the chemostat. The observed dynamics were verified by estimating the corresponding Lyapunov exponents. Such a defined microbial food web offers a new possibility for the experimental study of deterministic chaos in real biological systems.

The Allee Effect and Infectious Diseases: Extinction, Multistability, and the (Dis‐)Appearance of Oscillations

Infectious diseases that affect their host on a long timescale can regulate the host population dynamics. Here we show that a strong Allee effect can lead to complex dynamics in simple epidemic models. Generally, the Allee effect renders a population bistable, but we also identify conditions for tri‐ or monostability. Moreover, the disease can destabilize endemic equilibria and induce sustained oscillations. These disappear again for high transmissibilities, with eventually vanishing host population. Disease‐induced extinction is thus possible for density‐dependent transmission and without any alternative reservoirs. The overall complexity suggests that the system is very sensitive to perturbations and control methods, even in parameter regions with a basic reproductive ratio far beyond \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\encodingdefault{OT2} \normalfont \selectfont} \DeclareTextFontCommand{\textcyr}{\cyr} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \landscape

Pathogens can slow down or reverse invasion fronts of their hosts

R_{0}=1

Strange Periodic Attractors in a Prey-Predator System with Infected Prey

\end{document} . This may have profound implications for biological conservation as well as pest management. We identify important threshold quantities and attribute the dynamical behavior to the joint interplay of a strong Allee effect and infection.

Spatiotemporal patterns in an excitable plankton system with lysogenic viral infection

Parasites are an integral part of virtually all food webs and species communities. Here we consider the invasion of a resident predator-prey system by an infectious disease with frequency-dependent transmission spreading within the predator population. We derive biologically plausible and insightful quantities (demographic and epizootiological reproduction numbers) that allow us to completely determine community composition. Successful disease invasion can have two contrary effects in driving its host population to extinction or in stabilizing predator-prey cycles. Our findings contradict predictions from previous models suggesting a destabilizing effect of parasites. We show that predator infection counteracts the paradox of enrichment. In turn, parasite removal from food webs can have catastrophic effects. We discuss the implications for biological control and resource management on more than one trophic level.

Patterns of Patchy Spread in Deterministic and Stochastic Models of Biological Invasion and Biological Control

Infectious diseases are often regarded as possible explanations for the sudden collapse of biological invasions. This phenomenon is characterized by a host species, which firstly can successfully establish in a non-native habitat, but then spontaneously disappears again. This study proposes a reaction-diffusion model consisting of a simple SI disease with vital dynamics of Allee effect type. By way of travelling wave analysis, conditions are derived under which the invasion of the host population is slowed down, stopped or reversed as a consequence of a subsequently introduced disease. Hence, pathogens can dramatically control the rate of spread of invasive species.

Population collapse to extinction: the catastrophic combination of parasitism and Allee effect.

A flow regulator for liquid to be administered parenterally to a patient comprises a first member having a flow passage therein for the liquid and a second member arranged to be adjustably telescoped in the passage. The first and second members are constructed such that they can be telescopingly positioned to form a flow rate controlling channel which restricts the flow rate as a function of the length of the channel. The length of the channel is adjustable by changing the relative position of the first and second members. An adjustment force applied to the outside of the regulator is transmitted to the second member within the flow regulator for changing the channel length and therefore the flow rate. The flow regulator can include a drip chamber positioned immediately above the second member for convenient adjustment of the flow rate. Sealing against leakage of air into the flow regulator is attainable because the flow rate controlling second member is located entirely within the first member.

Preventing Extinction and Outbreaks in Chaotic Populations

Strange periodic attractors with complicated, long-lasting transient dynamics are found in a prey-predator model with disease transmission in the prey. The model describes viral infection of a phytoplankton population and grazing by zooplankton. The analysis of the three-dimensional system of ordinary differential equations yields several semi-trivial stationary states, among them two saddle-foci, and the sudden (dis-)appearance of a continuum of degenerated nontrivial equilibria. Along this continuum line, the equilibria undergo a fold-Hopf (zero-pair) bifurcation (also called zip bifurcation). The continuum only exists in the bifurcation point of the saddle-foci. Especially interesting is the emergence of strange periodic attractors, stabilizing themselves after a repeated torus-like oscillation. This form of coexistence is related to persistent and permanent ecological communities and to bursting phenomena.