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Frank M. Hilker

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Fields of research:

Selected research projects

Bifurcation sequence of two chaotic attractors (Credit: M. Sieber) Non-equilibrium coexistence in ecological communities
In collaboration with Michael Sieber and Horst Malchow (U Osnabrück, Germany)

The "principle of competitive exclusion" states, roughly speaking, that two or more consumer species cannot coexist on a single resource (Gause, 1934). We investigate mechanisms by which nonlinear interactions faciliate the cyclic or chaotic (i.e. non-equilibrium) coexistence of multiple consumer-resource communities.

Sample publications: Sieber and Hilker (2011 J. Anim. Ecol.), Hilker and Malchow (2006 Math. Popul. Stud.)

Travelling waves predator-prey dynamics in streams and rivers Population dynamics in streams and rivers
In collaboration with Mark Lewis (U Alberta, Canada)

Many organisms live in environments with a predominantly unidirectional flow. Alterations of natural flow regimes (e.g., due to human management or global warming) have put biological populations at risk. The analysis of a simple and general model provides a straight-forward method that can be used to asses the impact of flow regime alterations on the persistence (or extinction) of predator-prey communities. This provides a useful tool in the assessment of instream flow needs, estimating the flow speed necessary for preserving riverine populations.

Sample publications: Anderson et al. (2012 Ecol. Lett.), Hilker and Lewis (2010 Theor. Ecol.)

Effect of biological control by virus introduction on predator-prey dynamics (Credit: N. Oliveira) Disease spread in predators: Control of invasive cats with FIV
In collaboration with Kirsten Schmitz (U Osnabrück, Germany) and Nuno Oliveira (IGC and U Lisbon, Portugal)

Feral cats which have been introduced on remote oceanic islands now pose devastating threats on the native fauna, particularly on seabirds. We explore the prospects of the Feline Immunodeficiency Virus (FIV) as a potential biological control agent to regulate the cats (predators) and thus to support the birds (prey).

Sample publications: Hilker and Schmitz (2008 J. Theor. Biol.), Oliveira and Hilker (2010 Bull. Math. Biol.)

Extinction dynamics in the phase plane after a homoclinic bifurcation Population dynamics of wildlife diseases
In collaboration with Michel Langlais (U Bordeaux 2, France) and Horst Malchow (U Osnabrück, Germany)

Another example investigates the spread of infectious diseases in wildlife populations. Probably for historical reasons and an eminent interest in human epidemics, mathematical models have neglected the impact of an Allee effect in the host population. The Allee effect describes reduced population growth at small densities, for example due to difficulties in finding mating partners or predator defense. Epidemiological models including an Allee effect exhibit dynamics that are substantially more complex than previously thought. In particular, the synergy between disease and the Allee effect can drive the host population to extinction - even in situations which were previously regarded as safe for the host.

Sample publications: Hilker et al. (2009 Am. Nat.; 2007 Math. Biosci.; 2005 Biol. Invas.), Hilker (2010 J. Biol. Dyn.)

Bifurcation diagram chaos control Chaos control
In collaboration with Frank Westerhoff (U Bamberg, Germany), Daniel Franco (UNED Madrid), Eduardo Liz (U Vigo, Spain)

Many pest species such as forest or crop insects behave chaotically, i.e. they often have unpredictable outbreaks and fluctuate in an apparently erratic manner. Endangered species can also crash abruptly. Any management strategy seems therefore doomed to failure. However, a new method involving strategic harvest or restocking programs proves to be a powerful tool in preventing extinction and outbreaks. It has been shown to be very effective - even if only little data is available as is typical for ecological systems. Making a clever use of the short-term predictability of chaos, this method is regarded as one of the first to hold the promise that chaos theory can actually be applied to solve problems in pest control and biological conservation.

Sample publications: Dattani et al. (2011 Phys. Lett. A), Hilker and Westerhoff (2007 Am. Nat.; 2007 Phys. Lett. A; 2006 Phys. Rev. E)

Stochastic plankton outbreaks (blooms) in a stochastic reaction-diffusion model Spatiotemporal pattern formation in plankton communities with viral infection and noise
In collaboration with Horst Malchow (U Osnabrück, Germany) and Sergei Petrovskii (U Leicester, UK)

Viruses are evidently the most abundant entities in the sea and the question may arise whether they control ocean life. We investigate deterministic and stochastic partial differential equations which model lytic and lysogenic viral infections of phytoplankton and their interaction with zooplankton.

Sample publications: Malchow et al. (2004 Ecol. Complex.; 2005 Math. Comput. Model.), Hilker et al. (2006 Ecol. Complex.)
 

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Last updated: 25 September 2012
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