Research
(this site is permanently under construction, just as research itself)
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Frithjof Lutscher Research (this site is permanently under construction, just as research itself) |
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| Modeling
River
Ecosystems Individuals in rivers are constantly subject to unidirectional flow. However, populations persist in the face of this potential wash-out ("drift paradox"). I model dispersal mechanisms of individuals in rivers and study the effect of different mechanisms on the dynamics of populations. When can populations invade against the flow and how fast? How far upstream can a population invade? What are the effects of environmental heterogeneity? How are two competitors affected by drift? The following results on this topic are available at my publications page: Vasilyeva and Lutscher (accepted) Lutscher et al. (2010) Theor Ecol Lewis et al. (2009) Park City Mathematics Series 14 Pringle et al. (2009) MEPS Lutscher et al. (2007) TPB Lutscher et al. (2006) BMB Pachepsky et al. (2005) TPB Lutscher et al. (2005) SIAP/SIAM REV |
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| Invasion
and Conservation Biology: Modeling Dispersal in Discrete-Time Systems Dispersal is often modeled by reaction-diffusion equations in continuous time. But many species have distinct dispersal stages and dispersal times. The better modeling framework for these populations are integrodifference equations (IDEs). I am interested in the following questions. How does dispersal behavior influence invasion speeds? Which dispersal mechanisms allow population persistence? How big a habitat patch is required for persistence? How does dispersal influence the dynamics of interacting populations? The following results on this topic are available at my publications page: Samia and Lutscher (2010) BMB Lutscher (2010) Applicable Analysis Dewhirst and Lutscher (2009) Ecology Lutscher and Petrovskii (2008) J. Biol. Dynamics Lutscher (2008) JMB Fagan et al. (2007) Am. Nat. Lutscher (2007) BMB Fagan and Lutscher (2006) Ecol. Appl. Cobbold et al. (2005) TPB Lutscher and Lewis (2004) JMB |
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| Individual
Movement Behavior, Random Walks and Pattern Formation Diffusion equations result from position-jump processes. These might not always be a good description of the mechanisms of movement. Other processes that were suggested are for example velocity jump processes, which lead to transport equations, or the Langevin equations. I study the differences and similarities that result from these different processes, and in scaling relationships between them. I am particularly interested in pattern formation in these systems, such as alignment, aggregation, or rippling (myxobacteria). The following results on this topic are available at my publications page: Eftimie et al. (2007) BMB Hadeler et al. (2004) M3AS Lutscher (2003) Proceedings Lutscher and Stevens (2002) JNS Lutscher (2002) JMB Lutscher (2003) EJAM Hillen et al. (2001) JMAA |
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