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Vessman, B. (2015) *From pair-wise interactions to triplet dynamics*. Göteborg : Chalmers University of Technology

** BibTeX **

@mastersthesis{

Vessman2015,

author={Vessman, Björn},

title={From pair-wise interactions to triplet dynamics},

abstract={The present thesis investigates the properties of a system of ordinary di_erential
equations, that describes cross-feeding in two- and three-species systems of bacteria.
The system is studied statistically and the probability of permanence | a stable
state where no species is driven extinct | is computed under the assumption that
the energy-uptake parameters of the system are either independent or organised in a
hierarchy where any excreted metabolites carry less energy than previous nutrients.
For a system of two species, we derive the probability of permanence analytically.
For three-species systems, we di_erentiate between di_erent modes of coexistence
with respect to boundary behaviour of the system. We are able to show that the
a_ne _tness function described by Lundh & Gerlee (Lundh, T., Gerlee, P., Bull
Math Biol, 75, 2013) is equivalent to the linear _tness function investigated by
Bomze (Bomze, I. M., Biol Cybern, 48, 1983) and hence that the dynamics derived
by Bomze holds for the cross-feeding paradigm of Lundh & Gerlee. For the question
implicit in the title of the thesis, the pair-wise interactions of a three-species system
are not enough to draw any deterministic conclusions on permanence of the triplet.
We _nd, however, that the probability of permanence is close to 50% for systems
with three coexistent pairs on the boundary and for so-called intransitive systems.
Systems with two and one coexistent pairs on the boundary are more likely to exist
for random interactions parameters, but are not as likely to be permanent.
Keywords: Biomathematics, Population dynamics, Cross-feeding.
v
},

publisher={Institutionen för matematiska vetenskaper, Chalmers tekniska högskola},

place={Göteborg},

year={2015},

}

** RefWorks **

RT Generic

SR Electronic

ID 218643

A1 Vessman, Björn

T1 From pair-wise interactions to triplet dynamics

YR 2015

AB The present thesis investigates the properties of a system of ordinary di_erential
equations, that describes cross-feeding in two- and three-species systems of bacteria.
The system is studied statistically and the probability of permanence | a stable
state where no species is driven extinct | is computed under the assumption that
the energy-uptake parameters of the system are either independent or organised in a
hierarchy where any excreted metabolites carry less energy than previous nutrients.
For a system of two species, we derive the probability of permanence analytically.
For three-species systems, we di_erentiate between di_erent modes of coexistence
with respect to boundary behaviour of the system. We are able to show that the
a_ne _tness function described by Lundh & Gerlee (Lundh, T., Gerlee, P., Bull
Math Biol, 75, 2013) is equivalent to the linear _tness function investigated by
Bomze (Bomze, I. M., Biol Cybern, 48, 1983) and hence that the dynamics derived
by Bomze holds for the cross-feeding paradigm of Lundh & Gerlee. For the question
implicit in the title of the thesis, the pair-wise interactions of a three-species system
are not enough to draw any deterministic conclusions on permanence of the triplet.
We _nd, however, that the probability of permanence is close to 50% for systems
with three coexistent pairs on the boundary and for so-called intransitive systems.
Systems with two and one coexistent pairs on the boundary are more likely to exist
for random interactions parameters, but are not as likely to be permanent.
Keywords: Biomathematics, Population dynamics, Cross-feeding.
v

PB Institutionen för matematiska vetenskaper, Chalmers tekniska högskola,

LA eng

LK http://publications.lib.chalmers.se/records/fulltext/218643/218643.pdf

OL 30