Phylogenetic diversity (PD) is a measure of species biodiversity quantified by how
much of an evolutionary tree is spanned by a subset of species. In this thesis, we study
optimization problems that aim to find species sets with maximum PD in different scenarios,
and examine random extinction models under various assumptions to predict the
PD of species that will still be present in the future.
Optimizing PD with Dependencies is a combinatorial optimization problem in
which species form an ecological network. Here, we are interested in selecting species
sets of a given size that are ecologically viable and that maximize PD. The NP-hardness
of this problem is proved and it is established which special cases of the problem are
computationally easy and which are computationally hard. It is also shown that it is
NP-complete to decide whether the feasible solution obtained by the greedy algorithm is
optimal. We formulate the optimization problem as an integer linear program and find
exact solutions to the largest food web currently in the empirical literature. In addition,
we give a generalization of PD that can be used for example when we do not know the
true evolutionary history. Based on this measure, an optimization problem is formulated.
We discuss the complexity and the approximability properties of this problem.
In the generalized field of bullets model (g-FOB), species are assumed to become
extinct with possibly different probabilities, and extinction events are independent. We
show that under this model the distribution of future phylogenetic diversity converges to
a normal distribution as the number of species grows. When extinction probabilities are
influenced by some binary character on the tree, the state-based field of bullets model
(s-FOB) represents a more realistic picture. We compare the expected loss of PD under
this model to that under the associated g-FOB model and find that the former is always
greater than or equal to the latter. It is natural to further generalize the s-FOB model to
allow more than one binary character to affect the extinction probabilities. The expected
future PD obtained for the resulting trait-dependent field of bullets model (t-FOB) is
compared to that for the associated g-FOB model and our previous result is generalized.
| Identifer | oai:union.ndltd.org:canterbury.ac.nz/oai:ir.canterbury.ac.nz:10092/3985 |
| Date | January 2010 |
| Creators | Faller, Beáta |
| Publisher | University of Canterbury. Mathematics and Statistics |
| Source Sets | University of Canterbury |
| Language | English |
| Detected Language | English |
| Type | Electronic thesis or dissertation, Text |
| Rights | Copyright Beáta Faller, http://library.canterbury.ac.nz/thesis/etheses_copyright.shtml |
| Relation | NZCU |
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