Building Networks Using Phylogenetic Trees
Logan, T. M.
Allan Wilson Centre and Dept. of Mathematics and Statistics, University of Canterbury
Project supervisors: James, A. and Steel, M.
Keywords: Network architecture, ecological network, mutualism, phylogenetic tree, graph theory.
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INTRODUCTION
The world’s biota can be divided into interacting groups called ecosystems. Understanding ecological
dynamics has become increasingly important. Knowledge of the properties and structure of the ecosystem
means that the impacts of these perturbations can be approximated and conservation solutions found (James et
al., 2014). Interactions between species in an ecosystem can be represented by a network. Three types of
ecosystems are commonly used: predator-prey, host-parasite, and mutualistic. Mutualistic networks include
pollination networks, seed dispersal networks, and networks between ants and the plant species they protect.
In this study, pollination networks were analysed as data was readily available. The pollination network is also
bipartite as interactions only exist between two distinct, non-overlapping sets of species, but not within the
set: a pollinator can never be pollinated, unlike in a predator-prey network where a predator can be depredated
(Newman, 2009). Networks can be modelled as graphs:
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𝐶 = (1
0
0
0
1
1
1)
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Figure 1. a-left) A bipartite pollination network with the vertices (species) labelled. b-centre) A graphical matrix
representation of the network. c-right) A matrix of the network.
Although it is agreed that the architecture of ecological networks contributes to biodiversity persistence, little
is known about which evolutionary and ecological processes are involved. Rezende et al. (2007) encourages
the inclusion of evolutionary history into models of network formation and maintenance. The objective of this
study was to develop a model of an ecological network based on the phylogenetic distance between the species
and to compare its accuracy against commonly used random network models.
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THE PHYLOGENETIC NETWORK MODEL
The phylogenetic networks are generated to have a predetermined size and number of links. Then the network
is created using the phylogenetic distances determined from the Yule-Harding model (Harding, 1971; Steel
and McKenzie, 2001; Yule, 1925) and the preferential attachment method.
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Figure 2. The mutualistic pollination network.
The red dashed line is the seed link between the
plants and pollinators. The other links are
weighted (width) to show the likelihood of a
connection being formed between them.
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DISCUSSION
The phylogenetic network model was refined by varying the input parameters. Then, for each real set of
network data and the corresponding generated model, the metrics were compared. The phylogenetic network
performed better than the random network in all metrics, except of modularity. This is likely due to the
phylogenetic networks having an accurate nestedness, and the data collection method (of the networks which
the models were evaluated on) favoured modular network by excluding outlying species. One of the network’s
compiling author: “… in this initial survey we limit ourselves to relative importance of major vector types…”
(Arroyo et al., 1982) (p.84)
A further application for this work is to investigate the implications of a phylogenetic model on the study of
community evolution. It may be possible to determine genetic similarity based on species interactions, or
determine whether a currently unknown species should have existed by examining gaps in network
interactions.
Further work is to determine the suitability of the phylogenetic model for networks other than binary, bipartite,
pollination networks. Ultimately, the model may provide further insight into ecosystem responses to
perturbations and contribute to the conservation of ecological networks.
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ACKNOWLEDGEMENTS
Thank you to the Allan Wilson Centre for providing funding for this project.
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REFERENCES
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Andes of central Chile. I. Pollination mechanisms and altitudinal variation." American journal of botany, 82-97.
Harding, E. (1971). "The probabilities of rooted tree-shapes generated by random bifurcation." Advances in Applied
Probability, 44-77.
James, A., McLeod, J., and Pitchford, J. (2014). "Simple Cycles Underpin Ecological Complexity." Unpublished
manuscript.
Newman, M. (2009). Networks: an introduction, Oxford University Press.
Rezende, E. L., Lavabre, J. E., Guimarães, P. R., Jordano, P., and Bascompte, J. (2007). "Non-random coextinctions in
phylogenetically structured mutualistic networks." Nature, 448(7156), 925-928.
Steel, M., and McKenzie, A. (2001). "Properties of phylogenetic trees generated by Yule-type speciation models."
Mathematical biosciences, 170(1), 91-112.
Yule, G. U. (1925). "A mathematical theory of evolution, based on the conclusions of Dr. JC Willis, FRS." Philosophical
Transactions of the Royal Society of London. Series B, Containing Papers of a Biological Character, 213, 2187.
T. Logan