Evolutionary relationships between species are usually represented in
phylogenies, i.e. evolutionary trees, which are a type of networks. The
terminal nodes of these trees represent species, which are made of individuals
and populations among which gene flow occurs. This flow can also be represented
as a network. In this paper we briefly show some properties of these complex
networks of evolutionary and ecological relationships. First, we characterize
large scale evolutionary relationships in the Tree of Life by a degree
distribution. Second, we represent genetic relationships between individuals of
a Mediterranean marine plant, Posidonia oceanica, in terms of a Minimum
Spanning Tree. Finally, relationships among plant shoots inside populations are
represented as networks of genetic similarity.Comment: 6 pages, 5 figures. To appear in Proceedings of the Medyfinol06
  Conferenc

Arnaud-Haond, S.

Duarte, C. M.

Eguiluz, V. M.

Hernandez-Garcia, E.

Herrada, E. A.

Rozenfeld, A. F.

Serrao, E.

Tessone, C. J.

English

arXiv

Emilio Hernández-García

E. Alejandro Herrada

Alejandro F. Rozenfeld

Claudio J. Tessone

Víctor M. Eguíluz

Carlos M. Duarte

Sophie Arnaud-Haond

Ester Serrão

Crossref

Evolutionary and Ecological Trees and Networks

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Evolutionary and Ecological Trees and Networks
Emilio Hernández-García∗, E. Alejandro Herrada∗, Alejandro F. Rozenfeld†,
Claudio J. Tessone∗, Víctor M. Eguíluz∗, Carlos M. Duarte†, Sophie
Arnaud-Haond∗∗,‡ and Ester Serrão∗∗
∗Unidad de Física Interdisciplinar-IMEDEA (CSIC-UIB).
Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
†Instituto Mediterráneo de Estudios Avanzados IMEDEA (CSIC-U B).
C/ Miquel Marquès, 21, E-07190 Esporles, Mallorca, Spain
∗∗CCMAR, CIMAR-Laboratório Associado, Universidade do Algarve
Gambelas, 8005-139, Faro, Portugal
‡DEEP/LEP-Laboratoire Environnement Profond
IFREMER Centre de Brest, BP 70 29280, Plouzane, France
Abstract. Evolutionary relationships between species are usually represented in phylogenies, i.e. evolutionary trees, which
are a type of networks. The terminal nodes of these trees repres nt species, which are made of individuals and populations
among which gene flow occurs. This flow can also be representedas a network. In this paper we briefly show some properties
of these complex networks of evolutionary and ecological relationships. First, we characterize large scale evolutionary
relationships in the Tree of Life by a degree distribution. Second, we represent genetic relationships between individuals
of a Mediterranean marine plant, Posidonia oceanica, in terms of a Minimum Spanning Tree. Finally, relationships among
plant shoots inside populations are represented as networks of genetic similarity.
Keywords: Complex networks, Phylogenies, Tree of Life, Population structure, Genetic similarity, Posidonia oceanica
PACS: 89.75.Hc , 87.23.-n
INTRODUCTION
The study of complex networks, representing interactions among components, has become a central tool in the science
of complex systems [1, 2, 3]. Evolutionary relationships between species are usually represented in phylogenies, i.e.
evolutionary trees. One branching event represents the evolution of an ancestral species into descendent ones. The
whole set of relationships among all known species is conceptually represented as a hugeTree of Life. A tree is a
network in which there are no cycles, i.e., there is a unique path from one node to another inside the network. This
is probably a good approximation to the correct large scale structure of the Tree of Life, but processes such as lateral
gene transfer or hybridization would need a richer network structure to be properly represented [4]. If analyzing the
Tree of Life at a finer detail, entering the scale appropriatefor ecological interactions, we observe that species are
composed of different populations, and that those are made of individuals that interchange genes and recombine their
genomes in processes such as sexual reproduction. Thus, there are gene flow processes, particularly obvious when
looking at the intraspecific level, which add loops to the Tree of Life, and make the whole structure a rather complex
object.
In this paper we briefly analyze, at three different scales, some properties of this complex network of evolutionary
and ecological gene flow. Our aim is just to provide an overview of the many interesting features of genetic relation-
ships and phylogenies that can be addressed from the point ofview of complex systems, with the hope that this will
stimulate further and more detailed work. First, we characterize large scale evolutionary relationships, the ones more
traditionally represented in a tree topology. To this end weanalyze a large scale reconstruction of the Tree of Life and
characterize it by its degree distribution. Second, we represent the genetic relationships between individual shootsof a
Mediterranean marine plant, Posidonia oceanica, sampled across its entire geographical extent, in terms of a Minimum
Spanning Tree that would represent the most parsimonious pattern of gene flow between distant populations. Finally,
relationships among shoots in the same population are repres nt d as networks of genetic similarity.
FIGURE 1. A rendering of the first branchings of the “Tree of Life". Manyadditional subdivisions occur at each of the final
branches in this plot, where we can distinguish the three main Domains (Bacteria, Archaea, Eucarya) in which the different
organisms are classified.
SCALE-FREE DEGREE DISTRIBUTION IN THE TREE OF LIFE
Since the beginning of the studies on evolutionary biology,ne of the most ambitious goals has been the assemble and
comprehension of the complete evolutionary history of biodiversity. This assembly has produced a huge phylogenetic
tree, baptized with the name “Tree of Life". The data set analyzed here is the reconstruction of the Tree of Life which is
available at the database of theTree of Life Web Project(http://www.tolweb.org/). It contains about 6×105
nodes. A very small portion of it, showing the first ramifications, is shown in Fig. 1.
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FIGURE 2. Degree distribution in the Tree of Life. The fit is a power lawP(k) ∼ k−γ with the scaling exponentγ ≈ 2.33. The
inset shows it in cumulative form:Q(k) = 1−∑kr=1 P(r).
One of the first quantities to discuss when analyzing complexnetworks is the degree distribution,P(k), i.e. the
proportion of nodes in the network which are connected tok neighbors. For our tree, this function is plotted in Fig. 2
(together with the functionQ(k) = 1−∑kr=1P(r), giving an accumulated version of the distribution). We seethat the
probability of finding a node with degreek decays as a power lawP(k)∼ k−γ , with γ ≈ 2.33. Thus, this phylogenetic
tree has a broad degree distribution of the scale-free type.Th scaling exponentγ characterizing this distribution is
consistent with the results obtained by Cartozoet al.[5] from a previous taxonomic diversity analysis, where thevalues
obtained were in the range 1.9−2.7.
The use of the degree distribution to characterize a phylogenetic tree needs some qualification: It is generally
accepted that a true phylogenetic tree at high enough resolution will contain only binary branchings [6]. This
corresponds tok = 3 for all internal nodes, andk = 1 for the root and the terminal tips, that would constitute about
one half of the nodes. The presence of nodes with a very high deree (see Fig. 2) in our data set reveals a large amount
of polytomies. This would correspond to successive branchings of several species or groups in an order that can not
be resolved with the techniques used in the phylogenetic reconstruction, so that all of them are assigned the same
branching point. In this sense, it can be thought that a charateristic such as the degree distribution is quantifying more
the limitations of the methodology used to reconstruct the pylogenetic history than the true evolutionary branching
itself. The limitation would be clearer if considering the statistics of taxonomic classifications, in which branchings
are forced to fit into the restricted set of levels established by taxonomic science (Domain, Kingdom, Phyllum, Class,
Order, Family, Genera, Specie). TheTree of Life Web Projectused here does not use a strict taxonomic classification,
since new levels are added as needed. It is likely that the broad distribution of degrees obtained here reflects a property
of radiationprocesses during evolutionary history, i.e. events in which many new species appeared during a relatively
short period of time [7]. Clearly, further analysis is needed to establish which features of the degree distribution
arise from phenomena of biological relevance and which are consequences of the lack of resolution of available
reconstruction methods. In any case, it is seen in Fig. 2 thatthe proportion of nodes withk = 3, representing binary
branchings, stands up above the background power law behavior. We see also the presence of some nodes withk = 2
(they represent taxa which consist of only one subtaxon), although in a very small proportion.
INSIDE ONE LEAF OF THE TREE: GENETIC RELATIONSHIPS IN A PLANT
SPECIES
We now consider in more detail the genetic structures present at one of the tips of the above Tree of Life. We focus in
a particular species and analyze its internal genetic relationships, first across its whole geographical range, and then at
particular locations.
We consider the case of Posidonia oceanica, a marine angiosperm living in meadows submerged between 0 to 40
m in the Mediterranean Sea [8]. It combines clonal reproduction with episodes of sexual reproduction. This plant is
experiencing basin-wide decline and is subject to specific protection and conservation measures [8]. Genomic DNA
data are available from approximately 40 shoots sampled in each of 37 localities across the Mediterranean. A set of
seven microsatellite markers was used to characterize the genotype of each individual. This provides us with a data set
[9, 10, 11] consisting on the number of repetitions of the microsatellite motif at each locus of each shoot sampled. In
this set, a convenient genetic distancedi j can be defined [10, 11] which measures the degree of dissimilarity among
every pair{i, j} of sampled shoots. From this distance matrix, several treesand networks can be built and analyzed,
as described in the following.
The minimum spanning tree of plant shoots
We can consider the fully connected network linking all pairs of shoots in our data set. Given a connected, undirected
graph, a spanning tree of that graph is a subgraph which is a tree, i.e. contains no loops, and connects all the vertices
together. A single graph can have many different spanning trees. Our distance matrixdi j assigns a weight to each of
the links. We can use this information to assign a totallength to each of the possible spanning trees by computing
the sum of the distances of the edges which are kept in that spanning tree. A minimum spanning tree (MST) is then
a spanning tree with the minimum possible total length. In the case in which all edges have a different distance, the
MST is unique. But more generally, there could be several MSTs for a particular network and distance matrix. A MST
is in fact the minimum-cost subgraph connecting all vertices, since subgraphs containing cycles necessarily have more
FIGURE 3. Minimum spanning tree containing all sampled ramets of Posidonia oceanica. Each node represents a shoot, with
colors (or grey shades) indicating the sampling meadow, ande ch link has an associated distance. The minimum spanning tree
minimizes the total sum of distances.
total weight. This allows to interpret the MST as the main path of gene flow among the plant populations, as it links
all the specimens in the genetically shorter way.
Fig. 3 shows the MST associated to the set of shoots and the corr sp nding distances (it is in fact one of the
several equivalent MST with identical total length and similar shape that can be constructed from our distance matrix).
The nodes, representing shoots, are colored with the same shad if they have been collected from the same meadow.
The upper part of the tree contains shoots from populations in the Eastern and Central Mediterranean, and the lower
part from the Northern Spanish coast, in the Western Mediterran an. The central part of the MST is occupied by
populations in the Balearic Islands. The tightly packed balls of nodes group together genetically identical shoots,
arising from clonal reproduction. Although most of the shoots from the same location appear close together in the tree,
there is some scatter, indicating that there has been some migration between different populations. This would need to
be represented with additional links introducing cycles and transforming the tree into a more complex network.
Figure 4 shows the cumulative degree distribution characteizing the MST. It follows a power law with exponent
-1.95, so that the degree distribution is of the scale-free typ , satisfyingP(k)∼ k−2.95.
Intrapopulation networks
Still at a smaller scale, we can address the genetic relationsh p among shoots sampled inside the same meadow. It
is clear that a tree structure is not appropriate to represent th intense gene mixing that would be provided by sexual
reproduction at this scale. Starting from the fully connected network containing links among all pairs of shoots, we can
discard the links containing higher distances and retain only those that represent a sufficiently close genetic similarity.
This is related to the network construction methods based incorrelation thresholds [12, 13]. In [10] we constructed
networks of genetic similarity amonggenets(the set of clonally identical shoots) by choosing as the distance threshold
the so calledoutcrossing distance. This is the average distance between the genets in a population and its offspring
obtained from a simulation of outcrossing, i.e. sexual reproduction among genetically different individuals. The same
idea is applied here to obtain networks of shoots. Network lin s will join shoots which are genetically closer than
the typical outcrossing distance for their population. Figure 5 shows two examples of networks obtained in such a
way. The network representation visually highlights the main features of the population structure. For example the
population in Es Pujols (Fig. 5a) consists of a central core of interconnected shoots to which less central organisms
are linked. Campomanes (Fig. 5b), instead, is structured intwo main components. The size of these networks is too
small to search for scaling properties in the degree distribution, but the analysis in [10] at the genet level reveals that
they have the characteristics of small worlds [14], i.e. clustering significatively higher than a random network with
the same number of nodes and links, while at the same time keeping the same low diameter values characteristic of
random networks.
CONCLUSION
We have presented a brief overview of properties of trees andnetworks constructed in the context of phylogenetic and
genetic relationship at very different scales, from evoluti nary to ecological. The visual inspection of these structures
reveals interesting clues such as paths of gene flow, patterns of speciation, or population structure. The open challenge
is to relate more quantitative topological properties of these complex networks to relevant biological mechanisms.
ACKNOWLEDGMENTS
We acknowledge financial support from the Spanish MEC (Spain) and FEDER through projects CONOCE2 (FIS2004-
00953) and SICOFIB (FIS2006-09966), the Portuguese FCT through project NETWORK (POCI/MAR/57342/2004),
the BBVA Foundation (Spain), and the European Commission through the NEST-Complexity project EDEN (043251).
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Degree Distribution on MST
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FIGURE 4. Representation of the cumulative degree distributionQ(k) = 1−∑kr=1 P(r) characterizing the MST. The straight line
is a fit toQ(k)∼ k−γ+1, with γ ≈ 2.95
a) b)
FIGURE 5. Networks of genetic similarity constructed for the shoots sampled at a) Es Pujols (Formentera, Balearic Islands), and
b) Campomanes (Mediterranean Spanish coast).
REFERENCES
1. R. Albert and A.-L. Barabási,Rev. Mod. Phys.74, 47–97 (2002).
2. S. Dorogovtsev and J. Mendes,Adv. Phys.51, 1079–1187 (2002).
3. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.-U. Hwang,Phys. Rep.424, 175–308 (2006).
4. D. Posada and K. Crandall,Trends Ecol. Evol.16, 37–45 (2001).
5. C. C. Cartozo, D. Garlaschelli, C. Ricotta, M. Barthelemy, and G. Caldarelli, Quantifying the taxonomic diversity inreal
species communities (2006), URLhttp://arxiv.org/abs/q-bio.PE/0612023.
6. A. O. Mooers and S. B. Heard,Q. Rev. Biol.72, 31–54 (1997).
7. T. J. Givnish and K. J. Sytsma, editors,Molecular Evolution and Adaptive Radiation, Cambridge University Press, Cambridge,
1997.
8. M. A. Hemminga and C. M. Duarte,Seagrass Ecology, Cambridge University Press, Cambridge, 2000.
9. S. Arnaud-Haond, F. Alberto, G. Procaccini, E. A. Serrão,and C. M. Duarte,J. Heredity96, 434–440 (2005).
10. A. F. Rozenfeld, S. Arnaud-Haond, E. Hernández-García,V. M. Eguíluz, M. A. Matías, E. Serrão, and C. M. Duarte, to appear
in J. Royal Soc. Interface(2007), URLhttp://arxiv.org/abs/q-bio.PE/0605050.
11. E. Hernández-García, A. F. Rozenfeld, V. M. Eguíluz, S. Arnaud-Haond, and C. M. Duarte,Physica D224, 166–173 (2006).
12. J.-P. Onnela, A. Chakraborti, K. Kaski, J. Kertész, and A. Kanto,Phys. Rev. E68, 056110 (2003).
13. V. Eguíluz, D. Chialvo, G. Cecchi, M. Baliki, and A. Apkari n,Phys. Rev. Lett.94, 018102 (2005).
14. D. J. Watts and S. Strogatz,Nature393, 440–442 (1998).


Evolutionary relationships between species are usually represented in phylogenies, i.e. evolutionary trees, which are a type of networks. The terminal nodes of these trees represent species, which are made of individuals and populations among which gene flow occurs. This flow can also be represented as a network. In this paper we briefly show some properties of these complex networks of evolutionary and ecological relationships. First, we characterize large scale evolutionary relationships in the Tree of Life by a degree distribution. Second, we represent genetic relationships between individuals of a Mediterranean marine plant, Posidonia oceanica, in terms of a Minimum Spanning Tree. Finally, relationships among plant shoots inside populations are represented as networks of genetic similarity

Evolutionary and Ecological Trees and Networks

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