Nessun titolo diapositiva

1
Universal Scaling Relations in Biological Systems
Cecile Caretta, Diego Garlaschelli, Guido
Caldarelli, Luciano Pietronero Carlo
Ricotta University of RomeLa Sapienza
Coevolution and Self-Organization in Dynamical
Networks
2
Contents

• Two examples of Biological Networks
• Food webs
• Linnean trees

• Network Topological properties (degree
  distribution etc)
• give some new description of the phenomena
• allowing to detect new universal behaviour.

3
Food Web (ecological network)
Set of interconnected food chains resulting in a
much more complex topology
4
Examples of Food Webs
? Pamlico Estuary (North Carolina) 14 species
? Aggregated Food Web of Little Rock Lake
(Wisconsin) 182 species ? 93 trophic species
How to characterize the topology of Webs?
See Neo Martinez Group at http//userwww.sfsu.ed
u/webhead/lrl.html
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Degree Distribution P(k) in real Food Webs
Unaggregated versions of real webs
irregular or scale-free? P(k)? k-?
R.V. Solé, J.M. Montoya Proc. Royal Society
Series B 268 2039 (2001) J.M. Montoya, R.V. Solé,
Journal of Theor. Biology 214 405
(2002) J.Camacho, R. Guimera, L. A. N. Amaral PRE
(2002),PRL (2002)
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Spanning Trees of a Directed Graph
A spanning tree of a connected directed graph is
any of its connected directed subtrees with the
same number of vertices.
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How to characterize the topology of a tree?
1
1
1
1
1
1
3
1
1
5
5
2
3
11
1
8
22
1
10
33
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Allometric Relations in Vascular Systems
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Allometric Relations in River Networks
AX drained area of point X
Hacks Law
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Area Distribution in Real Food Webs
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Allometric Relations in Real Food Webs
(D.Garlaschelli, G. Caldarelli, L. Pietronero
Nature 423 165 (2003))
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Spanning Trees of the webs generated by Webworld
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Match between Little Rock Lake food web and a
simulation of the Webworld Model (R200 ?0.4)
Original Webs
Aggregated Webs
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Ecosystems around the world
Ecosystem
Set of all living organisms and environmental
properties of a restricted geographic area
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From Linnean trees to graph theory
Linnean Tree hierarchical structure organized
on different
levels, called taxonomic levels, representing

• classification and identification of different
  plants

• history of the evolution of different species

A Linnean tree already has the topological
structure of a tree graph

• each node in the graph represents a different
  taxa
• (specie, genus, family, and so on). All nodes
  are
• organized on levels representing the taxonomic
  one

• all link are up-down directed and each one
• represents the belonging of a taxon to the
  relative
• upper level taxon

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Scale-free properties
Degree distribution
P(k)
k
The best results for the exponent value are given
by ecosystems with greater number of species. For
smaller networks its value can increase reaching
? 2.8 - 2.9.
17
Geographical flora subsets
P(k)
P(k)
k
k
2.6 ? 2.8
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What about random subsets?
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Memory?
?
NO!
Particular rule to put a species in a genus, a
genus in a family.?
P(kf, kg) that a genus with degree kg belongs to
a family with degree kf
? kg? ?g kg P(kf,kg)
P(kf,kg)? kg -?
? 2.2 ? 0.2
? kf? ?f kf P(ko,kf)
P(ko,kf)? kf -?
? 1.8 ? 0.2
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A simple model
1) create N species to build up an ecosystem
2) Group the different species in genus, the
genus in families, then families in
orders and so on realizing a Linnean tree
- Each species is represented by a string with 40
characters representing 40 properties which
identify the single species (genes) - Each
character is chosen between 94 possibilities all
the characters and symbols that in the ASCII
code are associated to numbers from 33 to 126
Two species are grouped in the same genus
according to the extended Hamming distance dWH
c1i character of species 1 with
i1,.,40 c2i character of species
2 with i1,.,40
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dEH C
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Two ways of creating N species
No correlation species randomly created with
no relationship between them
Genetic correlation species are no more
independent but
descend from the same ancestor

• No correlation

• ecosystems of 3000 species
• each character of each string is chosen
• at random
• quite big distance between two different
• species

?dEH? 20
23

• Coevolution correlation

• single species ancestor of all species in the
  ecosystem
• at each time step t a new species appear
• - chose (randomly) one of the species
  already present in the ecosystem
• - change one of its character
• 3000 time steps

• Environment average of all species present in
  the
• the ecosystem at each
  time step t.
• At each time step t we calculate the distance
  between
• the environment and each species

dEH lt Csel
dEH gt Csel

• small distance between different species

?dEH? 0.5
P(k) k -? ? 2.8 ? 0.2
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A comparison
Correlated
Not Correlated
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Conclusions
Results

• universality (same statistical properties for
  food webs and
• ecosystems with different number of species
  and climatic
• environment) and scale-free properties

• (FOOD WEBS) A certain degree of optimization is
  reached,
• given as a constraint the presence of
  competition

• (LINNEAN TREES) comparison between geographical
  random
• subsets evidence of the existence of a
  correlation between
• species in a same ecosystem due to some
  coevolution process

Future

• models presented can be improved with
• particular attention to environment and
  natural selection

• new data

Applications

• prevent correlated plants/animal extinction due
  to human
• influence

• plant ecosystems structure and reafforestation

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COSIN COevolution and Self-organisation In
dynamical Networks
RTD Shared Cost Contract IST-2001-33555
http//www.cosin.org

• Nodes 6 in 5 countries
• Period of Activity April 2002-April 2005
• Budget 1.256 M
• Persons financed 8-10 researchers
• Human resources 371.5 Persons/months

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