The document describes a method called MusRank for ranking species in mutualistic networks based on their importance and vulnerability. Mutualistic networks involve mutually beneficial interactions between plants and animals, and play a key role in biodiversity. MusRank ranks species based on both their importance, determined by the number and vulnerability of their partners, and their own vulnerability, bounded by their least important partner. The ranking is robust and outperforms other methods. MusRank can help identify key species to focus on for conservation in these important ecosystems.

1. Ranking Species
in
Mutualistic Networks
Virginia Domínguez García and Miguel Á. Muñoz
Lake Como Quantitative Laws II – June 2016
Statistical Physics and
Complex Systems Group

2. Ranking Species in Mutualistic Networks – Mutualistic Interactions
Mutualistic interactions
Mutual beneficial interplay:
Bee obtains nutrients in exchange for its pollination
service

3. Mutualistic interactions
Ranking Species in Mutualistic Networks – Mutualistic Interactions
90 % tropical trees
Needs mutualism
70 % of crops
needs bees
Ubiquitous
90% of tropical trees are involved

4. Mutualistic interactions
Ubiquitous
90% of tropical trees are involved
Interactions can involve hundreds of
species
Tight coevolution: one to one
specialization
Mutualistic bipartite Networks
Ranking Species in Mutualistic Networks – Mutualistic Interactions

5. Mutualistic interactions
Bipartite: 2 Different set of nodes PlantsAnimals
Mutualistic bipartite networks
Ranking Species in Mutualistic Networks – Mutualistic Networks

6. Mutualistic interactions
Bipartite: 2 Different set of nodes PlantsAnimals
Interactions
Ranking Species in Mutualistic Networks – Mutualistic Networks

7. Ranking Species in Mutualistic Networks – Mutualistic Networks
specialistgeneralist
specialist

8. Specialist
(few partners)
Specialist
Specialist Generalist
(many partners)
specialistgeneralist
Ranking Species in Mutualistic Networks – Mutualistic Networks
specialist

9. Specialist
(few partners)
Specialist
Specialist Generalist
(many partners)
specialistgeneralist
Ranking Species in Mutualistic Networks – Mutualistic Networks
specialist
Measures number of shared
neighbours
=

10. Mutualistic Networks – External perturbation
The International Union for Conservation of
Nature has evaluated 52,205 species, depicted
here, for their ability to survive

11. Mutualistic Networks – External perturbation
How to identify the most important
species in the network?

12. If we identify important species the network will collapse fast
Ranking Species in Mutualistic Networks - Framework
FRAMEWORK: DECONSTRUCTING ECOSYSTEMS
We do not know how these networks are assembled Other strategy
Tear them down
Search for the most efficient way to destruction

13. PageRank
A node is
important if
linked to
important
nodes
Closeness
Less distance to
others
Ranking Species in Mutualistic Networks - Framework
FRAMEWORK: DECONSTRUCTING ECOSYSTEMS
WHICH
RANKING
? Degree
More
connections
Betweenness
Bottlenecks
Nestedness
Contribution to
nestedness
Eigenvector
Overlap with
leading
eigenvalue of
A

14. Ranking Species in Mutualistic Networks - Framework
FRAMEWORK: MusRank Ranking algorithm for mutualistic networks
Inspired in a recent work in
econometrics Products

15. Ranking Species in Mutualistic Networks - Framework
FRAMEWORK: MusRank Ranking algorithm for mutualistic networks
Inspired in a recent work in
econometrics
Active species
Passive species
Importance
Vulnerability
Determined by number and vulnerability of
partners
(Linear)
Bounded by the less important partner
(Non-linear)

16. Ranking Species in Mutualistic Networks
FRAMEWORK: MusRank
Adjacency
matrix
( )
( )
( )
( )
Active
Passive
-
Importance
Vulnerability
+
- +

17. ( )
( )
( )
( )
Ranking Species in Mutualistic Networks
FRAMEWORK: MusRank
FIX
PONT
Ranking of
Importance of Active
species
Ranking of
Vulnerability of
Passive species
Independent of initial
conditions
Active
Passive
-
Importance
Vulnerability
+
- +

18. ( )
( )
( )
( )
Ranking Species in Mutualistic Networks
FRAMEWORK: MusRank
FIX
PONT
Ranking of
Importance of Active
species
Ranking of
Vulnerability of
Passive species
Independent of initial
conditions

19. Ranking Species in Mutualistic Networks
FRAMEWORK: Evaluating a ranking
Extinction
curve
Active Passive
Decreasingrank

20. Ranking Species in Mutualistic Networks
FRAMEWORK: Evaluating a ranking
Extinction
Area
Active Passive
0 1
1
destructive ranking
0 1
1
not destructive ranking
OK!
Decreasingrank
Active Passive

21. Ranking Species in Mutualistic Networks
RESULTS: MusRank PERFORMANCE
Genetic Algorithm
best
RESULT:
The ranking provided by
MusRank outperforms all
others
RESULT:
Reversing Active/Passive roles
do not change results
Robust algorithm
Distance from each ranking to the genetic algorithm
over all dataset (60 networks)

22. Ranking Species in Mutualistic Networks
Take home message
Mutualistic networks
-mutual benefit interplay
-hundred of species involved
-characteristic features: Degree heterogeneity (Generalists and specialists),
robust core, phylogeny groups, nestedness,…
-Mutualistic interactions are very important for biodiversity manteinance.
Rankig species
-protocol to quantify “lethality” of a ranking
-MusRank: best method to asses species importance in mutualistic networks
WE ARE
IMPORTANT !!
Oh, No!!I’m more important
than you are ! hehehe
Thanks for Your
attention !!