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

Ranking Species in Mutualistic Networks – Mutualistic Interactions

Mutualistic interactions

Mutual beneficial interplay:

Bee obtains nutrients in exchange for its pollination

service

Mutualistic interactions

Ranking Species in Mutualistic Networks – Mutualistic Interactions

90 % tropical trees

Needs mutualism

70 % of cropsneeds bees

Ubiquitous 90% of tropical trees are involved

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

Mutualistic interactions

Bipartite: 2 Different set of nodes PlantsAnimals

Mutualistic bipartite networks

Ranking Species in Mutualistic Networks – Mutualistic Networks

Mutualistic interactions

Bipartite: 2 Different set of nodes PlantsAnimals

Interactions

Ranking Species in Mutualistic Networks – Mutualistic Networks

Ranking Species in Mutualistic Networks – Mutualistic Networks

specialistgeneralist

specialist

Specialist (few partners)

Specialist

Specialist Generalist(many partners)

specialistgeneralist

Ranking Species in Mutualistic Networks – Mutualistic Networks

specialist

Specialist (few partners)

Specialist

Specialist Generalist(many partners)

specialistgeneralist

Ranking Species in Mutualistic Networks – Mutualistic Networks

specialist

Measures number of shared

neighbours

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Mutualistic Networks – External perturbation

The International Union for Conservation of

Nature has evaluated 52,205 species, depicted

here, for their ability to survive

Mutualistic Networks – External perturbation

How to identify the most important species in the network?

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 strategyTear them down

Search for the most efficient way to destruction

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

Ranking Species in Mutualistic Networks - Framework

FRAMEWORK: MusRank Ranking algorithm for mutualistic networks

Inspired in a recent work in

econometrics Products

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)

Ranking Species in Mutualistic Networks

FRAMEWORK: MusRank

Adjacency matrix

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Act

ive

Passive

-Imp

ort

an

ce

Vulnerability

+

- +

�(���)

��(���)

�(�)

��(�)

Ranking Species in Mutualistic Networks

FRAMEWORK: MusRank

FIXPONT

Ranking of

Importance of Active

species

Ranking of

Vulnerability of

Passive species

Independent of initial

conditions

Act

ive

Passive

-Imp

ort

an

ce

Vulnerability

+

- +

�(���)

��(���)

�(�)

��(�)

Ranking Species in Mutualistic Networks

FRAMEWORK: MusRank

FIXPONT

Ranking of

Importance of Active

species

Ranking of

Vulnerability of

Passive species

Independent of initial

conditions

Ranking Species in Mutualistic Networks

FRAMEWORK: Evaluating a ranking

Extinction

curve

Active PassiveD

ecr

ea

sin

gra

nk

Ranking Species in Mutualistic Networks

FRAMEWORK: Evaluating a ranking

Extinction

Area

Active Passive

0 1

1destructive ranking

0 1

1not destructive ranking

OK!

De

cre

asi

ng

ran

kActive Passive

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)

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 AREIMPORTANT !!

Oh, No!!I’m more importantthan you are ! hehehe

Thanks for Your

attention !!