Localization in Ecological Mutualistic Networks (ECCS 2014)
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Localization in Mutualistic Ecological Networks [email protected] Physics and Astronomy Department, University of Padova CONTACTS
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There is an ongoing scientific debate about the relation about the architecture of mutualstic ecological interaction networks and their stability. Indeed, the role of this so called "nested" architecture in terms of robustness of the mutualistic community is an open and intriguing open question. Although it has been shown that the architecture of mutualistic networks minimizes competition and increases stability, several other works have demonstrated how structured mutualistic ecological networks are less stable than their random counterparts. In this work we show beside nestedness, there is another important feature of the network structure that is critical for establishing the stability of mutualistic ecosystems: the localization of the leading eigenvectors corresponding to the highest real part eigenvalue of the community matrix. We found that ecological networks are indeed localized systems, and that this localization lead to an attenuation of the amplitude of the over-all perturbations to systems. We also show that this e ffect increases as the size of the ecological community increases. In other words, the ecological communities seem to organize so that there is a trade off between the resilience of the system (time to return at the equilibrium state) and the net eff ect of the perturbations on species populations.
Transcript of Localization in Ecological Mutualistic Networks (ECCS 2014)
Localization in Mutualistic Ecological Networks
Physics and Astronomy Department,
University of Padova
Welcome to Amos Maritan Lab
Page 1 of 2http://www.pd.infn.it/~maritan/
!!!!!!!!!!!!!!!!!!!!!
Our! research! spans! from! statistical!mechanicsto!organization!of!ecosystems...
29#01#2013
Claudio!wrote!his!thesis.!Good!luck!with!it!
In!the!spirit!of!the!motto!"interdisciplinarity!is!dialog"!the!aim!of!the!Lab!is!toface!biological!and!ecological!problems!in!collaboration!with!experts!of!the!field.Not!mixing!our!expertises,!but!summing!them!up.!
!!!!!!!!!!!!!!!
ABOUT!US NEWS
Home Research People Publications Teaching Collaborators Opportunities Contacts
CONTACTS
# Species [S]
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Architecture of Mutualistic Networks
Null model 0 We keep fixed S and C, and place at random the edges
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NESTEDNESS
Why do we found this ubiquitous structure?
Time
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Nestedness correlates with species abundance
Suweis et al., Nature 2013
Are nested architecture more stable??
~̇x = �~x Max(Re[�(�)]) = �1 ) Resilience
Mutualistic Nested Networks are less resilient than their random counterpart!
!1
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maxA B C
MF [� = 0] CE [� = 0.5] OPT [� = �0.5]
ASSIGN INTERACTION STRENGTHS
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Null Model Bran ! �ran
Beyond Resilience: Localization
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St!1(C,�) ! persistence
vvv1(�, C, S)? ! spread of⇠⇠⇠
uuu1(�, C, S)? ! A1
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Eigenvecor components
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Amplification Envelope: ⇢(tmax) = Maxt2[0,1)||�xxx(t)||
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Stability: putting ingridients together (t=1)
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0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70
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NODF
Localization
Nestedness is not the whole story…
Take Home Messages
�1 ! Resilience
vvv1 ! Spreading of the perturbation
uuu1 ! Attenuation of the perturbation
{�H ,wwwH} ! Reactivity
⇢ ! Amplification Envelope
Asymptotic Stability
Transient Stability
Architecture of mutualistic ecological networks = Nestedness +Localization!
Thanks for your attention! Questions?
Join the LIVING Satellite!Thursday 25, 2 pm @ IMT library (San Ponziano Church)
Robustness, Adaptability and Critical Transitions in Living Systems
SamirSuweis
Optimization: Nature, 500 (449); 2013 Localization: soon in Arxiv
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Max@lD
g0=constant
TRADE-‐OFF between resilience and localiza5on
~̇x = �~x
Real
Imag
inary
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A
B
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(Allesina, Nature 2012)
�ij ⇠ N (0,�2) �ij ,�ji ⇠ |N (0,�2)|Random Structure Mutualis5c (nested) Structure
See also Staniczenko et al., Nat Comm.; Suweis et al. Oikos 2013
Robustness of the results
Nestedness [NODF] Relative Nestedness [NODF*]
i
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iii
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v
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Random
HTI total
HTII total
HTI individual species
HTII individual speciesi
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iii
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a b
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Optimization + AssemblingRandom Fully Optimized
Architecture of Ecological Networks
A =
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aPA 0
�
Fontaine et al., Eco. LeT, 2011
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Attempted Swaps [T]
Popu
latio
n [x
]
Pollinator*species
Plant*species
�c ⇠1pSC
�c ⇠1
SC
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Nestedness [NODF]
Mea
n Po
pula
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Optimiz Total Pop HTI
Null Model 0
Optimiz Total Pop HTII
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Nestedness [NODF]
Null Model 1
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8Nestedness [NODF]
Nestedness [NODF]
Null Model 0
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null model 0 Optimization Single Speciesnull model 1
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HTI HTII
Result 2: Op5mized Networks are nested
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NODF Data
NODF
CM
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<k1>, <k2>,…,<kS>
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# species
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Connec5vity
Holling Type II
Degree @kD »v1\ »z\ »x\
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se
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ffortCase
Summary
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