Limits...
Predicting the stability of large structured food webs.

Allesina S, Grilli J, Barabás G, Tang S, Aljadeff J, Maritan A - Nat Commun (2015)

Bottom Line: The stability of ecological systems has been a long-standing focus of ecology.Recently, tools from random matrix theory have identified the main drivers of stability in ecological communities whose network structure is random.For example, their degree distribution is broader, they contain few trophic cycles, and they are almost interval.

View Article: PubMed Central - PubMed

Affiliation: 1] Department of Ecology &Evolution, University of Chicago, 1101 E. 57th st., Chicago, IL 60637, USA [2] Computation Institute, University of Chicago, Chicago, IL 60637, USA.

ABSTRACT
The stability of ecological systems has been a long-standing focus of ecology. Recently, tools from random matrix theory have identified the main drivers of stability in ecological communities whose network structure is random. However, empirical food webs differ greatly from random graphs. For example, their degree distribution is broader, they contain few trophic cycles, and they are almost interval. Here we derive an approximation for the stability of food webs whose structure is generated by the cascade model, in which 'larger' species consume 'smaller' ones. We predict the stability of these food webs with great accuracy, and our approximation also works well for food webs whose structure is determined empirically or by the niche model. We find that intervality and broad degree distributions tend to stabilize food webs, and that average interaction strength has little influence on stability, compared with the effect of variance and correlation.

No MeSH data available.


Related in: MedlinePlus

Cascade model variants.Simulations performed as for Fig. 2, but with variants of the cascade model. Given that our prediction matches Re(λM,1) (the real part of the leading eigenvalue of M) very closely for matrices built using the cascade model, any deviation displayed here necessarily descends from the different structural models employed. Points above the dashed black line (the identity line) indicate networks with smaller Re(λM,1) than that we would predict using the cascade model approximation, indicating a stabilizing effect of the structure with respect to the cascade model. For each model, we display the predicted versus observed Re(λM,1), as well as the best-fitting linear model. All lines are reported in the Niche model panel for ease of comparison. In all the cases, the effect of the variation is stabilizing, with intervality having a stronger effect than the degree distribution.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4525179&req=5

f3: Cascade model variants.Simulations performed as for Fig. 2, but with variants of the cascade model. Given that our prediction matches Re(λM,1) (the real part of the leading eigenvalue of M) very closely for matrices built using the cascade model, any deviation displayed here necessarily descends from the different structural models employed. Points above the dashed black line (the identity line) indicate networks with smaller Re(λM,1) than that we would predict using the cascade model approximation, indicating a stabilizing effect of the structure with respect to the cascade model. For each model, we display the predicted versus observed Re(λM,1), as well as the best-fitting linear model. All lines are reported in the Niche model panel for ease of comparison. In all the cases, the effect of the variation is stabilizing, with intervality having a stronger effect than the degree distribution.

Mentions: To test whether these features can account for the small discrepancy between our expectation and that found in simulations, we built three variants of the cascade model: (i) a version of the cascade model producing the same degree distribution for the consumers as that of the niche model; (ii) a version producing interval food webs; (iii) a version yielding the same consumer degree distribution as the niche model, and producing interval food webs (that is, a cycle-less niche model). In Fig. 3 we show that all these modifications are slightly stabilizing, making the matrices built using these variants as likely to be stable as those for the niche model. Similarly, modifying the cascade model so that it matches the degree distribution of a given empirical network recapitulates the small deviation we observe between the predicted and observed Re(λM,1) for matrices generated using empirical food web structures (Supplementary Note 4).


Predicting the stability of large structured food webs.

Allesina S, Grilli J, Barabás G, Tang S, Aljadeff J, Maritan A - Nat Commun (2015)

Cascade model variants.Simulations performed as for Fig. 2, but with variants of the cascade model. Given that our prediction matches Re(λM,1) (the real part of the leading eigenvalue of M) very closely for matrices built using the cascade model, any deviation displayed here necessarily descends from the different structural models employed. Points above the dashed black line (the identity line) indicate networks with smaller Re(λM,1) than that we would predict using the cascade model approximation, indicating a stabilizing effect of the structure with respect to the cascade model. For each model, we display the predicted versus observed Re(λM,1), as well as the best-fitting linear model. All lines are reported in the Niche model panel for ease of comparison. In all the cases, the effect of the variation is stabilizing, with intervality having a stronger effect than the degree distribution.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4525179&req=5

f3: Cascade model variants.Simulations performed as for Fig. 2, but with variants of the cascade model. Given that our prediction matches Re(λM,1) (the real part of the leading eigenvalue of M) very closely for matrices built using the cascade model, any deviation displayed here necessarily descends from the different structural models employed. Points above the dashed black line (the identity line) indicate networks with smaller Re(λM,1) than that we would predict using the cascade model approximation, indicating a stabilizing effect of the structure with respect to the cascade model. For each model, we display the predicted versus observed Re(λM,1), as well as the best-fitting linear model. All lines are reported in the Niche model panel for ease of comparison. In all the cases, the effect of the variation is stabilizing, with intervality having a stronger effect than the degree distribution.
Mentions: To test whether these features can account for the small discrepancy between our expectation and that found in simulations, we built three variants of the cascade model: (i) a version of the cascade model producing the same degree distribution for the consumers as that of the niche model; (ii) a version producing interval food webs; (iii) a version yielding the same consumer degree distribution as the niche model, and producing interval food webs (that is, a cycle-less niche model). In Fig. 3 we show that all these modifications are slightly stabilizing, making the matrices built using these variants as likely to be stable as those for the niche model. Similarly, modifying the cascade model so that it matches the degree distribution of a given empirical network recapitulates the small deviation we observe between the predicted and observed Re(λM,1) for matrices generated using empirical food web structures (Supplementary Note 4).

Bottom Line: The stability of ecological systems has been a long-standing focus of ecology.Recently, tools from random matrix theory have identified the main drivers of stability in ecological communities whose network structure is random.For example, their degree distribution is broader, they contain few trophic cycles, and they are almost interval.

View Article: PubMed Central - PubMed

Affiliation: 1] Department of Ecology &Evolution, University of Chicago, 1101 E. 57th st., Chicago, IL 60637, USA [2] Computation Institute, University of Chicago, Chicago, IL 60637, USA.

ABSTRACT
The stability of ecological systems has been a long-standing focus of ecology. Recently, tools from random matrix theory have identified the main drivers of stability in ecological communities whose network structure is random. However, empirical food webs differ greatly from random graphs. For example, their degree distribution is broader, they contain few trophic cycles, and they are almost interval. Here we derive an approximation for the stability of food webs whose structure is generated by the cascade model, in which 'larger' species consume 'smaller' ones. We predict the stability of these food webs with great accuracy, and our approximation also works well for food webs whose structure is determined empirically or by the niche model. We find that intervality and broad degree distributions tend to stabilize food webs, and that average interaction strength has little influence on stability, compared with the effect of variance and correlation.

No MeSH data available.


Related in: MedlinePlus