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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

Accuracy of the approximation.(a) We parameterized 150 community matrices with structure determined by the cascade model. The predicted Re(λM,1) (real part of the leading eigenvalue of M, light blue squares) is much closer to the observed value than when approximating it using the method by Tang et al.5 (green triangles) or using May's criterion1 (purple dots). The coloured dashed lines are the best-fitting linear models, and the black dashed line is the bisector of the first quadrant, marking perfect predictions. (b) The bulk of the eigenvalues of M for one of the matrices. The light blue ellipse is that found for B, but centred at (Re(λA,1),0) (the red line indicates the curve describing the circle where we expect the eigenvalues of A to fall). The green ellipse is that predicted according to Tang et al.5, and the purple circle is that predicted using May's criterion1. (b and e) The same plots for matrices built using the niche model. (c and f) The same plots but for matrices built parameterizing 10 times each of 15 empirical food webs.
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f2: Accuracy of the approximation.(a) We parameterized 150 community matrices with structure determined by the cascade model. The predicted Re(λM,1) (real part of the leading eigenvalue of M, light blue squares) is much closer to the observed value than when approximating it using the method by Tang et al.5 (green triangles) or using May's criterion1 (purple dots). The coloured dashed lines are the best-fitting linear models, and the black dashed line is the bisector of the first quadrant, marking perfect predictions. (b) The bulk of the eigenvalues of M for one of the matrices. The light blue ellipse is that found for B, but centred at (Re(λA,1),0) (the red line indicates the curve describing the circle where we expect the eigenvalues of A to fall). The green ellipse is that predicted according to Tang et al.5, and the purple circle is that predicted using May's criterion1. (b and e) The same plots for matrices built using the niche model. (c and f) The same plots but for matrices built parameterizing 10 times each of 15 empirical food webs.

Mentions: To test the quality of our approximation, we built 150 adjacency matrices K using the cascade model9. The size of the matrix was randomly chosen among {500, 750, 1,000}, and the probability of interaction C was sampled uniformly between 0.1 and 0.3. We sampled the pairs (Mij,Mji) independently from the empirical distribution Z whenever Kij=1. The results are presented in Fig. 2. The approximation is very accurate, and clearly superior to what expected following the derivations by May1 or Tang et al.5.


Predicting the stability of large structured food webs.

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

Accuracy of the approximation.(a) We parameterized 150 community matrices with structure determined by the cascade model. The predicted Re(λM,1) (real part of the leading eigenvalue of M, light blue squares) is much closer to the observed value than when approximating it using the method by Tang et al.5 (green triangles) or using May's criterion1 (purple dots). The coloured dashed lines are the best-fitting linear models, and the black dashed line is the bisector of the first quadrant, marking perfect predictions. (b) The bulk of the eigenvalues of M for one of the matrices. The light blue ellipse is that found for B, but centred at (Re(λA,1),0) (the red line indicates the curve describing the circle where we expect the eigenvalues of A to fall). The green ellipse is that predicted according to Tang et al.5, and the purple circle is that predicted using May's criterion1. (b and e) The same plots for matrices built using the niche model. (c and f) The same plots but for matrices built parameterizing 10 times each of 15 empirical food webs.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f2: Accuracy of the approximation.(a) We parameterized 150 community matrices with structure determined by the cascade model. The predicted Re(λM,1) (real part of the leading eigenvalue of M, light blue squares) is much closer to the observed value than when approximating it using the method by Tang et al.5 (green triangles) or using May's criterion1 (purple dots). The coloured dashed lines are the best-fitting linear models, and the black dashed line is the bisector of the first quadrant, marking perfect predictions. (b) The bulk of the eigenvalues of M for one of the matrices. The light blue ellipse is that found for B, but centred at (Re(λA,1),0) (the red line indicates the curve describing the circle where we expect the eigenvalues of A to fall). The green ellipse is that predicted according to Tang et al.5, and the purple circle is that predicted using May's criterion1. (b and e) The same plots for matrices built using the niche model. (c and f) The same plots but for matrices built parameterizing 10 times each of 15 empirical food webs.
Mentions: To test the quality of our approximation, we built 150 adjacency matrices K using the cascade model9. The size of the matrix was randomly chosen among {500, 750, 1,000}, and the probability of interaction C was sampled uniformly between 0.1 and 0.3. We sampled the pairs (Mij,Mji) independently from the empirical distribution Z whenever Kij=1. The results are presented in Fig. 2. The approximation is very accurate, and clearly superior to what expected following the derivations by May1 or Tang et al.5.

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