An understanding of food-web persistence from local to global scales

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Daniel B. Stouffer

Integrative Ecology Group Estación Biológica de Doñana - CSIC

Sevilla, Spain [email protected]

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• A true complex system • Experimentation is

impossible (or impractical)

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• A true complex system • Experimentation is impossible (or impractical) • A modeling approach is imperative

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• Stability of small sub-webs

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• “Complexity-stability” debate

• More diversity and more connections = Greater stability • More diversity and more connections = Lower stability • Greater empirical realism increases stability

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• Omnivory is a stabilizing force • Weak interactions confer stability • Predator-prey body size ratios

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• “Complexity-stability” debate

• What is meant by stability?

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• What is meant by stability?

• Return to equilibrium after perturbation • Stabilization of dynamics

• Greater species persistence

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• What is the role of food-web modules?

• How does persistence of food-web modules in isolation

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• A key to the success of leading static food-web models 0 1 2 3 4 Number of prey, k/2z 0.0 0.2 0.4 0.6 0.8 1.0 Cumulative distribution 0 1 2 3 4 Number of predators, m/2z 0.0 0.2 0.4 0.6 0.8 1.0 0 1 2 3 4 Number of links, r/2z 0.0 0.2 0.4 0.6 0.8 1.0

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• Species can be ordered in one dimension • Prey selection

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• Prey selection: Random

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• Species can be ordered in one dimension • Prey selection: Contiguous

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• Prey selection: Contiguous

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• Species can be ordered in one dimension • Prey selection: Contiguous

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• Contiguous predation

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• Random predation

• Predators are indifferent to the identity of their prey

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• Predators specialize on species which have some

characteristic features

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• Random predation

• Predators specialize on species which have some

characteristic features

• Is there a signature in the data indicating the

empirically observed mechanism?

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• Just the appearance of motifs is not significant • Compare to null hypothesis of a randomized network

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• Compare to null hypothesis of a randomized network • Could the observed motif pattern occur at random?

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• Just the appearance of motifs is not significant • Compare to null hypothesis of a randomized network • Could the observed motif pattern occur at random?

S1 S2 S3 S4 S5 D1 D2 D3 D4 D5 D6 D7 D8 -1.0 -0.5 0.0 0.5 1.0 Normalized profile Stoufferet al._{, PRSB (2007)}

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• Just the appearance of motifs is not significant • Compare to null hypothesis of a randomized network • Could the observed motif pattern occur at random?

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• What is the relationship between persistence of

modules in isolation and their influence on community food-web persistence?

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• How does a module’s influence on community

food-web persistence relate to its presence in community food-webs?

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• We will model module and food-web dynamics and

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• Allometric scaling of metabolic parameters× dBi dt = riGiBi − X k=pred xkykBkFki eki dBi dt = −xiBi + xiBi X j=prey yiFij − X k=pred xkykBkFki eki

†_{Yodzis and Innes, Am. Nat. (1992)} ×_Broseet al._{, Ecol. Lett. (2006)}

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• Bioenergetic population dynamics model • Allometric scaling of metabolic parameters • Required inputs:

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• Allometric scaling of metabolic parameters • Required inputs:

• Network of interactions

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• Network of interactions • Species’ body masses

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• Network of interactions • Species’ body masses

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• Network of interactions • Species’ body masses • Interaction strengths

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• Network of interactions⋆ • Species’ body masses • Interaction strengths

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Tri−trophic chain Exploitative competition Apparent competition Omnivory

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0 1000 2000 3000 4000 Timesteps 0.00 0.20 0.40 0.60 0.80

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>

chain Tri−trophic Exploitative competition Apparent competition Omnivory

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• How does presence of modules relate to persistence?

• Generate a food web, assign masses, assign interaction

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strengths. . .

• The food web has some number of each module:

• Tri-trophic food chain • Omnivory

• Exploitative competition • Apparent competition

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strengths. . .

• The food web has some number of each module:

• Tri-trophic food chain • Omnivory

• Exploitative competition • Apparent competition

• How does the number of each module present

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10−6 10−5 10−4 10−3 0.0 500.0 1000.0 1500.0 2000.0 −1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2 C on d iti on al pr ob ab ilit y d en sit y Nmodule M o d el re si d u al s

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10−6 10−5 10−4 10−3 0.0 500.0 1000.0 1500.0 2000.0 −1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2 0.4 C on d iti on al pr ob ab ilit y d en sit y Nmodule M o d el re si d u al s

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10−6 10−5 10−4 10−3 0.0 500.0 1000.0 1500.0 2000.0 −1.0 −0.5 0.0 C on d iti on al pr ob ab ilit y d en sit y Nmodule M o d el re si d u al s

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10−6 10−5 10−4 10−3 0.0 500.0 1000.0 1500.0 −1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2 C on d iti on al pr ob ab ilit y d en sit y Nmodule M o d el re si d u al s

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10−6 10−5 10−4 10−3 0.0 1000.0 2000.0 3000.0 −1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2 C on d iti on al pr ob ab ilit y d en sit y Nmodule M o d el re si d u al s

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-0.2 -0.1 0.0 0.1 0.2 Persistence factor

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• Persistence of isolated modules is not the same as the

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• Presence of modules has clear influence on community

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• Presence of modules has clear influence on community

food web persistence

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• There may be significant dynamic justifications for

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observed food-web structure

• Caution must be taken when attempting to scale up

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• There may be significant dynamic justifications for

observed food-web structure

• Caution must be taken when attempting to scale up

from modules to community food webs

• Species appear to participate in interactions which

maximize community persistence and not necessarily their own persistence

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S1 S2 S3 S4 S5 D1 D2 D3 D4 D5 D6 D7 D8 -1.0 -0.5 0.0 0.5 1.0 Normalized profile

• Some empirical food webs exhibit fewer instances of

omnivory and greater instances of exploitative and apparent competition

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S1 S2 S3 S4 S5 D1 D2 D3 D4 D5 D6 D7 D8 -1.0 -0.5 0.0 0.5 1.0 Normalized profile

• We hypothesize that these food webs are less

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• Management decisions

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• What motifs does a species participate in?

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• What motifs does a species participate in?

• Invasive species

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• Lu´ıs Amaral, Juan Camacho, Wenxin Jiang • Jordi Bascompte

• Members of the Integrative Ecology Group and Amaral Lab • NSF IGERT Graduate Research Fellowship

• NU ChBE Teaching Apprenticeship fellowship • CSIC JAE Post-doctoral Fellowship