Elucidating the Relationship Between Indirect Effects and Ecosystem Stability - Presentation

7/27/2019 Elucidating the Relationship Between Indirect Effects and Ecosystem Stability - Presentation

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Elucidating the Relationship Between

Indirect Effects and Ecosystem Stability

Jessica Robbins

University of California Berkeley & The University of Georgia


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Indirect Effects

.5 .5

.25

A B C


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Indirect Effects Ratio

= [

+

+

]

= ==

G = Flow intensity matrix

Gij = the fraction of species js flow material that goes directly to

species i

T = Throughflow vector

Ti = all the energy species i obtains by consuming other species +

all the energy species i obtains from the environmentfij = Rate of direct flow from species j to species i


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Objective

Investigate the connection between the indirect effects

ratio of an ecosystem and the degree of its response

to environmental perturbation


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The Niche ModelImage Source: Williams, R.J., Martinez, N.D., 2000. Simple rules yield

complex food webs. Nature 404, 180-183.

1. Each species is assigned a niche value (ni) between 0 and 1

according to a Beta distribution with =1.5 and =5

2. Each species is assigned a feeding range size (ri), determined

by multiplying the result of a Beta function with mean 2C by ni3. The location of the center of each range (ci) is drawn uniformly

between the values ri/2 and ni

4. Species prey on those that fall within their feeding range, with a

higher probability of feeding on species near the center of their

range


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Possible Confounding Variables

Number of SpeciesFood webs that can exhibit a wide range of functional responses to

environmental change are often more stable

ConnectanceNetworks with higher connectance tend to be more stable

Number of basal speciesThere is thought to be a connection between abundance of basal

species and system stability

Body Mass RatioPredator-prey body-mass ratios between 10 and 100 tend topromote stability

Predator-Prey functional responseSystem stability is promoted when predator response to prey

abundance is not completely linear


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Change In Biomass

For basal species:

= ()=

For consumer species:

= + =

(

)

=

Bi= biomass of species ix

i= mass-specific metabolic rate

yij= maximum ingestion rate of prey species j by predator species i

eij= assimilation efficiencythe fraction of biomass of species j lost due toconsumption by species i that is actually metabolized

Gi(B) = normalized growth rate

Fij(B) = functional response of consumer i and resource j


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Results


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Conclusions

1. There is a strong correlation between indirect effects ratio andconnectance. This means that is difficult to delineate theirimpacts on ecosystem dynamics, and that stability that has beenpreviously been attributed to connectance may also result fromindirect effects

2. Both connectance and indirect effects promote ecosystemstability. However, this is not a guarantee that the ecosystemswith the highest levels of connectance or highest indirect effects

ratio will be the most stable, or vice versa

3. The indirect effects ratio may be a more informative metric thanconnectance

4. Increasing the abundance of basal species tends to decreasesystem stability

5. Increasing the network size both promotes instability andincreases the range of ecosystem response

6. However, the influence of network size and basal speciesabundance on network stability may be poorly represented bycomputational modeling techniques


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Avenues For Future Investigation

1. Adding parasite species to food web

2. Adding detrital compartment to food web

3. Modeling non-feeding interactions

4. Simulating larger webs


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Acknowledgments

This work would not have been possible without the

support, advice, and assistance of:Dr. Caner Kazanci

Qianqian Ma

Dr. Alice Boit

Dr. Rosalyn Rael

Dr. Kevin Lafferty

The University of Georgia

The Ohio State University


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1. Allesina, S., Tang, S., 2012. Stability criteria forcomplex ecosystems. Nature 483, 208-208.

2. Bellingeri, M., Cassi, D., Vincenzi, S., 2013.

Increasing the extinction risk of highly connectedspecies causes a sharp robust-to-fragile transitionin empirical food webs. Ecological Modeling251,1-8.

3. Brose, U., 2008. Complex food webs preventcompetitive exclusion among producer species.Proceedings of the Royal Society B: BiologicalSciences 275, 2507-2514.

4. Brose, U., Williams, R.J., Martinez, N.D., 2006.Allometric scaling enhances stability in complexfood webs. Ecology Letters 9, 1228-1236.

5. Dunne, J.A., Williams, R.J., Martinez, N.D, 2002.Network structure and biodiversity loss in foodwebs: robustness increases with connectance.Ecology Letters 5, 558-567.

6. Grimm, V., Schmidt, E., Wissel, C., 1992. On theapplication of stability concepts in ecology.Ecological Modeling63, 143-161.

7. Kalinkat, G., Scheider, F.D., Digel, C., Guill, C.,Rall, B.C., Brose, U., 2013. Body masses,functional responses and predator-prey stability.Ecology Letters 1-9.

8. Lin, Y., Sutherland, W.J., 2013. Color and degreeof interspecific synchrony of environmental noiseaffect the variability of complex ecologicalnetworks. Ecological Modeling263, 162-173.

1. Ma, Q., Kazanci, C., 2012. Analysis of indirecteffects within ecosystem models using pathway-based methodology. Ecological Modeling252,

238245.2. Martinez, N.D., Williams, R.J., Dunne, J.A., 2005.

Diversity, complexity, and persistence in largemodel ecosystems. Santa Fe Institute.

3. McCann, K.S., 2000. The diversity-stabilitydebate. Nature, 405 228-233.

4. Rall, B.C., Guill, C., Brose, U., 2008. Food-webconnectance and predator interference dampenthe paradox of enrichment. Oikos 117, 202-213.

5. Rip, J.M.K., McCann, K.S., 2011. Cross-ecosystem

differences in stability and the principle of energyflux. Ecology Letters, 14 733-740.

6. Williams, R.J., 2008. Effects of network anddynamical model structure on speciespersistence in large model food webs. TheoreticalEcology3, 285-294.

7. Williams, R.J., Anandanedesan, A., Purves, D.,2010. The probabilistic niche model reveals theniche structure and role of body size in complexfood webs. PLoS ONE5, e12092.

8. Williams, R.J., Martinez, N.D., 2000. Simple rules

yield complex food webs. Nature 404, 180-183.

9. Williams, R.J., Martinez, N.D., 2004. Stabilizationof chaotic and non-permanent food-websdynamics. European Physical Journal B 38. 297-303.

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Elucidating the Relationship Between Indirect Effects and Ecosystem Stability - Presentation