IJPAM: Volume 114, No. 1 (2017)




H.T. Banks$^1$, J.E. Banks$^2$, Riccardo Bommarco$^3$,
Alva Curtsdotter$^4$, Tomas Jonsson$^5$, A.N. Laubmeier$^6$
$^{1,6}$Center for Research in Scientific Computation
North Carolina State University
Raleigh, NC 27695, USA
$^2$Undergraduate Research Opportunities Center (UROC)
California State University, Monterey Bay
Seaside, CA 93955, USA
$^{3,4,5}$Department of Ecology
Swedish University of Agricultural Sciences
Uppsala, SE-75007, SWEDEN
$^5$School of Bioscience
University of Skövde
Skövde, SE-54128, SWEDEN


The application of mechanistic models to natural systems is of interest to ecological researchers. We use the mechanistic Allometric Trophic Network (ATN) model, which is well-studied for controlled and theoretical systems, to describe the dynamics of the aphid Rhopalosiphum padi in an agricultural field. We diagnose problems that arise in a first attempt at a least squares parameter estimation on this system, including formulation of the model for the inverse problem and information content present in the data. We seek to establish whether the field data, as it is currently collected, can support parameter estimation for the ATN model.


Received: March 27, 2017
Revised: April 20, 2017
Published: April 21, 2017

AMS Classification, Key Words

AMS Subject Classification: 92D25, 92D40, 65L09, 93C10
Key Words and Phrases: population models, Rhopalosiphum padi, allometric trophic network, parameter estimation, residual analysis, model selection

Download Section

Download paper from here.
You will need Adobe Acrobat reader. For more information and free download of the reader, see the Adobe Acrobat website.


P. Balvanera, A.B. Pfisterer, N. Buchmann, J.S. He, T. Nakashizuka, D. Raffaelli, and B. Schmid.
Quantifying the evidence for biodiversity effects on ecosystem functioning and services.
Ecology Letters, 9:1146-1156, 2006.

H.T. Banks, J.E. Banks, Riccardo Bommarco, Alva Curtsdotter, Tomas Jonsson, and A.N. Laubmeier.
Parameter estimation for an allometric food web model.
CRSC Technical Report, CRSC-TR16-03, May 2016.

H.T. Banks, J.E. Banks, J. Rosenheim, and K. Tillman. Modeling populations of Lygus Hesperus on cotton fields in the San Joaquin Valley of California: The importance of statistical and mathematical model choice. CRSC-TR15-04, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, May, 2015; J. Biological Dynamics, 11:25-39, 2017. DOI: 10.1080/17513758.2016.1143533.

H.T. Banks, J.E. Banks, Neha Murad, J. A Rosenheim, and K. Tillman. Modelling pesticide treatment effects on Lygus hesperus in cotton fields. CRSC-TR15-09, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, September, 2015; Proceedings, 27 th IFIP TC7 Conference 2015 on System Modelling and Optimization, L. Bociu et al (Eds.) CSMO 2015 IFIP AICT 494:1-12, 2017. Springer : DOI: 10.1007/978-3-319-55795-3-8.

H.T. Banks, E. Collins, K. Flores, P. Pershad, M. Stemkovski, and L. Stephenson. Statistical error model comparison for logistic growth of green algae (Raphidocelis subcapitata). CRSC-TR16-10, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, August, 2016; Applied Mathematical Letters, 64:213-222, 2017.

H.T. Banks, R.A. Everett, S. Hu, N. Murad, and H.T. Tran. Mathematical and statistical model misspecifications in modeling immune response in renal transplant recipients. CRSC-TR16-14, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, November, 2016; Inverse Problems in Science and Engineering, to appear.

H.T. Banks, Jared Catenacci, and Shuhua Hu.
Use of difference-based methods to explore statistical and mathematical model discrepancy in inverse problems.
Journal of Inverse and Ill-posed Problems, 23:491-509, 2015.

H.T. Banks and B.G. Fitzpatrick.
Statistical methods for model comparison in parameter estimation problems for distributed systems.
Journal of Mathematical Biology, 28:501-527, 1990.

H.T. Banks, S. Hu, and W.C. Thompson.
Modeling and Inverse Problems in the Presence of Uncertainty.
CRC Press, Boca Raton, 2014.

H.T. Banks and H.T. Tran.
Mathematical and Experimental Modeling of Physical and Biological Processes.
CRC Press, New York, 2009.

Eric L. Berlow, Jennifer A. Dunne, Neo D. Martinez, Phillip B. Stark, Richard J. Williams, Ulrich Brose, and Simon A. Levin.
Simple prediction of interaction strengths in complex food webs.
Proceedings of the National Academy of Sciences of the United States of America, 106:187-191, 2009.

Alice Boit, Neo D. Martinez, Richard J. Williams, and Ursula Gaedke.
Mechanistic theory and modelling of complex food-web dynamics in Lake Constance.
Ecology Letters, 15:594-602, 2012.

U. Brose, R.B. Ehnes, B.C. Rall, O. Vucic-Pestic, E.L. Berlow, and S. Scheu.
Foraging theory predicts predator-prey energy fluxes.
Journal of Animal Ecology, 77:1072-1078, 2008.

Ulrich Brose, Richard J. Williams, and Neo D. Martinez.
Allometric scaling enhances stability in complex food webs.
Ecology Letters, 9:1228-1236, 2006.

James H. Brown, James F. Gillooly, Andrew P. Allen, Van M. Savage, and Geoffrey B. West.
Toward a metabolic theory of ecology.
Ecology, 85:1771-1789, 2004.

B. Cardinale, E. Duffy, S. Srivastava, M. Loreau, M. Thomas, and M. Emmerson.
Towards a food web perspective on biodiversity and ecosystem functioning.
In S. Naeem, D.E. Bunker, A. Hector, M Loreau, and C. Perrings, editors, Biodiversity, Ecosystem Functioning, and Human Wellbeing, chapter 8, pages 105-120. Oxford University Press, Oxford, 2009.

B.J. Cardinale, J.E. Duffy, A. Gonzalez, C. Hooper, D.U. Perrings, P. Venail, A. Narwani, G.M. Mace, D. Tilman, D.A. Wardle, A.P. Kinzig, G.C. Daily, M. Loreau, J.B. Grace, A. Larigauderie, D.S. Srivastava, and S. Naeem.
Biodiversity loss and its impact on humanity.
Nature, 486:59-67, 2012.

G.C. Chang.
Comparison of single versus multiple species of generalist predators for biological control.
Environmental Ecology, 25:207-212, 1996.

Brian Dennis, José Miguel Ponciano, Subhash R. Lele, Mark L. Taper, and David F. Staples.
Estimating density dependence, process noise, and observation error.
Ecological Monographs, 76:323-341, 2006.

J.E. Duffy, B.J. Cardinale, K.E. France, P.B. McIntyre, E. Thebault, and M. Loreau.
The functional role of biodiversity in ecosystems: incorporating trophic complexity.
Ecology Letters, 10:522-538, 2007.

C.S. Elton.
The Ecology of Invasions by Plants and Animals, Volume 18.
Metheun, London, 1958.

Tessa B. Francis, Elizabeth M. Wolkovich, Mark D. Scheuerell, Stephen L. Katz, Elizabeth E. Holmes, and Stephanie E. Hampton.
Shifting regimes and changing interactions in the Lake Washington, U.S.A., plankton community from 1962–1994.
PLOS ONE, 9, 2014.

Stephanie E. Hampton, Elizabeth E. Holmes, Lindsay P. Scheef, Mark D. Scheuerell, Stephen L. Katz, Daniel E. Pendleton, and Eric J. Ward.
Quantifying effects of abiotic and biotic drivers on community dynamics with multivariate autoregressive (MAR) models.
Ecology, 94:2663-2669, 2013.

A.R. Ives, B. Dennis, K.L. Cottingham, and S.R. Carpenter.
Estimating community stability and ecological interactions from time-series data.
Ecological Monographs, 73:301-330, 2003.

Riikka Kaartinen, Tomas Jonsson, Mattias Jonsson, and Riccardo Bommarco.
Intraguild interactions modify the effect of body size on trophic interactions.
Unpublished manuscript.

D.K. Letourneau, J.A. Jedlicka, S.G. Bothwell, and C.R. Moreno.
Effects of natural enemy biodiversity on the suppression of arthropod herbivores in terrestrial ecosystems.
Annual Review of Ecology, Evolution, and Systematics, 40:573-592, 2009.

M. Loreau, S. Naeem, P. Inchausti, J. Bengtsson, J.P. Grime, A. Hector, D.U. Hooper, M.A. Huston, D. Raffaelli, B. Schmid, and D. Tilman.
Biodiversity and ecosystem functioning: current knowledge and future challenges.
Science, 294:804-808, 2001.

J.E. Losey and R.F. Denno.
Positive predator-predator interactions: enhanced predation rates and synergistic suppression of aphid populations.
Ecology, 79:2143-2152, 1998.

G.M. Mace, K. Norris, and A.H. Fitter.
Biodiversity and ecosystem services: a multilayered relationship.
Trends in Ecology and Evolution, 27:19-26, 2012.

R.M. May.
Stability and Complexity in Model Ecosystems. Volume 6.
Princeton University Press, 1973.

Shahid Naeem, Daniel E. Bunker, Andy Hector, Michel Loreau and Charles Perrings, Eds.
Biodiversity, Ecosystem Functioning, and Human Wellbeing: An Ecological and Economic Perspective.
Oxford University Press, 2009.

B.C. Rall, G. Kalinkat, O. Vucic-Pestic, and U. Brose.
Taxonomic versus allometric constraints on non-linear interaction strengths.
Oikos, 120:483-492, 2011.

Florian Dirk Schneider, Stefan Scheu, and Ulrich Brose.
Body mass constraints on feeding rates determine the consequences of predator loss.
Ecology Letters, 15:436-443, 2012.

W.E. Snyder and A.R. Ives.
Interactions between specialist and generalist natural enemies: parasitoids, predators, and pea aphid biocontrol.
Ecology, 84:91-107, 2003.

E. Thebault and M. Loreau.
Food-web constraints on biodiversity - ecosystem functioning relationships.
Proceedings of the National Academy of Sciences, 100:14949-14954, 2003.

D. Tilman.
The ecological consequences of changes in biodiversity: a search for general principles.
Ecology, 80:1455-1474, 1999.

P. Yodzis and S. Innes.
Body size and consumer-resource dynamics.
The American Naturalist, 139:1151-1175, 1992.

How to Cite?

DOI: 10.12732/ijpam.v114i1.12 How to cite this paper?

International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 114
Issue: 1
Pages: 143 - 160

Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).