zbMATH — the first resource for mathematics

Structural sensitivity of biological models revisited. (English) Zbl 1397.92565
Summary: Enhancing the predictive power of models in biology is a challenging issue. Among the major difficulties impeding model development and implementation are the sensitivity of outcomes to variations in model parameters, the problem of choosing of particular expressions for the parametrization of functional relations, and difficulties in validating models using laboratory data and/or field observations. In this paper, we revisit the phenomenon which is referred to as structural sensitivity of a model. Structural sensitivity arises as a result of the interplay between sensitivity of model outcomes to variations in parameters and sensitivity to the choice of model functions, and this can be somewhat of a bottleneck in improving the models predictive power. We provide a rigorous definition of structural sensitivity and we show how we can quantify the degree of sensitivity of a model based on the Hausdorff distance concept. We propose a simple semi-analytical test of structural sensitivity in an ODE modeling framework. Furthermore, we emphasize the importance of directly linking the variability of field/experimental data and model predictions, and we demonstrate a way of assessing the robustness of modeling predictions with respect to data sampling variability. As an insightful illustrative example, we test our sensitivity analysis methods on a chemostat predator-prey model, where we use laboratory data on the feeding of protozoa to parameterize the predator functional response.

92D25 Population dynamics (general)
92D40 Ecology
Full Text: DOI
[1] Abrams, P.A., The fallacies of ratio-dependent predation, Ecology, 75, 1842-1850, (1994)
[2] Arditi, R.; Ginzburg, L.R.; Akcakaya, H.R., Variations in plankton densities among lakes: a case for ratio-dependent models, American naturalist, 138, 1287-1296, (1991)
[3] Arhonditsis, G.B.; Brett, M.T., Evaluation of the current state of mechanistic aquatic biogeochemical modeling, Marine ecology progress series, 271, 13-26, (2004)
[4] Becks, L.; Hilker, F.M.; Malchow, H.; Jurgens, K.H.A., Experimental demonstration of chaos in a microbial food web, Nature, 435, June, 1226-1229, (2005)
[5] Begon, M.; Harper, J.L.; Townsend, C.R., Ecology, (2002), Blackwell Science Oxford
[6] Bendoricchio, G.; Jorgensen, S., Fundamentals of ecological modelling, (2001), Elsevier Science Ltd
[7] Brauer, F.; Castillo-Chavez, C., Mathematical models in population biology and epidemiology, (2000), Springer New-York · Zbl 0967.92015
[8] Butler, G.J.; Wolkowicz, G.S.K., Predator-mediated competition in the chemostat, Journal of mathematical biology, 24, 167-191, (1986) · Zbl 0604.92019
[9] Canale, R.P.; Lustig, T.D.; Kehrberger, P.M.; Salo, J.E., Experimental and mathematical modeling studies of protozoan predation on bacteria, Biotechnology and bioengineering, 15, 107-728, (1973)
[10] Carlotti, F.; Poggiale, J., Towards methodological approaches to implement the zooplankton component in “end to end” food-webs models, Progress in oceanography, 84, 20-38, (2010)
[11] Demongeot, J.; Francoise, J.P.; Nerini, D., From biological and clinical experiments to mathematical models, Philosophical transactions of the royal society A, 367, 4657-4663, (2009)
[12] Englund, G.; Leonardsson, K., Scaling up the functional response for spatially heterogeneous systems, Ecology letters, 11, 440-449, (2008)
[13] Freedman, H., Graphical stability, enrichment and pest control by a natural enemy, Mathematical biosciences, 31, 207-225, (1976) · Zbl 0373.92023
[14] Fulton, E.A.; Parslow, J.S.; Smith, A.D.M.; Johnson, C.R., Biogeochemical marine ecosystem models ii: the effect of physiological detail on model performance, Ecological modelling, 173, 371-406, (2004)
[15] Fussmann, G.; Ellner, S.; Shertzer, K.; Hairston Jr., N.G., Crossing the Hopf bifurcation in a live predator – prey system, Science, 290, 1358-1360, (2000)
[16] Fussmann, G.F.; Blasius, B., Community response to enrichment is highly sensitive to model structure, Biology letters, 1, 9-12, (2005)
[17] Jeschke, J.; Kopp, M.; Tollrian, R., Predator functional responses: discriminating between handling and digesting prey, Ecological monographs, 72, 95-112, (2002)
[18] Korobeinikov, A., Stability of ecosystem: global properties of a general predator – prey model, Mathematical medicine and biology, 26, 309-321, (2009) · Zbl 1178.92053
[19] Kuang, Y.; Freedman, H.I., Uniqueness of limit cycles in gause-type models of predator – prey systems, Mathematical biosciences, 88, 67-84, (1988) · Zbl 0642.92016
[20] Kuznetsov, Y.A., Elements of applied bifurcation theory, (2004), Springer New York · Zbl 1082.37002
[21] Lagarias, J.; Reeds, J.; Wright, M.; Wright, P., Convergence properties of the nelder – mead simplex method in low dimensions, SIAM journal on optimization, 9, 112-147, (1998) · Zbl 1005.90056
[22] Morozov, A., Emergence of Holling type iii zooplankton functional response: bringing together field evidence and mathematical modelling, Journal of theoretical biology, 265, 45-54, (2010) · Zbl 1406.92676
[23] Morozov, A.; Arashkevich, E., Towards a correct description of zooplankton feeding on models: taking into account food-mediated unsynchronized vertical migration, Journal of theoretical biology, 262, 346-360, (2010) · Zbl 1403.92335
[24] Myerscough, M.R.; Darwen, M.J.; Hogarth, W.L., Stability, persistence and structural stability in a classical predator-prey model, Ecological modelling, 89, 31-42, (1996)
[25] Nelder, J.; Mead, R., A simplex method for function minimization, Computer journal, 7, 308-313, (1965) · Zbl 0229.65053
[26] Pavlou, S., Dynamics of a chemostat in which one microbial population feeds on another, Biotechnology and bioengineering, 27, 1525-1532, (1985)
[27] Poggiale, J.C., Predator – prey models in heterogeneous environment: emergence of functional response, Mathematical and computer modelling, 27, 4, 63-71, (1998) · Zbl 1185.37197
[28] Poggiale, J.C.; Baklouti, M.; Queguiner, B.; Kooijman, S., How far details are important in ecosystem modelling: the case of multi-limiting nutrients in phytoplankton – zooplankton interactions, Philosophical transactions of the royal society B, 365, 3495-3507, (2010)
[29] Seber, C., Wild, C., 2003. Nonlinear Regression. Wiley, New-York
[30] Simonoff, J.S., Smoothing methods in statistics, (1996), Springer New-York · Zbl 0859.62035
[31] Smith, H.L.; Waltman, P., The theory of the chemostat, (1995), Cambridge University Press · Zbl 0860.92031
[32] Thébault, E.; Loreau, M., Trophic interactions and the relationship between species diversity and ecosystem stability, American naturalist, 166, E95-E114, (2005)
[33] Thieme, H.R., Asymptotically autonomous differential equations in the plane, Rocky mountain journal of mathematics, 24, 351-380, (1994) · Zbl 0811.34036
[34] Truscott, J.E.; Brindley, J., Equilibria, stability and excitability in a general class of plankton population models, Philosophical transactions of the royal society A, 347, 703-718, (1994) · Zbl 0857.92017
[35] Williams, B.K.; Nichols, J.D.; Conroy, M.J., Analysis and management of animal populations, (2002), Academic Press
[36] Wood, S.N.; Thomas, M.B., Super-sensitivity to structure in biological models, Proceedings of the royal society London B, 266, 565-570, (1999)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.