Review: To be or not to be an identifiable model. Is this a relevant question in animal science modelling?
Open accessAbstract
What is a good (useful) mathematical model in animal science? For models constructed for prediction purposes, the question of model adequacy (usefulness) has been traditionally tackled by statistical analysis applied to observed experimental data relative to model-predicted variables. However, little attention has been paid to analytic tools that exploit the mathematical properties of the model equations. For example, in the context of model calibration, before attempting a numerical estimation of the model parameters, we might want to know if we have any chance of success in estimating a unique best value of the model parameters from available measurements. This question of uniqueness is referred to as structural identifiability; a mathematical property that is defined on the sole basis of the model structure within a hypothetical ideal experiment determined by a setting of model inputs (stimuli) and observable variables (measurements). Structural identifiability analysis applied to dynamic models described by ordinary differential equations (ODEs) is a common practice in control engineering and system identification. This analysis demands mathematical technicalities that are beyond the academic background of animal science, which might explain the lack of pervasiveness of identifiability analysis in animal science modelling. To fill this gap, in this paper we address the analysis of structural identifiability from a practitioner perspective by capitalizing on the use of dedicated software tools. Our objectives are (i) to provide a comprehensive explanation of the structural identifiability notion for the community of animal science modelling, (ii) to assess the relevance of identifiability analysis in animal science modelling and (iii) to motivate the community to use identifiability analysis in the modelling practice (when the identifiability question is relevant). We focus our study on ODE models. By using illustrative examples that include published mathematical models describing lactation in cattle, we show how structural identifiability analysis can contribute to advancing mathematical modelling in animal science towards the production of useful models and, moreover, highly informative experiments via optimal experiment design. Rather than attempting to impose a systematic identifiability analysis to the modelling community during model developments, we wish to open a window towards the discovery of a powerful tool for model construction and experiment design.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
This integration task is far from trivial due to multiple time scales and parameter identifiability.
“This integration task is far from trivial due to multiple time scales, among other aspects such as parameter identifiability (Muñoz-Tamayo et al., 2018).”
From Addressing global ruminant agricultural challenges through understanding the rumen microbiome: past, present, and future (2018) · cites this paper as Muñoz-Tamayo et al., 2018
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Raue, A., Kreutz, C., Maiwald, T., Bachmann, J., Schilling, M., Klingmüller, U., & Timmer, J. (2009) · Bioinformatics · doi:10.1093/bioinformatics/btp358 · Cited by 1,442 · see citing works
Universally Sloppy Parameter Sensitivities in Systems Biology Models
Gutenkunst, R. N., Waterfall, J. J., Casey, F. P., Brown, K. S., Myers, C. R., & Sethna, J. P. (2007) · PLoS Computational Biology · doi:10.1371/journal.pcbi.0030189 · Cited by 1,261 · see citing works
Identification of parametric models : from experimental data
Walter, E. D., & Pronzato, L. (1997) · Cited by 1,204 · see citing works
Algebraic Model of the Lactation Curve in Cattle
Wood, P. D. P. (1967) · Nature · doi:10.1038/216164a0 · Cited by 1,123 · see citing works
Bellman, R., & Åström, K. J. (1970) · Mathematical Biosciences · doi:10.1016/0025-5564(70)90132-x · Cited by 871 · see citing works
Assessment of the adequacy of mathematical models
Tedeschi, L. O. (2006) · Agricultural Systems · doi:10.1016/j.agsy.2005.11.004 · Cited by 756 · see citing works
DAISY: A new software tool to test global identifiability of biological and physiological systems
Bellu, G., Saccomani, M. P., Audoly, S., & D’Angiò, L. (2007) · Computer Methods and Programs in Biomedicine · doi:10.1016/j.cmpb.2007.07.002 · Cited by 452 · see citing works
Structural identifiability of systems biology models: a critical comparison of methods
Chis, O.-T., Banga, J. R., & Balsa-Canto, E. (2011) · PLoS ONE · doi:10.1371/journal.pone.0027755 · Cited by 448 · see citing works
Structural Identifiability of Dynamic Systems Biology Models
Villaverde, A. F., Barreiro, A., & Papachristodoulou, A. (2016) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1005153 · Cited by 278 · see citing works
Mills, J. A. N., Dijkstra, J., Bannink, A., Cammell, S. B., Kebreab, E., & France, J. (2001) · Journal of Animal Science · doi:10.2527/2001.7961584x · Cited by 253 · see citing works
Locke, J. C. W., Millar, A. J., & Turner, M. S. (2005) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2004.11.038 · Cited by 238 · see citing works
Parameter identifiability of nonlinear systems: the role of initial conditions
Saccomani, M. P., Audoly, S., & D’Angiò, L. (2003) · Automatica · doi:10.1016/s0005-1098(02)00302-3 · Cited by 233 · see citing works
Dynamical modeling and multi-experiment fitting with PottersWheel
Maiwald, T., & Timmer, J. (2008) · Bioinformatics · doi:10.1093/bioinformatics/btn350 · Cited by 231 · see citing works
Metabolism of the lactating cow: II. Digestive elements of a mechanistic model
Baldwin, R. L., Thornley, J. H. M., & Beever, D. E. (1987) · Journal of Dairy Research · doi:10.1017/s0022029900025231 · Cited by 228 · see citing works
Modelling nutrient utilization in farm animals.
(2000) · CABI Publishing eBooks · doi:10.1079/9780851994499.0000 · Cited by 185 · see citing works
Comparison of approaches for parameter identifiability analysis of biological systems
Raue, A., Karlsson, J., Saccomani, M. P., Jirstrand, M., & Timmer, J. (2014) · Bioinformatics · doi:10.1093/bioinformatics/btu006 · Cited by 179 · see citing works
A Model to Describe Growth Patterns of the Mammary Gland During Pregnancy and Lactation
Dijkstra, J., France, J., Dhanoa, M. S., et al. (1997) · Journal of Dairy Science · doi:10.3168/jds.s0022-0302(97)76185-x · Cited by 172 · see citing works
On the identifiability and distinguishability of nonlinear parametric models
Walter, E., & Pronzato, L. (1996) · Mathematics and Computers in Simulation · doi:10.1016/0378-4754(95)00123-9 · Cited by 148 · see citing works
Effects of parameterization on the performance of empirical models used in `predictive microbiology'
Baranyi, J., Ross, T., McMeekin, T., et al. (1996) · Food Microbiology · doi:10.1006/fmic.1996.0011 · Cited by 148 · see citing works
An Efficient Method for Structural Identifiability Analysis of Large Dynamic Systems
Karlsson, J., Anguelova, M., & Jirstrand, M. (2012) · IFAC Proceedings Volumes · doi:10.3182/20120711-3-be-2027.00381 · Cited by 133 · see citing works
GenSSI: a software toolbox for structural identifiability analysis of biological models
Chis, O., Banga, J. R., & Balsa‐Canto, E. (2011) · Bioinformatics · doi:10.1093/bioinformatics/btr431 · Cited by 126 · see citing works
Carson, E. R., Cobelli, C., & Finkelstein, L. (1983) · Medical Entomology and Zoology · Cited by 94 · see citing works
On the relationship between sloppiness and identifiability
Chis, O.-T., Villaverde, A. F., Banga, J. R., & Balsa-Canto, E. (2016) · Mathematical Biosciences · doi:10.1016/j.mbs.2016.10.009 · Cited by 84 · see citing works
Cedersund, G. (2012) · The FEBS Journal · doi:10.1111/j.1742-4658.2012.08725.x · Cited by 81 · see citing works
AMIGO, a toolbox for advanced model identification in systems biology using global optimization
Balsa‐Canto, E., & Banga, J. R. (2011) · Bioinformatics · doi:10.1093/bioinformatics/btr370 · Cited by 79 · see citing works
Friggens, N. C., Brun-Lafleur, L., Faverdin, P., et al. (2011) · animal · doi:10.1017/s1751731111001820 · Cited by 76 · see citing works
Minimal output sets for identifiability
Anguelova, M., Karlsson, J., & Jirstrand, M. (2012) · Mathematical Biosciences · doi:10.1016/j.mbs.2012.04.005 · Cited by 74 · see citing works
Modelling of Livestock Production Systems
Korver, S., & Korver, S. (1992) · Wageningen Academic Publishers eBooks · doi:10.1163/9789004684607_005 · Cited by 63 · see citing works
Wu, X., Heringstad, B., & Daniel Gianola, B. (2010) · Journal of Animal Breeding and Genetics · doi:10.1111/j.1439-0388.2009.00835.x · Cited by 53 · see citing works
Friggens, N. C., Emmans, G. C., & Veerkamp, R. F. (1999) · Livestock Production Science · doi:10.1016/s0301-6226(99)00110-4 · Cited by 49 · see citing works
Martin, O., & Sauvant, D. (2010) · animal · doi:10.1017/s1751731110001357 · Cited by 49 · see citing works
Self-citationMechanistic modelling of in vitro fermentation and methane production by rumen microbiota
Muñoz‐Tamayo, R., Giger‐Reverdin, S., & Sauvant, D. (2016) · Animal Feed Science and Technology · doi:10.1016/j.anifeedsci.2016.07.005 · Cited by 49 · see citing works
Self-citationIdentifiability of large nonlinear biochemical networks
Villaverde, A. F., & Barreiro, A. (2016) · Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT) · Cited by 38 · see citing works
Moate, P. J., Boston, R. C., Jenkins, T. C., et al. (2008) · Journal of Dairy Science · doi:10.3168/jds.2007-0398 · Cited by 36 · see citing works
Schaber, J., & Klipp, E. (2011) · Current Opinion in Biotechnology · doi:10.1016/j.copbio.2010.09.014 · Cited by 33 · see citing works
Getting the most out of it: Optimal experiments for parameter estimation of microalgae growth models
Muñoz‐Tamayo, R., Martinon, P., Bougaran, G., Mairet, F., & Olivier Bernard, A. (2014) · Journal of Process Control · doi:10.1016/j.jprocont.2014.04.021 · Cited by 33 · see citing works
Self-citationModelling homeostatic and homeorhetic regulations in lactating animals
Sauvant, D. (1994) · Livestock Production Science · doi:10.1016/0301-6226(94)90162-7 · Cited by 30 · see citing works
Self-citationHanigan, M. D., Ríus, A. G., Kolver, E. S., et al. (2007) · Journal of Dairy Science · doi:10.3168/jds.2007-0028 · Cited by 24 · see citing works
Muñoz‐Tamayo, R., Laroche, B., Leclerc, M., & Walter, E. (2009) · IFAC Proceedings Volumes · doi:10.3182/20090706-3-fr-2004.00211 · Cited by 23 · see citing works
Self-citationPuillet, L., Martin, O., Tichit, M., et al. (2008) · animal · doi:10.1017/s1751731107001140 · Cited by 21 · see citing works
Self-citationThe art of catchment modeling: What is a good model?
Barnes, C. J. (1995) · Environment International · doi:10.1016/0160-4120(95)00082-v · Cited by 18 · see citing works
Cellular signaling identifiability analysis: A case study
Roper, R. T., Saccomani, M. P., & Vicini, P. (2010) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2010.02.029 · Cited by 11 · see citing works
Guaranteed numerical alternatives to structural identifiability testing
Braems, I., Jaulin, L., Kieffer, M., et al. (2002) · Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes · doi:10.1109/.2001.980298 · Cited by 11 · see citing works
Doeschl-Wilson, A. B. (2011) · animal · doi:10.1017/s1751731110002557 · Cited by 11 · see citing works
Mathematical modelling in agricultural science
France, J. (1988) · Weed Research · doi:10.1111/j.1365-3180.1988.tb00822.x · Cited by 9 · see citing works
Guaranteed numerical alternatives to structural identifiability testing
Braems, I., Jaulin, L., Kieffer, M., et al. (2003) · Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes · doi:10.1109/cdc.2001.980298 · Cited by 9 · see citing works
Boer, H. M. T., Butler, S. T., Stötzel, C., et al. (2017) · animal · doi:10.1017/s175173111700026x · Cited by 8 · see citing works
White, L. J., Evans, N. D., Lam, T. J. G. M., Schukken, Y. H., Medley, G. F., Godfrey, K. R., & Chappell, M. J. (2002) · Mathematical Biosciences · doi:10.1016/s0025-5564(02)00130-x · Cited by 6 · see citing works
Vargas-Villamil, L. M., & Tedeschi, L. O. (2014) · Animal Production Science · doi:10.1071/an14568 · Cited by 4 · see citing works
Flagged first, then by citations
Research works printed but not linked: 2
- Boston RC, Wilkins P and Tedeschi LO 2007. Identifiability and accuracy: two critical problems associated with the application of models in nutrition and the health sciences. In Mathematical modeling for nutrition and health sciences (ed. M Hanigan), pp. 161-193.
- Khalil HK 2000. Nonlinear systems. Pearson Education International Inc, Upper Saddle River, NJ.
Cited by
Sorted by citations
Huws, S. A., Creevey, C. J., Oyama, L. B., Mizrahi, I., Denman, S. E., Popova, M., Muñoz-Tamayo, R., Forano, E., Waters, S. M., Hess, M., et al. (2018) · Frontiers in Microbiology · doi:10.3389/fmicb.2018.02161 · Cited by 487 · see citing works
Self-citation
- Authors
- Muñoz-Tamayo, R., Puillet, L., Daniel, J. B., Sauvant, D., Martin, O., Taghipoor, M., & Blavy, P.
- Affiliations
- AgroParisTech (FR)
- Institut Agro Rennes-Angers (FR)
- Venue
- animal
- Publisher
- Elsevier BV
- Published
- 2018
- Volume
- 12
- Issue
- 4
- Pages
- 701-712
- ISSN
- 1751-7311 (ISSN-L)
- OpenAlex
- W2641287658
- Cited by
- 56
- References
- 49
- Citations by year
- 2026: 2 · 2025: 9 · 2024: 3 · 2023: 9 · 2022: 8 · 2021: 3 · 2020: 9 · 2019: 9 · 2018: 4
- FWCI
- 0.99
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- animal (publishedVersion, cc-by-nc-nd)
- PubMed (publishedVersion)
- HAL (submittedVersion, other-oa)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Funders
- Università degli Studi di Padova
- AgroParisTech
- Institut National de la Recherche Agronomique
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Control Systems and Identification
- Physical Sciences › Mathematics › Applied Mathematics › Statistical and numerical algorithms
- Life Sciences › Agricultural and Biological Sciences › Ecology, Evolution, Behavior and Systematics › Agriculture, Soil, Plant Science
- Keywords
- structural identifiability, ordinary differential equation model, model calibration, parameter estimation, cattle, optimal experiment design, model adequacy
- MeSH terms
- Animals, Cattle, Female, Laboratory Animal Science, Lactation, Models, Biological, Research Design, Software, Models, Statistical, Models, Animal, Animal Nutrition Sciences
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
