Using active subspaces to explore discrepancies between global and local parameter sensitivities in a Lotka-Volterra system

Huiyan Zou; Allison L. Lewis; Huiyan Zou; Allison L. Lewis

doi:10.3934/mbe.2026079

Mathematical Biosciences and Engineering

2026, Volume 23, Issue 7: 2178-2207. doi: 10.3934/mbe.2026079

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Using active subspaces to explore discrepancies between global and local parameter sensitivities in a Lotka-Volterra system

Huiyan Zou ,
Allison L. Lewis ^,

Department of Mathematical Sciences, Lafayette College, 730 High Street, Easton, PA 18042, USA

Received: 10 March 2026 Revised: 30 June 2026 Accepted: 02 July 2026 Published: 16 July 2026

Global sensitivity metrics are essential tools for assessing parameter importance in complex models, particularly when precise information about parameter values is unavailable. In many cases, such metrics are used to provide parameter rankings that allow for necessary dimension reduction in moderate-to-high dimensional systems. However, globally derived sensitivity results may obscure localized variability in parameter sensitivities, resulting in misleading conclusions about parameter importance and ensuing consequences for subsequent tasks such as model calibration and surrogate model construction. In this study, we illustrated how discrepancies between globally and locally based sensitivity information may arise for an emerging sensitivity metric based on active subspace methodology, as well as for other commonly used sensitivity techniques. In response, we outlined a framework that exploits the active subspace to evaluate the stability of parameter sensitivities over the admissible parameter space. This analysis allows one to determine the subregions of the parameter space in which a globally derived sensitivity metric may be considered representative of local behavior. The proposed framework was illustrated on a collection of simple examples for ease of visualization, as well as a variation of the Lotka-Volterra model used to study interactions between competing tumor cell lines, for which we demonstrated how these issues may be exacerbated in higher dimensions. Our findings suggest that globally derived sensitivity information should be treated with caution, and that incorporating analysis on local subregions may improve robustness and accuracy in downstream modeling tasks.
- active subspaces,
- global sensitivity analysis,
- dimension reduction,
- model calibration,
- surrogate model construction
Citation: Huiyan Zou, Allison L. Lewis. Using active subspaces to explore discrepancies between global and local parameter sensitivities in a Lotka-Volterra system[J]. Mathematical Biosciences and Engineering, 2026, 23(7): 2178-2207. doi: 10.3934/mbe.2026079

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Abstract

Global sensitivity metrics are essential tools for assessing parameter importance in complex models, particularly when precise information about parameter values is unavailable. In many cases, such metrics are used to provide parameter rankings that allow for necessary dimension reduction in moderate-to-high dimensional systems. However, globally derived sensitivity results may obscure localized variability in parameter sensitivities, resulting in misleading conclusions about parameter importance and ensuing consequences for subsequent tasks such as model calibration and surrogate model construction. In this study, we illustrated how discrepancies between globally and locally based sensitivity information may arise for an emerging sensitivity metric based on active subspace methodology, as well as for other commonly used sensitivity techniques. In response, we outlined a framework that exploits the active subspace to evaluate the stability of parameter sensitivities over the admissible parameter space. This analysis allows one to determine the subregions of the parameter space in which a globally derived sensitivity metric may be considered representative of local behavior. The proposed framework was illustrated on a collection of simple examples for ease of visualization, as well as a variation of the Lotka-Volterra model used to study interactions between competing tumor cell lines, for which we demonstrated how these issues may be exacerbated in higher dimensions. Our findings suggest that globally derived sensitivity information should be treated with caution, and that incorporating analysis on local subregions may improve robustness and accuracy in downstream modeling tasks.

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