Disentangling different sources of variation in functional responses: between-individual variability, measurement error and inherent stochasticity of the prey-predator interaction process
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Abstract
The consumption rate of prey by predators, or functional responses, are known to be highly variable even within a single population. Identifying and estimating the different sources of variation of functional responses is a long-standing challenge. We develop here a statistical framework derived from a mechanistic stochastic process model that explicitly accounts for different sources of variation. We apply it to disentangle and estimate in particular 1) residual variance due to measurement errors and model misspecification, 2) between-predator variability, and 3) the interaction stochasticity , i.e. the intrinsic and mechanistic variability due to interactions processes between prey and predators. We show that it is possible to estimate these sources of variation under realistic experimental conditions. Our results also show that model fitting can compensate by overestimating residual source of variation, leading to biased parameter estimates when interaction stochasticity is misspecified. Applied to empirical data, the model reveals that standard assumptions, such as prey renewal and lack of spatial structure, fail to capture observed variability. We also show how experimental design affects parameter identifiability, highlighting the trade-off between the number of individuals and repeated observations.
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Functional responses have been used to describe and model species’ consumption rates for more than half a century. These rates are typically measured through experimental feeding trials, but also field data. The FoRAGE database (Uiterwaal et al. 2022) now contains data on over 3,000 functional responses. Meanwhile, mathematical models and statistical approaches are continuously being developed to better estimate density-dependent feeding rates.
A statistical model commonly consists of a deterministic prediction model (number of eaten prey based on available prey density density) and a stochastic part (distribution of observations around the mean prediction). Research has been active on the prediction component (e.g., Okuyama & Ruyle 2011, Pritchard et al. 2017, Rosenbaum & Rall 2018, Uszko et al. 2020, Novak et al. 2025). However, …
Functional responses have been used to describe and model species’ consumption rates for more than half a century. These rates are typically measured through experimental feeding trials, but also field data. The FoRAGE database (Uiterwaal et al. 2022) now contains data on over 3,000 functional responses. Meanwhile, mathematical models and statistical approaches are continuously being developed to better estimate density-dependent feeding rates.
A statistical model commonly consists of a deterministic prediction model (number of eaten prey based on available prey density density) and a stochastic part (distribution of observations around the mean prediction). Research has been active on the prediction component (e.g., Okuyama & Ruyle 2011, Pritchard et al. 2017, Rosenbaum & Rall 2018, Uszko et al. 2020, Novak et al. 2025). However, while strong variation in observed feeding rates between replicates is a known problem, empirical research frequently overlooks the fact that Binomial or Gaussian distributions often fail to describe the dispersion of experimental responses. While few studies have addressed observed variation (Fenlon & Faddy 2006, Billiard et al 2018, Coblentz & DeLong 2021, Coblentz et al. 2021, DeLong 2021), a unified approach is still lacking.
Here, Baey et al. (2025) developed a framework that can attribute three sources of error: not only (1) classical measurement error, but also (2) between-predator individual variability and (3) the underlying stochastic dynamics of the feeding process. Using a simulation study and an experimental dataset with substantial variation in feeding rates, they demonstrate that neglecting these sources of error can bias parameter estimates.
By treating feeding events as a stochastic process, they derive a mathematical formulation describing mean and variance of eaten prey, that can be fitted to the data. Although the mathematical model is reasonably complex, the authors also provide a tailored model fitting approach: a stochastic gradient descent method implemented in Python.
The reviewers welcomed the new approach and acknowledged the significance of the issue of strong variation in experimentally observed responses. While fitting nonlinear models is already a nontrivial task, experimental researchers should be aware that their statistical model should be able to replicate observed variation to get the best possible inference out of their data.
To be able to disentangle all three sources of variation, the suggested framework comes with practically relevant assumptions: The number of offered prey should substantially succeed the number of eaten prey, and the length of each feeding trial should be sufficiently long. Future studies could explore how well the method performs when these conditions cannot be met due to logistical limitations, or further develop the approach to account for substantial prey depletion.
References
Baey, C., Billiard, S., & Delattre, M. (2025). Disentangling different sources of variation in functional responses: between-individual variability, measurement error and inherent stochasticity of the prey-predator interaction process. bioRxiv. ver.3 peer-reviewed and recommended by PCI Ecology. https://doi.org/10.1101/2025.07.09.663660
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