A macro-ecological approach to predators’ functional response

  1. Matthieu Barbier
  2. Laurie Wojcik
  3. Michel Loreau

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Abstract

Predation often deviates from the law of mass action: many micro- and meso-scale experiments have shown that consumption saturates with resource abundance, and decreases due to interference between consumers. But does this observation hold at macro-ecological scales, spanning many species and orders of magnitude in biomass? If so, what are its consequences for large-scale ecological patterns and dynamics?

We perform a meta-analysis of predator-prey pairs of mammals, birds and reptiles, and show that predation losses appear to increase, not as the product of predator and prey densities following the Lotka-Volterra (mass action) model, but rather as the square root of that product. This suggests a phenomenological power-law expression of the effective cross-ecosystem functional response. We discuss whether the same power-law may hold dynamically within an ecosystem, and assuming that it does, we explore its consequences in a simple food chain model. The empirical exponents fall close to the boundary between regimes of donor and consumer limitation. Exponents on this boundary are singular in multiple ways. First, they maximize predator abundance and some stability metrics. Second, they create proportionality relations between biomass and productivity, both within and between trophic levels. These intuitive relations do not hold in general in mass action models, yet they are widely observed empirically. These results provide evidence of mechanisms limiting predation across multiple ecological scales. Some of this evidence was previously associated with donor control, but we show that it supports a wider range of possibilities, including forms of consumer control. As limiting consumption counter-intuitively allows larger populations, it is worthwhile to reconsider whether the observed functional response arises from microscopic mechanisms, or could hint at selective pressure at the population level.

This article has been peer-reviewed and recommended by Peer Community In Ecology (DOI: 10.24072/pci.ecology.100051)

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  1. Peer Community in Ecology

    Species interactions are classically derived from the law of mass action: the probability that, for example, a predation event occurs is proportional to the product of the density of the prey and predator species. In order to describe how predator and prey species populations grow, is then necessary to introduce functional response, describing the intake rate of a consumer as a function of food (e.g. prey) density.
    Linear functional responses shapes are typically introduced in the ecological modeling of population dynamics for both predator-prey and mutualistic systems [1,2]. Recently some works have proposed alternatives to the classic approach for mutualistic systems [3,4], both because cooperative interactions also model effect not directly related to mass action [3] and for analytical tractability [4,5].
    In this work [6] the authors challenge the classic modeling of functional response also for predator-prey systems. In particular, they use a meta-analysis of several observational studies of predator-prey ecosystems to infer a generic predator functional response, fitting a phenomenological generalization of the mass-action law. Using advanced statistical analysis, they show that the functional response obtained from data is clearly different from the mass-action assumption. In fact, they found that it scales sub-linearly as the square root of the ratio between predator and prey biomass. They further argue that, from a macro-ecological point of view, using such a phenomenological relationship might be more valuable than relying on various mechanistic functional response formulations.
    The manuscript thus provides an interesting different perspective on how to approach predator-prey modelling and for this reason, I have recommended the work for PCI Ecology.

    References

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    [2] Bastolla, U., Fortuna, M. A., Pascual-García, A., Ferrera, A., Luque, B., and Bascompte, J. (2009). The architecture of mutualistic networks minimizes competition and increases biodiversity. Nature, 458(7241), 1018–1020. doi: 10.1038/nature07950
    [3] Tu, C., Suweis, S., Grilli, J., Formentin, M., and Maritan, A. (2019). Reconciling cooperation, biodiversity and stability in complex ecological communities. Scientific Reports, 9(1), 1–10. doi: 10.1038/s41598-019-41614-2
    [4] García-Algarra, J., Galeano, J., Pastor, J. M., Iriondo, J. M., and Ramasco, J. J. (2014). Rethinking the logistic approach for population dynamics of mutualistic interactions. Journal of Theoretical Biology, 363, 332–343. doi: 10.1016/j.jtbi.2014.08.039
    [5] Suweis, S., Simini, F., Banavar, J. R., and Maritan, A. (2013). Emergence of structural and dynamical properties of ecological mutualistic networks. Nature, 500(7463), 449–452. doi: 10.1038/nature12438
    [6] Barbier, M., Wojcik, L., and Loreau, M. (2020). A macro-ecological approach to predators’ functional response. BioRxiv, 832220, ver. 4 recommended and peer-reviewed by Peer Community in Ecology. doi: 10.1101/832220

  2. Version published to 10.1101/832220 on bioRxiv