How does assimilation efficiency work?

[nicolasmerino41]

Hey there,

Firstly, great package, love it! :)

I'm probably missing something very obvious, but I've looked at the Bio-energetic version equation of Lajaaiti et al. 2024 and I do not understand why the assimilation efficiency is used in the substracting part of the equation. It seems intuitive to me that it should be affecting the additve part since it limits how much biomass from the prey is effectively transferred into predator biomass.

I guess I can see that lower efficiencies lead to predators needing to consume/prey more so that's why it's in the denominator in the substracting part? Idk :/

I've checked Delmas2017 and I see they used the same equation, so I'm sure there's an explanation, so I'd appreciate if you could share it with me :)

However, the Classic version aligns more with what I mentioned before, right?

Nico

[alaindanet]

Hi Nico,

Thank you for your question, that is not obvious at all.

Short answer is that the difference between the bioenergetic version and the classic version is the presence of the maximal assimilation rate $y_i$ and of the metabolic rate $x_i$ in the bioenergetic version of the model, and it is where the assimilation rate is contained.

This transformation from the classic version to the bioenergetic version happens when one applies allometric scaling of the physiological rates in the classic version. This transformation is best explained in Williams et al. (2006)
. In the paper, this is explained from equations (2.8, 2.9, where you will recognise the classic form) to the equations (2.17, 2.18, where you will recognise the bioenergetic form).

Note that from the bioenergetic version presented in Williams et al. (2006), $y_i$ was $y_{ij}$ meaning that the maximal assimilation rate was historically depending on the prey $j$, an assumption that was relaxed since Brose et al. (2006). A second difference that you might notice is the presence of $f_{ji}$ in Williams et al. (2006). It is the biomass fraction of the prey $j$ effectively eaten by the predator $i$ but it is assumed to be equal to unity since implementation of Brose et al. (2006), then it disappeared from the equations.

Hope this helps and once again, not a obvious question :)

Cited references

Brose, U., Williams, R. J., & Martinez, N. D. (2006). Allometric scaling enhances stability in complex food webs. Ecology Letters, 9(11), 1228–1236. https://doi.org/10.1111/j.1461-0248.2006.00978.x

Williams, R. J., Brose, U., & Martinez, N. D. (2006). Homage to Yodzis and Innes 1992: Scaling up Feeding-Based Population Dynamics to Complex Ecological Networks. In N. Rooney, K. S. McCann, & D. L. G. Noakes (Eds.), From Energetics to Ecosystems: The Dynamics and Structure of Ecological Systems (pp. 37–51). Springer Netherlands. https://doi.org/10.1007/978-1-4020-5337-5_2