# Effects of intraspecific cooperative interactions in large ecosystems

### Submission summary

 As Contributors: Ada Altieri Preprint link: scipost_202109_00017v2 Date accepted: 2021-11-08 Date submitted: 2021-10-20 16:45 Submitted by: Altieri, Ada Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory Statistical and Soft Matter Physics Approach: Theoretical

### Abstract

We analyze the role of the Allee effect, a positive correlation between population density and mean individual fitness, for ecological communities formed by a large number of species. Our study is performed using the generalized Lotka-Volterra model with random interactions between species. We obtain the phase diagram and analyze the nature of the multiple equilibria phase. Remarkable differences emerge with respect to the logistic growth case, thus revealing the major role played by the functional response in determining aggregate behaviours of ecosystems.

###### Current status:
Publication decision taken: accept

Editorial decision: For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)

### List of changes

The part that we added during the resubmission process (on September 14) is, to a large extent, a result of computations and numerical analysis done long ago. In any case, to take some recent comments into account, we have added
i) In the first paragraph of Sec. 5, after
"Thus we naturally expect, and find, a marginality condition akin to the one of mean-field Ising spin-glasses, e.g. the Sherrington-Kirkpatrick model.”
the sentence “This was first analyzed in the context of soft-spins in [Folena & Urbani]”.

ii) In the last paragraph of Sec. 5.1: we have modified the sentence "We won't give more details since this kind of marginality is well studied and understood in the context of mean-field spin-glasses \cite{MPV}.”
in
"We won't give more details since this kind of marginality has been already well studied in the context of mean-field spin-glasses \cite{MPV, Muller2015}. For more details and a thorough analysis of the similarity with mean-field spin-glasses see the recent work [Folena & Urbani].”

iii) In the last sentence of Appendix E, we have changed: "Nonetheless, thanks to the Gaussian form of the integrals, the reader can keep going in the analysis and show that the replicon expression would diverge irrespective of the parameters $a$, $b$, $c$, $\rho$, as $\beta \gg 1$."
in
"Nonetheless, thanks to the Gaussian form of the integrals, the reader can keep going in the analysis and show that the replicon expression would diverge irrespective of the parameters $a$, $b$, $c$, $\rho$, as $\beta \gg 1$. We have verified it numerically in our case. For an analytical explanation see the recent work [Folena and Urbani]."