nucleation

LIT-1824: Tractable models of ecological assembly

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StatusActive — read 2026-10-29 (NOTE-1422) in full, from its first author's dissertation in the University of Chicago's repository (chapter 3, appendix included); worth reading as the result that, for symmetric competitive Lotka–Volterra communities, MacArthur's Lyapunov function orders every sub-community, so the assembly graph is acyclic, every feasible sub-community can be built by invasions without extinctions, and sequential and all-at-once assembly reach the same end-points. Read it knowing that the copy read is the dissertation chapter of August 2020, not the Ecology Letters version, which was not compared; that order-independence (a single end-point) needs the interaction matrix positive definite, and an indefinite one still has priority effects; and that the step from the Lyapunov function to acyclicity is asserted, not written out.
Version2
Tagsecology, mathematics
Cited as “paper” byNOTE-1422 — Serván and Allesina — Tractable models of ecological assembly
Cited as “source” byTHEORY-1168 — In a Lotka–Volterra community with a symmetric interaction matrix, the growth-weighted biomass rᵀx strictly increases along every edge of the invasion graph, so the invasion graph has no cycles

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Serván, C. A. & Allesina, S. (2021). Tractable models of ecological assembly. Ecology Letters 24(5), 1029–1037. doi:10.1111/ele.13702. Preprint bioRxiv 2020.09.02.279943 (3 September 2020).

Read in full on 2026-10-29 (NOTE-1422), in the first author’s dissertation version. One account was drawn from it: THEORY-1168.

Why this is here

The triage of 2026-10-29 put it in the File tier for CLAIM-369. That claim’s note of 2026-10-29 said that in its symmetric class the objective L decreases along every trajectory, “which should rule out heteroclinic cycles and so cyclic invasion graphs”, and that neither Hofbauer and Schreiber (LIT-1233) nor the reading proved it. This paper builds the assembly graph for symmetric competitive Lotka–Volterra communities. It also bears on QUESTION-083’s entrenchment by order of arrival and on QUESTION-132’s requirement that coexistence be judged by invasion graphs, in the potential case.

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