nucleation

LIT-1233: Permanence via invasion graphs: incorporating community assembly into modern coexistence theory

1 min read

Properties5
StatusActive — read 2026-10-29 (NOTE-1379) in full, from arXiv 2204.03773v2; worth reading as the theorem that says when signs of invasion growth rates decide coexistence: with an acyclic invasion graph, robust permanence holds exactly when each species can invade each of its −i communities. Read it knowing that it is deterministic, that its sign-parity assumption excludes common non-Lotka–Volterra cases, that cycles are left open, and that its switching-predator example swaps the labels of two invasion conditions.
Version2
Tagsecology, mathematics
Cited as “paper” byNOTE-1379 — Hofbauer and Schreiber — Permanence via invasion graphs
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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Hofbauer, J. & Schreiber, S. J. (2022). Permanence via invasion graphs: incorporating community assembly into modern coexistence theory. Journal of Mathematical Biology 85(5): 54. doi:10.1007/s00285-022-01815-2. arXiv:2204.03773.

Read in full on 2026-10-29 (NOTE-1379).

Why this is here

The synthesis the owner relayed on 2026-10-18, connecting the record’s distributed-agency line to statistical feature learning and ecological coexistence theory, recommended it for reading. It makes rigorous the recovery-from-rarity criterion that Chesson’s framework (LIT-1219) rests on, and ties it to the order in which a community is assembled, which the synthesis read as a model of how early entrants shape which roles later ones can hold. Bears on QUESTION-083.

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