PT - JOURNAL ARTICLE AU - Haas, Pierre A. AU - Goldstein, Raymond E. TI - Turing’s diffusive threshold in random reaction-diffusion systems AID - 10.1101/2020.11.09.374934 DP - 2020 Jan 01 TA - bioRxiv PG - 2020.11.09.374934 4099 - http://biorxiv.org/content/early/2020/11/09/2020.11.09.374934.short 4100 - http://biorxiv.org/content/early/2020/11/09/2020.11.09.374934.full AB - Turing instabilities of reaction-diffusion systems can only arise if the diffusivities of the chemical species are sufficiently different. This threshold is unphysical in generic systems with N = 2 diffusing species, forcing experimental realizations of the instability to rely on fluctuations or additional non-diffusing species. Here we ask whether this diffusive threshold lowers for N > 2 to allow “true” Turing instabilities. Inspired by May’s analysis of the stability of random ecological communities, we analyze the threshold for reactiondiffusion systems whose linearized dynamics near a homogeneous fixed point are given by a random matrix. In the numerically tractable cases of N ⩽ 6, we find that the diffusive threshold generically decreases as N increases and that these many-species instabilities generally require all species to be diffusing.Competing Interest StatementThe authors have declared no competing interest.