Competitive exclusion and Hebbian couplings in random generalised LotkaVolterra systems
Abstract
We study communities emerging from generalised random LotkaVolterra dynamics with a large number of species and with competitive exclusion. Each species is endowed with a number of traits, and competition between pairs of species increases with their similarity in trait space. This leads to a model with random Hebbian interactions. We use tools from the theory of disordered systems, notably dynamic mean field theory, to characterise the statistics of the resulting communities at stable fixed points and determine analytically when stability breaks down. Two distinct types of transition are identified in this way, both marked by diverging abundances, but differing in the behaviour of the integrated response function. At fixed points only a fraction of the initial pool of species survives. We numerically study the eigenvalue spectra of the interaction matrix between extant species. We find evidence that the two types of dynamical transition are, respectively, associated with the bulk spectrum or an outlier eigenvalue crossing into the right half of the complex plane.
 Publication:

arXiv eprints
 Pub Date:
 January 2023
 DOI:
 10.48550/arXiv.2301.11703
 arXiv:
 arXiv:2301.11703
 Bibcode:
 2023arXiv230111703R
 Keywords:

 Quantitative Biology  Populations and Evolution;
 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Statistical Mechanics
 EPrint:
 14 pages, 9 figures + Supplement