RT Journal Article T1 Statistical mechanics of ecosystem assembly A1 Capitán, José A. A1 Cuesta, José A. A1 Bascompte, Jordi AB We introduce a toy model of ecosystem assembly for which we are able to map out all assembly pathways generated by external invasions. The model allows us to display the whole phase space in the form of an assembly graph whose nodes are communities of species and whose directed links are transitions between them induced by invasions. We characterize the process as a finite Markov chain and prove that it exhibits a unique set of recurrent states (the end state of the process), which is therefore resistant to invasions. This also shows that the end state is independent of the assembly history. The model shares all features with standard assembly models reported in the literature, with the advantage that all observables can be computed in an exact manner. PB The American Physical Society SN 0031-9007 (Print) SN 1079-7114 (Online) YR 2009 FD 2009-10-16 LK http://hdl.handle.net/10016/7167 UL http://hdl.handle.net/10016/7167 LA eng NO 4 pages, 3 figures.-- PACS nrs.: 87.23.Cc, 64.60.De, 87.23.Kg, 89.75.Fb.-- ArXiv pre-print available at: http://arxiv.org/abs/0903.2691 NO This work is funded by projects MOSAICO (Ministerio de Educación y Ciencia) and MOSSNOHO-CM (Comunidad de Madrid), by the European Heads ofResearch Councils, the European Science Foundation, and the EC Sixth Framework Programme through an EURYI grant (J. B.), and by a contract from Comunidad de Madrid and Fondo Social Europeo (J. A. Capitán). DS e-Archivo RD 27 abr. 2024