{"id":1121,"date":"2017-06-01T10:38:01","date_gmt":"2017-06-01T10:38:01","guid":{"rendered":"http:\/\/physics-complex-systems.fr\/?p=1121"},"modified":"2025-07-04T19:13:13","modified_gmt":"2025-07-04T19:13:13","slug":"complex-networks","status":"publish","type":"post","link":"https:\/\/physics-complex-systems.fr\/en\/complex-networks.html","title":{"rendered":"Statistical physics of ecosystems"},"content":{"rendered":"<p>[vc_row][vc_column css=&#8221;.vc_custom_1496399944725{margin-top: -40px !important;margin-bottom: -20px !important;}&#8221;][vc_separator][\/vc_column][\/vc_row][vc_row equal_height=&#8221;yes&#8221; content_placement=&#8221;top&#8221;][vc_column width=&#8221;1\/2&#8243;][vc_column_text]Many natural ecosystems are home to a staggering diversity of species. How do so many species coexist? What principles underly the organization of ecosystems? How do they evolve over time or respond to perturbations? The aim of this course is to show how tools coming from the statistical physics of nonequilibrium and disordered systems can be used to approach such questions.<\/p>\n<div class=\"page\" title=\"Page 1\">\n<div class=\"layoutArea\">\n<div class=\"column\">\n<p><span style=\"color: #339966;\"><strong>Outline<\/strong><\/span><\/p>\n<p><strong>1. Introduction<br \/>\n<\/strong>(a) What can statistical physics possibly teach us about ecosystems?<br \/>\n(b) Some generic ecological patterns through scales and biomes.<\/p>\n<p><strong>2. Fluctuating dynamics of a single population<br \/>\n<\/strong>(a) Logistic growth and demographic fluctuations. Extinction times.<br \/>\n(b) Spatially structured populations. Connection with directed percolation.<\/p>\n<p><strong>3. Many-species dynamics<br \/>\n<\/strong>(a) Models of interacting populations (Lotka-Volterra, MacArthur). Few-species examples.<br \/>\n(b) Equilibrium coexistence: stability, invadability, susceptibility.<br \/>\n(c) Models with random interactions: May instability, transition to chaos, dynamical mean-field theory.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>[\/vc_column_text][vc_column_text]<img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-1986 alignnone\" src=\"https:\/\/physics-complex-systems.fr\/wp-content\/uploads\/2025\/07\/Arnoulx-Thibaut.jpg\" alt=\"\" width=\"150\" height=\"100\" \/> Thibaut Arnoulx de Pirey, IPhT, CEA[\/vc_column_text][\/vc_column][vc_column width=&#8221;1\/2&#8243; css=&#8221;.vc_custom_1496308532682{background-color: #fcfcfc !important;}&#8221;][vc_single_image image=&#8221;1994&#8243; img_size=&#8221;full&#8221; alignment=&#8221;center&#8221;][\/vc_column][\/vc_row][vc_row css=&#8221;.vc_custom_1496827430783{margin-top: 20px !important;}&#8221;][vc_column][vc_column_text]<\/p>\n<div class=\"displaytags\" style=\"color: #363131;\">keywords: <span data-olk-copy-source=\"MessageBody\">theoretical ecology, population dynamics, nonlinear dynamics, disordered systems, random matrices, stochastic processes<\/span><\/div>\n<p>[\/vc_column_text][\/vc_column][\/vc_row][vc_row][vc_column][vc_column_text]<\/p>\n<p>[\/vc_column_text][\/vc_column][\/vc_row]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>[vc_row][vc_column css=&#8221;.vc_custom_1496399944725{margin-top: -40px !important;margin-bottom: -20px !important;}&#8221;][vc_separator][\/vc_column][\/vc_row][vc_row equal_height=&#8221;yes&#8221; content_placement=&#8221;top&#8221;][vc_column width=&#8221;1\/2&#8243;][vc_column_text]Many natural ecosystems are home to a staggering diversity of species. How do so many species coexist?&#8230;<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[83,10],"tags":[],"translation":{"provider":"WPGlobus","version":"2.12.2","language":"en","enabled_languages":["fr","en"],"languages":{"fr":{"title":true,"content":true,"excerpt":false},"en":{"title":false,"content":false,"excerpt":false}}},"_links":{"self":[{"href":"https:\/\/physics-complex-systems.fr\/en\/wp-json\/wp\/v2\/posts\/1121"}],"collection":[{"href":"https:\/\/physics-complex-systems.fr\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/physics-complex-systems.fr\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/physics-complex-systems.fr\/en\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/physics-complex-systems.fr\/en\/wp-json\/wp\/v2\/comments?post=1121"}],"version-history":[{"count":23,"href":"https:\/\/physics-complex-systems.fr\/en\/wp-json\/wp\/v2\/posts\/1121\/revisions"}],"predecessor-version":[{"id":7073,"href":"https:\/\/physics-complex-systems.fr\/en\/wp-json\/wp\/v2\/posts\/1121\/revisions\/7073"}],"wp:attachment":[{"href":"https:\/\/physics-complex-systems.fr\/en\/wp-json\/wp\/v2\/media?parent=1121"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/physics-complex-systems.fr\/en\/wp-json\/wp\/v2\/categories?post=1121"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/physics-complex-systems.fr\/en\/wp-json\/wp\/v2\/tags?post=1121"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}