{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T19:12:06Z","timestamp":1770837126122,"version":"3.50.1"},"reference-count":50,"publisher":"Public Library of Science (PLoS)","issue":"4","license":[{"start":{"date-parts":[[2025,4,15]],"date-time":"2025-04-15T00:00:00Z","timestamp":1744675200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100005990","name":"Australian Mathematical Sciences Institute","doi-asserted-by":"publisher","award":["Liftoff Fellowship"],"award-info":[{"award-number":["Liftoff Fellowship"]}],"id":[{"id":"10.13039\/501100005990","id-type":"DOI","asserted-by":"publisher"}]},{"name":"The University of Bath"}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Collective behaviour occurs at all levels of the natural world, from cells aggregating to form tissues, to locusts interacting to form large and destructive plagues. These complex behaviours arise from relatively simple interactions amongst individuals and between individuals and their environment. For simplicity, mathematical models of these phenomena often assume that the population is homogeneous. However, population heterogeneity arising due to the internal state of individuals can affect these interactions and thus plays a role in the dynamics of group formation. In this paper, we present a partial differential equation model that accounts for this heterogeneity by introducing a state space that models an individual\u2019s internal state (<jats:italic>e.g.<\/jats:italic> age, level of hunger) which affects its movement characteristics. We then apply the model to a concrete example of locust foraging to investigate the dynamic interplay of food availability, hunger, and degree of gregarisation (level of sociability) on locust group formation and structure. We find that including hunger lowers group density and raises the percentage of the population that needs to be gregarious for group formation. Within the group structure itself we find that the most gregarious and satiated locusts tend to be located towards the centre with hunger driving locusts towards the edges of the group. These two effects may combine to give a simple mechanism for locust group dispersal, in that hunger lowers the group density, which in turn lowers the gregarisation, further lowering density and creating a feedback loop. We also note that a previously found optimal food patch size for group formation may be driven by hunger. In addition to our locust results, we provide more general results and methods in the attached appendices.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1011469","type":"journal-article","created":{"date-parts":[[2025,4,15]],"date-time":"2025-04-15T20:06:13Z","timestamp":1744747573000},"page":"e1011469","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":2,"title":["Including population and environmental dynamic heterogeneities in continuum models of collective behaviour with applications to locust foraging and group structure"],"prefix":"10.1371","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4588-5319","authenticated-orcid":true,"given":"Fillipe","family":"Georgiou","sequence":"first","affiliation":[]},{"given":"Camille","family":"Buhl","sequence":"additional","affiliation":[]},{"given":"J. E. 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Population kinetics, differential adhesiveness and the absence of directed migration. Proc Natl Acad Sci U S A"},{"issue":"2","key":"pcbi.1011469.ref005","first-page":"135","article-title":"A Revision of the Genus Locusta, L","volume":"12","author":"BP Uvarov","year":"1921","journal-title":"(= Pachytylus, Fieb.), with a New Theory as to the Periodicity and Migrations of Locusts. Bull Entomol Res"},{"key":"pcbi.1011469.ref006","first-page":"1","article-title":"Variability and Heterogeneity in Natural Swarms: Experiments and Modeling","volume-title":"Modeling and Simulation in Science, Engineering and Technology","author":"G Ariel","year":"2022"},{"issue":"8","key":"pcbi.1011469.ref007","doi-asserted-by":"crossref","first-page":"e1002642","DOI":"10.1371\/journal.pcbi.1002642","article-title":"Locust dynamics: behavioral phase change and swarming","volume":"8","author":"CM Topaz","year":"2012","journal-title":"PLoS Comput Biol"},{"issue":"7","key":"pcbi.1011469.ref008","doi-asserted-by":"crossref","first-page":"e1008353","DOI":"10.1371\/journal.pcbi.1008353","article-title":"Modelling locust foraging: How and why food affects group formation","volume":"17","author":"F Georgiou","year":"2021","journal-title":"PLoS Comput Biol"},{"issue":"8","key":"pcbi.1011469.ref009","doi-asserted-by":"crossref","first-page":"1573","DOI":"10.1007\/s00265-011-1167-5","article-title":"Group leadership depends on energetic state in a nomadic collective foraging caterpillar","volume":"65","author":"M McClure","year":"2011","journal-title":"Behav Ecol Sociobiol"},{"issue":"2","key":"pcbi.1011469.ref010","doi-asserted-by":"crossref","first-page":"e0148334","DOI":"10.1371\/journal.pone.0148334","article-title":"Crimson spotted rainbowfish (Melanotaenia duboulayi) change their spatial position according to nutritional requirement","volume":"11","author":"MJ Hansen","year":"2016","journal-title":"PLoS One"},{"issue":"23","key":"pcbi.1011469.ref011","doi-asserted-by":"crossref","first-page":"3132","DOI":"10.1016\/j.cub.2015.10.044","article-title":"Speed determines leadership and leadership determines learning during pigeon flocking","volume":"25","author":"B Pettit","year":"2015","journal-title":"Curr Biol"},{"key":"pcbi.1011469.ref012"},{"issue":"2","key":"pcbi.1011469.ref013","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/0022-1910(94)90089-2","article-title":"Parental effects on the behaviour and colouration of nymphs of the desert locust Schistocerca gregaria","volume":"40","author":"M Saiful Islam","year":"1994","journal-title":"J Insect Physiol"},{"key":"pcbi.1011469.ref014","doi-asserted-by":"crossref","unstructured":"Schmidt GH, Albutz R. Identification of solitary and gregarious populations of the desert locust, Schistocerca gregaria, by experimental breeding (Caelifera: Acrididae). Entomologia generalis. 1999.","DOI":"10.1127\/entom.gen\/24\/1999\/161"},{"issue":"4","key":"pcbi.1011469.ref015","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1111\/j.1469-185X.1999.tb00038.x","article-title":"A behavioural analysis of phase change in the desert locust","volume":"74","author":"SJ Simpson","year":"1999","journal-title":"Biol Rev"},{"key":"pcbi.1011469.ref016"},{"issue":"5914","key":"pcbi.1011469.ref017","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1126\/science.1165939","article-title":"Serotonin mediates behavioral gregarization underlying swarm formation in desert locusts","volume":"323","author":"ML Anstey","year":"2009","journal-title":"Science"},{"issue":"1","key":"pcbi.1011469.ref018","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1111\/j.1365-3032.1996.tb00838.x","article-title":"Separating food and water deprivation in locusts: effects on the patterns of consumption, locomotion and growth","volume":"21","author":"D Raubenheimer","year":"1996","journal-title":"Physiol Entomol"},{"key":"pcbi.1011469.ref019"},{"issue":"3","key":"pcbi.1011469.ref020","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/s10905-019-09727-8","article-title":"Effects of starvation and vegetation distribution on locust collective motion","volume":"32","author":"J Dkhili","year":"2019","journal-title":"J Insect Behav"},{"key":"pcbi.1011469.ref021","first-page":"1","article-title":"The derivation of swarming models: Mean-field limit and Wasserstein distances","volume-title":"CISM International Centre for Mechanical Sciences","author":"JA Carrillo","year":"2014"},{"issue":"5778","key":"pcbi.1011469.ref022","doi-asserted-by":"crossref","first-page":"1402","DOI":"10.1126\/science.1125142","article-title":"From disorder to order in marching locusts","volume":"312","author":"C Buhl","year":"2006","journal-title":"Science"},{"issue":"6","key":"pcbi.1011469.ref023","doi-asserted-by":"crossref","first-page":"757","DOI":"10.1098\/rsfs.2012.0024","article-title":"Using field data to test locust migratory band collective movement models","volume":"2","author":"C Buhl","year":"2012","journal-title":"Interface Focus"},{"issue":"12","key":"pcbi.1011469.ref024","doi-asserted-by":"crossref","first-page":"e1004522","DOI":"10.1371\/journal.pcbi.1004522","article-title":"Locust collective motion and its modeling","volume":"11","author":"G Ariel","year":"2015","journal-title":"PLoS Comput Biol"},{"issue":"2","key":"pcbi.1011469.ref025","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1007\/s00265-010-1041-x","article-title":"Group structure in locust migratory bands","volume":"65","author":"C Buhl","year":"2010","journal-title":"Behav Ecol 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