Editing Theoretical ecology (section)

==Behavioral ecology==
{{main|Behavioral ecology}}

===Swarm behaviour===
[[File:A wedge of starlings - geograph.org.uk - 1069366.jpg|thumb|right|Flocks of birds can abruptly change their direction in unison, and then, just as suddenly, make a unanimous group decision [[Bird landings|to land]].<ref name="Bhattacharya">Bhattacharya K and Vicsek T (2010) [https://arxiv.org/abs/1007.4453 "Collective decision making in cohesive flocks"]</ref>]]
{{See also|Swarm models}}

[[Swarm behaviour]] is a [[Collective animal behaviour|collective behaviour]] exhibited by animals of similar size which aggregate together, perhaps milling about the same spot or perhaps [[Animal migration|migrating]] in some direction. Swarm behaviour is commonly exhibited by insects, but it also occurs in the [[flocking (behavior)|flocking]] of birds, the [[shoaling and schooling|schooling]] of fish and the [[herd behaviour]] of quadrupeds. It is a complex [[emergent organization|emergent]] behaviour that occurs when [[Agent-based model in biology|individual agents]] follow simple behavioral rules.

Recently, a number of mathematical models have been discovered which explain many aspects of the emergent behaviour. Swarm algorithms follow a [[Lagrangian mechanics|Lagrangian]] approach or an [[Euler equations (fluid dynamics)|Eulerian]] approach.<ref name="Li et al">{{cite journal | author = Li YX | year = 2007 | title = Minimal mechanisms for school formation in self-propelled particles | url = http://www.iam.ubc.ca/~lukeman/fish_school_f.pdf | archive-url = https://web.archive.org/web/20111001032730/http://www.iam.ubc.ca/~lukeman/fish_school_f.pdf | url-status = dead | archive-date = 2011-10-01 | journal = Physica D: Nonlinear Phenomena | volume = 237 | issue = 5 | pages = 699–720 | doi = 10.1016/j.physd.2007.10.009 | author2 = Lukeman R | author3 = Edelstein-Keshet L | bibcode = 2008PhyD..237..699L }}</ref> The Eulerian approach views the swarm as a [[Field (physics)|field]], working with the density of the swarm and deriving mean field properties. It is a hydrodynamic approach, and can be useful for modelling the overall dynamics of large swarms.<ref>Toner J and Tu Y (1995) "Long-range order in a two-dimensional xy model: how birds fly together" ''Physical Revue Letters,'' '''75''' (23)(1995), 4326–4329.</ref><ref>{{cite journal |vauthors=Topaz C, Bertozzi A | year = 2004 | title = Swarming patterns in a two-dimensional kinematic model for biological groups | journal = SIAM J Appl Math | volume = 65 | issue = 1| pages = 152–174 | doi = 10.1137/S0036139903437424 | citeseerx = 10.1.1.88.3071 | bibcode = 2004APS..MAR.t9004T | s2cid = 18468679 }}</ref><ref>{{cite journal |vauthors=Topaz C, Bertozzi A, Lewis M | year = 2006 | title = A nonlocal continuum model for biological aggregation | journal = Bull Math Biol | volume = 68 | issue = 7| pages = 1601–1623 | doi = 10.1007/s11538-006-9088-6 | arxiv = q-bio/0504001 | pmid=16858662| s2cid = 14750061 }}</ref> However, most models work with the Lagrangian approach, which is an [[agent-based model]] following the individual agents (points or particles) that make up the swarm. Individual particle models can follow information on heading and spacing that is lost in the Eulerian approach.<ref name="Li et al"/><ref>{{cite book | last1 = Carrillo | first1 = J | last2 = Fornasier | first2 = M | last3 = Toscani | first3 = G | title = Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences | chapter = Particle, kinetic, and hydrodynamic models of swarming | series = Modeling and Simulation in Science, Engineering and Technology | year = 2010 | url = http://mate.unipv.it/~toscani/publi/swarming.pdf | volume = 3 | pages = 297–336 | doi = 10.1007/978-0-8176-4946-3_12 | isbn = 978-0-8176-4945-6 | citeseerx = 10.1.1.193.5047 }}</ref> Examples include [[ant colony optimization]], [[self-propelled particles]] and [[particle swarm optimization]].

On cellular levels, individual organisms also demonstrated swarm behavior. [[Decentralised system|Decentralized systems]] are where individuals act based on their own decisions without overarching guidance. Studies have shown that individual ''[[Trichoplax adhaerens]]'' behave like [[self-propelled particles]] (SPPs) and collectively display phase transition from ordered movement to disordered movements.<ref>{{Cite journal |last1=Davidescu |first1=Mircea R. |last2=Romanczuk |first2=Pawel |last3=Gregor |first3=Thomas |last4=Couzin |first4=Iain D. |date=2023-03-14 |title=Growth produces coordination trade-offs in Trichoplax adhaerens, an animal lacking a central nervous system |journal=Proceedings of the National Academy of Sciences |language=en |volume=120 |issue=11 |pages=e2206163120 |doi=10.1073/pnas.2206163120 |issn=0027-8424 |pmc=10089153 |pmid=36897970|bibcode=2023PNAS..12006163D }}</ref> Previously, it was thought that the surface-to-volume ratio was what limited the animal size in the evolutionary game. Considering the collective behaviour of the individuals, it was suggested that order is another limiting factor. [[Central nervous system]]s were indicated to be vital for large multicellular animals in the evolutionary pathway.

=== Synchronization ===
The coexistence of the [[synchronization]] and asynchronization in the flashings in the system composed of multiple fireflies could be characterized by the chimera states. Synchronization could spontaneously occur.<ref>{{Cite journal |last1=Sarfati |first1=Raphaël |last2=Peleg |first2=Orit |date=2022-11-18 |title=Chimera states among synchronous fireflies |journal=Science Advances |language=en |volume=8 |issue=46 |pages=eadd6690 |doi=10.1126/sciadv.add6690 |issn=2375-2548 |pmc=9668303 |pmid=36383660|bibcode=2022SciA....8D6690S }}</ref> The [[agent-based model]] has been useful in describing this unique phenomenon. The flashings of individual fireflies could be viewed as oscillators and the global coupling models were similar to the ones used in [[condensed matter physics]].