Editing Food web (section)

=== Complexity and stability ===
[[File:Food web in the Gulf of Naples in eutrophic and oligotrophic summer conditions - oo 297117.jpg|thumb|A simplified version of a food web in the [[Gulf of Naples]] in eutrophic (green) and oligotrophic (blue) summer conditions. In the Green system state, both copepods and microzooplankton exert a strong grazing pressure on phytoplankton, while in the Blue state, copepods increase their predation over microzooplankton, which in turn shifts its predation from phytoplankton to bacterial plankton or picoplankton. These trophic mechanisms stabilize the delivery of organic matter from copepods to fish.]]
Food webs are extremely complex. [[Complex system|Complexity]] is a term that conveys the mental intractability of understanding all possible higher-order effects in a food web. Sometimes in food web terminology, complexity is defined as product of the number of species and connectance.,<ref name="Neutel02">{{cite journal | last1=Neutel | first1=A. | last2=Heesterbeek | first2=J. A. P. | last3=de Ruiter | first3=P. D. | title=Stability in real food webs: Weak link in long loops | year=2002 | journal=Science | volume=295 | issue=550 | pages=1120–1123 | doi=10.1126/science.1068326 | pmid=12004131 | url=http://igitur-archive.library.uu.nl/vet/2006-0321-200233/heesterbeek_02_stability_webs.pdf | url-status=dead | archive-url=https://web.archive.org/web/20110928044042/http://igitur-archive.library.uu.nl/vet/2006-0321-200233/heesterbeek_02_stability_webs.pdf | archive-date=2011-09-28 | bibcode=2002Sci...296.1120N | hdl=1874/8123 | s2cid=34331654 | accessdate=2011-07-04 }}</ref><ref name="Leveque03">{{cite book | editor-last=Leveque | editor-first=C. | title= Ecology: From ecosystem to biosphere | year=2003 | page=490 | publisher=Science Publishers | isbn=978-1-57808-294-0 | url= https://books.google.com/books?id=-h3AFlmGS_kC&q=Ecology+from+ecosystem+to+biosphere }}</ref><ref name="Proctor05">{{cite journal | last1=Proctor | first1=J. D. | last2=Larson | first2=B. M. H. | title=Ecology, complexity, and metaphor | journal=BioScience | volume=55 | issue=12 | pages=1065–1068 | year=2005 | doi=10.1641/0006-3568(2005)055[1065:ECAM]2.0.CO;2 | doi-access=free }}</ref> though there have been criticisms of this definition and other proposed methods for measuring network complexity.<ref>{{Cite journal |last1=Strydom |first1=Tanya |last2=Dalla Riva |first2=Giulio V. |last3=Poisot |first3=Timothée |date=2021 |title=SVD Entropy Reveals the High Complexity of Ecological Networks |journal=Frontiers in Ecology and Evolution |volume=9 |doi=10.3389/fevo.2021.623141 |issn=2296-701X|doi-access=free }}</ref> Connectance is "the fraction of all possible links that are realized in a network".<ref name="Dunne02">{{cite journal | last1=Dunne | first1=J. A. | last2=Williams | first2=R. J. | last3=Martinez | first3=N. D. | title=Food-web structure and network theory: The role of connectance and size | journal=Proceedings of the National Academy of Sciences | volume=99 | issue=20 | pages=12917–12922 | year=2002 | doi=10.1073/pnas.192407699 | pmid=12235364 | pmc=130560| bibcode=2002PNAS...9912917D | doi-access=free }}</ref>{{rp|12917}} These concepts were derived and stimulated through the suggestion that complexity leads to stability in food webs, such as increasing the number of trophic levels in more species rich ecosystems. This hypothesis was challenged through mathematical models suggesting otherwise, but subsequent studies have shown that the premise holds in real systems.<ref name="Neutel02" /><ref name="Banasek-Richter09" />

At different levels in the hierarchy of life, such as the stability of a food web, "the same overall structure is maintained in spite of an ongoing flow and change of components."<ref name="Capra07">{{cite journal | last1=Capra | first1=F. | title=Complexity and life | journal=Syst. Res. | volume=24 | issue=5 | pages=475–479 | year=2007 | doi=10.1002/sres.848}}</ref>{{rp|476}} The farther a living system (e.g., ecosystem) sways from equilibrium, the greater its complexity.<ref name="Capra07" /> Complexity has multiple meanings in the life sciences and in the public sphere that confuse its application as a precise term for analytical purposes in science.<ref name="Proctor05" /><ref name="Peters88">{{cite journal | last1=Peters | first1=R. H. | title=Some general problems for ecology illustrated by food web theory | journal=Ecology | volume=69 | issue=6 | pages=1673–1676 | year=1988 | jstor=1941145 | doi=10.2307/1941145| bibcode=1988Ecol...69.1673P }}</ref> Complexity in the life sciences (or [[biocomplexity]]) is defined by the "properties emerging from the interplay of behavioral, biological, physical, and social interactions that affect, sustain, or are modified by living organisms, including humans".<ref name="Michener01">{{cite journal | last1=Michener | first1=W. K. | last2=Baerwald | first2=T. J. | last3=Firth | first3=P. | last4=Palmer | first4=M. A. | last5=Rosenberger | first5=J. L. | last6=Sandlin | first6=E. A. | last7=Zimmerman | first7=H. | year=2001 | title=Defining and unraveling biocomplexity | journal=BioScience | volume=51 | issue=12 | pages=1018–1023 | doi=10.1641/0006-3568(2001)051[1018:daub]2.0.co;2 | doi-access=free }}</ref>{{rp|1018}}

Several concepts have emerged from the study of complexity in food webs. Complexity explains many principals pertaining to self-organization, non-linearity, interaction, cybernetic feedback, discontinuity, emergence, and stability in food webs. Nestedness, for example, is defined as "a pattern of interaction in which specialists interact with species that form perfect subsets of the species with which generalists interact",<ref name="Bascompte07">{{cite journal | last1=Bascompte | first1=J. | last2=Jordan | first2=P. | title=Plant-animal mutualistic networks: The architecture of biodiversity. | year=2007 | journal=Annu. Rev. Ecol. Evol. Syst. | volume=38 | pages=567–569 | url=http://ieg.ebd.csic.es/JordiBascompte/Publications/AREES-07.pdf | archive-url=https://web.archive.org/web/20091025023353/http://ieg.ebd.csic.es/JordiBascompte/Publications/AREES-07.pdf | url-status=dead | archive-date=2009-10-25 | doi=10.1146/annurev.ecolsys.38.091206.095818 | hdl=10261/40177 | hdl-access=free | accessdate=2011-07-03 }}</ref>{{rp|575}} "—that is, the diet of the most specialized species is a subset of the diet of the next more generalized species, and its diet a subset of the next more generalized, and so on."<ref name="Montoya06">{{cite journal | last1=Montoya | first1=J. M. | last2=Pimm | first2=S. L. | last3=Solé | first3=R. V. | title=Ecological networks and their fragility | journal=Nature | volume=442 | issue=7100 | pages=259–264 | year=2006 | doi=10.1038/nature04927 | pmid=16855581 | url=http://eeb19.biosci.arizona.edu/Faculty/Dornhaus/courses/materials/papers/Montoya%20Pimm%20Sole%20networks%20ecol.pdf | archive-url=https://web.archive.org/web/20100706235030/http://eeb19.biosci.arizona.edu/Faculty/Dornhaus/courses/materials/papers/Montoya%20Pimm%20Sole%20networks%20ecol.pdf | url-status=dead | archive-date=2010-07-06 | bibcode=2006Natur.442..259M | s2cid=592403 | accessdate=2011-07-04 }}</ref> Until recently, it was thought that food webs had little nested structure, but empirical evidence shows that many published webs have nested subwebs in their assembly.<ref name="Michio10">{{cite journal | last1=Michio | first1=K. | last2=Kato | first2=S. | last3=Sakato | first3=Y. | year=2010 | title=Food webs are built up with nested subwebs | journal=Ecology | volume=91 | issue=11 | pages=3123–3130 | doi=10.1890/09-2219.1 | pmid=21141173 | doi-access=free | bibcode=2010Ecol...91.3123K }}</ref>

Food webs are complex [[ecological network|networks]]. As networks, they exhibit similar structural properties and mathematical laws that have been used to describe other complex systems, such as [[small-world network|small world]] and [[scale-free network|scale free properties]]. The small world attribute refers to the many loosely connected nodes, non-random dense clustering of a few nodes (i.e., trophic or [[keystone species]] in ecology), and small path length compared to a regular lattice.<ref name="Dunne02" /><ref name="Montoya02">{{cite journal | last1=Montoya | first1=J. M. | last2=Solé | first2=R. V. | title=Small world patterns in food webs | journal=Journal of Theoretical Biology | volume=214 | issue=3 | pages=405–412 | year=2002 | doi=10.1006/jtbi.2001.2460 | pmid=11846598 | url=http://complex.upf.es/papers/Small_World_Patterns_in_Food_Webs.pdf | url-status=dead | archive-url=https://web.archive.org/web/20110905095528/http://complex.upf.es/papers/Small_World_Patterns_in_Food_Webs.pdf | archive-date=2011-09-05 | arxiv=cond-mat/0011195 | bibcode=2002JThBi.214..405M | accessdate=2011-07-05 }}</ref> "Ecological networks, especially mutualistic networks, are generally very heterogeneous, consisting of areas with sparse links among species and distinct areas of tightly linked species. These regions of high link density are often referred to as cliques, hubs, compartments, cohesive sub-groups, or modules...Within food webs, especially in aquatic systems, nestedness appears to be related to body size because the diets of smaller predators tend to be nested subsets of those of larger predators (Woodward & Warren 2007; YvonDurocher et al. 2008), and phylogenetic constraints, whereby related taxa are nested based on their common evolutionary history, are also evident (Cattin et al. 2004)."<ref name="Montoya09">{{cite journal | last1=Montoya | first1=J. M. | last2=Blüthgen | first2=N | last3=Brown | first3=L. | last4=Dormann | first4=C. F. | last5=Edwards | first5=F. | last6=Figueroa | first6=D. | title=Ecological networks: beyond food webs | year=2009 | journal=Journal of Animal Ecology | volume=78 | issue=1 | pages=253–269 | doi=10.1111/j.1365-2656.2008.01460.x | pmid=19120606 | display-authors=etal | doi-access=free }}</ref>{{rp|257}} "Compartments in food webs are subgroups of taxa in which many strong interactions occur within the subgroups and few weak interactions occur between the subgroups. Theoretically, compartments increase the stability in networks, such as food webs."<ref name="Krause03" />

Food webs are also complex in the way that they change in scale, seasonally, and geographically. The components of food webs, including organisms and mineral nutrients, cross the thresholds of ecosystem boundaries. This has led to the concept or area of study known as [[cross-boundary subsidy]].<ref name="Bormann67">{{cite journal | last1=Bormann | first1=F. H. | last2=Likens | first2=G. E. | year=1967 | title=Nutrient cycling | journal=Science | volume=155 | issue=3761 | pages=424–429 | doi=10.1126/science.155.3761.424 | pmid=17737551 | url=http://www.biology.duke.edu/upe302/pdf%20files/Emily_BormannLikens1967.pdf | url-status=dead | archive-url=https://web.archive.org/web/20110927182833/http://www.biology.duke.edu/upe302/pdf%20files/Emily_BormannLikens1967.pdf | archive-date=2011-09-27 | bibcode=1967Sci...155..424B | s2cid=35880562 | accessdate=2011-06-29 }}</ref><ref name="Polis97">{{cite journal | last1=Polis | first1=G. A. | last2=Anderson | first2=W. B. | last3=Hold | first3=R. D. | title=Toward an integration of landscape and food web ecology: The dynamics of spatially subsidized food webs | journal=Annual Review of Ecology and Systematics | volume=28 | year=1997 | pages=289–316 | url=http://limnology.wisc.edu/courses/zoo955/Fall2006/Papers/Polis_1997_Toward.pdf | doi=10.1146/annurev.ecolsys.28.1.289 | url-status=dead | archive-url=https://web.archive.org/web/20111002090844/http://limnology.wisc.edu/courses/zoo955/Fall2006/Papers/Polis_1997_Toward.pdf | archive-date=2011-10-02 | hdl=1808/817 | hdl-access=free | accessdate=2011-06-29 }}</ref> "This leads to anomalies, such as food web calculations determining that an ecosystem can support one half of a top carnivore, without specifying which end."<ref name="O'Neil01">{{cite journal | last1=O'Neil | first1=R. V. | title=Is it time to bury the ecosystem concept? (With full military honors, of course!) | year=2001 | journal=Ecology | volume=82 | issue=12 | pages=3275–3284 | url=http://ss1.webkreator.com.mx/4_2/000/000/00c/04a/Concepto%20de%20Ecosistema.pdf | doi=10.1890/0012-9658(2001)082[3275:IITTBT]2.0.CO;2 | url-status=dead | archive-url=https://web.archive.org/web/20120425235406/http://ss1.webkreator.com.mx/4_2/000/000/00c/04a/Concepto%20de%20Ecosistema.pdf | archive-date=2012-04-25 }}</ref> Nonetheless, real differences in structure and function have been identified when comparing different kinds of ecological food webs, such as terrestrial vs. aquatic food webs.<ref name="Shurin06">{{cite journal | last1=Shurin | first1=J. B. | last2=Gruner | first2=D. S. | last3=Hillebrand | first3=H. | title=All wet or dried up? Real differences between aquatic and terrestrial food webs | journal=Proc. R. Soc. B | year=2006 | volume=273 | pages=1–9 | doi=10.1098/rspb.2005.3377 | issue=1582 | pmid=16519227 | pmc=1560001}}</ref>