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Coexistence theory

Coexistence theory is a framework to understand how competitor traits can maintain species diversity and stave-off competitive exclusion even among similar species living in ecologically similar environments. Coexistence theory explains the stable coexistence of species as an interaction between two opposing forces: fitness differences between species, which should drive the best-adapted species to exclude others within a particular ecological niche, and stabilizing mechanisms, which maintains diversity via niche differentiation. For many species to be stabilized in a community, population growth must be negative density-dependent, i.e. all participating species have a tendency to increase in density as their populations decline. In such communities, any species that becomes rare will experience positive growth, pushing its population to recover and making local extinction unlikely. As the population of one species declines, individuals of that species tend to compete predominantly with individuals of other species. Thus, the tendency of a population to recover as it declines in density reflects reduced intraspecific competition (within-species) relative to interspecific competition (between-species), the signature of niche differentiation (see Lotka-Volterra competition).

Coexistence theory attempts to explain the paradox of the plankton -- how can ecologically similar species coexist without competitively excluding each other?

Types of coexistence mechanisms edit

 
Groundhog and a raccoon eating together

Two qualitatively different processes can help species to coexist: a reduction in average fitness differences between species or an increase in niche differentiation between species. These two factors have been termed equalizing and stabilizing mechanisms, respectively.[1] For species to coexist, any fitness differences that are not reduced by equalizing mechanisms must be overcome by stabilizing mechanisms.

Equalizing mechanisms edit

Equalizing mechanisms reduce fitness differences between species. As its name implies, these processes act in a way that push the competitive abilities of multiple species closer together. Equalizing mechanisms affect interspecific competition (the competition between individuals of different species).

For example, when multiple species compete for the same resource, competitive ability is determined by the minimum level of resources a species needs to maintain itself (known as an R*, or equilibrium resource density).[2] Thus, the species with the lowest R* is the best competitor and excludes all other species in the absence of any niche differentiation. Any factor that reduces R*s between species (like increased harvest of the dominant competitor) is classified as an equalizing mechanism.

Environmental variation (which is the focus of the Intermediate Disturbance Hypothesis) can be considered an equalizing mechanism. Since the fitness of a given species is intrinsically tied to a specific environment, when that environment is disturbed (e.g. through storms, fires, volcanic eruptions, etc.) some species may lose components of their competitive advantage which were useful in the previous version of the environment.

Stabilizing mechanisms edit

Stabilizing mechanisms promote coexistence by concentrating intraspecific competition relative to interspecific competition. In other words, these mechanisms "encourage" an individual to compete more with other individuals of its own species, rather than with individuals of other species. Resource partitioning (a type of niche differentiation) is a stabilizing mechanism because interspecific competition is reduced when different species primarily compete for different resources. Similarly, if species are differently affected by environmental variation (e.g., soil type, rainfall timing, etc.), this can create a stabilizing mechanism (see the storage effect). Stabilizing mechanisms increase the low-density growth rate of all species.[citation needed]

Chesson's categories of stabilizing mechanisms edit

In 1994, Chesson proposed that all stabilizing mechanisms could be categorized into four categories.[3][4] These mechanisms are not mutually exclusive, and it is possible for all four to operate in any environment at a given time.

  1. Variation-independent mechanisms (also called fluctuation-independent mechanisms) are any stabilizing mechanism that functions within a local place and time.[3][4] Resource partitioning, predator partitioning, and frequency-dependent predation are three classic examples of variation-independent mechanisms. When a species is at very low density, individuals gain an advantage, because they are less constrained by competition across the landscape. For example, under frequency-dependent predation, a species is less likely to be consumed by predators when they are very rare.
  2. The storage effect occurs when species are affected differently by environmental variation in space or time.[3][4] For example, coral reef fishes have different reproductive rates in different years, plants grow differently in different soil types, and desert annual plants germinate at different rates in different years. When a species is at low density, individuals gain an advantage because they experience less competition in times or locations that they grow best. For example, if annual plants germinate in different years, then when it is a good year to germinate, species will be competing predominately with members of the same species. Thus, if a species becomes rare, individuals will experience little competition when they germinate whereas they would experience high competition if they were abundant. For the storage effect to function, species must be able to "store" the benefits of a productive time period or area, and use it to survive during less productive times or areas.[5] This can occur, for example, if species have a long-lived adult stage, a seed bank or diapause stage, or if they are spread out over the environment.
  3. A fitness-density covariance occurs when species are spread out non-uniformly across the landscape.[3] Most often, it occurs when species are found in different areas. For example, mosquitoes often lay eggs in different locations, and plants who partition habitat are often found predominately where they grow best. Species can gain two possible advantages by becoming very rare. First, because they are physically separated from other species, they mainly compete with members of the same species (and thus experience less competition when they become very rare). Second, species are often more able to concentrate in favorable habitat as their densities decline. For example, if individuals are territorial, then members of an abundant species may not have access to ideal habitat; however, when that species becomes very rare, then there may be enough ideal habitat for all of the few remaining individuals. The Janzen-Connell hypothesis is an excellent example of a stabilizing mechanism that operates (in part) through fitness-density covariance.
  4. Relative nonlinearity occurs when species benefit in different ways from variation in competitive factors.[3][4] For example, two species might coexist if one can grow better when resources are rare, and the other grows better when resources are abundant. Species will be able to coexist if the species which benefits from variation in resources tends to reduce variation in resources. For example, a species which can rapidly consume excess resources tends to quickly reduce the level of excess resources favoring the other species, whereas a species which grows better when resources are rare is more likely to cause fluctuations in resource density favoring the other species.[6]

Quantifying stabilizing mechanisms edit

A general way of measuring the effect of stabilizing mechanisms is by calculating the growth rate of species i in a community as[7] 

where:

  •   is the long-term average growth rate of the species i when at low density. Because species are limited from growing indefinitely, viable populations have an average long-term growth rate of zero. Therefore, species at low-density can increase in abundance when their long-term average growth rate is positive.
  •   is a species-specific factor that reflects how quickly species i responds to a change in competition. For example, species with faster generation times may respond more quickly to a change in resource density than longer lived species. In an extreme scenario, if ants and elephants were to compete for the same resources, elephant population sizes would change much more slowly to changes in resource density than would ant populations.
  •   is the difference between the fitness of species i when compared to the average fitness of the community excluding species i. In the absence of any stabilizing mechanisms, species i will only have a positive growth rate if its fitness is above its average competitor, i.e. where this value is greater than zero.
  •   measures the effect of all stabilizing mechanisms acting within this community.
Example calculation: Species competing for resource edit

In 2008 Chesson and Kuang showed how to calculate fitness differences and stabilizing mechanisms when species compete for shared resources and competitors. Each species j captures resource type l at a species-specific rate, cjl. Each unit of resource captured contributes to species growth by value vl. Each consumer requires resources for the metabolic maintenance at rate μi.[8]

In conjunction, consumer growth is decreased by attack from predators. Each predator species m attacks species j at rate ajm.

Given predation and resource capture, the density of species i, Ni, grows at rate

 

where l sums over resource types and m sums over all predator species. Each resource type exhibits logistic growth with intrinsic rate of increase, rRl, and carrying capacity, KRl = 1/αRl, such that growth rate of resource l is

 

Similarly, each predator species m exhibits logistic growth in the absence of the prey of interest with intrinsic growth rate rPm and carrying capacity KPm = 1/αPm. The growth rate of a predator species is also increased by consuming prey species where again the attack rate of predator species m on prey j is ajm. Each unit of prey has a value to predator growth rate of w. Given these two sources of predator growth, the density of predator m, Pm, has a per-capita growth rate

 

where the summation terms is contributions to growth from consumption over all j focal species. The system of equations describes a model of trophic interactions between three sets of species: focal species, their resources, and their predators.

Given this model, the average fitness of a species j is

 

where the sensitivity to competition and predation is

 

The average fitness of a species takes into account growth based on resource capture and predation as well as how much resource and predator densities change from interactions with the focal species.

The amount of niche overlap between two competitors i and j is

 

which represents the amount to which resource consumption and predator attack are linearly related between two competing species, i and j.

This model conditions for coexistence can be directly related to the general coexistence criterion: intraspecific competition, αjj, must be greater than interspecific competition, αij. The direct expressions for intraspecific and interspecific competition coefficients from the interaction between shared predators and resources are

 

and

 

Thus, when intraspecific competition is greater than interspecific competition,

 

which, for two species leads to the coexistence criteria

 

Notice that, in the absence of any niche differences (i.e. ρ = 1), species cannot coexist.

Empirical evidence edit

A 2012 study[9] reviewed different approaches which tested coexistence theory, and identified three main ways to separate the contributions of stabilizing and equalizing mechanisms within a community. These are:

  1. Experimental manipulations, which involved determining the effect of relative fitness or stabilizing mechanisms by manipulating resources or competitive advantages.
  2. Trait-Phylogeny-Environment relationships, in which the phylogeny of members of a set of communities can be tested for evidence of trait clustering, which would suggest that certain traits are important (and perhaps necessary) to thrive in that environment, or trait overdispersion, which would suggest a high ability of species to exclude close relatives. Such tests have been widely used, although they have also been criticized as simplistic and flawed.[10]
  3. Demographic analyses, which can be used to recognize frequency- or density-dependent processes simply by measuring the number and per-capita growth rates of species in natural communities over time. If such processes are operating, the per-capita growth rate would vary with the number of individuals in species comprising the community.

A 2010 review[11] argued that an invasion analysis should be used as the critical test of coexistence. In an invasion analysis, one species (termed the "invader") is removed from the community, and then reintroduced at a very low density. If the invader shows positive population growth, then it cannot be excluded from the community. If every species has a positive growth rate as an invader, then those species can stably coexist. An invasion analysis could be performed using experimental manipulation, or by parameterizing a mathematical model. The authors argued that in the absence of a full-scale invasion analysis, studies could show some evidence for coexistence by showing that a trade-off produced negative density-dependence at the population level. The authors reviewed 323 papers (from 1972 to May 2009), and claimed that only 10 of them met the above criteria (7 performing an invasion analysis, and 3 showing some negative-density dependence).

However, an important caveat is that invasion analysis may not always be sufficient for identifying stable coexistence. For example, priority effects or Allee effects may prevent species from successfully invading a community from low density even if they could persist stably at a higher density. Conversely, high order interactions in communities with many species can lead to complex dynamics following an initially successful invasion, potentially preventing the invader from persisting stably in the long term.[12] For example, an invader that can only persist when a particular resident species is present at high density could alter community structure following invasion such that that resident species' density declines or that it goes locally extinct, thereby preventing the invader from successfully establishing in the long term.

Neutral theory and coexistence theory edit

The 2001 Neutral theory by Stephen P. Hubbell[13] attempts to model biodiversity through a migration-speciation-extinction balance, rather through selection.[14] It assumes that all members within a guild are inherently the same, and that changes in population density are a result of random births and deaths. Particular species are lost stochastically through a random walk process, but species richness is maintained via speciation or external migration. Neutral theory can be seen as a particular case of coexistence theory: it represents an environment where stabilizing mechanisms are absent (i.e.,  ), and there are no differences in average fitness (i.e.,   for all species).[15]

It has been hotly debated how close real communities are to neutrality. Few studies have attempted to measure fitness differences and stabilizing mechanisms in plant communities, for example in 2009[16] or in 2015 [17] These communities appear to be far from neutral, and in some cases, stabilizing effects greatly outweigh fitness differences.

Cultural coexistence theory edit

Cultural Coexistence Theory (CCT), also called Social-ecological Coexistence Theory, expands on coexistence theory to explain how groups of people with shared interests in natural resources (e.g., a fishery) can come to coexist sustainably.[18] Cultural Coexistence Theory draws on work by anthropologists such as Frederik Barth and John Bennett, both of whom studied the interactions among culture groups on shared landscapes. In addition to the core ecological concepts described above, which CCT summarizes as limited similarity, limited competition, and resilience, CCT argues the following features are essential for cultural coexistence:

  1. Adaptability describes the ability of people to respond to change or surprise. It is essential to CCT because it helps capture the importance of human agency.
  2. Pluralism describes where people value cultural diversity and recognize the fundamental rights of people not like them to live in the same places and access shared resources.
  3. Equity as used in CCT describes whether social institutions exist that ensure that people's basic human rights, including the ability to meet basic needs, are protected, and whether people are protected from being marginalized in society.

Cultural Coexistence Theory fits in under the broader area of sustainability science, common pool resources theory, and conflict theory.

References edit

  1. ^ Chesson, Peter (2000). "Mechanisms of maintenance of species diversity". Annual Review of Ecology and Systematics. 31: 343–366. doi:10.1146/annurev.ecolsys.31.1.343. S2CID 403954.
  2. ^ Tilman, David (1980-09-01). "Resources: A Graphical-Mechanistic Approach to Competition and Predation". The American Naturalist. 116 (3): 362–393. doi:10.1086/283633. JSTOR 2463311. S2CID 85411812.
  3. ^ a b c d e Chesson, P. (2000). "General Theory of Competitive Coexistence in Spatially-Varying Environments". Theoretical Population Biology. 58 (3): 211–37. doi:10.1006/tpbi.2000.1486. PMID 11120650.
  4. ^ a b c d Chesson, Peter (June 1994). "Multispecies Competition in Variable Environments". Theoretical Population Biology. 45 (3): 227–276. doi:10.1006/Tpbi.1994.1013.
  5. ^ Chesson, Peter; Warner, Robert (1981). "Environmental Variability Promotes Coexistence in Lottery Competitive Systems". The American Naturalist. 117 (6): 923–943. doi:10.1086/283778. S2CID 84164336.
  6. ^ Armstrong, Robert A.; McGehee, Richard (February 1980). "Competitive Exclusion". The American Naturalist. 115 (2): 151–170. doi:10.1086/283553. S2CID 222329963.
  7. ^ Chesson, Peter (January 2008). "Chapter 6: Quantifying and testing species coexistence mechanisms". In Valladares, F.; Camacho, A.; Elosegui, A.; Garcia, C.; Estrada, M.; Senar, J.; Gili, J. (eds.). Unity in Diversity. A Conference on Ecology after the Legacy of Ramon Margalef. Bilbao: Fundación BBVA. pp. 119–164. ISBN 978-84-96515-53-6.
  8. ^ Chesson, Peter; Kuang, Jessica J. (2008-01-01). "The interaction between predation and competition". Nature. 456 (7219): 235–8. Bibcode:2008Natur.456..235C. doi:10.1038/nature07248. PMID 19005554. S2CID 4342701.
  9. ^ HilleRisLambers, J.; Adler, P. B.; Harpole, W. S.; Levine, J. M.; Mayfield, M. M. (2012). "Rethinking Community Assembly through the Lens of Coexistence Theory". Annual Review of Ecology, Evolution, and Systematics. 43: 227–248. doi:10.1146/annurev-ecolsys-110411-160411.
  10. ^ Mayfield, M. M.; Levine, J. M. (2010). "Opposing effects of competitive exclusion on the phylogenetic structure of communities". Ecology Letters. 13 (9): 1085–93. Bibcode:2010EcolL..13.1085M. doi:10.1111/j.1461-0248.2010.01509.x. PMID 20576030.
  11. ^ Seipielski, Adam; McPeek, Mark (2010). "On the evidence for species coexistence: A critique of the coexistence program". Ecology. 91 (11): 3153–3164. Bibcode:2010Ecol...91.3153S. doi:10.1890/10-0154.1. PMID 21141177. S2CID 24771175.
  12. ^ Levine, Jonathan; Bascompte, Jordi; Adler, Peter; Allesina, Stefano (2017). "Beyond pairwise mechanisms of species coexistence in complex communities" (PDF). Nature. 546 (7656): 56–64. Bibcode:2017Natur.546...56L. doi:10.1038/nature22898. PMID 28569813. S2CID 205257096.
  13. ^ Hubbell, Stephen P. (2001). The Unified Neutral Theory of Biodiversity and Biogeography (MPB-32). Princeton: Princeton University Press. ISBN 9781400837526.
  14. ^ Vellend, Mark (2010). "Conceptual synthesis in community ecology". The Quarterly Review of Biology. 85 (2): 183–206. doi:10.1086/652373. PMID 20565040. S2CID 10026873.
  15. ^ Adler, Peter B.; HilleRisLambers, Janneke; Levine, Jonathan M. (February 2007). "A niche for neutrality". Ecology Letters. 10 (2): 95–104. Bibcode:2007EcolL..10...95A. doi:10.1111/J.1461-0248.2006.00996.X. PMID 17257097.
  16. ^ Levine, Jonathan M.; HilleRisLambers, Janneke (12 August 2009). "The importance of niches for the maintenance of species diversity". Nature. 461 (7261): 254–257. Bibcode:2009Natur.461..254L. doi:10.1038/Nature08251. PMID 19675568. S2CID 1768121.
  17. ^ Chu, Chengjin; Adler, Peter B. (August 2015). "Large niche differences emerge at the recruitment stage to stabilize grassland coexistence". Ecological Monographs. 85 (3): 373–392. Bibcode:2015EcoM...85..373C. doi:10.1890/14-1741.1.
  18. ^ Loring, Philip A. (23 January 2016). "Toward a Theory of Coexistence in Shared Social-ecological Systems: The Case of Cook Inlet Salmon Fisheries". Human Ecology. 44 (2): 153–165. doi:10.1007/s10745-016-9806-0. PMC 4832003. PMID 27122652.

coexistence, theory, been, suggested, that, this, article, should, split, into, articles, titled, cultural, coexistence, theory, discuss, october, 2021, framework, understand, competitor, traits, maintain, species, diversity, stave, competitive, exclusion, eve. It has been suggested that this article should be split into articles titled Coexistence theory and Cultural coexistence theory discuss October 2021 Coexistence theory is a framework to understand how competitor traits can maintain species diversity and stave off competitive exclusion even among similar species living in ecologically similar environments Coexistence theory explains the stable coexistence of species as an interaction between two opposing forces fitness differences between species which should drive the best adapted species to exclude others within a particular ecological niche and stabilizing mechanisms which maintains diversity via niche differentiation For many species to be stabilized in a community population growth must be negative density dependent i e all participating species have a tendency to increase in density as their populations decline In such communities any species that becomes rare will experience positive growth pushing its population to recover and making local extinction unlikely As the population of one species declines individuals of that species tend to compete predominantly with individuals of other species Thus the tendency of a population to recover as it declines in density reflects reduced intraspecific competition within species relative to interspecific competition between species the signature of niche differentiation see Lotka Volterra competition Coexistence theory attempts to explain the paradox of the plankton how can ecologically similar species coexist without competitively excluding each other Contents 1 Types of coexistence mechanisms 1 1 Equalizing mechanisms 1 2 Stabilizing mechanisms 1 2 1 Chesson s categories of stabilizing mechanisms 1 2 2 Quantifying stabilizing mechanisms 1 2 2 1 Example calculation Species competing for resource 2 Empirical evidence 3 Neutral theory and coexistence theory 4 Cultural coexistence theory 5 ReferencesTypes of coexistence mechanisms edit nbsp Groundhog and a raccoon eating togetherTwo qualitatively different processes can help species to coexist a reduction in average fitness differences between species or an increase in niche differentiation between species These two factors have been termed equalizing and stabilizing mechanisms respectively 1 For species to coexist any fitness differences that are not reduced by equalizing mechanisms must be overcome by stabilizing mechanisms Equalizing mechanisms edit Equalizing mechanisms reduce fitness differences between species As its name implies these processes act in a way that push the competitive abilities of multiple species closer together Equalizing mechanisms affect interspecific competition the competition between individuals of different species For example when multiple species compete for the same resource competitive ability is determined by the minimum level of resources a species needs to maintain itself known as an R or equilibrium resource density 2 Thus the species with the lowest R is the best competitor and excludes all other species in the absence of any niche differentiation Any factor that reduces R s between species like increased harvest of the dominant competitor is classified as an equalizing mechanism Environmental variation which is the focus of the Intermediate Disturbance Hypothesis can be considered an equalizing mechanism Since the fitness of a given species is intrinsically tied to a specific environment when that environment is disturbed e g through storms fires volcanic eruptions etc some species may lose components of their competitive advantage which were useful in the previous version of the environment Stabilizing mechanisms edit Stabilizing mechanisms promote coexistence by concentrating intraspecific competition relative to interspecific competition In other words these mechanisms encourage an individual to compete more with other individuals of its own species rather than with individuals of other species Resource partitioning a type of niche differentiation is a stabilizing mechanism because interspecific competition is reduced when different species primarily compete for different resources Similarly if species are differently affected by environmental variation e g soil type rainfall timing etc this can create a stabilizing mechanism see the storage effect Stabilizing mechanisms increase the low density growth rate of all species citation needed Chesson s categories of stabilizing mechanisms edit In 1994 Chesson proposed that all stabilizing mechanisms could be categorized into four categories 3 4 These mechanisms are not mutually exclusive and it is possible for all four to operate in any environment at a given time Variation independent mechanisms also called fluctuation independent mechanisms are any stabilizing mechanism that functions within a local place and time 3 4 Resource partitioning predator partitioning and frequency dependent predation are three classic examples of variation independent mechanisms When a species is at very low density individuals gain an advantage because they are less constrained by competition across the landscape For example under frequency dependent predation a species is less likely to be consumed by predators when they are very rare The storage effect occurs when species are affected differently by environmental variation in space or time 3 4 For example coral reef fishes have different reproductive rates in different years plants grow differently in different soil types and desert annual plants germinate at different rates in different years When a species is at low density individuals gain an advantage because they experience less competition in times or locations that they grow best For example if annual plants germinate in different years then when it is a good year to germinate species will be competing predominately with members of the same species Thus if a species becomes rare individuals will experience little competition when they germinate whereas they would experience high competition if they were abundant For the storage effect to function species must be able to store the benefits of a productive time period or area and use it to survive during less productive times or areas 5 This can occur for example if species have a long lived adult stage a seed bank or diapause stage or if they are spread out over the environment A fitness density covariance occurs when species are spread out non uniformly across the landscape 3 Most often it occurs when species are found in different areas For example mosquitoes often lay eggs in different locations and plants who partition habitat are often found predominately where they grow best Species can gain two possible advantages by becoming very rare First because they are physically separated from other species they mainly compete with members of the same species and thus experience less competition when they become very rare Second species are often more able to concentrate in favorable habitat as their densities decline For example if individuals are territorial then members of an abundant species may not have access to ideal habitat however when that species becomes very rare then there may be enough ideal habitat for all of the few remaining individuals The Janzen Connell hypothesis is an excellent example of a stabilizing mechanism that operates in part through fitness density covariance Relative nonlinearity occurs when species benefit in different ways from variation in competitive factors 3 4 For example two species might coexist if one can grow better when resources are rare and the other grows better when resources are abundant Species will be able to coexist if the species which benefits from variation in resources tends to reduce variation in resources For example a species which can rapidly consume excess resources tends to quickly reduce the level of excess resources favoring the other species whereas a species which grows better when resources are rare is more likely to cause fluctuations in resource density favoring the other species 6 Quantifying stabilizing mechanisms edit A general way of measuring the effect of stabilizing mechanisms is by calculating the growth rate of species i in a community as 7 r i b i k i k A displaystyle hat r i b i k i hat k A nbsp where r i displaystyle hat r i nbsp is the long term average growth rate of the species i when at low density Because species are limited from growing indefinitely viable populations have an average long term growth rate of zero Therefore species at low density can increase in abundance when their long term average growth rate is positive b i displaystyle b i nbsp is a species specific factor that reflects how quickly species i responds to a change in competition For example species with faster generation times may respond more quickly to a change in resource density than longer lived species In an extreme scenario if ants and elephants were to compete for the same resources elephant population sizes would change much more slowly to changes in resource density than would ant populations k i k displaystyle k i hat k nbsp is the difference between the fitness of species i when compared to the average fitness of the community excluding species i In the absence of any stabilizing mechanisms species i will only have a positive growth rate if its fitness is above its average competitor i e where this value is greater than zero A displaystyle A nbsp measures the effect of all stabilizing mechanisms acting within this community Example calculation Species competing for resource edit This section may be too technical for most readers to understand Please help improve it to make it understandable to non experts without removing the technical details June 2017 Learn how and when to remove this template message In 2008 Chesson and Kuang showed how to calculate fitness differences and stabilizing mechanisms when species compete for shared resources and competitors Each species j captures resource type l at a species specific rate cjl Each unit of resource captured contributes to species growth by value vl Each consumer requires resources for the metabolic maintenance at rate mi 8 In conjunction consumer growth is decreased by attack from predators Each predator species m attacks species j at rate ajm Given predation and resource capture the density of species i Ni grows at rate1 N j d N j d t l c j l v l R l m a j m P m m j displaystyle frac 1 N j frac dN j dt sum l c jl v l R l sum m a jm P m mu j nbsp where l sums over resource types and m sums over all predator species Each resource type exhibits logistic growth with intrinsic rate of increase rRl and carrying capacity KRl 1 aRl such that growth rate of resource l is1 R l d R l d t r l R 1 a l R R l j c j l N j displaystyle frac 1 R l frac dR l dt r l R left 1 alpha l R R l right sum j c jl N j nbsp Similarly each predator species m exhibits logistic growth in the absence of the prey of interest with intrinsic growth rate rPm and carrying capacity KPm 1 aPm The growth rate of a predator species is also increased by consuming prey species where again the attack rate of predator species m on prey j is ajm Each unit of prey has a value to predator growth rate of w Given these two sources of predator growth the density of predator m Pm has a per capita growth rate1 P m d P m d t r m P 1 a m P P m j w N j a j m displaystyle frac 1 P m frac dP m dt r m P 1 alpha m P P m sum j wN j a jm nbsp where the summation terms is contributions to growth from consumption over all j focal species The system of equations describes a model of trophic interactions between three sets of species focal species their resources and their predators Given this model the average fitness of a species j isk j 1 s j l 1 c j l v l K l R m a j m K m P m i displaystyle k j frac 1 s j left sum l 1 c jl v l K l R sum m a jm K m P mu i right nbsp where the sensitivity to competition and predation iss j l c j l 2 v l K l R r l R m a j m 2 w K m P r m P displaystyle s j sqrt left sum l frac c jl 2 v l K l R r l R sum m frac a jm 2 wK m P r m P right nbsp The average fitness of a species takes into account growth based on resource capture and predation as well as how much resource and predator densities change from interactions with the focal species The amount of niche overlap between two competitors i and j isr l c i l v l c j l a l R r l R m a i m w a j m a m P r m P s i s j displaystyle rho left sum l frac c il v l c jl alpha l R r l R sum m frac a im wa jm alpha m P r m P right s i s j nbsp which represents the amount to which resource consumption and predator attack are linearly related between two competing species i and j This model conditions for coexistence can be directly related to the general coexistence criterion intraspecific competition ajj must be greater than interspecific competition aij The direct expressions for intraspecific and interspecific competition coefficients from the interaction between shared predators and resources area j j s j k j displaystyle alpha jj s j k j nbsp anda i j r s j k i displaystyle alpha ij rho s j k i nbsp Thus when intraspecific competition is greater than interspecific competition a j j gt a i j s j k j gt r s j k i displaystyle alpha jj gt alpha ij frac s j k j gt rho frac s j k i nbsp which for two species leads to the coexistence criteriar lt k 1 k 2 lt 1 r displaystyle rho lt frac k 1 k 2 lt frac 1 rho nbsp Notice that in the absence of any niche differences i e r 1 species cannot coexist Empirical evidence editA 2012 study 9 reviewed different approaches which tested coexistence theory and identified three main ways to separate the contributions of stabilizing and equalizing mechanisms within a community These are Experimental manipulations which involved determining the effect of relative fitness or stabilizing mechanisms by manipulating resources or competitive advantages Trait Phylogeny Environment relationships in which the phylogeny of members of a set of communities can be tested for evidence of trait clustering which would suggest that certain traits are important and perhaps necessary to thrive in that environment or trait overdispersion which would suggest a high ability of species to exclude close relatives Such tests have been widely used although they have also been criticized as simplistic and flawed 10 Demographic analyses which can be used to recognize frequency or density dependent processes simply by measuring the number and per capita growth rates of species in natural communities over time If such processes are operating the per capita growth rate would vary with the number of individuals in species comprising the community A 2010 review 11 argued that an invasion analysis should be used as the critical test of coexistence In an invasion analysis one species termed the invader is removed from the community and then reintroduced at a very low density If the invader shows positive population growth then it cannot be excluded from the community If every species has a positive growth rate as an invader then those species can stably coexist An invasion analysis could be performed using experimental manipulation or by parameterizing a mathematical model The authors argued that in the absence of a full scale invasion analysis studies could show some evidence for coexistence by showing that a trade off produced negative density dependence at the population level The authors reviewed 323 papers from 1972 to May 2009 and claimed that only 10 of them met the above criteria 7 performing an invasion analysis and 3 showing some negative density dependence However an important caveat is that invasion analysis may not always be sufficient for identifying stable coexistence For example priority effects or Allee effects may prevent species from successfully invading a community from low density even if they could persist stably at a higher density Conversely high order interactions in communities with many species can lead to complex dynamics following an initially successful invasion potentially preventing the invader from persisting stably in the long term 12 For example an invader that can only persist when a particular resident species is present at high density could alter community structure following invasion such that that resident species density declines or that it goes locally extinct thereby preventing the invader from successfully establishing in the long term Neutral theory and coexistence theory editMain article Unified neutral theory of biodiversity The 2001 Neutral theory by Stephen P Hubbell 13 attempts to model biodiversity through a migration speciation extinction balance rather through selection 14 It assumes that all members within a guild are inherently the same and that changes in population density are a result of random births and deaths Particular species are lost stochastically through a random walk process but species richness is maintained via speciation or external migration Neutral theory can be seen as a particular case of coexistence theory it represents an environment where stabilizing mechanisms are absent i e A 0 displaystyle A 0 nbsp and there are no differences in average fitness i e k i k 0 displaystyle k i hat k 0 nbsp for all species 15 It has been hotly debated how close real communities are to neutrality Few studies have attempted to measure fitness differences and stabilizing mechanisms in plant communities for example in 2009 16 or in 2015 17 These communities appear to be far from neutral and in some cases stabilizing effects greatly outweigh fitness differences Cultural coexistence theory editCultural Coexistence Theory CCT also called Social ecological Coexistence Theory expands on coexistence theory to explain how groups of people with shared interests in natural resources e g a fishery can come to coexist sustainably 18 Cultural Coexistence Theory draws on work by anthropologists such as Frederik Barth and John Bennett both of whom studied the interactions among culture groups on shared landscapes In addition to the core ecological concepts described above which CCT summarizes as limited similarity limited competition and resilience CCT argues the following features are essential for cultural coexistence Adaptability describes the ability of people to respond to change or surprise It is essential to CCT because it helps capture the importance of human agency Pluralism describes where people value cultural diversity and recognize the fundamental rights of people not like them to live in the same places and access shared resources Equity as used in CCT describes whether social institutions exist that ensure that people s basic human rights including the ability to meet basic needs are protected and whether people are protected from being marginalized in society Cultural Coexistence Theory fits in under the broader area of sustainability science common pool resources theory and conflict theory References edit Chesson Peter 2000 Mechanisms of maintenance of species diversity Annual Review of Ecology and Systematics 31 343 366 doi 10 1146 annurev ecolsys 31 1 343 S2CID 403954 Tilman David 1980 09 01 Resources A Graphical Mechanistic Approach to Competition and Predation The American Naturalist 116 3 362 393 doi 10 1086 283633 JSTOR 2463311 S2CID 85411812 a b c d e Chesson P 2000 General Theory of Competitive Coexistence in Spatially Varying Environments Theoretical Population Biology 58 3 211 37 doi 10 1006 tpbi 2000 1486 PMID 11120650 a b c d Chesson Peter June 1994 Multispecies Competition in Variable Environments Theoretical Population Biology 45 3 227 276 doi 10 1006 Tpbi 1994 1013 Chesson Peter Warner Robert 1981 Environmental Variability Promotes Coexistence in Lottery Competitive Systems The American Naturalist 117 6 923 943 doi 10 1086 283778 S2CID 84164336 Armstrong Robert A McGehee Richard February 1980 Competitive Exclusion The American Naturalist 115 2 151 170 doi 10 1086 283553 S2CID 222329963 Chesson Peter January 2008 Chapter 6 Quantifying and testing species coexistence mechanisms In Valladares F Camacho A Elosegui A Garcia C Estrada M Senar J Gili J eds Unity in Diversity A Conference on Ecology after the Legacy of Ramon Margalef Bilbao Fundacion BBVA pp 119 164 ISBN 978 84 96515 53 6 Chesson Peter Kuang Jessica J 2008 01 01 The interaction between predation and competition Nature 456 7219 235 8 Bibcode 2008Natur 456 235C doi 10 1038 nature07248 PMID 19005554 S2CID 4342701 HilleRisLambers J Adler P B Harpole W S Levine J M Mayfield M M 2012 Rethinking Community Assembly through the Lens of Coexistence Theory Annual Review of Ecology Evolution and Systematics 43 227 248 doi 10 1146 annurev ecolsys 110411 160411 Mayfield M M Levine J M 2010 Opposing effects of competitive exclusion on the phylogenetic structure of communities Ecology Letters 13 9 1085 93 Bibcode 2010EcolL 13 1085M doi 10 1111 j 1461 0248 2010 01509 x PMID 20576030 Seipielski Adam McPeek Mark 2010 On the evidence for species coexistence A critique of the coexistence program Ecology 91 11 3153 3164 Bibcode 2010Ecol 91 3153S doi 10 1890 10 0154 1 PMID 21141177 S2CID 24771175 Levine Jonathan Bascompte Jordi Adler Peter Allesina Stefano 2017 Beyond pairwise mechanisms of species coexistence in complex communities PDF Nature 546 7656 56 64 Bibcode 2017Natur 546 56L doi 10 1038 nature22898 PMID 28569813 S2CID 205257096 Hubbell Stephen P 2001 The Unified Neutral Theory of Biodiversity and Biogeography MPB 32 Princeton Princeton University Press ISBN 9781400837526 Vellend Mark 2010 Conceptual synthesis in community ecology The Quarterly Review of Biology 85 2 183 206 doi 10 1086 652373 PMID 20565040 S2CID 10026873 Adler Peter B HilleRisLambers Janneke Levine Jonathan M February 2007 A niche for neutrality Ecology Letters 10 2 95 104 Bibcode 2007EcolL 10 95A doi 10 1111 J 1461 0248 2006 00996 X PMID 17257097 Levine Jonathan M HilleRisLambers Janneke 12 August 2009 The importance of niches for the maintenance of species diversity Nature 461 7261 254 257 Bibcode 2009Natur 461 254L doi 10 1038 Nature08251 PMID 19675568 S2CID 1768121 Chu Chengjin Adler Peter B August 2015 Large niche differences emerge at the recruitment stage to stabilize grassland coexistence Ecological Monographs 85 3 373 392 Bibcode 2015EcoM 85 373C doi 10 1890 14 1741 1 Loring Philip A 23 January 2016 Toward a Theory of Coexistence in Shared Social ecological Systems The Case of Cook Inlet Salmon Fisheries Human Ecology 44 2 153 165 doi 10 1007 s10745 016 9806 0 PMC 4832003 PMID 27122652 Retrieved from https en wikipedia org w index php title Coexistence theory amp oldid 1213458157, wikipedia, wiki, book, books, library,

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