Coexistence theory

Last updated
Coexistence theory attempts to explain the paradox of the plankton -- how can ecologically similar species coexist without competitively excluding each other? Diatoms through the microscope.jpg
Coexistence theory attempts to explain the paradox of the plankton -- how can ecologically similar species coexist without competitively excluding each other?

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).

Contents

Types of coexistence mechanisms

Groundhog and a raccoon eating together Coexist animals.jpg
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

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

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

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

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

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

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

The 2008 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

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.

Related Research Articles

<span class="mw-page-title-main">Theoretical ecology</span>

Theoretical ecology is the scientific discipline devoted to the study of ecological systems using theoretical methods such as simple conceptual models, mathematical models, computational simulations, and advanced data analysis. Effective models improve understanding of the natural world by revealing how the dynamics of species populations are often based on fundamental biological conditions and processes. Further, the field aims to unify a diverse range of empirical observations by assuming that common, mechanistic processes generate observable phenomena across species and ecological environments. Based on biologically realistic assumptions, theoretical ecologists are able to uncover novel, non-intuitive insights about natural processes. Theoretical results are often verified by empirical and observational studies, revealing the power of theoretical methods in both predicting and understanding the noisy, diverse biological world.

<span class="mw-page-title-main">Mutualism (biology)</span> Mutually beneficial interaction between species

Mutualism describes the ecological interaction between two or more species where each species has a net benefit. Mutualism is a common type of ecological interaction, one that can come from a parasitic interaction. Prominent examples include most vascular plants engaged in mutualistic interactions with mycorrhizae, flowering plants being pollinated by animals, vascular plants being dispersed by animals, and corals with zooxanthellae, among many others. Mutualism can be contrasted with interspecific competition, in which each species experiences reduced fitness, and exploitation, or parasitism, in which one species benefits at the expense of the other.

<span class="mw-page-title-main">Ecological niche</span> Fit of a species living under specific environmental conditions

In ecology, a niche is the match of a species to a specific environmental condition. It describes how an organism or population responds to the distribution of resources and competitors and how it in turn alters those same factors. "The type and number of variables comprising the dimensions of an environmental niche vary from one species to another [and] the relative importance of particular environmental variables for a species may vary according to the geographic and biotic contexts".

This glossary of ecology is a list of definitions of terms and concepts in ecology and related fields. For more specific definitions from other glossaries related to ecology, see Glossary of biology, Glossary of evolutionary biology, and Glossary of environmental science.

In population ecology and economics, maximum sustainable yield (MSY) is theoretically, the largest yield that can be taken from a species' stock over an indefinite period. Fundamental to the notion of sustainable harvest, the concept of MSY aims to maintain the population size at the point of maximum growth rate by harvesting the individuals that would normally be added to the population, allowing the population to continue to be productive indefinitely. Under the assumption of logistic growth, resource limitation does not constrain individuals' reproductive rates when populations are small, but because there are few individuals, the overall yield is small. At intermediate population densities, also represented by half the carrying capacity, individuals are able to breed to their maximum rate. At this point, called the maximum sustainable yield, there is a surplus of individuals that can be harvested because growth of the population is at its maximum point due to the large number of reproducing individuals. Above this point, density dependent factors increasingly limit breeding until the population reaches carrying capacity. At this point, there are no surplus individuals to be harvested and yield drops to zero. The maximum sustainable yield is usually higher than the optimum sustainable yield and maximum economic yield.

Liebig's law of the minimum, often simply called Liebig's law or the law of the minimum, is a principle developed in agricultural science by Carl Sprengel (1840) and later popularized by Justus von Liebig. It states that growth is dictated not by total resources available, but by the scarcest resource. The law has also been applied to biological populations and ecosystem models for factors such as sunlight or mineral nutrients.

The Lotka–Volterra equations, also known as the Lotka–Volterra predator–prey model, are a pair of first-order nonlinear differential equations, frequently used to describe the dynamics of biological systems in which two species interact, one as a predator and the other as prey. The populations change through time according to the pair of equations:

<span class="mw-page-title-main">Unified neutral theory of biodiversity</span> Theory of evolutionary biology

The unified neutral theory of biodiversity and biogeography is a theory and the title of a monograph by ecologist Stephen P. Hubbell. It aims to explain the diversity and relative abundance of species in ecological communities. Like other neutral theories of ecology, Hubbell assumes that the differences between members of an ecological community of trophically similar species are "neutral", or irrelevant to their success. This implies that niche differences do not influence abundance and the abundance of each species follows a random walk. The theory has sparked controversy, and some authors consider it a more complex version of other null models that fit the data better.

The Allee effect is a phenomenon in biology characterized by a correlation between population size or density and the mean individual fitness of a population or species.

<span class="mw-page-title-main">Intraspecific competition</span> Species members compete for resources

Intraspecific competition is an interaction in population ecology, whereby members of the same species compete for limited resources. This leads to a reduction in fitness for both individuals, but the more fit individual survives and is able to reproduce. By contrast, interspecific competition occurs when members of different species compete for a shared resource. Members of the same species have rather similar requirements for resources, whereas different species have a smaller contested resource overlap, resulting in intraspecific competition generally being a stronger force than interspecific competition.

The paradox of enrichment is a term from population ecology coined by Michael Rosenzweig in 1971. He described an effect in six predator–prey models where increasing the food available to the prey caused the predator's population to destabilize. A common example is that if the food supply of a prey such as a rabbit is overabundant, its population will grow unbounded and cause the predator population to grow unsustainably large. That may result in a crash in the population of the predators and possibly lead to local eradication or even species extinction.

<span class="mw-page-title-main">Competition (biology)</span> Interaction where the fitness of one organism is lowered by the presence of another organism

Competition is an interaction between organisms or species in which both require a resource that is in limited supply. Competition lowers the fitness of both organisms involved since the presence of one of the organisms always reduces the amount of the resource available to the other.

<span class="mw-page-title-main">Interspecific competition</span> Form of competition

Interspecific competition, in ecology, is a form of competition in which individuals of different species compete for the same resources in an ecosystem. This can be contrasted with mutualism, a type of symbiosis. Competition between members of the same species is called intraspecific competition.

The storage effect is a coexistence mechanism proposed in the ecological theory of species coexistence, which tries to explain how such a wide variety of similar species are able to coexist within the same ecological community or guild. The storage effect was originally proposed in the 1980s to explain coexistence in diverse communities of coral reef fish, however it has since been generalized to cover a variety of ecological communities. The theory proposes one way for multiple species to coexist: in a changing environment, no species can be the best under all conditions. Instead, each species must have a unique response to varying environmental conditions, and a way of buffering against the effects of bad years. The storage effect gets its name because each population "stores" the gains in good years or microhabitats (patches) to help it survive population losses in bad years or patches. One strength of this theory is that, unlike most coexistence mechanisms, the storage effect can be measured and quantified, with units of per-capita growth rate.

Relative species abundance is a component of biodiversity and is a measure of how common or rare a species is relative to other species in a defined location or community. Relative abundance is the percent composition of an organism of a particular kind relative to the total number of organisms in the area. Relative species abundances tend to conform to specific patterns that are among the best-known and most-studied patterns in macroecology. Different populations in a community exist in relative proportions; this idea is known as relative abundance.

Limiting similarity is a concept in theoretical ecology and community ecology that proposes the existence of a maximum level of niche overlap between two given species that will allow continued coexistence.

Relative nonlinearity is a coexistence mechanism that maintains species diversity via differences in the response to and effect on variation in resource density or some other factor mediating competition. Relative nonlinearity depends on two processes: 1) species have to differ in the curvature of their responses to resource density and 2) the patterns of resource variation generated by each species must favor the relative growth of another species. In its most basic form, one species grows best under equilibrium competitive conditions and another performs better under variable competitive conditions. Like all coexistence mechanisms, relative nonlinearity maintains species diversity by concentrating intraspecific competition relative to interspecific competition. Because resource density can be variable, intraspecific competition is the reduction of per-capita growth rate under variable resources generated by conspecifics. Interspecific competition is the reduction of per-capita growth rate under variable resources generated by heterospecifics. Like some other coexistence mechanisms, relative nonlinearity can allow coexistence of at least two species on a single resource.

The R* rule is a hypothesis in community ecology that attempts to predict which species will become dominant as the result of competition for resources. The hypothesis was formulated by American ecologist David Tilman. It predicts that if multiple species are competing for a single limiting resource, then whichever species can survive at the lowest equilibrium resource level can outcompete all other species. If two species are competing for two resources, then coexistence is only possible if each species has a lower R* on one of the resources. For example, two phytoplankton species may be able to coexist if one is more limited by nitrogen, and the other is more limited by phosphorus.

The fitness-density covariance is a coexistence mechanism that can allow similar species to coexist because they are in different locations. This effect will be the strongest if species are completely segregated, but can also work if their populations overlap somewhat. If a fitness-density covariance is operating, then when a species becomes very rare, its population will shift to predominantly locations with favorable conditions. Similarly, when a species becomes very common, then conditions will worsen where they are most common, and they will spread into areas where conditions are less favorable. This negative feedback can help species avoid being driven extinct by competition, and it can prevent stronger species from becoming too common and crowding out other species.

<span class="mw-page-title-main">Competition–colonization trade-off</span>

In ecology, the competition–colonization trade-off is a stabilizing mechanism that has been proposed to explain species diversity in some biological systems, especially those that are not in equilibrium. In which case some species are particularly good at colonizing and others have well-established survival abilities. The concept of the competition-colonization trade-off was originally proposed by Levins and Culver, the model indicated that two species could coexist if one had impeccable competition skill and the other was excellent at colonizing. The model indicates that there is typically a trade-off, in which a species is typically better at either competing or colonizing. A later model, labelled The Lottery Model was also proposed, in which interspecific competition is accounted for within the population.

References

  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. 1 2 3 4 5 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. 1 2 3 4 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. (2008). 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.