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Coexistence theory

Coexistence theory, often referred to as modern coexistence theory (MCT), is a foundational framework in ecology that elucidates the mechanisms enabling multiple species to persist indefinitely in shared habitats despite interspecific competition for limited resources. It posits that stable coexistence requires a balance between stabilizing mechanisms, which arise from niche differences that allow rarer species to grow faster than dominant ones when infrequent, and equalizing mechanisms, which diminish fitness disparities to prevent any single species from outcompeting others. This theory, formalized through the analysis of invasion growth rates—the per-capita growth rate of a focal species at low density while competitors are at equilibrium—provides a quantitative basis for predicting community assembly and diversity maintenance.^[1] Pioneered by ecologist Peter Chesson in his seminal 2000 review, MCT builds on classical ecological principles like the competitive exclusion principle, which suggests that superior competitors should displace others, by incorporating fluctuations in environmental conditions, species interactions, and demographic stochasticity as key drivers of coexistence. Stabilizing mechanisms include resource partitioning, where species exploit distinct niches, and frequency-dependent predation or disease that disproportionately affect common species, thereby promoting negative density dependence. Equalizing mechanisms, in contrast, operate through factors like temporal variability in birth and death rates or spatial heterogeneity that level competitive advantages, ensuring no species has an overwhelming edge.^[2] The theory's invasion criterion states that coexistence occurs when each species' invasion growth rate exceeds zero, a condition met only if stabilizing effects outweigh fitness differences.^[1] MCT has broad applications across ecological subfields, including restoration ecology, where it guides interventions by assessing whether target species can invade restored communities based on niche and fitness metrics.^[3] In microbial ecology, it disentangles fluctuation-independent processes like resource competition from dependent ones such as predation, aiding predictions of microbiome stability.^[4] The framework also integrates with priority effects—the influence of species arrival order on community outcomes—by linking them to frequency-dependent interactions that align with stabilizing dynamics.^[2] Recent extensions emphasize community assembly processes, using invasion graphs to map transitions between subcommunities and identify exclusion risks in diverse systems like plant or yeast assemblages.^[1] By prioritizing empirical measurement of invasion rates and mechanism decomposition, MCT remains a cornerstone for testing hypotheses on biodiversity persistence amid global change.^[5]

Fundamentals

Definition and principles

Coexistence theory in ecology investigates the conditions under which multiple species that overlap in resource use can persist indefinitely within the same community, thereby maintaining biodiversity over long timescales.^[6] This framework stands in contrast to the competitive exclusion principle, also known as Gause's law, which posits that two species competing for the same resources cannot coexist stably if one has even a slight competitive advantage, leading to the exclusion of the inferior competitor.^[7] Coexistence thus requires specific ecological processes that counteract such exclusionary dynamics, ensuring that no single species dominates the community.^[6] At its core, long-term species persistence in coexistence theory depends on mechanisms that prevent competitive exclusion, operating under the fundamental assumption of density-dependent competition where population growth rates decline as densities increase due to resource limitation.^[6] These mechanisms are broadly distinguished into equalizing processes, which reduce fitness inequalities between species in the short term by minimizing differences in competitive ability, and stabilizing processes, which promote long-term coexistence by enhancing species' abilities to recover from rarity through negative feedback on their own densities relative to others.^[6] A key prerequisite is the prevalence of intraspecific competition—interactions within the same species—over interspecific competition—interactions between different species—as stronger intraspecific effects foster self-limitation and prevent any one species from overwhelming others.^[6] Central concepts in the theory include the differential strengths of intraspecific versus interspecific competition, which underpin the potential for stable equilibria, and the roles of environmental heterogeneity—such as spatial or temporal variability in conditions—and species-specific traits, like resource acquisition strategies or dispersal abilities, in facilitating niche differentiation that allows coexistence.^[8] These elements enable species to exploit resources or respond to the environment in ways that reduce overlap and competitive pressure. The theoretical foundations of coexistence trace back to the Lotka-Volterra competition models developed in the 1920s and 1930s, which formalized interspecific interactions through differential equations describing population dynamics under competition.^[6] These early models highlighted conditions for stable coexistence but were refined in modern ecology from the 1970s onward to incorporate more realistic ecological complexities, such as fluctuating environments and trait-mediated interactions.^[8]

Historical development

The foundations of coexistence theory emerged in the early 20th century with the development of the Lotka-Volterra equations, which modeled interspecies competition and demonstrated the potential for competitive exclusion when species overlap significantly in resource use.^[9] These deterministic models, extended to competition scenarios, predicted that one species would dominate under constant conditions, setting the stage for understanding limits to diversity. In 1934, G.F. Gause's laboratory experiments with Paramecium caudatum and Paramecium aurelia provided empirical support, showing exclusion in mixed cultures with uniform resources, thus formalizing the competitive exclusion principle. Mid-20th-century advances shifted focus toward mechanisms enabling diversity despite competition. Robert MacArthur's 1958 study of warbler foraging behaviors introduced niche partitioning, suggesting that species coexist by exploiting distinct resources within shared habitats.^[10] This idea gained prominence through G.E. Hutchinson's 1961 "paradox of the plankton," which questioned how numerous phytoplankton species persist in seemingly resource-limited aquatic environments, challenging the strict application of exclusion principles and prompting exploration of environmental heterogeneity.^[11] The 1970s saw heated debates on niche-based versus neutral processes, exemplified by Robert May's 1973 analysis, which used random matrix models to argue that increasing species interactions in complex communities often reduce stability, influencing discussions on diversity maintenance.^[12] Post-1980s developments incorporated stochasticity to address variability in real ecosystems, marking a transition from purely deterministic frameworks. Influential figures like Robert MacArthur, Robert May, and Peter Chesson drove this evolution, with Chesson's 1994 model of multispecies competition in fluctuating environments integrating invasion analysis to evaluate coexistence potential through long-term growth rates.^[13] In the 1990s and 2000s, Chesson synthesized these ideas, distinguishing stabilizing mechanisms that promote negative density dependence from equalizing mechanisms that reduce fitness differences, as detailed in his seminal 2000 review. These 1970s debates on niche versus neutral processes laid groundwork for later neutral theory formulations, though coexistence theory emphasized niche roles.

Mechanisms of coexistence

Equalizing mechanisms

Equalizing mechanisms in coexistence theory are ecological processes that diminish differences in the average fitness of competing species, thereby slowing competitive exclusion and enabling species to persist together for extended periods by rendering their demographic performances more equivalent despite intrinsic disparities in competitive abilities. These mechanisms operate by reducing the long-term growth rate advantages of superior competitors, creating a more level playing field without necessarily altering the relative impacts of intra- versus interspecific interactions. As articulated by Chesson (2000), equalizing mechanisms are crucial because they counteract large fitness inequalities that could otherwise overwhelm the benefits of other coexistence processes.^[6] Prominent biological processes underlying equalizing mechanisms include trade-offs in life-history traits, where species exhibit complementary strengths across varying conditions—for instance, one species may outperform in resource-scarce environments while another excels in resource-rich ones, leading to averaged fitness similarities when resources fluctuate spatially or temporally. Spatial heterogeneity in resources or environmental conditions can also equalize fitness by allowing species to achieve comparable overall performance across a landscape, as differential success in distinct patches offsets advantages elsewhere. Temporal environmental fluctuations similarly contribute by periodically favoring different species in a way that balances their long-term average growth rates, independent of their relative abundances. Frequency-dependent predation, such as when predators preferentially target more abundant prey species, can function as an equalizing mechanism by curtailing the dominance of common species, although it often exhibits dual equalizing and stabilizing properties.^[14]^[15] However, equalizing mechanisms alone cannot sustain long-term stable coexistence, as they merely narrow fitness gaps without generating the negative frequency dependence required to favor rare species; instead, they complement stabilizing mechanisms by setting the preconditions for such dynamics to take effect.

Stabilizing mechanisms

Stabilizing mechanisms in species coexistence theory refer to ecological processes that generate negative frequency dependence, whereby the per capita growth rate of a rare species exceeds that of a common one, thereby promoting long-term persistence of multiple species at stable equilibria. These mechanisms arise when intraspecific competition is stronger than interspecific competition, contrasting with destabilizing positive frequency dependence that drives competitive exclusion. In essence, they enhance niche differentiation, allowing species to coexist even when average fitness differences exist, provided the stabilizing forces are sufficiently strong.^[16] Key types of stabilizing mechanisms include resource partitioning, where species reduce overlap in resource use, such as through differences in optimal foraging niches or habitat preferences, thereby limiting interspecific interference. For instance, Darwin's finches on the Galápagos Islands partition seeds by beak size, with larger-beaked species targeting harder seeds and smaller-beaked ones focusing on softer varieties, fostering coexistence via reduced competition. Another prominent type involves differential responses to environmental fluctuations, exemplified by the storage effect, in which species-specific buffering against variability—often through persistent life stages like seed banks—allows rare species to capitalize on favorable periods while surviving unfavorable ones. This mechanism is particularly evident in desert annual plants, where one species may germinate primarily after heavy rainfall events, storing resources in seeds to endure dry spells, while another thrives in milder conditions with different recruitment cues. A classic example of a stabilizing mechanism is the Janzen-Connell effect in tropical forests, where host-specific pathogens and herbivores impose higher mortality on seedlings near conspecific adults, disproportionately impacting denser, more common species and generating negative frequency dependence that favors rare species and promotes diverse seedling establishment (Janzen 1970; Connell 1971). This density-dependent mortality ensures stronger intraspecific than interspecific competition, preventing rapid exclusion.^[6] A specific concept within stabilizing mechanisms is relative nonlinearity in competition responses, where the per capita competitive effect on a species varies nonlinearly with competitor density, often benefiting rare invaders by altering interaction strengths at low abundances. Biological examples of stabilizing mechanisms include competitive trade-offs tied to environmental conditions, such as one plant species outperforming others in wet soils due to specialized root morphology, while a trade-off partner dominates in drier habitats through efficient water conservation.^[17] Predator-mediated stabilization also plays a role, particularly through frequency-dependent predation, where predators disproportionately target abundant prey, thereby reducing the dominance of common species and aiding rare ones via apparent competition dynamics. Conceptually, these mechanisms ensure the invasibility criterion—each species can increase when rare—and establish a threshold for coexistence wherein stabilizing benefits must surpass any equalizing deficits from unequal average fitness. While equalizing mechanisms primarily mitigate initial fitness disparities, stabilizing ones are crucial for maintaining dynamic stability over time.^[16]

Mathematical frameworks

Chesson's categories of stabilizing mechanisms

Peter Chesson's framework for understanding stabilizing mechanisms in species coexistence, introduced in 1994 and expanded in 2000, provides a structured taxonomy that categorizes these mechanisms into three primary types based on their effects on invasion growth rates—the long-term growth rates of rare species invading a community dominated by a resident species.^[18]^[19] These categories emphasize how niche differences and environmental variability can promote coexistence by making intraspecific competition stronger than interspecific competition on average, thereby allowing rare species to recover from low densities.^[19] Each type is derived from analyses of invasion dynamics, where positive invasion growth rates for all species indicate stable coexistence, and the framework indirectly incorporates equalizing mechanisms by considering relative fitness differences alongside stabilization.^[18] The first category, resource partitioning or stabilizing niche differences, arises when species exploit resources in disproportionately different ways, leading to reduced interspecific overlap in resource use compared to intraspecific overlap.^[19] This mechanism stabilizes coexistence by allowing each species to limit its own population more effectively through self-competition for preferred resources, while competitors affect them less due to niche separation.^[19] Niche overlap metrics, such as those measuring the similarity in resource consumption proportions between species, quantify the strength of this stabilization, with lower overlap promoting higher invasion growth rates.^[19] A representative example is found in desert annual plant communities, where species partition soil nutrients or water availability differently, enabling persistent coexistence despite similar overall habitats.^[19] The second category, the storage effect, operates through temporal fluctuations in the environment or population densities, coupled with species-specific responses that create covariance between environmental conditions and the intensity of interspecific competition.^[19] In favorable periods for a species, it experiences reduced competition from others if the latter perform poorly, allowing the focal species to "store" reproductive output (such as seeds or long-lived stages) for survival during unfavorable times.^[20] This mechanism enhances invasion growth rates by buffering rare species against extinction during downturns, provided species have differing phenologies or tolerances that desynchronize their competitive impacts.^[19] The storage effect is quantified by the term \Delta I = \gamma \Cov(E_i(t), C_i(t)), where \gamma measures the nonadditivity of fitness to environment and competition, and negative covariance (favorable environment coinciding with low competition) for the invader promotes stabilization. Classic examples include desert annual plants, where variable rainfall leads to species-specific recruitment success, as demonstrated in lottery competition models where seedlings compete for fixed adult sites.^[20]^[19] The third category, relative nonlinearity or fitness-density covariance, stems from nonlinear responses in species fitness to changes in their own or competitors' densities, often driven by trade-offs in competitive abilities across density regimes.^[19] Here, a species may have higher fitness at low densities relative to competitors but lower at high densities, or vice versa, creating a covariance between fitness and total community density that favors coexistence when rare species benefit disproportionately.^[19] This nonlinearity stabilizes communities by promoting recovery of rare invaders before density escalates to disadvantage them, integrating elements of frequency-dependent selection.^[18] In desert annual plant systems, this mechanism manifests through density-dependent growth rates influenced by resource depletion, where superior competitors at high densities are offset by inferior performance at low densities, supporting overall diversity.^[19]

Quantifying coexistence mechanisms

Quantifying coexistence mechanisms relies on mathematical metrics derived from ecological models to assess the balance between stabilizing and equalizing processes that permit long-term species persistence. These tools, primarily developed within frameworks like the Lotka-Volterra competition equations and extended by modern coexistence theory, evaluate invasibility and the relative strengths of niche differentiation versus fitness asymmetries. By partitioning invasion growth rates into mechanistic components, researchers can predict community outcomes and attribute diversity to specific processes. A foundational metric is the invasion growth rate, which measures a species' long-term per capita growth when rare in a resident community at equilibrium. In the Lotka-Volterra competition model, this is expressed as

\rho_i = r_i - \sum_j \alpha_{ij} N_j,

where r_i is the intrinsic growth rate of species i, \alpha_{ij} is the per capita competitive effect of species j on i, and N_j is the equilibrium abundance of j. Positive \rho_i > 0 indicates invasibility, a necessary condition for stable coexistence across all species; derivation follows from linearizing the Lotka-Volterra dynamics around the resident equilibrium, where the rare species experiences negligible self-limitation. Stabilizing mechanisms are quantified through indices that capture how niche differences promote recovery from rarity. For the storage effect, the contribution to the difference in invasion rates between resident and invader arises from species-specific responses to environmental fluctuations, generating negative frequency dependence.^[19] Equalizing mechanisms, which mitigate fitness differences to prevent exclusion, are often measured by the log fitness ratio \delta = \log(r_1 / r_2), quantifying demographic equivalence between two species; smaller absolute values of \delta reflect reduced competitive dominance, allowing closer approach to neutrality without requiring exact equivalence. This metric stems from comparing intrinsic growth rates in isolation, integrated into broader invasion analyses to assess asymmetry. For two-species systems in classical competition theory, stable coexistence requires intraspecific competition to exceed interspecific competition, given by \alpha_{12} < K_1 / K_2 and \alpha_{21} < K_2 / K_1, where K_i are carrying capacities; in normalized units (K_i = 1, \alpha_{ii} = 1), this simplifies to \alpha_{12} < 1 and \alpha_{21} < 1. This ensures mutual invasibility, derived from the eigenvalues of the Jacobian matrix in the Lotka-Volterra system having negative real parts at the coexistence equilibrium. More generally, coexistence holds when stabilizing variance exceeds fitness differences, as stabilizing effects amplify niche partitioning to overcome equalizing deficits. Stochastic extensions incorporate demographic noise into these frameworks, particularly via Levins' metapopulation models, where random local extinctions and colonizations replace deterministic rates; coexistence persists if colonization rates exceed extinction thresholds under variability, extending invasion criteria to patchy, uncertain environments.^[21] These quantification methods allow decomposition of observed species diversity into stabilizing and equalizing contributions, revealing how mechanisms interact to sustain communities.

Empirical support

Field and experimental evidence

Field studies have provided substantial evidence for coexistence mechanisms in natural ecosystems, particularly through the lens of environmental fluctuations and host-specific interactions. In desert annual plant communities, the storage effect has been demonstrated as a key stabilizing mechanism, where interannual variability in rainfall allows species to persist via differential responses to moisture availability and seed dormancy. For instance, Chesson et al. (2004) analyzed long-term data from arid environments, showing that resource pulses from erratic rainfall promote coexistence by enabling species-specific recovery during favorable periods, preventing competitive exclusion. Similarly, in tropical forests, the Janzen-Connell hypothesis explains high tree diversity through density-dependent mortality from specialized pathogens and herbivores, which disproportionately affect conspecifics near parent trees. Terborgh (2012) reviewed field observations from Amazonian plots, confirming that these enemy-mediated effects maintain hyperdiversity by reducing recruitment success of common species, thus stabilizing community composition over decades. Experimental evidence from controlled settings further corroborates these mechanisms, highlighting the role of predation in facilitating coexistence. Laboratory microcosms using protists and bacteria have illustrated frequency-dependent predation, where predators preferentially attack abundant prey species, promoting persistence of rarer ones. Lawler (1993) conducted experiments with bacterivorous and predatory protists, finding that such predation dynamics led to stable coexistence in multi-species assemblages by equalizing competitive advantages through selective pressure on dominant populations. Classic studies on flour beetles (Tribolium spp.) in controlled arenas demonstrated how environmental conditions can tip outcomes from exclusion to coexistence under interspecific competition. Park (1948) initiated mixed cultures varying temperature, humidity, and initial densities, revealing that cannibalic interactions and resource overlap often resulted in exclusion of one species, but certain conditions allowed long-term coexistence via subtle niche differences. Earlier foundational examples underscore the resolution of apparent paradoxes in coexistence through spatial and resource heterogeneity. The "paradox of the plankton," which questions how diverse phytoplankton species coexist on few limiting nutrients, has been addressed by patchiness in ocean currents and mixing, preventing uniform competitive dominance. Steele (1974) integrated field data from marine surveys, arguing that spatial variability in nutrient distribution and grazing maintains diversity by creating transient refugia for inferior competitors. In terrestrial systems, grassland experiments have shown niche partitioning along resource gradients as a stabilizing force. Tilman's (1982) long-term manipulations at Cedar Creek Natural History Area demonstrated that plant species coexist by exploiting different ratios of light, nitrogen, and water, with diversity increasing as resource supply heterogeneity allows partitioning without exclusion. Across these studies, stabilizing mechanisms, such as storage effects and niche partitioning, emerge as dominant in maintaining diversity in complex, species-rich systems like forests and grasslands, where they counteract fitness inequalities. In contrast, equalizing mechanisms, including herbivory, play a prominent role in insect communities by reducing dominance of superior competitors through shared predation pressure. A meta-analysis of competition in plant communities from 35 studies confirmed the prevalence of stabilizing effects, with intraspecific competition exceeding interspecific in the majority of species pairs analyzed.^[22] This underscores their broad empirical support in promoting long-term coexistence.

Challenges in empirical testing

Empirical testing of coexistence theory is hindered by observational biases that arise from the slow dynamics of natural communities. Detecting competitive exclusion, a key process underlying coexistence predictions, often requires monitoring over long timescales, as the time to exclusion can extend for decades or even centuries when species have similar competitive abilities or when equalizing mechanisms are strong.^[23] Short-term observational data exacerbate this issue by making it challenging to differentiate stabilizing niche mechanisms from neutral ecological drift, where random fluctuations in population sizes can produce patterns resembling coexistence without underlying fitness differences.^[24] Experimental approaches to validate coexistence theory encounter constraints related to scale and confounding variables. Laboratory experiments, while allowing precise control, often mismatch the spatial and temporal scales of field conditions, leading to results that fail to capture real-world dynamics such as dispersal or large-scale environmental heterogeneity.^[25] In field experiments, factors like migration, evolutionary adaptation, or unmeasured biotic interactions can alter predicted outcomes, complicating the isolation of specific coexistence mechanisms.^[26] Measurement challenges further impede accurate empirical assessment of coexistence processes. Quantifying niche overlap and environmental fluctuations demands high-resolution data, but infrequent sampling can underestimate the storage effect, a stabilizing mechanism reliant on temporal variability in species performance, by missing critical periods of fluctuation.^[27] Similarly, precise estimation of fitness differences and interaction strengths is prone to error in complex communities, where indirect effects obscure direct competitive signals.^[28] Specific hurdles include the role of stochasticity in small populations, which can mask underlying coexistence mechanisms, as highlighted in critiques of niche-based approaches emphasizing neutral drift's dominance in low-abundance scenarios.^[29] Spatial structure adds complexity to invasion analyses, the cornerstone of coexistence tests, by introducing neighborhood effects and dispersal gradients that violate assumptions of well-mixed populations.^[30] Advances in long-term monitoring, such as the Cedar Creek Ecosystem Science Reserve plots established in 1982, have provided valuable data on plant community dynamics and mechanism partitioning over decades, enabling detection of slow processes like exclusion.^[31] However, persistent gaps remain, particularly in microbial systems, where rapid generation times and high diversity challenge the application of standard frameworks, with few studies successfully quantifying mechanisms amid complex interactions.^[25] Reviews of the literature reveal that only about 2% of empirical studies on community assembly robustly test invasibility criteria essential for validating coexistence, underscoring the scarcity of rigorous partitioning of mechanisms across taxa.^[32]

Theoretical comparisons

Relation to neutral theory

Neutral theory, as proposed by Hubbell, assumes that species in a community are ecologically equivalent, with individual-level demographic rates such as birth, death, immigration, and speciation being independent of species identity.^[29] In this framework, biodiversity patterns emerge from stochastic processes including ecological drift, dispersal limitation, and speciation, operating under zero-sum dynamics where the total number of individuals in the community remains constant.^[33] A key parameter in neutral theory is θ, defined as θ = 2 J v, where J is the community size and v is the speciation rate; this dimensionless quantity governs the expected diversity in the metacommunity. The dispersal probability (m) is a separate key parameter.^[29] In contrast, coexistence theory emphasizes niche differences among species to achieve stable coexistence, relying on stabilizing mechanisms that favor rare species through differential responses to environmental fluctuations or interactions, rather than demographic stochasticity alone. Neutral theory predicts no fitness inequalities between species, treating all individuals as demographically interchangeable, whereas coexistence theory incorporates fitness differences but requires them to be counterbalanced by niche partitioning for long-term persistence. Neutral theory serves as a null model against which niche-based explanations can be tested, highlighting how stochastic equivalence alone can generate observed diversity patterns in homogeneous environments, while coexistence theory better accounts for elevated diversity in heterogeneous settings where stabilizing mechanisms dominate.^[34] Hybrid models integrate elements of both, positing a continuum where neutrality emerges at one extreme and strong niche differentiation at the other, as explored by Gravel et al. who demonstrated how varying strengths of biotic interactions can bridge the two perspectives. In neutral theory, diversity is quantified via parameters like θ and invasion rates driven by drift, whereas coexistence theory focuses on invasion growth rates that reflect niche-mediated recovery of rare species relative to common ones.^[29] Empirically, neutral models fit species abundance distributions in some tropical forest communities, such as those on Barro Colorado Island, where dispersal and drift explain much of the observed structure without invoking niches.^[29] However, neutral theory often fails in systems exhibiting clear stabilizing mechanisms, such as the storage effect in annual plant communities, where species-specific responses to temporal environmental variability—buffered by long-lived seed banks—promote coexistence beyond what stochastic equivalence predicts.^[35] The debate between the two theories intensified following the publication of Hubbell's Unified Neutral Theory in 2001, with subsequent critiques, including those by Clark et al. in 2010, arguing that the assumption of ecological equivalence is implausible given pervasive evidence for species-specific fitness and niche differences.

Relation to niche theory

Classical niche theory, as articulated by G. Evelyn Hutchinson, conceptualizes the ecological niche as an n-dimensional hypervolume representing the range of environmental conditions under which a species can persist, including resources, temperature, and other biotic and abiotic factors.^[36] In this framework, complete overlap in niches between species typically leads to competitive exclusion, as predicted by the competitive exclusion principle, unless niches are partitioned along resource axes or other dimensions to reduce overlap and allow coexistence. Coexistence theory builds upon and refines classical niche concepts by integrating them into mechanistic models that emphasize stabilizing and equalizing processes. Stabilizing mechanisms, such as resource partitioning, arise from niche differences that allow species to limit their own populations more than those of competitors through differential access to resources. Equalizing mechanisms, in turn, involve shifts in realized niches that reduce fitness inequalities, enabling species with similar fundamental niches to persist together by minimizing competitive dominance. A key distinction between classical niche theory and coexistence theory lies in their approaches: niche theory is largely descriptive, differentiating between fundamental niches (potential range without competitors) and realized niches (actual range influenced by interactions), whereas coexistence theory is predictive, relying on fitness differences and negative density dependence to forecast long-term persistence. For instance, Robert MacArthur's consumer-resource model bridges these views by demonstrating how niche partitioning along resource gradients can stabilize consumer coexistence, particularly in heterogeneous environments, but highlights limitations in uniform settings where high overlap precludes stable outcomes without additional mechanisms. Niche differentiation is often quantified using metrics like Levins' overlap index, defined as B_{ij} = \sum_k p_{ik} p_{jk}, where p_{ik} is the proportion of resource k used by species i, providing a measure of niche similarity that directly informs competition coefficients \alpha_{ij} in Lotka-Volterra models. This linkage underscores how static niche overlap translates into dynamic competitive interactions central to coexistence predictions. Coexistence theory addresses limitations in classical niche theory, such as the "ghost of competition past" proposed by Joseph Connell, by shifting focus from historical or static niche adjustments—where past competition might have already partitioned niches—to ongoing dynamic mechanisms that actively maintain diversity in contemporary assemblages.^[37]

Extensions and applications

Coexistence theory, originally developed in ecology to explain species diversity, has been conceptually transferred to social-ecological systems to analyze how competing human groups maintain sustainable interactions over shared resources. In such adaptations, equalizing mechanisms—such as policies that reduce disparities in resource access—parallel ecological processes that minimize fitness differences among competitors, while stabilizing mechanisms—like targeted management interventions—promote recovery of disadvantaged groups by limiting dominance. For instance, in the Cook Inlet salmon fisheries of Alaska, state laws prioritizing subsistence users equalize access for indigenous communities, and periodic fishing closures stabilize coexistence among commercial, sport, and subsistence sectors by preventing overexploitation by any one group.^[38] Cultural pluralism emerges as a key equalizing mechanism in these social applications, fostering resilience by valuing diverse knowledge systems and practices within communities. In the Pamir Mountains of Afghanistan, pluralism enables ethnic groups to draw on varied ecological strategies for survival, such as complementary agricultural and pastoral systems, which buffer against environmental variability and support long-term group coexistence. This cultural value reduces competitive imbalances by encouraging mutual recognition and integration of diverse lifeways, akin to how equalizing forces in ecology prevent exclusion.^[38] In the realm of multiculturalism, ecological niche concepts have informed analyses of ethnic group interactions, particularly through partitioning of social and economic roles to sustain diversity in plural societies. Fredrik Barth's work on ethnic boundaries highlights how groups occupy distinct "niches" defined by occupational specializations and cultural markers, allowing coexistence without assimilation; for example, in Swat, Pakistan, Pathan, Kohistani, and Gujar groups partition herding, farming, and trading roles, maintaining boundaries while sharing the landscape. Such partitioning parallels niche differentiation in ecology, enabling stable ethnic pluralism by reducing direct competition over resources. Applications in conflict resolution and peace studies draw on stabilizing mechanisms to promote resource sharing and frequency-dependent cooperation. Johan Galtung's concept of positive peace, developed in the late 1960s, emphasizes equity through cooperative resource distribution to achieve harmony beyond mere absence of violence; this involves structural reforms for mutual benefit, stabilizing social equilibria by countering dominance and fostering interdependence among groups. Similarly, Robert Axelrod's 1984 model of cooperation evolution demonstrates how frequency-dependent strategies, like tit-for-tat reciprocity, lead to stable social outcomes in iterated interactions, analogous to intraspecific advantages that prevent group exclusion in diverse settings.^[39]^[40] Developments in applying coexistence principles to social sciences gained traction in the 2000s and 2010s, building on earlier analogs like Axelrod's work, with formal extensions in social-ecological theory emphasizing human adaptability. However, mathematical formalizations remain limited compared to ecology; instead, agent-based simulations in cultural evolution reveal patterns analogous to negative frequency dependence, where rare norms or practices gain advantages, preventing dominance by prevalent ones and sustaining diversity. For example, models of cultural transmission show that anti-conformity biases lead to balanced trait distributions, supporting long-term social pluralism.^[41]^[42] In multicultural policy contexts, measures like targeted support for immigrant communities can promote equitable coexistence by addressing competitive disadvantages, drawing parallels to stabilizing interventions that enhance establishment of minority groups.

Applications in conservation and management

Coexistence theory informs conservation strategies by promoting stabilizing mechanisms, such as the storage effect, through habitat heterogeneity restoration. For instance, in wetland ecosystems, creating heterogeneous patches with varying hydrology and soil conditions enhances temporal niche partitioning, allowing rare species like Lasthenia conjugens to persist by buffering against unfavorable periods.^[3] This approach has been applied in vernal pool restorations, where competitor removal and depth variation facilitate low-density invasion and long-term coexistence.^[43] In ecosystem management, the theory guides invasive species control by leveraging equalizing mechanisms to reduce fitness advantages of exotics over natives. Biological controls, such as introducing natural enemies, can equalize competitive asymmetries in interaction networks, promoting stable coexistence in invaded communities.^[44] In agroecology, principles of niche differentiation and resource partitioning are used to foster crop-weed coexistence, where landscape heterogeneity supports diverse weed communities that provide ecosystem services like soil protection without yield losses.^[45] For example, semi-natural habitats act as sources for beneficial weed dispersal, regulating populations through natural enemies and reducing reliance on herbicides.^[45] Specific applications include designing protected areas with invasion criteria derived from coexistence theory, where Chesson's metrics of niche and fitness differences predict multispecies persistence in fragmented landscapes.^[46] These metrics, such as normalized niche overlap indices, help configure habitat patches to balance local competition and regional dispersal, achieving up to 96% accuracy in coexistence forecasts for communities like Daphnia in rock pools.^[46] In climate change adaptation, the theory supports buffering environmental fluctuations via storage effects, where diverse life-history strategies in restored sites mitigate variability impacts on community composition.^[3] Initiatives like the EU Natura 2000 network, established in 1992, advance niche partitioning by protecting heterogeneous habitats that sustain biodiversity through varied ecological niches.^[47] Recent rewilding models integrate these principles to restore trophic complexity and dispersal, enhancing self-sustaining ecosystems.^[48] The theory aids in predicting community responses to perturbations by quantifying resilience through stabilizing indices, such as invasion growth rates in fisheries. In Cook Inlet salmon systems, equalizing mechanisms like resource access laws and stabilizing factors like density-dependent predation maintain sector coexistence amid harvest pressures, buffering against declines post-disasters.^[49] A unique application lies in metacommunity management, where controlled dispersal equalizes regional differences, optimizing connectivity to support biodiversity in riverine networks. For example, adjusting barriers in restored streams prevents invasive recolonization while promoting native dispersal.^[50]

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Comparing the Deterministic Levins Model with its Stochastic ...
In this paper, we examine, for small metapopulations, the stochastic analog of the classical Levins metapopulation model.
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May 9, 2014 · The theory of competitive exclusion predicts that inferior competitors for a limiting resource will be driven to extinction.Methods · Results · Discussion
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Coexistence Theory for Microbial Ecology, and Vice Versa - PMC
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Widespread analytical pitfalls in empirical coexistence studies and a ...
Feb 28, 2024 · A key challenge is that interaction coefficients between species ( terms) are more difficult to accurately estimate than intrinsic ...
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Quantifying and testing coexistence mechanisms arising from ...
Warner and Chesson (1985) developed a method for partitioning long-term population growth rates into components due to recruitment fluctuations and components ...
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[PDF] An Expanded Modern Coexistence Theory for Empirical Applications
Oct 11, 2018 · Spatial coexistence mechanisms in the Chesson (2000) model. To highlight our approach's generality we show how it can be used to analyze ...
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Toward a “modern coexistence theory” for the discrete and spatial
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Long-Term and Large-Scale Perspectives on the Relationship ...
At the Cedar Creek LTER site, a long-term N-addition experiment initiated in grassland fields in 1982 resulted in plots with plant species richness levels ...
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Aug 22, 2006 · “Storage effect” theory derives the conditions under which climate variability will have stabilizing or destabilizing effects on species ...Abstract · Sign Up For Pnas Alerts · Materials And Methods
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Hutchinson-CSHSymQunBio-1957.pdf
No information is available for this page. · Learn whyMissing: multidimensional theory
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Diversity and the Coevolution of Competitors, or the Ghost of ... - jstor
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Toward a Theory of Coexistence in Shared Social-Ecological Systems
Jan 23, 2016 · Coexistence theory (CT) in community ecology provides a functional perspective on how multiple competing species coexist.
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[PDF] THEORIES OF PEACE A Synthetic Approach to Peace Thinking By ...
3. PREFACE. The present work is an effort to make a comprehensive and relatively exhaustive survey of thinking about peace. It has been carried out.
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[PDF] The Evolution of Cooperation* - Stanford University
Therefore, the problem is that each country has an incentive to retain trade barriers, leading to a worse outcome than would have been possible had both.Missing: coexistence | Show results with:coexistence
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Global perspectives, local solutions: Improving human–predator ...
Jul 19, 2025 · Human–predator coexistence is a complex and dynamic relationship influenced by a variety of social–ecological factors.
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Measuring frequency-dependent selection in culture - PubMed
Our analysis of cultural evolution through frequency-dependent selection provides a quantitative account of social pressures to conform or to be different.
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Random copying, frequency-dependent copying and culture change
Negative frequency-dependent copying, or anti-conformity, is where agents adopt the least common trait in the population with a certain probability.
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Multiculturalism - Stanford Encyclopedia of Philosophy
Sep 24, 2010 · Will Kymlicka has developed the most influential liberal theory of multiculturalism by marrying the liberal values of autonomy and equality with ...
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Application of modern coexistence theory to rare plant restoration ...
May 13, 2022 · Here, we re-purpose tools developed from modern coexistence theory to address these questions, and apply them to an effort to restore the ...
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Coexistence theory as a tool to understand biological invasions in ...
Apr 11, 2019 · Coexistence theory fundamentally aims to determine the mechanisms by which some species do not exclude others when they interact for shared ...
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Landscape perspectives for agroecological weed management. A ...
Jan 25, 2024 · We did not represent feedback between weeds and their environment (modern coexistence and feedback theories: HilleRisLambers et al. 2012 ...
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Multispecies coexistence in fragmented landscapes - PNAS
Specifically, coexistence theory clarifies that the outcome of interspecific competition is determined by the balance of two key ecological processes: the niche ...Multispecies Coexistence In... · Results · A Spatially Explicit...
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Assessing the Heterogeneity and Conservation Status of the Natura ...
Apr 22, 2025 · Priority habitat types (HTs) within the Natura 2000 network are of the highest importance for conservation in Europe. However, they often occur ...
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Rewilding complex ecosystems - Science
Apr 26, 2019 · The practice of “rewilding” has emerged as a method for returning wild lands, and wildness, to landscapes we have altered.
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The application of metacommunity theory to the management of ...
Metacommunity theory describes how multiple species from different communities potentially interact with local-scale environmental drivers to influence ...Missing: equalization | Show results with:equalization