# Limiting similarity

Limiting similarity (informally "limsim") 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.

This concept is a corollary of the competitive exclusion principle, which states that, controlling for all else, two species competing for exactly the same resources cannot stably coexist. It assumes normally-distributed resource utilization curves ordered linearly along a resource axis, and as such, it is often considered to be an oversimplified model of species interactions. Moreover, it has theoretical weakness, and it is poor at generating real-world predictions or falsifiable hypotheses. Thus, the concept has fallen somewhat out of favor except in didactic settings (where it is commonly referenced), and has largely been replaced by more complex and inclusive theories.

## History

In 1932, Georgii Gause created the competitive exclusion principle based on experiments with cultures of yeast and paramecium.[1] The principle maintains that two species with the same ecological niches cannot stably coexist. That is to say, when two species compete for identical resource access, one will be competitively superior and it will ultimately supplant the other. Over the next half century, limiting similarity slowly emerged as a natural outgrowth of this principle, aiming (but not necessarily succeeding) to be more quantitative and specific.

Noted ecologist and evolutionary biologist David Lack said retrospectively that he had already begun to mull around with the ideas of limiting similarity as early as the 1940s, but it wasn't until the end of the 1950s that the theory began to be built up and articulated.[2] G. Evelyn Hutchinson's famous "Homage to Santa Rosalia" was the next foundational paper in the history of the theory. Its subtitle famously asks, "Why are there so many kinds of animals?", and the address attempts to answer this question by suggesting theoretical bounds to speciation and niche overlap. For the purposes of understanding limiting similarity, the key portion of Hutchinson's address is the end where he presents the observation that a seemingly ubiquitous ratio (1.3:1) defines the upper bound of morphological character similarity between closely related species.[3] While this so-called Hutchinson ratio and the idea of a universal limit have been overturned by later research, the address was still foundational to the theory of limiting similarity.

MacArthur and Levins were the first to introduce the term 'limiting similarity' in their 1967 paper. They attempted to lay out a rigorous quantitative basis for the theory using probability theory and the Lotka–Volterra competition equations.[4] In doing so, they provided the ultimate theoretical framework on which many subsequent studies were based.

## Theory

As proposed by MacArthur and Levins in 1967, the theory of limiting similarity is rooted in the Lotka–Volterra competition model. This model describes two or more populations with logistic dynamics, adding in an additional term to account for their biological interactions. Thus for two populations, x1 and x2:

{\displaystyle {\begin{aligned}{dx_{1} \over dt}&=r_{1}x_{1}\left({K_{1}-x_{1}-\alpha _{12}x_{2} \over K_{1}}\right),\\[6pt]{dx_{2} \over dt}&=r_{2}x_{2}\left({K_{2}-x_{2}-\alpha _{21}x_{1} \over K_{2}}\right).\end{aligned}}}

where

• α12 represents the effect species 2 has on the population of species 1
• α21 represents the effect species 1 has on the population of species 2
• dy/dt and dx/dt represent the growth of the two populations with time;
• K1 and K2 represent these species’ respective carrying capacities
• r1 and r2 represent these species’ respective growth rates

MacArthur and Levins examine this system applied to three populations, also visualized as resource utilization curves, depicted below. In this model, at some upper limit of competition α, between two species x1 and x3, the survival of a third species x2 between the other two is not possible. This phenomenon is termed limiting similarity. Evolutionary, if two species are more similar than some limit L, a third species will converge towards the nearer of the two competitors. If the two species are less similar than some limit L, a third species will evolve an intermediate phenotype.

[embedded graph: U v R. x1, x2, x3 curves.]

For each resource R, U represents the probability of utilization per unit time by an individual. At some level of overlap between species x1 and x3, the survival of a third species x2 is no longer possible.

May[5] extended this theory when considering species with different carrying capacities, concluding that coexistence was unlikely if the distance between the modes of competing resource utilization curves d was less than the standard deviation of the curves w.

## Applied examples

It is of note that the theory of limiting similarity does not easily generate falsifiable predictions about natural phenomenon. However, many studies have tried to test the theory by making the highly suspect assumption that character displacement can be used as a close proxy for niche incongruence.[6] One recent paleoecological study, for example, used fossil proxies of gastropod body size to determine levels of character displacement over 42,500 years during the Quaternary. They found little evidence of character displacement, and they concluded that "limiting similarity, as seen in both ecological character displacement and community-wide character displacement, is a transient ecological phenomenon rather than a long-term evolutionary process".[7] Other theoretical and empirical studies tend to find results that similarly play down the strength and role of limiting similarity in ecology and evolution. For example, Abrams (who is prolific on the subject of limiting similarity) and Rueffler find in 2009 that "there is no absolute limit to similarity; there is always some range of mortality rates of one species allowing coexistence, given a fixed mortality of the other species".[8]

What a lot of studies examining limiting similarity find are the weaknesses in the original theory that are addressed below.

## Criticism

The key weakness of the theory of limiting similarity is that it is highly system specific and thus difficult to test in practice. In actual environments, one resource axis is inadequate and a specific analysis must be done for each given pair of species. In practice it is necessary to take into account:

• individual variations in resource utilization curves within a species and how these should be weighted in calculating a common curve
• whether the resource in question is a present in a deterministic or stochastic distribution and if this changes over time
• effects of intraspecific competition vs interspecific competition

While these complications don't invalidate the concept, they render limiting similarity exceedingly difficult to test in practice and useful for little more than didacticism.

Furthermore, Hubbell and Foster point out that extinction via competition can take an extremely long time and the importance of limiting similarity in extinction may even be superseded by speciation.[9] Also, from a theoretical standpoint, small changes in carrying capacities can allow for nearly completely overlapping resource utilization curves and in practice carrying capacity can be difficult to determine. Many studies that attempt to explore limiting similarity (including Huntley et al. 2007) resort to examining character displacement as a proxy for niche overlap, which is suspect at best. While a useful-if simple-model, limiting similarity is nearly untestable in reality.

## References

1. ^ Gause, GF. 1932. Experimental studies on the struggle for existence. Journal of Experimental Biology 9: 389–402.
2. ^ Lack, D. 1973. My life as an amateur ornithologist. Ibis 115: 421–434.
3. ^ Hutchinson, GE. 1959. Homage to Santa Rosalia, or Why are there so many kinds of animals?. The American Naturalist 93(870): 145–159.
4. ^ MacArthur, R and R Levins. 1967. The Limiting Similarity, Convergence, and Divergence of Coexisting Species. The American Naturalist 101(921): 377–385.
5. ^ May, R. M. 1973. Stability and Complexity in Model Ecosystems. Princeton: Princeton Univ. Press
6. ^ Abrams P. 1983. The Theory of Limiting Similarity. Annual Review of Ecology, Evolution, and Systematics 14: 359–376.
7. ^ Huntley JW, Yanes Y, Kowalewski M, Castillo C, Delgado-Huertas A, Ibanez M, Alonso MR, Ortiz JE and T de Torres. 2008. Testing limiting similarity in Quaternary terrestrial gastropods. Paleobiology 34(3): 378–388.
8. ^ Abrams PA and C Rueffler. 2009. Coexistence and limiting similarity of consumer species competing for a linear array of resources. Ecology 90(3): 812–822.
9. ^ Hubbell, S. P. and Foster, R.B. (1986). Biology, chance, and history and the structure of tropical rain forest tree communities. In: Diamond, J. and Case, T.J. eds. Community ecology. Harper and Row, New York, pp. 314–329.
Abiotic component

In biology and ecology, abiotic components or abiotic factors are non-living chemical and physical parts of the environment that affect living organisms and the functioning of ecosystems. Abiotic factors and the phenomena associated with them underpin all biology.

Abiotic components include physical conditions and non-living resources that affect living organisms in terms of growth, maintenance, and reproduction. Resources are distinguished as substances or objects in the environment required by one organism and consumed or otherwise made unavailable for use by other organisms.

Component degradation of a substance occurs by chemical or physical processes, e.g. hydrolysis. All non-living components of an ecosystem, such as atmospheric conditions and water resources, are called abiotic components.

Bacterivore

Bacterivores are free-living, generally heterotrophic organisms, exclusively microscopic, which obtain energy and nutrients primarily or entirely from the consumption of bacteria. Many species of amoeba are bacterivores, as well as other types of protozoans. Commonly, all species of bacteria will be prey, but spores of some species, such as Clostridium perfringens, will never be prey, because of their cellular attributes.

Competitive exclusion principle

In ecology, the competitive exclusion principle, sometimes referred to as Gause's law, is a proposition named for Georgy Gause that two species competing for the same limiting resource cannot coexist at constant population values. When one species has even the slightest advantage over another, the one with the advantage will dominate in the long term. This leads either to the extinction of the weaker competitor or to an evolutionary or behavioral shift toward a different ecological niche. The principle has been paraphrased in the maxim "complete competitors can not coexist".

Copiotroph

A copiotroph is an organism found in environments rich in nutrients, particularly carbon. They are the opposite to oligotrophs, which survive in much lower carbon concentrations.

Copiotrophic organisms tend to grow in high organic substrate conditions. For example, copiotrophic organisms grow in Sewage lagoons. They grow in organic substrate conditions up to 100x higher than oligotrophs.

Decomposer

Decomposers are organisms that break down dead or decaying organisms, and in doing so, they carry out the natural process of decomposition. Like herbivores and predators, decomposers are heterotrophic, meaning that they use organic substrates to get their energy, carbon and nutrients for growth and development. While the terms decomposer and detritivore are often interchangeably used, detritivores must ingest and digest dead matter via internal processes while decomposers can directly absorb nutrients through chemical and biological processes hence breaking down matter without ingesting it. Thus, invertebrates such as earthworms, woodlice, and sea cucumbers are technically detritivores, not decomposers, since they must ingest nutrients and are unable to absorb them externally.

Depensation

In population dynamics, depensation is the effect on a population (such as a fish stock) whereby, due to certain causes, a decrease in the breeding population (mature individuals) leads to reduced production and survival of eggs or offspring. The causes may include predation levels rising per offspring (given the same level of overall predator pressure) and the allee effect, particularly the reduced likelihood of finding a mate.

Dominance (ecology)

Ecological dominance is the degree to which a taxon is more numerous than its competitors in an ecological community, or makes up more of the biomass.

Most ecological communities are defined by their dominant species.

In many examples of wet woodland in western Europe, the dominant tree is alder (Alnus glutinosa).

In temperate bogs, the dominant vegetation is usually species of Sphagnum moss.

Tidal swamps in the tropics are usually dominated by species of mangrove (Rhizophoraceae)

Some sea floor communities are dominated by brittle stars.

Exposed rocky shorelines are dominated by sessile organisms such as barnacles and limpets.

Ecological threshold

Ecological threshold is the point at which a relatively small change or disturbance in external conditions causes a rapid change in an ecosystem. When an ecological threshold has been passed, the ecosystem may no longer be able to return to its state by means of its inherent resilience . Crossing an ecological threshold often leads to rapid change of ecosystem health. Ecological threshold represent a non-linearity of the responses in ecological or biological systems to pressures caused by human activities or natural processes.Critical load, tipping point and regime shift are examples of other closely related terms.

Energy Systems Language

The Energy Systems Language, also referred to as Energese, Energy Circuit Language, or Generic Systems Symbols, was developed by the ecologist Howard T. Odum and colleagues in the 1950s during studies of the tropical forests funded by the United States Atomic Energy Commission. They are used to compose energy flow diagrams in the field of systems ecology.

Feeding frenzy

In ecology, a feeding frenzy occurs when predators are overwhelmed by the amount of prey available. For example, a large school of fish can cause nearby sharks, such as the lemon shark, to enter into a feeding frenzy. This can cause the sharks to go wild, biting anything that moves, including each other or anything else within biting range. Another functional explanation for feeding frenzy is competition amongst predators. This term is most often used when referring to sharks or piranhas. It has also been used as a term within journalism.

Lithoautotroph

A lithoautotroph or chemolithoautotroph is a microbe which derives energy from reduced compounds of mineral origin. Lithoautotrophs are a type of lithotrophs with autotrophic metabolic pathways. Lithoautotrophs are exclusively microbes; macrofauna do not possess the capability to use mineral sources of energy. Most lithoautotrophs belong to the domain Bacteria, while some belong to the domain Archaea. For lithoautotrophic bacteria, only inorganic molecules can be used as energy sources. The term "Lithotroph" is from Greek lithos (λίθος) meaning "rock" and trōphos (τροφοσ) meaning "consumer"; literally, it may be read "eaters of rock". Many lithoautotrophs are extremophiles, but this is not universally so.

Lithoautotrophs are extremely specific in using their energy source. Thus, despite the diversity in using inorganic molecules in order to obtain energy that lithoautotrophs exhibit as a group, one particular lithoautotroph would use only one type of inorganic molecule to get its energy.

Mesotrophic soil

Mesotrophic soils are soils with a moderate inherent fertility. An indicator of soil fertility is its base status, which is expressed as a ratio relating the major nutrient cations (calcium, magnesium, potassium and sodium) found there to the soil's clay percentage. This is commonly expressed in hundredths of a mole of cations per kilogram of clay, i.e. cmol (+) kg−1 clay.

Mycotroph

A mycotroph is a plant that gets all or part of its carbon, water, or nutrient supply through symbiotic association with fungi. The term can refer to plants that engage in either of two distinct symbioses with fungi:

Many mycotrophs have a mutualistic association with fungi in any of several forms of mycorrhiza. The majority of plant species are mycotrophic in this sense. Examples include Burmanniaceae.

Some mycotrophs are parasitic upon fungi in an association known as myco-heterotrophy.

Organotroph

An organotroph is an organism that obtains hydrogen or electrons from organic substrates. This term is used in microbiology to classify and describe organisms based on how they obtain electrons for their respiration processes. Some organotrophs such as animals and many bacteria, are also heterotrophs. Organotrophs can be either anaerobic or aerobic.

Antonym: Lithotroph, Adjective: Organotrophic.

Overpopulation

Overpopulation occurs when a species' population exceeds the carrying capacity of its ecological niche. It can result from an increase in births (fertility rate), a decline in the mortality rate, an increase in immigration, or an unsustainable biome and depletion of resources. When overpopulation occurs, individuals limit available resources to survive.

The change in number of individuals per unit area in a given locality is an important variable that has a significant impact on the entire ecosystem.

Planktivore

A planktivore is an aquatic organism that feeds on planktonic food, including zooplankton and phytoplankton.

Recruitment (biology)

In biology, especially marine biology, recruitment occurs when a juvenile organism joins a population, whether by birth or immigration, usually at a stage whereby the organisms are settled and able to be detected by an observer.There are two types of recruitment: closed and open.In the study of fisheries, recruitment is "the number of fish surviving to enter the fishery or to some life history stage such as settlement or maturity".

Relative abundance distribution

In the field of ecology, the relative abundance distribution (RAD) or species abundance distribution describes the relationship between the number of species observed in a field study as a function of their observed abundance. The graphs obtained in this manner are typically fitted to a Zipf–Mandelbrot law, the exponent of which serves as an index of biodiversity in the ecosystem under study.

Species homogeneity

In ecology, species homogeneity is a lack of biodiversity. Species richness is the fundamental unit in which to assess the homogeneity of an environment. Therefore, any reduction in species richness, especially endemic species, could be argued as advocating the production of a homogenous environment.

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