Quantum contextuality

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Quantum_contextuality

Quantum contextuality is a feature of the phenomenology of quantum mechanics whereby measurements of quantum observables cannot simply be thought of as revealing pre-existing values. Any attempt to do so in a realistic hidden-variable theory leads to values that are dependent upon the choice of the other (compatible) observables which are simultaneously measured (the measurement context). More formally, the measurement result (assumed pre-existing) of a quantum observable is dependent upon which other commuting observables are within the same measurement set.

Contextuality was first demonstrated to be a feature of quantum phenomenology by the Bell–Kochen–Specker theorem. The study of contextuality has developed into a major topic of interest in quantum foundations as the phenomenon crystallises certain non-classical and counter-intuitive aspects of quantum theory. A number of powerful mathematical frameworks have been developed to study and better understand contextuality, from the perspective of sheaf theory, graph theory, hypergraphs, algebraic topology, and probabilistic couplings.

Nonlocality, in the sense of Bell's theorem, may be viewed as a special case of the more general phenomenon of contextuality, in which measurement contexts contain measurements that are distributed over spacelike separated regions. This follows from Fine's theorem.

Quantum contextuality has been identified as a source of quantum computational speedups and quantum advantage in quantum computing. Contemporary research has increasingly focused on exploring its utility as a computational resource.

Kochen and Specker

Main article: Kochen–Specker theorem

The need for contextuality was discussed informally in 1935 by Grete Hermann, but it was more than 30 years later when Simon B. Kochen and Ernst Specker, and separately John Bell, constructed proofs that any realistic hidden-variable theory able to explain the phenomenology of quantum mechanics is contextual for systems of Hilbert space dimension three and greater. The Kochen–Specker theorem proves that realistic noncontextual hidden variable theories cannot reproduce the empirical predictions of quantum mechanics. Such a theory would suppose the following.

1. All quantum-mechanical observables may be simultaneously assigned definite values (this is the realism postulate, which is false in standard quantum mechanics, since there are observables which are undefinite in every given quantum state). These global value assignments may deterministically depend on some 'hidden' classical variable which, in turn, may vary stochastically for some classical reason (as in statistical mechanics). The measured assignments of observables may therefore finally stochastically change. This stochasticity is however epistemic and not ontic as in the standard formulation of quantum mechanics.
2. Value assignments pre-exist and are independent of the choice of any other observables which, in standard quantum mechanics, are described as commuting with the measured observable, and they are also measured.
3. Some functional constraints on the assignments of values for compatible observables are assumed (e.g., they are additive and multiplicative, there are however several versions of this functional requirement).

In addition, Kochen and Specker constructed an explicitly noncontextual hidden variable model for the two-dimensional qubit case in their paper on the subject, thereby completing the characterisation of the dimensionality of quantum systems that can demonstrate contextual behaviour. Bell's proof invoked a weaker version of Gleason's theorem, reinterpreting the theorem to show that quantum contextuality exists only in Hilbert space dimension greater than two.

Frameworks for contextuality

Sheaf-theoretic framework

The sheaf-theoretic, or Abramsky–Brandenburger, approach to contextuality initiated by Samson Abramsky and Adam Brandenburger is theory-independent and can be applied beyond quantum theory to any situation in which empirical data arises in contexts. As well as being used to study forms of contextuality arising in quantum theory and other physical theories, it has also been used to study formally equivalent phenomena in logic, relational databases, natural language processing, and constraint satisfaction.

In essence, contextuality arises when empirical data is locally consistent but globally inconsistent.

This framework gives rise in a natural way to a qualitative hierarchy of contextuality.

• (Probabilistic) contextuality may be witnessed in measurement statistics, e.g. by the violation of an inequality. A representative example is the KCBS proof of contextuality.
• Logical contextuality may be witnessed in the 'possibilistic' information about which outcome events are possible and which are not possible. A representative example is Hardy's nonlocality proof of nonlocality.
• Strong contextuality is a maximal form of contextuality. Whereas (probabilistic) contextuality arises when measurement statistics cannot be reproduced by a mixture of global value assignments, strong contextuality arises when no global value assignment is even compatible with the possible outcome events. A representative example is the original Kochen–Specker proof of contextuality.

Each level in this hierarchy strictly includes the next. An important intermediate level that lies strictly between the logical and strong contextuality classes is all-versus-nothing contextuality, a representative example of which is the Greenberger–Horne–Zeilinger proof of nonlocality.

Graph and hypergraph frameworks

Adán Cabello, Simone Severini, and Andreas Winter introduced a general graph-theoretic framework for studying contextuality of different physical theories. Within this framework experimental scenarios are described by graphs, and certain invariants of these graphs were shown have particular physical significance. One way in which contextuality may be witnessed in measurement statistics is through the violation of noncontextuality inequalities (also known as generalized Bell inequalities). With respect to certain appropriately normalised inequalities, the independence number, Lovász number, and fractional packing number of the graph of an experimental scenario provide tight upper bounds on the degree to which classical theories, quantum theory, and generalised probabilistic theories, respectively, may exhibit contextuality in an experiment of that kind. A more refined framework based on hypergraphs rather than graphs is also used.

Contextuality-by-Default (CbD) framework

In the CbD approach, developed by Ehtibar Dzhafarov, Janne Kujala, and colleagues, (non)contextuality is treated as a property of any system of random variables, defined as a set ${\displaystyle {\mathcal {R}}=\left\{R_{q}^{c}:q\in Q,q\prec c,c\in C\right\}}$ in which each random variable ${\displaystyle R_{q}^{c}}$ is labeled by its content ${\displaystyle q}$, the property it measures, and its context ${\displaystyle c}$, the set of recorded circumstances under which it is recorded (including but not limited to which other random variables it is recorded together with); ${\displaystyle q\prec c}$ stands for "${\displaystyle q}$ is measured in ${\displaystyle c}$". The variables within a context are jointly distributed, but variables from different contexts are stochastically unrelated, defined on different sample spaces. A (probabilistic) coupling of the system ${\displaystyle {\mathcal {R}}}$ is defined as a system ${\displaystyle S}$ in which all variables are jointly distributed and, in any context ${\displaystyle c}$, ${\displaystyle R^{c}=\left\{R_{q}^{c}:q\in Q,q\prec c\right\}}$ and ${\displaystyle S^{c}=\left\{S_{q}^{c}:q\in Q,q\prec c\right\}}$ are identically distributed. The system  is considered noncontextual if it has a coupling ${\displaystyle S}$ such that the probabilities ${\displaystyle \Pr \left[S_{q}^{c}=S_{q}^{c'}\right]}$ are maximal possible for all contexts ${\displaystyle c,c'}$ and contents ${\displaystyle q}$ such that ${\displaystyle q\prec c,c'}$. If such a coupling does not exist, the system is contextual. For the important class of cyclic systems of dichotomous (${\displaystyle \pm 1}$) random variables,  ${\displaystyle {\mathcal {C}}_{n}=\left\{\left(R_{1}^{1},R_{2}^{1}\right),\left(R_{2}^{2},R_{3}^{2}\right),\ldots ,\left(R_{n}^{n},R_{1}^{n}\right)\right\}}$ (${\displaystyle n\geq 2}$), it has been shown that such a system is noncontextual if and only if

$${\displaystyle D\left({\mathcal {C}}_{n}\right)\leq \Delta \left({\mathcal {C}}_{n}\right),}$$

where

$${\displaystyle \Delta \left({\mathcal {C}}_{n}\right)=\left(n-2\right)+\left|R_{1}^{1}-R_{1}^{n}\right|+\left|R_{2}^{1}-R_{2}^{2}\right|+\ldots \left|R_{n}^{n-1}-R_{n}^{n}\right|,}$$

and

$${\displaystyle D\left({\mathcal {C}}_{n}\right)=\max \left(\lambda _{1}\left\langle R_{1}^{1}R_{2}^{1}\right\rangle +\lambda _{2}\left\langle R_{2}^{2}R_{3}^{2}\right\rangle +\ldots +\lambda _{n}\left\langle R_{n}^{n},R_{1}^{n}\right\rangle \right),}$$

with the maximum taken over all ${\displaystyle \lambda _{i}=\pm 1}$ whose product is ${\displaystyle -1}$. If ${\displaystyle R_{q}^{c}}$ and ${\displaystyle R_{q}^{c'}}$, measuring the same content in different context, are always identically distributed, the system is called consistently connected (satisfying "no-disturbance" or "no-signaling" principle). Except for certain logical issues, in this case CbD specializes to traditional treatments of contextuality in quantum physics. In particular, for consistently connected cyclic systems the noncontextuality criterion above reduces to ${\displaystyle D\left({\mathcal {C}}_{n}\right)\leq n-2,}$which includes the Bell/CHSH inequality (${\displaystyle n=4}$), KCBS inequality (${\displaystyle n=5}$), and other famous inequalities. That nonlocality is a special case of contextuality follows in CbD from the fact that being jointly distributed for random variables is equivalent to being measurable functions of one and the same random variable (this generalizes Arthur Fine's analysis of Bell's theorem). CbD essentially coincides with the probabilistic part of Abramsky's sheaf-theoretic approach if the system is strongly consistently connected, which means that the joint distributions of ${\displaystyle \left\{R_{q_{1}}^{c},\ldots ,R_{q_{k}}^{c}\right\}}$ and ${\displaystyle \left\{R_{q_{1}}^{c'},\ldots ,R_{q_{k}}^{c'}\right\}}$ coincide whenever ${\displaystyle q_{1},\ldots ,q_{k}}$ are measured in contexts ${\displaystyle c,c'}$. However, unlike most approaches to contextuality, CbD allows for inconsistent connectedness, with ${\displaystyle R_{q}^{c}}$ and ${\displaystyle R_{q}^{c'}}$ differently distributed. This makes CbD applicable to physics experiments in which no-disturbance condition is violated, as well as to human behavior where this condition is violated as a rule. In particular, Vctor Cervantes, Ehtibar Dzhafarov, and colleagues have demonstrated that random variables describing certain paradigms of simple decision making form contextual systems, whereas many other decision-making systems are noncontextual once their inconsistent connectedness is properly taken into account.

Operational framework

An extended notion of contextuality due to Robert Spekkens applies to preparations and transformations as well as to measurements, within a general framework of operational physical theories. With respect to measurements, it removes the assumption of determinism of value assignments that is present in standard definitions of contextuality. This breaks the interpretation of nonlocality as a special case of contextuality, and does not treat irreducible randomness as nonclassical. Nevertheless, it recovers the usual notion of contextuality when outcome determinism is imposed.

Spekkens' contextuality can be motivated using Leibniz's law of the identity of indiscernibles. The law applied to physical systems in this framework mirrors the entended definition of noncontextuality. This was further explored by Simmons et al, who demonstrated that other notions of contextuality could also be motivated by Leibnizian principles, and could be thought of as tools enabling ontological conclusions from operational statistics.

Other frameworks and extensions

A form of contextuality that may present in the dynamics of a quantum system was introduced by Shane Mansfield and Elham Kashefi, and has been shown to relate to computational quantum advantages. As a notion of contextuality that applies to transformations it is inequivalent to that of Spekkens. Examples explored to date rely on additional memory constraints which have a more computational than foundational motivation. Contextuality may be traded-off against Landauer erasure to obtain equivalent advantages.

Fine's theorem

The Kochen–Specker theorem proves that quantum mechanics is incompatible with realistic noncontextual hidden variable models. On the other hand Bell's theorem proves that quantum mechanics is incompatible with factorisable hidden variable models in an experiment in which measurements are performed at distinct spacelike separated locations. Arthur Fine showed that in the experimental scenario in which the famous CHSH inequalities and proof of nonlocality apply, a factorisable hidden variable model exists if and only if an noncontextual hidden variable model exists. This equivalence was proven to hold more generally in any experimental scenario by Samson Abramsky and Adam Brandenburger. It is for this reason that we may consider nonlocality to be a special case of contextuality.

Measures of contextuality

Contextual fraction

A number of methods exist for quantifying contextuality. One approach is by measuring the degree to which some particular noncontextuality inequality is violated, e.g. the KCBS inequality, the Yu–Oh inequality, or some Bell inequality. A more general measure of contextuality is the contextual fraction.

Given a set of measurement statistics e, consisting of a probability distribution over joint outcomes for each measurement context, we may consider factoring e into a noncontextual part e^NC and some remainder e',

$${\displaystyle e=\lambda e^{NC}+(1-\lambda )e'\,.}$$

The maximum value of λ over all such decompositions is the noncontextual fraction of e denoted NCF(e), while the remainder CF(e)=(1-NCF(e)) is the contextual fraction of e. The idea is that we look for a noncontextual explanation for the highest possible fraction of the data, and what is left over is the irreducibly contextual part. Indeed for any such decomposition that maximises λ the leftover e' is known to be strongly contextual. This measure of contextuality takes values in the interval [0,1], where 0 corresponds to noncontextuality and 1 corresponds to strong contextuality. The contextual fraction may be computed using linear programming.

It has also been proved that CF(e) is an upper bound on the extent to which e violates any normalised noncontextuality inequality. Here normalisation means that violations are expressed as fractions of the algebraic maximum violation of the inequality. Moreover, the dual linear program to that which maximises λ computes a noncontextual inequality for which this violation is attained. In this sense the contextual fraction is a more neutral measure of contextuality, since it optimises over all possible noncontextual inequalities rather than checking the statistics against one inequality in particular.

Measures of (non)contextuality within the Contextuality-by-Default (CbD) framework

Several measures of the degree of contextuality in contextual systems were proposed within the CbD framework, but only one of them, denoted CNT₂, has been shown to naturally extend into a measure of noncontextuality in noncontextual systems, NCNT₂. This is important, because at least in the non-physical applications of CbD contextuality and noncontextuality are of equal interest. Both CNT₂ and NCNT₂ are defined as the ${\displaystyle L_{1}}$-distance between a probability vector ${\displaystyle \mathbf {p} }$ representing a system and the surface of the noncontextuality polytope ${\displaystyle \mathbb {P} }$ representing all possible noncontextual systems with the same single-variable marginals. For cyclic systems  of dichotomous random variables, it is shown that if the system is contextual (i.e., ${\displaystyle D\left({\mathcal {C}}_{n}\right)>\Delta \left({\mathcal {C}}_{n}\right)}$),

$${\displaystyle \mathrm {CNT} _{2}=D\left({\mathcal {C}}_{n}\right)-\Delta \left({\mathcal {C}}_{n}\right),}$$

and if it is noncontextual ( ${\displaystyle D\left({\mathcal {C}}_{n}\right)\leq \Delta \left({\mathcal {C}}_{n}\right)}$),

$${\displaystyle \mathrm {NCNT} _{2}=\min \left(\Delta \left({\mathcal {C}}_{n}\right)-D\left({\mathcal {C}}_{n}\right),m\left({\mathcal {C}}_{n}\right)\right),}$$

where ${\displaystyle m\left({\mathcal {C}}_{n}\right)}$ is the ${\displaystyle L_{1}}$-distance from the vector ${\displaystyle \mathbf {p} \in \mathbb {P} }$ to the surface of the box circumscribing the noncontextuality polytope. More generally, NCNT₂ and CNT₂ are computed by means of linear programming. The same is true for other CbD-based measures of contextuality. One of them, denoted CNT₃, uses the notion of a quasi-coupling, that differs from a coupling in that the probabilities in the joint distribution of its values are replaced with arbitrary reals (allowed to be negative but summing to 1). The class of quasi-couplings ${\displaystyle S}$ maximizing the probabilities ${\displaystyle \Pr \left[S_{q}^{c}=S_{q}^{c'}\right]}$ is always nonempty, and the minimal total variation of the signed measure in this class is a natural measure of contextuality.

Contextuality as a resource for quantum computing

Recently, quantum contextuality has been investigated as a source of quantum advantage and computational speedups in quantum computing.

Magic state distillation

Magic state distillation is a scheme for quantum computing in which quantum circuits constructed only of Clifford operators, which by themselves are fault-tolerant but efficiently classically simulable, are injected with certain "magic" states that promote the computational power to universal fault-tolerant quantum computing. In 2014, Mark Howard, et al. showed that contextuality characterises magic states for qudits of odd prime dimension and for qubits with real wavefunctions. Extensions to the qubit case have been investigated by Juani Bermejo-Vega et al. This line of research builds on earlier work by Ernesto Galvão, which showed that Wigner function negativity is necessary for a state to be "magic"; it later emerged that Wigner negativity and contextuality are in a sense equivalent notions of nonclassicality.

Measurement-based quantum computing

Measurement-based quantum computation (MBQC) is a model for quantum computing in which a classical control computer interacts with a quantum system by specifying measurements to be performed and receiving measurement outcomes in return. The measurement statistics for the quantum system may or may not exhibit contextuality. A variety of results have shown that the presence of contextuality enhances the computational power of an MBQC.

In particular, researchers have considered an artificial situation in which the power of the classical control computer is restricted to only being able to compute linear Boolean functions, i.e. to solve problems in the Parity L complexity class ⊕L. For interactions with multi-qubit quantum systems a natural assumption is that each step of the interaction consists of a binary choice of measurement which in turn returns a binary outcome. An MBQC of this restricted kind is known as an l2-MBQC.

Anders and Browne

In 2009, Janet Anders and Dan Browne showed that two specific examples of nonlocality and contextuality were sufficient to compute a non-linear function. This in turn could be used to boost computational power to that of a universal classical computer, i.e. to solve problems in the complexity class P. This is sometimes referred to as measurement-based classical computation. The specific examples made use of the Greenberger–Horne–Zeilinger nonlocality proof and the supra-quantum Popescu–Rohrlich box.

Raussendorf

In 2013, Robert Raussendorf showed more generally that access to strongly contextual measurement statistics is necessary and sufficient for an l2-MBQC to compute a non-linear function. He also showed that to compute non-linear Boolean functions with sufficiently high probability requires contextuality.

Abramsky, Barbosa and Mansfield

A further generalisation and refinement of these results due to Samson Abramsky, Rui Soares Barbosa and Shane Mansfield appeared in 2017, proving a precise quantifiable relationship between the probability of successfully computing any given non-linear function and the degree of contextuality present in the l2-MBQC as measured by the contextual fraction. Specifically,

$${\displaystyle (1-p_{s})\geq \left(1-CF(e)\right).\nu (f)}$$

where ${\displaystyle p_{s},CF(e),\nu (f)\in [0,1]}$ are the probability of success, the contextual fraction of the measurement statistics e, and a measure of the non-linearity of the function to be computed ${\displaystyle f}$, respectively.

Further examples

• The above inequality was also shown to relate quantum advantage in non-local games to the degree of contextuality required by the strategy and an appropriate measure of the difficulty of the game.
• Similarly the inequality arises in a transformation-based model of quantum computation analogous to l2-MBQC where it relates the degree of sequential contextuality present in the dynamics of the quantum system to the probability of success and the degree of non-linearity of the target function.
• Preparation contextuality has been shown to enable quantum advantages in cryptographic random-access codes and in state-discrimination tasks.
• In classical simulations of quantum systems, contextuality has been shown to incur memory costs.

Biological interaction

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Biological_interaction 

The black walnut secretes a chemical from its roots that harms neighboring plants, an example of competitive antagonism.

In ecology, a biological interaction is the effect that a pair of organisms living together in a community have on each other. They can be either of the same species (intraspecific interactions), or of different species (interspecific interactions). These effects may be short-term, like pollination and predation, or long-term; both often strongly influence the evolution of the species involved. A long-term interaction is called a symbiosis. Symbioses range from mutualism, beneficial to both partners, to competition, harmful to both partners. Interactions can be indirect, through intermediaries such as shared resources or common enemies. This type of relationship can be shown by net effect based on individual effects on both organisms arising out of relationship.

Several recent studies have suggested non-trophic species interactions such as habitat modification and mutualisms can be important determinants of food web structures. However, it remains unclear whether these findings generalize across ecosystems, and whether non-trophic interactions affect food webs randomly, or affect specific trophic levels or functional groups.

History

Although biological interactions, more or less individually, were studied earlier, Edward Haskell (1949) gave an integrative approach to the thematic, proposing a classification of "co-actions", later adopted by biologists as "interactions". Close and long-term interactions are described as symbiosis; symbioses that are mutually beneficial are called mutualistic.

Short-term interactions

Predation is a short-term interaction, in which the predator, here an osprey, kills and eats its prey.

Short-term interactions, including predation and pollination, are extremely important in ecology and evolution. These are short-lived in terms of the duration of a single interaction: a predator kills and eats a prey; a pollinator transfers pollen from one flower to another; but they are extremely durable in terms of their influence on the evolution of both partners. As a result, the partners coevolve.

Predation

Main article: Predation

In predation, one organism, the predator, kills and eats another organism, its prey. Predators are adapted and often highly specialized for hunting, with acute senses such as vision, hearing, or smell. Many predatory animals, both vertebrate and invertebrate, have sharp claws or jaws to grip, kill, and cut up their prey. Other adaptations include stealth and aggressive mimicry that improve hunting efficiency. Predation has a powerful selective effect on prey, causing them to develop antipredator adaptations such as warning coloration, alarm calls and other signals, camouflage and defensive spines and chemicals. Predation has been a major driver of evolution since at least the Cambrian period.

Over the last several decades, microbiologists have discovered a number of fascinating microbes that survive by their ability to prey upon others. Several of the best examples are members of the genera Daptobacter (Campylobacterota), Bdellovibrio, and Vampirococcus.

Bdellovibrios are active hunters that are vigorously motile, swimming about looking for susceptible Gram-negative bacterial prey. Upon sensing such a cell, a bdellovibrio cell swims faster until it collides with the prey cell. It then bores a hole through the outer membrane of its prey and enters the periplasmic space. As it grows, it forms a long filament that eventually forms septae and produces progeny bacteria. Lysis of the prey cell releases new bdellovibrio cells. Bdellovibrios will not attack mammalian cells, and Gram-negative prey bacteria have never been observed to acquire resistance to bdellovibrios.

This has raised interest in the use of these bacteria as a "probiotic" to treat infected wounds. Although this has not yet been tried, one can imagine that with the rise in antibiotic-resistant pathogens, such forms of treatments may be considered viable alternatives.

Pollination

Pollination has driven the coevolution of flowering plants and their animal pollinators for over 100 million years.

 

See also: Pollination and Plant-pollinator interactions

In pollination, pollinators including insects (entomophily), some birds (ornithophily), and some bats, transfer pollen from a male flower part to a female flower part, enabling fertilisation, in return for a reward of pollen or nectar. The partners have coevolved through geological time; in the case of insects and flowering plants, the coevolution has continued for over 100 million years. Insect-pollinated flowers are adapted with shaped structures, bright colours, patterns, scent, nectar, and sticky pollen to attract insects, guide them to pick up and deposit pollen, and reward them for the service. Pollinator insects like bees are adapted to detect flowers by colour, pattern, and scent, to collect and transport pollen (such as with bristles shaped to form pollen baskets on their hind legs), and to collect and process nectar (in the case of honey bees, making and storing honey). The adaptations on each side of the interaction match the adaptations on the other side, and have been shaped by natural selection on their effectiveness of pollination.

Seed dispersal

Main article: Seed dispersal

Seed dispersal is the movement, spread or transport of seeds away from the parent plant. Plants have limited mobility and rely upon a variety of dispersal vectors to transport their propagules, including both abiotic vectors such as the wind and living (biotic) vectors like birds. Seeds can be dispersed away from the parent plant individually or collectively, as well as dispersed in both space and time. The patterns of seed dispersal are determined in large part by the dispersal mechanism and this has important implications for the demographic and genetic structure of plant populations, as well as migration patterns and species interactions. There are five main modes of seed dispersal: gravity, wind, ballistic, water, and by animals. Some plants are serotinous and only disperse their seeds in response to an environmental stimulus. Dispersal involves the letting go or detachment of a diaspore from the main parent plant.

Symbiosis: long-term interactions

Main article: Symbiosis

 

The six possible types of symbiotic relationship, from mutual benefit to mutual harm

The six possible types of symbiosis are mutualism, commensalism, parasitism, neutralism, amensalism, and competition. These are distinguished by the degree of benefit or harm they cause to each partner.

Mutualism

Main article: Mutualism (biology)

Mutualism is an interaction between two or more species, where species derive a mutual benefit, for example an increased carrying capacity. Similar interactions within a species are known as co-operation. Mutualism may be classified in terms of the closeness of association, the closest being symbiosis, which is often confused with mutualism. One or both species involved in the interaction may be obligate, meaning they cannot survive in the short or long term without the other species. Though mutualism has historically received less attention than other interactions such as predation, it is an important subject in ecology. Examples include cleaning symbiosis, gut flora, Müllerian mimicry, and nitrogen fixation by bacteria in the root nodules of legumes.

Commensalism

Main article: Commensalism

Commensalism benefits one organism and the other organism is neither benefited nor harmed. It occurs when one organism takes benefits by interacting with another organism by which the host organism is not affected. A good example is a remora living with a manatee. Remoras feed on the manatee's faeces. The manatee is not affected by this interaction, as the remora does not deplete the manatee's resources.

Parasitism

Main article: Parasitism

Parasitism is a relationship between species, where one organism, the parasite, lives on or in another organism, the host, causing it some harm, and is adapted structurally to this way of life. The parasite either feeds on the host, or, in the case of intestinal parasites, consumes some of its food.

Neutralism

Neutralism (a term introduced by Eugene Odum) describes the relationship between two species that interact but do not affect each other. Examples of true neutralism are virtually impossible to prove; the term is in practice used to describe situations where interactions are negligible or insignificant.

Amensalism

Further information: Symbiosis § Amensalism

Amensalism (a term introduced by Haskell) is an interaction where an organism inflicts harm to another organism without any costs or benefits received by itself. Amensalism describes the adverse effect that one organism has on another organism (figure 32.1). This is a unidirectional process based on the release of a specific compound by one organism that has a negative effect on another. A classic example of amensalism is the microbial production of antibiotics that can inhibit or kill other, susceptible microorganisms.

A clear case of amensalism is where sheep or cattle trample grass. Whilst the presence of the grass causes negligible detrimental effects to the animal's hoof, the grass suffers from being crushed. Amensalism is often used to describe strongly asymmetrical competitive interactions, such as has been observed between the Spanish ibex and weevils of the genus Timarcha which feed upon the same type of shrub. Whilst the presence of the weevil has almost no influence on food availability, the presence of ibex has an enormous detrimental effect on weevil numbers, as they consume significant quantities of plant matter and incidentally ingest the weevils upon it.

Amensalisms can be quite complex. Attine ants (ants belonging to a New World tribe) are able to take advantage of an interaction between an actinomycete and a parasitic fungus in the genus Escovopsis. This amensalistic relationship enables the ant to maintain a mutualism with members of another fungal genus, Leucocoprinus. Amazingly, these ants cultivate a garden of Leucocoprinus fungi for their own nourishment. To prevent the parasitic fungus Escovopsis from decimating their fungal garden, the ants also promote the growth of an actinomycete of the genus Pseudonocardia, which produces an antimicrobial compound that inhibits the growth of the Escovopsis fungi.

Competition

Main article: Competition (biology)

 

Male-male interference competition in red deer.

Competition can be defined as an interaction between organisms or species, in which the fitness of one is lowered by the presence of another. Competition is often for a resource such as food, water, or territory in limited supply, or for access to females for reproduction. Competition among members of the same species is known as intraspecific competition, while competition between individuals of different species is known as interspecific competition. According to the competitive exclusion principle, species less suited to compete for resources should either adapt or die out. According to evolutionary theory, this competition within and between species for resources plays a critical role in natural selection.

Non-trophic interactions

See also: Non-trophic networks

 

Foundation species enhance food web complexity
In a 2018 study by Borst et al...

(A) Seven ecosystems with foundation species were sampled: coastal (seagrass, blue mussel, cordgrass), freshwater (watermilfoil, water-starwort) and terrestrial (Spanish moss, marram grass).
(B) Food webs were constructed for both bare and foundation species-dominated replicate areas.
(C) From each foundation species structured-food web, nodes (species) were randomly removed until the species number matched the species number of the bare food webs.

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It was found the presence of foundation species strongly enhanced food web complexity, facilitating particularly species higher in the food chains.

Some examples of non-trophic interactions are habitat modification, mutualism and competition for space. It has been suggested recently that non-trophic interactions can indirectly affect food web topology and trophic dynamics by affecting the species in the network and the strength of trophic links. A number of recent theoretical studies have emphasized the need to integrate trophic and non-trophic interactions in ecological network analyses. The few empirical studies that address this suggest food web structures (network topologies) can be strongly influenced by species interactions outside the trophic network. However these studies include only a limited number of coastal systems, and it remains unclear to what extent these findings can be generalized. Whether non-trophic interactions typically affect specific species, trophic levels, or functional groups within the food web, or, alternatively, indiscriminately mediate species and their trophic interactions throughout the network has yet to be resolved. Some studies suggest sessile species with generally low trophic levels seem to benefit more than others from non-trophic facilitation, while other studies suggest facilitation benefits higher trophic and more mobile species as well.

A 2018 study by Borst et al.. tested the general hypothesis that foundation species — spatially dominant habitat-structuring organisms – modify food webs by enhancing their size as indicated by species number, and their complexity as indicated by link density, via facilitation of species, regardless of ecosystem type (see diagram). Additionally, they tested that any change in food web properties caused by foundation species occurs via random facilitation of species throughout the entire food web or via targeted facilitation of specific species that belong to certain trophic levels or functional groups. It was found that species at the base of the food web are less strongly, and carnivores are more strongly facilitated in foundation species' food webs than predicted based on random facilitation, resulting in a higher mean trophic level and a longer average chain length. This indicates foundation species strongly enhance food web complexity through non-trophic facilitation of species across the entire trophic network.

Although foundation species are part of the food web like any other species (e.g. as prey or predator), numerous studies have shown that they strongly facilitate the associated community by creating new habitat and alleviating physical stress. This form of non-trophic facilitation by foundation species has been found to occur across a wide range of ecosystems and environmental conditions. In harsh coastal zones, corals, kelps, mussels, oysters, seagrasses, mangroves, and salt marsh plants facilitate organisms by attenuating currents and waves, providing aboveground structure for shelter and attachment, concentrating nutrients, and/or reducing desiccation stress during low tide exposure. In more benign systems, foundation species such as the trees in a forest, shrubs and grasses in savannahs, and macrophytes in freshwater systems, have also been found to play a major habitat-structuring role. Ultimately, all foundation species increase habitat complexity and availability, thereby partitioning and enhancing the niche space available to other species.