mutualism (biology)
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Mutualism describes the ecological
interaction Interaction is a kind of action that occurs as two or more objects have an effect upon one another. The idea of a two-way effect is essential in the concept of interaction, as opposed to a one-way causal effect. Closely related terms are interac ...
between two or more
species In biology, a species is the basic unit of biological classification, classification and a taxonomic rank of an organism, as well as a unit of biodiversity. A species is often defined as the largest group of organisms in which any two individu ...

species
where each species has a net benefit. Mutualism is a common type of ecological interaction. Prominent examples include most vascular plants engaged in mutualistic interactions with
mycorrhizae A mycorrhiza (from Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is appro ...
, flowering plants being pollinated by animals, vascular plants being dispersed by animals, and
coral Corals are marine invertebrates Marine invertebrates are the invertebrates that live in marine habitats. Invertebrate is a blanket term that includes all animals apart from the vertebrate members of the chordate phylum. Invertebrates lack a ver ...

coral
s with
zooxanthellae Zooxanthellae is a colloquial term for single-celled dinoflagellates that are able to live in symbiosis with diverse marine invertebrates including demosponges, corals, jellyfish, and nudibranchs. Most known zooxanthellae are in the genus ''Symbi ...

zooxanthellae
, among many others. Mutualism can be contrasted with
interspecific competition Interspecific competition, in ecology Ecology (from el, οἶκος, "house" and el, -λογία, label=none, "study of") is the study of the relationships between living organisms, including humans, and their physical environment. Ecology ...
, in which each species experiences ''reduced'' fitness, and
exploitation Exploitation may refer to: *Exploitation of natural resources *Exploitation of labour *Exploitation fiction *Exploitation film *Exploitation (film), ''Exploitation'' (film), a 2012 film *Sexual slavery and other forms of slavery *Oppression See al ...
, or
parasitism Parasitism is a close relationship between species In biology, a species is the basic unit of biological classification, classification and a taxonomic rank of an organism, as well as a unit of biodiversity. A species is often defined ...

parasitism
, in which one species benefits at the "expense" of the other. The term ''mutualism'' was introduced by
Pierre-Joseph van Beneden Pierre-Joseph van Beneden FRS FRS may also refer to: Government and politics * Facility Registry System, a centrally managed Environmental Protection Agency database that identifies places of environmental interest in the United States * Family R ...

Pierre-Joseph van Beneden
in his 1876 book ''Animal Parasites and Messmates'' to mean "mutual aid among species". Mutualism is often conflated with two other types of ecological phenomena: cooperation and symbiosis.
Cooperation Cooperation (written as co-operation in British English British English (BrE) is the standard dialect A standard language (also standard variety, standard dialect, and standard) is a language variety that has undergone substantial ...

Cooperation
most commonly refers to increases in fitness through within-species (intraspecific) interactions, although it has been used (especially in the past) to refer to mutualistic interactions, and it is sometimes used to refer to mutualistic interactions that are not obligate.
Symbiosis Symbiosis (from Ancient Greek, Greek , , "living together", from , , "together", and , bíōsis, "living") is any type of a close and long-term biological interaction between two different Organism, biological organisms, be it Mutualism (biolog ...

Symbiosis
involves two species living in close physical contact over a long period of their existence and may be mutualistic, parasitic, or
commensal Commensalism is a long-term biological interaction In ecology Ecology (from el, οἶκος, "house" and el, -λογία, label=none, "study of") is the study of the relationships between living organisms, including humans, and their ph ...

commensal
, so symbiotic relationships are not always mutualistic, and mutualistic interactions are not always symbiotic. Despite a different definition between mutualistic interactions and symbiosis, mutualistic and symbiosis have been largely used interchangeably in the past, and confusion on their use has persisted. Mutualism plays a key part in
ecology Ecology (from el, οἶκος, "house" and el, -λογία, label=none, "study of") is the study of the relationships between living organisms, including humans, and their physical environment. Ecology considers organisms In biol ...
and
evolution Evolution is change in the heritable Heredity, also called inheritance or biological inheritance, is the passing on of Phenotypic trait, traits from parents to their offspring; either through asexual reproduction or sexual reproduction, ...

evolution
. For example, mutualistic interactions are vital for terrestrial
ecosystem An ecosystem (or ecological system) consists of all the organisms and the physical environment with which they interact. These biotic and abiotic components are linked together through nutrient cycles and energy flows. Energy enters the syst ...

ecosystem
function as about 80% of land plants species rely on
mycorrhizal A mycorrhiza (from Ancient Greek, Greek μύκης ', "fungus", and ῥίζα ', "root"; pl. mycorrhizae, mycorrhiza or mycorrhizas) is a mutual symbiosis, symbiotic association between a fungus and a plant. The term mycorrhiza refers to the role ...
relationships with
fungi A fungus (plural The plural (sometimes abbreviated An abbreviation (from Latin ''brevis'', meaning ''short'') is a shortened form of a word or phrase, by any method. It may consist of a group of letters, or words taken from the full ...

fungi
to provide them with inorganic compounds and trace elements. As another example, the estimate of tropical rainforest plants with seed dispersal mutualisms with animals ranges at least from 70–93.5%.Jordano, P. 2000. Fruits and frugivory. pp. 125–166 in: Fenner, M. (Ed) ''Seeds: the ecology of regeneration in plant communities''. CABI. In addition, mutualism is thought to have driven the evolution of much of the biological diversity we see, such as
flower A flower, sometimes known as a bloom or blossom Image:Cerisier du Japon Prunus serrulata.jpg, Cherry blossoms in Paris in full bloom. In botany, blossoms are the flowers of stone fruit fruit tree, trees (genus ''Prunus'') and of some other plan ...

flower
forms (important for
pollination Pollination is the transfer of pollen Pollen is a powdery substance consisting of pollen grains which are Sporophyte, microsporophytes of spermatophyta, seed plants, which produce male gametes (sperm cells). Pollen grains have a hard coat ...

pollination
mutualisms) and
co-evolution In biology, coevolution occurs when two or more species In biology, a species is the basic unit of biological classification, classification and a taxonomic rank of an organism, as well as a unit of biodiversity. A species is often defined ...
between groups of species. Mutualism has also been linked to major evolutionary events, such as the evolution of the eukaryotic cell (
symbiogenesis Symbiogenesis, endosymbiotic theory, or serial endosymbiotic theory is the leading evolutionary theory of the origin of eukaryotic cells from prokaryotic organisms. The theory holds that mitochondria, plastids such as chloroplasts, and possibly oth ...

symbiogenesis
) or the colonization of land by plants in association with mycorrhizal fungi.


Types


Resource-resource relationships

Mutualistic relationships can be thought of as a form of "biological barter" in
mycorrhizal A mycorrhiza (from Ancient Greek, Greek μύκης ', "fungus", and ῥίζα ', "root"; pl. mycorrhizae, mycorrhiza or mycorrhizas) is a mutual symbiosis, symbiotic association between a fungus and a plant. The term mycorrhiza refers to the role ...
associations between plant
root In vascular plant Vascular plants (from Latin ''vasculum'': duct), also known as Tracheophyta (the tracheophytes , from Greek τραχεῖα ἀρτηρία ''trācheia artēria'' 'windpipe' + φυτά ''phutá'' 'plants'), form a large grou ...

root
s and
fungi A fungus (plural The plural (sometimes abbreviated An abbreviation (from Latin ''brevis'', meaning ''short'') is a shortened form of a word or phrase, by any method. It may consist of a group of letters, or words taken from the full ...

fungi
, with the plant providing
carbohydrates A carbohydrate () is a biomolecule , showing alpha helices, represented by ribbons. This poten was the first to have its suckture solved by X-ray crystallography by Max Perutz and Sir John Cowdery Kendrew in 1958, for which they received a ...
to the
fungus A fungus (plural The plural (sometimes abbreviated An abbreviation (from Latin ''brevis'', meaning ''short'') is a shortened form of a word or phrase, by any method. It may consist of a group of letters, or words taken from the full ...

fungus
in return for primarily
phosphate In chemistry, a phosphate is an anion, salt (chemistry), salt, functional group or ester derived from a phosphoric acids and phosphates, phosphoric acid. It most commonly means orthophosphate, a derivative of phosphoric acid, orthophosphoric a ...

phosphate
but also
nitrogenous Nitrogen is the chemical element In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, properties, b ...
compounds. Other examples include
rhizobia Rhizobia are diazotrophic bacteria Bacteria (; common noun bacteria, singular bacterium) are a type of biological cell The cell (from Latin ''cella'', meaning "small room") is the basic structural, functional, and biological unit o ...

rhizobia
bacteria that fix nitrogen for
leguminous A legume () is a plant Plants are predominantly photosynthetic Photosynthesis is a process used by plants and other organisms to Energy transformation, convert light energy into chemical energy that, through cellular respiration, can ...
plants (family Fabaceae) in return for energy-containing
carbohydrates A carbohydrate () is a biomolecule , showing alpha helices, represented by ribbons. This poten was the first to have its suckture solved by X-ray crystallography by Max Perutz and Sir John Cowdery Kendrew in 1958, for which they received a ...
.


Service-resource relationships

Service-resource relationships are common. Three important types are pollination, cleaning symbiosis, and zoochory. In
pollination Pollination is the transfer of pollen Pollen is a powdery substance consisting of pollen grains which are Sporophyte, microsporophytes of spermatophyta, seed plants, which produce male gametes (sperm cells). Pollen grains have a hard coat ...

pollination
, a plant trades food resources in the form of
nectar Nectar is a sugar Sugar is the generic name for , soluble s, many of which are used in food. Simple sugars, also called s, include , , and . Compound sugars, also called s or double sugars, are molecules made of two monosaccharides jo ...

nectar
or
pollen Pollen is a powdery substance consisting of pollen grains which are microsporophytes of seed plants The spermatophytes (; ), also known as phanerogams (taxon Phanerogamae) or phaenogams (taxon Phaenogamae), comprise those plant Plant ...

pollen
for the service of pollen dispersal.
Phagophile Phagophilia or phagophily is feeding on parasites. German zoologist M. Beier reported that phagophilia is the feeding behavior of some pseudoscorpions. It was reported that many pseudoscorpions species co-exist with some packrat species, and two o ...
s feed (resource) on
ectoparasite Parasitism is a close relationship between species In biology, a species is the basic unit of biological classification, classification and a taxonomic rank of an organism, as well as a unit of biodiversity. A species is often defined ...
s, thereby providing anti-pest service, as in
cleaning symbiosis Cleaning symbiosis is a mutualism (biology), mutually beneficial association between individuals of two species, where one (the cleaner) removes and eats parasites and other materials from the surface of the other (the client). Cleaning symbiosi ...
. ''
Elacatinus ''Elacatinus'' is a genus Genus /ˈdʒiː.nəs/ (plural genera /ˈdʒen.ər.ə/) is a taxonomic rank In biological classification In biology, taxonomy () is the scientific study of naming, defining (Circumscription (taxonomy), circ ...
'' and ''
Gobiosoma ''Gobiosoma'' is a genus Genus /ˈdʒiː.nəs/ (plural genera /ˈdʒen.ər.ə/) is a taxonomic rank In biological classification In biology, taxonomy () is the scientific study of naming, defining (Circumscription (taxonomy), circum ...
'', genera of
gobies Gobiidae is a family In , family (from la, familia) is a of people related either by (by recognized birth) or (by marriage or other relationship). The purpose of families is to maintain the well-being of its members and of society. Id ...

gobies
, feed on ectoparasites of their clients while cleaning them.
Zoochory 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 li ...
is the dispersal of the seeds of plants by animals. This is similar to pollination in that the plant produces food resources (for example, fleshy fruit, overabundance of seeds) for animals that disperse the seeds (service). Plants may advertise these resources using colour and a variety of other fruit characteristics. Another type is
ant Ants are eusocial Eusociality (from Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population i ...

ant
protection of
aphids Aphids are small sap SAP SE () is a German multinational software corporation based in Walldorf, Baden-Württemberg Baden-Württemberg (; ) is a States of Germany, state (''Land'') in southwest Germany, east of the Rhine, which for ...

aphids
, where the aphids trade
sugar Sugar is the generic name for sweet-tasting, soluble carbohydrate is a disaccharide A disaccharide (also called a double sugar or ''biose'') is the sugar formed when two monosaccharides are joined by glycosidic linkage. Like monosacc ...

sugar
-rich honeydew (a by-product of their mode of feeding on plant
sap SAP SE () is a German multinational Multinational may refer to: * Multinational corporation, a corporate organization operating in multiple countries * Multinational force, a military body from multiple countries * Multinational state, a sove ...

sap
) in return for defense against
predator Predation is a biological interaction In ecology Ecology (from el, οἶκος, "house" and el, -λογία, label=none, "study of") is the study of the relationships between living organisms, including humans, and their physical en ...

predator
s such as
ladybug Coccinellidae () is a widespread family (biology), family of small beetles ranging in size from . The family is commonly known as ladybugs in North America and ladybirds in Great Britain and other parts of the English-speaking world. Entomolog ...

ladybug
s.


Service-service relationships

Strict service-service interactions are very rare, for reasons that are far from clear. One example is the relationship between
sea anemone Sea anemones are the marine, predatory Predation is a biological interaction In ecology Ecology (from el, οἶκος, "house" and el, -λογία, label=none, "study of") is the study of the relationships between living organisms ...

sea anemone
s and
anemone fish Clownfish or anemonefish are fish Fish are aquatic Aquatic means relating to water Water (chemical formula H2O) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main co ...

anemone fish
in the family
Pomacentridae Pomacentridae is a family (biology), family of ray-finned fish, comprising the damselfishes and clownfishes. This family were formerly placed in the order Perciformes but are now regarded as being ''incertae sedis'' in the subseries Ovalentaria ...
: the anemones provide the fish with protection from
predator Predation is a biological interaction In ecology Ecology (from el, οἶκος, "house" and el, -λογία, label=none, "study of") is the study of the relationships between living organisms, including humans, and their physical en ...

predator
s (which cannot tolerate the stings of the anemone's tentacles) and the fish defend the anemones against
butterflyfish The butterflyfish are a group of conspicuous tropical The tropics are the region of Earth Earth is the third planet from the Sun and the only astronomical object known to harbour and support life. 29.2% of Earth's surface is land ...

butterflyfish
(family ), which eat anemones. However, in common with many mutualisms, there is more than one aspect to it: in the anemonefish-anemone mutualism, waste
ammonia Ammonia is a chemical compound, compound of nitrogen and hydrogen with the chemical formula, formula NH3. A Binary compounds of hydrogen, stable binary hydride, and the simplest pnictogen hydride, ammonia is a colourless gas with a distinct ch ...

ammonia
from the fish feeds the
symbiotic Symbiosis (from Ancient Greek, Greek , , "living together", from , , "together", and , bíōsis, "living") is any type of a close and long-term biological interaction between two different Organism, biological organisms, be it Mutualism (biolog ...
algae Algae (; singular alga ) is an informal term for a large and diverse group of photosynthetic Photosynthesis is a process used by plants and other organisms to convert Conversion or convert may refer to: Arts, entertainment, and media * Co ...

algae
that are found in the anemone's tentacles. Therefore, what appears to be a service-service mutualism in fact has a service-resource component. A second example is that of the relationship between some
ants Ants are eusocial Eusociality (from Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is ...

ants
in the genus ''
Pseudomyrmex ''Pseudomyrmex'' is a genus Genus /ˈdʒiː.nəs/ (plural genera /ˈdʒen.ər.ə/) is a taxonomic rank In biological classification In biology, taxonomy () is the scientific study of naming, defining (Circumscription (taxonomy), cir ...
'' and trees in the
genus Genus /ˈdʒiː.nəs/ (plural genera /ˈdʒen.ər.ə/) is a taxonomic rank In biological classification In biology, taxonomy () is the scientific study of naming, defining (Circumscription (taxonomy), circumscribing) and classifying gr ...
''
Acacia ''Acacia'', commonly known as the wattles or acacias, is a large genus Genus /ˈdʒiː.nəs/ (plural genera /ˈdʒen.ər.ə/) is a taxonomic rank In biological classification In biology, taxonomy () is the scientific study of nam ...

Acacia
'', such as the
whistling thorn ''Vachellia drepanolobium'', commonly known as whistling thorn, is a swollen-thorn Acacia sensu lato, acacia native to East Africa. The whistling thorn grows up to 6 meters tall. It produces a pair of straight spines at each node, some of which h ...

whistling thorn
and
bullhorn acacia Bull horn acacia is a common name for several plants with large thorns resembling a bull's horns: *''Acacia collinsii'', native to Central America and parts of Africa *''Acacia cornigera'', native to Mexico and Central America *''Acacia sphaeroceph ...
. The
ants Ants are eusocial Eusociality (from Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is ...

ants
nest inside the plant's thorns. In exchange for shelter, the ants protect acacias from attack by
herbivores A herbivore is an animal Animals (also called Metazoa) are multicellular A multicellular organism is an organism In biology, an organism () is any organic, life, living system that functions as an individual entity. All ...
(which they frequently eat when those are small enough, introducing a resource component to this service-service relationship) and competition from other plants by trimming back vegetation that would shade the acacia. In addition, another service-resource component is present, as the ants regularly feed on
lipid In biology Biology is the natural science that studies life and living organisms, including their anatomy, physical structure, Biochemistry, chemical processes, Molecular biology, molecular interactions, Physiology, physiological mechanis ...
-rich food-bodies called
Beltian bodies A Beltian body is a detachable tip found on the pinnules of some species of ''Acacia'' and closely related genera. Beltian bodies, named after Thomas Belt, are rich in lipids, sugars and proteins and often red in colour. They are believed to have e ...
that are on the ''Acacia'' plant. In the
neotropics The Neotropical realm is one of the eight biogeographic realm A biogeographic realm or ecozone is the broadest biogeographic Biogeography is the study of the distribution of species In biology, a species is the basic unit of bio ...
, the ant ''
Myrmelachista schumanni ''Myrmelachista schumanni'', also known as the lemon ant, is a species of ant Ants are eusocial Eusociality (from Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officiall ...
'' makes its nest in special cavities in '' Duroia hirsute''. Plants in the vicinity that belong to other species are killed with
formic acid Formic acid, systematically named methanoic acid, is the simplest carboxylic acid A carboxylic acid is an organic acid An organic acid is an organic compound with acidic properties. The most common organic acids are the carboxylic acid ...

formic acid
. This selective gardening can be so aggressive that small areas of the rainforest are dominated by ''Duroia hirsute''. These peculiar patches are known by local people as "
devil's garden Devils Garden is an area of Arches National Park, located near Moab, Utah, Moab, Utah, United States, that features a series of rock (geology), rock Fin (geology), fins and natural arch, arches formed by erosion. The Devils Garden Trail, including ...

devil's garden
s". Piper, Ross (2007), ''Extraordinary Animals: An Encyclopedia of Curious and Unusual Animals'',
Greenwood Press Greenwood Publishing Group, Inc. (GPG), also known as ABC-Clio/Greenwood (stylized ABC-CLIO/Greenwood), is an educational and academic publisher (middle school A middle school (also known as intermediate school, junior high school, or lower ...
.
In some of these relationships, the cost of the ant's protection can be quite expensive. ''
Cordia ''Cordia'' is a genus Genus /ˈdʒiː.nəs/ (plural genera /ˈdʒen.ər.ə/) is a taxonomic rank In biological classification In biology, taxonomy () is the scientific study of naming, defining (Circumscription (taxonomy), circumsc ...
'' sp. trees in the
Amazonian rainforest The Amazon rainforest, alternatively, the Amazon jungle or ; es, Selva amazónica, , or usually ; french: Forêt amazonienne; nl, Amazoneregenwoud. In English, the names are sometimes capitalized further, as Amazon Rainforest, Amazon Forest ...

Amazonian rainforest
have a kind of partnership with ''
Allomerus ''Allomerus'' is a Neotropical genus of small ants in the subfamily Myrmicinae. Its eight species are known from the forests of South America, where they live in plant cavities and structures. Species *''Allomerus brevipilosus'' Fernández, 200 ...
'' sp. ants, which make their nests in modified leaves. To increase the amount of living space available, the ants will destroy the tree's flower buds. The flowers die and leaves develop instead, providing the ants with more dwellings. Another type of ''Allomerus'' sp. ant lives with the '' Hirtella'' sp. tree in the same forests, but in this relationship, the tree has turned the tables on the ants. When the tree is ready to produce flowers, the ant abodes on certain branches begin to wither and shrink, forcing the occupants to flee, leaving the tree's flowers to develop free from ant attack. The term "species group" can be used to describe the manner in which individual organisms group together. In this non-taxonomic context one can refer to "same-species groups" and "mixed-species groups." While same-species groups are the norm, examples of mixed-species groups abound. For example, zebra ('' Equus burchelli'') and wildebeest ('''') can remain in association during periods of long distance wikt:migration, migration across the Serengeti as a strategy for thwarting predators. ''Cercopithecus mitis'' and ''Cercopithecus ascanius'', species of monkey in the Kakamega Forest of Kenya, can stay in close proximity and travel along exactly the same routes through the forest for periods of up to 12 hours. These mixed-species groups cannot be explained by the coincidence of sharing the same habitat. Rather, they are created by the active behavioural choice of at least one of the species in question.


Mathematical modeling

Mathematical treatments of mutualisms, like the study of mutualisms in general, has lagged behind those of predation, or predator-prey, consumer-resource, interactions. In models of mutualisms, the terms "type I" and "type II" functional responses refer to the linear and saturating relationships, respectively, between ''benefit'' provided to an individual of species 1 (''y''-axis) on the ''density'' of species 2 (''x''-axis).


Type I functional response

One of the simplest frameworks for modeling species interactions is the Lotka–Volterra equations.May, R., 1981. Models for Two Interacting Populations. In: May, R.M., Theoretical Ecology. Principles and Applications, 2nd ed. pp. 78–104. In this model, the change in population density of the two mutualists is quantified as: : \begin \frac &=r_1 N_1 - \alpha_ N_1^2 + \beta _N_1N_2 \\[8pt] \frac &=r_2 N_2 - \alpha_ N_2^2 + \beta _N_1N_2 \end where * N_i = the population densities. * r_i = the intrinsic growth rate of the population. * \alpha _ = the negative effect of within-species crowding. * \beta _ = the beneficial effect of a mutualistic partner's density. Mutualism is in essence the Logistic function, logistic growth equation + mutualistic interaction. The mutualistic interaction term represents the increase in population growth of species one as a result of the presence of greater numbers of species two, and vice versa. As the mutualistic term is always positive, it may lead to unrealistic unbounded growth as it happens with the simple model. So, it is important to include a saturation mechanism to avoid the problem.


Type II functional response

In 1989, David Hamilton Wright modified the Lotka–Volterra equations by adding a new term, ''βM''/''K'', to represent a mutualistic relationship. Wright also considered the concept of saturation, which means that with higher densities, there are decreasing benefits of further increases of the mutualist population. Without saturation, species' densities would increase indefinitely. Because that is not possible due to environmental constraints and carrying capacity, a model that includes saturation would be more accurate. Wright's mathematical theory is based on the premise of a simple two-species mutualism model in which the benefits of mutualism become saturated due to limits posed by handling time. Wright defines handling time as the time needed to process a food item, from the initial interaction to the start of a search for new food items and assumes that processing of food and searching for food are mutually exclusive. Mutualists that display foraging behavior are exposed to the restrictions on handling time. Mutualism can be associated with symbiosis. Handling time interactions In 1959, C. S. Holling performed his classic disc experiment that assumed the following: that (1), the number of food items captured is proportional to the allotted Search time, searching time; and (2), that there is a variable of handling time that exists separately from the notion of search time. He then developed an equation for the Type II functional response, which showed that the feeding rate is equivalent to : \cfrac where, * a=the instantaneous discovery rate * x=food item density * TH=handling time The equation that incorporates Type II functional response and mutualism is: : \frac=N\left[r(1-cN)+\cfrac\right] where * ''N'' and ''M''=densities of the two mutualists * ''r''=intrinsic rate of increase of ''N'' * ''c''=coefficient measuring negative intraspecific interaction. This is equivalent to inverse of the carrying capacity, 1/''K'', of ''N'', in the Logistic function#Logistic differential equation, logistic equation. * ''a''=instantaneous discovery rate * ''b''=coefficient converting encounters with ''M'' to new units of ''N'' or, equivalently, : \frac=N[r(1-cN)+\beta M/(X+M)] where * ''X''=1/''a'' ''T''H * ''β''=''b''/''T''H This model is most effectively applied to free-living species that encounter a number of individuals of the mutualist part in the course of their existences. Wright notes that models of biological mutualism tend to be similar qualitatively, in that the featured isoclines generally have a positive decreasing slope, and by and large similar isocline diagrams. Mutualistic interactions are best visualized as positively sloped isoclines, which can be explained by the fact that the saturation of benefits accorded to mutualism or restrictions posed by outside factors contribute to a decreasing slope. The type II functional response is visualized as the graph of \cfrac ''vs.'' ''M''.


Structure of networks

Mutualistic networks made up out of the interaction between plants and pollinators were found to have a similar structure in very different ecosystems on different continents, consisting of entirely different species. The structure of these mutualistic networks may have large consequences for the way in which pollinator communities respond to increasingly harsh conditions and on the community carrying capacity. Mathematical models that examine the consequences of this network structure for the stability of pollinator communities suggest that the specific way in which plant-pollinator networks are organized minimizes competition between pollinators, reduce the spread of indirect effects and thus enhance ecosystem stability and may even lead to strong indirect facilitation between pollinators when conditions are harsh. This means that pollinator species together can survive under harsh conditions. But it also means that pollinator species collapse simultaneously when conditions pass a critical point. This simultaneous collapse occurs, because pollinator species depend on each other when surviving under difficult conditions. Such a community-wide collapse, involving many pollinator species, can occur suddenly when increasingly harsh conditions pass a critical point and recovery from such a collapse might not be easy. The improvement in conditions needed for pollinators to recover could be substantially larger than the improvement needed to return to conditions at which the pollinator community collapsed.


Humans

Humans are involved in mutualisms with other species: their gut flora is essential for efficient digestion. Infestations of head lice ''might'' have been beneficial for humans by fostering an immune response that helps to reduce the threat of body louse borne lethal diseases. Some relationships between humans and domestication, domesticated animals and plants are to different degrees mutualistic. For example, agricultural varieties of maize provide food for humans and are unable to reproduce without human intervention because the leafy sheath does not fall open, and the seedhead (the "corn on the cob") does not Shattering (agriculture), shatter to scatter the seeds naturally. In traditional agriculture, some plants have mutualist as Companion planting, companion plants, providing each other with shelter, soil fertility and/or natural pest control. For example, beans may grow up Maize, cornstalks as a trellis, while fixing nitrogen in the soil for the corn, a phenomenon that is used in Three Sisters (agriculture), Three Sisters farming. One researcher has proposed that the key advantage ''Homo sapiens'' had over Neanderthals in competing over similar habitats was the former's mutualism with dogs.


Evolution of mutualism


Evolution by type

Every generation of every organism needs nutrients and similar nutrients more than they need particular defensive characteristics, as the fitness benefit of these vary heavily especially by environment. This may be the reason that hosts are more likely to evolve to become dependent on vertically transmitted bacterial mutualists which provide nutrients than those providing defensive benefits. This pattern is generalized beyond bacteria by Yamada et al 2015's demonstration that undernourished ''Drosophila melanogaster, Drosophila'' are heavily dependent on their fungal symbiont ''Issatchenkia Issatchenkia orientalis, orientalis'' for amino acids.


Mutualism breakdown

Mutualisms are not static, and can be lost by evolution. Sachs and Simms (2006) suggest that this can occur via four main pathways: # One mutualist shifts to parasitism, and no longer benefits its partner, such as headlice # One partner abandons the mutualism and lives autonomously # One partner may go extinct # A partner may be switched to another species There are many examples of mutualism breakdown. For example, plant lineages inhabiting nutrient-rich environments have evolutionarily abandoned mycorrhizal mutualisms many times independently.


Measuring and defining mutualism

Measuring the exact Fitness (biology), fitness benefit to the individuals in a mutualistic relationship is not always straightforward, particularly when the individuals can receive benefits from a variety of species, for example most plant-pollinator mutualisms. It is therefore common to categorise mutualisms according to the closeness of the association, using terms such as obligate and facultative. Defining "closeness", however, is also problematic. It can refer to mutual dependency (the species cannot live without one another) or the biological intimacy of the relationship in relation to physical closeness (''e.g.'', one species living within the tissues of the other species).Ollerton, J. 2006. "Biological Barter": Interactions of Specialization Compared across Different Mutualisms. pp. 411–435 in: Waser, N.M. & Ollerton, J. (Eds) ''Plant-Pollinator Interactions: From Specialization to Generalization''. University of Chicago Press.


See also

* Arbuscular mycorrhiza * Co-adaptation * Coevolution * Ecological facilitation * Frugivore * Greater honeyguide – has a mutualism with humans * Interspecies communication * Müllerian mimicry * Mutualisms and conservation * ''Mutual Aid: A Factor of Evolution'' * Symbiogenesis


References


Further references

* * * * * * * Bronstein JL. 2001. The costs of mutualism. ''American Zoologist'' 41 (4): 825-839 S * * * * * * * * * Ollerton, J. 2006. "Biological Barter": Patterns of Specialization Compared across Different Mutualisms. pp. 411–435 in: Waser, N.M. & Ollerton, J. (Eds) Plant-Pollinator Interactions: From Specialization to Generalization. University of Chicago Press. * * * * Thompson, J. N. 2005. ''The Geographic Mosaic of Coevolution''. University of Chicago Press. *


Further reading

* * Boucher, D. H. (editor) (1985) ''The Biology of Mutualism : Ecology and Evolution'' London : Croom Helm 388 p.  {{DEFAULTSORT:Mutualism (Biology) Mutualism (biology), Biological interactions Symbiosis Ethology