Mutualism (biology)

Mutualistic relationships can be thought of as a form of "biological barter"[10] in mycorrhizal associations between plant roots and fungi, with the plant providing carbohydrates to the fungus in return for primarily phosphate but also nitrogenous compounds. Other examples include rhizobia bacteria that fix nitrogen for leguminous plants (family Fabaceae) in return for energy-containing carbohydrates.[11]

The red-billed oxpecker eats ticks on the impala's coat, in a cleaning symbiosis.

Service-resource relationships are common. Three important types are pollination, cleaning symbiosis, and zoochory.

In pollination, a plant trades food resources in the form of nectar or pollen for the service of pollen dispersal.

Phagophiles feed (resource) on ectoparasites, thereby providing anti-pest service, as in cleaning symbiosis. Elacatinus and Gobiosoma, genera of gobies, feed on ectoparasites of their clients while cleaning them.[12]

Zoochory 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).

Another type is ant protection of aphids, where the aphids trade sugar-rich honeydew (a by-product of their mode of feeding on plant sap) in return for defense against predators such as ladybugs.

Ocellaris clownfish and Ritter's sea anemones live in a mutual service-service symbiosis, the fish driving off butterflyfish and the anemone's tentacles protecting the fish from predators.

Strict service-service interactions are very rare, for reasons that are far from clear.[10] One example is the relationship between sea anemones and anemone fish in the family Pomacentridae: the anemones provide the fish with protection from predators (which cannot tolerate the stings of the anemone's tentacles) and the fish defend the anemones against butterflyfish (family Chaetodontidae), which eat anemones. However, in common with many mutualisms, there is more than one aspect to it: in the anemonefish-anemone mutualism, waste ammonia from the fish feeds the symbiotic algae that are found in the anemone's tentacles.[13][14] 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 in the genus Pseudomyrmex and trees in the genus Acacia, such as the whistling thorn and bullhorn acacia. The ants nest inside the plant's thorns. In exchange for shelter, the ants protect acacias from attack by herbivores (which they frequently eat, 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-rich food-bodies called Beltian bodies that are on the Acacia plant.[15]

In the neotropics, the ant Myrmelachista schumanni makes its nest in special cavities in Duroia hirsute. Plants in the vicinity that belong to other species are killed with 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 gardens".[16]

In some of these relationships, the cost of the ant's protection can be quite expensive. Cordia sp. trees in the Amazonian rainforest have a kind of partnership with Allomerus 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.[16]

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 (Connochaetes taurinus) can remain in association during periods of long distance 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.[17]

One of the simplest frameworks for modeling species interactions is the Lotka–Volterra equations.[18] In this model, the change in population density of the two mutualists is quantified as:

${\displaystyle {\begin{aligned}{\frac {dN_{1}}{dt}}&=r_{1}N_{1}-\alpha _{11}N_{1}^{2}+\beta _{12}N_{1}N_{2}\\[8pt]{\frac {dN_{2}}{dt}}&=r_{2}N_{2}-\alpha _{22}N_{2}^{2}+\beta _{21}N_{1}N_{2}\end{aligned}}}$

where

• ${\displaystyle N_{i}}$ = the population densities.
• ${\displaystyle r_{i}}$ = the intrinsic growth rate of the population.
• ${\displaystyle \alpha _{ii}}$ = the negative effect of within-species crowding.
• ${\displaystyle \beta _{ij}}$ = the beneficial effect of a mutualistic partner's density.

Mutualism is in essence the 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.[19] So, it is important to include a saturation mechanism to avoid the problem.

In 1989, David Hamilton Wright modified the Lotka–Volterra equations by adding a new term, βM/K, to represent a mutualistic relationship.[20] 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 isn't 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 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

${\displaystyle {\cfrac {ax}{1+axT_{H}}}}$

where,

• a=the instantaneous discovery rate
• x=food item density
• T_H=handling time

The equation that incorporates Type II functional response and mutualism is:

${\displaystyle {\frac {dN}{dt}}=N\left[r(1-cN)+{\cfrac {baM}{1+aT_{H}M}}\right]}$

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 equation.
• a=instantaneous discovery rate
• b=coefficient converting encounters with M to new units of N

or, equivalently,

${\displaystyle {\frac {dN}{dt}}=N[r(1-cN)+\beta M/(X+M)]}$

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 ${\displaystyle {\cfrac {baM}{1+aT_{H}M}}}$ vs. M.

Mutualisms are not static, and can be lost by evolution.[32] Sachs and Simms (2006) suggest that this can occur via 4 main pathways:

1. One mutualist shifts to parasitism, and no longer benefits its partner,[32] such as headlice
2. One partner abandons the mutualism and lives autonomously[32]
3. One partner may go extinct[32]
4. A partner may be switched to another species[33]

There are many examples of mutualism breakdown. For example, plant lineages inhabiting nutrient-rich environments have evolutionarily abandoned mycorrhizal mutualisms many times independently.[34]