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Self-Organized Patchiness in Ecosystems Information

General definition

Formation of patchiness

The formation of self-orgninzed patches is driven by the intercations between organisms which lead to the emergence of higher order spatial structures. Organisms in nature interact in in many ways. These interactions can be positve e.g organisms support each other and cooperatively facilitate growth or negative by restraining each other e.g by competiton for resources. Self-organized patchiness is supposed to be caused by a combination of positive and negative interactions, where positive interactions have to be short-range and the negative interaction longe-range. The local facilitation of growth leads to areas with high species densities interupted by areas of low species densities caused by the long-range negative interactions: the occurence of patches. Those patches often have a typical size set by the range of the interactions. The different length scales of positive and negative interactions are often caused by different diffusion constants of the activator and inhibitor, slow diffusion of the activator (e.g the cooperating organisms) and fast diffusion of the growth inhibitor. Instead of an inhibitor often the depleiton of fast diffusing resources can mediate the long diestance competition. This situation gives rise to reaction-diffusion patterns also known as Turing patterns.

Examples of Self-Organized Patchiness Information

Self-organized patches can be found in large variety of terrestial and aquatic ecosystems. They are very often rather rough ecosystems, with scarce resources and extreme weather or water-flow conditions. Those demanding conditions make positive, cooperative interactions between the organisms beneficial and leads to strong competitions for rare resources, the ingredients for self-organized patches.

Patterned Vegetation

Arid Ecosystems

Self-oranized Pattern foramton has been observed in a large variety of arid ecosystems like savanna grass and bushland ^{[1] [2] [3] [4]}. Leading to regular pattern in the shape of stripes ( tiger bush), spots, gaps and labyrinths. The formation of those patches in dry ecosystems is explained by the increased retention of surface water by vegetation and thus an increase of water infiltration into the ground. Local high density of vegetation causes an increased water supply for itself. The water is correspodingly missing in the neighbourhood of those patches and vegetation can not sustain there. In some cases not water but nutrient has be suggested as limiting factor: in savannas groups of trees support each other in growth, but deplete the nutrients around these groups by long roots causing growth inhibition over some distance.

Wetland Ecosystems

In wetlands patterns can occur as strings or maze like structures with areas of higher plant growth separated by wetter zones with less vegetation ^[5]. The formation of line patterns can be explained by a slow downhill flow of water. Places with higher density of plants retain and accumulate solid material on which further plants can grow (Checkk and CITE), they basically form small string like islands which supports their own growth. Correspondingly those string are perpendicular to the flow direction of the water.

For the formation of maze like structures it has been suggested that the transpiration of locally growing spots of vegetation causes a water flow. This flow transports nutrient to the plants over some distance and thus leads to nutrient depletion and thus inhibition of growth in the neighbourhood of those vegetatinos spots. (Check and cite)

Fir Waves

see also main article: Fir Waves

Mussel beds

Mussels that live on soft sediment can form regular stripes and patches. The suggested mechanism is that mussels adhere to each other forming clusters that prevents them from being washed away by the water flow and protects them from predation. These clusters remove a high amount of plancton from the surrounding water which leads to long-range negative interaction beweenn the mussels, limiting the size of the mussel clusters and thus causing the spacing between them. Thus formation of clusters leads to high resilicence against water movement while allowing high food-uptake by minimizing competiton for food ^[6]

Coral reefs

Coral reefs show self-organized on different scales. Single corals grow adopt their growth to local flows by adjusting their shape and orientation. In the reef often distinct pillars formed from corals apperear that are divied by channels with high water flow. And, as whole whole reefs can be arranged along ocean currents. A combination of local amplification of growth and long - distance inhibitoin have been proposed to explain the formation of those patterns. The autocatalytic growth of the corals leads to a depletion of nutrient in the surrounding water giving rise to self-oganized patterns. ^[7]

Microbes

Many microbes are known to form spatial structures, however those structures are often causes by active directed movement towards each other like in the case of the slime mold Dictyostelium discoideum or by limited dispersal of expanding microbes like the patterns that many bacterial colonies form upon growth, but self-organized patchiness is not formed by active, directed movement ( the movement of all agenst is described as undirected diffusion, see below). Nevertheless examples of self- organized patchiness can be found in the microbial realm.

Patches in free living microbes

many bacteria are known to cooperatively interact by the production of public goods, e.g. goods that are accessible by the whole population. Examples of are the the secretion of enzymes or chemical substance. The presence of such public goods leads to cooperative interaction between the bacteria, the more bacteria are present the more public goods are produces which is beneficial for each bacterium in the populaion. However, bacteria also compete for nutrients in their environment. Is the diffusionof the public goods slowert thatn that of the public good this results in a local activation by the public good in compbiaton with a long-rane negatie interaction by competition. In Bacillus subtilils the presecne of a public good ( in this case the enzyme amylase that allows cooperative break down of starch ) causes the ermgence of patchiness. Those patches allows for surival under conditions that would be lethal for homogenounsly distributed bacteria ^[8] .

Patches in bacterial biofilms

Bacteria can secrete mucoid sticky substances that allow the cells to stick together and to form biofilms on surfaces. Since the formation of biofilms depends on the collective secretion of the mucoid substance ( name it?) the formation of biofilms is much easier at high cellular denities since the amunt of mucus a single cell has to produce is lower, leading to a positiv interaction. However, those biofilms are often not homogenous but consist of cluster - often in the shape of mushrooms - separated by areas free of biofilm. THe formation of clusters appears at low nutrient conditions letting suggest that a competition for nutrient causes long-scale negative interactions liting the size of the clusters and setting the spacing between them. Applying flow to those patches results in their elongation - called streamers - and also the formatio of ripple like structures. ^[9]

Microbial mats and stromatolites

Thick biofilms with mutliple layers of microbes are often called microbial mats and appear in mostly in wet enviroments. Those mats can also incorporate sand grains or precipiated caused by biocementation by the microbes and thus can form rather solid structures. The most prominent examples of those mats are likly stromatolites that appear as rather regular patchy, rock like structures. They are normally formed by photosynthetic bacteria like cyanobacteria. The spacing between the single stromatlithes is supposed to be caused by resource depletion during the - photosyntetic active - day. The distance of the spacing is set by the lenght over which the nutrients can diffuse during the day period and accourding varies with illumjination time. ^[10]

Theories and mathematical modelling

Reaction - diffusion models

A common appraoch to model self-organized patches in ecosystems is the usage of differential equations describing the growth (reaction) and movement (diffusion) of the organisms and the resource they consume (e.g. water, nutrient). The time-development of at least the organisms (o) and the resource (r) they use is described with one differential equation each, leading to a two-component reaction–diffusion equation.

${\displaystyle {\begin{pmatrix}\partial _{t}o&\partial _{t}r\end{pmatrix}}={\begin{pmatrix}D_{o}&0\\0&D_{r}\end{pmatrix}}{\begin{pmatrix}\partial _{xx}o\\\partial _{xx}r\end{pmatrix}}+{\begin{pmatrix}F(o,r)\\G(o,r)\end{pmatrix}}}$

The growth of the organisms depends positively on itself (local activation) and the presence of the resource, the resource is consumed by the organims.

The diffusion of the resource is normally faster than that of the organism (${\displaystyle D_{o}<D_{r}}$) and thus the area of resource depletion is much bigger than the area in which the organisms grow ( lateral inhibiton). The combination of local growth activation and lateral resourrce depletion and thus growth inhibition gives rise to Turing type self-organized patterns.

Cellular automata models

Ising type cellular automata have been used to model the emergence of self-organized patchiness. Initially spots of vegetation and vegetation free spots are randomly placed on a regular grid. This virtual ecosystem evolves in time in and round-based way (discrete time). At every round vegetation spots are removed and added. Both proceses are randomly, but weighted for every place on the grid based on the neighborhood of that place. A high amount of vegetation in the neighborhood makes establishment of vegetation more likely, whereas a high amount of vegetation space makes its dissappearanc more likely. The simulation gives rise to the formation of self-organized patches. A basic difference to reaction diffusio based models is that the size distribution of the appreacing patches does not show a typical size. But the size distribution of the patches follows a powerlaw, which could also be found for vegetation clusters in nature ^[2].

Ecological meaning of patchiness Information

Although self-orgnaizhed patchiness is observed in many cases and many theoretical models can explain it, its ecologial function is less clear.

Self-Organized patchiness as survival strategy

Self-organized patchess are supposed to be caused by cooperative interactions between the individuals that form them. Accorddingly those organissm benefit from a high population density because it allows them to cooperative with more other individuals ( Allee effect). In a situation where the environmental conditoins are too rough to keep up a global high density that ensures cooperation the formation of local high density patches allows at least for local cooperation and thus increases the individual fitness, which may allows survivial under conditions that would be lethal for a equally dispersed organisms. Indeed it could be shown in cooeprativiely gowing bacteria that forming self-organized patches drastically increases survival.

name some examples: mussels are more resilient towards preationa and waves,bsubitlis survives lower cell densities,

Self-organized patchiness as a tool for ecosystem restoration

Once an ecosystem is destroyd e.g by desertificaon and deforestration it may be brought back into its natural state by restoration. However it often turnes out that this process is quite difficult since newly introduces organisms fails to established e.g. because of too strong soil erosion in the absence of a covering vegetations. Since vegetation may thrive better at local high densities and thus in patches an idea to overcome this issue is to reintroduce vegetation not uniformly distributed, but in local patches to allow the plants to supports each other e.g. by locally restrain water inthe ground or avoid erosion of soil.

Catastrophic shifts and self-organized patchiness

Ecosystems change over time often driven by external factors, like change of climate, nutrient conditions or anthropogenic influnce. In many cases the ecosystems do not change continously but in a catastrphic shifts, by suddenly jumping between aternating states (--> article Catastrophic shifts in ecosystems). The reasons for this behaviour are likly cooperative interactions between the organisms of an ecosystem that give rise to positive feedback loops, which cause strongly nonlinear behavior. Cooperative interactions are also the driving force behind the formation of self-organized patchiness which lead to the idea that catastrophic shifts and self-organized patchiness may be linked. Several theoretical works propose the onset of spatial patterns as an ecosystem approaches an catastrophic shift which makes self-organized patches a potential early warning factor that allows to estimate how close a ecosystem is to an catastrophic shift and thus identify endangered ecosystems. Indeed many ecosystems that show self-organized patches are systems that face rather extreme conditons like dryness or low nutrient levels.

Public goods and self organized patches

patchiness and evolution? Information

References

External links

• www.example.com