Proteolysis

From Wikipedia, the free encyclopedia

The hydrolysis of a protein (red) by the nucleophilic attack of water (blue). The uncatalysed half-life is several hundred years.

Proteolysis is the breakdown of proteins into smaller polypeptides or amino acids. Uncatalysed, the hydrolysis of peptide bonds is extremely slow, taking hundreds of years. Proteolysis is typically catalysed by cellular enzymes called proteases, but may also occur by intra-molecular digestion. Low pH or high temperatures can also cause proteolysis non-enzymatically. 

Proteolysis in organisms serves many purposes; for example, digestive enzymes break down proteins in food to provide amino acids for the organism, while proteolytic processing of a polypeptide chain after its synthesis may be necessary for the production of an active protein. It is also important in the regulation of some physiological and cellular processes, as well as preventing the accumulation of unwanted or abnormal proteins in cells. Consequently, dis-regulation of proteolysis can cause disease and is used by some venoms. 

Proteolysis is important as an analytical tool for studying proteins in the laboratory, as well as industrially, for example in food processing and stain removal.

Biological functions

Post-translational proteolytic processing

Limited proteolysis of a polypeptide during or after translation in protein synthesis often occurs for many proteins. This may involve removal of the N-terminal methionine, signal peptide, and/or the conversion of an inactive or non-functional protein to an active one. The precursor to the final functional form of protein is termed proprotein, and these proproteins may be first synthesized as preproprotein. For example, albumin is first synthesized as preproalbumin and contains an uncleaved signal peptide. This forms the proalbumin after the signal peptide is cleaved, and a further processing to remove the N-terminal 6-residue propeptide yields the mature form of the protein.

Removal of N-terminal methionine

The initiating methionine (and, in prokaryotes, fMet) may be removed during translation of the nascent protein. For E. coli, fMet is efficiently removed if the second residue is small and uncharged, but not if the second residue is bulky and charged. In both prokaryotes and eukaryotes, the exposed N-terminal residue may determine the half-life of the protein according to the N-end rule.

Removal of the signal sequence

Proteins that are to be targeted to a particular organelle or for secretion have an N-terminal signal peptide that directs the protein to its final destination. This signal peptide is removed by proteolysis after their transport through a membrane.

Cleavage of polyproteins

Some proteins and most eukaryotic polypeptide hormones are synthesized as a large precursor polypeptide known as a polyprotein that requires proteolytic cleavage into individual smaller polypeptide chains. The polyprotein pro-opiomelanocortin (POMC) contains many polypeptide hormones. The cleavage pattern of POMC, however, may vary between different tissues, yielding different sets of polypeptide hormones from the same polyprotein. 

Many viruses also produce their proteins initially as a single polypeptide chain that were translated from a polycistronic mRNA. This polypeptide is subsequently cleaved into individual polypeptide chains.

Cleavage of precursor proteins

Many proteins and hormones are synthesized in the form of their precursors - zymogens, proenzymes, and prehormones. These proteins are cleaved to form their final active structures. Insulin, for example, is synthesized as preproinsulin, which yields proinsulin after the signal peptide has been cleaved. The proinsulin is then cleaved at two positions to yield two polypeptide chains linked by two disulfide bonds. Removal of two C-terminal residues from the B-chain then yields the mature insulin. Protein folding occurs in the single-chain Proinsulin form which facilitates formation of the ultimately inter-peptide disulfide bonds, and the ultimately intra-peptide disulfide bond, found in the native structure of insulin. 

Proteases in particular are synthesized in the inactive form so that they may be safely stored in cells, and ready for release in sufficient quantity when required. This is to ensure that the protease is activated only in the correct location or context, as inappropriate activation of these proteases can be very destructive for an organism. Proteolysis of the zymogen yields an active protein; for example, when trypsinogen is cleaved to form trypsin, a slight rearrangement of the protein structure that completes the active site of the protease occurs, thereby activating the protein.

Proteolysis can, therefore, be a method of regulating biological processes by turning inactive proteins into active ones. A good example is the blood clotting cascade whereby an initial event triggers a cascade of sequential proteolytic activation of many specific proteases, resulting in blood coagulation. The complement system of the immune response also involves a complex sequential proteolytic activation and interaction that result in an attack on invading pathogens.

Protein degradation

Protein degradation may take place intracellularly or extracellularly. In digestion of food, digestive enzymes may be released into the environment for extracellular digestion whereby proteolytic cleavage breaks down proteins into smaller peptides and amino acids so that they may be absorbed and used by an organism. In animals the food may be processed extracellularly in specialized digestive organs or guts, but in many bacteria the food may be internalized into the cell via phagocytosis. Microbial degradation of protein in the environment can be regulated by nutrient availability. For example, limitation for major elements in proteins (carbon, nitrogen, and sulfur) has been shown to induce proteolytic activity in the fungus Neurospora crassa as well as in whole communities of soil organisms.

Proteins in cells are also constantly being broken down into amino acids. This intracellular degradation of protein serves a number of functions: It removes damaged and abnormal protein and prevent their accumulation, and it also serves to regulate cellular processes by removing enzymes and regulatory proteins that are no longer needed. The amino acids may then be reused for protein synthesis. 

Structure of a proteasome. Its active sites are inside the tube (blue) where proteins are degraded.

Lysosome and proteasome

The intracellular degradation of protein may be achieved in two ways - proteolysis in lysosome, or a ubiquitin-dependent process that targets unwanted proteins to proteasome. The autophagy-lysosomal pathway is normally a non-selective process, but it may become selective upon starvation whereby proteins with peptide sequence KFERQ or similar are selectively broken down. The lysosome contains a large number of proteases such as cathepsins. 

The ubiquitin-mediated process is selective. Proteins marked for degradation are covalently linked to ubiquitin. Many molecules of ubiquitin may be linked in tandem to a protein destined for degradation. The polyubiquinated protein is targeted to an ATP-dependent protease complex, the proteasome. The ubiquitin is released and reused, while the targeted protein is degraded.

Rate of intracellular protein degradation

Different proteins are degraded at different rates. Abnormal proteins are quickly degraded, whereas the rate of degradation of normal proteins may vary widely depending on their functions. Enzymes at important metabolic control points may be degraded much faster than those enzymes whose activity is largely constant under all physiological conditions. One of the most rapidly degraded proteins is ornithine decarboxylase, which has a half-life of 11 minutes. In contrast, other proteins like actin and myosin have a half-life of a month or more, while, in essence, haemoglobin lasts for the entire life-time of an erythrocyte.

The N-end rule may partially determine the half-life of a protein, and proteins with segments rich in proline, glutamic acid, serine, and threonine (the so-called PEST proteins) have short half-life. Other factors suspected to affect degradation rate include the rate deamination of glutamine and asparagine and oxidation of cystein, histidine, and methionine, the absence of stabilizing ligands, the presence of attached carbohydrate or phosphate groups, the presence of free α-amino group, the negative charge of protein, and the flexibility and stability of the protein. Proteins with larger degrees of intrinsic disorder also tend to have short cellular half-life, with disordered segments having been proposed to facilitate efficient initiation of degradation by the proteasome.

The rate of proteolysis may also depend on the physiological state of the organism, such as its hormonal state as well as nutritional status. In time of starvation, the rate of protein degradation increases.

Digestion

In human digestion, proteins in food are broken down into smaller peptide chains by digestive enzymes such as pepsin, trypsin, chymotrypsin, and elastase, and into amino acids by various enzymes such as carboxypeptidase, aminopeptidase, and dipeptidase. It is necessary to break down proteins into small peptides (tripeptides and dipeptides) and amino acids so they can be absorbed by the intestines, and the absorbed tripeptides and dipeptides are also further broken into amino acids intracellularly before they enter the bloodstream. Different enzymes have different specificity for their substrate; trypsin, for example, cleaves the peptide bond after a positively charged residue (arginine and lysine); chymotrypsin cleaves the bond after an aromatic residue (phenylalanine, tyrosine, and tryptophan); elastase cleaves the bond after a small non-polar residue such as alanine or glycine. 

In order to prevent inappropriate or premature activation of the digestive enzymes (they may, for example, trigger pancreatic self-digestion causing pancreatitis), these enzymes are secreted as inactive zymogen. The precursor of pepsin, pepsinogen, is secreted by the stomach, and is activated only in the acidic environment found in stomach. The pancreas secretes the precursors of a number of proteases such as trypsin and chymotrypsin. The zymogen of trypsin is trypsinogen, which is activated by a very specific protease, enterokinase, secreted by the mucosa of the duodenum. The trypsin, once activated, can also cleave other trypsinogens as well as the precursors of other proteases such as chymotrypsin and carboxypeptidase to activate them. 

In bacteria, a similar strategy of employing an inactive zymogen or prezymogen is used. Subtilisin, which is produced by Bacillus subtilis, is produced as preprosubtilisin, and is released only if the signal peptide is cleaved and autocatalytic proteolytic activation has occurred.

Cellular regulation

Proteolysis is also involved in the regulation of many cellular processes by activating or deactivating enzymes, transcription factors, and receptors, for example in the biosynthesis of cholesterol, or the mediation of thrombin signalling through protease-activated receptors.

Some enzymes at important metabolic control points such as ornithine decarboxylase is regulated entirely by its rate of synthesis and its rate of degradation. Other rapidly degraded proteins include the protein products of proto-oncogenes, which play central roles in the regulation of cell growth.

Cell cycle regulation

Cyclins are a group of proteins that activate kinases involved in cell division. The degradation of cyclins is the key step that governs the exit from mitosis and progress into the next cell cycle. Cyclins accumulate in the course the cell cycle, then abruptly disappear just before the anaphase of mitosis. The cyclins are removed via a ubiquitin-mediated proteolytic pathway.

Apoptosis

Caspases are an important group of proteases involved in apoptosis or programmed cell death. The precursors of caspase, procaspase, may be activated by proteolysis through its association with a protein complex that forms apoptosome, or by granzyme B, or via the death receptor pathways.

Proteolysis and diseases

Abnormal proteolytic activity is associated with many diseases. In pancreatitis, leakage of proteases and their premature activation in the pancreas results in the self-digestion of the pancreas. People with diabetes mellitus may have increased lysosomal activity and the degradation of some proteins can increase significantly. Chronic inflammatory diseases such as rheumatoid arthritis may involve the release of lysosomal enzymes into extracellular space that break down surrounding tissues. Abnormal proteolysis and generation of peptides that aggregate in cells and their ineffective removal may result in many age-related neurological diseases such as Alzheimer's.

Proteases may be regulated by antiproteases or protease inhibitors, and imbalance between proteases and antiproteases can result in diseases, for example, in the destruction of lung tissues in emphysema brought on by smoking tobacco. Smoking is thought to increase the neutrophils and macrophages in the lung which release excessive amount of proteolytic enzymes such as elastase, such that they can no longer be inhibited by serpins such as α₁-antitrypsin, thereby resulting in the breaking down of connective tissues in the lung. Other proteases and their inhibitors may also be involved in this disease, for example matrix metalloproteinases (MMPs) and tissue inhibitors of metalloproteinases (TIMPs).

Other diseases linked to aberrant proteolysis include muscular dystrophy, degenerative skin disorders, respiratory and gastrointestinal diseases, and malignancy.

Non-enzymatic proteolysis

Protein backbones are very stable in water at neutral pH and room temperature, although the rate of hydrolysis of different peptide bonds can vary. The half life of a peptide bond under normal conditions can range from 7 years to 350 years, even higher for peptides protected by modified terminus or within the protein interior. The rate of proteolysis however can be significantly increased by extremes of pH and heat. 

Strong mineral acids can readily hydrolyse the peptide bonds in a protein (acid hydrolysis). The standard way to hydrolyze a protein or peptide into its constituent amino acids for analysis is to heat it to 105 °C for around 24 hours in 6M hydrochloric acid. However, some proteins are resistant to acid hydrolysis. One well-known example is ribonuclease A, which can be purified by treating crude extracts with hot sulphuric acid so that other proteins become degraded while ribonuclease A is left intact.

Certain chemicals cause proteolysis only after specific residues, and these can be used to selectively break down a protein into smaller polypeptides for laboratory analysis. For example, cyanogen bromide cleaves the peptide bond after a methionine. Similar methods may be used to specifically cleave tryptophanyl, aspartyl, cysteinyl, and asparaginyl peptide bonds. Acids such as trifluoroacetic acid and formic acid may also be used. 

Like other biomolecules, proteins can also be broken down by high heat alone. At 250 °C, the peptide bond may be easily hydrolyzed, with its half-life dropping to about a minute. Protein may also be broken down without hydrolysis through pyrolysis; small heterocyclic compounds may start to form upon degradation, above 500 °C, polycyclic aromatic hydrocarbon may also form, which is of interest in the study of generation of carcinogens in tobacco smoke and cooking at high heat.

Laboratory applications

Proteolysis is also used in research and diagnostic applications:

• Cleavage of fusion protein so that the fusion partner and protein tag used in protein expression and purification may be removed. The proteases used have high degree of specificity, such as thrombin, enterokinase, and TEV protease, so that only the targeted sequence may be cleaved.
• Complete inactivation of undesirable enzymatic activity or removal of unwanted proteins. For example, proteinase K, a broad-spectrum proteinase stable in urea and SDS, is often used in the preparation of nucleic acids to remove unwanted nuclease contaminants that may otherwise degrade the DNA or RNA.
• Partial inactivation, or changing the functionality, of specific protein. For example, treatment of DNA polymerase I with subtilisin yields the Klenow fragment, which retains its polymerase function but lacks 5'-exonuclease activity.
• Digestion of proteins in solution for proteome analysis by liquid chromatography-mass spectrometry (LC-MS). This may also be done by in-gel digestion of proteins after separation by gel electrophoresis for the identification by mass spectrometry.
• Analysis of the stability of folded domain under a wide range of conditions.
• Increasing success rate of crystallisation projects 
• Production of digested protein used in growth media to culture bacteria and other organisms, e.g. tryptone in Lysogeny Broth.

Protease enzymes

Proteases may be classified according to the catalytic group involved in its active site.

• Cysteine protease
• Serine protease
• Threonine protease
• Aspartic protease
• Glutamic protease
• Metalloprotease
• Asparagine peptide lyase

Venoms

Certain types of venom, such as those produced by venomous snakes, can also cause proteolysis. These venoms are, in fact, complex digestive fluids that begin their work outside of the body. Proteolytic venoms cause a wide range of toxic effects, including effects that are:

• cytotoxic (cell-destroying)
• hemotoxic (blood-destroying)
• myotoxic (muscle-destroying)
• hemorrhagic (bleeding)

Ecological niche

From Wikipedia, the free encyclopedia

The flightless dung beetle occupies an ecological niche exploiting animal droppings as a food source.

In ecology, a niche (CanE, UK: /ˈniːʃ/ or US: /ˈnɪtʃ/) is the fit of a species living under specific environmental conditions. The ecological niche describes how an organism or population responds to the distribution of resources and competitors (for example, by growing when resources are abundant, and when predators, parasites and pathogens are scarce) and how it in turn alters those same factors (for example, limiting access to resources by other organisms, acting as a food source for predators and a consumer of prey). "The type and number of variables comprising the dimensions of an environmental niche vary from one species to another [and] the relative importance of particular environmental variables for a species may vary according to the geographic and biotic contexts".

A Grinnellian niche is determined by the habitat in which a species lives and its accompanying behavioral adaptations. An Eltonian niche emphasizes that a species not only grows in and responds to an environment, it may also change the environment and its behavior as it grows. The Hutchinsonian niche uses mathematics and statistics to try to explain how species coexist within a given community. 

The notion of ecological niche is central to ecological biogeography, which focuses on spatial patterns of ecological communities. "Species distributions and their dynamics over time result from properties of the species, environmental variation..., and interactions between the two—in particular the abilities of some species, especially our own, to modify their environments and alter the range dynamics of many other species." Alteration of an ecological niche by its inhabitants is the topic of niche construction.

The majority of species exist in a standard ecological niche, sharing behaviors, adaptations, and functional traits similar to the other closely related species within the same broad taxonomic class, but there are exceptions. A premier example of a non-standard niche filling species is the flightless, ground-dwelling kiwi bird of New Zealand, which feeds on worms and other ground creatures, and lives its life in a mammal-like niche. Island biogeography can help explain island species and associated unfilled niches.

Grinnellian niche

A niche: the place where a statue may stand

 

The ecological meaning of niche comes from the meaning of niche as a recess in a wall for a statue, which itself is probably derived from the Middle French word nicher, meaning to nest. The term was coined by the naturalist Roswell Hill Johnson but Joseph Grinnell was probably the first to use it in a research program in 1917, in his paper "The niche relationships of the California Thrasher".

The Grinnellian niche concept embodies the idea that the niche of a species is determined by the habitat in which it lives and its accompanying behavioral adaptations. In other words, the niche is the sum of the habitat requirements and behaviors that allow a species to persist and produce offspring. For example, the behavior of the California thrasher is consistent with the chaparral habitat it lives in—it breeds and feeds in the underbrush and escapes from its predators by shuffling from underbrush to underbrush. Its 'niche' is defined by the felicitous complementing of the thrasher's behavior and physical traits (camouflaging color, short wings, strong legs) with this habitat.

This perspective of niche allows for the existence of both ecological equivalents and empty niches. An ecological equivalent to an organism is an organism from a different taxonomic group exhibiting similar adaptations in a similar habitat, an example being the different succulents found in American and African deserts, cactus and euphorbia, respectively. As another example, the anole lizards of the Greater Antilles are a rare example of convergent evolution, adaptive radiation, and the existence of ecological equivalents: the anole lizards evolved in similar microhabitats independently of each other and resulted in the same ecomorphs across all four islands.

Eltonian niche

In 1927 Charles Sutherland Elton, a British ecologist, defined a niche as follows: "The 'niche' of an animal means its place in the biotic environment, its relations to food and enemies."

Elton classified niches according to foraging activities ("food habits"):

For instance there is the niche that is filled by birds of prey which eat small animals such as shrews and mice. In an oak wood this niche is filled by tawny owls, while in the open grassland it is occupied by kestrels. The existence of this carnivore niche is dependent on the further fact that mice form a definite herbivore niche in many different associations, although the actual species of mice may be quite different.

Conceptually, the Eltonian niche introduces the idea of a species' response to and effect on the environment. Unlike other niche concepts, it emphasizes that a species not only grows in and responds to an environment based on available resources, predators, and climatic conditions, but also changes the availability and behavior of those factors as it grows. In an extreme example, beavers require certain resources in order to survive and reproduce, but also construct dams that alter water flow in the river where the beaver lives. Thus, the beaver affects the biotic and abiotic conditions of other species that live in and near the watershed. In a more subtle case, competitors that consume resources at different rates can lead to cycles in resource density that differ between species. Not only do species grow differently with respect to resource density, but their own population growth can affect resource density over time.

Hutchinsonian niche

The shape of the bill of this purple-throated carib is complementary to the shape of the flower and coevolved with it, enabling it to exploit the nectar as a resource.

The Hutchinsonian niche is an "n-dimensional hypervolume", where the dimensions are environmental conditions and resources, that define the requirements of an individual or a species to practice "its" way of life, more particularly, for its population to persist. The "hypervolume" defines the multi-dimensional space of resources (e.g., light, nutrients, structure, etc.) available to (and specifically used by) organisms, and "all species other than those under consideration are regarded as part of the coordinate system."

The niche concept was popularized by the zoologist G. Evelyn Hutchinson in 1957. Hutchinson inquired into the question of why there are so many types of organisms in any one habitat. His work inspired many others to develop models to explain how many and how similar coexisting species could be within a given community, and led to the concepts of 'niche breadth' (the variety of resources or habitats used by a given species), 'niche partitioning' (resource differentiation by coexisting species), and 'niche overlap' (overlap of resource use by different species).

Where three species eat some of the same prey, a statistical picture of each niche shows overlap in resource usage between three species, indicating where competition is strongest.

Statistics were introduced into the Hutchinson niche by Robert MacArthur and Richard Levins using the 'resource-utilization' niche employing histograms to describe the 'frequency of occurrence' as a function of a Hutchinson coordinate. So, for instance, a Gaussian might describe the frequency with which a species ate prey of a certain size, giving a more detailed niche description than simply specifying some median or average prey size. For such a bell-shaped distribution, the position, width and form of the niche correspond to the mean, standard deviation and the actual distribution itself. One advantage in using statistics is illustrated in the figure, where it is clear that for the narrower distributions (top) there is no competition for prey between the extreme left and extreme right species, while for the broader distribution (bottom), niche overlap indicates competition can occur between all species. The resource-utilization approach consists in postulating that not only competition can occur, but also that it does occur, and that overlap in resource utilization directly enables the estimation of the competition coefficients. This postulate, however, can be misguided, as it ignores the impacts that the resources of each category have on the organism and the impacts that the organism has on the resources of each category. For instance, the resource in the overlap region can be non-limiting, in which case there is no competition for this resource despite niche overlap.

An organism free of interference from other species could use the full range of conditions (biotic and abiotic) and resources in which it could survive and reproduce which is called its fundamental niche. However, as a result of pressure from, and interactions with, other organisms (i.e. inter-specific competition) species are usually forced to occupy a niche that is narrower than this, and to which they are mostly highly adapted; this is termed the realized niche. Hutchinson used the idea of competition for resources as the primary mechanism driving ecology, but overemphasis upon this focus has proved to be a handicap for the niche concept. In particular, overemphasis upon a species' dependence upon resources has led to too little emphasis upon the effects of organisms on their environment, for instance, colonization and invasions.

The term "adaptive zone" was coined by the paleontologist George Gaylord Simpson to explain how a population could jump from one niche to another that suited it, jump to an 'adaptive zone', made available by virtue of some modification, or possibly a change in the food chain, that made the adaptive zone available to it without a discontinuity in its way of life because the group was 'pre-adapted' to the new ecological opportunity.

As a hemi-parasitic plant, the mistletoe in this tree exploits its host for nutrients and as a place to grow.

Hutchinson's "niche" (a description of the ecological space occupied by a species) is subtly different from the "niche" as defined by Grinnell (an ecological role, that may or may not be actually filled by a species—see vacant niches). 

A niche is a very specific segment of ecospace occupied by a single species. On the presumption that no two species are identical in all respects (called Hardin's 'axiom of inequality') and the competitive exclusion principle, some resource or adaptive dimension will provide a niche specific to each species. Species can however share a 'mode of life' or 'autecological strategy' which are broader definitions of ecospace. For example, Australian grasslands species, though different from those of the Great Plains grasslands, exhibit similar modes of life.

Once a niche is left vacant, other organisms can fill that position. For example, the niche that was left vacant by the extinction of the tarpan has been filled by other animals (in particular a small horse breed, the konik). Also, when plants and animals are introduced into a new environment, they have the potential to occupy or invade the niche or niches of native organisms, often outcompeting the indigenous species. Introduction of non-indigenous species to non-native habitats by humans often results in biological pollution by the exotic or invasive species. 

The mathematical representation of a species' fundamental niche in ecological space, and its subsequent projection back into geographic space, is the domain of niche modelling.

Parameters

The different dimensions, or plot axes, of a niche represent different biotic and abiotic variables. These factors may include descriptions of the organism's life history, habitat, trophic position (place in the food chain), and geographic range. According to the competitive exclusion principle, no two species can occupy the same niche in the same environment for a long time. The parameters of a realized niche are described by the realized niche width of that species. Some plants and animals, called specialists, need specific habitats and surroundings to survive, such as the spotted owl, which lives specifically in old growth forests. Other plants and animals, called generalists, are not as particular and can survive in a range of conditions, for example the dandelion.

Unified neutral theory of biodiversity

From Wikipedia, the free encyclopedia

The Unified Neutral Theory of Biodiversity and Biogeography

Author	Stephen P. Hubbell
Country	U.S.
Language	English
Series	Monographs in Population Biology
Release number	32
Publisher	Princeton University Press
Publication date	2001
Pages	375
ISBN	0-691-02129-5

The unified neutral theory of biodiversity and biogeography (here "Unified Theory" or "UNTB") is a hypothesis and the title of a monograph by ecologist Stephen Hubbell. The hypothesis aims to explain the diversity and relative abundance of species in ecological communities, although like other neutral theories of ecology, Hubbell's hypothesis assumes that the differences between members of an ecological community of trophically similar species are "neutral", or irrelevant to their success. This implies that biodiversity arises at random, as each species follows a random walk. The hypothesis has sparked controversy, and some authors consider it a more complex version of other null models that fit the data better.

Neutrality means that at a given trophic level in a food web, species are equivalent in birth rates, death rates, dispersal rates and speciation rates, when measured on a per-capita basis. This can be considered a null hypothesis to niche theory. Hubbell built on earlier neutral concepts, including MacArthur & Wilson's theory of island biogeography and Gould's concepts of symmetry and null models.

An ecological community is a group of trophically similar, sympatric species that actually or potentially compete in a local area for the same or similar resources. Under the Unified Theory, complex ecological interactions are permitted among individuals of an ecological community (such as competition and cooperation), provided that all individuals obey the same rules. Asymmetric phenomena such as parasitism and predation are ruled out by the terms of reference; but cooperative strategies such as swarming, and negative interaction such as competing for limited food or light are allowed (so long as all individuals behave in the same way).

The Unified Theory also makes predictions that have profound implications for the management of biodiversity, especially the management of rare species.

The theory predicts the existence of a fundamental biodiversity constant, conventionally written θ, that appears to govern species richness on a wide variety of spatial and temporal scales.

Saturation

Although not strictly necessary for a neutral theory, many stochastic models of biodiversity assume a fixed, finite community size. There are unavoidable physical constraints on the total number of individuals that can be packed into a given space (although space per se isn't necessarily a resource, it is often a useful surrogate variable for a limiting resource that is distributed over the landscape; examples would include sunlight or hosts, in the case of parasites). 

If a wide range of species are considered (say, giant sequoia trees and duckweed, two species that have very different saturation densities), then the assumption of constant community size might not be very good, because density would be higher if the smaller species were monodominant.

However, because the Unified Theory refers only to communities of trophically similar, competing species, it is unlikely that population density will vary too widely from one place to another.

Hubbell considers the fact that population densities are constant and interprets it as a general principle: large landscapes are always biotically saturated with individuals. Hubbell thus treats communities as being of a fixed number of individuals, usually denoted by J.

Exceptions to the saturation principle include disturbed ecosystems such as the Serengeti, where saplings are trampled by elephants and Blue wildebeests; or gardens, where certain species are systematically removed.

Species abundances

When abundance data on natural populations are collected, two observations are almost universal:

1. The most common species accounts for a substantial fraction of the individuals sampled;
2. A substantial fraction of the species sampled are very rare. Indeed, a substantial fraction of the species sampled are singletons, that is, species which are sufficiently rare for only a single individual to have been sampled.

Such observations typically generate a large number of questions. Why are the rare species rare? Why is the most abundant species so much more abundant than the median species abundance? 

A non neutral explanation for the rarity of rare species might suggest that rarity is a result of poor adaptation to local conditions. The UNTB implies that such considerations may be neglected from the perspective of population biology (because the explanation cited implies that the rare species behaves differently from the abundant species). 

Species composition in any community will change randomly with time. However, any particular abundance structure will have an associated probability. The UNTB predicts that the probability of a community of J individuals composed of S distinct species with abundances ${\displaystyle n_{1}}$ for species 1, ${\displaystyle n_{2}}$ for species 2, and so on up to ${\displaystyle n_{S}}$ for species S is given by

${\displaystyle \Pr(n_{1},n_{2},\ldots ,n_{S}|\theta ,J)={\frac {J!\theta ^{S}}{1^{\phi _{1}}2^{\phi _{2}}\cdots J^{\phi _{J}}\phi _{1}!\phi _{2}!\cdots \phi _{J}!\Pi _{k=1}^{J}(\theta +k-1)}}}$

where ${\displaystyle \theta =2J\nu }$ is the fundamental biodiversity number (${\displaystyle \nu }$ is the speciation rate), and ${\displaystyle \phi _{i}}$ is the number of species that have i individuals in the sample. 

This equation shows that the UNTB implies a nontrivial dominance-diversity equilibrium between speciation and extinction. 

As an example, consider a community with 10 individuals and three species "a", "b", and "c" with abundances 3, 6 and 1 respectively. Then the formula above would allow us to assess the likelihood of different values of θ. There are thus S = 3 species and ${\displaystyle \phi _{1}=\phi _{3}=\phi _{6}=1}$, all other ${\displaystyle \phi }$'s being zero. The formula would give

${\displaystyle \Pr(3,6,1|\theta ,10)={\frac {10!\theta ^{3}}{1^{1}\cdot 3^{1}\cdot 6^{1}\cdot 1!1!1!\cdot \theta (\theta +1)(\theta +2)\cdots (\theta +9)}}}$

which could be maximized to yield an estimate for θ (in practice, numerical methods are used). The maximum likelihood estimate for θ is about 1.1478. 

We could have labelled the species another way and counted the abundances being 1,3,6 instead (or 3,1,6, etc. etc.). Logic tells us that the probability of observing a pattern of abundances will be the same observing any permutation of those abundances. Here we would have

${\displaystyle \Pr(3;3,6,1)=\Pr(3;1,3,6)=\Pr(3;3,1,6)}$

and so on.

To account for this, it is helpful to consider only ranked abundances (that is, to sort the abundances before inserting into the formula). A ranked dominance-diversity configuration is usually written as ${\displaystyle \Pr(S;r_{1},r_{2},\ldots ,r_{s},0,\ldots ,0)}$ where ${\displaystyle r_{i}}$ is the abundance of the ith most abundant species: ${\displaystyle r_{1}}$ is the abundance of the most abundant, ${\displaystyle r_{2}}$ the abundance of the second most abundant species, and so on. For convenience, the expression is usually "padded" with enough zeros to ensure that there are J species (the zeros indicating that the extra species have zero abundance). 

It is now possible to determine the expected abundance of the ith most abundant species:

${\displaystyle E(r_{i})=\sum _{k=1}^{C}r_{i}(k)\cdot \Pr(S;r_{1},r_{2},\ldots ,r_{s},0,\ldots ,0)}$

where C is the total number of configurations, ${\displaystyle r_{i}(k)}$ is the abundance of the ith ranked species in the kth configuration, and ${\displaystyle Pr(\ldots )}$ is the dominance-diversity probability. This formula is difficult to manipulate mathematically, but relatively simple to simulate computationally. 

The model discussed so far is a model of a regional community, which Hubbell calls the metacommunity. Hubbell also acknowledged that on a local scale, dispersal plays an important role. For example, seeds are more likely to come from nearby parents than from distant parents. Hubbell introduced the parameter m, which denotes the probability of immigration in the local community from the metacommunity. If m = 1, dispersal is unlimited; the local community is just a random sample from the metacommunity and the formulas above apply. If m < 1, however, dispersal is limited and the local community is a dispersal-limited sample from the metacommunity for which different formulas apply. 

It has been shown that ${\displaystyle \langle \phi _{n}\rangle }$, the expected number of species with abundance n, may be calculated by

${\displaystyle \theta {\frac {J!}{n!(J-n)!}}{\frac {\Gamma (\gamma )}{\Gamma (J+\gamma )}}\int _{y=0}^{\gamma }{\frac {\Gamma (n+y)}{\Gamma (1+y)}}{\frac {\Gamma (J-n+\gamma -y)}{\Gamma (\gamma -y)}}\exp(-y\theta /\gamma )\,dy}$

where θ is the fundamental biodiversity number, J the community size, ${\displaystyle \Gamma }$ is the gamma function, and ${\displaystyle \gamma =(J-1)m/(1-m)}$. This formula is however an approximation. The correct formula is derived in a series of papers, reviewed and synthesized by Etienne & Alonso 2005:

${\displaystyle {\frac {\theta }{(I)_{J}}}{J \choose n}\int _{0}^{1}(Ix)_{n}(I(1-x))_{J-n}{\frac {(1-x)^{\theta -1}}{x}}\,dx}$

where ${\displaystyle I=(J-1)*m/(1-m)}$ is a parameter that measures dispersal limitation. 

${\displaystyle \langle \phi _{n}\rangle }$ is zero for n > J, as there cannot be more species than individuals. 

This formula is important because it allows a quick evaluation of the Unified Theory. It is not suitable for testing the theory. For this purpose, the approptiate likelihood function should be used. For the metacommunity this was given above. For the local community with dispersal limitation it is given by:

${\displaystyle \Pr(n_{1},n_{2},\ldots ,n_{S}|\theta ,m,J)={\frac {J!}{\prod _{i=1}^{S}n_{i}\prod _{j=1}^{J}\Phi _{j}!}}{\frac {\theta ^{S}}{(I)_{J}}}\sum _{A=S}^{J}K({\overrightarrow {D}},A){\frac {I^{A}}{(\theta )_{A}}}}$

Here, the ${\displaystyle K({\overrightarrow {D}},A)}$ for ${\displaystyle A=S,...,J}$ are coefficients fully determined by the data, being defined as

${\displaystyle K({\overrightarrow {D}},A):=\sum _{\{a_{1},...,a_{S}|\sum _{i=1}^{S}a_{i}=A\}}\prod _{i=1}^{S}{\frac {{\overline {s}}\left(n_{i},a_{i}\right){\overline {s}}\left(a_{i},1\right)}{{\overline {s}}\left(n_{i},1\right)}}}$

This seemingly complicated formula involves Stirling numbers and Pochhammer symbols, but can be easily calculated.^[9]

An example of a species abundance curve can be found in Scientific American.

Stochastic modelling of species abundances under the UNTB

UNTB distinguishes between a dispersal-limited local community of size ${\displaystyle J}$ and a so-called metacommunity from which species can (re)immigrate and which acts as a heat bath to the local community. The distribution of species in the metacommunity is given by a dynamic equilibrium of speciation and extinction. Both community dynamics are modelled by appropriate urn processes, where each individual is represented by a ball with a color corresponding to its species. With a certain rate ${\displaystyle r}$ randomly chosen individuals reproduce, i.e. add another ball of their own color to the urn. Since one basic assumption is saturation, this reproduction has to happen at the cost of another random individual from the urn which is removed. At a different rate ${\displaystyle \mu }$ single individuals in the metacommunity are replaced by mutants of an entirely new species. Hubbell calls this simplified model for speciation a point mutation, using the terminology of the Neutral theory of molecular evolution. The urn scheme for the metacommunity of ${\displaystyle J_{M}}$ individuals is the following. 

At each time step take one of the two possible actions :

1. With probability ${\displaystyle (1-\nu )}$ draw an individual at random and replace another random individual from the urn with a copy of the first one.
2. With probability ${\displaystyle \nu }$ draw an individual and replace it with an individual of a new species.

Note that the size ${\displaystyle J_{M}}$ of the metacommunity does not change. Note also that this is a point process in time. The length of the time steps is distributed exponentially. For simplicity one can, however, assume that each time step is as long as the mean time between two changes which can be derived from the reproduction and mutation rates ${\displaystyle r}$ and ${\displaystyle \mu }$. The probability ${\displaystyle \nu }$ is given as ${\displaystyle \nu =\mu /(r+\mu )}$. 

The species abundance distribution for this urn process is given by Ewens's sampling formula which was originally derived in 1972 for the distribution of allele under neutral mutations. The expected number ${\displaystyle S_{M}(n)}$ of species in the metacommunity having exactly ${\displaystyle n}$ individuals is:

${\displaystyle S_{M}(n)={\frac {\theta }{n}}{\frac {\Gamma (J_{M}+1)\Gamma (J_{M}+\theta -n)}{\Gamma (J_{M}+1-n)\Gamma (J_{M}+\theta )}}}$

where ${\displaystyle \theta =(J_{M}-1)\nu /(1-\nu )\approx J_{M}\nu }$ is called the fundamental biodiversity number. For large metacommunities and ${\displaystyle n\ll J_{M}}$ one recovers the Fisher Log-Series as species distribution.

${\displaystyle S_{M}(n)\approx {\frac {\theta }{n}}\left({\frac {J_{M}}{J_{M}+\theta }}\right)^{n}}$

The urn scheme for the local community of fixed size ${\displaystyle J}$ is very similar to the one for the metacommunity. 

At each time step take one of the two actions :

1. With probability ${\displaystyle (1-m)}$ draw an individual at random and replace another random individual from the urn with a copy of the first one.
2. With probability ${\displaystyle m}$ replace a random individual with an immigrant drawn from the metacommunity.

The metacommunity is changing on a much larger timescale and is assumed to be fixed during the evolution of the local community. The resulting distribution of species in the local community and expected values depend on four parameters, ${\displaystyle J}$, ${\displaystyle J_{M}}$, ${\displaystyle \theta }$ and ${\displaystyle m}$ (or ${\displaystyle I}$) and are derived in Etienne & Alonso (2005), including several simplifying limit cases like the one presented in the previous section (there called ${\displaystyle \langle \phi _{n}\rangle }$). The parameter ${\displaystyle m}$ is a dispersal parameter. If ${\displaystyle m=1}$ then the local community is just a sample from the metacommunity. For ${\displaystyle m=0}$ the local community is completely isolated from the metacommunity and all species will go extinct except one. This case has been analyzed by Hubbell himself. The case ${\displaystyle 0$ is characterized by a unimodal species distribution in a Preston Diagram and often fitted by a log-normal distribution. This is understood as an intermediate state between domination of the most common species and a sampling from the metacommunity, where singleton species are most abundant. UNTB thus predicts that in dispersal limited communities rare species become even rarer. The log-normal distribution describes the maximum and the abundance of common species very well but underestimates the number of very rare species considerably which becomes only apparent for very large sample sizes.

Species-area relationships

The Unified Theory unifies biodiversity, as measured by species-abundance curves, with biogeography, as measured by species-area curves. Species-area relationships show the rate at which species diversity increases with area. The topic is of great interest to conservation biologists in the design of reserves, as it is often desired to harbour as many species as possible. 

The most commonly encountered relationship is the power law given by

${\displaystyle S=cA^{z}}$

where S is the number of species found, A is the area sampled, and c and z are constants. This relationship, with different constants, has been found to fit a wide range of empirical data. 

From the perspective of Unified Theory, it is convenient to consider S as a function of total community size J. Then ${\displaystyle S=kJ^{z}}$ for some constant k, and if this relationship were exactly true, the species area line would be straight on log scales. It is typically found that the curve is not straight, but the slope changes from being steep at small areas, shallower at intermediate areas, and steep at the largest areas. 

The formula for species composition may be used to calculate the expected number of species present in a community under the assumptions of the Unified Theory. In symbols

${\displaystyle E\left\{S|\theta ,J\right\}={\frac {\theta }{\theta }}+{\frac {\theta }{\theta +1}}+{\frac {\theta }{\theta +2}}+\cdots +{\frac {\theta }{\theta +J-1}}}$

where θ is the fundamental biodiversity number. This formula specifies the expected number of species sampled in a community of size J. The last term, ${\displaystyle \theta /(\theta +J-1)}$, is the expected number of new species encountered when adding one new individual to the community. This is an increasing function of θ and a decreasing function of J, as expected. 

By making the substitution ${\displaystyle J=\rho A}$ (see section on saturation above), then the expected number of species becomes ${\displaystyle \Sigma \theta /(\theta +\rho A-1)}$. 

The formula above may be approximated to an integral giving

${\displaystyle S(\theta )=1+\theta \ln \left(1+{\frac {J-1}{\theta }}\right).}$

This formulation is predicated on a random placement of individuals.

Example

Consider the following (synthetic) dataset, of 27 individuals:

a, a,a, a,a, a,a, a,a, a,b, b,b, b,c, c,c, c,d, d,d, d,e, f,g, h,i

There are thus 27 individuals of 9 species ("a" to "i") in the sample. Tabulating this would give: 

 a  b  c  d  e  f  g  h  i
10  4  4  4  1  1  1  1  1

indicating that species "a" is the most abundant with 10 individuals and species "e" to "i" are singletons. Tabulating the table gives:

species abundance    1    2    3    4    5    6    7    8    9    10
number of species    5    0    0    3    0    0    0    0    0     1

On the second row, the 5 in the first column means that five species, species "e" through "i", have abundance one. The following two zeros in columns 2 and 3 mean that zero species have abundance 2 or 3. The 3 in column 4 means that three species, species "b", "c", and "d", have abundance four. The final 1 in column 10 means that one species, species "a", has abundance 10. 

This type of dataset is typical in biodiversity studies. Observe how more than half the biodiversity (as measured by species count) is due to singletons. 

For real datasets, the species abundances are binned into logarithmic categories, usually using base 2, which gives bins of abundance 0-1, abundance 1-2, abundance 2-4, abundance 4-8, etc. Such abundance classes are called octaves; early developers of this concept included F. W. Preston and histograms showing number of species as a function of abundance octave are known as Preston diagrams. 

These bins are not mutually exclusive: a species with abundance 4, for example, could be considered as lying in the 2-4 abundance class or the 4-8 abundance class. Species with an abundance of an exact power of 2 (i.e. 2,4,8,16, etc.) are conventionally considered as having 50% membership in the lower abundance class 50% membership in the upper class. Such species are thus considered to be evenly split between the two adjacent classes (apart from singletons which are classified into the rarest category). Thus in the example above, the Preston abundances would be 

abundance class 1    1-2   2-4   4-8  8-16
species         5     0    1.5   1.5   1

The three species of abundance four thus appear, 1.5 in abundance class 2-4, and 1.5 in 4-8. 

The above method of analysis cannot account for species that are unsampled: that is, species sufficiently rare to have been recorded zero times. Preston diagrams are thus truncated at zero abundance. Preston called this the veil line and noted that the cutoff point would move as more individuals are sampled.

Dynamics under neutral hypothesis

All biodiversity patterns previously described are related to time-independent quantities. However, for biodiversity evolution and species preservation, it is crucial to compare the dynamics of ecosystems with models (Leigh, 2007). An easily accessible index of the underlying evolution is the so-called species turnover distribution (STD), defined as the probability P(r,t) that the population of any species has varied by a fraction r after a given time t. 

A neutral model that can analytically predict both the relative species abundance (RSA) at steady-state and the STD at time t has been presented in Azaele et al. (2006). Within this framework the population of any species is represented by a continuous (random) variable x, whose evolution is governed by the following Langevin equation:

${\displaystyle {\dot {x}}=b-x/\tau +{\sqrt {Dx}}\xi (t)}$

where b is the immigration rate from a large regional community, ${\displaystyle -x/\tau }$ represents competition for finite resources and D is related to demographic stochasticity; ${\displaystyle \xi (t)}$ is a Gaussian white noise. The model can also be derived as a continuous approximation of a master equation, where birth and death rates are independent of species, and predicts that at steady-state the RSA is simply a gamma distribution. 

From the exact time-dependent solution of the previous equation, one can exactly calculate the STD at time t under stationary conditions:

${\displaystyle P(r,t)=A{\frac {\lambda +1}{\lambda }}{\frac {(e^{t/\tau })^{b/2D}}{1-e^{-t/\tau }}}\left({\frac {\sinh({\frac {t}{2\tau }})}{\lambda }}\right)^{{\frac {b}{D}}+1}\left({\frac {4\lambda ^{2}}{(\lambda +1)^{2}e^{t/\tau }-4\lambda }}\right)^{{\frac {b}{D}}+{\frac {1}{2}}}.}$

This formula provides good fits of data collected in the Barro Colorado tropical forest from 1990 to 2000. From the best fit one can estimate ${\displaystyle \tau }$ ~ 3500 years with a broad uncertainty due to the relative short time interval of the sample. This parameter can be interpreted as the relaxation time of the system, i.e. the time the system needs to recover from a perturbation of species distribution. In the same framework, the estimated mean species lifetime is very close to the fitted temporal scale ${\displaystyle \tau }$. This suggests that the neutral assumption could correspond to a scenario in which species originate and become extinct on the same timescales of fluctuations of the whole ecosystem.

Testing the theory

The theory has provoked much controversy as it "abandons" the role of ecology when modelling ecosystems. The theory has been criticized as it requires an equilibrium, yet climatic and geographical conditions are thought to change too frequently for this to be attained. Tests on bird and tree abundance data demonstrate that the theory is usually a poorer match to the data than alternative null hypotheses that use fewer parameters (a log-normal model with two tunable parameters, compared to the neutral theory's three), and are thus more parsimonious. The theory also fails to describe coral reef communities and is a poor fit to data in intertidal communities. It also fails to explain why families of tropical trees have statistically highly correlated numbers of species in phylogenetically unrelated and geographically distant forest plots in Central and South America, Africa, and South East Asia.

While the theory has been heralded as a valuable tool for palaeontologists, little work has so far been done to test the theory against the fossil record.