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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.^[1] 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.^[2] The hypothesis has sparked controversy, and some authors consider it a more complex version of other null models that fit the data better.^[3]

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.^[4] This can be considered a null hypothesis to niche theory. Hubbell built on earlier neutral concepts, including MacArthur & Wilson's theory of island biogeography^[1] and Gould's concepts of symmetry and null models.^[4]

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.^[1] 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.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park.

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 is 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:

The most common species accounts for a substantial fraction of the individuals sampled;
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 $n_{1}$ for species 1, $n_{2}$ for species 2, and so on up to $n_{S}$ for species S is given by

\Pr (n_{1}, n_{2}, \dots, n_{S} | θ, J) = \frac{J! θ^{S}}{1^{ϕ_{1}} 2^{ϕ_{2}} \dots J^{ϕ_{J}} ϕ_{1}! ϕ_{2}! \dots ϕ_{J}! Π_{k = 1}^{J} (θ + k - 1)}

where $θ = 2 J ν$ is the fundamental biodiversity number ( $ν$ is the speciation rate), and $ϕ_{i}$ 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 $ϕ_{1} = ϕ_{3} = ϕ_{6} = 1$ , all other $ϕ$ 's being zero. The formula would give

\Pr (3, 6, 1 | θ, 10) = \frac{10! θ^{3}}{1^{1} \cdot 3^{1} \cdot 6^{1} \cdot 1! 1! 1! \cdot θ (θ + 1) (θ + 2) \dots (θ + 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

\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 $\Pr (S; r_{1}, r_{2}, \dots, r_{s}, 0, \dots, 0)$ where $r_{i}$ is the abundance of the ith most abundant species: $r_{1}$ is the abundance of the most abundant, $r_{2}$ 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:

E (r_{i}) = \sum_{k = 1}^{C} r_{i} (k) \cdot \Pr (S; r_{1}, r_{2}, \dots, r_{s}, 0, \dots, 0)

where C is the total number of configurations, $r_{i} (k)$ is the abundance of the ith ranked species in the kth configuration, and $P r (\dots)$ 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.

In a paper in Nature in 2003 [1], it is shown that $⟨ ϕ_{n} ⟩$ , the expected number of species with abundance n, may be calculated by

θ \frac{J!}{n! (J - n)!} \frac{Γ (γ)}{Γ (J + γ)} \int_{y = 0}^{γ} \frac{Γ (n + y)}{Γ (1 + y)} \frac{Γ (J - n + γ - y)}{Γ (γ - y)} \exp (- y θ / γ) d y

where θ is the fundamental biodiversity number, J the community size, $Γ$ is the gamma function, and $γ = (J - 1) m / (1 - m)$ . This formula is however an approximation. The correct formula is derived in a series of papers, reviewed and synthesized by Etienne & Alonso 2005 [2]:

\frac{θ}{(I)_{J}} (\binom{J}{n}) \int_{0}^{1} (I x)_{n} (I (1 - x))_{J - n} \frac{(1 - x)^{θ - 1}}{x} d x

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

$⟨ ϕ_{n} ⟩$ 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:

\Pr (n_{1}, n_{2}, \dots, n_{S} | θ, m, J) = \frac{J!}{\prod_{i = 1}^{S} n_{i} \prod_{j = 1}^{J} Φ_{j}!} \frac{θ^{S}}{(I)_{J}} \sum_{A = S}^{J} K (\vec{D}, A) \frac{I^{A}}{(θ)_{A}}

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

K (\vec{D}, A) : = \sum_{{a_{1}, . . ., a_{S} | \sum_{i = 1}^{S} a_{i} = A}} \prod_{i = 1}^{S} \frac{\overline{s} (n_{i}, a_{i}) \overline{s} (a_{i}, 1)}{\overline{s} (n_{i}, 1)}

This seemingly complicated formula involves Stirling numbers and Pochhammer symbols, but can be easily calculated. See [3]

An example of a species abundance curve can be found here: [4].

Stochastic modelling of species abundances under the UNTB

UNTB distinguishes between a dispersal-limited local community of size $J$ 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 $r$ 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 $μ$ 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 $J_{M}$ individuals is the following.

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

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

Note that the size $J_{M}$ 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 $r$ and $μ$ . The probability $ν$ is given as $ν = μ / (r + μ)$ .

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 $S_{M} (n)$ of species in the metacommunity having exactly $n$ individuals is [Vallade, Houchmandzadeh 2003 [5]

S_{M} (n) = \frac{θ}{n} \frac{Γ (J_{M} + 1) Γ (J_{M} + θ - n)}{Γ (J_{M} + 1 - n) Γ (J_{M} + θ)}

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

S_{M} (n) \approx \frac{θ}{n} {(\frac{J_{M}}{J_{M} + θ})}^{n}

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

At each time step take one of the two actions :

With probability $(1 - m)$ draw an individual at random and replace another random individual from the urn with a copy of the first one.
With probability $m$ 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, $J$ , $J_{M}$ , $θ$ and $m$ (or $I$ ) and are derived in [Etienne, Alonso 2005 [6], including several simplifying limit cases like the one presented in the previous section (there called $⟨ ϕ_{n} ⟩$ ). The parameter $m$ is a dispersal parameter. If $m = 1$ then the local community is just a sample from the metacommunity. For $m = 0$ 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 [Hubbell 2001]. The case $0 < m < 1$ 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 [Hubbell 2001].

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

S = c A^{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 $S = k J^{z}$ 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

E {S | θ, J} = \frac{θ}{θ} + \frac{θ}{θ + 1} + \frac{θ}{θ + 2} + \dots + \frac{θ}{θ + 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, $θ / (θ + J - 1)$ , 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 $J = ρ A$ (see section on saturation above), then the expected number of species becomes $Σ θ / (θ + ρ A - 1)$ .

The formula above may be approximated to an integral giving

S (θ) = 1 + θ \ln (1 + \frac{J - 1}{θ}) .

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 [7]. 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:

\dot{x} = b - x / τ + \sqrt{D x} ξ (t)

where b is the immigration rate from a large regional community, $- x / τ$ represents competition for finite resources and D is related to demographic stochasticity; $ξ (t)$ 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:

P (r, t) = A \frac{λ + 1}{λ} \frac{(e^{t / τ})^{b / 2 D}}{1 - e^{- t / τ}} {(\frac{\sinh (\frac{t}{2 τ})}{λ})}^{\frac{b}{D} + 1} {(\frac{4 λ^{2}}{(λ + 1)^{2} e^{t / τ} - 4 λ})}^{\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 $τ$ ~ 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 $τ$ . 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.^[5] 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.^[5] 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^[3]), and are thus more parsimonious.^[2] The theory also fails to describe coral reef communities^[6] and is a poor fit to data in intertidal communities.^[7] 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 ^[8]

Application

While the theory has been heralded as a valuable tool for palaeontologists,^[4] little work has so far been done to test the theory against the fossil record.^[9]

External links

References

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In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang)
One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

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Giuseppe Vitali: Difference between revisions

Latest revision as of 01:47, 26 February 2013

Contents

Saturation

Species abundances

Stochastic modelling of species abundances under the UNTB

Species-area relationships

Example

Dynamics under neutral hypothesis

Testing the theory

Application

See also

External links

References

Navigation menu

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-Introduction! I am Dalton. Acting often is a thing that I'm totally addicted to. Vermont is just where my home was. Managing the public has been my big day job for a even while but I plan using changing it. I've been toiling on my website for the some time now. Investigate it out here: http://circuspartypanama.com<br><br>Feel free to surf to my page :: [http://circuspartypanama.com clash of clans hack ifunbox]
+The '''unified neutral theory of biodiversity and biogeography''' (here '''"Unified Theory"''' or '''"UNTB"''') is a hypothesis and the title of a monograph by [[ecology|ecologist]] [[Stephen Hubbell]].<ref name=Hubbell2001>{{Cite web
+| author = Hubbell, SP
+| year = 2001
+| title = The Unified Neutral Theory of Biodiversity and Biogeography (MPB-32)
+| url = https://pup.princeton.edu/chapters/s7105.html
+}}</ref> 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 [[trophic]]ally similar species are "neutral," or irrelevant to their success.  This implies that biodiversity arises at random, as each species follows a [[random walk]].<ref name="McGill2003">{{cite doi|10.1038/nature01583}}</ref> The hypothesis has sparked controversy, and some authors consider it a more complex version of other null models that fit the data better.<ref name="Nee2003"/>
+''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.<ref name=Hubbell2005>{{cite doi|10.1666/0094-8373(2005)031[0122:TNTOBA]2.0.CO;2}}</ref>  This can be considered a [[null hypothesis]] to [[ecological niche|niche theory]].  Hubbell built on earlier neutral concepts, including [[Robert MacArthur|MacArthur]] & [[E.O. Wilson|Wilson]]'s theory of [[island biogeography]]<ref name="Hubbell2001"/> and [[Steven Jay Gould|Gould]]'s concepts of symmetry and null models.<ref name=Hubbell2005/>
+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.<ref name=Hubbell2001/>  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 [[parasite|parasitism]] and [[predator|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.{{Citation needed|date=November 2007}}
+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 is 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 [[elephant]]s and [[Blue wildebeest]]s; or [[garden]]s, where certain species are systematically removed.
+===Species abundances===
+When abundance data on natural populations are collected, two observations are almost universal:
+*  The most common species accounts for a substantial fraction of the individuals sampled;
+*  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 <math>n_1</math> for species 1, <math>n_2</math> for  species 2, and so on up to <math>n_S</math> for species ''S'' is given by
+:<math>
+\Pr(n_1,n_2,\ldots,n_S| \theta, J)=
+\frac{J!\theta^S}
+{
+^{\phi_1}2^{\phi_2}\cdots J^{\phi_J}
+  \phi_1!\phi_2!\cdots\phi_J!
+  \Pi_{k=1}^J(\theta+k-1)
+}
+</math>
+where <math>\theta=2J\nu</math> is the fundamental biodiversity number (<math>\nu</math> is the speciation rate), and <math>\phi_i</math> 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 function|likelihood]] of different values of ''θ''.  There are thus ''S''&nbsp;=&nbsp;3 species and <math>\phi_1=\phi_3=\phi_6=1</math>, all other <math>\phi</math>'s being zero.  The formula would give
+:<math>
+\Pr(3,6,1| \theta,10)=
+\frac{10!\theta^3}{
+^1\cdot 3^1\cdot 6^1
+\cdot
+!1!1!
+\cdot
+\theta(\theta+1)(\theta+2)\cdots(\theta+9)}
+</math>
+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
+: <math>\Pr(3;3,6,1)=\Pr(3;1,3,6)=\Pr(3;3,1,6)</math>
+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 <math>\Pr(S;r_1,r_2,\ldots,r_s,0,\ldots,0)</math> where <math>r_i</math> is the abundance of the ''i''th most abundant species: <math>r_1</math> is the abundance of the most abundant, <math>r_2</math> 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 value|expected]] abundance of the ''i''th most abundant species:
+:<math>
+E(r_i)=\sum_{k=1}^C
+r_i(k)\cdot \Pr(S;r_1,r_2,\ldots,r_s,0,\ldots,0)
+</math>
+where ''C'' is the total number of configurations, <math>r_i(k)</math> is the abundance of the ''i''th ranked species in the ''k''th configuration,  and <math>Pr(\ldots)</math> 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.
+In a paper in [[Nature (journal)|Nature]] in 2003 [http://www.nature.com/nature/journal/v424/n6952/abs/nature01883.html], it is shown that <math>\langle \phi_n \rangle </math>, the expected number of species with abundance n, may be calculated by
+:<math>
+\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
+</math>
+where ''θ'' is the fundamental biodiversity number, ''J'' the community size,  <math>\Gamma</math> is the [[gamma function]], and <math>\gamma=(J-1)m/(1-m)</math>. This formula is however an approximation.  The correct formula is derived in a series of papers, reviewed and synthesized by Etienne & Alonso 2005 [http://www.blackwell-synergy.com/doi/abs/10.1111/j.1461-0248.2005.00817.x]:
+:<math>
+\frac{\theta }{(I)_{J}} {J \choose n}
+\int_{0}^{1}(Ix)_{n}(I(1-x))_{J-n}\frac{(1-x)^{\theta -1}}{x}\,dx
+</math>
+where <math>I = (J-1)*m/(1-m)</math> is a parameter that measures dispersal limitation.
+<math>\langle \phi_n \rangle</math> is zero for ''n''&nbsp;>&nbsp;''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:
+:<math>
+\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}}
+</math>
+Here, the <math>K(\overrightarrow{D},A)</math> for <math>A=S,...,J</math> are coefficients fully determined by the data, being defined as
+:<math>
+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) }
+</math>
+This seemingly complicated formula involves [[Stirling number]]s and [[Pochhammer symbol]]s, but can be easily calculated. See [http://www.blackwellpublishing.com/products/journals/suppmat/ELE/ELE717/ELE717sm.htm]
+An example of a species abundance curve can be found here: [http://www.sciam.com/article.cfm?articleID=000656C3-8F00-1CDA-B4A8809EC588EEDF].
+==Stochastic modelling of species abundances under the UNTB==
+UNTB distinguishes between a dispersal-limited local community of size <math>J</math> 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 problem|urn processes]], where each individual is represented by a ball with a color corresponding to its species. With a certain rate <math>r</math> 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 <math>\mu</math> 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 <math>J_M</math> individuals is the following.
+At each time step take one of the two possible actions :
+# With probability <math>(1-\nu)</math> draw an individual at random and replace another random individual from the urn with a copy of the first one.
+# With probability <math>\nu</math> draw an individual and replace it with an individual of a new species.
+Note that the size <math>J_M</math> 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 <math>r</math> and <math>\mu</math>. The probability <math>\nu</math> is given as <math>\nu=\mu/(r+\mu)</math>.
+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 <math>S_M(n)</math> of species in the metacommunity having exactly <math>n</math> individuals is [Vallade, Houchmandzadeh 2003 [http://prola.aps.org/abstract/PRE/v68/i6/e061902]
+:<math>
+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)}
+</math>
+where <math>\theta=(J_M-1)\nu/(1-\nu)\approx J_M\nu</math> is called the fundamental biodiversity number. For large
+metacommunities and <math>n\ll J_M</math> one recovers the [[Logarithmic distribution|Fisher Log-Series]] as species distribution.
+:<math>
+S_M(n) \approx \frac{\theta}{n} \left( \frac{J_M}{J_M+\theta} \right)^n
+</math>
+The urn scheme for the local community of fixed size <math>J</math> is very similar to the one for the metacommunity.
+At each time step take one of the two actions :
+# With probability <math>(1-m)</math> draw an individual at random and replace another random individual from the urn with a copy of the first one.
+# With probability <math>m</math> 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, <math>J</math>, <math>J_M</math>, <math>\theta</math> and <math>m</math> (or <math>I</math>) and are derived in [Etienne, Alonso 2005 [http://www.blackwell-synergy.com/doi/full/10.1111/j.1461-0248.2005.00817.x], including several simplifying limit cases like the one presented in the previous section (there called <math>\langle\phi_n\rangle</math>). The parameter <math>m</math> is a dispersal parameter. If <math>m=1</math> then the local community is just a sample from the metacommunity. For <math>m=0</math> 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 [Hubbell 2001]. The case <math>0<m<1</math> 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 [Hubbell 2001].
+==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
+:<math>
+S=cA^z</math>
+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 <math>S=kJ^z</math> 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 <!--derived above ('''not done this bit yet''')--> may be used to calculate the expected number of species present in a community under the assumptions of the Unified Theory.  In symbols
+:<math>
+E\left\{S|\theta,J\right\}=
+\frac{\theta}{\theta  }+
+\frac{\theta}{\theta+1}+
+\frac{\theta}{\theta+2}+
+\cdots +
+\frac{\theta}{\theta+J-1}
+</math>
+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, <math>\theta/(\theta+J-1)</math>, 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 <math>J=\rho A</math> (see section on saturation above), then the expected number of species becomes <math>\Sigma\theta/(\theta+\rho A-1)</math>.
+The formula above may be approximated to an [[integral]] giving
+:<math>
+S(\theta)=
++\theta\ln\left(1+\frac{J-1}{\theta}\right).
+</math>
+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
+  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 [[Frank W. Preston|F. W. Preston]] and histograms showing number of species as a function of abundance octave are known as [[Preston diagram]]s.
+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. [[Frank W. Preston|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 [http://www.nature.com/nature/journal/v444/n7121/abs/nature05320.html]. 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:
+:<math>
+\dot{x}=b-x/\tau+\sqrt{Dx}\xi(t)
+</math>
+where b is the immigration rate from a large regional community, <math>-x/\tau</math> represents competition for finite resources and D is related to demographic stochasticity; <math>\xi(t)</math> 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:
+:<math>
+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)^2e^{t/\tau}-4\lambda}\right)^{\frac{b}{D}+\frac{1}{2}}.
+</math>
+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 <math>\tau</math> ~ 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 <math>\tau</math>. 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.<ref name="Ricklefs2006">{{cite doi|10.1890/0012-9658(2006)87[1424:TUNTOB]2.0.CO;2}}</ref> 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.<ref name="Ricklefs2006" />
+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<ref name="Nee2003">{{cite doi|10.1016/S0169-5347(03)00196-4}}</ref>), and are thus more parsimonious.<ref name="McGill2003" />  The theory also fails to describe coral reef communities<ref name="Dornelas2006">{{cite doi|10.1038/nature04534}}</ref> and is a poor fit to data in intertidal communities.<ref name="Timothy Wootton2005">{{cite doi|10.1038/nature03211}}</ref> 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 <ref name="Ricklefs2012">{{cite DOI: 10.1126/science.1215182}}</ref>
+== Application ==
+While the theory has been heralded as a valuable tool for palaeontologists,<ref name=Hubbell2005/> little work has so far been done to test the theory against the fossil record.<ref name="Bonuso2007">{{cite doi|10.2110/palo.2007.S05}}</ref>
+==See also==
+* [[Biodiversity Action Plan]]
+* [[Warren Ewens]]
+* [[Ewens's sampling formula]]
+* [[Metabolic theory of ecology]]
+* [[Neutral theory of molecular evolution]]
+==External links==
+* [http://www.sciam.com/article.cfm?articleID=000D401A-8D9D-1CDA-B4A8809EC588EEDF Scientific American Interview with Steve Hubbell]
+* [http://finzi.psych.upenn.edu/R/library/untb/html/untb.package.html R package for implementing UNTB]
+* [http://news.cell.com/discussions/trends-in-ecology-and-evolution/ecological-neutral-theory-useful-model-or-statement-of-ignorance "Ecological neutral theory: useful model or statement of ignorance?" in Cell Press Discussions]
+==References==
+{{reflist|33em}}
+* {{cite journal|last=Azaele|first=S.|coauthors=Pigolotti, S., Banavar, J. R., Maritan, A.|title=Dynamical evolution of ecosystems|journal=Nature|volume=444|pages=926–928|doi=10.1038/nature05320| year=2006|pmid=17167485|issue=7121|bibcode = 2006Natur.444..926A }}
+* {{cite journal|last=Etienne|first=R.S. |coauthors=Alonso, D.|title=A dispersal-limited sampling theory for species and alleles|journal=Ecology Letters|volume=8|pages=1147–1156|year=2005|doi=10.1111/j.1461-0248.2005.00817.x|url=http://www.ourbiosphere.org/~dalonso/SelectPubl/ecoLet05_EtienneAlonso.pdf|issue=11|pmid=21352438}} ({{cite journal|title=Errata |journal=Ecology Letters|volume=9|pages=500|doi=10.1111/j.1461-0248.2006.00917.x|year=2006|issue=4}})
+*{{cite journal|last=Gilbert|first=B |coauthor=Lechowicz MJ|year=2004|title=Neutrality, niches, and dispersal in a temperate forest understory|journal=PNAS|volume=101|pages=7651–7656|doi=10.1073/pnas.0400814101|pmid=15128948|issue=20|pmc=419661|bibcode = 2004PNAS..101.7651G }}
+* {{cite book |author=[[Stephen P. Hubbell|Hubbell, S.P.]] |year=2001 |title=The Unified Neutral Theory of Biodiversity and Biogeography|publisher=[[Princeton University Press]]| isbn=0-691-02128-7}}
+* {{cite journal|author=Leigh E.G. (Jr) | year=2007| title=Neutral theory: a historical perspective| journal=[[Journal of Evolutionary Biology]] |volume=20 |pages=2075–2091| doi=10.1111/j.1420-9101.2007.01410.x|pmid=17956380|issue=6|url=http://si-pddr.si.edu/dspace/bitstream/10088/6669/1/Leigh0305neutral_theory_a_historic.pdf}}
+* {{cite journal|last=Preston|first=F. W.|title=The Canonical Distribution of Commonness and Rarity: Part I|journal=Ecology|volume=43|issue=2|pages=185–215|year=1962|doi=10.2307/1931976|publisher=Ecology, Vol. 43, No. 2|jstor=1931976}}
+* {{cite journal |last=Pueyo |first=S. |coauthors=He, F.; Zillio, T. |year=2007 |title= The maximum entropy formalism and the idiosyncratic theory of biodiversity |journal=Ecology Letters |volume=10 |pages=1017–1028 |url=http://www.blackwell-synergy.com/doi/pdf/10.1111/j.1461-0248.2007.01096.x |doi=10.1111/j.1461-0248.2007.01096.x |pmid=17692099 |issue=11 |pmc=2121135}}
+* {{cite journal|last=Vallade|first=M.|coauthors=Houchmandzadeh, B.|title=Analytical solution of a neutral model of biodiversity|journal=Phys. Rev. E|volume=68|issue=061902|year=2003|doi=10.1103/PhysRevE.68.061902|pages=061902|bibcode = 2003PhRvE..68f1902V }}
+* {{cite journal|last=Volkov|first=I.|coauthors=Banavar, J. R.,Hubbell, S. P., Maritan, A.|title=Neutral theory and relative species abundance in ecology|journal=Nature|volume=424|pages=1017–1028|doi=10.1038/nature01883| year=2003|pmid=12944964|issue=6952|url=http://sirismm.si.edu/ctfs/volkov_et_al_2003_nature.pdf|arxiv = q-bio/0504018 |bibcode = 2003Natur.424.1035V }}
+{{modelling ecosystems|expanded=other}}
+[[Category:Biodiversity]]
+[[Category:Ecological theories]]

Giuseppe Vitali: Difference between revisions

Latest revision as of 01:47, 26 February 2013

Saturation

Species abundances

Stochastic modelling of species abundances under the UNTB

Species-area relationships

Example

Dynamics under neutral hypothesis

Testing the theory

Application

See also

External links

References

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