Unified neutral theory of biodiversity Guide, Meaning , Facts, Information and Description
The unified neutral theory of biodiversity (here UNTB) is a scientific hypothesis that aims to explain the relative abundance of species in ecological communities. The theory is named in analogy to the neutral theory of molecular evolution, to which it is closely related. The theory has been applied successfully to many diverse ecosystems including forest tree species, bacterial populations, moths, British birds, and vascular plants.The UNTB states that ecological communities are neutral.
Neutrality is defined as per capita ecological equivalence among all individuals of every species at a given trophic level in a food web; "per capita equivalence" means that all species are held to behave (ie reproduce and die) in the same way as one another; and individuals of a particular species reproduce and die (behave) in the same way. Early neutral theories include the broken stick hypothesis of R. H. MacArthur and the island biogeography theories of MacArthur and E. O. Wilson.
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 (Hubbell 2001). Under the UNTB, complex ecological interactions are permitted among individuals of an ecological community (such as competition and cooperation), provided that all individuals obey the same rules. 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 UNTB makes a large number of falsifiable hypotheses. Differences between predictions of the UNTB and observations are of very small magnitude. The UNTB also makes predictions that have profound implications for the management of biodiversity, especially the management of rare species.
Non-neutral theories of biodiversity would include niche assembly and dispersal assembly. These theories are non-neutral because they hold that different species behave in different ways from one another. Other examples of non-neutral explanations would be to hold that older organisms are fitter in the Darwinian sense.
Under the UNTB, species drift is allowed to occur via speciation, which would occur with a specific probablity per birth. The neutrality of the UNTB implies that this probability would be independent of the parent's species (note that common species have a higher birth rate, and thus the UNTB predicts that speciation occurs more frequently for common species than 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.
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2 UNTB and species-area relationships 3 Stochastic modelling of species abundances under the UNTB |
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 for if the smaller species were monodominant.
However, because the UNTB 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 ecosysems such as
the Serengeti, where saplings are trampled by elephants; or gardens, where certain species are systematically removed.
When abundance data on natural populations are collected, two
observations are almost universal:
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 for species 1, for species 2, and so on up to for species S is given by
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
, all other
's being zero. The formula would give
Note that 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 probablity of observing a pattern of abundances will be the same observing any permutation of those abundances. Here we would have 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
where is the abundance of the ith most abundant species:
is the abundance of the most abundant, 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:
In a paper in Nature in 2003, it is shown that , the expected abundance of the n-th most abundant species, may be calculated by
UNTB and saturation
Species abundances
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?
where is the fundamental biodiversity number
( is the speciation rate), and is the
number of species that have i individuals in the sample.
which could be maximized to yield an estimate for θ (in practice,
numerical methods are used). The R programming language can be used to show that the maximum likelihood estimate for θ is about 1.1478.
where C is the total number of configurations, is the abundance of the ith ranked species in the kth configuration, and is the dominance-diversity probability. This formula is difficult to manipulate mathematically, but relatively simple to simulate computationally.
where θ is the fundamental biodiversity number, J the community size, is the gamma function, and (m is the immigration rate). This integral may be evaluated numerically, but no analytical solution is known.
This formula is important because it allows the UNTB to be tested using, for example, the chi square test.
Note that is zero for n>J, as there cannot be more species than individuals.
The species-area relationship is the rate at which species accumulate as the area surveyed
increases. 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
From the perspective of UNTB, it is convenient to consider S as a function of total community
size J. Then 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 dont this bit yet) may be used to
calculate the expected number of species present in a community under the assumptions of the
UNTB. In symbols
By making the substitution (see section on saturation above), then
the expected number of species becomes .
The formula above may be approximated to an integral giving
The UNTB is perhaps best understood using stochastic process modelling. Consider a community, of fixed size, consisting of J individuals.
Although in reality individuals die and reproduce, it is often realistic to assume that the community changes at regular intervals, the timestep being J times an individual's lifespan. At each timestep, one individual dies and one is born (community size remaining constant at J); the dynamical process simulated is known as "zero-sum", by analogy with zero sum game theory.
Each individual occupies one space or unit of limiting resources. The individual dies with probability μ per timestep and is replaced by a new individual. Under the UNTB, the replacing species is drawn randomly from the community. It is possible to use this fact to calculate the probabilities of species' abundance changing with time:
Consider species i, which at time t has abundance . For the species to increase abundance to at time t+1, two separate events must happen: firstly, the individual that dies must be of species i; and secondly, the individual that is born must be of some other species.
For the species to decrease abundance to , then again two separate events must happen: the individual that dies must not be species i, and the individual that is born must be of species i.
For the species to remain at abundance , one of two things might happen:
UNTB and species-area relationships
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.
where &theta is the fundamental biodiversity number. This formula specifies the expected
number of species sampled in a community of size J. The last term,
, is the expected number of new species
encountered when adding one new individual to the community. Note that this is an
increasing function of &theta and a decreasing function of J, as expected.Stochastic modelling of species abundances under the UNTB
In symbols,
It is always possible to choose the time increment so that . Note that the probability of species i increasing is equal to the probability of it decreasing. The abundance of species i, if viewed as a discrete time sequence of random variables, is thus a martingale because the expectation of species i 's abundance at time t+1 is equal to its abundance at time t.
Consider the following (synthetic) dataset, of 23 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:
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.
Note that 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 (ie 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
Note that 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 Fisher called this the veil line and noted that the cutoff point would move as more individuals are sampled.
Notable proponents of the UNTB include Stephen Hubbell. This is an Article on Unified neutral theory of biodiversity. Page Contains Information, Facts Details or Explanation Guide About Unified neutral theory of biodiversity Example
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 "d" to "h" 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.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.