The unified neutral theory of biodiversity and biogeography (here "Unified Theory" or "UNTB") is a theory and the title of a monograph by
ecologist
Ecology () is the study of the relationships between living organisms, including humans, and their physical environment. Ecology considers organisms at the individual, population, community, ecosystem, and biosphere level. Ecology overlaps wi ...
Stephen P. Hubbell
Stephen P. Hubbell (born 17 February 1942) is an American ecologist on the faculty of the University of California, Los Angeles. He is author of the unified neutral theory of biodiversity and biogeography (UNTB), which seeks to explain the divers ...
.
It aims to explain the diversity and relative abundance of species in ecological communities. Like other neutral theories of ecology, Hubbell assumes that the differences between members of an ecological community of
trophically similar species are "neutral", or irrelevant to their success. This implies that
niche
Niche may refer to:
Science
*Developmental niche, a concept for understanding the cultural context of child development
*Ecological niche, a term describing the relational position of an organism's species
*Niche differentiation, in ecology, the ...
differences do not influence abundance and the abundance of each species follows a
random walk
In mathematics, a random walk is a random process that describes a path that consists of a succession of random steps on some mathematical space.
An elementary example of a random walk is the random walk on the integer number line \mathbb Z ...
.
The theory has sparked controversy,
and some authors consider it a more complex version of other null models that fit the data better.
"Neutrality" means that at a given
trophic level
The trophic level of an organism is the position it occupies in a food web. A food chain is a succession of organisms that eat other organisms and may, in turn, be eaten themselves. The trophic level of an organism is the number of steps it ...
in a
food web
A food web is the natural interconnection of food chains and a graphical representation of what-eats-what in an ecological community. Another name for food web is consumer-resource system. Ecologists can broadly lump all life forms into one o ...
, species are equivalent in birth rates, death rates, dispersal rates and speciation rates, when measured on a per-capita basis.
This can be considered a
null hypothesis
In scientific research, the null hypothesis (often denoted ''H''0) is the claim that no difference or relationship exists between two sets of data or variables being analyzed. The null hypothesis is that any experimentally observed difference is d ...
to
niche theory. Hubbell built on earlier neutral models, including
Robert MacArthur
Robert Helmer MacArthur (April 7, 1930 – November 1, 1972) was a Canadian-born American ecologist who made a major impact on many areas of community and population ecology.
Early life and education
MacArthur was born in Toronto, Ontario, ...
and
E.O. Wilson's theory of
island biogeography Insular biogeography or island biogeography is a field within biogeography that examines the factors that affect the species richness and diversification of isolated natural communities. The theory was originally developed to explain the pattern of ...
and
Stephen Jay Gould
Stephen Jay Gould (; September 10, 1941 – May 20, 2002) was an American paleontologist, evolutionary biologist, and historian of science. He was one of the most influential and widely read authors of popular science of his generation. Gould sp ...
's concepts of symmetry and null models.
An "ecological community" is a group of trophically similar,
sympatric
In biology, two related species or populations are considered sympatric when they exist in the same geographic area and thus frequently encounter one another. An initially interbreeding population that splits into two or more distinct species sh ...
species
In biology, a species is the basic unit of classification and a taxonomic rank of an organism, as well as a unit of biodiversity. A species is often defined as the largest group of organisms in which any two individuals of the appropriate s ...
that actually or potentially compete in a local area for the same or similar resources.
Under the Unified Theory, complex
ecological
Ecology () is the study of the relationships between living organisms, including humans, and their physical environment. Ecology considers organisms at the individual, population, community, ecosystem, and biosphere level. Ecology overlaps wi ...
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
Parasitism is a Symbiosis, close relationship between species, where one organism, the parasite, lives on or inside another organism, the Host (biology), host, causing it some harm, and is Adaptation, adapted structurally to this way of lif ...
and
predation
Predation is a biological interaction where one organism, the predator, kills and eats another organism, its prey. It is one of a family of common feeding behaviours that includes parasitism and micropredation (which usually do not kill the ...
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 alike).
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 (total number of individual organisms). 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
Sunlight is a portion of the electromagnetic radiation given off by the Sun, in particular infrared, visible, and ultraviolet light. On Earth, sunlight is scattered and filtered through Earth's atmosphere, and is obvious as daylight when t ...
or hosts, in the case of parasites).
If a wide range of species are considered (say,
giant sequoia
''Sequoiadendron giganteum'' (giant sequoia; also known as giant redwood, Sierra redwood, Sierran redwood, California big tree, Wellingtonia or simply big treea nickname also used by John Muir) is the sole living species in the genus ''Sequoiade ...
trees and
duckweed
Lemnoideae is a subfamily of flowering aquatic plants, known as duckweeds, water lentils, or water lenses. They float on or just beneath the surface of still or slow-moving bodies of fresh water and wetlands. Also known as bayroot, they arose ...
, 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. 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 community sizes 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
The Serengeti ( ) ecosystem is a Geography of Africa, geographical region in Africa, spanning northern Tanzania. The protected area within the region includes approximately of land, including the Serengeti National Park and several game res ...
, where saplings are trampled by
elephant
Elephants are the largest existing land animals. Three living species are currently recognised: the African bush elephant, the African forest elephant, and the Asian elephant. They are the only surviving members of the family Elephantidae an ...
s and
Blue wildebeest
The blue wildebeest (''Connochaetes taurinus''), also called the common wildebeest, white-bearded gnu or brindled gnu, is a large antelope and one of the two species of wildebeest. It is placed in the genus '' Connochaetes'' and family Bovidae, a ...
s; or
garden
A garden is a planned space, usually outdoors, set aside for the cultivation, display, and enjoyment of plants and other forms of nature. The single feature identifying even the wildest wild garden is ''control''. The garden can incorporate bot ...
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 suggests that it is not necessary to invoke adaptation or niche differences because neutral dynamics alone can generate such patterns.
Species composition in any community will change randomly with time. 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
:
where
is the fundamental biodiversity number (
is the speciation rate), and
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
The likelihood function (often simply called the likelihood) represents the probability of random variable realizations conditional on particular values of the statistical parameters. Thus, when evaluated on a given sample, the likelihood functi ...
of different values of ''θ''. There are thus ''S'' = 3 species and
, all other
's being zero. The formula would give
:
which could be maximized to yield an estimate for ''θ'' (in practice,
numerical methods
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods th ...
are used). The
maximum likelihood
In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed stat ...
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
:
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 ''i''th 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 ''i''th most abundant species:
:
where ''C'' is the total number of configurations,
is the abundance of the ''i''th ranked species in the ''k''th configuration, and
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
An ecological metacommunity is a set of interacting communities which are linked by the dispersal of multiple, potentially interacting species. The term is derived from the field of community ecology, which is primarily concerned with patterns of ...
. 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, dispersal is limited and the local community is a dispersal-limited sample from the metacommunity for which different formulas apply.
It has been shown
that
, the expected number of species with abundance n, may be calculated by
:
where ''θ'' is the fundamental biodiversity number, ''J'' the community size,
is the
gamma function
In mathematics, the gamma function (represented by , the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except ...
, and
. This formula is an approximation. The correct formula is derived in a series of papers, reviewed and synthesized by Etienne and Alonso in 2005:
:
where
is a parameter that measures dispersal limitation.
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 appropriate likelihood function should be used. For the metacommunity this was given above. For the local community with dispersal limitation it is given by:
:
Here, the
for
are coefficients fully determined by the data, being defined as
:
This seemingly complicated formula involves
Stirling numbers and
Pochhammer symbol
In mathematics, the falling factorial (sometimes called the descending factorial, falling sequential product, or lower factorial) is defined as the polynomial
:\begin
(x)_n = x^\underline &= \overbrace^ \\
&= \prod_^n(x-k+1) = \prod_^(x-k) \,.
\e ...
s, but can be very easily calculated.
An example of a species abundance curve can be found in Scientific American.
Stochastic modelling of species abundances
UNTB distinguishes between a dispersal-limited local community of size
and a so-called metacommunity from which species can (re)immigrate and which acts as a
heat bath
In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is al ...
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
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
single individuals in the metacommunity are replaced by mutants of an entirely new species. Hubbell calls this simplified model for
speciation
Speciation is the evolutionary process by which populations evolve to become distinct species. The biologist Orator F. Cook coined the term in 1906 for cladogenesis, the splitting of lineages, as opposed to anagenesis, phyletic evolution within ...
a
point mutation
A point mutation is a genetic mutation where a single nucleotide base is changed, inserted or deleted from a DNA or RNA sequence of an organism's genome. Point mutations have a variety of effects on the downstream protein product—consequence ...
, using the terminology of the
Neutral theory of molecular evolution
The neutral theory of molecular evolution holds that most evolutionary changes occur at the molecular level, and most of the variation within and between species are due to random genetic drift of mutant alleles that are selectively neutral. The ...
. The urn scheme for the metacommunity of
individuals is the following.
At each time step take one of the two possible actions :
# With probability
draw an individual at random and replace another random individual from the urn with a copy of the first one.
# With probability
draw an individual and replace it with an individual of a new species.
The size
of the metacommunity does not change. This is a
point process
In statistics and probability theory, a point process or point field is a collection of mathematical points randomly located on a mathematical space such as the real line or Euclidean space. Kallenberg, O. (1986). ''Random Measures'', 4th editio ...
in time. The length of the time steps is distributed exponentially. For simplicity one can 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
and
. The probability
is given as
.
The species abundance distribution for this urn process is given by
Ewens's sampling formula
In population genetics, Ewens's sampling formula, describes the probabilities associated with counts of how many different alleles are observed a given number of times in the sample.
Definition
Ewens's sampling formula, introduced by Warren Ewens ...
which was originally derived in 1972 for the distribution of
allele
An allele (, ; ; modern formation from Greek ἄλλος ''állos'', "other") is a variation of the same sequence of nucleotides at the same place on a long DNA molecule, as described in leading textbooks on genetics and evolution.
::"The chro ...
s under neutral mutations. The expected number
of species in the metacommunity having exactly
individuals is:
:
where
is called the fundamental biodiversity number. For large
metacommunities and
one recovers the
Fisher Log-Series as species distribution.
:
The urn scheme for the local community of fixed size
is very similar to the one for the metacommunity.
At each time step take one of the two actions :
# With probability
draw an individual at random and replace another random individual from the urn with a copy of the first one.
# With probability
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,
,
,
and
(or
) and are derived by Etienne and Alonso (2005),
including several simplifying limit cases like the one presented in the previous section (there called
). The parameter
is a dispersal parameter. If
then the local community is just a sample from the metacommunity. For
the local community is completely isolated from the metacommunity and all species will go extinct except one. This case has been analyzed by Hubbell himself.
The case