Unified neutral theory of biodiversity

From Wikipedia, the free encyclopedia

The Unified Neutral Theory of Biodiversity and Biogeography

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

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

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

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

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

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

Saturation

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

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

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

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

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

Species abundances

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

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

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

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

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

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

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

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

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

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

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

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

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

and so on.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Stochastic modelling of species abundances under the UNTB

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

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

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

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

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

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

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

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

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

At each time step take one of the two actions :

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

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

Species-area relationships

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

The most commonly encountered relationship is the power law given by

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

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

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

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

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

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

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

The formula above may be approximated to an integral giving

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

This formulation is predicated on a random placement of individuals.

Example

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

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

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

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

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

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

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

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

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

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

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

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

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

Dynamics under neutral hypothesis

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

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

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

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

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

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

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

Testing the theory

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

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

Habitat

From Wikipedia, the free encyclopedia

This coral reef in the Phoenix Islands Protected Area is a rich habitat for sea life.

 

Few creatures make the ice shelves of Antarctica their habitat.

 

Ibex in alpine habitat

In ecology, a habitat is the type of natural environment in which a particular species of organism lives. It is characterized by both physical and biological features. A species' habitat is those places where it can find food, shelter, protection and mates for reproduction. 

The physical factors are for example soil, moisture, range of temperature, and light intensity as well as biotic factors such as the availability of food and the presence or absence of predators. Every organism has certain habitat needs for the conditions in which it will thrive, but some are tolerant of wide variations while others are very specific in their requirements. A habitat is not necessarily a geographical area, it can be the interior of a stem, a rotten log, a rock or a clump of moss, and for a parasitic organism it is the body of its host, part of the host's body such as the digestive tract, or a single cell within the host's body. 

Habitat types include polar, temperate, subtropical and tropical. The terrestrial vegetation type may be forest, steppe, grassland, semi-arid or desert. Fresh water habitats include marshes, streams, rivers, lakes, ponds and estuaries, and marine habitats include salt marshes, the coast, the intertidal zone, reefs, bays, the open sea, the sea bed, deep water and submarine vents. 

Habitats change over time. This may be due to a violent event such as the eruption of a volcano, an earthquake, a tsunami, a wildfire or a change in oceanic currents; or the change may be more gradual over millennia with alterations in the climate, as ice sheets and glaciers advance and retreat, and as different weather patterns bring changes of precipitation and solar radiation. Other changes come as a direct result of human activities; deforestation, the ploughing of ancient grasslands, the diversion and damming of rivers, the draining of marshland and the dredging of the seabed. The introduction of alien species can have a devastating effect on native wildlife, through increased predation, through competition for resources or through the introduction of pests and diseases to which the native species have no immunity.

Definition and etymology

The word "habitat" has been in use since about 1755 and derives from the Latin habitāre, to inhabit, from habēre, to have or to hold. Habitat can be defined as the natural environment of an organism, the type of place in which it is natural for it to live and grow. It is similar in meaning to a biotope; an area of uniform environmental conditions associated with a particular community of plants and animals.

Environmental factors

The chief environmental factors affecting the distribution of living organisms are temperature, humidity, climate, soil type and light intensity, and the presence or absence of all the requirements that the organism needs to sustain it. Generally speaking, animal communities are reliant on specific types of plant communities.

Some plants and animals are generalists, and their habitat requirements are met in a wide range of locations. The small white butterfly (Pieris rapae) for example is found on all the continents of the world apart from Antarctica. Its larvae feed on a wide range of Brassicas and various other plant species, and it thrives in any open location with diverse plant associations. The large blue butterfly is much more specific in its requirements; it is found only in chalk grassland areas, its larvae feed on Thymus species and because of complex lifecycle requirements it inhabits only areas in which Myrmica ants live.

Disturbance is important in the creation of biodiverse habitats. In the absence of disturbance, a climax vegetation cover develops that prevents the establishment of other species. Wildflower meadows are sometimes created by conservationists but most of the flowering plants used are either annuals or biennials and disappear after a few years in the absence of patches of bare ground on which their seedlings can grow. Lightning strikes and toppled trees in tropical forests allow species richness to be maintained as pioneering species move in to fill the gaps created. Similarly coastal habitats can become dominated by kelp until the seabed is disturbed by a storm and the algae swept away, or shifting sediment exposes new areas for colonisation. Another cause of disturbance is when an area may be overwhelmed by an invasive introduced species which is not kept under control by natural enemies in its new habitat.

Types

Rich rainforest habitat in Dominica

 

Terrestrial habitat types include forests, grasslands, wetlands and deserts. Within these broad biomes are more specific habitats with varying climate types, temperature regimes, soils, altitudes and vegetation types. Many of these habitats grade into each other and each one has its own typical communities of plants and animals. A habitat may suit a particular species well, but its presence or absence at any particular location depends to some extent on chance, on its dispersal abilities and its efficiency as a coloniser.

Wetland habitats in Borneo

Freshwater habitats include rivers, streams, lakes, ponds, marshes and bogs. Although some organisms are found across most of these habitats, the majority have more specific requirements. The water velocity, its temperature and oxygen saturation are important factors, but in river systems, there are fast and slow sections, pools, bayous and backwaters which provide a range of habitats. Similarly, aquatic plants can be floating, semi-submerged, submerged or grow in permanently or temporarily saturated soils besides bodies of water. Marginal plants provide important habitat for both invertebrates and vertebrates, and submerged plants provide oxygenation of the water, absorb nutrients and play a part in the reduction of pollution.

Marine habitats include brackish water, estuaries, bays, the open sea, the intertidal zone, the sea bed, reefs and deep / shallow water zones. Further variations include rock pools, sand banks, mudflats, brackish lagoons, sandy and pebbly beaches, and seagrass beds, all supporting their own flora and fauna. The benthic zone or seabed provides a home for both static organisms, anchored to the substrate, and for a large range of organisms crawling on or burrowing into the surface. Some creatures float among the waves on the surface of the water, or raft on floating debris, others swim at a range of depths, including organisms in the demersal zone close to the seabed, and myriads of organisms drift with the currents and form the plankton.

Desert scene in Egypt

A desert is not the kind of habitat that favours the presence of amphibians, with their requirement for water to keep their skins moist and for the development of their young. Nevertheless, some frogs live in deserts, creating moist habitats underground and hibernating while conditions are adverse. Couch's spadefoot toad (Scaphiopus couchii) emerges from its burrow when a downpour occurs and lays its eggs in the transient pools that form; the tadpoles develop with great rapidity, sometimes in as little as nine days, undergo metamorphosis, and feed voraciously before digging a burrow of their own.

Other organisms cope with the drying up of their aqueous habitat in other ways. Vernal pools are ephemeral ponds that form in the rainy season and dry up afterwards. They have their specially-adapted characteristic flora, mainly consisting of annuals, the seeds of which survive the drought, but also some uniquely adapted perennials. Animals adapted to these extreme habitats also exist; fairy shrimps can lay "winter eggs" which are resistant to desiccation, sometimes being blown about with the dust, ending up in new depressions in the ground. These can survive in a dormant state for as long as fifteen years. Some killifish behave in a similar way; their eggs hatch and the juvenile fish grow with great rapidity when the conditions are right, but the whole population of fish may end up as eggs in diapause in the dried up mud that was once a pond.

Many animals and plants have taken up residence in urban environments. They tend to be adaptable generalists and use the town's features to make their homes. Rats and mice have followed man around the globe, pigeons, peregrines, sparrows, swallows and house martins use the buildings for nesting, bats use roof space for roosting, foxes visit the garbage bins and squirrels, coyotes, raccoons and skunks roam the streets. About 2,000 coyotes are thought to live in and around Chicago. A survey of dwelling houses in northern European cities in the twentieth century found about 175 species of invertebrate inside them, including 53 species of beetle, 21 flies, 13 butterflies and moths, 13 mites, 9 lice, 7 bees, 5 wasps, 5 cockroaches, 5 spiders, 4 ants and a number of other groups. In warmer climates, termites are serious pests in the urban habitat; 183 species are known to affect buildings and 83 species cause serious structural damage.

Microhabitats

A microhabitat is the small-scale physical requirements of a particular organism or population. Every habitat includes large numbers of microhabitats with subtly different exposure to light, humidity, temperature, air movement, and other factors. The lichens that grow on the north face of a boulder are different to those that grow on the south face, from those on the level top and those that grow on the ground nearby; the lichens growing in the grooves and on the raised surfaces are different from those growing on the veins of quartz. Lurking among these miniature "forests" are the microfauna, each species of invertebrate with its own specific habitat requirements.

There are numerous different microhabitats in a wood; coniferous forest, broad-leafed forest, open woodland, scattered trees, woodland verges, clearings and glades; tree trunk, branch, twig, bud, leaf, flower and fruit; rough bark, smooth bark, damaged bark, rotten wood, hollow, groove and hole; canopy, shrub layer, plant layer, leaf litter and soil; buttress root, stump, fallen log, stem base, grass tussock, fungus, fern and moss. The greater the structural diversity in the wood, the greater the number of microhabitats that will be present. A range of tree species with individual specimens of varying sizes and ages, and a range of features such as streams, level areas, slopes, tracks, clearings and felled areas will provide suitable conditions for an enormous number of biodiverse plants and animals. For example, in Britain it has been estimated that various types of rotting wood are home to over 1700 species of invertebrate.

For a parasitic organism, its habitat is the particular part of the outside or inside of its host on or in which it is adapted to live. The life cycle of some parasites involves several different host species, as well as free-living life stages, sometimes providing vastly different microhabitats. One such organism is the trematode (flatworm) Microphallus turgidus, present in brackish water marshes in the southeastern United States. Its first intermediate host is a snail and the second, a glass shrimp. The final host is the waterfowl or mammal that consumes the shrimp.

Extreme habitats

An Antarctic rock split apart to show an endolithic lifeform showing as a green layer a few millimetres thick

Although the vast majority of life on Earth lives in mesophyllic (moderate) environments, a few organisms, most of them microbes, have managed to colonise extreme environments that are unsuitable for most higher life forms. There are bacteria, for example, living in Lake Whillans, half a mile below the ice of Antarctica; in the absence of sunlight, they must rely on organic material from elsewhere, perhaps decaying matter from glacier melt water or minerals from the underlying rock. Other bacteria can be found in abundance in the Mariana Trench, the deepest place in the ocean and on Earth; marine snow drifts down from the surface layers of the sea and accumulates in this undersea valley, providing nourishment for an extensive community of bacteria.

Other microbes live in habitats lacking in oxygen, and are dependent on chemical reactions other than photosynthesis. Boreholes drilled 300 m (1,000 ft) into the rocky seabed have found microbial communities apparently based on the products of reactions between water and the constituents of rocks. These communities have been little studied, but may be an important part of the global carbon cycle. Rock in mines two miles deep also harbour microbes; these live on minute traces of hydrogen produced in slow oxidizing reactions inside the rock. These metabolic reactions allow life to exist in places with no oxygen or light, an environment that had previously been thought to be devoid of life.

The intertidal zone and the photic zone in the oceans are relatively familiar habitats. However the vast bulk of the ocean is unhospitable to air-breathing humans, with scuba divers limited to the upper 50 m (160 ft) or so. The lower limit for photosynthesis is 100 to 200 m (330 to 660 ft) and below that depth the prevailing conditions include total darkness, high pressure, little oxygen (in some places), scarce food resources and extreme cold. This habitat is very challenging to research, and as well as being little studied, it is vast, with 79% of the Earth's biosphere being at depths greater than 1,000 m (3,300 ft). With no plant life, the animals in this zone are either detritivores, reliant on food drifting down from surface layers, or they are predators, feeding on each other. Some organisms are pelagic, swimming or drifting in mid-ocean, while others are benthic, living on or near the seabed. Their growth rates and metabolisms tend to be slow, their eyes may be very large to detect what little illumination there is, or they may be blind and rely on other sensory inputs. A number of deep sea creatures are bioluminescent; this serves a variety of functions including predation, protection and social recognition. In general, the bodies of animals living at great depths are adapted to high pressure environments by having pressure-resistant biomolecules and small organic molecules present in their cells known as piezolytes, which give the proteins the flexibility they need. There are also unsaturated fats in their membranes which prevent them from solidifying at low temperatures.

Dense mass of white crabs at a hydrothermal vent, with stalked barnacles on right

Hydrothermal vents were first discovered in the ocean depths in 1977. They result from seawater becoming heated after seeping through cracks to places where hot magma is close to the seabed. The under-water hot springs may gush forth at temperatures of over 340 °C (640 °F) and support unique communities of organisms in their immediate vicinity. The basis for this teeming life is chemosynthesis, a process by which microbes convert such substances as hydrogen sulfide or ammonia into organic molecules. These bacteria and Archaea are the primary producers in these ecosystems and support a diverse array of life. About 350 species of organism, dominated by molluscs, polychaete worms and crustaceans, had been discovered around hydrothermal vents by the end of the twentieth century, most of them being new to science and endemic to these habitats.

Besides providing locomotion opportunities for winged animals and a conduit for the dispersal of pollen grains, spores and seeds, the atmosphere can be considered to be a habitat in its own right. There are metabolically active microbes present that actively reproduce and spend their whole existence airborne, with hundreds of thousands of individual organisms estimated to be present in a cubic metre of air. The airborne microbial community may be as diverse as that found in soil or other terrestrial environments, however these organisms are not evenly distributed, their densities varying spatially with altitude and environmental conditions. Aerobiology has been little studied, but there is evidence of nitrogen fixation in clouds, and less clear evidence of carbon cycling, both facilitated by microbial activity.

There are other examples of extreme habitats where specially adapted lifeforms exist; tar pits teeming with microbial life; naturally occurring crude oil pools inhabited by the larvae of the petroleum fly; hot springs where the temperature may be as high as 71 °C (160 °F) and cyanobacteria create microbial mats; cold seeps where the methane and hydrogen sulfide issue from the ocean floor and support microbes and higher animals such as mussels which form symbiotic associations with these anaerobic organisms; salt pans harbour salt-tolerant microorganisms and also Wallemia ichthyophaga, a basidomycotous fungus; ice sheets in Antarctica which support fungi Thelebolus spp., and snowfields on which algae grow.

Habitat change

Twenty five years after the devastating eruption at Mount St. Helens, United States, pioneer species have moved in.

Whether from natural processes or the activities of man, landscapes and their associated habitats change over time. There are the slow geomorphological changes associated with the geologic processes that cause tectonic uplift and subsidence, and the more rapid changes associated with earthquakes, landslides, storms, flooding, wildfires, coastal erosion, deforestation and changes in land use. Then there are the changes in habitats brought on by alterations in farming practices, tourism, pollution, fragmentation and climate change.

Loss of habitat is the single greatest threat to any species. If an island on which an endemic organism lives becomes uninhabitable for some reason, the species will become extinct. Any type of habitat surrounded by a different habitat is in a similar situation to an island. If a forest is divided into parts by logging, with strips of cleared land separating woodland blocks, and the distances between the remaining fragments exceeds the distance an individual animal is able to travel, that species becomes especially vulnerable. Small populations generally lack genetic diversity and may be threatened by increased predation, increased competition, disease and unexpected catastrophe. At the edge of each forest fragment, increased light encourages secondary growth of fast-growing species and old growth trees are more vulnerable to logging as access is improved. The birds that nest in their crevices, the epiphytes that hang from their branches and the invertebrates in the leaf litter are all adversely affected and biodiversity is reduced. Habitat fragmentation can be ameliorated to some extent by the provision of wildlife corridors connecting the fragments. These can be a river, ditch, strip of trees, hedgerow or even an underpass to a highway. Without the corridors, seeds cannot disperse and animals, especially small ones, cannot travel through the hostile territory, putting populations at greater risk of local extinction.

Habitat disturbance can have long-lasting effects on the environment. Bromus tectorum is a vigorous grass from Europe which has been introduced to the United States where it has become invasive. It is highly adapted to fire, producing large amounts of flammable detritus and increasing the frequency and intensity of wildfires. In areas where it has become established, it has altered the local fire regimen to such an extant that native plants cannot survive the frequent fires, allowing it to become even more dominant. A marine example is when sea urchin populations "explode" in coastal waters and destroy all the macroalgae present. What was previously a kelp forest becomes an urchin barren that may last for years and this can have a profound effect on the food chain. Removal of the sea urchins, by disease for example, can result in the seaweed returning, with an over-abundance of fast-growing kelp.

Habitat protection

The protection of habitats is a necessary step in the maintenance of biodiversity because if habitat destruction occurs, the animals and plants reliant on that habitat suffer. Many countries have enacted legislation to protect their wildlife. This may take the form of the setting up of national parks, forest reserves and wildlife reserves, or it may restrict the activities of humans with the objective of benefiting wildlife. The laws may be designed to protect a particular species or group of species, or the legislation may prohibit such activities as the collecting of bird eggs, the hunting of animals or the removal of plants. A general law on the protection of habitats may be more difficult to implement than a site specific requirement. A concept introduced in the United States in 1973 involves protecting the critical habitat of endangered species, and a similar concept has been incorporated into some Australian legislation.

International treaties may be necessary for such objectives as the setting up of marine reserves. Another international agreement, the Convention on the Conservation of Migratory Species of Wild Animals, protects animals that migrate across the globe and need protection in more than one country. However, the protection of habitats needs to take into account the needs of the local residents for food, fuel and other resources. Even where legislation protects the environment, a lack of enforcement often prevents effective protection. Faced with food shortage, a farmer is likely to plough up a level patch of ground despite it being the last suitable habitat for an endangered species such as the San Quintin kangaroo rat, and even kill the animal as a pest. In this regard, it is desirable to educate the community on the uniqueness of their flora and fauna and the benefits of ecotourism.

Monotypic habitat

A monotypic habitat is one in which a single species of animal or plant is so dominant as to virtually exclude all other species. An example would be sugarcane; this is planted, burnt and harvested, with herbicides killing weeds and pesticides controlling invertebrates. The monotypic habitat occurs in botanical and zoological contexts, and is a component of conservation biology. In restoration ecology of native plant communities or habitats, some invasive species create monotypic stands that replace and/or prevent other species, especially indigenous ones, from growing there. A dominant colonization can occur from retardant chemicals exuded, nutrient monopolization, or from lack of natural controls such as herbivores or climate, that keep them in balance with their native habitats. The yellow starthistle, Centaurea solstitialis, is a botanical monotypic-habitat example of this, currently dominating over 15,000,000 acres (61,000 km²) in California alone. The non-native freshwater zebra mussel, Dreissena polymorpha, that colonizes areas of the Great Lakes and the Mississippi River watershed, is a zoological monotypic-habitat example; the predators that control it in its home-range in Russia are absent and it proliferates abundantly. Even though its name may seem to imply simplicity as compared with polytypic habitats, the monotypic habitat can be complex. Aquatic habitats, such as exotic Hydrilla beds, support a similarly rich fauna of macroinvertebrates to a more varied habitat, but the creatures present may differ between the two, affecting small fish and other animals higher up the food chain.

Google AI Princeton: Current and Future Research

Tuesday, December 18, 2018  

Posted by Elad Hazan and Yoram Singer, Research Scientists, Google AI and Princeton University

Original link:  https://ai.googleblog.com/2018/12/google-ai-princeton-current-and-future.html

Google has long partnered with academia to advance research, collaborating with universities all over the world on joint research projects which result in novel developments in Computer Science, Engineering, and related fields. Today we announce the latest of these academic partnerships in the form of a new lab, across the street from Princeton University’s historic Nassau Hall, opening early next year. By fostering closer collaborations with faculty and students at Princeton, the lab aims to broaden research in multiple facets of machine learning, focusing its initial research efforts on optimization methods for large-scale machine learning, control theory and reinforcement learning. 

Below we give a brief overview of the research progress thus far.Large-Scale Optimization Imagine you have gone for a mountain hike and have run out of water. You need to get to a lake. How can you do so most efficiently? This is a matter of optimizing your route, and the mathematical analogue of this is the gradient descent method. You therefore move in the direction of steepest descent until you find the nearest lake at the bottom of your path. In the language of optimization, the location of the lake is referred to as a (local) minimum. The trajectory of gradient descent resembles the path, shown below, a thirsty yet avid hiker would take in order to get down to a lake as fast as she can.

Gradient descent (GD), and its randomized version, stochastic gradient descent (SGD), are the methods of choice for optimizing the weights of neural networks. Stacking all of the parameters together, we form a set of cells organized into vectors Let us take a simplistic view and assume that our neural net merely has 5 different parameters. Taking a gradient descent step amounts to subtracting the gradient vector (red) from the current set of parameters (blue) and putting the result back into the parameter vector.

Going back to our avid hiker, suppose she finds an unmarked path that is long and narrow, with limited visibility as she gazes down. If she follows the descent method her path would zig-zag down the hill, as shown in the illustration below on the left. However, she can now make faster progress by exploiting the skewed geometry of the terrain. That is, she can make a bigger leap forward than to the sides. In the context of gradient descent, pacing up is called acceleration. A popular class of acceleration methods is named adaptive regularization, or adaptive preconditioning, first introduced by the AdaGrad algorithm devised in collaboration with Prof. John Duchi from Stanford while he was at Google.

The idea is to change the geometry of the landscape of the optimization objective to make it easier for gradient descent to work. In order to do so, preconditioning methods stretch and rotate the space. The terrain after preconditioning looks like the serene, perfectly spherical lake above on the right, and the descent trajectory is a straight line! Procedurally, instead of subtracting the gradient vectors from the parameters vector per-se, adaptive preconditioning first multiplies the gradient by a 5×5 multicell structure, called a matrix preconditioner, as shown below.

This preconditioning operation yields a stretched and rotated gradient which is then subtracted as before, allowing much faster progress toward a basin. However, there is a downside to preconditioning, namely, its computational cost. Instead of subtracting a 5-dimensional gradient vector from a 5-dimensional parameter vector, the preconditioning transformation itself requires 5×5=25 operations. Suppose we would like to precondition gradients in order to learn a deep network with 10 million parameters. A single preconditioning step would require 100 trillion operations. In order to save computation, a diagonal version in which preconditioning amounts to stretching sans rotation was also introduced in the original AdaGrad paper. The diagonal version was later adopted and modified, yielding another very successful algorithm called Adam. This simplified diagonal preconditioning imposes only a marginal additional cost to gradient descent. However, oversimplification has its own downside: we are no longer able to rotate our space. Going back to our hiker, if the deep-and-narrow canyon runs from southeast to northwest, she can no longer take large westward leaps. Had we provided her with a “rigged” compass in which the north pole is in the northwest, she could have followed her descent procedure as before. In high dimensions, the analog of compass rigging is full-matrix preconditioning. We thus asked ourselves whether we could devise a preconditioning method that is computationally efficient while allowing for the equivalent of coordinate rotations. At Google AI Princeton, we developed a new method for full-matrix adaptive preconditioning at roughly the same computational cost as the commonly-used diagonal restriction. 

Details can be found in the paper, but the key idea behind the method is depicted below. Instead of using a full matrix, we replace the preconditioning matrix by a product of three matrices: a tall, thin matrix, a (small) square matrix, and a short, fat matrix. The vast amount of computation is performed using the smaller matrix. If we have d parameters, instead of a single large d × d matrix, the matrices maintained by GGT (shorthand for the operation Gradient Gradient^T), the proposed method, are of sizes d × k, k × k, k × d respectively.

For reasonable choices of k, which can be thought of as the “window size” of the algorithm, the computational bottleneck has been mitigated from a single large matrix, to that of a much smaller kkmatrix. In our implementation we typically choose k to be, say, 50, and maintaining the smaller square matrix is significantly less expensive while yielding good empirical performance. When compared to other adaptive methods on standard deep learning tasks, GGT is competitive with AdaGrad and Adam.Spectral Filtering for Control and Reinforcement Learning Another broad mission of Google’s research group in Princeton is to develop principled building blocks for decision-making systems. In particular, the group strives to leverage provable guarantees from the field of online learning, which studies the robust (worst-case) guarantees of decision-making algorithms under uncertainty. An online algorithm is said to attain a no-regret guarantee if it learns to make decisions as well as the best "offline" decision in hindsight. Ideas from this field have already enabled many innovations within theoretical computer science, and provide a mathematically elegant framework to study a widely-used technique called boosting.

We envision using ideas from online learning to broaden the toolkit of modern reinforcement learning. With that goal in mind, and in collaboration with researchers and students at Princeton, we developed the algorithmic technique of spectral filtering for estimation and control of linear dynamical systems (see severalrecentpublications). In this setting, noisy observations (e.g., location sensor measurements) are being streamed from an unknown source. The source of the signal is a system whose state evolves over time following a set of linear equations (e.g. Newton's laws). To forecast future signals (prediction), or to perform actions which bring the system to a desired state (control), the usual approach starts with learning the model explicitly (a task termed system identification), which is often slow and inaccurate. Spectral filtering circumvents the need to model the dynamics explicitly, by reformulating prediction and control as convex programs, enabling provable no-regret guarantees. A major component of the technique is that of a new signal processing transformation. The idea is to summarize the long history of past input signals through convolution with a tailored bank of filters, and then use this representation to predict the dynamical system’s future outputs. Each filter compresses the input signal into a single real number, by taking a weighted combination of the previous inputs.

A set of filters depicted in a plot of filter amplitude versus time. With our technique of spectral filtering, multiple filters are used to predict the state of a linear dynamical system at any given time. Each filter is a set of weights used to summarize past observations, such that combining them in a weighted fashion, over time allows us to accurately predict the system. 

The mathematical derivation of these weights (filters) has an interesting connection to the spectral theory of Hankel matrices. Looking Forward We are excited about the progress we have made thus far in partnership with Princeton’s faculty and students, and we look forward to the official opening of the lab in the coming weeks. It has long been Google’s view that both industry and academia benefit significantly from an open research culture, and we look forward to our continued close collaboration.AcknowledgmentsThe research and results discussed in this post would not have been possible without contributions from the following researchers: Naman Agarwal, Brian Bullins, Xinyi Chen, Udaya Ghai, Tomer Koren, Karan Singh, Cyril Zhang, Yi Zhang, and visiting professor Sham Kakade. Since joining Google earlier this year, the research team has been working remotely from both the Google NYC office as well as the Princeton University campus, and they look forward to moving into the new Google space across from the Princeton campus in the weeks to come.