macroecology Macroecology is the subfield of ecology that deals with the study of relationships between organisms and their environment at large spatial scales to characterise and explain statistical patterns of abundance, distribution and diversity. The term ...

and

community ecology In ecology, a community is a group or association of populations of two or more different species occupying the same geographical area at the same time, also known as a biocoenosis, biotic community, biological community, ecological community, ...

, an occupancy frequency distribution (OFD) is the distribution of the numbers of species occupying different numbers of areas. It was first reported in 1918 by the Danish botanist

Christen C. Raunkiær Christen Christensen Raunkiær (29 March 1860 – 11 March 1938) was a Danish botanist, who was a pioneer of plant ecology. He is mainly remembered for his scheme of plant strategies to survive an unfavourable season ("life forms") and his demons ...

in his study on plant communities. The OFD is also known as the species-range size distribution in literature.

Bimodality

A typical form of OFD is a

bimodal distribution In statistics, a multimodal distribution is a probability distribution with more than one mode. These appear as distinct peaks (local maxima) in the probability density function, as shown in Figures 1 and 2. Categorical, continuous, and dis ...

, indicating the

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 ...

in a community is either rare or common, known as Raunkiaer's law of distribution of frequencies. That is, with each species assigned to one of five 20%-wide occupancy classes, Raunkiaer's law predicts bimodal distributions within homogenous plant formations with

modes Mode ( la, modus meaning "manner, tune, measure, due measure, rhythm, melody") may refer to: Arts and entertainment * '' MO''D''E (magazine)'', a defunct U.S. women's fashion magazine * ''Mode'' magazine, a fictional fashion magazine which is ...

in the first (0-20%) and last (81-100%) classes. Although Raunkiaer's law has long been discounted as an index of plant community homogeneity, the method of using occupancy classes to construct OFDs is still commonly used for both plant and animal assemblages.

Henry Gleason Henry Allan Gleason (1882–1975) was an American ecologist, botanist, and taxonomist. He was known for his endorsement of the individualistic or open community concept of ecological succession, and his opposition to Frederic Clements's concept ...

commented on this law in a 1929 ''

Ecology 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 ...

'' article: "In conclusion we may say that Raunkiaer's law is merely an expression of the fact that in any association there are more species with few individuals than with many, that the law is most apparent when

quadrat A quadrat is a frame, traditionally square, used in ecology, geography and biology to isolate a standard unit of area for study of the distribution of an item over a large area. Modern quadrats can for example be rectangular, circular, or irregul ...

s are chosen of the most serviceable size to show frequency, and that it is obscured or lost if the quadrats are either too large or too small." Evidently, there are different shapes of OFD found in literature. Tokeshi reported that approximately 46% of observations have a right-skewed unimodal shape, 27% bimodal, and 27%

uniform A uniform is a variety of clothing worn by members of an organization while participating in that organization's activity. Modern uniforms are most often worn by armed forces and paramilitary organizations such as police, emergency services, se ...

. A recent study reaffirms about 24% bimodal OFDs in among 289 real communities.

Factors

As pointed out by Gleason, the variety shapes of OFD can be explained, to a large degree, by the size of the sampling interval. For instance, McGeoch and Gaston (2002) show that the number of satellite (rare) species declines with the increase of sampling grains, but the number of core (common) species increases, showing a tendency from a bimodal OFD towards a right-skewed unimodal distribution. This is because species range, measured as occupancy, is strongly affected by the spatial scale and its aggregation structure, known often as the

scaling pattern of occupancy In spatial ecology and macroecology, scaling pattern of occupancy (SPO), also known as the area-of-occupancy (AOO) is the way in which species distribution changes across spatial scales. In physical geography and image analysis, it is similar to t ...

. Such scale dependence of occupancy has a profound effect on other macroecological patterns, such as the occupancy-abundance relationship. Other factors that have been proposed to be able to affect the shape of OFD include the degree of habitat heterogeneity, species specificity, landscape productivity, position in the geographic range, species dispersal ability and the extinction–colonization dynamics.

Mechanisms

Three basic models have been proposed to explain the bimodality found in occupancy frequency distributions.

Sampling results

Random sampling of individuals from either

lognormal In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable is log-normally distributed, then has a normal ...

or log-series rank abundance distributions (where random choice of an individual from a given species was proportional to its frequency) may produce bimodal occupancy distributions. This model is not particularly sensitive or informative as to the mechanisms generating bimodality in occupancy frequency distributions, because the mechanisms generating the lognormal species abundance distribution are still under heavy debate.

Core-satellite hypothesis

Bimodality may be generated by colonization-extinction metapopulation dynamics associated with a strong

rescue effect The rescue effect is a phenomenon which was first described by Brown and Kodric-Brown,Brown JH, Kodric-Brown A. 1977 Turnover rates in insular biogeography: effect of immigration on extinction. Ecology 58, 445– 449. (doi:10.2307/ 1935620) and is ...

. This model is appropriate to explain the range structure of a community that is influenced by metapopulation processes, such as dispersal and

local extinction Local extinction, also known as extirpation, refers to a species (or other taxon) of plant or animal that ceases to exist in a chosen geographic area of study, though it still exists elsewhere. Local extinctions are contrasted with global extinct ...

. However, it is not robust because the shape of the occupancy frequency distribution generated by this model is highly sensitive to species immigration and extinction parameters. The metapopulation model does also not explain scale dependence in the occupancy frequency distribution.

Occupancy probability transition

The third model that describes bimodality in the occupancy frequency distribution is based on the

under a self-similar assumption of species distributions (called the occupancy probability transition PTmodel). The OPT model is based on Harte et al.'s bisection scheme (although not on their probability rule) and the recursion probability of occupancy at different scales. The OPT model has been shown to support two empirical observations: #That bimodality is prevalent in interspecific occupancy frequency distributions. #that the number of satellite species in the distribution increases towards finer scales. The OPT model demonstrates that the sample grain of a study, sampling adequacy, and the distribution of species saturation coefficients (a measure of the fractal dimensionality of a species distribution) in a community are together largely able to explain the patterns commonly found in empirical occupancy distributions.

Hui The Hui people ( zh, c=, p=Huízú, w=Hui2-tsu2, Xiao'erjing: , dng, Хуэйзў, ) are an East Asian ethnoreligious group predominantly composed of Chinese-speaking adherents of Islam. They are distributed throughout China, mainly in the n ...

and McGeoch (2007) further show that the self-similarity in species distributions breaks down according to a power relationship with spatial scales, and we therefore adopt a power-scaling assumption for modeling species occupancy distributions. The bimodality in occupancy frequency distributions that is common in species communities, is confirmed to a result for certain mathematical and statistical properties of the probability distribution of occupancy. The results thus demonstrate that the use of the bisection method in combination with a power-scaling assumption is more appropriate for modeling species distributions than the use of a self-similarity assumption, particularly at fine scales. This model further provokes the Harte-Maddux debate: Harte et al. demonstrated that the

power law In statistics, a power law is a Function (mathematics), functional relationship between two quantities, where a Relative change and difference, relative change in one quantity results in a proportional relative change in the other quantity, inde ...

form of the

species–area relationship The species-area relationship or species-area curve describes the relationship between the area of a habitat, or of part of a habitat, and the number of species found within that area. Larger areas tend to contain larger numbers of species, and e ...

may be derived from a bisected, self-similar landscape and a community-level probability rule. However, Maddux showed that this self-similarity model generates biologically unrealistic predictions.

and McGeoch (2008) resolve the Harte–Maddux debate by demonstrating that the problems identified by Maddux result from an assumption that the probability of occurrence of a species at one scale is independent of its probability of occurrence at the next, and further illustrate the importance of considering patterns of species co-occurrence, and the way in which species occupancy patterns change with scale, when modeling species distributions.

References

{{Reflist, 2, refs= {{cite journal , doi=10.1086/284267 , last=Brown , first=James H. , date=August 1994 , title=On the relationship between abundance and distribution of species , journal=

The American Naturalist ''The American Naturalist'' is the monthly peer-reviewed scientific journal of the American Society of Naturalists, whose purpose is "to advance and to diffuse knowledge of organic evolution and other broad biological principles so as to enhance ...

, volume=124 , issue=4 , pages=255–279 , jstor=2461494 , url=http://biology.unm.edu/jhbrown/Documents/Publications/1980s/Brown1984AN.pdf , access-date=2010-08-10 {{cite journal , doi=10.2307/1941678 , last=Brown , first=James H. , author2=David W. Mehlman , author3=George C. Stevens , date=October 1995 , title=Spatial variation in abundance , journal=

, volume=76 , issue=7 , pages=2028–2043 , jstor=1941678 {{cite journal , last=Collins , first=Scott L. , author2=Susan M. Glenn , date=May 1997 , title= Effects of organismal and distance scaling on analysis of species distribution and abundance, journal=Ecological Applications , volume= 7, issue=2 , pages=543–551 , doi=10.1890/1051-0761(1997)007 543:EOOADS.0.CO;2, jstor=2269519 {{cite journal , last=Gaston , first=Kevin J. , date=May 1996 , title=Species-range size distributions: patterns, mechanisms and implications , journal=Trends in Ecology and Evolution , volume=11 , issue=5 , pages=197–201 , doi=10.1016/0169-5347(96)10027-6, pmid=21237808 {{cite journal , last=Gaston , first=Kevin J. , date=February 1998 , title=Species-range size distributions: products of speciation, extinction and transformation , journal= Philosophical Transactions of the Royal Society B: Biological Sciences , volume=353 , issue=1366 , pages=219–230 , doi=10.1098/rstb.1998.0204 , pmc=1692215, jstor=56474 {{cite journal , last=Gleason , first=H.A. , date=October 1929 , title=The significance of Raunkiaer's law of frequency , journal=

, volume=10 , issue=4 , pages=406–408 , doi=10.2307/1931149 , jstor=1931149 {{cite journal , doi=10.2307/3544021 , last=Hanski , first=Ilkka , date=March 1982 , title=Dynamics of regional distributions: the core and satellite species hypothesis , journal=

Oikos The ancient Greek word ''oikos'' (ancient Greek: , plural: ; English prefix: eco- for ecology and economics) refers to three related but distinct concepts: the family, the family's property, and the house. Its meaning shifts even within texts. The ...

, volume=38 , issue=2 , pages=210–221 , url=http://www.helsinki.fi/science/metapop/Publications/articles/Oikos%201982%20Hanski.pdf , jstor=3544021 {{cite journal , doi=10.1086/285527 , last=Hanski , first=Ilkka , author2=Mats Gyllenberg , date=July 1993 , title=Two general metapopulation models and the core-satellite species hypothesis , journal=The American Naturalist , volume=142 , issue=1 , pages=17–41 , jstor=2462632 {{cite journal , last= Harte, first=John , author2=Ann Kinzig , author3=Jessica Green , date=April 1999 , title=Self-similarity in the distribution and abundance of species , journal=

Science Science is a systematic endeavor that builds and organizes knowledge in the form of testable explanations and predictions about the universe. Science may be as old as the human species, and some of the earliest archeological evidence for ...

, volume=284 , issue=5412 , pages=334–336 , pmid=10195901 , doi= 10.1126/science.284.5412.334 , bibcode=1999Sci...284..334H , url=http://biology.uoregon.edu/people/green/publications/Harte%20et%20al.%201999%20Science%20Self-Similarity.pdf {{cite journal , last=Hui , first=Cang , author2=Melodie A. McGeoch , date=February 2007 , title=A self-similarity model for the occupancy frequency distribution , journal=Theoretical Population Biology , volume=71 , issue=1 , pages=61–70 , doi=10.1016/j.tpb.2006.07.007 , pmid=16979203, hdl=10019.1/117491 , hdl-access=free {{cite journal , last=Hui , first=Cang , author2=Melodie A. McGeoch , date=December 2007 , title=Modeling species distributions by breaking the assumption of self-similarity , journal=Oikos , volume=116 , issue=12 , pages= 2097–2107, doi=10.1111/j.2007.0030-1299.16149.x, hdl=10019.1/117512 , hdl-access=free {{cite journal , last=Hui , first=Cang , author2=Melodie A. McGeoch , date=October 2008 , title=Does the Self-Similar Species Distribution Model Lead to Unrealistic Predictions? , journal=Ecology , volume=89 , issue=10 , pages=2946–2952 , doi=10.1890/07-1451.1 , pmid=18959331, hdl=10019.1/117506 , hdl-access=free {{cite journal , last=Hui , first=Cang , author2=Ruan Veldtman , author3=Melodie A. McGeoch , date=February 2010 , title=Measures, perceptions and scaling patterns of aggregated species distributions , journal=Ecography , volume=33 , issue=1 , pages= 95–102, doi=10.1111/j.1600-0587.2009.05997.x, hdl=10019.1/117498 , hdl-access=free {{cite journal , last=Maddux , first=Robert D. , author2=Krishna Athreya , year=1999 , title=On the distribution and abundance of species , journal=Science , volume=286 , issue=5445 , pages=1647a–1647 , doi=10.1126/science.286.5445.1647a {{cite journal , last=Maddux , first=Robert D. , date=April 2004 , title=Self-similarity and the species–area relationship , journal=The American Naturalist , volume=163 , issue=4 , pages=616–626 , doi=10.1086/382660 , url=http://www.math.iastate.edu/maddux/papers/ms01-0371v3.pdf , pmid=15122507 , jstor=3473305, citeseerx=10.1.1.7.809 {{cite journal , doi=10.2307/3545425 , last=Maurer , first=Brian A. , date=June 1990 , title=The relationship between distribution and abundance in a patchy environment , journal=Oikos , volume=58 , issue=2 , pages=181–189 , jstor=3545425 {{cite journal , last=McGeoch , first=Melodie A. , author2=Kevin J. Gaston , date=August 2002 , title=Occupancy frequency distributions: patterns, artefacts and mechanisms , journal=

Biological Reviews The Cambridge Philosophical Society (CPS) is a scientific society at the University of Cambridge. It was founded in 1819. The name derives from the medieval use of the word philosophy to denote any research undertaken outside the fields of law ...

, volume=77 , issue= 3, pages=311–331 , doi= 10.1017/S1464793101005887 , pmid=12227519 {{cite journal , doi=10.2307/1933384 , last=McIntosh , first=Robert P. , date=July 1962 , title=Raunkiaer's 'Law of Frequency' , journal=Ecology , volume=43 , issue=3 , pages=533–535 , jstor=1933384 {{cite journal , doi=10.2307/3545450 , last=Nee , first=Richard D. Gregory , author2=Robert M. May , date=October 1991 , title= Core and satellite species: theory and artefacts , journal=Oikos , volume=62 , issue=1 , pages=83–87 , jstor=3545450 {{cite journal , last= Ostling , first=Annette , author2=John Harte , author3=Jessica L. Green , author4=Ann P. Kinzig , date=April 2004 , title=Self-similarity, the power law form of the species–area relationship, and a probability rule: a reply to Maddux , journal=The American Naturalist , volume=163 , issue=4 , pages=627–633 , doi=10.1086/382663 , pmid=15122508 , jstor=3473306 {{cite journal , doi=10.2307/3546107 , last=Papp , first=László , author2=János Izsák , date=May 1997 , title=Bimodality in occurrence classes: a direct consequence of lognormal or logarithmic series distribution of abundances: a numerical experimentation , journal=Oikos , volume=79 , issue=1 , pages=191–194 , jstor=3546107 {{cite book , last=Raunkiær , first=Christen C. , author-link=Christen C. Raunkiær , year=1934 , title=The life forms of plants and statistical plant geography: Being the collected papers of C. Raunkiær, others=Humphrey Gilbert-Carter et al., translators , location=Oxford , publisher=Clarendon Press {{cite journal , last=Scheiner , first=Samuel M. , author2=José M. Rey-Benayas , year=1997 , title=Placing empirical limits on metapopulation models for terrestrial plants , journal=Evolutionary Ecology , volume=11 , pages= 275–288 , doi=10.1023/A:1018464319460 , issue=3 {{cite journal , last=Storch , first=David , author2=Arnošt L. Šizling , date=August 2002 , title= Patterns of commonness and rarity in central European birds: reliability of the core-satellite hypothesis within a large scale, journal=Ecography , volume=25 , issue=4 , pages= 405–416, doi=10.1034/j.1600-0587.2002.250403.x , url=http://www.cts.cuni.cz/reports/2001/CTS-01-18.pdf , jstor=3683551 {{cite journal , last=Tokeshi , first=Mutsunori , year=1992 , title=Dynamics of distribution in animal communities: theory and analysis , journal=Researches on Population Ecology , volume=34 , issue=2 , pages=249–273 , doi=10.1007/BF02514796 , url=http://meme.biology.tohoku.ac.jp/popecol/RP%20PDF/34(2)/pp.249.pdf {{cite journal , last=Williams , first=Paul H. , date=May 1988 , title=Habitat use by bumble bees (''Bombus'' spp.) , journal=Ecological Entomology , volume=13 , issue=2 , pages= 223–237 , doi=10.1111/j.1365-2311.1988.tb00350.x Types of probability distributions Ecology Systems ecology Environmental statistics