Occupancy frequency distribution
Encyclopedia
In macroecology
and community ecology, 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
in his study on plant communities. The OFD is also known as the species-range size distribution in literature.
, indicating the species
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
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
commented on this law in a 1929 Ecology
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
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
.
. 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.
. 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.
under a self-similar
assumption of species distributions (called the occupancy probability transition [OPT] model). 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:
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 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
form of the species–area relationship
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. Hui 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.
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...
and community ecology, 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 C. Raunkiær
Christen Christensen Raunkiær 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 and his demonstration that the relative abundance of strategies in floras largely corresponded to the Earth's...
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 distributionBimodal distribution
In statistics, a bimodal distribution is a continuous probability distribution with two different modes. These appear as distinct peaks in the probability density function, as shown in Figure 1....
, indicating the species
Species
In biology, a species is one of the basic units of biological classification and a taxonomic rank. A species is often defined as a group of organisms capable of interbreeding and producing fertile offspring. While in many cases this definition is adequate, more precise or differing measures are...
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 (statistics)
In statistics, the mode is the value that occurs most frequently in a data set or a probability distribution. In some fields, notably education, sample data are often called scores, and the sample mode is known as the modal score....
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 Gleason
Henry Allan Gleason was a noted American ecologist, botanist, and taxonomist, most recognized for his endorsement of the individualistic/open community concept of ecological succession.- Life and work :...
commented on this law in a 1929 Ecology
Ecology (journal)
Ecology is a scientific journal publishing research and synthesis papers in the field of ecology. It was founded in 1920, and is published by the Ecological Society of America.- External links :**...
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
Quadrat
A quadrat is a square used in ecology and geography to isolate a sample, usually about 1m2 or 0.25m2. The quadrat is suitable for sampling plants, slow-moving animals , and some aquatic organisms.When an ecologist wants to know how many organisms there are in a particular habitat, it would not be...
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
Skewness
In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable. The skewness value can be positive or negative, or even undefined...
unimodal shape, 27% bimodal, and 27% uniform
Uniform distribution (continuous)
In probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of probability distributions such that for each member of the family, all intervals of the same length on the distribution's support are equally probable. The support is defined by...
.
Factors
As pointed out by Gleason, the variety shapes of OFD can be explained, to a large degree, by the sampling grain, extent and intensity. 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 occupancyScaling pattern of occupancy
In spatial ecology and macroecology, scaling pattern of occupancy , also known as the area-of-occupancy is the way in which species distribution changes across spatial scales. In physical geography and image analysis, it is similar to the modifiable areal unit problem. Simon A...
. Such scale dependence of occupancy has a profound effect on other macroecological patterns, such as the occupancy-abundance relationship
Occupancy-abundance relationship
In macroecology, the occupancy-abundance relationship is the relationship between the abundance of species and the size of their ranges within a region. This relationship is perhaps one of the most well-documented relationships in macroecology, and applies both intra- and interspecifically . In...
.
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 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-statellite hypothesis
Bimodality may be generated by colonization-extinction metapopulation dynamics associated with a strong rescue effect. This model is appropriate to explain the range structure of a community that is influenced by metapopulation processes, such as dispersal and local extinctionLocal extinction
Local extinction, also known as extirpation, is the condition of a species which ceases to exist in the chosen geographic area of study, though it still exists elsewhere...
. 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 scaling pattern of occupancyScaling pattern of occupancy
In spatial ecology and macroecology, scaling pattern of occupancy , also known as the area-of-occupancy is the way in which species distribution changes across spatial scales. In physical geography and image analysis, it is similar to the modifiable areal unit problem. Simon A...
under a self-similar
Self-similarity
In mathematics, a self-similar object is exactly or approximately similar to a part of itself . Many objects in the real world, such as coastlines, are statistically self-similar: parts of them show the same statistical properties at many scales...
assumption of species distributions (called the occupancy probability transition [OPT] model). 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 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
Power law
A power law is a special kind of mathematical relationship between two quantities. When the frequency of an event varies as a power of some attribute of that event , the frequency is said to follow a power law. For instance, the number of cities having a certain population size is found to vary...
form of the species–area relationship
Species-area curve
In ecology, a species-area curve is a 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 empirically, the relative numbers seem to follow systematic mathematical...
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. Hui 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.