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A typical form of OFD is a bimodal distribution, indicating the species in a community is either rare or common, known as Raunkiaer's law of distribution of frequencies. With each
A typical form of OFD is a bimodal distribution, indicating the species in a community is either rare or common, known as Raunkiaer's law of distribution of frequencies. With each
species assigned to one of five 20%-wide occupancy classes, this law predicted bimodal distributions within homogenous plant formations with modes in the first and last classes. Although Raunkiaer's law has long been discounted as an index of plant community homogeneity<ref>McIntosh, R. P. (1962). Raunkiaer's `Law of Frequency'. Ecology 43:533-535.</ref>, the method of using occupancy classes to construct OFDs is still commonly used for both plant and animal assemblages. [[Henry A. Gleason]] commented on this law in his 1929 Ecology article that "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 quadrats are chosen of the most serviceable size to show frequency, and that it is obscurred or lost if the quadrats are either too large or too small." Evidently, there are different shapes of OFD found in literature. Tokeshi (1992)<ref>Tokeshi, M. (1992). Dynamics of distribution in animal communities: theory and analysis. Researches on Population Ecology 34:249-273</ref> reported approximately 46% observations have a right-skewed unimodal shape, 27% bimodal and 27% uniform.
species assigned to one of five 20%-wide occupancy classes, this law predicted bimodal distributions within homogenous plant formations with modes in the first and last classes. Although Raunkiaer's law has long been discounted as an index of plant community homogeneity<ref>McIntosh, R. P. (1962). Raunkiaer's `Law of Frequency'. Ecology 43:533-535.</ref>, the method of using occupancy classes to construct OFDs is still commonly used for both plant and animal assemblages. [[Henry A. Gleason]] commented on this law in his 1929 Ecology article that "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 quadrats are chosen of the most serviceable size to show frequency, and that it is obscurred or lost if the quadrats are either too large or too small." Evidently, there are different shapes of OFD found in literature. Tokeshi (1992)<ref name="tok">Tokeshi, M. (1992). Dynamics of distribution in animal communities: theory and analysis. Researches on Population Ecology 34:249-273</ref> reported approximately 46% observations have a right-skewed unimodal shape, 27% bimodal and 27% uniform.


== Factors ==
== Factors ==
Line 24: Line 24:
'''Core-statellite hypothesis'''<br />
'''Core-statellite hypothesis'''<br />
Bimodality may be generated by colonization-extinction metapopulation dynamics associated with a strong rescue effect<ref name="Hanski 1982">Hanski, I., 1982. Dynamics of regional distributions: the core and satellite species hypothesis. Oikos 38, 210–221.</ref><ref>Hanski, I. and Gyllenberg, M. 1993. Two general metapopulation models and the core-satellite species hypothesis. Am. Nat. 142:17-41.</ref>. This model is appropriate to explain the range structure of a community that is influenced by metapopulation processes, such as dispersal and local extinction<ref>Storch, D. and Sizling, A. L. 2002. Patterns of commonness and rarity in central European birds: reliability of the coresatellite hypothesis within a large scale. Ecography 25:405-416.</ref>. However, it is not robust because the shape of the occupancy frequency distribution generated by this model is highly sensitive
Bimodality may be generated by colonization-extinction metapopulation dynamics associated with a strong rescue effect<ref name="Hanski 1982">Hanski, I., 1982. Dynamics of regional distributions: the core and satellite species hypothesis. Oikos 38, 210–221.</ref><ref>Hanski, I. and Gyllenberg, M. 1993. Two general metapopulation models and the core-satellite species hypothesis. Am. Nat. 142:17-41.</ref>. This model is appropriate to explain the range structure of a community that is influenced by metapopulation processes, such as dispersal and local extinction<ref>Storch, D. and Sizling, A. L. 2002. Patterns of commonness and rarity in central European birds: reliability of the coresatellite hypothesis within a large scale. Ecography 25:405-416.</ref>. 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<ref>Tokeshi, M. 1992. Dynamics of distribution in animal communities: theory and analysis. Res. Popul. Ecol. 34:249-273.</ref><ref>Scheiner, S. M. and Rey-Benayas, J. M. 1997. Placing empirical limits on metapopulation models for terrestrial plants. Evol. Ecol. 11:275-288.</ref>. The metapopulation model does also not explain scale dependence in the occupancy frequency distribution.<br />
to species immigration and extinction parameters<ref name="tok">Tokeshi, M. (1992). Dynamics of distribution in animal communities: theory and analysis. Researches on Population Ecology 34:249-273</ref><ref>Scheiner, S. M. and Rey-Benayas, J. M. 1997. Placing empirical limits on metapopulation models for terrestrial plants. Evol. Ecol. 11:275-288.</ref>. The metapopulation model does also not explain scale dependence in the occupancy frequency distribution.<br />


'''Occupancy probability transition'''<br />
'''Occupancy probability transition'''<br />
The third model that describes bimodality in the occupancy frequency distribution is based on the scaling pattern of occupancy under a self-similar assumption of species
The third model that describes bimodality in the occupancy frequency distribution is based on the scaling pattern of occupancy under a self-similar assumption of species
⚫
distributions (called the occupancy probability transition [OPT] model)<ref name="Hui 1">Hui, C. & McGeoch, M.A. (2007) A self-similarity model for the occupancy frequency distribution. Theoretical Population Biology, 71, 61-70.</ref><ref name="Hui 2">Hui, C. & McGeoch, M.A. (2007) Modeling species distributions by breaking the assumption of self-similarity. Oikos, 116, 2097-2107.</ref>. The OPT model is based on Harte et al.’s bisection scheme<ref name="Harte 1">Harte, J., Kinzig, A., Green, J., 1999. Self-similarity in the distribution and abundance of species. Science 284, 334–336.</ref> (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, i.e. (1) that bimodality is prevalent in interspecific occupancy frequency distributions and (2) that the number of satellite species in the distribution increases towards finer scales<ref name="Hui 1">Hui, C. & McGeoch, M.A. (2007) A self-similarity model for the occupancy frequency distribution. Theoretical Population Biology, 71, 61-70.</ref>. 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<ref name="Hui 2">Hui, C. & McGeoch, M.A. (2007) Modeling species distributions by breaking the assumption of self-similarity. Oikos, 116, 2097-2107.</ref>. The bimodality in occupancy frequency distributions that is common in species communities, is confirmed to a reult 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.<ref name="Harte 1">Harte, J., Kinzig, A., Green, J., 1999. Self-similarity in the distribution and abundance of species. Science 284, 334–336.</ref> 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<ref>Ostling, A., J. Harte, J. L. Green, and A. P. Kinzig. 2004. Self-similarity, the power law form of the species–area relationship, and a probability rule: a reply to Maddux. American Naturalist 163:627–633.</ref>. However, Maddux<ref>Maddux, R. D. 2004. Self-similarity and the species–area relationship. American Naturalist 163:616–626.</ref><ref>Maddux, R. D., and K. Athreya. 1999. On the distribution and abundance of species. Science 286:1647a.</ref>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<ref>Hui, C. & McGeoch, M.A. (2008) Does the Self-Similar Species Distribution Model Lead to Unrealistic Predictions? Ecology, 89, 2946-2952.</ref>.
distributions (called the occupancy probability transition [OPT] model)<ref>Hui, C. & McGeoch, M.A. (2007) A self-similarity model for the occupancy frequency distribution. Theoretical Population Biology, 71, 61-70.</ref><ref>Hui, C. & McGeoch, M.A. (2007) Modeling species distributions by breaking the assumption of self-similarity. Oikos, 116, 2097-2107.</ref>. The OPT model is based on Harte et al.’s bisection scheme<ref>Harte, J., Kinzig, A., Green, J., 1999. Self-similarity in the distribution and abundance of species. Science 284, 334–336.</ref> (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, i.e. (1) that bimodality is prevalent in interspecific occupancy frequency distributions and (2) that the number of satellite species in the
⚫
distribution increases towards finer scalesref>Hui, C. & McGeoch, M.A. (2007) A self-similarity model for the occupancy frequency distribution. Theoretical Population Biology, 71, 61-70.</ref>. 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<ref>Hui, C. & McGeoch, M.A. (2007) Modeling species distributions by breaking the assumption of self-similarity. Oikos, 116, 2097-2107.</ref>. The bimodality in occupancy frequency distributions that is common in species communities, is confirmed to a reult 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.<ref>Harte, J., Kinzig, A., Green, J., 1999. Self-similarity in the distribution and abundance of species. Science 284, 334–336.</ref> 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<ref>Ostling, A., J. Harte, J. L. Green, and A. P. Kinzig. 2004. Self-similarity, the power law form of the species–area relationship, and a probability rule: a reply to Maddux. American Naturalist 163:627–633.</ref>. However, Maddux<ref>Maddux, R. D. 2004. Self-similarity and the species–area relationship. American Naturalist 163:616–626.</ref><ref>Maddux, R. D., and K. Athreya. 1999. On the distribution and abundance of species. Science 286:1647a.</ref>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<ref>Hui, C. & McGeoch, M.A. (2008) Does the Self-Similar Species Distribution Model Lead to Unrealistic Predictions? Ecology, 89, 2946-2952.</ref>.


== References ==
== References ==

Revision as of 13:49, 22 April 2010

Definition

In macroecology and community ecology, an occupancy frequency distribution (OFD) refers to the distribution of the numbers of species occupying different numbers of areas[1]. 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[2][3].

Bimodality

A typical form of OFD is a bimodal distribution, indicating the species in a community is either rare or common, known as Raunkiaer's law of distribution of frequencies. With each species assigned to one of five 20%-wide occupancy classes, this law predicted bimodal distributions within homogenous plant formations with modes in the first and last classes. Although Raunkiaer's law has long been discounted as an index of plant community homogeneity[4], the method of using occupancy classes to construct OFDs is still commonly used for both plant and animal assemblages. Henry A. Gleason commented on this law in his 1929 Ecology article that "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 quadrats are chosen of the most serviceable size to show frequency, and that it is obscurred or lost if the quadrats are either too large or too small." Evidently, there are different shapes of OFD found in literature. Tokeshi (1992)[5] reported approximately 46% observations have a right-skewed unimodal shape, 27% bimodal and 27% uniform.

Factors

As pointed out by Henry A. 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)[1] 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 shape. This is because species range, measured as occupancy, is strongly affected by the spatial scale and its aggregation structure[6], known often as the scaling pattern of occupancy. 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[7][8], species specificity[9], landscape productivity[10], position in the geographic range[11], species dispersal ability[12] and the extinction–colonization dynamics[13].

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[14][15]. 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[13][16]. This model is appropriate to explain the range structure of a community that is influenced by metapopulation processes, such as dispersal and local extinction[17]. 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[5][18]. 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 occupancy under a self-similar assumption of species distributions (called the occupancy probability transition [OPT] model)[19][20]. The OPT model is based on Harte et al.’s bisection scheme[21] (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, i.e. (1) that bimodality is prevalent in interspecific occupancy frequency distributions and (2) that the number of satellite species in the distribution increases towards finer scales[19]. 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[20]. The bimodality in occupancy frequency distributions that is common in species communities, is confirmed to a reult 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.[21] 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[22]. However, Maddux[23][24]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[25].

References

  1. ^ a b McGeoch MA, Gaston KJ. 2002. Occupancy frequency distributions: patterns, artefacts and mechansims. Biological Reviews 77:311-331.
  2. ^ Gaston, K. J. (1996). Species-range size distributions: patterns, mechanisms and implications. Trends in Ecology and Evolution 11:197-201.
  3. ^ Gaston, K. J. (1998). Species-range size distributions: products of speciation, extinction and transformation. Philosophical Transactions of the Royal Society of London B 353:219-230.
  4. ^ McIntosh, R. P. (1962). Raunkiaer's `Law of Frequency'. Ecology 43:533-535.
  5. ^ a b Tokeshi, M. (1992). Dynamics of distribution in animal communities: theory and analysis. Researches on Population Ecology 34:249-273
  6. ^ Hui, C., Veldtman, R. & McGeoch, M.A. (2010) Measures, perceptions and scaling patterns of aggregated species distributions. Ecography, 33, 95-102.
  7. ^ Raunkiaer, C., 1934. The life forms of plants and statistical plant geography being the collected papers of C Raunkiaer. Claredon Press, Oxford.
  8. ^ Brown, J.H., 1984. On the relationship between abundance and distribution of species. Am. Nat. 124, 255–279.
  9. ^ Brown, J.H., Mehlman, D.W., Stevens, G.C., 1995. Spatial variation in abundance. Ecology 76, 2028–2043.
  10. ^ Maurer, B.A., 1990. The relationship between distribution and abundance in a patchy environment. Oikos 58, 181–189.
  11. ^ Williams, P.H., 1988. Habitat use by bumble bees (Bombus spp.). Ecol. Entomol. 13, 223–237.
  12. ^ Collins, S.L., Glenn, S.M., 1997. Effects of organismal and distance scaling on analysis of species distribution and abundance. Ecol. Appl. 7, 543–551.
  13. ^ a b Hanski, I., 1982. Dynamics of regional distributions: the core and satellite species hypothesis. Oikos 38, 210–221.
  14. ^ Nee, S. et al. 1991. Core and satellite species: theory and artefacts. Oikos 62:83-87.
  15. ^ Papp, L. and Izsak, J. 1997. Bimodality in occurrence classes: a direct consequence of lognormal or logarithmic series distribution of abundances: a numerical experimentation. Oikos 79:191-194.
  16. ^ Hanski, I. and Gyllenberg, M. 1993. Two general metapopulation models and the core-satellite species hypothesis. Am. Nat. 142:17-41.
  17. ^ Storch, D. and Sizling, A. L. 2002. Patterns of commonness and rarity in central European birds: reliability of the coresatellite hypothesis within a large scale. Ecography 25:405-416.
  18. ^ Scheiner, S. M. and Rey-Benayas, J. M. 1997. Placing empirical limits on metapopulation models for terrestrial plants. Evol. Ecol. 11:275-288.
  19. ^ a b Hui, C. & McGeoch, M.A. (2007) A self-similarity model for the occupancy frequency distribution. Theoretical Population Biology, 71, 61-70.
  20. ^ a b Hui, C. & McGeoch, M.A. (2007) Modeling species distributions by breaking the assumption of self-similarity. Oikos, 116, 2097-2107.
  21. ^ a b Harte, J., Kinzig, A., Green, J., 1999. Self-similarity in the distribution and abundance of species. Science 284, 334–336.
  22. ^ Ostling, A., J. Harte, J. L. Green, and A. P. Kinzig. 2004. Self-similarity, the power law form of the species–area relationship, and a probability rule: a reply to Maddux. American Naturalist 163:627–633.
  23. ^ Maddux, R. D. 2004. Self-similarity and the species–area relationship. American Naturalist 163:616–626.
  24. ^ Maddux, R. D., and K. Athreya. 1999. On the distribution and abundance of species. Science 286:1647a.
  25. ^ Hui, C. & McGeoch, M.A. (2008) Does the Self-Similar Species Distribution Model Lead to Unrealistic Predictions? Ecology, 89, 2946-2952.
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