Binomial proportion confidence interval: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
Newer edit →
No edit summary
 
No edit summary
Line 1: Line 1:
Ed is what people contact me and my spouse doesn't like it at all. To perform lacross is something I truly enjoy performing. He is an purchase clerk and it's something he really appreciate. My wife and I reside in Mississippi and I adore each day residing right here.<br><br>my blog - [http://www.herandkingscounty.com/content/information-and-facts-you-must-know-about-hobbies psychic readings online]
The term '''alpha diversity''' (α-diversity) was introduced by R. H. Whittaker<ref name=Whittaker1960>Whittaker, R. H. (1960) Vegetation of the Siskiyou Mountains, Oregon and California. Ecological Monographs, 30, 279–338. {{doi|10.2307/1943563}}</ref><ref name=Whittaker1972>Whittaker, R. H. (1972). Evolution and Measurement of Species Diversity. Taxon, 21, 213-251. {{doi|10.2307/1218190}}</ref> together with the terms [[beta diversity]] (β-diversity) and [[gamma diversity]] (γ-diversity). Whittaker's idea was that the total [[species diversity]] in a landscape (gamma diversity) is determined by two different things, the mean species diversity in sites or habitats at a more local scale (alpha diversity) and the differentiation among those habitats ([[beta diversity]]).
 
==Scale considerations==
 
Both the area or [[landscape]] of interest and the sites or [[habitat]]s within it may be of very different sizes in different situations, and no consensus has been reached on what [[Scale (spatial)|spatial scales]] are appropriate to quantify alpha diversity.<ref>Whittaker, R. J. et al. (2001). Scale and species richness: towards a general, hierarchical theory of species diversity. Journal of Biogeography, 28, 453-470. {{doi|10.1046/j.1365-2699.2001.00563.x}}</ref> It has therefore been proposed that the definition of alpha diversity does not need to be tied to a specific spatial scale: alpha diversity can be measured for an existing dataset that consists of subunits at any scale.<ref name=Tuomisto2010a>Tuomisto, H. (2010) A diversity of beta diversities: straightening up a concept gone awry. Part 1. Defining beta diversity as a function of alpha and gamma diversity. Ecography, 33, 2-22. {{doi|10.1111/j.1600-0587.2009.05880.x}}</ref> The subunits can be, for example, sampling units that were already used in the field when carrying out the inventory, or grid cells that are delimited just for the purpose of analysis. If results are extrapolated beyond the actual observations, it needs to be taken into account that the [[species diversity]] in the subunits generally gives an underestimation of the species diversity in larger areas.<ref>Colwell, R. K. and Coddington, J. A. (1994) Estimating terrestrial biodiversity through extrapolation. Philosophical Transactions: Biological Sciences, 345, 101-118.</ref><ref>Tuomisto, H. (2010) A diversity of beta diversities: straightening up a concept gone awry. Part 2. Quantifying beta diversity and related phenomena. Ecography, 33, 23-45. {{doi|10.1111/j.1600-0587.2009.06148.x}}</ref>
 
==Different alpha diversity concepts==
 
Ecologists have used several slightly different definitions of alpha diversity. Whittaker himself used the term both for the species diversity in a single subunit and for the mean species diversity in a collection of subunits.<ref name=Whittaker1960 /><ref name=Whittaker1972 /> It has been argued that defining alpha diversity as a mean across all relevant subunits is preferable, because it agrees better with Whittaker's idea that total species diversity consists of alpha and beta components.<ref name=Tuomisto2011>Tuomisto, H. (2011) Commentary: do we have a consistent terminology for species diversity? Yes, if we choose to use it. Oecologia, 167, 903-911.</ref>
 
Definitions of alpha diversity can also differ in what they assume [[species diversity | diversity]] to be. Often researchers use the values given by one or more [[diversity index|diversity indices]], such as species richness, the Shannon index or the Simpson index.<ref name=Whittaker1960 /><ref>Lande, R. (1996) Statistics and partitioning of species diversity, and similarity among multiple communities. Oikos, 76, 5-13.</ref><ref>Veech, J. A. et al. (2002) The additive partitioning of species diversity: recent revival of an old idea. Oikos, 99, 3-9.</ref> However, it has been argued that it would be better to use the effective number of species as the universal measure of species diversity. This measure allows weighting rare and abundant species in different ways, just as the diversity indices collectively do, but its meaning is intuitively easier to understand. The effective number of species is the number of equally-abundant species needed to obtain the same mean proportional species abundance as that observed in the dataset of interest (where all species may not be equally abundant).<ref name=Tuomisto2010a /><ref name=Tuomisto2011 /><ref>Hill, M. O. (1973) Diversity and evenness: a unifying notation and its consequences. Ecology, 54, 427–432</ref><ref name=Jost2006>Jost, L. (2006) Entropy and diversity. Oikos, 113, 363–375</ref><ref>Jost, L. (2007) Partitioning diversity into independent alpha and beta components. Ecology, 88, 2427–2439.</ref><ref name=Tuomisto2010c>Tuomisto, H. 2010. A consistent terminology for quantifying species diversity? Yes, it does exist. Oecologia 4: 853–860. {{doi|10.1007/s00442-010-1812-0}}</ref>
 
==Calculating alpha diversity==
 
Suppose species diversity is equated with the effective number of species, and alpha diversity with the mean species diversity per subunit. Then alpha diversity can be calculated in two different ways that give the same result. The first approach is to calculate a weighted [[generalized mean]] of the within-subunit species proportional abundances, and then take the inverse of this mean. The second approach is to calculate the species diversity for each subunit separately, and then take a weighted generalized mean of these.<ref name=Tuomisto2010a /><ref name=Tuomisto2010c />
 
If the first approach is used, the equation is:
 
:<math>{}^q\!D_{\alpha}=\dfrac{1}{\sqrt[q-1]{\sum_{j=1}^N{\sum_{i=1}^S p_{ij} p_{i|j}^{q-1}}}}</math>
 
In the equation, ''N'' is the total number of subunits and ''S'' is the total number of species (species richness) in the dataset. The proportional abundance of the ''i''th species in the ''j''th subunit is <math>p_{i|j}</math>. These proportional abundances are weighted by the proportion of data that each contributes to the dataset, which equals <math>p_{ij}</math>. The denominator hence equals mean proportional species abundance within the subunits (mean <math>p_{i|j}</math>) as calculated with the weighted generalized mean with exponent ''q'' - 1.
 
If the second approach is used, the equation is:
 
:<math>{}^q\!D_{\alpha}=\sqrt[1-q]{\sum_{j=1}^N w_j ({}^q\!D_{\alpha j})^{1-q}}</math>
 
This also equals a weighted generalized mean but with exponent 1 - ''q''. Here the mean is taken of the <sup>''q''</sup>''D''<sub>α''j''</sub> values, each of which represents the effective species density (species diversity per subunit) in one subunit ''j''. The nominal weight of the ''j''th subunit is <math>w_j</math>, which equals the proportion of data that the subunit contributes to the dataset.
 
Large values of ''q'' lead to smaller alpha diversity than small values of ''q'', because increasing ''q'' increases the effective weight given to those species with the highest proportional abundance and to those subunits with the lowest species diversity.<ref name=Tuomisto2010a /><ref name=Tuomisto2010c />
 
==See also==
 
* [[Beta diversity]]
* [[Gamma diversity]]
* [[Diversity index]]
* [[Phylogenetic diversity]]
* [[Global biodiversity]]
 
==References==
{{reflist|2}}
 
==External links==
* [http://www.uwsp.edu/geo/faculty/heywood/geog358/Diversity/Biodiversity.htm An explanation of many specific biodiversity terms using illustrations], [[University of Wisconsin–Stevens Point]]
 
[[Category:Biodiversity]]
[[Category:Measurement of biodiversity]]
[[Category:Summary statistics for categorical data]]

Revision as of 12:34, 22 December 2013

The term alpha diversity (α-diversity) was introduced by R. H. Whittaker[1][2] together with the terms beta diversity (β-diversity) and gamma diversity (γ-diversity). Whittaker's idea was that the total species diversity in a landscape (gamma diversity) is determined by two different things, the mean species diversity in sites or habitats at a more local scale (alpha diversity) and the differentiation among those habitats (beta diversity).

Scale considerations

Both the area or landscape of interest and the sites or habitats within it may be of very different sizes in different situations, and no consensus has been reached on what spatial scales are appropriate to quantify alpha diversity.[3] It has therefore been proposed that the definition of alpha diversity does not need to be tied to a specific spatial scale: alpha diversity can be measured for an existing dataset that consists of subunits at any scale.[4] The subunits can be, for example, sampling units that were already used in the field when carrying out the inventory, or grid cells that are delimited just for the purpose of analysis. If results are extrapolated beyond the actual observations, it needs to be taken into account that the species diversity in the subunits generally gives an underestimation of the species diversity in larger areas.[5][6]

Different alpha diversity concepts

Ecologists have used several slightly different definitions of alpha diversity. Whittaker himself used the term both for the species diversity in a single subunit and for the mean species diversity in a collection of subunits.[1][2] It has been argued that defining alpha diversity as a mean across all relevant subunits is preferable, because it agrees better with Whittaker's idea that total species diversity consists of alpha and beta components.[7]

Definitions of alpha diversity can also differ in what they assume diversity to be. Often researchers use the values given by one or more diversity indices, such as species richness, the Shannon index or the Simpson index.[1][8][9] However, it has been argued that it would be better to use the effective number of species as the universal measure of species diversity. This measure allows weighting rare and abundant species in different ways, just as the diversity indices collectively do, but its meaning is intuitively easier to understand. The effective number of species is the number of equally-abundant species needed to obtain the same mean proportional species abundance as that observed in the dataset of interest (where all species may not be equally abundant).[4][7][10][11][12][13]

Calculating alpha diversity

Suppose species diversity is equated with the effective number of species, and alpha diversity with the mean species diversity per subunit. Then alpha diversity can be calculated in two different ways that give the same result. The first approach is to calculate a weighted generalized mean of the within-subunit species proportional abundances, and then take the inverse of this mean. The second approach is to calculate the species diversity for each subunit separately, and then take a weighted generalized mean of these.[4][13]

If the first approach is used, the equation is:

qDα=1∑j=1N∑i=1Spijpi|jq−1q−1

In the equation, N is the total number of subunits and S is the total number of species (species richness) in the dataset. The proportional abundance of the ith species in the jth subunit is pi|j. These proportional abundances are weighted by the proportion of data that each contributes to the dataset, which equals pij. The denominator hence equals mean proportional species abundance within the subunits (mean pi|j) as calculated with the weighted generalized mean with exponent q - 1.

If the second approach is used, the equation is:

qDα=∑j=1Nwj(qDαj)1−q1−q

This also equals a weighted generalized mean but with exponent 1 - q. Here the mean is taken of the qDαj values, each of which represents the effective species density (species diversity per subunit) in one subunit j. The nominal weight of the jth subunit is wj, which equals the proportion of data that the subunit contributes to the dataset.

Large values of q lead to smaller alpha diversity than small values of q, because increasing q increases the effective weight given to those species with the highest proportional abundance and to those subunits with the lowest species diversity.[4][13]

See also

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

External links

  1. ↑ 1.0 1.1 1.2 Whittaker, R. H. (1960) Vegetation of the Siskiyou Mountains, Oregon and California. Ecological Monographs, 30, 279–338. 21 year-old Glazier James Grippo from Edam, enjoys hang gliding, industrial property developers in singapore developers in singapore and camping. Finds the entire world an motivating place we have spent 4 months at Alejandro de Humboldt National Park.
  2. ↑ 2.0 2.1 Whittaker, R. H. (1972). Evolution and Measurement of Species Diversity. Taxon, 21, 213-251. 21 year-old Glazier James Grippo from Edam, enjoys hang gliding, industrial property developers in singapore developers in singapore and camping. Finds the entire world an motivating place we have spent 4 months at Alejandro de Humboldt National Park.
  3. ↑ Whittaker, R. J. et al. (2001). Scale and species richness: towards a general, hierarchical theory of species diversity. Journal of Biogeography, 28, 453-470. 21 year-old Glazier James Grippo from Edam, enjoys hang gliding, industrial property developers in singapore developers in singapore and camping. Finds the entire world an motivating place we have spent 4 months at Alejandro de Humboldt National Park.
  4. ↑ 4.0 4.1 4.2 4.3 Tuomisto, H. (2010) A diversity of beta diversities: straightening up a concept gone awry. Part 1. Defining beta diversity as a function of alpha and gamma diversity. Ecography, 33, 2-22. 21 year-old Glazier James Grippo from Edam, enjoys hang gliding, industrial property developers in singapore developers in singapore and camping. Finds the entire world an motivating place we have spent 4 months at Alejandro de Humboldt National Park.
  5. ↑ Colwell, R. K. and Coddington, J. A. (1994) Estimating terrestrial biodiversity through extrapolation. Philosophical Transactions: Biological Sciences, 345, 101-118.
  6. ↑ Tuomisto, H. (2010) A diversity of beta diversities: straightening up a concept gone awry. Part 2. Quantifying beta diversity and related phenomena. Ecography, 33, 23-45. 21 year-old Glazier James Grippo from Edam, enjoys hang gliding, industrial property developers in singapore developers in singapore and camping. Finds the entire world an motivating place we have spent 4 months at Alejandro de Humboldt National Park.
  7. ↑ 7.0 7.1 Tuomisto, H. (2011) Commentary: do we have a consistent terminology for species diversity? Yes, if we choose to use it. Oecologia, 167, 903-911.
  8. ↑ Lande, R. (1996) Statistics and partitioning of species diversity, and similarity among multiple communities. Oikos, 76, 5-13.
  9. ↑ Veech, J. A. et al. (2002) The additive partitioning of species diversity: recent revival of an old idea. Oikos, 99, 3-9.
  10. ↑ Hill, M. O. (1973) Diversity and evenness: a unifying notation and its consequences. Ecology, 54, 427–432
  11. ↑ Jost, L. (2006) Entropy and diversity. Oikos, 113, 363–375
  12. ↑ Jost, L. (2007) Partitioning diversity into independent alpha and beta components. Ecology, 88, 2427–2439.
  13. ↑ 13.0 13.1 13.2 Tuomisto, H. 2010. A consistent terminology for quantifying species diversity? Yes, it does exist. Oecologia 4: 853–860. 21 year-old Glazier James Grippo from Edam, enjoys hang gliding, industrial property developers in singapore developers in singapore and camping. Finds the entire world an motivating place we have spent 4 months at Alejandro de Humboldt National Park.
Retrieved from "https://en.formulasearchengine.com/index.php?title=Binomial_proportion_confidence_interval&oldid=12457"