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Group size measures

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Many animals, including humans, tend to live in groups, herds, flocks, bands, packs, shoals, or colonies hereafter: groups of conspecific individuals The size of these groups, as expressed by the number of participant individuals, is an important aspect of their social environment Group size tend to be highly variable even within the same species, thus we often need statistical measures to quantify group size and statistical tests to compare these measures between two or more samples Group size measures are notoriously hard to handle statistically since groups sizes typically follow an aggregated right-skewed distribution: most groups are small, few are large, and a very few are very large

Statistical measures of group size roughly fall into two categories

Contents

  • 1 Outsiders' view of group size
  • 2 Insiders' view of group size
  • 3 Example
  • 4 Statistical methods
  • 5 Literature
  • 6 See also
  • 7 External links
  • 8 Gallery

Outsiders' view of group size

Colony size measures for rooks breeding in Normandy The distribution of colonies vertical axis above and the distribution of individuals vertical axis below across the size classes of colonies horizontal axis The number of individuals is given in pairs Animal group size data tend to exhibit aggregated right-skewed distributions, ie most groups are small, a few are large, and a very few are very large Note that average individuals live in colonies larger than the average colony size Data from Normandy, 1999-2000 smoothed, Debout, 2003
  • Group size is the number of individuals within a group;
  • Mean group size , the arithmetic mean of group sizes averaged over groups;
  • Confidence interval for mean group size;
  • Median group size, the median of group sizes calculated over groups;
  • Confidence interval for median group size

Insiders' view of group size

As Jarman 1974 pointed out, average individuals live in groups larger than average Therefore, when we wish to characterize a typical average individual’s social environment, we should apply non-parametric estimations of group size Reiczigel et al 2008 proposed the following measures:

  • Crowding is the size the number of individuals of a group that a particular individual lives in equals to group size: 1 for a solitary individual, 2 for both individuals in a group of 2, etc Practically, it describes the social environment of one particular individual This was called Individual Group Size in Jovani & Mavor's 2011 paper;
  • Mean crowding, ie the arithmetic mean of crowding measures averaged over individuals this was called "Typical Group Size" according to Jarman's 1974 terminology;
  • Confidence interval for mean crowding

Example

Imagine a sample with 3 groups, where group sizes are 1, 2, and 6 individuals, respectively, then

mean group size group sizes averaged over groups equals 1 + 2 + 6 / 3 = 3 ; mean crowding group sizes averaged over individuals equals 1 + 2 + 2 + 6 + 6 + 6 + 6 + 6 + 6 / 9 = 4555

Generally speaking, given there are G groups with sizes n1, n2, , nG, mean crowding can be calculated as:

mean crowding= ∑ i = 1 G n i 2 / ∑ i = 1 G n i ^n_^/\sum _^n_

Statistical methods

Due to the aggregated right-skewed distribution of group members among groups, the application of parametric statistics would be misleading Another problem arises when analyzing crowding values Crowding data consist of non-independent values, or ties, which show multiple and simultaneous changes due to a single biological event Say, all group members' crowding values change simultaneously whenever an individual joins or leaves

Reiczigel et al 2008 discuss the statistical problems associated with group size measures calculating confidence intervals, 2-sample tests, etc and offer a free statistical toolset Flocker 11

Literature

  • Debout G 2003 Le corbeau freux Corvus frugilegus nicheur en Normandie: recensement 1999 & 2000 Cormoran, 13, 115–121
  • Jarman PJ 1974 The social organisation of antelope in relation to their ecology Behaviour, 48, 215–268
  • Jovani R, Mavor R 2011 Group size versus individual group size frequency distributions: a nontrivial distinction Animal Behaviour, 82, 1027–1036
  • Lengyel S, Tar J, Rozsa L 2012 Flock size measures of migrating Lesser White-fronted Geese Anser erythropus Acta Zoologica Academiae Scientiarum Hungaricae, 58, 297–303 2012
  • Reiczigel J, Lang Z, Rózsa L, Tóthmérész B 2008 Measures of sociality: two different views of group size Animal Behaviour, 75, 715–721
  • Reiczigel J, Mejía Salazar MF, Bollinger TK, Rozsa L 2015 Comparing radio-tracking and visual detection methods to quantify group size measures European Journal of Ecology, 12, 1–4

See also

Size of groups, organizations, and communities

External links

  • Flocker 11 – a statistical toolset to analyze group size measures with all the abovementioned calculations available

Gallery

group measures, group measures tableau, group size measures converter


Group size measures Information about

Group size measures


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    Group size measures beatiful post thanks!

    29.10.2014


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