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 people/etc in a group such as eight groups of nine people in each one, 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.
A group acts as a social environment of individuals: a flock of nine common cranes.
Statistical measures of group size roughly fall into two categories.
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, i.e. 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;
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: one for a solitary individual, two for both individuals in a group of two, 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, i.e. the arithmetic mean of crowding measures averaged over individuals (this was called "Typical Group Size" according to Jarman's 1974 terminology);
Imagine a sample with three groups, where group sizes are one, two, and six individuals, respectively, then
mean group size (group sizes averaged over groups) equals ;
mean crowding (group sizes averaged over individuals) equals .
Generally speaking, given there are G groups with sizes n1, n2, ..., nG, mean crowding can be calculated as:
mean crowding=
Statistical methodsedit
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, two-sample tests, etc.) and offer a free statistical toolset (Flocker 1.1).
Literatureedit
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, 1(2), 1–4.
group, size, measures, many, animals, including, humans, tend, live, groups, herds, flocks, bands, packs, shoals, colonies, hereafter, groups, conspecific, individuals, size, these, groups, expressed, number, people, group, such, eight, groups, nine, people, e. 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 people etc in a group such as eight groups of nine people in each one 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 A group acts as a social environment of individuals a flock of nine common cranes 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 GalleryOutsiders view of group size edit nbsp 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 i e 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 editAs 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 one for a solitary individual two for both individuals in a group of two etc Practically it describes the social environment of one particular individual This was called Individual Group Size in Jovani amp Mavor s 2011 paper Mean crowding i e 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 editImagine a sample with three groups where group sizes are one two and six individuals respectively then mean group size group sizes averaged over groups equals 1 2 6 3 3 displaystyle 1 2 6 3 3 nbsp mean crowding group sizes averaged over individuals equals 1 2 2 6 6 6 6 6 6 9 4 555 displaystyle 1 2 2 6 6 6 6 6 6 9 4 555 nbsp 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 displaystyle sum i 1 G n i 2 sum i 1 G n i nbsp Statistical methods editDue 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 two sample tests etc and offer a free statistical toolset Flocker 1 1 Literature editDebout G 2003 Le corbeau freux Corvus frugilegus nicheur en Normandie recensement 1999 amp 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 Rozsa L Tothmeresz B 2008 Measures of sociality two different views of group size Animal Behaviour 75 715 721 Reiczigel J Mejia Salazar MF Bollinger TK Rozsa L 2015 Comparing radio tracking and visual detection methods to quantify group size measures European Journal of Ecology 1 2 1 4 See also editSize of groups organizations and communitiesExternal links editFlocker 1 1 a statistical toolset to analyze group size measures with all the abovementioned calculations available Gallery edit nbsp An aphid colony nbsp European paper wasp colony nbsp Bluestripe snapper schooling nbsp Flamingos nbsp Gannet colony nbsp Common coots nbsp Great woodswallows allopreening nbsp Red billed quelea flock nbsp Wolf pack hunting nbsp African wild dogs nbsp Elephant seals nbsp Vicunas nbsp Bottlenose dolphins nbsp African buffalo herd nbsp Sheep flock Retrieved from https en wikipedia org w index php title Group size measures amp oldid 1185898773, wikipedia, wiki, book, books, library,
