Group size measures
Encyclopedia
Herd
Herd refers to a social grouping of certain animals of the same species, either wild or domestic, and also to the form of collective animal behavior associated with this or as a verb, to herd, to its control by another species such as humans or dogs.The term herd is generally applied to mammals,...
s, flocks
Flock (birds)
A flock is a group of birds conducting flocking behavior in flight, or while foraging. The term is akin to the herd amongst mammals. The benefits of aggregating in flocks are varied and flocks will form explicitly for specific purposes...
, bands, packs
Pack (canine)
Pack is a social group of conspecific canids. Not all species of canids - notably the red fox - form packs. Pack size and social behaviour within packs varies across species.-Species which exhibit pack behavior:...
, shoals
Shoaling and schooling
In biology, any group of fish that stay together for social reasons are said to be shoaling , and if, in addition, the group is swimming in the same direction in a coordinated manner, they are said to be schooling . In common usage, the terms are sometimes used rather loosely...
, or colonies
Bird colony
A bird colony is a large congregation of individuals of one or more species of bird that nest or roost in close proximity at a particular location. Many kinds of birds are known to congregate in groups of varying size; a congregation of nesting birds is called a breeding colony...
(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. Unfortunately, group size measures are notoriously hard to handle statistically since groups size values typically exhibit an aggregated (right-skewed) distribution
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...
: most groups are small, few are large, and a very few are very large.
Statistical measures of group size roughly fall into two categories.
Outsiders’ view of group size
- Group size is the number of individuals within a group;
- Mean group size , i.e. the arithmetic meanArithmetic meanIn mathematics and statistics, the arithmetic mean, often referred to as simply the mean or average when the context is clear, is a method to derive the central tendency of a sample space...
of group sizes averaged across groups; - Confidence intervalConfidence intervalIn statistics, a confidence interval is a particular kind of interval estimate of a population parameter and is used to indicate the reliability of an estimate. It is an observed interval , in principle different from sample to sample, that frequently includes the parameter of interest, if the...
for mean group size; - Median group size, i.e. the medianMedianIn probability theory and statistics, a median is described as the numerical value separating the higher half of a sample, a population, or a probability distribution, from the lower half. The median of a finite list of numbers can be found by arranging all the observations from lowest value to...
of group sizes calculated across groups; - Confidence intervalConfidence intervalIn statistics, a confidence interval is a particular kind of interval estimate of a population parameter and is used to indicate the reliability of an estimate. It is an observed interval , in principle different from sample to sample, that frequently includes the parameter of interest, if the...
for median group size.
Insiders’ view of group size
As Jarman (1974) pointed out, average individuals live in groups larger than average – simply because the groups smaller than average have fewer individuals than the groups larger than average. (Except for an unrealistic case when all groups are of equal size.) Therefore, when we wish to characterize a typical (average) individual’s social environment, we should not apply the outsiders’ view of group size. Reiczigel et al. (2008) proposed the following measures:- Crowding is the number of individuals within a group (equals to group size: 1 for a solitary individual, 2 for both individuals in a group of 2, etc.);
- Mean crowding, i.e. the arithmetic meanArithmetic meanIn mathematics and statistics, the arithmetic mean, often referred to as simply the mean or average when the context is clear, is a method to derive the central tendency of a sample space...
of crowding measures averaged across individuals (this was called "Typical Group Size" according to Jarman's 1974 terminology); - Confidence intervalConfidence intervalIn statistics, a confidence interval is a particular kind of interval estimate of a population parameter and is used to indicate the reliability of an estimate. It is an observed interval , in principle different from sample to sample, that frequently includes the parameter of interest, if the...
for mean crowding.
Statistical methods
Due to the aggregated (right-skewed) distributionSkewness
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...
of group members among groups, the application of parametric statistics
Parametric statistics
Parametric statistics is a branch of statistics that assumes that the data has come from a type of probability distribution and makes inferences about the parameters of the distribution. Most well-known elementary statistical methods are parametric....
would be misleading. Another problem arises when analyzing crowding values. Crowding data consist of nonindependent 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.)
The paper by Reiczigel et al. (2008) discusses the statistical problems associated with group size measures (calculating confidence interval
Confidence interval
In statistics, a confidence interval is a particular kind of interval estimate of a population parameter and is used to indicate the reliability of an estimate. It is an observed interval , in principle different from sample to sample, that frequently includes the parameter of interest, if the...
s, 2-sample tests, etc.) and offers a free statistical toolset (Flocker 1.1) to handle them in a user-friendly manner.
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.
- Reiczigel J, Lang Z, Rózsa L, Tóthmérész B 2008. Measures of sociality: two different views of group size. Animal Behaviour, 75, 715–721.