56
4 StatistIcal Models and Technique;,
pattern, thus there are no generally applicable recipes for how to analyse patterns
statistically. If constancy (see Chap. 9) of a pattern or process is to be used as a
stability property, then it is necessary to define the pattern or process in such a way
that it is possible to decide whether a situation has or has not changed between two
different points in time. In ELA W AT the following patterns and processes were
investigated among others.
4.3.1.1
Small-Scale Distribution Patterns
Questions: In what way are individuals arranged in an area? Are they aggregated?
Are there repeated structures')
Sampling was done with a multi corer, with single corers arranged in a quadrate
without spaces in-between.
In the language of statistics, the arrangement of individuals is a stochastic process in two-dimensional space. The Poisson Process serves as a null model. It is
clearly defined by the statement that the probability for a certain number of individuals in an area only depends upon the size of the area, but not upon its location
within a larger area or other intluences. Such a pattern is sometimes called purely
random arrangement. To test the hypothesis, whether an observed arrangement is
purely random, aggregated or regular, the index of dispersion may be used. It distinguishes itself from other measures of aggregation by the fact that its statistical
distribution under the null model is known, so that a statistical test is possible
(Pfeifer et al. 1994).
For a description of the spatial pattern of the arrangement with respect to abundance, autocorrelogram- and variogram-analysis may be applied (Matheron 1971;
Jongman et al. 1995). For an example see Blome et al. (1999). Computationally,
autocorrelogram and variogram are equivalent, mathematically they are not. A
discussion on the use of autocorrelogram and variogram can be found in Journel &
Huijbregts (1991).
4.3.1.2
Spatial and Temporal Patterns
Questions: How variable are patterns in aggregations of L. conchi/ega') In which
way can the dynamics and the spatial aggregation of wading birds be modelled?
A criterion for the decision between equality and inequality of patterns derives
from the way in which the pattern has been described. If the model for the pattern
is a Poisson Process with parameter A, then change in pattern will be change of the
parameter A and/or change in the statistical distribution. If the pattern has been
described by means of the variogram, then this function is the criterion for constancy in the pattern. If more sophisticated models are used, specially designed
techniques will be necessary (see e.g. Ver Hoef & Cressie 1993). Borovkov et al.
(1996) show in which way stochastic networks can be used to model spatial and
temporal patterns.
4 StatistIcal Models and Technique;,
pattern, thus there are no generally applicable recipes for how to analyse patterns
statistically. If constancy (see Chap. 9) of a pattern or process is to be used as a
stability property, then it is necessary to define the pattern or process in such a way
that it is possible to decide whether a situation has or has not changed between two
different points in time. In ELA W AT the following patterns and processes were
investigated among others.
4.3.1.1
Small-Scale Distribution Patterns
Questions: In what way are individuals arranged in an area? Are they aggregated?
Are there repeated structures')
Sampling was done with a multi corer, with single corers arranged in a quadrate
without spaces in-between.
In the language of statistics, the arrangement of individuals is a stochastic process in two-dimensional space. The Poisson Process serves as a null model. It is
clearly defined by the statement that the probability for a certain number of individuals in an area only depends upon the size of the area, but not upon its location
within a larger area or other intluences. Such a pattern is sometimes called purely
random arrangement. To test the hypothesis, whether an observed arrangement is
purely random, aggregated or regular, the index of dispersion may be used. It distinguishes itself from other measures of aggregation by the fact that its statistical
distribution under the null model is known, so that a statistical test is possible
(Pfeifer et al. 1994).
For a description of the spatial pattern of the arrangement with respect to abundance, autocorrelogram- and variogram-analysis may be applied (Matheron 1971;
Jongman et al. 1995). For an example see Blome et al. (1999). Computationally,
autocorrelogram and variogram are equivalent, mathematically they are not. A
discussion on the use of autocorrelogram and variogram can be found in Journel &
Huijbregts (1991).
4.3.1.2
Spatial and Temporal Patterns
Questions: How variable are patterns in aggregations of L. conchi/ega') In which
way can the dynamics and the spatial aggregation of wading birds be modelled?
A criterion for the decision between equality and inequality of patterns derives
from the way in which the pattern has been described. If the model for the pattern
is a Poisson Process with parameter A, then change in pattern will be change of the
parameter A and/or change in the statistical distribution. If the pattern has been
described by means of the variogram, then this function is the criterion for constancy in the pattern. If more sophisticated models are used, specially designed
techniques will be necessary (see e.g. Ver Hoef & Cressie 1993). Borovkov et al.
(1996) show in which way stochastic networks can be used to model spatial and
temporal patterns.