The COCKTAIL algorithm (Bruelheide 1995, 2000) was designed for statistical forming of sociological species groups. It proceeds iteratively as follows:
Step 1. The algorithm can be used either to 1a – select species differential for a vegetation unit, or 1b – define a vegetation unit characterised by a group of differential species.
Step 1a. Starting with preselected relevés (typical of a known vegetation unit) the algorithm begins by calculating all species fidelities to that vegetation unit and takes the species with the highest fidelity values as the starting species group.
Step 1b. Starting with a preselected species group which is user-defined, based on literature or previous analysis.
Step 2. The number of species of the species group is calculated in each relevé. The expected and observed cumulative distribution functions for relevés having 0 to k species are calculated. The distributions’ intersection defines the required minimum number m of species for a relevé to belong to the vegetation unit. The vegetation unit is defined by all relevés having m or more species belonging to the species group. If there is no intersection between observed and expected cumulative distribution then the algorithm aborts. This is the case when species having fewer co-occurrences than expected form the starting group.
Step 3. The occurrences of each species in the vegetation unit are counted and the fidelity is calculated.
Step 4. For all species in the species group fidelity value is tested against an (initially) fixed threshold fidelity. If fidelity exceeds the threshold the algorithm proceeds to step 5. If not there are two possibilities:
Step 4a. One of the initially selected species does not exceed the threshold. The group is rejected and the algorithm aborts.
Step 4b. The last species added has caused a previous species’ fidelity to decrease below the threshold. The previous species is removed, and the algorithm does not try to add this species again until the group has been changed by adding a further species.
Step 5. All species not belonging to the species group are sorted according to their fidelity value. If any exceed the threshold fidelity the algorithm proceeds to step 6. If not the algorithm stops. The species group is optimised when all species above the threshold are included.
Step 6. The species group is enlarged by including the (single) species with highest fidelity. Iteration continues at step 2.
Note that step 4a guarantees that the species group composition is not changed to such a degree that the initial species no longer have the highest fidelity. This restriction allows the formation of a number of species groups, some with lower maximal fidelity than others. Not every such group can be optimised. This is the case if species which do not co-occur with the vegetation type more than expected form the starting group.
When starting with preselected relevés (belonging to a known syntaxon) the vegetation unit is optimized in such a way that it is defined by differential species groups a posteriori, and the final composition of relevés in the group may be different than at the beginning. Not all syntaxa can be defined by groups of differential species – some are defined by dominance rather than by floristic composition.
Contrary to the original description of the COCKTAIL algorithm, JUICE allows the user to be more directly involved into the process of species group formation. Instead of automatical checking the species group composition in each step against the initially fixed fidelity value, it can be checked by the user if its give sense in phytosociological terms.
finds species, which are most frequent in the relevés
where selected species occurs. The species must be
selected by mouse click in the Species table part before
the running the function. The function is called from the
menu ANALYSIS and CO-OCCURRING SPECIES.
The selected species is shown at the top of the Co-occurring species window, with the number of relevés in which it occurs below. The list of the most frequently co-occurring species is sorted by decreasing frequency in the relevés where the selected species occurs. The value shown in the first column is the percentage of relevés of the selected species also containing the listed species. The next columns are: species name, layer, species frequency in the dataset, and frequency of joint occurrence of current and selected species.
procedure is the basic step of COCKTAIL method; it tests
interspecific association between the selected species
and each other species in the table. A fidelity measure
is calculated for each pair of species, which gives
information on their reciprocal affinity in the dataset.
Fig. 17 shows the display form of this function, with a
sorted list of species positively and negatively
associated with the species previously selected by
clicking in the Species part of the table. The list with
positive associations can be exported to the current
export *.RTF file (see Section 10).
All species in the list box can be marked by shift or control button and mouse click by using the button MARK SELECTED SPECIES IN THE TABLE.
The function INTERSPECIFIC ASSOCIATIONS is also used in the other parts of the program – Export of all interspecific associations (Section 10.3), Calculation of indicator values for species II (Section 7.4), Dependence sorting (Section 6) and INI groups (Section 9.5).
Explanation of list columns: fidelity measure, species name, layer, species frequency in the data set, frequency of joint occurrence of current and selected species in the data set.
An example of difference between mentioned functions
The maximum value (100 %) in the function Co-occuring species has a comparison of the species A with both B and C, while the function Interspecific associations gives a maximum fidelity value only for comparison of species A with C.
searches for an appropriate species combination as a
starting group for the function COCKTAIL groups, i. e. a
group of two or more species which frequently occur
together. Select one or a few species and add them into
the form. State the number of species to be added to the
group (1-10 can be added at a time) and press the Run
button. The function calculates interspecific
associations of the first species from the list with all
the other species, sorts them by decreasing values, and
selects the one or more most associated species. These
most associated species are added to the list. The
procedure is repeated with the second species and with
all subsequent species now in the list, and is terminated
after testing all listed species. Mark backwards in the
table marks the listed species with the specified colour.
Warning! High number of species to be added in larger tables can cause a very long cycle, so the program will have to be manually interrupted.
COCKTAIL GROUPS searches for optimal combinations of
species, which have similar distributions in the data set
and can be used as sociological species groups in
vegetation classification. The reciprocal test of species
associations is based on the fidelity calculation. A
relevé is considered to contain the species group if
more than half of species of the group occur in it.
How to create a species group:
Terminate the process when the group seems to be optimal for syntaxonomic classification. This may be when it is similar to a group of diagnostic species traditionally recognized in the syntaxonomic literature.
An optimized group with relatively high fidelity values (see bellow) can be saved by writing its name into the combo box and using the function ADD GROUP INTO THE TABLE. If you wish to see the percentage synoptic column only for coloured relevés, select the SYNOPTIC COL button.
Species groups can be added directly into the table as a pseudospecies (with ### before the group name). Such groups can be treated and analysed in the same way as proper species and can be combined with other species in the function Group aggregation. The column defined by selected species group can be tested for constants and dominants displayed after setting of cover threshold parameter (Header data analysis).
The group aggregation function selects relevé groups by combining presence of species groups and dominance of individual species. It uses species groups loaded in the table and dominant species which are defined by cover values exceeding a selected threshold. Species groups and dominant species are combined by the logical operators AND, OR, AND NOT, with the hierarchy defined by parentheses.
The query contains logical operators AND, OR and NOT (= AND NOT). Species group names consist of the characters ### followed by the species group name. Names of dominant species are not preceded by characters ###, but they have suffixes such as UP05 or UP25. For example, UP05 means that species is considered if its cover in the given relevé is higher than 5 % (UP25 means higher than 25 %).
Before running the query it can be checked by Show definition.
Warning: All pairs of logical variables associated by one operator must be put in parentheses!
For details of the procedures described in Sections 9.6 and 9.7, see Bruelheide (1995, 1997, 2000) or Bruelheide & Jandt (1995).
Expert system can automatically assign a relevé to a vegetation type, if there is already a classification based on species groups. The classification algorithm must be included in *.ESY file. This file should preferably be created as a product of the classification in a large dataset and must include all required information on aggregated species, species groups and their combinations into vegetation types. A result of the expert system run is shown in Fig. 21. The *.ESY file has a text structure and can be created manually.