Additional Material for

Kampichler C, Platen R (2004) Ground beetle occurrence and moor degradation: modelling a bioindication system by automated decision-tree induction and fuzzy logic. Ecological Indicators 4, 99-109

1. Material and Methods / Transformation into the fuzzy model
 2. Appendix A : Carabid beetles encountered in the study
3. Appendix B : Fuzzy model derived from main decision tree (Fig. 3a in Kampichler & Platen 2004)
4. Appendix C : Fuzzy model derived from the first additional decision tree (boosting) (Fig. 3b in Kampichler & Platen 2004)
5. Appendix D : Fuzzy model derived from the second additional decision tree (boosting) (Fig. 3c in Kampichler & Platen 2004)


Material and Methods

Transformation into the fuzzy model

A decision tree as in Fig. 1b in Kampichler & Platen (2004) is a classifier with discrete decision criteria. For example, a moor with 50 individuals of species A and with 101 individuals of species B in a sample of a defined size would be classified as belonging to class X. If only one specimen of species B was missed, the moor would be assigned to another class, Y, despite the obvious similarity between the two cases. Where ecologists have previously drawn this kind of artificially sharp distinction, they can now draw more realistic boundaries by means of fuzzy sets. In classical ('crisp') set theory, there are only two possibilities; either an object is member of a set or is not; thus, the only possible membership values are 0 and 1. In the example above, the moor has the membership 1 in class X (is a member of the class) and the membership 0 in class Y (is not a member of the class).The central idea in fuzzy set theory is that members of a set may have only partial membership, which consequently may possess all possible values between 0 and 1. The closer the membership of an element is to 1, the more it belongs to the set; the closer the membership of an element is to 0, the less it belongs to the set. Let, for example, the possible numbers of individuals of a species in a defined sample lie within 0 and 100 ( Fig. A ). Sharp boundaries between sets necessarily mean, that counts that differ as close as 1 may be assigned to different sets (here, 50 and 51). Through fuzzy sets, a region of overlap may be defined; numbers around 50 belong to both sets, the respective membership values depending on whether the observed numbers are lower or larger than 50.

fuzzy sets

Fig A. Example for discrete and fuzzy sets. Membership of the discrete sets "rare" (dotted line) and "frequent" (unbroken line) have a sharp upper and lower boarder, respectively (left), while membership of the fuzzy set "rare" (dotted line) and "frequent" (unbroken line) increase and decrease gradually, respectively (right).

The decision trees yielded by automated tree induction were broken down into a set of rules by representing each possible path through the trees by a rule. (See5 uses a more parsimonious approach for generating rules out of a tree; however, for a fuzzy model, the rule base must explicitly cover the entire variable space.) Subsequently, sharp boundaries (e.g., a rule including the antecedent IF species A <= n versus a rule including IF species A > n, where n defines a split in the tree) were translated into fuzzy boundaries (e.g. into rules with the antecedents IF species A is rare versus IF species A is frequent with an overlapping zone between the sets "rare" and "frequent" around n) in a manner similar to that demonstrated in Fig. A. The amount of overlap chosen was based on biological plausibility and was open to modification while adjusting the model. Fuzzy models can be tuned by modifying the shape of the fuzzy sets until the model output eventually fits the desired output. Presence-absence splits in the decision trees were translated into discrete sets. For development of the fuzzy model, we chose only 15 of the plots according to a stratified random drawing from the full list of plots in order to ensure an equal representation of each degradation stage in the subset; we used the ten plots not chosen for development as unseen cases for validation of the model (Rykiel 1996).

For a hypothetical example, let there be two species (A and B) and two fuzzy sets denoting the abundance of A and B ("rare" and "frequent") ( Fig. B ), and let X, Y and Z be three classes of increasing moor degradation. There are four possible combinations of variable states, and they can be described by four rules (as it would be if the sets were discrete); let them, hypothetically, be:

Rule 1: IF species A is rare and species B is rare THEN moor belongs to class X.
Rule 2: IF species A is rare and species B is frequent THEN moor belongs to class Y.
Rule 3: IF species A is frequent and species B is rare THEN moor belongs to class Z.
Rule 4: IF species A is frequent and species B is frequent THEN moor belongs to class Z.

Logically, rules 3 and 4 could be replaced by the simpler rule IF species A is frequent THEN moor belongs to class Z, but the procedures involved in running a fuzzy rule-based model need the explicit addressing of all possible variable states. Let the observed numbers n of the two species be n A=10 and nB =60. In a process called fuzzification (Fig. B ), the observed numbers of individuals of A and B are translated into membership values in the sets "rare" and "frequent". Of the four rules, rule 3 and 4 are not activated, since nA =10 is not a member of the class "frequent", the respective membership value is 0. Both rule 1 and 2 are activated, because -- due to the fuzzy nature of the sets -- n B=60 belongs to set "rare" as well as to set "frequent" and this is a fundamental difference to a rule base with discrete sets: Whereas in a discrete rule-set each possible combination of attributes is represented by only one rule, in a fuzzy rule-set several rules may address the same combination of attributes.


fuzzification - fuzzy inference - defuzzification
Fig. B. Hypothetical example for fuzzy control consisting of the processes fuzzification, fuzzy inference and defuzzification. The abundance of species A and B is 10 and 60 individuals, respectively. See text for detailed description.


In a process called fuzzy inference (Fig. B ), the membership values of the moor in the classes X, Y and Z are calculated. This is done by use of the minimum-operator: the lower value of the membership values of A and B is assigned to the class that is addressed by the rule (this is the simplest possibility for the logical AND in fuzzy logic). Subsequently, the results of rule 1 and 2 are merged by use of the maximum-operator: the higher value of the membership determined by the different rules is assigned to each class (this is the simplest possibility for the logical OR in fuzzy logic) (Fig. B ). In a final step called defuzzification (Fig.B ), the result of the fuzzy inference can be transformed (when necessary) into a discrete output. The method most widely used is to calculate the centre of gravity of the output polygon and to project it onto the x-axis. This value can be used for assigning a case (i.e., moor) to a certain class (e.g., the x co-ordinate of the centre of gravity is closest to class Y, this means that the moor with nA=10 and n B =60 is assigned to class Y). Thus, classes must be expressed at least on an ordinal scale.

The entire process embracing fuzzification, fuzzy interference and defuzzification is called fuzzy control. The simple example above shows only a few of the possibilities available for fuzzy control; the operators used and the shape of the fuzzy sets (trapezoid, triangular, overlapping vs. non-overlapping etc.) are subject to the expertise of the modeller (see Bothe (1995) or Zimmermann (1996) for an introduction to fuzzy control).

(See Kampichler & Platen (2004) for references cited in this text.)

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Appendix

Appendix A.
Carabid beetles encountered in the study.

Table A.1. Number of individuals encountered in the 25 study sites (their degradation stage is given in the column headers).

Species
 1
 1
 1
 1
 1
 2
 2
 2
 2
 2
 3
 3
 3
 3
 3
 4
 4
 4
 4
 4
 5
 5
 5
 5
 5
Abax parallelepipedus (Piller & Mitterpacher, 1783)








1



7









Acupalpus dubius Schilsky, 1888




1
1

1










1

Acupalpus flavicollis (Sturm, 1825)





17
 1



1
 1







2

Acupalpus parvulus (Sturm, 1825)





1







2





7

Agonum afrum (Duftschmid, 1812)



















1
 65
 1

Agonum fuliginosum (Panzer, 1809)
 1
 3
 3
 2

2
 25
 4
 15

1
 1
 1
 1
 58
 29
 24
 11
 10
 44
 32

Agonum gracile (Gyllenhal, 1827)
 1








1









1


Agonum piceum (Linnaeus, 1758)









1













Agonum sexpunctatum (Linnaeus, 1758)










3
 1

1






67
 24
Agonum thoreyi Dejean, 1828
1


1
3













1

Agonum versutum (Gyllenhal, 1827)




















1


Agonum viduum (Panzer, 1797)




















11
 3

Amara aenea (De Geer, 1774)













1









Amara aulica (Panzer, 1797)























1
Amara bifrons (Gyllenhal, 1810)











2










1
Amara brunnea (Gyllenhal, 1810)













1
14
 1
38


10
 85
Amara communis (Panzer, 1797)







2



4
 4

1
 3
 51


78
 21
Amara consularis (Duftschmid, 1812)


















1




Amara convexior Stephens, 1828























2
Amara familiaris (Duftschmid, 1812)








1


1








1
 1
Amara lunicollis Schiödte, 1837












1
 1


1



86
 13
Amara ovata (Fabricius, 1792)













3







1
Amara plebeja (Gyllenhal, 1810)

2


1


1
 1
 2
 2




1
2


Amara similata (Gyllenhal, 1810)


















2


1
Amara spreta Dejean, 1831























1
Amara tibialis (Paykull, 1798)













1









Anisodactylus binotatus (Fabricius, 1787)









1
1






1



Anthracus consputus (Duftschmid, 1812)









1



1








Badister bullatus (Schrank, 1798)






















1
Badister dilatatus Chaudoir, 1827





1







1



4
 2


Badister lacertosus Sturm, 1815











1


1







Badister sodalis (Duftschmid, 1812)




















21


Bembidion articulatum (Panzer, 1796)























20
Bembidion assimile Gyllenhal, 1810

1


1


3



12




7
 66

Bembidion biguttatum (Fabricius, 1779)




















2


Bembidion doris (Panzer, 1797)









1



2



8
 1
 4

Bembidion gilvipes Sturm, 1825









2









1


Bembidion guttula (Fabricius, 1792)















1



2
 1

Bembidion humerale Sturm, 1825









3











1
Bembidion lampros (Herbst, 1784)

















1
 11


11
 122
Bembidion mannerheimii C.R. Sahlberg, 1827
















1


1


Bembidion properans Stephens, 1829























44
Bembidion tetracolum Say, 1823




















1


Bembidion varium (Olivier, 1795)









1













Blethisa multipunctata (Linnaeus, 1758)
 1








3
 1






1




Bradycellus csikii Laczó, 1912














1




2
 1
 2
Bradycellus harpalinus (Serville, 1821)





1
2
 1
1
1








4
 1
Broscus cephalotes (Linnaeus, 1758)













1









Calathus fuscipes (Goeze, 1777)










1




1




2
 18
Calathus melanocephalus (Linnaeus, 1758)














1







2
Calathus micropterus (Duftschmid, 1812)
2
 1










1
 1
 19
 2
 3



4
 8
Calathus rotundicollis Dejean, 1828



1
1










2





Carabus granulatus Linnaeus, 1758





1

1

27
7
 3
3
19
 71
 431
 53
 1
Carabus hortensis Linnaeus, 1758













77

5
2




Carabus nemoralis O.F. Müller, 1764








6
 2


4

6
 1
 11

1
 33
 86
Carabus violaceus Linnaeus, 1758












1
 25

23
 4
 12




Chlaenius nigricornis (Fabricius, 1787)










1












Chlaenius tristis (Schaller, 1783)















2







Clivina fossor (Linnaeus, 1758)








4


11



3

20


Cychrus caraboides (Linnaeus, 1758)
 1







1


2
 4

2
 10
 2




Dromius sigma (Rossi, 1790)




















1


Dyschirius aeneus (Dejean, 1825)














1








Dyschirius globosus (Herbst, 1783)





15
1
 7
 3
76
 9
 14
 55
 5
 39
 1
 27
 14
 99
 14
 166
 86
Dyschirius luedersi Wagner, 1915

1






6








2



Elaphrus cupreus Duftschmid, 1812
 8
 1
 10



1
 2
10
 8



7
 2

4
 4
9
 3
Elaphrus riparius (Linnaeus, 1758)









4













Elaphrus uliginosus Fabricius, 1775









1













Epaphius rivularis (Gyllenhal, 1810)




249

5
1
12


16


5
 6
 1

Epaphius secalis (Paykull, 1790)











3
6



1




Harpalus affinis (Schrank, 1781)























1
Harpalus anxius (Duftschmid, 1812)




















1


Harpalus distinguendus (Duftschmid, 1812)








1














Harpalus latus (Linnaeus, 1758)











1
 1


2
 3
 4
1
8
Harpalus rufipalpis Sturm, 1818













1

1




1
Harpalus signaticornis (Duftschmid, 1812)



















1



Harpalus smaragdinus (Duftschmid, 1812)





1

















Harpalus tardus (Panzer, 1797)









1







1



1
Harpalus xanthopus winkleri Schauberger, 1923













16

1
1



2
Leistus ferrugineus (Linnaeus, 1758)












2
 1

1
 2
 2




Leistus rufomarginatus Duftschmid, 1812
















4
 2
 17



3
Leistus terminatus (Hellwig in Panzer, 1793)
 1
4








1
 5
 1

28
 27
 36
 2
 3
 2
 81
 22
Loricera pilicornis (Fabricius, 1775)




5


9
 2
 1
3

5
 147
 1
 1
48
 1
 12
 5
Microlestes minutulus (Goeze, 1777)











3

1







2
Nebria brevicollis (Fabricius, 1792)
 1
3


1

1
 17
 3




121
 1
 19
1
 3
 6
 3
Notiophilus aquaticus (Linnaeus, 1758)






















1
Notiophilus biguttatus (Fabricius, 1779)
















10
11


9
 56
Notiophilus palustris (Duftschmid, 1812)




1

2



1
 4

4
 8
 11


11
 49
Oodes helopioides (Fabricius, 1792)
 2
 2
 12
 3
1
 8
 14
 14
1



7
 6


14
 44
 28

Oxypselaphus obscurus (Herbst, 1794)



3

3
 7
 99
 25
44
 82
 20
 22
 2
 226
 197
 69
 8
 12
 21
 12
Panagaeus cruxmajor (Linnaeus, 1758)




1


















Patrobus assimilis Chaudoir, 1844




1


6














Patrobus atrorufus (Stroem, 1768)




3
 1
35
10
 5


2
 15

1
4
 16
 13
 6
Poecilus cupreus (Linnaeus, 1758)









3





1


3
 1
2
Poecilus versicolor (Sturm, 1824)
1
1




2

3





1


2
 2
Pseudoophonus rufipes (De Geer, 1774)





1
1





6
2
8


4
 17
Pterostichus anthracinus (Illiger, 1798)




















65
 35

Pterostichus aterrimus (Herbst, 1794)
 7
 33
 6







43
 1


2


13



Pterostichus diligens (Sturm, 1824)

2
25
 137
 75
 27
 58
 68
 277
 5
 194
 197
 335
 50
 91
 143
 51
 80
 32
 45
 50
 209
Pterostichus guentheri Sturm, 1824




















1


Pterostichus melanarius (Illiger, 1798)









1


10


2
 1
29
2
 2
Pterostichus minor (Gyllenhal, 1827)
 3
 13
 9
 1
 4
 31
 35
 13
 19
 31
 94
 19
 69
 51
 2
 35
 64
 15
 9
 5
 96
 172
 98
 50
 1
Pterostichus niger (Schaller, 1783)
 1
 9
1
 3
1
 25
15
 6
 4
 21
 19
 304

178
 106
 111
 1
 5
 18
 10
 3
Pterostichus nigrita (Paykull, 1790)
 3
 9
 14
1

1


7
 2
13
 1
80
3
 10
 24
 17

Pterostichus oblongopunctatus (Fabricius, 1787)






1

3

2
 35
5
 102
 32
 141


248
 186
Pterostichus rhaeticus Heer, 1837
 16
 22
 19
 10
 18
 4
 17
 19
 34
 520
 55
 99
 22
 114
 4
 4
 118
 372
 22
 77
 21
 4
58
 20
Pterostichus strenuus (Panzer, 1797)
1
 2
2


2

4

3
2
 16
 5
 88
4
2
Pterostichus vernalis (Panzer, 1796)
 1



1
 2



6


4




2
 3
1
Stenolophus mixtus (Herbst, 1784-1785)
 3
 2



8


1
2

3



6
 9
 10

Stenolophus teutonus (Schrank, 1781)








1

1











Stomis pumicatus (Panzer, 1796)











2




1
 7


1
Syntomus truncatellus (Linné, 1761)























3
Synuchus vivalis (Illigier, 1798)


















1


1
 2
Trechoblemus micros (Herbst, 1783)












1










Trechus obtusus Erichson, 1837












1



8


1
1
Trechus quadristriatus (Schrank, 1781)























1
Trichocellus placidus (Gyllenhal, 1827)








1



3

53
27
3
 3
 7
 1
Zabrus tenebrioides (Goeze, 1777)


1





















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Table A.2. Ecological characteristics of encountered species.

Species
 Prefered habitat types
 Ecological tolerance
 Trophic Guild
 Feeding Items
Abax parallelepipedus (Piller & Mitterpacher, 1783)
 moist deciduous forests
 stenotopic a
 carnivorous
Acupalpus dubius Schilsky, 1888
 vegetationless river banks
 stenotopic a
 unclear
Acupalpus flavicollis (Sturm, 1825)
 vegetationless river banks
 intermediate c
 unclear
Acupalpus parvulus (Sturm, 1825)
 vegetationless river banks
 stenotopic a
 unclear
Agonum afrum (Duftschmid, 1812)
 eutrophic mires
 stenotopic a
 mainly carnivorous
Agonum fuliginosum (Panzer, 1809)
 wet forests (incl. floodplains)
 intermediate c
 carnivorous
 Collembola
Agonum gracile (Gyllenhal, 1827)
 oligotrophic or mesotrophic mires
 stenotopic a
 mainly carnivorous
Agonum piceum (Linnaeus, 1758)
 eutrophic mires
 stenotopic a
 mainly carnivorous
Agonum sexpunctatum (Linnaeus, 1758)
 oligotrophic or mesotrophic mires
 intermediate c
 mainly carnivorous
Agonum thoreyi Dejean, 1828
 eutrophic mires
 intermediate c
 mainly carnivorous
Agonum versutum (Gyllenhal, 1827)
 eutrophic mires
 intermediate c
 mainly carnivorous
Agonum viduum (Panzer, 1797)
 eutrophic mires
 stenotopic a
 mainly carnivorous
Amara aenea (De Geer, 1774)
 dry grasslands
 intermediate c
 herbivorous, carnivorous
 seeds, soft roots, insects, small worms
Amara aulica (Panzer, 1797)
 ruderal sites (incl. fallows)
 intermediate c
 herbivorous
 seeds
Amara bifrons (Gyllenhal, 1810)
 ruderal sites (incl. fallows)
 intermediate c
 herbivorous, carnivorous
 seeds, soft roots, insects, small worms
Amara brunnea (Gyllenhal, 1810)
 drier deciduous or coniferous forests
 intermediate c
 herbivorous, carnivorous
 seeds, soft roots, insects, small worms
Amara communis (Panzer, 1797)
 fresh, intensively managed meadows or pastures
 eurytopic b
 herbivorous
 seeds
Amara consularis (Duftschmid, 1812)
 arable land
 intermediate c
 herbivorous
 seeds
Amara convexior Stephens, 1828
 dry grasslands
 intermediate c
 herbivorous, carnivorous
 seeds, soft roots, insects, small worms
Amara familiaris (Duftschmid, 1812)
 arable land
 intermediate c
 herbivorous
 seeds
Amara lunicollis Schiödte, 1837
 dry grasslands
 intermediate c
 herbivorous, carnivorous
 seeds, soft roots, insects, small worms
Amara ovata (Fabricius, 1792)
 moist deciduous forests
 intermediate c
 herbivorous, carnivorous
 seeds, soft roots, insects, small worms
Amara plebeja (Gyllenhal, 1810)
 arable land
 eurytopic b
 herbivorous
 seeds
Amara similata (Gyllenhal, 1810)
 arable land
 intermediate c
 herbivorous, carnivorous
 seeds, soft roots, insects, small worms
Amara spreta Dejean, 1831
 arable land
 intermediate c
 herbivorous, carnivorous
 seeds, soft roots, insects, small worms
Amara tibialis (Paykull, 1798)
 dry grasslands
 intermediate c
 herbivorous, carnivorous
 seeds, soft roots, insects, small worms
Anisodactylus binotatus (Fabricius, 1787)
 unmanaged moist or wet meadows
 intermediate c
 unclear
Anthracus consputus (Duftschmid, 1812)
 eutrophic mires
 intermediate c
 unclear
Badister bullatus (Schrank, 1798)
 drier deciduous or coniferous forests
 intermediate c
 unclear
Badister dilatatus Chaudoir, 1827
 oligotrophic or mesotrophic mires
 intermediate c
 unclear
Badister lacertosus Sturm, 1815
 moist deciduous forests
 intermediate c
 unclear
Badister sodalis (Duftschmid, 1812)
 unmanaged moist or wet meadows
 intermediate c
 unclear
Bembidion articulatum (Panzer, 1796)
 unmanaged moist or wet meadows
 intermediate c
 unclear
 d
Bembidion assimile Gyllenhal, 1810
 eutrophic mires
 intermediate c
 unclear
 d
Bembidion biguttatum (Fabricius, 1779)
 eutrophic mires
 intermediate c
 unclear
 d
Bembidion doris (Panzer, 1797)
 oligotrophic or mesotrophic mires
 intermediate c
 unclear
 d
Bembidion gilvipes Sturm, 1825
 unmanaged moist or wet meadows
 intermediate c
 unclear
 d
Bembidion guttula (Fabricius, 1792)
 eutrophic mires
 intermediate c
 unclear
 d
Bembidion humerale Sturm, 1825
 oligotrophic or mesotrophic mires
 stenotopic a
 unclear
 d
Bembidion lampros (Herbst, 1784)
 arable land
 intermediate c
 unclear
 d
Bembidion mannerheimii C.R. Sahlberg, 1827
 wet forests (incl. floodplains)
 intermediate c
 unclear
 d
Bembidion properans Stephens, 1829
 arable land
 intermediate c
 unclear
 d
Bembidion tetracolum Say, 1823
 arable land
 intermediate c
 unclear
 d
Bembidion varium (Olivier, 1795)
 vegetationless river banks
 intermediate c
 carnivorous
 Nematoda, insect larvae
Blethisa multipunctata (Linnaeus, 1758)
 eutrophic mires
 intermediate c
 unclear
Bradycellus csikii Laczó, 1912
 ruderal sites (incl. fallows)
 intermediate c
 unclear
Bradycellus harpalinus (Serville, 1821)
 oligotrophic or mesotrophic mires
 intermediate c
 herbivorous
 seeds
Broscus cephalotes (Linnaeus, 1758)
 arable land
 intermediate c
 carnivorous
Calathus fuscipes (Goeze, 1777)
 ruderal sites (incl. fallows)
 intermediate c
 herbivorous
 seeds, germinating pine seeds
Calathus melanocephalus (Linnaeus, 1758)
 ruderal sites (incl. fallows)
 intermediate c
 herbivorous
 seeds
Calathus micropterus (Duftschmid, 1812)
 drier deciduous or coniferous forests
 stenotopic a
 unclear
Calathus rotundicollis Dejean, 1828
 moist deciduous forests
 intermediate c
 unclear
Carabus granulatus Linnaeus, 1758
 wet forests (incl. floodplains)
 eurytopic b
 carnivorous
 insects, larvae
Carabus hortensis Linnaeus, 1758
 moist deciduous forests
 stenotopic a
 carnivorous
 insects, snails, fresh carrion
Carabus nemoralis O.F. Müller, 1764
 moist deciduous forests
 intermediate c
 carnivorous, herbivorous
 insects, snails, worms, fresh fruit
Carabus violaceus Linnaeus, 1758
 drier deciduous or coniferous forests
 intermediate c
 mainly carnivorous
 snails, fresh carrion, mushrooms
Chlaenius nigricornis (Fabricius, 1787)
 eutrophic mires
 stenotopic a
 unclear
Chlaenius tristis (Schaller, 1783)
 eutrophic mires
 stenotopic a
 unclear
Clivina fossor (Linnaeus, 1758)
 arable land
 intermediate c
 mainly carnivorous
Cychrus caraboides (Linnaeus, 1758)
 moist deciduous forests
 intermediate c
 carnivorous
 snails, worms
Dromius sigma (Rossi, 1790)
 wet forests (incl. floodplains)
 intermediate c
 unclear
Dyschirius aeneus (Dejean, 1825)
 vegetationless river banks
 stenotopic a
 carnivorous
 Staphilinidae and their larvae
Dyschirius globosus (Herbst, 1783)
 wet forests (incl. floodplains)
 eurytopic b
 carnivorous
 Staphilinidae and their larvae
Dyschirius luedersi Wagner, 1915
 eutrophic mires
 intermediate c
 carnivorous
 Staphilinidae and their larvae
Elaphrus cupreus Duftschmid, 1812
 wet forests (incl. floodplains)
 intermediate c
 carnivorous
Elaphrus riparius (Linnaeus, 1758)
 vegetationless river banks
 stenotopic a
 carnivorous
Elaphrus uliginosus Fabricius, 1775
 eutrophic mires
 intermediate c
 carnivorous
Epaphius rivularis (Gyllenhal, 1810)
 oligotrophic or mesotrophic mires
 intermediate c
 unclear
Epaphius secalis (Paykull, 1790)
 wet forests (incl. floodplains)
 stenotopic a
 unclear
Harpalus affinis (Schrank, 1781)
 arable land
 intermediate c
 herbivorous
 seeds of deciduous and coniferous trees
Harpalus anxius (Duftschmid, 1812)
 dry grasslands
 intermediate c
 mainly herbivorous
Harpalus distinguendus (Duftschmid, 1812)
 arable land
 stenotopic a
 herbivorous
Harpalus latus (Linnaeus, 1758)
 fresh, intensively managed meadows or pastures
 intermediate c
 mainly herbivorous
Harpalus rufipalpis Sturm, 1818
 dry grasslands
 intermediate c
 mainly herbivorous
Harpalus signaticornis (Duftschmid, 1812)
 arable land
 intermediate c
 mainly herbivorous
Harpalus smaragdinus (Duftschmid, 1812)
 dry grasslands
 intermediate c
 mainly herbivorous
Harpalus tardus (Panzer, 1797)
 ruderal sites (incl. fallows)
 intermediate c
 herbivorous
Harpalus xanthopus winkleri Schauberger, 1923
 moist deciduous forests
 intermediate c
 mainly herbivorous
Leistus ferrugineus (Linnaeus, 1758)
 drier deciduous or coniferous forests
 intermediate c
 carnivorous
 Collembola
Leistus rufomarginatus Duftschmid, 1812
 moist deciduous forests
 intermediate c
 carnivorous
 Collembola
Leistus terminatus (Hellwig in Panzer, 1793)
 oligotrophic or mesotrophic mires
 intermediate c
 carnivorous
 Collembola
Loricera pilicornis (Fabricius, 1775)
 arable land
 eurytopic b
 carnivorous
 Collembola
Microlestes minutulus (Goeze, 1777)
 ruderal sites (incl. fallows)
 intermediate c
 unclear
Nebria brevicollis (Fabricius, 1792)
 moist deciduous forests
 eurytopic b
 carnivorous
 Collembola
Notiophilus aquaticus (Linnaeus, 1758)
 dry grasslands
 stenotopic a
 carnivorous
 Collembola, mites
Notiophilus biguttatus (Fabricius, 1779)
 moist deciduous forests
 intermediate c
 carnivorous
 Collembola, mites
Notiophilus palustris (Duftschmid, 1812)
 wet forests (incl. floodplains)
 intermediate c
 carnivorous
 Collembola, mites
Oodes helopioides (Fabricius, 1792)
 eutrophic mires
 intermediate c
 unclear
Oxypselaphus obscurus (Herbst, 1794)
 wet forests (incl. floodplains)
 intermediate c
 unclear
Panagaeus cruxmajor (Linnaeus, 1758)
 eutrophic mires
 stenotopic a
 unclear
Patrobus assimilis Chaudoir, 1844
 oligotrophic or mesotrophic mires
 stenotopic a
 unclear
Patrobus atrorufus (Stroem, 1768)
 wet forests (incl. floodplains)
 intermediate c
 unclear
Poecilus cupreus (Linnaeus, 1758)
 arable land
 intermediate c
 carnivorous
Poecilus versicolor (Sturm, 1824)
 arable land
 intermediate c
 carnivorous
Pseudoophonus rufipes (De Geer, 1774)
 arable land
 intermediate c
 carnivorous, herbivorous
Pterostichus anthracinus (Illiger, 1798)
 wet forests (incl. floodplains)
 intermediate c
 carnivorous
Pterostichus aterrimus (Herbst, 1794)
 oligotrophic or mesotrophic mires
 stenotopic a
 carnivorous
Pterostichus diligens (Sturm, 1824)
 oligotrophic or mesotrophic mires
 intermediate c
 carnivorous
Pterostichus guentheri Sturm, 1824
 eutrophic mires
 intermediate c
 carnivorous
Pterostichus melanarius (Illiger, 1798)
 fresh, intensively managed meadows or pastures
 eurytopic b
 carnivorous, herbivorous
 insects, cereals, fruit
Pterostichus minor (Gyllenhal, 1827)
 oligotrophic or mesotrophic mires
 intermediate c
 carnivorous
Pterostichus niger (Schaller, 1783)
 moist deciduous forests
 eurytopic b
 carnivorous
Pterostichus nigrita (Paykull, 1790)
 wet forests (incl. floodplains)
 intermediate c
 carnivorous
Pterostichus oblongopunctatus (Fabricius, 1787)
 moist deciduous forests
 intermediate c
 carnivorous
Pterostichus rhaeticus Heer, 1837
 oligotrophic or mesotrophic mires
 intermediate c
 carnivorous
Pterostichus strenuus (Panzer, 1797)
 moist deciduous forests
 intermediate c
 carnivorous, herbivorous
 insects, rotting plants
Pterostichus vernalis (Panzer, 1796)
 unmanaged noist or wet meadows
 intermediate c
 carnivorous
Stenolophus mixtus (Herbst, 1784-1785)
 eutrophic mires
 intermediate c
 unclear
Stenolophus teutonus (Schrank, 1781)
 vegetationless river banks
 intermediate c
 unclear
Stomis pumicatus (Panzer, 1796)
 moist deciduous forests
 intermediate c
 unclear
Syntomus truncatellus (Linné, 1761)
 ruderal sites (incl. fallows)
 intermediate c
 unclear
Synuchus vivalis (Illigier, 1798)
 ruderal sites (incl. fallows)
 intermediate c
 unclear
Trechoblemus micros (Herbst, 1783)
 eutrophic mires
 intermediate c
 unclear
Trechus obtusus Erichson, 1837
 ruderal sites (incl. fallows)
 intermediate c
 unclear
Trechus quadristriatus (Schrank, 1781)
 arable land
 intermediate c
 unclear
Trichocellus placidus (Gyllenhal, 1827)
 wet forests (incl. floodplains)
 intermediate c
 unclear
Zabrus tenebrioides (Goeze, 1777)
 arable land
 stenotopic a
 herbivorous, carnivorous
 cereals, young plants

a stenotopic, here: occurring in not more than two habitat types (e.g., oligotrophic and mesotrophic mires)
b eurytopic, here: occurring in more than seven habitat types of any kind
c intermediate, between stenotopic and eurytopic
d Many Bembidion species are known as insect egg predators .

Ecological information about Carabid species were drawn from:

Barndt, D., Brase, S., Glauche, M., Gruttke, H., Kegel, B., Platen, R.  & Winkelmann, H. (1991): Die Laufkäferfauna von Berlin (West) - mit Kennzeichnung und Auswertung der verschollenen und gefährdeten Arten (Rote Liste, 3. Fassung). In: Auhagen, A., Platen, R. & Sukopp, H., Rote Liste der gefährdeten Pflanzen und Tiere in Berlin. Landschaftsentwicklung und Umweltforschung S 6: 243-275.
Bauer, T. (1974): Ethologische, autökologische und ökophysiologische Untersuchungen an Elaphrus cupreus Dft. und Elaphrus riparius L. (Coleoptera, Carabidae). Zum Lebensformtyp des optisch jagenden Räubers unter den Laufkäfern. Oecologia (Berlin) 14: 139-196.
Bauer, T. (1975): Zur Biologie und Autökologie von Notiophilus biguttatus F. und Bembidion foraminosum Strm. (Coleoptera, Carabidae) als Bewohner ökologisch extremer Standorte. Zum Lebensformtyp des visuell jagenden Räubers unter den Laufkäfern (11). Zool. Anz. 194: 305-318.
Bauer, T. (1985): Beetles which use a setal trap to hunt springtails: The hunting strategy and apparatus of Leistus (Coleoptera, Carabidae). Pedobiologia 28: 275-287.
Bauer, T. (1990): Laufkäfer und Collembolen: Räuber-Beute-Beziehungen unter den Bodentieren. Sber. Ges. Naturf. Freunde Berlin (N.F.) 29/30: 29-43.
Faasch, H. (1968): Beobachtungen zur Biologie und zum Verhalten von Cicindela hybrida L. und Cicindela campestris L. und experimentelle Analyse ihres Beutefangverhaltens. Zool. Jb. Syst. 95: 477-522.
Hintzpeter, U. & Bauer, T. (1986): The antennal setal trap of the ground beetle Loricera pilicornis: a specialization for feeding on Collembola. J. Zool. 208: 615-630.
Kane, T. C. (1976): Foraging by cave beetles: Spatial and temporal heterogenity of prey. Ecology 57: 793-800.
Koch, K. (1989): Die Käfer Mitteleuropas. Ökologie, Vol. 1. Goecke & Evers, Krefeld, 440 pp.
Scheffler, I., Kielhorn, K.-H., Wrase, D. W., Korge, H. & Braasch, D. (1999): Rote Liste und Artenliste der Laufkäfer des Landes Brandenburg (Coleoptera, Carabidae). Natursch. u. Landschaftspfl. i. Brandenburg 8 (1). Supplement, 19 S., Potsdam.
Siepel, H. & Brunsting, A. M. H. (1984): The stability of Carabid predator-prey systems and the potential role in Biological Control. XVII Int. Congr. Of Entomol. Hamburg, Abstr. Vol. 363.
Thiele, H.-U. (1977): Carabid beetles in their Environments. A Study on Habitat Selection by Adaptions in Physiology and Behaviour. Springer Vlg., Berlin, Heidelberg, New York, 369 pp.
Wachmann, E., Platen, R. & Barndt, D. (1995): Laufkäfer. Beobachtung-Lebensweise. Naturbuch Verlag, Augsburg, 295 pp.
Weseloh, R. M. (1958): Predation by Calosoma sycophanta (Coleoptera, Carabidae): evidence for a large impact on gypsy moth, Lymantria dispar L. pupae. Can. Ent. 117: 1117-1126.

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Appendix B.
Fuzzy model derived from main decision tree (Fig. 3a in Kampichler & Platen 2004)

The table "Fuzzy sets" shows the intersection points of the set boarders with the isolines "membership = 0" and "membership = 1". For example, the triangle representing the fuzzy set "is_absent" for Agonum afrum is is defined by the lower left point (0/0), the upper point (0/1) and lower right point (1/0). In analogy, trapezoid sets are defined by four points. The numbers in parentheses behind the names of the fuzzy sets are used for listing the rules in the table "Rule base".

Table B.1. Fuzzy sets

Species

Fuzzy Set

Shape

Points

Agonum afrum

is_absent (1)

triangle

[0 0 1]


is_present (2)

trapezoid

[0 1 500 500]

Amara lunicollis

is_rare_or_absent (1)

triangle

[0 0 4]


is_present (2)

trapezoid

[0 4 500 500]

Pterostichus diligens

is_moderately_abundant_or_absent (1)

trapezoid

[0 0 10 50]


is_abundant (2)

trapezoid

[10 50 110 176]


is_very_abundant (3)

trapezoid

[110 176 1000 1000]

Calathus micropterus

is_absent (1)

triangle

[0 0 1]


is_present (2)

trapezoid

[0 1 500 500]


Table B.2. Rule-base

Rule no.

A. afrum

A. lunicollis

P. diligens

C. micropterus

Degradation stage

1

2

1

1

1

1

2

2

1

1

2

1

3

2

1

2

1

2

4

2

1

2

2

4

5

2

1

3

1

3

6

2

1

3

2

3

7

2

2

1

1

5

8

2

2

1

2

5

9

2

2

2

1

5

10

2

2

2

2

5

11

2

2

3

1

5

12

2

2

3

2

5

13

1

1

1

1

5

14

1

1

2

1

5

15

1

1

2

2

5

16

1

1

2

2

5

17

1

1

3

1

5

18

1

1

3

2

5

19

1

2

1

1

5

20

1

2

1

2

5

21

1

2

2

1

5

22

1

2

2

2

5

23

1

2

3

1

5

24

1

2

3

2

5


For example, rule 1 is to be read as

IF Agonum afrum is_present AND IF Amara lunicollis is_rare_or_absent AND IF Pterostichus diligens is_moderately_abundant_or_absent AND IF Calathus micropterus is_absent THEN moor belongs to degradation stage 1.

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Appendix C.
Fuzzy model derived from first additional decision tree (boosting) (Fig. 3b in Kampichler & Platen 2004). See explanations in Appendix B .

Table C.1. Fuzzy sets

Species

Fuzzy set

Shape

Points

Chlaenius nigricornis

is_absent (1)

triangle

[0 0 1]


is_present (2)

trapezoid

[0 1 500 500]

Agonum afrum

is_absent (1)

triangle

[0 0 1]


is_present (2)

trapezoid

[0 1 500 500]

Pterostichus diligens

is_moderately_abundant_or_absent (1)

trapezoid

[0 0 10 50]


is_abundant (2)

trapezoid

[10 50 110 176]


is_very_abundant (3)

trapezoid

[110 176 1000 1000]

Bradycellus harpalinus

is_absent (1)

triangle

[0 0 1]


is_present (2)

trapezoid

[0 1 500 500]


Table C.2. Rule-base

Rule no.

C. nigricornis

A. afrum

P. diligens

B. harpalinus

Degradation stage

1

1

1

1

1

1

2

1

1

1

2

1

3

1

1

2

1

4

4

1

1

2

2

2

5

1

1

3

2

3

6

1

2

1

1

5

7

1

2

1

1

5

8

1

2

1

2

5

9

1

2

2

1

5

10

1

2

2

2

5

11

1

2

3

1

5

12

1

2

3

2

5

13

2

1

1

1

3

14

2

1

1

2

3

15

2

1

2

1

3

16

2

1

2

2

3

17

2

1

3

2

3

18

2

1

3

2

3

19

2

2

1

1

3

20

2

2

1

2

3

21

2

2

2

1

3

22

2

2

2

2

3

23

2

2

3

1

3

24

2

2

3

2

3


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Appendix D.
Fuzzy model derived from second additional decision tree (boosting) (Fig. 3c in Kampichler & Platen 2004). See explanations in Appendix B .

Table D.1. Fuzzy sets

Species

Fuzzy set

Shape

Points

Amara consularis

is_absent (1)

triangle

[0 0 1]


is_present (2)

trapezoid

[0 1 500 500]

Synuchus vivalis

is_absent (1)

triangle

[0 0 1]


is_present (2)

trapezoid

[0 1 500 500]

Chlaenius nigricornis

is_absent (1)

triangle

[0 0 1]


is_present (2)

trapezoid

[0 1 500 500]

Calathus micropterus

is_absent (1)

triangle

[0 0 1]


is_present (2)

trapezoid

[0 1 500 500]

Oxypselaphus obscurus

is_rare_or_absent (1)

trapezoid

[0 0 4 10]


is_present (2)

trapezoid

[4 10 500 500]


Table D.2. Rule-base

Rule no.

A. consularis

S. vivalis

C. nigricornis

C. micropterus

P. obscurus

Degradation stage

1

1

1

1

1

1

3

2

1

1

1

1

2

3

3

1

1

1

2

1

1

4

1

1

1

2

2

2

5

1

1

2

1

1

2

6

1

1

2

1

2

2

7

1

1

2

2

1

2

8

1

1

2

2

2

2

9

1

2

1

1

1

4

10

1

2

1

1

2

4

11

1

2

1

2

1

4

12

1

2

1

2

2

4

13

1

2

2

1

1

4

14

1

2

2

1

2

4

15

1

2

2

2

1

4

16

1

2

2

2

2

4

17

2

1

1

1

1

3

18

2

1

1

1

2

3

19

2

1

1

2

1

3

20

2

1

1

2

2

3

21

2

1

2

1

1

3

22

2

1

2

1

2

3

23

2

1

2

2

1

3

24

2

1

2

2

2

3

25

2

2

1

1

1

3

26

2

2

1

1

2

3

27

2

2

1

2

1

3

28

2

2

1

2

2

3

29

2

2

2

1

1

3

30

2

2

2

1

2

3

31

2

2

2

2

1

3

32

2

2

2

2

2

3

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