Journal of General Microbiology (1988), 134, 301 1-3018.
Printed in Great Britain
301 1
A Frequency Matrix for Probabilistic Identification of Some Bacilli
By F E R G U S G . P R I E S T * A N D B R I A N A L E X A N D E R
Department of Brewing and Biological Sciences, Heriot- Watt University, Chambers Street,
Edinburgh EHl IHX, UK
(Received 13 May 1988; revised 29 July 1988)
A matrix comprising frequencies for positive results for 44 Bacillus taxa for 30 characters has
been constructed. The 44 taxa include most of the common species and several clusters of
environmental isolates including those described as B.firmus--B. lentus intermediates. The tests,
which were chosen for their high diagnostic value, included some of the traditional tests used for
identification of bacilli supplemented with a range of sugar fermentations and other
characterization tests. The matrix was evaluated by identifying hypothetical median organisms,
cluster representatives and a panel of 23 reference strains. All reference strains achieved Willcox
probabilities above 0.995. Fifty-eight environmental isolates were also subjected to the 30 tests
and identification was attempted. Forty-one strains (70 %) achieved a Willcox probability
>0.95, which was considered an acceptable identification, and were assigned to 12 taxa. If the
SE of taxonomic distance was also considered in the identification score (an acceptable value
being <7.0), the number of acceptable identifications was reduced to 34 (59%). It was
encouraging that bacteria from garden soils identified to the common species such as B. subtilis,
B. cereus and B. licheniformis whereas some of the bacteria from an estuarine habitat were
identified as species such as B. Jirmus which are normally identified with that habitat.
INTRODUCTION
The aerobic endospore-forming bacteria of the genus Bacillus are important as pathogens of
man and animals and have considerable value as sources of industrial enzymes, insect toxins for
biological control and antibiotics (Debabov, 1982; Priest, 1988). They are distributed widely in
the environment and are physiologically diverse with alkaliphilic, acidophilic, halophilic,
thermophilic and psychrophilic species described in the literature (Claus & Berkeley, 1986). It is
therefore surprising that little is known of their ecology (Slepecky & Leadbetter, 1983;
Goodfellow & Dickinson, 1985); largely due to the difficulty of identifying environmental
isolates.
The traditional identification schemes rely on the use of spore morphology to assign a Bacillus
isolate to one of three groups based on spore shape and relative size in the sporangium.
Physiological tests are then used in dichotomous keys or polythetic tables to identify the
organism to the species level (Gordon et al., 1973; Hobbs & Cross, 1983). This approach has
several drawbacks; in particular it is often difficult to decide spore morphology unequivocally
and the monothetic nature of the keys leads to mis-identification. Moreover, the number of
Bacillus species has increased dramatically over recent years and the traditional identification
schemes cannot cope with the greater diversity of types.
In an attempt to improve identification of bacilli, Logan & Berkeley (1984) adopted the API
5OCHB trays. A comprehensive database was established using these miniaturized kits
supplemented with some traditional characters and a computerized identification scheme was
developed (Bryant et al., 1985). However, the system is expensive for routine use.
Abbreviation : HMOs, hypothetical median organisms.
0001-4895 0 1988 SGM
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F . G . PRIEST A N D B. ALEXANDER
Frequency matrices contain results in the form of percentage positive reactions for the most
diagnostic characters of the taxa in question. This information can be used for probabilistic
identification of unknown strains (Willcox et al., 1980). This approach has been very successful
for various Gram-negative bacteria (Holmes et al., 1986a, b ; Dawson & Sneath, 1985) and has
been increasingly used for Gram-positive organisms such as slow-growing mycobacteria
(Wayne et al., 1980), Streptomyces (Williams et al., 1983), Streptoverticilliurn (Williams et al.,
1985) and Micrococcus species (Feltham & Sneath, 1982). In view of the need for a reliable, costeffective and simple scheme for the identification of bacilli, we have prepared and tested a
frequency matrix derived from a recent numerical classification of the genus (Priest et al., 1988).
METHODS
Organisms used. Reference strains of Bacillus (Table 2) were obtained from the German Collection of Micro-
organisms, Braunschweig, FRG. Environmental isolates (Table 3) were obtained from samples of garden soil (EL
strains) and estuarine muds (T strains) by plating heat-treated (80 "C for 10 min) suspensions in sterile
physiological saline onto nutrient agar and incubating at 30 "C for 1 to 5 d. Colonies of various morphology were
selected, taking care to avoid picking more than one type from any individual sample. Isolates were stored at
- 20 "C in 20% (v/v) glycerol.
Selection of taxa and tests. The clusters were based on those described by Priest et al. (1988). Forty-four of the 49
clusters were included. The test methods have been described in detail (Priest et al., 1988).
Construction and theoretical evaluation of the matrix. To assist the selection of the most diagnostic tests for the
matrix, the CHARSEP program (Sneath, 19796)was used initially. This calculates five separation indices for each
test (see Williams et al., 1983). The DIACHAR program (Sneath, 1980a) was used to determine the most
characteristic features of clusters. Having made an initial choice of tests, the OVERMAT program (Sneath,
1980c) was used to calculate overlap between taxa in the matrix and the matrix was further tested by calculation
and subsequent identification of hypothetical median organisms using MOSTTYP (Sneath, 19806).
Determination of identijcation scores. Strains were identified from the matrix using the MATIDEN program
(Sneath, 1979~)which calculates five identification indices of which we routinely used Willcox probabilities
(Willcox et al., 1973) and standard error (SE) of taxonomic distance (Sneath, 1978). Unless otherwise indicated, all
test results were determined in this study.
RESULTS
Selection of characters
When the database, comprising result frequencies for 118 tests for 49 Bacillus clusters (see
Priest et al,, 1988) was examined using the CHARSEP program, 70 tests conformed to the
criteria of CSP index >50% and VSP index >25% as suggested for acceptable diagnostic
characters by Sneath (19793). The DIACHAR program, which ranks the most diagnostic
characters for taxa, was used to indicate the most characteristic features for all 49 taxa recovered
in the original classification. Visual comparison of the CHARSEP and DIACHAR outputs was
sufficient to enable a choice of 55 from the 70 'acceptable' characters, to produce a 49 (taxa) x
55 (tests) matrix. Since carrying out 55 tests is expensive and time-consuming, a second smaller
matrix comprising a subset of thirty characters (Table 1) was devised. This comprised 25 tests
which had VSP scores of 34 to 87% (mean 65%) and which required some form of inoculation
and five cellular morphology features that were included, not because of their diagnostic value
(VSP scores 2 to 83%),but because this information will probably have been used to allocate the
unknown organism to the genus Bacillus. The output from the DIACHAR program for this
matrix indicated sums of diagnostic scores for taxa ranging from 12-34 to 18.46.
Theoretical evaluation of the matrices
Cluster overlap in the two matrices was estimated using OVERMAT. In the 49 x 55 matrix at
the selected critical overlap level (V,) of 5 % there was no significant overlap between any pair of
taxa. In four cases, standard deviations (SDS) of taxa were greater than 0.3, indicative of
heterogeneity. These were unidentified clusters (taxa 10 and 17), B. psychrosaccharolyticus
(taxon 12) and B. macquariensis (taxon 45) which contained three, two, two and two members
respectively and had SDS of 0.32, 0-39, 0.36 and 0.45.
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Identification of bacilli
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When the 49 x 30 matrix was evaluated with OVERMAT, several pairs of taxa displayed
significant overlap ; these were almost exclusively restricted to the taxa with unacceptable SDS
noted above. These four taxa again showed high SDS as did B . subtilis var. niger (taxon 16, three
members, SD = 0.315) and the five taxa were deleted from the matrix until more strains and
better diagnostic features become available. Taxon 27 also had a high SD (six members, SD =
0.316) but was retained because it represented a major taxon in the original classification. In the
resultant 44 x 30 matrix (Table 1), significant overlap was calculated between two pairs of taxa;
B. licheniformiswith taxon 21 (V, = 2.9%) and taxon 42 (B.fusiformis) with B. sphaericus ( Vg =
2.6%). It was considered that this would be acceptable for general usage.
The MOSTTYP program calculates hypothetical median organisms (HMOs) for each taxon
in an identification matrix and then attempts to identify them. The results from this analysis
were satisfactory with the larger matrix obtaining Willcox probabilities of 0-999or 1.0 coupled
with low SES of taxonomic distance for all HMOs. The smaller matrix did not perform so well,
but the Willcox probability was below 0.999 only for B . amyloliquefaciens(0.9987) and the HMO
of taxon 27 (0.9989). The range for SE of taxonomic distance for this matrix was - 1.0 to - 6.9.
The smaller matrix was therefore considered satisfactory for most purposes and we now use it
routinely for identification of bacilli.
The final evaluation of the 44 x 30 matrix involved identifying representative organisms
using the data that had been generated in the numerical classification study and on which the
identification matrix was based. Most strains identified with a high Willcox probability
( > 0.999) and low SE of taxonomic distance ( < 3.5). Strains representing B. azotoformans, 8.
brevis, B. laterosporus, B. subtilis and taxon 27 achieved Willcox probabilities of 0.996 to 0.998.
Equally importantly, with the exception of ‘ B . subtilis var. niger’ strain S225 which was
identified as B. lichenformis, single member clusters from the numerical classification which
had not been included in the matrix failed to identify. Finally, some strains were examined with
and without spore morphology data. The omission of these data had virtually no effect on the
identification scores. For example, B. arnyloliquefaciens, B. sphaericus and B. subtilis retained
scores of 0-999; the largest reduction, from 0.999 to 0.997 was for B. lichenformis.
Practical evaluation of the selected matrix
We examined 22 reference strains including type and neotype cultures where possible, for the
30 tests. All these reference strains identified to their taxon with high Willcox probabilities and
low SE of taxonomic distance (Table 2). Phenotypically, B . cereus, B . mycoides and B .
thuringiensis are indistinguishable (Priest et al., 1988). Therefore the matrix does not contain
separate entries for these bacteria and consequently B. mycoides and B. thuringiensis strains
identified to B. cereus.
Bacillus strains were isolated from garden soils (EL strains) and estuarine muds (T strains) (see
Methods). These strains were examined using the 30 tests listed in Table 1 and identified using
MATIDEN. Of the 58 strains, 25 scored a Willcox probability >0.99 and 16 achieved a score of
0.95 to 0.99. Three strains scored 0-90to 0.949 and 14 obtained low scores below 0.90. It therefore
seemed reasonable to accept an identification as a Willcox probability >0.95 and using this
criterion alone, 41 (70%) of the strains were identified.
If the SE of taxonomic distance is also considered in the identification, the results are not so
good. A low SE of taxonomic distance indicates that the organism lies close to the centroid of the
group and an acceptable score is below 3 (Sneath, 1979a). Only 11 strains achieved this.
However, if the requirement is relaxed such that a Willcox probability of > 0.95 coupled with a
SE of taxonomic distance of <7.0 is accepted as an identification, then the results are more
promising and 34 of the 58 strains (59%) were identified to 12 different taxa. Since many
identification systems use the Willcox criterion alone, we do not consider that we are being overlenient in setting these limits.
DISCUSSION
Traditional schemes for the identification of aerobic, spore-forming bacteria have suffered
the problems typically associated with monothetic systems, namely inability to proceed past a
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F . G . PRIEST A N D B . A L E X A N D E R
Table 1. A frequency matrix for the identification of bacilli
d
ss
C
4
Cluster number*
...
Cell morphology :
1. Length > 3 pm
2. Gram-positive
3. Spores oval
4. Spores central
5. Spores bulging
Degradation of :
6. Aesculin
7. Casein
8. Hippurate
9. Starch
10. Urea
Resistance to (pg ml-l):
11. Chloramphenicol(4)
12. Nalidixic acid (32)
13. Polymyxin (16)
14. Streptomycin (8)
Acid from :
15. Cellobiose
16. Fructose
17. Galactose
18. Lactose
19. Mannose
20. Raffinose
21. Salicin
22. Xylose
Utilization o f :
23. Citrate
24. Succinate
Miscellaneous:
25. Growth at 50°C
26. Growth in 10% NaCl
27. Anaerobic growth
28. Nitrate reduction
29. Oxidase reaction
30. Voges-Proskauer test
1
95
39
99
23
92
2
3
4
5
6
7
8
9 11 13 14 15 18 19 20 21 22 23 24
99 1 67 70 40 99 82 99
1 1 1 1 20 1 1 1
99 99 99 99 99 99 99 99
99 1 1 1 20 50 64 1
99 99 99 99 99 99 91 99
99 99 99
99 99 99
99 99 99
99 99 99
319999
98
99
99
99
1
67 1 1 1 1 1 1
99 99 99 99 90 90 99
99 95 99 99 95 99 50
99 99 99 99 95 99 50
89 1 1 1 1 1 99
99 99 99 99 99 60 99 60 99 99 99 99 99 99 99 1 99
83 1 1 99 99 33 99 60 99 99 99 99 99 99 99 99 99
99 50 1 1 1 33 2 67 11 27 1 99 1 1 9 1 1
99 99 99 99 99 99 86 1 99 99 99 1 99 99 99 99 50
1 1 1 1 1 1 2 1 1 1 1 1 13299829999
1 1 1 99 10 1 99 9 3 15 22 11 1 1 99 90 99
1 1 99 1 1 99 1 1 99 2 1 1 1 1 1 42 99
99 99 99 17 99 80 99 99 1 99 99 99 99 99 99 99 99
92 99 1 99 99 1 99 64 1 60 20 11 73 99 1 95 99
92
1
54
1
15
99
1
1
1
1
99
99
90
99
90
90
99
99
99
99
99
99
99
80
99
99
1 50 50 1
1 1 33 80
1
1
99
1
99
1
1
99
99
1
99
99
99
99
99
99
99
1
50 1
99 99
99 99
99 99
1 1 1
54
99
99
99
99
99
99
99
99
99
99
99
1 1 117
1 1 1 1
99 99 99 99
1 99 99 33
99 99 99 99
77 1 1 1
99
99
50
99
99
99
99
99
99
99
91
91
82
99
99
91
99
99
99
99
33
99
99
99
9
1
1
1
1
1
1
1
84 20 99 99 1 99 99 99 99
86 60 99 99 99 99 99 99 99
3 1 1 33 1 90 95 99 99
2 1 99 13 1 45 68 1 27
21 1 89 99 1 99 99 99 45
3 1 99 99 1 75 95 99 1
91 40 99 99 1 99 99 99 99
1 1 11 80 1 95 95 99 99
99
99
99
1
99
50
1
1
1
1
1
1 50
99
99
1
99
99
99
1
1 18 1 80 11 22 87 1 90 95 99 99 99 50
1 46 99 14 99 78 87 99 99 99 99 99 99 99
996050 133 1
1 1 1 9 1 40
99 99 99 99 99 99
99 20 1 99 99 97
99 1 99 1 99 69
1 1 1 99 1 91
1 8 9 8 7 16095 1
1 89 80 99 99 5 1
99 1 1 1 1 99 99
99 78 99 99 1 99 99
11 1 1 1 10 10 1
1 99 99 99 99 19 99
1 1 1
1 99 99
1 1 1
1 1 1
1 1 1
1 1 1
particular point in the key because of a missing character and mis-identification due to an
organism being aberrant in one or more features. Polythetic tables overcome these shortcomings
but, because of the size of the genus Bacillus and the paucity of good diagnostic phenotypic data,
they have their limitations when applied to this genus and are cumbersome. The database
provided here offers Baciffusidentifications using relatively few and inexpensive tests. The tests
were chosen with two criteria in mind. From the diagnostic viewpoint, they should conform to
the minimum VSP and CSP scores suggested by Sneath (1979b) and second, they should
represent the full range of biological attributes. Thus biochemical, physiological, morphological
and antibiotic resistance tests were included. Although the prevalence of plasmids in bacilli
might argue against the use of antibiotic resistance tests, resistance to antibiotics such as
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Table 1 (continued)
* Cluster designations are the same as those in Priest et al. (1988). Taxon 9 (previously B. circulans) has been
named B. amylolyticus (Nakamura, 1984). The other unnamed taxa comprise the following strains: taxon 4,
Bxirculans; taxon 18, B. subtilis; taxa 21 and 24 to 29, isolates from marine muds and salt marshes; taxon 33,
B.megaterium; taxon 41, B. breuis.
t B. cereus includes B. mycoides and B. thuringiensis.
$ B. badius includes ‘B.freudenreichii’.
5 For details of B. smithii see Nakamura et al. (1988).
chloramphenicol is not commonly plasmid-borne in Bacillus, (Gryczan, 1982). For example, in
bacilli chloramphenicol acetyltransferase and streptomycin resistance can be chromosomally
encoded (Williams et al., 1981 ; Yousten et al., 1985) and offer useful identification criteria for
B. pumilus and B. sphaericus respectively as well as other taxa. The morphological tests are
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F . G . P R I E S T AND B . A L E X A N D E R
Table 2. IdentiJicationscores for reference strains using the 44 taxon x 30 character matrix and
characters determined in this study
Strain
DSM no.*
Identity (cluster no.)
Willcox
probability
B. alvei
B. amyloliquefaciens
B. badius
B. brevis
B. cereus
B. circulans
B. coagulans
B. firmus
B. laterosporus
B . lentus
B. licheniformis
B. macerans
B. megaterium
B. mycoides
B. pantothenticus
B. polymyxa
B. pumilus
B. psychrophilus
B. sphaericus
B . stearothermophilus
B. subtilis
B. thuringiensis
7
29
23
30
31
11
1
12
25
9
13
24
32
2048
26
36
27
3
28
22
10
2046
B. alvei (1)
B. amyloliquefaciens (14)
B . badius (39)
B. brevis (37)
B . cereus (1 1)
B. circulans (6)
B. coagulans (47)
B. firmus (25)
B. laterosporus (13)
B. lentus (44)
B. licheniformis (20)
B. macerans ( 5 )
B. megaterium (22)
B. cereus (1 1)
B. pantothenticus (30)
B. polymyxa (8)
B. pumilus (19)
B. psychrophilus (40)
B. sphaericus (43)
B . stearothermophilus (48)
B. subtilis (15)
B. cereus (1 1)
0.999
1,000
0.999
1.000
0-999
0-995
0.999
0.999
0.997
0.999
0.999
0.999
1.000
0.999
1.000
0.999
1so00
0.998
0.999
0.999
0.999
0.999
* German Collection of
SE of taxonomic
-
distance
2-784
3.038
2.324
- 0.219
2.35 1
6-763
- 0.228
0.704
1.800
3.577
0.683
2.293
4.989
4.63 1
6.963
3.563
2.235
5.126
2.993
0.606
2-625
1.997
Micro-organisms.
Table 3, Summary of identijication scores for the environmental isolates
Identification
B. badius
‘B. carotarum’
B. cereus
B. licheniformis
B. megaterium
B. polymyxa
B. pumilus
B. sphaericus
B. fusiformis
B. subtilis
Taxon 27
Taxon 29
Totals
No. of
isolates
identified*
2
2
6
2
4
4
3
1
1
6
2
1
34
Willcox probability
>0-995
0.9900-994
0.9500.989
1
1
1
4
23
1
2
2
2
2
1
9
* An identificationcomprises a Willcox probability > 0.95 and SE of taxonomic distance <7.0. Twenty-four of
the 58 strains failed to reach these criteria.
supplementary since several did not achieve acceptable VSP and CSP levels and were not
essential for successful identification. They were included simply because when handling an
unknown Bacillus, these data are usually available from the initial examination of the strain. The
number of tests was chosen as the minimum consistent with acceptable overlap figures. Little
significant overlap was calculated using 5 % as the critical value which is similar to the successful
matrices for Streptomyces (Williams et al., 1983) and streptoverticillia (Williams et al., 1985).
Moreover, the MOSTTYP program indicated efficient functioning of the matrix despite the
relatively low number of tests.
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IdentiJicationof bacilli
3017
The identification rate for reference strains was acceptable indicating that reliable
reproducible tests were incorporated in the matrix. Identification of environmental isolates was
58%. This compares with 50% for field strains of ‘coryneform’bacteria (Hill et a f . , 1978), 47%
for slow-growingmycobacteria (Wayne et al., 1980) and 81.3% for Streptomyces (Williams etal.,
1983). Although the figure for successful identifications of bacilli was lower than that for the
streptomycetes, we adopted a more stringent Willcox probability than Williams et a f . (0.95
against 0.85). If Williams et al. (1983) had used > 0.995, the identification rate would have been
reduced to 42%. This point regarding an ‘acceptable identification score’ is important in
probabilistic identification since various levels of Willcox probability have been adopted in
different studies. Generally, higher levels (>0.999) can be adopted for well-characterized taxa
in which species are homogeneous such as the Enterobacteriaceae, but where species are more
diverse and show less uniformity of test results a lower level is appropriate. Thus >045 was
considered an acceptable identification for streptomycetes (Williams et al., 1983). We have
approached this problem by setting an intermediate Willcox probability level ( >0.95) and also a
definite, but somewhat relaxed score for SE of taxonomic distance ( <7.0). By ignoring the SE of
taxonomic distance a higher success rate could be obtained (70%) but this was probably
achieved at the expense of some mis-identifications. It is well-known that Willcox probabilities
can sometimes be misleadingly high for an unrelated taxon when the correct taxon for the
unknown is not represented in the matrix (Willcox et al., 1980). The SE of taxonomic distance
does not have this problem and so by combining the two criteria a more reliable identification
should be obtained.
It is difficult to assess the accuracy of the identifications since most of the environmental
isolates could not be identified using traditional schemes. However, it is encouraging that
‘common’ bacteria such as B. Zicheniformis, B. pumilus and B. cereus were isolated from garden
soils and halotolerant organisms related to B . firmus and B. badius, and including the various
B.firmus-B. lentus ‘intermediates’ originally isolated from salt marsh soils (Gordon et d.,
1977),
were recovered from the estuarine mud samples. This indicates that the system is providing
similar identifications to the traditional schemes and should be useful in industrial, medical and
ecological applications.
We are grateful to Dr Colin Moore for assistance with computing, Part of this work was supported by a grant
from Gesellschaft fur BiotechnologischeForschung for research of relevance to the German Collection of Microorganisms.
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