Quantification of Nonproteolytic Clostridium botulinum ... · inimally processed chilled foods, or partially processed chilled foods, are foods that have fresh-food-like character-istics

Quantification of Nonproteolytic Clostridium botulinum Spore Loadsin Food Materials

Gary C Barker Pradeep K Malakar June Plowman Michael W Peck

Institute of Food Research Norwich Research Park Colney Norwich United Kingdom

We have produced data and developed analysis to build representations for the concentration of spores of nonproteolytic Clos-tridium botulinum in materials that are used during the manufacture of minimally processed chilled foods in the United King-dom Food materials are categorized into homogenous groups which include meat fish shellfish cereals fresh plant materialdairy liquid dairy nonliquid mushroom and fungi and dried herbs and spices Models are constructed in a Bayesian frameworkand represent a combination of information from a literature survey of spore loads from positive-control experiments that es-tablish a detection limit and from dedicated microbiological tests for real food materials The detection of nonproteolytic C bot-ulinum employed an optimized protocol that combines selective enrichment culture with multiplex PCR and the majority oftests on food materials were negative Posterior beliefs about spore loads center on a concentration range of 1 to 10 spores kg1Posterior beliefs for larger spore loads were most significant for dried herbs and spices and were most sensitive to the detailedresults from control experiments Probability distributions for spore loads are represented in a convenient form that can be usedfor numerical analysis and risk assessments

Minimally processed chilled foods or partially processedchilled foods are foods that have fresh-food-like character-

istics and satisfy consumer demand for foods that are mildlyheated without added preservatives higher in nutritional valueand easy to prepare (1ndash3) These foods form an increasing part ofthe diet in many parts of Europe and in the United Kingdom thechilled food sector employs a substantial fraction of the food man-ufacturing workforce Estimates indicate that in the United King-dom in 2014 the value of the market for chilled prepared foodexceeded pound12 billion (httpwwwchilledfoodorgMEDIA)

Clostridium botulinum is a diverse species that comprises fourdistinct groups of bacteria all of which form botulinum neuro-toxin There are seven types of botulinum neurotoxin (A to G)and it is the most potent toxin known with as little as 30 to 100 ngof neurotoxin potentially being fatal (4ndash7) Proteolytic C botuli-num (group I) and nonproteolytic C botulinum (group II) areassociated with food-borne botulism Strains of proteolytic C bot-ulinum form neurotoxin of types A B andor F form very heat-resistant spores and have a minimum growth temperature of10degC to 12degC while strains of nonproteolytic C botulinum formneurotoxin of type B E or F form spores of moderate heat resis-tance and multiply and form neurotoxin at 30degC to 33degC in 5 to7 weeks but not at 25degC or below in 12 weeks (4ndash6 8ndash10) Non-proteolytic C botulinum has been identified as a hazard in mini-mally processed chilled foods Mild thermal processing conditionscannot guarantee complete inactivation of spores and typical re-frigeration conditions may permit spore germination populationgrowth and toxin production by nonproteolytic C botulinumThe consumption of even small amounts of preformed botulinumneurotoxin in food can cause severe illness and potentially deathThe safety of these foods relies on a combination of good-qualityraw materials mild heat treatment manufacturing hygiene chilledstorage and a restricted shelf life (1 2) The safety record formass-produced minimally processed chilled food is very strongbut there have been occasional incidents that have involved timeandor temperature abuse of the final product or home-prepared

foods (1 2 8 11 12) These sporadic incidents drive exceptionalvigilance

A crucial piece of information in quantifying the risk fromnonproteolytic C botulinum concerns the initial spore loads infood materials but detection of these spores is particularly chal-lenging Currently the optimized protocol developed by Peck etal (13) is considered a very sensitive enumeration method forspores of nonproteolytic C botulinum in food materials Withthis method 400 spores kg1 were observed in scallops How-ever loads typically are smaller and 1 spore kg1 could be con-sidered a significant contamination level for food materials (14)As a contribution to risk assessment an effective quantification ofspore loads for nonproteolytic C botulinum must embrace thelarge variations in concentration but importantly must also rep-resent uncertainties such as those associated with the experimen-tal detection limit (15)

For nonproteolytic C botulinum the origins of spore contam-ination in food materials are unclear Spores are ubiquitous in theenvironment but the steps and processes leading to food contam-ination have not been identified explicitly In addition the actualloads in food materials generally are very small and very difficult todetect so that observations failing to detect spores predominateTogether these factors ensure that the statistical properties ofnonproteolytic C botulinum spore loads in food materials vari-

Received 6 November 2015 Accepted 24 December 2015

Accepted manuscript posted online 4 January 2016

Citation Barker GC Malakar PK Plowman J Peck MW 2016 Quantification ofnonproteolytic Clostridium botulinum spore loads in food materials Appl EnvironMicrobiol 821675ndash1685 doi101128AEM03630-15

Editor D W Schaffner Rutgers The State University of New Jersey

Address correspondence to Michael W Peck Mikepeckifracuk

Supplemental material for this article may be found at httpdxdoiorg101128AEM03630-15

Copyright copy 2016 Barker et al This is an open-access article distributed under theterms of the Creative Commons Attribution 40 International license

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ability and uncertainty are not well established In many respectsa Bayesian approach using gathered evidence to build on broadprior beliefs is suited to address this problem Creacutepet et al (16)employed a Bayesian scheme to build a representation for thecontamination of fresh vegetables with Listeria monocytogenesbased on distinct observations describing both concentration andprevalence Gonzales-Barron et al (17) used a Bayesian frame-work to model belief concerning the contamination of sausages bySalmonella enterica serovar Typhimurium and Daelman et al(18) report a Bayesian model for Bacillus cereus spore contamina-tion of food materials that are used in the production of minimallyprocessed chilled foods Alternative but comparable approachesfor estimating probability distributions that represent bacterialcontamination in food based on maximum likelihood have beenreported by Busschaert et al (19) and by Pouillot et al (20) bothstudies concentrate on Listeria contamination

Here we develop a quantitative representation of beliefs con-cerning the concentration of nonproteolytic C botulinum sporesin a range of food materials that are used for manufacturing min-imally processed chilled foods in the United Kingdom Initialsteps correspond with a literature survey and the formation of aknowledge base of reported spore loads in foods In turn thisinformation is aggregated in a probabilistic representation ex-pressing the variability and uncertainty of spore loads in nine rep-resentative food categories Finally evidence from a large set ofcontrolled laboratory observations of real food materials is used toupdate beliefs about spore concentrations using a Bayesian ap-proach The posterior distribution of spore loads represents quan-titative beliefs and currently gives the best support for the assess-ment of risks

MATERIALS AND METHODSLiterature survey for information concerning spore loads in food ma-terials Information about C botulinum spore loads in food materials wasaccessed from a variety of sources including scientific journals bookstechnical reports and expert opinions A search in scientific databasessuch as the Thomson Reuters Web of Science and PubMed (based on keywords) as well as contributions from experts with personal documentcollections and from the Institute of Food Research botulinum databaseidentified more than 700 appropriate references (we thank B M Lundand T A Roberts for allowing access to their collections of papers on Cbotulinum) Foreign-language reports were included in the list when prac-tical The initial list was filtered by a microbiologist to recover 100sources that could contribute primary evidence on spore concentration

(ie not reviews or summarized data) These sources are included as acomma-separated variable file in the supplemental material

Most experimental investigations included enrichment in microbio-logical media followed by the mouse test or enzyme-linked immunosor-bent assay (ELISA) to detect botulinum neurotoxin or PCR to detect theneurotoxin gene In many cases the reported presence of type B or F toxindid not allow differentiation between proteolytic C botulinum and non-proteolytic C botulinum For those records either was assumed to bepresent

Primary data on the origin of materials the food type the experimen-tal methods the microbiology (including type information) and the re-sults were systematically extracted from these sources and entered into adatabase with approximately 30 fields The selected sources contributedapproximately 1200 records to the database Each record corresponds toa single test applied to a particular food material Expert microbiologistsscored each record on a scale of 1 to 5 according to the quality of themicrobiological method The details of the scoring system are presented inTable 1

For each data record that has a quality score above two ie 1089records an estimate of spore concentration and an associated standarderror were constructed by using a most-probable-number (MPN) calcu-lation (21) based on the reported number of tests the number of positivetests and the quantity of material tested (for records where all tests arenegative a single positive test result for the most sensitive test was addedto obtain a conservative MPN estimate eg see Carlin et al [22]) Notethat for food materials we use volume (V) and mass interchangeably Thedatabase represents an extensive source of information on spore loads fornonproteolytic C botulinum in food materials The database descriptionand the details of spore loads are included as comma-separated variablefiles in the supplemental material

Categorization of food materials Commercial minimally processedchilled foods are constructed from a wide variety of raw materials andingredients often from many different production systems and frommany different locations so that it is impractical to establish statisticalbeliefs concerning the nonproteolytic C botulinum spore loads for eachindividual food product However reports of active surveillance and ex-pressed opinions suggest that the aggregation of spore load informationusing a relatively small number of food groups or categories can success-fully represent beliefs about the contamination levels in primary foodmaterials

An expert group consisting of microbiologists modelers and special-ists involved in the manufacture of minimally processed chilled foodsprovided guidance on the organization of spore load information Theexperts suggested nine distinct aggregated groups of food materials tosupport a quantitative representation of nonproteolytic C botulinumspore load information meat (ME) fish (FI) shellfish (SH) cereals in-cluding pasta and rice (CE) fresh plant material including fresh herbs

TABLE 1 Scoring system for microbial methods used to prioritize records for the food materials C botulinum database

Score Description

1 Not adequately described2 Can be clearly identified as unlikely to recover nonproteolytic C botulinum spores eg where the heat treatment included temperatures of 80degC

the use of such a heat treatment to inactivate competing vegetative bacteria is valuable for isolation of proteolytic C botulinum spores but mayinactivate nonproteolytic C botulinum spores

3 Can recover most nonproteolytic C botulinum spores but is suboptimal eg incubation at 35ndash37degC weak anaerobically or trypsin was not usedin the mouse test optimum growth temp for nonproteolytic C botulinum is 25ndash30degC and that of proteolytic C botulinum is 37degC toxins ofnonproteolytic C botulinum may not exhibit maximum toxicity until they are activated by trypsin

4 Suitable for recovering nonproteolytic C botulinum spores but is not fully quantified eg the detection limit is not determined if samples arepositive an MPN technique should be included to estimate the numbers present

5 Suitable for recovering and quantifying nonproteolytic C botulinum spores and includes controls to calculate the detection limit for eachfood material parallel samples should be inoculated with spores from mixtures of nonproteolytic C botulinum strains and subjectedto the same procedure

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(PL) dairy liquid (DL) dairy nonliquid (DN) mushroom and fungi(MF) and dried herbs and spices (HS) The categorization matched theneeds of the manufacturers of chilled foods (in the United Kingdom) andalso took into account the distribution of available data across food cate-gories Thus although spore loads are believed to be high in honey (14)manufacturers of chilled thermally processed foods rarely include honeyas an ingredient so it is excluded from the categorization scheme Simi-larly information concerning spore loads in oils and fats is unavailable sothese materials are excluded from the assessment Two hundred sevenrecords from the database do not fit into the categorization scheme thatrepresents materials used in minimally processed chilled foods in theUnited Kingdom Carlin et al (22) used a similar aggregation of foods intheir survey of C botulinum in raw food materials used in minimallyprocessed chilled foods in France and Daelman et al (18) reported the useof five food groups to represent B cereus spore contamination in materialsused for the production of minimally processed chilled foods in Belgium

Variability and uncertainty for C botulinum spore loads in foodmaterials A representation for C botulinum spore contamination in foodmaterials begins with the spore concentration s (per kilogram) In foodsC botulinum spore loads are very small (typically an s of 1 kg1) so thatconcentration is well defined (ie it is a continuous variable) only inrelatively large volumes (ie V 1 kg) In this case a (batch) processingvolume typically 103 kg can be identified as the primary element forconsideration A batch is often identified uniquely for product tracingpurposes In this representation each batch is considered homogenous sothat the contamination of smaller volumes can be considered in terms ofindependent random samples but the contamination of batches from asingle food category is variable This contamination structure expressingwithin-batch variability as small compared to between-batch variability isconsistent with the aggregation property of the food material categoriza-tion scheme and with the stochastic nature of detection that generallyapplies to small numbers of spores of C botulinum In relation to thecontamination of food by pathogenic microorganisms the role of be-tween-batch and within-batch variability has been considered in detail byCommeau et al (23)

A practical representation is based on log-normal variability for thebatch concentration of C botulinum

where the parameters and are the means and the standard deviationsof ln(s) These parameters are related to s and s the mean and stan-

dard deviation of s [ie s e22 and ss e21] The

variability of the spore concentration accounts for different loads in dis-tinct batches of materials The log-normal form of the variability corre-sponds to many multiplicative effects on contamination but in realisticsituations where the origin of contamination is simply unknown it is alsoa convenient method of expressing the variation of a numerical quantityover several orders of magnitude We choose to parameterize the variabil-ity of the spore concentration by the mean value (location) s (perkilogram) and by the coefficient of variation (spread) ss This pa-rameterization is particularly convenient for considering spore loads infood materials for two reasons first when the load is small the meanvalue of concentration is more easily interpreted than second the co-efficient of variation is directly related to the standard deviation of thelogarithm of the concentration and is independent of the actual value

In turn the parameters of the variability are considered to be uncer-tain ie each parameter has a single value but we do not have sufficientinformation to make a precise estimate We choose to represent priorbelief about the mean spore concentration with a BetaPert uncertaintydistribution

s BetaPertsmin smod smaxwhere for each food category smin smod and smax (per kilo-gram) are the minimum modal and maximum values for the mean con-

centration respectively The BetaPert distribution is a unimodal form (aconstrained beta distribution) that is traditionally used for representingnumeric values within a finite range but other unimodal distributionswould be equally valid Prior beliefs concerning the coefficient of variationof the spore concentration are represented by a uniform uncertainty dis-tribution

s Uniform s

where (ss)min and (ss)max are the limiting values In the ma-jority of situations the coefficient of variation for batch concentration islargely unquantified and the uniform distribution represents uninformedbeliefs other featureless distributions are equally valid A uniform distri-bution of the coefficient of variation emphasizes the larger values in thecorresponding distribution of

We assume that the parameter values for the uncertainty distributionof the mean spore load can be established from the database and in turnthe uncertainty distributions can be considered informative priors in aBayesian framework In practice the database records contain an insepa-rable mixture of variability and uncertainty Although there are manyways to evaluate the records we have used the following consistentscheme for estimating the parameters for the uncertainty distributionof the mean batch concentration (i) Records were extracted from thedatabase according to material category (ii) For each record an MPNmeasure and an associated standard error for the spore concentrationwere established (iii) For each material category the estimate forsmod was set as the uniformly weighted average of the MPN values(spores per kilogram) (iv) For each material category the estimate forsmax was set as the uniformly weighted average of the values for theupper 95 confidence limit for the MPN (spores per kilogram) (v)We fixed smin as a spore load of zero

Table 2 indicates parameter values for uncertainty distributions of themean spore concentration that have been extracted from the collecteddata set Each database record includes a number of distinct tests Forexample the 81 shellfish records include 3874 distinct tests and the 13mushroom and fungus records represent 1410 individual tests

For three material categories we have compared the beta prior withan alternative construction that uses the average of many log-normaldistributions each constructed from an individual database record(again using derived MPN values) The comparison indicates that theparameterization scheme provides a suitable representation of databaseinformation The informative beta prior consistently gives a smootherdistribution over a range similar to that of the composite prior Althoughthe parameterization scheme truncates the uncertainty distribution of the

TABLE 2 Prior belief concerning parameter values for uncertaintydistribution of mean batch concentrations of nonproteolytic Cbotulinum sporesa

Food category Nb

Valuec (kg1)

smod smax

Meat 73 78 459Fish 574 514 2688Shellfish 81 1459 5433Cereals 12 86 607Plants 91 246 1719Dairy liquid 9 75 547Dairy nonliquid 20 340 1255Mushroom and fungi 13 2287 6668Herbs and spices 9 278 1500a The values shown are based on data from the literatureb N is the number of database recordsc smod and smax are the modal and maximum values respectively for the meanconcentration

C botulinum Spore Loads in Food Materials

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mean value of the batch concentration at large values it is important toappreciate that by including log-normal variability all nonzero sporeconcentrations are assigned a finite prior probability

It is practical to assume prior beliefs about the coefficient of variationfor the spore concentration that are independent of the material categoryTo represent prior belief about variability we have used single values of(ss)min 05 and (ss)max 4 The maximum value for thecoefficient of variation corresponds to a 10 of 073 so that it is clear thatprior belief for the spore concentration includes the possibility of log-normalvariability distributions for which 95 of the probability mass extends overthree orders of magnitude [10 ln(10) is the standard deviation oflog10(s)] The standard deviation 10 varies at a very low rate (logarithmi-cally) with the coefficient of variation so that prior beliefs are relatively insen-sitive to the choice for (ss)max Limpert et al (24) lists the coefficient ofvariation for numerous natural populations that occupy this range

Parameter uncertainty can be combined with log-normal popula-tion variability to give a representation for belief concerning the con-centration of nonproteolytic C botulinum in food materials A sche-matic illustration of the structure for the joint probability of theparameters and the variables is illustrated on the left side of Fig 1Marginal (prior) beliefs about the logarithm of the concentration ofnonproteolytic C botulinum spores in food materials are illustrated bybroken dark lines in Fig 2 The separation of uncertainty and variabil-ity imposed by this quantification scheme is not unique but it is ro-bust reproducible and flexible

Tests for spores of nonproteolytic C botulinum in real food mate-rials A total of 483 samples of food materials obtained from companiesinvolved in chilled food manufacturing in the United Kingdom weretested for the presence of nonproteolytic C botulinum spores The sam-ples were chosen to represent the nine different food categories high-lighted during a literature review concerning the natural occurrence ofspores in food and where possible reflected the significance of each cat-egory for United Kingdom chilled food manufacturing Additionally thesamples were selected to be as diverse as possible eg reflecting differentsources seasons and species For example the 54 samples of fish testedincluded salmon (18 samples) haddock (15) cod (12) hake (3) coley (3)and monkfish (3) Similarly the 50 meat samples included chicken (21samples) beef (16) lamb (5) pork (5) and turkey (3) while the 70 shell-fish samples included prawns (48 samples) mussels (10) crab meat (9)

and lobster (3) Samples that had been treated in any way that mightreduce the spore load were excluded from testing

An optimized protocol that combines selective enrichment culturewith multiplex PCR was used to test the food materials for the presence ofnonproteolytic C botulinum (13) Detection of proteolytic C botulinumusing this protocol is unlikely as its detection limit is reported as 107

spores kg1 (13) Additionally type B E and F strains each form a uniquePCR band and the type B4 and F6 neurotoxin genes exclusively presentin nonproteolytic C botulinum types B and F (8 9) can be identifiedthrough sequencing The PCR test was based on a multiplex PCR methodfor simultaneous detection of type A B E and F botulinum neurotoxingenes initially developed by Lindstroumlm et al (25) and later modified (13)New primers (forward 5=-CGGCTTCATTAGAGAACGGATGTCGTGCCAGCTGCATTAA-3= reverse 5=-TAACTCCCCTAGCCCCGTATGCCGGATCAAGAGCTACCAAC-3=) were included for the internal amplifi-cation control to give an 800-bp product Each food material sample was100 to 200 g except for dried porcini mushrooms (which absorbed waterto reach 200 g wet weight) and dried herbs and spices (for which thesample size was reduced to 50 g) For samples that appeared positive in thePCR test the toxin gene PCR product was purified and then sequencedThe gene sequence was confirmed as that of the C botulinum neurotoxingene through a BLAST search of all available sequence data

There is evidence that many herbs and spices possess antimicrobialactivity (26 27) Since there were concerns that herbs and spices couldinhibit spore detection the procedure for preparing these samples beforeadding the enrichment medium was modified The method used wasbased on that described by Bianco et al (28) for determining the preva-lence of C botulinum in fresh and dried chamomile In this case 50-gsamples of herbs and spices were stirred in 200 ml saline solution for 30 to60 min to aid the separation of any spores present The suspensions thenwere filtered through sterile cotton gauze and the filtrates were centri-fuged (12000 g for 15 min) to concentrate any spores in the samplesAfter discarding the supernatants pellets were resuspended in 10 ml an-aerobic saline before adding the enrichment medium

The detection limit for spores of nonproteolytic C botulinum wasdetermined for each food material using a protocol essentially as de-scribed previously (13) For each food category 14 sample bottles wereprepared from composite foods (some foods used multiple series of 14bottles see Table 3) Bottles were inoculated with a mixture of type B

FIG 1 Network representation for a statistical model of spore concentration in food materials The labeled objects (nodes) represent uncertain quantities andarrows indicate dependency In the first panel s and s are the means and the standard deviations of the spore concentration s (kg1) In the second panelWXi and SXi are the size and the load of the ith sample and Xi is the outcome of the ith test (positive or negative) In the third panel S (number of spores) is thelimit of detection and Si and Si are the expectation and the actual load in the ith control experiment respectively The second and third panels extend toinclude the complete set of samples and controls

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(Eklund 2B and Kapchunka B2) type E (Beluga and CB-K-18E) and typeF (Eklund 202F and Craig 610) strains of nonproteolytic C botulinumwith target loads of 4 (six replicates) 10 (four replicates) 30 (three repli-cates) and 100 (one replicate) spores bottle1 The spores were producedusing a two-phase cooked meat medium and washed as described previ-ously (29) and nominal inoculum concentrations were determined foreach spiking procedure using plate counts (29)

RESULTSThe limit of detection for nonproteolytic C botulinum spores infood materials For many bacteria and particularly for C botuli-num it is essential to appreciate the significance of negative testresults in order to establish quantitative beliefs about spore loadsin raw materials A standard method for estimating the limit ofdetection in food microbiology is to observe the presence or ab-sence of bacteria or spores using a prescribed protocol in a seriesof test samples with a range of known bacterial loads We assumethat each test is independent and that a well-defined but uncertain

load S spores partitions the outcomes (ie the test indicates thepresence of spores only for loads S where S S) The limit ofdetection S can be estimated (using a maximum likelihoodmethod or a Bayesian approach) from a series of test results (m)i 1 which indicate ri the number of positives from Ni tests eachwith a nominal load Si In this approach the threshold fordetection is considered a number of spores rather than as a sporeconcentration For a range of volumes this assumption is consis-tent with the nature of the experimental protocol used to detectspores Based on a sample volume it is possible to transform thisdetection limit into a concentration value (or a range of values)and then interpret the detection of contamination in natural ma-terials Details of the maximum likelihood method for the deter-mination of the limit of detection are included in the appendixFigure 1 right illustrates schematically how the results of the pos-itive-control tests are combined in a representation of the jointprobability to facilitate a Bayesian estimate for the full uncertainty

FIG 2 Beliefs concerning the logarithm of the concentration for nonproteolytic C botulinum spores in nine categories of food materials (fish [FI] meat [ME]dairy liquids [DL] dairy nonliquids [DN] cereals [CE] plant materials [PL] shellfish [SH] mushroom and fungi [MF] and herbs and spices [HS]) Broken linesrepresent prior beliefs and full lines represent posterior beliefs Additional dotted lines indicate the posterior belief given perfect detection of spores and verticalarrows indicate an approximate 95 confidence interval for the maximum likelihood estimate of the limit of detection For shellfish the gray line indicatesposterior beliefs following a hypothetical positive result of an additional test For mushroom and fungi the gray line indicates posterior belief following ahypothetical case in which two positive test results are absent In the meat panel two gray lines indicate spore concentration in 8020 and 2080 mixtures of meatand plant material In the cereal panel the gray line indicates posterior belief for the spore loads when a conflict arising from a rare case in the evidence frompositive controls is removed For fish two gray lines indicate posterior beliefs for alternative forms of prior information first when the prior probability for thecoefficient of variation of the batch spore load is uniformly distributed in the range of 05 to 8 and second when the prior probability for the mean value of thebatch spore load is uniformly distributed in the range of 250 to 260 spores kg1

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distribution of S (a Bayesian inference uses a broad uninforma-tive prior distribution for S)

Results from positive controls in each of nine food categoriesand maximum likelihood estimates for the detection limit are in-dicated in Table 3 The results show that for many food materialsit is possible to detect just a few spores of C botulinum The max-imum likelihood analyses indicate that estimated detection limitsare typically in the range of 1 to 10 spores per test sample andthese values vary across food material categories The interpreta-tion of the estimated detection limit (which is a discrete load in aparticular volume) in terms of limiting concentration (which is acontinuous variable) is not always straightforward However ap-proximate 95 confidence intervals (CI) based on maximumlikelihood analyses are indicated in Fig 2 for each food categoryby two arrows These ranges indicate the potential influence ofnew information on beliefs concerning spore loads in food mate-rials

Evidence relating to nonproteolytic C botulinum sporeloads in food materials Targeted observations provide specificevidence relating to the actual spore loads in food materials andthis evidence can be used to update beliefs about uncertain sporeconcentrations Ten egg samples tested negative for nonproteo-lytic C botulinum but only 114 corresponding control samplestested positive A variety of approaches were used to extract DNAfrom these samples to try to eliminate possible inhibitory compo-nents Since a reasonable limit of detection could not be estab-lished eggs were not considered further From the remaining 473tests 471 samples were negative indicating spore concentrationsbelow a detection limit that is typically 60 spores kg1 (Tables 3and 4) Two samples of mushrooms (both dried porcini mush-rooms) tested positive in the PCR test for the type B neurotoxingene Sequencing of the PCR product revealed a 100 match tothe type B4 neurotoxin gene of nonproteolytic C botulinumstrains IFR 05025 and CDC3875 and a 99 match to that ofstrains Eklund 17B and Eklund 2B (30 31) Note that strains IFR05025 and CDC3875 belonged to a class of European isolates

while other nonproteolytic C botulinum type B4 strains were fromNorth America (30)

The two samples giving a positive PCR result for C botulinumtoxin genes were examined further The concentration of spores ofnonproteolytic C botulinum in dried porcini mushrooms was de-termined using a three-tube MPN method that followed the opti-mized protocol described earlier again with appropriate positivecontrols to estimate the detection limit The samples were reducedto a fine homogenous grit using a sterile mechanical blender and40-g samples were tested at the first level together with a furtherfive 10-fold dilutions Three control series were prepared from aporcini mushroom sample that tested negative in the initial testsThey were inoculated at 105 103 and 102 spores kg1 with themixed spore suspension used in the positive-control experimentsBoth test samples were negative in all MPN tubes which equatedto a spore concentration of less than 65 spores kg1 (95 CI 11to 548) Therefore the concentration of spores in these two sam-ples is within the likely range of 60 to 65 spores kg1 Attempts

TABLE 3 Results from positive-control tests measuring the presence of spores of nonproteolytic C botulinum in food materialsa

Food material Weight (g)

Value for positive control Detection limit

r1 r2 r3 r4 S s (kg1) 95 CI

Meat 200 6 4 3 1 1 5 5 10Fish 200 4 3 2 1 5 25 20 30Fish 100 6 4 3 1 1 10 10 20Shellfish 200 4 3 3 1 3 15 10 25Cereals 100 5 4 3 0 5 50 30 60Cereals 100 6 4 3 1 1 10 10 20Cereals 100 6 3 1 1 5 50 40 60Plant 200 4 1 0 1 9 45 35 50Plant 200 6 4 3 1 1 5 5 10Plant 100 2 4 2 1 6 60 40 80Dairy liquid 100 6 4 3 1 1 10 10 20Dairy liquid 100 5 4 2 1 3 30 20 50Dairy nonliquid 100 6 3 3 1 2 20 10 30Dairy nonliquid 100 6 3 3 1 2 20 10 30Mushroom and fungi 200 3 4 3 1 3 15 10 25Herbs and spices 50 5 3 3 1 3 60 20 80a The control samples have nominal populations Si 38 96 30 and 94 with test size (Ni) of 6 4 3 and 1 where i is 1 4 and ri is the number of positive observations Thetest size is weight and the maximum likelihood estimates for the limit of detection are S spores The limit of detection is converted to a concentration s kg1 (with a 95confidence interval) based on the sample size

TABLE 4 Laboratory tests for the presence of nonproteolytic Cbotulinum spores in food materials

Category Weight (g)

No of samples

Total Positive Negative

Meat 200 50 0 50Fish 200 54 0 54Shellfish 200 70 0 70Cereals 100 60 0 60Plant 200 60 0 60Dairy liquid 100 46 0 46Dairy nonliquid 100 37 0 37Mushroom and fungia 200 57 0 57Mushroom and fungib 50 3 2 1Herbs and spices 50 36 0 36a Fresh mushroomsb Dried porcini mushrooms

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were made to isolate nonproteolytic C botulinum from the origi-nal enrichment cultures by streaking onto plates of Trypticasepeptone glucose yeast extract (TPGY) agar containing 10 (volvol) egg yolk emulsion and culturing anaerobically at 30degC butthese were unsuccessful

Assuming that food samples are independent and that in eachsample the contamination is representative of spore loads in aparticular food category the test results have a simple statisticalinterpretation The number of spores in a test sample is distrib-uted as Sx Poisson(sWX) where s is the batch concentration ofspores and WX is the sample size In turn the probability of apositive result in the ith test is expressed as

PXi veSXi S SXi Swhere is a unit step function This dependence relationship be-tween the test results and the limit of detection for spores is rep-resented schematically by the central portion of Fig 1

Posterior belief concerning nonproteolytic C botulinumspore concentrations in food materials Extensive evidence frommicrobiological tests on food samples can be used to update es-tablished prior beliefs concerning the spore concentration in foodmaterials The test results are dominant negative so that generallythey increase beliefs relating to small batch loads at the expense ofbeliefs about large loads however this change is conditioned byevidence indicating that the limit of detection for spores in foodmaterials is finite Consistent updated beliefs can be established asBayesian posterior distributions

The technical process of Bayesian inference (combining obser-vational evidence with prior beliefs) has become practical forcomplex information systems because of recent advances in algo-rithmic and computing power (eg see Kjaerulff and Madsen[32]) In complex scenarios it is convenient and instructive torepresent the relationships between distinct sources of informa-tion as a network structure (where nodes represent variables andarrows depict dependency) The network in Fig 1 is a structurethat highlights the relationship between information about sporeloads in food materials and information about microbial tests ap-plied to food samples In addition the network structure showshow information about a detection limit (for a test with a pre-scribed protocol) and the results from positive-control experi-ments are integrated into the estimation of uncertain spore loadsThe results of Bayesian inference for the uncertain batch load s ofspores of nonproteolytic C botulinum in nine distinct categoriesof food materials are illustrated by the full lines in Fig 2 Theresults were established using a Bayesian belief network imple-mentation of the statistical model (Hugin Expert AS AalborgDenmark) but could be obtained with alternative tools for Bayes-ian inference such as Markov chain Monte Carlo simulation TheBayesian network implementation uses a message-passing algo-rithm to implement the Bayes theorem consistently within thejoint probability of all uncertain variables

In general for each food category the posterior belief expressesthe impact of dominant-negative tests for nonproteolytic C bot-ulinum spores Repeated negative tests make large spore concen-trations increasingly unlikely so that posterior probability is con-centrated on loads that are smaller than the limit of detectionDistributions of posterior probability for spore loads are relativelyasymmetric (cf prior beliefs) reflecting the one-sided influenceof the limit of detection In this respect posterior beliefs concern-ing spore loads in materials from the meat category are slightly

anomalous because in this case all control tests gave a positiveresult so there is no evidence to indicate a lower bound for thelimit of detection For clarity dotted lines in Fig 2 show for eachfood category posterior beliefs that would correspond to similartest results obtained using a technique with perfect sensitivity (iea limit of detection of S 1) For assistance with computationssuch as those that might contribute to quantitative risk assess-ments for C botulinum hazards a precise representation of theposterior beliefs in terms of cubic B splines is included in thesupplemental material Some elements of the cumulative proba-bility representing posterior beliefs for spore concentration (iethe probability that the spore concentration exceeds a particularconcentration) are indicated in Table 5 For each food categorythe probability that the concentration exceeds s 1 spore kg1given the evidence is greater than 017 In contrast for all foodcategories except herbs and spices the probability that the sporeconcentration exceeds s 30 spores kg1 given the evidence isless than 61 109 A higher probability for herbs and spicesreflects the smaller sample sizes used for microbiological tests (thisconstraint is imposed by practical considerations) Appreciatingthis limitation is straightforward since for test sizes of 50 gnegative tests leading to reduced belief only relate to concentra-tions that exceed 20 spores kg1 (this limit would be lower fortests that use larger sample sizes) For herbs and spices a similarnumber of negative tests involving sample sizes of 200 g wouldgive a posterior belief (cumulative probability P) of P(s 30kg1 | Xi -ve i 1 36 WX 200 g HS) 24 1013which is in line with the other materials (Xi -ve indicates anegative result for the ith test)

Posterior probabilities for the logarithm of the concentrationof nonproteolytic C botulinum spores in food materials representa consistent combination of prior beliefs with gathered evidenceThe top right portion of Fig 2 (shellfish) illustrates the typicalsensitivity of the established posterior belief with respect to evi-dence The gray line is a posterior distribution which follows fromthe addition of evidence from a further hypothetical microbiolog-ical test (with test size of 200 g) that gives a positive result The(hypothetical) positive result reduces beliefs relating to very lowloads and increases belief for spore concentrations (s) of 15 kg1

(which is the concentration that corresponds to a detection limitof S 3 spores) Within the belief network representation prob-abilities can be combined so that this hypothetical evidence hasthe probability P(X71 ve | Xi -ve i 1 70 WX 200 gSH) 5 103

TABLE 5 Elements of the cumulative posterior probability for batchspore concentration in food materialsa

CategoryP(s 1 kg1

| X)P(s 10 kg1

| X)P(s 30 kg1

Meat 017 21 107 38 1020

Fish 085 21 102 19 109

Shellfish 079 85 104 21 1013

Cereals 072 14 102 61 109

Plant 082 11 102 53 1015

Dairy liquid 051 92 104 26 1010

Dairy nonliquid 065 16 103 98 1010

Mushroom and fungi 087 33 104 83 1014

Herbs and spices 084 15 101 37 103

a [X] indicates a complex combination of evidence from systematic surveillance andfrom positive controls

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In Fig 2 the irregular posterior distribution for spore loads inmushroom and fungi includes additional complexity because inthis case microbiological tests were performed for samples of dif-ferent sizes Since for the defined test the limit of detection corre-sponds to a discrete number of spores the evidence from sampleswith sizes of 200 g and 50 g has an impact on different parts of theposterior distribution of spore concentration (ie tests that uselarger sample sizes can provide evidence that relates to lower sporeconcentrations) The consistency of Bayesian updating is unaf-fected by multiple test sizes and the complex posterior distribu-tion for mushroom and fungi reflects a differential influence ofevidence from different sample sizes It also is important to appre-ciate that for the statistical model that represents beliefs aboutspore loads illustrated in Fig 1 positive test results can contributeto the development of posterior beliefs about the limit of detection(ie positive tests on small test sizes increase beliefs for a smalldetection limit) In the portion of Fig 2 that corresponds to mush-room and fungi a full gray line represents hypothetical posteriorbeliefs concerning spore loads in mushroom and fungi in the ab-sence of any positive test results For mushroom and fungi asexpected beliefs concerning small spore loads are reduced by twopositive test results but at the same time a small number of posi-tive tests causes a small decrease in belief concerning spore loadsthat are in the tail of the observed limit of detection This coun-terintuitive effect corresponds to increased beliefs about lowervalues for the limit of detection following observations of positivetest results for small test sizes (this shift in the limit of detection isnot indicated by the arrows in Fig 2 which are based on a maxi-mum likelihood analysis of the control experiments)

DISCUSSION

Posterior beliefs concerning concentrations of C botulinumspores in food materials indicate typical loads that are smaller thanmany reported in the scientific literature This shift reflects newevidence from significant numbers of negative results followingmicrobiological tests on food samples combined with detailed ev-idence concerning the limit of detection Current beliefs cannotrule out undetected spore loads with concentrations smaller than10 spores kg1 but they provide confidence concerning thesmall probability for very heavily contaminated food materials

Posterior beliefs concerning C botulinum spore concentra-tions in food materials may contribute to decision-making in re-lation to food safety Decision-making under uncertainty is acomplex process and in most cases posterior beliefs about loadsare combined with other information in developing safety out-comes However the posterior probabilities and their numericalrepresentation established above can lead directly to severalquantifications with immediate interpretations

For example the probability that a particular volume of mate-rial V contains spore numbers S beyond a particular thresholdS0 is given by

pS S0V food material 0

13 S S01

PoissonSsVpsds

where p(s) is the probability density for spore concentration infood material For dairy nonliquids the probability of exceeding aload of 10 spores in 100 g of material is p(S 10| 100 g DN) 3 1010 This calculation can easily be extended to mixtures offood materials (see the appendix) Based on the numerical repre-sentation in the supplemental material the uncertainty distribu-

tion for spore loads in binary mixtures of food materials can beestablished by simple quadrature (see the appendix) In the por-tion of Fig 2 corresponding to meat two full gray lines representbeliefs concerning spore density for nonproteolytic C botulinumin simple 8020 and 2080 mixtures of meat and plant materials

For each food material the development of belief concerningspore concentration involves the assessment of complex multi-component evidence (ie results from many controls and tests)Belief network structures include the facility to measure the inter-nal consistency of complex evidence and make it possible to iden-tify and trace any potential conflicts A conflict measure is given as

log2i1n pip

where p(ε) is the joint probability of the evidence ε εi i 1 nthat is composed from n components εi which have individualprobabilities p(εi) (32) When pieces of evidence are positivelycorrelated ie not in conflict we expect the probability of jointevidence to exceed the product of the probabilities for the individ-ual pieces (ie one piece of evidence makes another element inthe evidence set more likely) so that the logarithm is negativeAlternatively in conflict situations we expect 13(ε) to be positiveFor seven of the nine food material categories the conflict measureis negative indicating no significant conflicts in the evidence setsused to develop posterior beliefs about spore loads The positivetest results for mushroom and fungi are not in conflict with therest of the relevant evidence However for cereals and for plantmaterials the conflict measurements are positive ie 42 and 26respectively Within a belief network structure it is possible toexamine the origins of conflicts by looking at components of themeasure at different nodes of the junction tree (a structure that iscomplementary to the network itself and facilitates rapid compu-tations concerning elements of joint probability)

For cereals a single piece of evidence is responsible for themajority of the measured conflict Conflict is associated with asingle anomalous (negative) control result at high nominal sporeloads (Table 3) Further searching within the belief networkstructure it is possible to ascertain that the conflict would be ex-plained (and the total conflict measure would become negative) ifthe actual spore load in the control experiment was less than 7spores (Fig 1 right indicates the position of the actual spore loadin control experiments) In this case the expected load for thecontrol experiment was 100 spores and the actual load is Poissondistributed so the explanation involves a rare case Nonethelessthis reasoning is able to explain the conflict The significance ofthis rare case is illustrated by a gray line in the cereal portion of Fig2 which indicates posterior belief for spore loads in the absence ofthe spurious control result

Similarly for plant materials conflict is associated with evidencefrom control experiments but in this case conflict is not dominantlyassociated with a single result (there are many partial conflicts) and itis not possible to develop a hypothesis that explains the conflict as theresult of a rare case For plant materials conflict suggests that themodel describing spore loads does not fully align with the evidenceand more specifically that this category of food materials is inhomo-geneous (ie the limit of detection for spores of nonproteolytic Cbotulinum has significant variation within this category) In prac-tice the complex evidence leads to considerable uncertainty in theposterior belief for the limit of detection which in turn ensures

Barker et al

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that negative tests are not as effective in reducing beliefs concern-ing intermediate spore loads

In this development of belief some prior distributions are con-sidered to be informative (ie they are part of the informationsupply) but it is important to appreciate that nonetheless theobserved evidence is dominant in the formation of posteriorprobability concerning spore loads In particular posterior beliefsconcerning spore loads in food materials are relatively insensitiveto the range used for the uncertainty distribution of the coefficientof variation of batch spore concentration In Fig 2 the portioncorresponding to fish includes a gray line that represents posteriorbeliefs based on an alternative prior distribution for the coefficientof variation of batch spore concentration with ss uni-form[058] Alternative forms for prior belief concerning thevariability of batch spore concentrations ie a uniform uncer-tainty for may change the shape of the posterior distribution forsmall loads but do not disturb the sharp decline of probabilitydensity in the vicinity of the limit of detection (ie there is a strongeffect from the observed evidence) It is important to appreciatethat at fixed s the mean value of the logarithm of the concen-tration decreases as the standard deviation increases Posteriorbeliefs concerning spore loads in food materials are more sensitiveto prior beliefs concerning the mean value of the batch concentra-tion of spores but again this effect is significant only at moderateand low concentrations Within a belief network structure it ispossible to calculate exact derivatives that reflect the variation ofan output probability with respect to any input probability calleda sensitivity value (33) As an example for fish the output prob-ability p(s 30 kg1 | FI X) depends on the input probabilityp(100 kg1 s 110 kg1) an element of the prior uncer-tainty distribution but the corresponding sensitivity value is verysmall 10 109 (X represents the full evidence used to de-velop a posterior belief about spore concentration in fish) In con-trast posterior (output) probabilities for lower values of sporeload p(s 10 kg1 | FI X) and p(s 1 kg1 | FI X) have

stronger sensitivity with sensitivity values of 59 103 and41 101 with respect to the input probability (note that theinput probability corresponds to a spore concentration largerthan the modal value of s for fish [Table 2]) In Fig 2 theportion corresponding to fish includes a gray line that representsposterior beliefs based on a prior distribution for the mean batchconcentration of spores with s uniform[250260] spores perkilogram positioned around the 95th percentile of the informativeprior This distribution supports the conclusions based on the mea-sured changes in sensitivity values obtained across the range of sporeconcentration values A consistent sensitivity assessment is obtainedby similar tests across all nine material categories

Most active surveillance operations such as observations ofspore loads in samples of food materials can be extended in manydifferent ways but invariably this incurs additional costs For astructured belief system it is practical to evaluate the potentialimpact of additional findings using a value-of-information ap-proach hence it may be possible to direct the use of new re-sources For the posterior distribution of spore load establishedfor each food material it is possible to evaluate an ldquoinformationentropyrdquo as the expectation of log(p(log(s)) The entropy repre-sents the disorder associated with the distribution of log(s) andquantifies the information deficit that exists for current beliefs(information entropy is widely used to quantify uncertainty inprobabilistic scenarios) In turn a decrease of entropy followingnew findings quantifies the value that can be attributed to newinformation and directs choices for prospective investigations(even though the results of new investigations remain uncertain)The change in the entropy of log(s) following a new (single) ob-servation for another variable is called mutual information or thevalue of information this quantity can be computed easily withina belief network structure (32) For our nine food materials theentropy of the posterior distribution of log(s) was in the range of18 to 24 and the entropy reduction (value of information) cor-responding to additional tests on food samples or additional con-

TABLE 6 Value of information calculated for new findings in relation to the posteriorprobability for the logarithm of the spore load in nine food materialsa

a New findings from tests of independent food samples or from control experiments Values represent mutualinformation and for each material the most valuable (dark shading) and second most valuable (pale shading)findings are highlighted

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trol experiments is indicated in Table 6 It is clear that for four ofthe food materials (meat fish shellfish and mushroom andfungi) additional control experiments involving expected loads ofs 4 are the most valuable source of new information For theother materials testing additional food samples (with a samplesize of 200 g) has the most value (note that for all food materialsadditional control tests with large expected numbers of sporeshave very little value ie there is a strong belief that the result isalready known) Unsurprisingly additional tests for spores in200-g samples of herbs and spices represent the most valuablesource of new information relating to C botulinum loads in foods(however these tests will require additional method develop-ment) In contrast for mushroom and fungi further controls us-ing small expected numbers of spores represent the most valuableway to extend the quantification

An appreciation of this model for nonproteolytic C botulinumspore loads in food materials should include in addition to theevaluation of numerical sensitivities a clear picture of underlyingassumptions that relate to the nature of the information supply Inparticular the development of belief concerning spore loads isbased on a strong assumption that the sources of evidence (iesamples of food materials) are independent and that these sourcesare representative of the model variables (ie food samples arerepresentative of the associated [homogeneous] food category)Crucially this development assumes that the concentrations ofspores in food materials behave in a regular fashion and can berepresented by smooth unimodal probability distributions It isimportant to appreciate that the nine food categories used in thisdevelopment are not exhaustive so this construction cannot beused to represent belief concerning common food materials suchas honey or egg

The posterior probability distributions for nonproteolytic Cbotulinum spore concentrations in foods provide a robust andflexible representation of accumulated information that is rele-vant for consideration of botulism hazards The Bayesian schemeused to develop beliefs attempts to minimize the influence ofmodels and to highlight the impact of gathered evidence Numer-ical representations facilitate the use of extensive informationabout spore loads in quantitative risk assessments and in decisionsupport processes and analysis of sensitivities supports ongoingdevelopments or translation toward other objectives

APPENDIXMaximum likelihood estimation of the limit of detection forspores of C botulinum in food materials The limit of detectionS can be estimated from a series of test results i 1 m whichindicate ri-positive results from Ni tests each with a nominal loadof Si

We assume that the actual loads S in the test materials arePoisson distributed with the expectation Si In a test withnominal load Si the probability that the actual load exceedsthe detection limit is

pS SSi S qi 1 S0

In turn the likelihood of the test is given as

Pri13Ni13 Si S i1

BinomialNi ri qiwhere each test at level i is considered a Bernoulli trial The loga-

rithm of the likelihood has m contributions and can be maximizedwith respect to the threshold value S

lnPri13Ni13 Si S Constant i1

rilnqi

Ni riln1 qiThe constant which depends only on the data and not the thresh-old is irrelevant for maximum likelihood determination Theanalysis implies a single test volume v and a correspondingthreshold load S but could be extended to heterogeneous tests

A confidence interval can be established from the likelihoodratio (difference in log likelihood around the maximum value)The ratio

2lnPri13Ni13 Si S

lnPri13Ni13 Si Sis assumed to be distributed as 132 with 1 df so that 132

defines a 100 (1 ) percent confidence intervalSpore populations in mixtures of food materials For two in-

dependent homogeneous materials with batch spore concentra-tions s1 and s2 (kg1) and volumes V1 and V2 (kg) the conditionalprobability for the logarithm of the density of a mixture is

plogslogs1 logs2 V1 V2

logs logV1s1 V2s2

where is a Dirac delta function and s s1 where V1(V1 V2) is a partial volume Marginalization leads to

plogs 13

s s1plogs1plogs2

log s s1

1 dlogs1Similarly the total number of spores S in a mixture is the sum ofthe contributory numbers S1 and S2 in volumes V1 and V2 Indi-vidually S1 and S2 are Poisson distributed with parameters s1V1

and s2V2 so the cumulative probability of the total number can becomputed as a sum

P(S1 S2 Ss1 s2 V1 V2 P(S1 Ss1V1

PS1 is1V1PS2 S is2V2where on the right all of the probabilities are Poisson To includeuncertainty from batch concentrations this expression has to beintegrated over both s1 and s2 with appropriate density but theform of this expression ensures that double integrals are not re-quired

ACKNOWLEDGMENTS

We are grateful to Helen Sisson Martin Cole Peter McClure KaarinGoodburn Roy Betts and John Stanford for their helpful advice and toSandra Stringer Clare Aldus Andrew Carter and Catherine Channon fortheir contribution to aspects of the practical work

FUNDING INFORMATIONThis work was supported by the Department of Environment Food andRural Affairs United Kingdom the Biotechnology and Biological Sci-ences Research Council United Kingdom the Chilled Food Associationand Unilever as part of an Advanced Food Manufacture LINK projectAdditionally GCB and MWP acknowledge support from the Biotech-

Barker et al

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nology and Biological Sciences Research Council as part of the BBSRCInstitute Strategic Programme on Gut Health and Food Safety BBJ0045291

REFERENCES1 Peck MW 2006 Clostridium botulinum and the safety of minimally

heated chilled foods an emerging issue J Appl Microb 101556 ndash570 httpdxdoiorg101111j1365-2672200602987x

2 Peck MW Goodburn KE Betts RP Stringer SC 2008 Assessment of thepotential for growth and toxin formation by non-proteolytic Clostridiumbotulinum in commercial chilled foods Trends Food Sci Technol 19207ndash216 httpdxdoiorg101016jtifs200712006

3 Peck MW Stringer SC 2005 The safety of pasteurised in-pack chilledmeat products with respect to the foodborne botulism hazard Meat Sci70461ndash 475 httpdxdoiorg101016jmeatsci200407019

4 Johnson EA 2007 Clostridium botulinum p 401ndash 421 In Doyle MP Beu-chat LR (ed) Food microbiology fundamentals and frontiers 3rd edASM Press Washington DC

5 Lindstroumlm M Fredriksson-Ahomaa M Korkeala H 2009 Molecularepidemiology of group I and group II Clostridium botulinum p 103ndash130In Bruggemann H Gottschalk G (ed) Clostridia molecular biology in thepost-genomic era Caister Academic Press Norfolk United Kingdom

6 Peck MW 2009 Biology and genomic analysis of Clostridium botulinumAdv Microb Physiol 55183ndash265 httpdxdoiorg101016S0065-2911(09)05503-9

7 Peck MW Stringer SC Carter AT 2011 Clostridium botulinum in thepost-genomic era Food Microbiol 28183ndash191 httpdxdoiorg101016jfm201003005

8 Carter AT Peck MW 2015 Genomes neurotoxins and biology of Clos-tridium botulinum group I and group II Res Microbiol 166303ndash317 httpdxdoiorg101016jresmic201410010

9 Hill KK Smith TJ 2013 Genetic diversity within Clostridium botulinumserotypes botulinum neurotoxin gene clusters and toxin subtypes CurrTop Microbiol Immunol 3641ndash20

10 Graham AF Mason DR Maxwell FJ Peck MW 1997 Effect of pH andNaCl on growth from spores of non-proteolytic Clostridium botulinum atchill temperatures Lett Appl Microbiol 2495ndash100 httpdxdoiorg101046j1472-765X199700348x

11 King LA Niskanen T Junnikkala M Moilanen M Lindstroumlm MKorkeala H Korhonen T Popoff M Mazuet C Callon H Pihier NPeloux F Ichai C Quintard H Dellamonica P Cua E Lasfargue MPierre F de Valk H 2009 Botulism and hot-smoked whitefish a familycluster of type E botulism in France September 2009 EuroSurveill 147httpwwweurosurveillanceorgViewArticleaspxArticleId19394

12 Stringer SC Webb MD Peck MW 2011 Lag time variability in individ-ual spores of Clostridium botulinum Food Microbiol 28228 ndash235 httpdxdoiorg101016jfm201003003

13 Peck MW Plowman J Aldus CF Wyatt GW Penaloza Izurieta WStringer SC Barker GC 2010 Development and application of a newmethod for specific and sensitive enumeration of spores of non-proteolytic Clostridium botulinum types B E and F in foods and foodmaterials Appl Environ Microbiol 766607ndash 6614 httpdxdoiorg101128AEM01007-10

14 Dodds KL 1992 Clostridium botulinum in foods p 53ndash 68 In HauschildAHW Dodds KL (ed) Clostridium botulinum ecology and control infoods Marcel Dekker New York NY

15 Malakar PK Barker GC Peck MW 2011 Quantitative risk assessmentfor hazards that arise from non-proteolytic Clostridium botulinum in min-imally processed chilled dairy-based foods Food Microbiol 28321ndash330httpdxdoiorg101016jfm201004004

16 Creacutepet A Albert I Dervin C Carlin F 2007 Estimation of microbialcontamination of food from prevalence and concentration data applica-tion to Listeria monocytogenes in fresh vegetables Appl Environ Microbiol73250 ndash258 httpdxdoiorg101128AEM00351-06

17 Gonzales-Barron U Redmond G Butler F 2010 Modelling prevalence

and counts from most probable number in a Bayesian Framework anapplication to Salmonella Typhimurium in fresh pork sausages J FoodProt 731416 ndash1422

18 Daelman J Membre J-M Jacxsens L Devlieghere F 2012 A Bayesianmodel for Bacillus cereus contamination in raw materials used for REPFEDproduction httpwwwbenelearn2012ugentbeproceedingsBeneLearn2012_Proceedingspdf Accessed June 2015

19 Busschaert P Geeraerd AH Uyttendaele M Van Impe JF 2010 Esti-mating distributions out of qualitative and (semi) quantitative microbio-logical contamination data for use in risk assessment Int J Food Microbiol138260 ndash269 httpdxdoiorg101016jijfoodmicro201001025

20 Pouillot R Hoelzer K Chen K Dennis S 2013 Estimating probabilitydistributions of bacterial concentrations in food based on data generatedusing the most probable number (MPN) method for use in risk assess-ment Food Control 29350 ndash357 httpdxdoiorg101016jfoodcont201205041

21 Halvorson HH Ziegler NR 1933 Application of statistics to problems inbacteriology I A means of determining populations by the dilutionmethod J Bacteriol 25101ndash121

22 Carlin F Broussolle V Perelle S Litman S Fach P 2004 Prevalence ofClostridium botulinum in food raw materials used in REPFEDs manufac-tured in France Int J Food Microbiol 91141ndash145 httpdxdoiorg101016S0168-1605(03)00371-4

23 Commeau N Cornu M Albert I Denis J-B Parent E 2012 HierarchicalBayesian models to assess between- and within-batch variability of patho-gen contamination in food Risk Anal 32395ndash 415 httpdxdoiorg101111j1539-6924201101699x

24 Limpert E Stahel WA Abbt M 2001 Log-normal distributions acrossthe sciences keys and clues Bioscience 51341ndash352 httpdxdoiorg1016410006-3568(2001)051[0341LNDATS]20CO2

25 Lindstroumlm M Keto R Markkula A Nevas M Hielm S Korkeala H2001 A multiplex PCR assay for detection and identification of Clostrid-ium botulinum types A B E and F in food and fecal material Appl Envi-ron Microbiol 675694 ndash5699 httpdxdoiorg101128AEM67125694-56992001

26 Ismaiel AA Pierson MD 1990 Effect of sodium nitrite and origanum oilon growth and toxin production of Clostridium botulinum in TYG brothand ground pork J Food Prot 11958 ndash960

27 Zaika LL 1987 Spices and herbs their antimicrobial activity and itsdetermination J Food Saf 997ndash118

28 Bianco MI Luacutequez C de Jong LIT Fernaacutendez RA 2008 Presence ofClostridium botulinum spores in Matricaria chamomilla (chamomile) andits relationship with infant botulism Int J Food Microbiol 121357ndash360httpdxdoiorg101016jijfoodmicro200711008

29 Stringer SC Webb MD Peck MW 2009 Contrasting effects of heat-treatment and incubation temperature on germination and outgrowth ofindividual spores of nonproteolytic Clostridium botulinum Appl EnvironMicrobiol 752712ndash2719 httpdxdoiorg101128AEM02572-08

30 Carter AT Austin JW Weedmark KA Corbett C Peck MW 2014Three classes of plasmid (47-63 kb) carry the type B neurotoxin genecluster of group II Clostridium botulinum Genome Biol Evol 62076 ndash2087 httpdxdoiorg101093gbeevu164

31 Stringer SC Carter AT Webb MD Wachnicka E Crossman LCSebaihia M Peck MW 2013 Genomic and physiological variabilitywithin group II (non-proteolytic) Clostridium botulinum BMC Genomics14333 httpdxdoiorg1011861471-2164-14-333

32 Kjaerulff UB Madsen AL 2008 Bayesian networks and influence dia-grams Springer New York NY

33 Coupeacute VMH van der Gaag LC 1998 Practicable sensitivity analysis ofbayesian belief networks p 81ndash 86 In Huskova M Lachout P Visek JA(ed) Proceedings of the Joint Session of the 6th Prague Symposium ofAsymptotic Statistics and the 13th Prague Conference on InformationTheory Statistical Decision Functions and Random Processes Union ofCzech Mathematicians and Physicists Prague Czech Republic

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MATERIALS AND METHODS

Literature survey for information concerning spore loads in food materials

Categorization of food materials

Variability and uncertainty for C botulinum spore loads in food materials

Tests for spores of nonproteolytic C botulinum in real food materials

RESULTS

The limit of detection for nonproteolytic C botulinum spores in food materials

Evidence relating to nonproteolytic C botulinum spore loads in food materials

Posterior belief concerning nonproteolytic C botulinum spore concentrations in food materials

DISCUSSION

APPENDIX

Maximum likelihood estimation of the limit of detection for spores of C botulinum in food materials

Spore populations in mixtures of food materials

ACKNOWLEDGMENTS

REFERENCES