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Fitting of colony diameter and ergosterol as indicators of food borne mould
growth to known growth models in solid medium
Sonia Marn, Dolors Cuevas, Antonio J. Ramos, Vicente Sanchis
PII: S0168-1605(07)00464-3
DOI: doi: 10.1016/j.ijfoodmicro.2007.08.030
Reference: FOOD 4118
To appear in: International Journal of Food Microbiology
Received date: 30 June 2006
Revised date: 3 July 2007
Accepted date: 10 August 2007
Please cite this article as: Marn, Sonia, Cuevas, Dolors, Ramos, Antonio J., Sanchis,Vicente, Fitting of colony diameter and ergosterol as indicators of food borne mouldgrowth to known growth models in solid medium, International Journal of Food Microbiol-ogy (2007), doi: 10.1016/j.ijfoodmicro.2007.08.030
This is a PDF file of an unedited manuscript that has been accepted for publication.As a service to our customers we are providing this early version of the manuscript.The manuscript will undergo copyediting, typesetting, and review of the resulting proofbefore it is published in its final form. Please note that during the production processerrors may be discovered which could affect the content, and all legal disclaimers thatapply to the journal pertain.
http://dx.doi.org/10.1016/j.ijfoodmicro.2007.08.030http://dx.doi.org/10.1016/j.ijfoodmicro.2007.08.030http://dx.doi.org/10.1016/j.ijfoodmicro.2007.08.030http://dx.doi.org/10.1016/j.ijfoodmicro.2007.08.0307/29/2019 Ergosterol and Colony Diameter
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FITTING OF COLONY DIAMETER AND ERGOSTEROL AS INDICATORS OF FOOD
BORNE MOULD GROWTH TO KNOWN GROWTH MODELS IN SOLID MEDIUM
Running title: Fitting mould growth to models
Sonia Marn*, Dolors Cuevas, Antonio J. Ramos and Vicente Sanchis
Food Technology Department, Lleida University, CeRTA-UTPV, Rovira Roure 191, 25198
Lleida, Spain
*Corresponding author. Mailing address: Food Technology Department, Lleida University,
CeRTA-UTPV, Rovira Roure 191, 25198 Lleida, Spain. Phone: 34 973702555. Fax: 34
973702596. E-mail: [email protected]
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ABSTRACT
Growth of a range of 14 common food spoilage fungal species was evaluated along
time as a function of both colony diameter and ergosterol content on malt extract agar.
Growth was assessed under different environmental conditions following a central composite
design. The suitability of using either linear, Gompertzs or Baranyis models for primary
modelling of the results was tested. Regarding colony diameters, using either linear or
asymptotic Baranyis function gave better estimations of growth rate and lag phase when no
asymptotic trend was observed. When a decrease in growth rate was observed with time,
standard Baranyis model was chosen, although the search for new mechanistic models
specific for moulds would probably improve the estimations. The use of Gompertz equation
led, in general, to overestimated parameters. Ergosterol showed good performance as a
fungal growth indicator for the whole range of species. Finally, significant correlation
coefficients were found between ergosterol and colony diameters, suggesting that both
parameters may be useful for primary modelling and thus for subsequent secondary
modelling.
Keywords: fungi, food spoilage, growth, modelling, sigmoidal
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INTRODUCTION
Predictive microbiology has traditionally dealt with prediction of food spoilage by bacteria.
The non-pathogenic nature of moulds together with the lack of good methods for assessing
their growth are the reasons why they have been neglected in predictive microbiology
researches. However, moulds are important causative agents of economical losses mainly
regarding cereals and their derivatives. In indoor environments fungal volatiles/mycotoxins
have been shown to provoke adverse health effects (Samson et al., 1994). In addition, the
increasing concern regarding the presence of mycotoxins in foods, and the difficulty of
eliminating them from the foodstuffs once produced, has highlighted the importance of
preventing growth of toxigenic fungal growth as the main alternative for preventing mycotoxin
contamination in foodstuffs.
Mould growth (expressed as increase in colony diameter) was first empirically
modelled against time using the model of Baranyi et al. (1993) originally developed for
bacterial growth. This model has been successfully used to fit growth of bacteria and yeast,
and filamentous fungi such as Penicilliumroqueforti(Valik et al., 1999) andAspergillus flavus
(Gibson et al., 1994). The modified version of the Gompertz model (Zwietering et al., 1990)
has been sometimes selected for empirically modelling mould growth on the basis of its
proven flexibility to different asymmetrical growth data (Char et al., 2005). In addition, the
maximum growth rate (m) estimated by a modelling step is equivalent to the slope of the
straight line observed on the plot. From these primary models some parameters are usually
estimated such as m and lag phase (), which are subsequently used for secondary
modelling.
Modelling of colony diameter may be useful for research purposes; however, it is not
a measurable parameter in routine food analysis. Ergosterol analysis, which accounts for the
total fungal population in food samples, may be an alternative, although its determination
may be tedious and lengthy. In previous kinetic studies with Penicillium expansum,
ergosterol determination showed lower repeatability and sensitivity than colony diameters
measurements (Marn et al., 2006).
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The objective of this study was to compare the commonly used growth models for
primary modelling in order to assess their usefulness for estimation of growth parameters.
Also the use of ergosterol, besides colony diameters, as mould growth indicator for primary
modelling was assessed. Secondary modelling was not studied in the present work.
MATERIALS AND METHODS
Fungal isolates
The strains belonged to 14 fungal species representing general common food contaminants
found in intermediate moisture foods:Alternaria alternata (Fr.) Keissl. CECT2662,
Aspergillus carbonarius (Bainier) Thom CECT2086,A. flavus Link CECT2687,A. ochraceus
K. Wilh. NRRL3174,A. parasiticus Speare CECT2688, Cladosporium cladosporioides
(Fresen.) G.A. de Vries CECT2110, Eurotium amstelodamiL. Mangin CECT2586, Fusarium
graminearum Schwabe CECT2150, F. verticillioides (Sacc.) Nirenberg 25N, Mucor
racemosus Fresen. CECT2253, Penicillium chrysogenum Thom CECT2802, P. expansum
Thom CECT2278, P. verrucosum Dierckx CECT2906, and Rhizopus oryzae Went & Prins.
Geerl. CECT2339 (CECT: Spanish Type Culture Collection).
Experimental design
Experimental runs were generated by a Central Composite Design (circumscribed, alpha=2)
by means of The Unscrambler version 7.6. The factors entered were aw (0.85-0.95),
temperature (15-30C), pH (5-7) and potassium sorbate concentration (0.5-1.5%), and the
program generated a model with a centre point which was tested seven times as well as 24
test samples which were prepared and carried out in a random sequence (Table 1). The
levels of the factors were chosen to simulate those of intermediate moisture foods kept at
room temperature, thus susceptible of fungal spoilage. Five different sets of inoculated Petri
plates were prepared which were assessed for fungal growth diameters periodically and
analysed for ergosterol content when colonies attained approximately 15, 30, 45, 60 and 75
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mm of diameter (31 experiments x 14 isolates x 5 sampling times = 2170 ergosterol assays).
Experiments lasted for no more than 6 months.
Media
Malt Extract Agar (MEA) was used as medium. The pH of the medium was adjusted to pH
levels of 4-7 by using McIlvaines buffer consisting of 0.1M citric acid and 0.2 M Na2HPO4,
while pH 8 was achieved by means of NaOH. Glycerol was added to the media in order to
prepare media at 0.95, 0.90, 0.85 and 0.80 aw levels. Experimental curves were built in order
to calculate the amount of buffer solutions and glycerol to be added to the media. For the
later purpose initial medium was prepared with different glycerol concentrations and final aw
measured in each case with an Aqualab (Decagon, Pullman, USA), subsequently g of
glycerol added were plotted against aw and a suitable calibration curve was fitted. Finally,
potassium sorbate was added at the required concentrations. All 31 media were prepared
separately, autoclaved and plated onto 9-cm Petri plates. Water activity values were checked
in the prepared plates, as well as pH (Crison micropH2000 pH meter, Crison, Barcelona,
Spain).
Inoculation and incubation
The strains were grown on Malt Extract Agar (MEA) for 14 days and suspensions (105CFU
ml-1) were prepared in 0.005% Tween 80 solutions. Petri plates were single point inoculated
(101-102 CFU) in the middle for each fungal suspension. Petri plates with the same water
activity level were enclosed in sealed polyethylene bags and placed in suitable incubators
following the experimental design.
Measurement of colony diameters
Periodically, daily or as required, Petri plates were observed and colony diameters recorded.
When colonies achieved approximately 15, 30, 45, 60 and 75 mm of diameter, one Petri
plate per experiment and strain (434 in total) was taken and analyzed for ergosterol content.
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Ergosterol analysis
Colonies (on agar) were cut in small squares and extraction carried out. A modification of the
method by Gourama and Bullerman (1995) was applied. Recovery rates were calculated and
found to be around 84% for the concentrations found in the study; limit of detection was of 1-
2 g per plate. Briefly, fungal colony was extracted with 40 ml (or 20 ml in case of tiny
colonies) of 10% KOH in methanol by magnetically stirring for 30 min. A 10-ml aliquot was
transferred to a screw cap tube and placed in a hot water bath (55-60 C) for 20 min. The
tubes were then allowed to cool to room temperature. Three milliliters of water and 2 ml of
hexane were added to the tubes, which were then agitated in a Vortex mixer for 1 min. After
separation of layers, the upper layer (hexane) was transferred to a 10-ml vial. Hexane
extraction was repeated twice using 2 ml each time. The extracts were combined and
evaporated to dryness under a stream of nitrogen. The dry extracts were dissolved in 2 ml of
methanol, and forced through 0.45 m acetate filters. The HPLC equipment consisted of a
Waters 515 isocratic pump (Waters Associated, Milford, MA), a Waters 717plus autoinjector,
a Waters Spherisorb ODS2 C18 column (4.6 x 250 mm). The Waters 2487 variable
wavelength UV detector was set at 282 nm. The mobile phase was methanol at 1 ml min
-1
.
Ergosterol standard was purchased from Sigma (St. Louis, Mo) for calibration line (R2=0.99).
Statistical analyses
From the 434 experiments, those carried out with Fusarium species, C. cladosporioides, A.
alternata andA. carbonarius led to no-growth after 180 days in more than 74% of the cases,
and erratic under most of the remaining conditions, thus the authors decided not to use them
in this study. From the remaining strains (279 experiments), 142 experimental data
corresponded to growth kinetics, 137 to no-growth after 180 days.
Root-square ergosterol content and colony diameters were plotted against time. For
each treatment, diameters were adjusted to the sigmoidal Baranyis function [1] (Baranyi et
al., 1993), and to the Gompertz model modified by Zwietering et al. (1990) [2] by using
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Statgraphics Plus 5.1; also the linear model was adjusted using Microsoft Excel 2000.
Additionally, a biphasic Baranyis function was used in which the logarithmic term where Dmax
appears was deleted in order to omit the upper asymptote, as suggested by Valik et al.
(1999) [3].
[1]
+=
)exp(D
1-A)*exp(1log-A*diametercolony
max
mm
where [ ])**exp()*exp()*exp(log*1
mmmmm
tt
tA ++=
t=time (d)
m= maximum growth rate (mm d-1)
= lag phase before visible growth (d)
Dmax= maximum diameter attained, in most of the cases, the diameter of the Petri dish
[2]
+= 1)(*
*expexp*diametercolony
max
max tD
eD m
[3] [ ]
++= )**exp()*exp()*exp(log*1*diametercolony m mmmm
m
tt
t
Maximum growth rates, lag phases and final diameter attained were estimated from
the sigmoidal models, while maximum growth rates and lag phases were estimated from the
linear and Baranyis biphasic ones. In the linear case, lag phase was estimated through the
intercept of the regression line with the X-axis.
RESULTS
Primary modelling of colony diameters: comparison of sigmoidal, linear and Baranyis
biphasic models
Firstly, modelling was carried out in colony diameter data. In general, data plots showed,
after a lag phase, a linear trend with time. Only treatments 4, 13, 19 and 31 (0.85 aw) and
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those at 0.90 aw and 22.5C led in some cases to asymptotic curves (Fig. 1, 2), due to the
difficulty of maintaining a constant aw for such long periods of time. Thus under normal
circumstances convergence of the sigmoidal models relied on the diameter of the Petri dish
as upper asymptote; this means that the use of these models has no biological support as
growth functions in this case as the upper asymptote is an external parameter. Easier
convergence was found when using modified Gompertz model, than with Baranyis one.
However, the former led to overestimations of the final diameter, although this point is not
important due to the poor relevance of this parameter for practical issues, as long as it does
not interfere in m and estimations. Regarding linear model, plotting of the results against
time and manual (and subjective) selection of the straight part of the line (avoiding lag
phase and asymptotic one, if any) was required. Finally, Baranyis biphasic model seemed to
be the best choice in most of the cases (no subjectivity involved). R2 obtained for the 31
treatments and 9 strains ranged from 94 to 100%, 87 to 99%, 94 to 100%, and 78 to 100%
for the Gompertz, Baranyi, biphasic Baranyi and linear models, respectively. However, it is
known that, depending on the distribution of the experimental points, good R2 do not
necessarily mean accurate estimation of parameters.
In general, higher growth rates and lag phases were obtained when using modified
Gompertz model than with the others, the confidence intervals (P
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biphasic model is the best alternative, while complete Baranyis model may be the best when
an asymptotic stage is achieved.
Fig 4 shows two examples of the variability of the observed data and their respective
adjusted functions for the 7 replicates of the centerpoint (0.90 aw, 22.5C, pH 6, 1%) adjusted
to biphasic Baranyis model. Coefficients of variation of the observed values along time were
high around the lag phase but they decreased to less than 18% after 13-15 days of
incubation.
Primary modelling of ergosterol content
Ergosterol content did not show an exponential trend versus time, but a potential one (Fig 5).
Thus log transformation of the data was less useful than root-square one, which led to both
homogenisation of variance and linearisation of the data versus time. Data were
subsequently adjusted to either Baranyis or Baranyis biphasic model, depending on each
set of data. In this case regression analyses were carried out with 6 observed values over
time, and this resulted in high error levels of the estimations when compared to diameter
models (Table 2 and 3). Fig 5 also shows two examples of the variability of the observed
data for the 7 replicates of the centerpoint adjusted to either standard or biphasic Baranyis
model.
Fig 6 shows the experimental points adjusted to either standard or biphasic Baranyis
model for 4 different treatments. Ergosterol accumulation along time followed a similar trend
to diameter increase for the different treatments.
Correlation between colony diameters and ergosterol content
Significant Pearson correlation coefficients were found between colony diameters and root-
square (ergosterol content) of colonies of each of the strains tested under the 31 treatments
tested ranging from 0.66 to 0.91. The rate root-square(ergosterol)/diameter was rather
constant (between 0.20-0.24 forAspergillus species, 0.18-0.21 forPenicillium species, 0.16
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forE. amstelodami, while R. oryzae and M. racemosus, with a few observations, showed
rates of 0.13 and 0.29, respectively) (Fig. 7).
DISCUSSION
One challenge when working with moulds is their explorative and exploitative nature for
colonising solid substrates (Robinson et al., 1993), thus using liquid media for modelling their
growth (as generally done for bacteria) is not realistic. In the literature, the most common
used method to assess mould growth in solid substrates is colony diameter measurement,
with some authors using CFU counts (Vindelov and Arneborg, 2002), although it has been
shown that this latter parameter is linked to sporulating abilities of the species tested and has
poor correlation to biomass weight (Marn et al., 2005). Although easily assessed, colony
diameter measurement is difficult to be applied to real food substrates. Alternatively,
ergosterol content has been used for mould contamination in cereals and other food products
(Gourama and Bullerman, 1995; Saxena et al., 2001). This parameter, which accounts for
total fungal biomass has been shown to be correlated to biomass dry weight for the same
strains tested in the present study; a ratio between 0.6 to 1.6 mg dry biomass per g
ergosterol was found depending on the species tested (Marn et al., 2005).
In this study the total pool of data obtained represent most of the situations one can
encounter when dealing with fungal growth kinetics (from optimum growth to no-growth,
through erratic growth under certain limiting conditions). The responses of the 9 strains to the
31 treatments assayed were observed to be either sigmoidal or just have a lag phase
followed by a linear one. In general mould colony diameters have been primary modelled in
the past by Baranyis, linear and modified Gompertz models, both linear and Baranyi
approaches being the most common, but no study has compared before the usefulness of
each of them. This study shows that under favourable growth conditions, the linear model
may be the best alternative, however if the experimental design includes suboptimal
conditions, the lag phase makes the linear model not convenient. On the other hand, both
Baranyi and Gompertz models have been taken from bacterial growth curves in which log
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(N/No) is plotted against time in the presence of limited nutrients; thus after an initial lag
phase, an exponential multiplication of bacterial cells is observed after which, and due to the
shortage of nutrients or the accumulation of toxic metabolites the growth rate becomes
constant and eventually decreases. In this study, and from our previous experience, when
plotting diameters (or radiuses) of a mould colony growing in an agar Petri plate against time,
a lag phase is observed, followed by a linear phase, but in most of the cases no decrease in
growth rate is observed before the edge of the Petri plate is reached. Under constant
conditions a fungal colony would then probably grow indefinitely, if the agar plate was
unlimited; thus, in the absence of the edge of the plate, the Baranyis biphasic model would
be probably the best one (or the linear one in the absence of lag phase). This hypothesis
contradicts the results obtained by Valik et al. (1999), who described forPenicillium
roquefortidiameter a growth curve typical of microbial growth with lag-phase, linear phase
and upper asymptote when using 17 cm Petri plates with asymptotic values between 2 and
12 cm, well before the edge was reached.
Equivalent estimated parameters (m, ) were found using the different models except
for Gompertz one which was shown to overestimate both of them. Sigmoidal models other
than the ones traditionally used may have better potential to describe fungal growth process.
Under many circumstances, primary modelling yields reliable information on the value of m,
but poor estimates are often obtained for the lag time (McKellar, 1997).
Ergosterol was primary modelled for a range of food borne moulds for the first time.
Mould colonies, while growing at a constant growth rate in diameter, yield by branching an
exponential amount of biomass and consequently, of ergosterol amount. Thus ergosterol
content over time should show a lag phase, followed by an exponential increase phase, and
if log transformed, the curve should show a lag phase followed by a linear increase. In our
case, when ergosterol results were log transformed, a final phase in which ergosterol did not
increase exponentially anymore or even stopped was observed, while a clear decrease in
diameter growth rate was not observed, suggesting that even the colony extended in area, a
decrease in the rate of ergosterol accumulation occurred. This supports the work by Koch
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(1975), who reported that moulds form mycelium whose weight, except at the early stage of
growth, does not increase exponentially. For this reason, the square-root transformation was
chosen in the present work for data transformation in order to homogenise variance of
ergosterol data.
A previous work on growing colonies ofP. expansum and relationship with ergosterol
accumulation showed that ergosterol determination leaded to increased differences among
replicates compared to diameter measurements (Marn et al., 2006). However, in this study,
variation within replicates observed for colony diameters and ergosterol content was similar,
suggesting that the latter could be a good alternative. Also primary modelling of both square-
root ergosterol and colony diameters led to similar R2 values.
Primary models are the first step for estimation of parameters such as m, or time
for a certain colony size to be observed. Time for visible growth can also be directly observed
with no need for primary modeling. Lag phase and time for visible growth should have similar
values, the latter being slightly higher, and the former being always estimated through a
regression process. Dantigny et al. (2002) stated that lag time coincided with the completion
of the germination process; say more than 99% of germination. Germination has also been
studied by mycologists, from the predictive point of view, because prevention of germination
invariably leads to prevention of growth. However studies are lengthy and tedious, thus
prediction of lag time for growth would substitute parameters such as lag phase for
germination, germination rate and time for 10 or 90% germination.
This work has shown that, among the commonly used models, all of them showing
similar goodness of fit, Baranyis model, either biphasic or not, depending on the observed
kinetics, may be the best alternative for an accurate estimation of m and . Both growth rate
and lag phase have been used in the past for secondary modelling; m being used for
secondary modelling in about 75% of the publications. m may be a useful parameters to
compare treatments, and also complements lag phase data. However, when dealing with
prediction and prevention of fungal growth in food products, two parameters could be
considered: i) the lapse of time to reach a visible colony which makes a product rejectable,
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and ii) the lapse of time to reach a colony size which might be conducive to mycotoxin
accumulation; as it is not possible to establish such a correlation, in case of mycotoxigenic
species any growth should be prevented. Thus in this context growth rate may be of poor
application, and other parameters such as lag phase, time for a 2-3 mm visible colony, etc,
may be of interest. Secondary modelling will be the next step in this research. Also it is of
great importance the validation of secondary models obtained in real food matrices.
ACKNOWLEDGEMENTS
This work was supported by the Spanish Government (CICYT, Comisin Interministerial de
Ciencia y Tecnologa, project AGL 2004-06413/ALI, and Ramon y Cajal program).
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Marn, S., Morales, H., Ramos, A.J. Sanchis, V., 2006. Evaluation of growth quantification
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Saxena, J., Munimbazi, C., Bullerman, L.B., 2001. Relationship of mould count ergosterol
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Valik, L., Baranyi, J., Grner, F., 1999. Predicting fungal growth: the effect of water activity
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FIGURE CAPTIONS
Figure 1. Run1 (0.90 aw, 22.5C, pH 6, 1% sorbate) and run14 (1.00 aw, 22.5C, pH 6, 1%
sorbate) colony diameters raw data and adjusted to (a) Baranyi, (b), Gompertz, and (c) linear
models forA. flavus (), A. ochraceus ({), P. expansum (), P. verrucosum (U), E.
amstelodami() and R. oryzae ().
Figure 2. Run3 (0.95 aw, 15C, pH 7, 0.5% sorbate) and run16 (0.95 aw, 30C, pH 7, 0.5%
sorbate) colony diameters raw data and adjusted (a) Baranyi, (b), Gompertz, and (c) linear
models forA. flavus (), A. ochraceus ({), P. expansum (), P. verrucosum (U), E.
amstelodami() and R. oryzae ().
Figure 3. Estimated m and through modified Gompertz (), Baranyis (z) and linear ()
models for 10 sets of raw data generated by (a) Baranyis biphasic function, (b) standard
Baranyis function and (c) modified Gompertz model (m=3; =10) with data points distributed
as a normal distribution with 1 variance. Error bars are the confidence intervals of the
estimated parameters (P
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sorbate) square-root ergosterol raw data and adjusted to Baranyis model forA. flavus (),
A. ochraceus ({), P. expansum (), P. verrucosum (U), E. amstelodami() and R. oryzae
().
Figure 7. Relationship between colony diameter and square-root ergosterol content for (a)A.
parasiticus and (b) P. chrysogenum.
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Table 1. Central composite design with 4 designed variables and 31 run samples.
Run Water activity Temperature
(C)
pH Potassium sorbate
concentration (%)
1 0.90 22.5 6 1.0
2 0.95 15.0 5 1.53 0.95 15.0 7 0.5
4 0.85 30.0 7 1.5
5 0.80 22.5 6 1.0
6 0.95 15.0 7 1.5
7 0.90 7.5 6 1.0
8 0.90 22.5 6 1.0
9 0.90 22.5 6 1.0
10 0.85 15.0 5 0.5
11 0.95 30.0 5 0.5
12 0.90 22.5 6 1.0
13 0.85 15.0 7 0.5
14 1.00 22.5 6 1.0
15 0.85 30.0 5 0.5
16 0.95 30.0 7 0.5
17 0.90 22.5 6 2.0
18 0.85 15.0 5 1.5
19 0.85 15.0 7 1.520 0.90 22.5 6 1.0
21 0.90 22.5 6 1.0
22 0.90 22.5 6 0.0
23 0.85 30.0 5 1.5
24 0.90 22.5 6 1.0
25 0.95 30.0 5 1.5
26 0.95 15.5 5 0.5
27 0.95 30.0 7 1.5
28 0.90 22.5 8 1.0
29 0.90 37.5 6 1.0
30 0.90 22.5 4 1.0
31 0.85 30.0 7 0.5
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Table 2. Examples of the estimated parameters (, growth rate, mm d-1; , lag phase, d; A, upper asymptote va
colony diameter by linear, Baranyis and Gompertz models forA. ochraceus, P. verrucosum, E. amstelodamian
Linear Baranyis biphasic Baranyi
run S.E. R2 S.E. S.E. R
2 S.E. S.E. A S.E. R
2 S.E
1 3.340.08 2.80 99.7 3.340.08 2.800.32 99.8 NC NC NC NC 4.300.3
14 5.130.10 0.12 99.7 5.180.13 0.210.19 99.7 NC NC NC NC 5.960.3
3 3.420.09 3.77 99.2 3.540.09 4.220.30 99.5 NC NC NC NC 4.170.0
16 8.210.08 1.19 100.0 8.210.07 1.190.05 100 NC NC NC NC 9.060.3
13 0.260.01 14.95 98.3 NC NC NC 0.330.01 21.411.47 83.30.4 99.7 0.380.
A. och
31 0.310.05 18.62 89.9 NC NC NC 0.590.17 24.822.47 9.30.4 94.8 0.820.2
1 0.570.02 18.04 98.3 0.570.02 17.951.63 97.9 NC NC NC NC 0.630.0
14 1.090.07 0.09 94.5 1.090.08 0.131.57 94.5 NC NC NC NC 1.550.6
3 2.500.06 2.59 99.4 2.860.17 3.560.69 97.0 NC NC NC NC 4.560.9
16 1.340.07 -3.15 94.6 1.320.07 -3.691.47 94.8 NC NC NC NC 1.750.
13 0.230.02 2.41 94.0 NC NC NC 0.290.02 11.253.95 42.12.0 98.4 0.360.
P. ver
31 - - - - - - - - - - -
1 1.370.09 23.63 95.5 NC NC NC 1.700.09 26.861.04 83.31.7 99.1 1.970.
14 - - - - - - - - - - -
E. 3 1.810.13 5.03 94.8 1.820.10 5.071.05 96.4 NC NC NC NC 2.730.
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16 6.210.19 2.11 99.3 6.0410.18 1.850.23 99.3 NC NC NC NC 6.630.2
13 - - - - - - - - - - -
ams
31 1.260.09 7.39 98.2 NC NC NC 1.530.08 13.791.40 83.31.7 99.5 1.930.
1 1.180.04 8.17 99.1 NC NC NC 1.200.03 8.730.74 74.01.4 99.6 1.480.
14 4.700.62 0.76 90.4 3.330.38 -1.681.47 92.4 NC NC NC NC 5.120.7
3 2.690.09 4.48 99.2 3.160.29 5.451.02 94.3 NC NC NC NC 10.727
16 1.080.01 -3.69 99.6 1.190.05 -2.031.11 96.5 NC NC NC NC 1.20.04
13 - - - - - - - - - -
P. exp
31 - - -- - - - - - -
S.E., standard error of the estimated parameters
-, no growth
NC, no convergence
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Table 3. Estimated parameters (, increase in root-square ergosterol per day; , lag
phase till ergosterol detection and A, maximum asymptotic value of root square
ergosterol) through modelling of root-square ergosterol by Baranyis (either biphasic or
standard) model forA. ochraceus, P. verrucosum, E. amstelodamiand P. expansum.
run S.E. S.E. AS.E. R2
1 1.470.07 5.280.28 17.950.22 99.9
14 1.300.28 -0.151.47 20.951.41 97.8
3 0.560.04 4.830.94 98.6
16 1.160.07 0.810.35 99.3
13 2.690.34 8.890.39 20.590.50 99.7
A. ochraceus
31 - - - -
1 0.240.08 23.1614.28 84.2
14 0.440.10 1.044.33 12.861.51 95.5
3 0.270.00 -2.440.25 100.0
16 0.270.05 -6.723.90 12.670.53 99.2
13 NC NC NC NC
P. verrucosum
31 - - - -
1 0.420.13 22.747.65 18.732.42 93.6
14 - - - -
3 0.210.04 -1.526.72 91.516 0.780.07 0.250.75 98.5
13 - - - -
E.amstelodami
31 0.570.04 15.090.80 15.170.12 100.0
1 0.740.67 14.6912.49 16.841.81 89.9
14 2.040.31 2.090.79 25.361.67 98.2
3 0.510.05 3.381.62 98.1
16 0.340.04 -10.544.00 19.121.58 98.9
13 - - - -
P. expansum
31 - - - -
S.E., standard error of the estimated parameters
-, no growth
NC, no convergence
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