Advances in Food Mycology

Probabilistic Modelling of Aspergillus Growth 293
a circular inoculum (1 mm diameter). For every tested pH and a w ,
growth controls without antimicrobial were prepared and inoculated
as above, including one control without pH adjustment (pH = 5.5) or
a w change (a w = 0.998). Three plates of each system were maintained
without inoculation for a w and pH measurement. The inoculated
plates and controls were incubated for 1 month at selected temperatures
(Tables 1 and 2) in hermetically closed plastic containers to avoid
dehydration. A sufficient headspace was left in the containers to avoid
anoxic conditions. Periodically, inoculated plates were removed briefly
to observe them and determine if growth had occurred and immediately
re-incubated. Water activity was measured with a Decagon CX-
1 instrument (Decagon Devices, Inc., Pullman, WA) calibrated and
operated following the procedure described by López-Malo et al.
(1993). pH was determined with a Beckman pH meter model 50
(Beckman Instruments, Inc., Fullerton, CA). Measurements were
made by triplicate. The pH and a w of the PDA systems without inoculation
determined at the beginning and at the end of incubation
demonstrated that the desired values remained constant under
incubation conditions.
2.5. Mould Growth Response
The inoculated systems were examined daily using a stereoscopic
microscope (American Optical, model Forty). A diameter of approximately
2 mm was defined as a positive sign of growth (López-Malo
et al., 1998) and registered as “1.” If no growth was observed during
the incubation period (one month), the response was registered as “0”.
2.6. Model Construction
A logistic regression model relates the probability of occurrence of
an event, Y, conditional on a vector, x, of explanatory variables
(Hosmer and Lemeshow, 1989). The quantity p (x) = E (Y⎪x) represents
the conditional mean of Y given x when the logistic distribution
is used. The specific model of the logistic regression is as follows:
p (x) = [exp (Σ b i x i )] / [1+ exp (Σ b i x i )] (1)
The logit transformation of p (x) is defined as:
logit (p) = g (x) = ln {[p (x) ] / [1-p (x)]} = Σ b x (2)
i i
For our particular case, a , pH, incubation temperature (T),
w
antimicrobial type (A), antimicrobial concentration (C) and their