The Handbook of Predictive Microbiology Growth Models in R is a resource book covering some units of the International Workshop Predictive Modelling in Foods, a two-level course designed by the authors and imparted in 2014, 2017 and 2019. It provides an overview of the classical predictive microbiology models used to describe the growth of microbial populations, and the responses of their kinetic parameters to environmental conditions and intrinsic food properties. This handbook is divided into three sections, Experimental Design, Growth Primary Models and Growth Secondary Models, comprising a total of 20 chapters. Through the many R scripts explained in this handbook, the reader will learn how to address typical issues in
predictive microbiology, such as design of experiments, fitting of linear and nonlinear models, assessment and comparison of models, prediction from fitted models and graph building. The present handbook is intended to be the accompanying book for future workshops/courses taught by the authors or other predictive microbiology practitioners, or a beginner’s guide for self-study. It was published using the bookdown package of the R software.
About the Book
About the Authors
Preface
SECTION I: Experimental Design
1 Introduction to experimental design
2 Factorial designs
2.1 Complete factorial design
2.2 2?? Complete factorial design
2.3 3?? Complete factorial design
2.4 Fractional factorial design
2.4.1 2??-1 Half-fraction design
2.4.2 2??-2 Quarter-fraction design
2.4.3 3??-1 One-third-fraction design
3 Box-Behnken design
4 Central composite design
5 Latin-square design
6 Optimal design
SECTION II: Growth Primary Models
7 Introduction to growth primary models
7.1 Empirical and mechanistic models
7.2 Deterministic and stochastic models
7.3 Kinetic and probability models
7.4 Static and dynamic models
7.5 Primary, secondary and tertiary models
8 Linear models
8.1 Normality
8.2 Independence
8.3 Homocedasticity
9 First-order growth kinetics model
9.1 Fitting a first-order growth kinetics model
10 Non-linear models
10.1 Method of steepest descent
10.2 Gauss-Newton method
10.3 Levenberg-Marquardt method
10.4 Assessing adequacy and comparing nonlinear models
10.4.1 Deviance
10.4.2 Log-likelihood value
10.4.3 Akaike’s information criterion
10.4.4 Bayesian information criterion
10.4.5 F-test
11 Nonlinear models applied to microbial growth
11.1 Modified Gompertz model
11.2 Modified logistic models
11.3 Buchanan’s three-phase model
11.4 Baranyi model
11.5 Huang model
12 Fitting a nonlinear model to a single growth curve
12.1 Fitting modified Gompertz model to a single growth curve
12.2 Fitting Buchanan’s log-linear three-phase model to a single growth curve
12.3 Fitting Buchanan’s log-linear two-phase model to a single growth curve
12.4 Fitting Baranyi’s mechanistic model to a single growth curve
13 Fitting a nonlinear model to multiple growth curves
13.1 Fitting a logistic model to multiple growth curves
SECTION III: Growth Secondary Models
14 Introduction to growth secondary models
15 Modelling growth rate as a function of environmental factors
15.1 Belehradek-type or square-root models
15.2 Cardinal parameter models
16 Fitting secondary growth models
16.1 Fitting a square-root model
16.2 Fitting a cardinal parameter model
17 An application of determination of shelf-life using a cardinal parameter model
18 Modelling lag time as a function of environmental factors
18.1 Lag time modelled independently
18.2 Lag time modelled proportional to growth rate
18.3 Lag time modelled also as a function of pre-growth conditions
19 An application of comparison of lag times as influenced by temperature
19.1 Fitting the model to the breast data
19.2 Fitting the model to the thigh data
19.3 Fitting a model to the joint data
20 Polynomial models for growth kinectics parameters
20.1 Fitting a response surface model
20.2 Producing contour plots and surface graphs
References
Ursula Gonzales-Barron
Ursula Gonzales-Barron obtained her BSc degree (Honours) in Food Industries at the National Agricultural University La Molina (UNALM), Peru in 1998; and her PhD degree in Biosystems Engineering at the Faculty of Engineering of University College Dublin (UCD), Ireland in 2006.
She then took on the positions of Associate Researcher at the University of Manchester, UK, and Senior Researcher at UCD Biosystems Engineering until 2012. Currently, she is Senior Investigator at CIMO Mountain Research Centre based at the Polytechnic Institute of Bragança (IPB), Portugal. Her expertise resides in diverse areas of food quality and microbiological safety, including mathematical modelling, predictive microbiology, risk assessment, meta-analysis, product and process optimisation, development of food quality monitoring tools and Bayesian statistics. She is leader or participates in a number of EU and international research projects; has been in receipt of 10 grants from competitive European calls; and has published over 80 peer-reviewed articles and over 100 in conference proceedings. She is Associate Editor of the LWT Food Science and Technology journal, and member of the editorial boards of the journals Food Research International, Microbial Risk Analysis and open-access MDPI Foods. She teaches as Visiting Professor in the Food Science PhD Programme at UNALM.
Vasco Cadavez
Vasco Cadavez holds a BSc degree in Animal Husbandry Engineering, an MSc degree in Animal Production with specialisation in Feed and Nutrition, and a PhD degree in Animal Science from the Portuguese University of Trás-Os-Montes e Alto Douro. He is Coordinator Professor in the Animal Science Department of the Polytechnic Institute of Bragança (IPB), Portugal, where he teaches Animal Breeding, Biotechnology, Animal Production Systems and Experimental Design and Data Analysis. He is also an active Investigator of the Research Group Sustainable Agriculture and Innovative Agro-food Chains at CIMO-IPB. He has ample experience in robust, logistic and multiple regression analyses, multivariate analysis, general linear models, count
data models, linear and non-linear mixed models, dynamic modelling and meta-analysis, which he has applied to the fields of animal science, agriculture and food safety. He has published 60 peer-reviewed articles, has authored/edited 4 books, has written 18 book chapters, and has presented his research at over 100 international conferences. Along with Ursula Gonzales-Barron, he leads the Food Quality and Safety Modelling research team at CIMO-IPB.