Ž . International Journal of Food Microbiology 71 2001 219–234 www.elsevier.comrlocaterijfoodmicro Recovery of an oscillatory mode of batch yeast growth in water for a pure culture A.S. Vadasz, P. Vadasz ) , M.E. Abashar, A.S. Gupthar Faculty of Science and Engineering, UniÕersity of Durban-WestÕille, PriÕate Bag X54001, Durban 4000, South Africa Received 22 January 2001; received in revised form 7 May 2001; accepted 29 June 2001 Abstract New experiments that we conducted show an oscillatory mode of batch yeast growth in water, for a pure culture of the T206 strain of Saccharomyces cereÕisiae. The oscillations are damped over time, allowing the cell concentration to stabilize at the stationary equilibrium. A new proposed model that includes the complete cell growth dynamics is introduced and showed to recover the experimental oscillatory results. In addition the proposed model recovers effects that are frequently encountered in experiments such as a ALag PhaseB as well as an inflection point in the Aln curveB of the cell concentration. The proposed model recovers also the Logistic Growth Curve as a special case. For purposes of providing some interesting contrast we present additional experimental as well as computational results for the growth of the VIN7 strain of S. cereÕisiae in a 5% grape juice medium. The latter indicates even stronger oscillations during the growth process. In order to Ž . capture experimentally the oscillatory growth behavior, very frequent readings are required every 15–30 min and the Ž . measurement process needs to be extended to longer than usual periods over 250 h . q 2001 Elsevier Science B.V. All rights reserved. Keywords: Oscillations; Yeast growth; Nutritional stress; Logistic growth; Population dynamics 1. Introduction The importance of mathematical modeling in food microbiology was discussed extensively by Roberts Ž . Ž . 1995 and Baranyi and Roberts 1995 . In particu- lar, the growth of yeast is reported widely in connec- tion to classical as well as more modern develop- ments of mathematical models. Quite from the very early stages of application of models in population dynamics, yeast growth was used to validate such Ž . models. Pearl 1927 , whose Logistic Growth Model ) Corresponding author. Tel.: q 27-31-204-4873; fax: q 27-31- 204-4002. Ž . E-mail address: vadasz@pixie.udw.ac.za P. Vadasz . Ž . LGM is still widely used, reported experimental Ž . results of yeast growth based on Carlson 1913 and compared them to his proposed Logistic Growth Ž . Model LGM results. The experimental results fitted excellently with Pearl’s logistic curve that repre- Ž . sented the solution of the LGM. Pearl 1927 sug- gested the LGM as a universal model for population growth and not only for yeast. However, experiments carried out in populations other than yeast indicated that the LGM does not recover essential features and therefore might not be appropriate in all cases, reduc- ing therefore its general applicability as well as the claim of its universality. As a result, some authors Ž . see Krebs, 1978; Strogatz, 1994 suggested that the LGM might be a good model for bacteria, yeast or 0168-1605r01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. Ž . PII: S0168-1605 01 00618-3