Taib, Ziad A note on modelling the dynamics of budding yeast populations using branching processes. (English) Zbl 0777.92017 J. Math. Biol. 31, No. 8, 805-815 (1993). Summary: A multitype branching process is proposed as a model for the behaviour of populations of the budding yeast Saccaromyces Cerevisiae. Using the idea of branching processes counted by random characteristics, we are able to obtain explicit expressions describing different aspects of the asymptotic composition of such populations. The main purpose of this note is to show that the branching process approach is an alternative to deterministic population models based on differential equation methods. Cited in 1 Document MSC: 92D25 Population dynamics (general) 60J85 Applications of branching processes Keywords:budding yeast populations; stable scar distribution; stable size distribution; multitype branching process; Saccaromyces Cerevisiae; explicit expressions; asymptotic composition PDFBibTeX XMLCite \textit{Z. Taib}, J. Math. Biol. 31, No. 8, 805--815 (1993; Zbl 0777.92017) Full Text: DOI References: [1] Asmussen, S., Hering, H.: Branching Processes. Boston Basel Stuttgart: Birkhäuser 1983 · Zbl 0516.60095 [2] Beran, K.: Budding yeast cells, their scars and ageing. Adv. Microbiol. Physiol. 2, 143-171 (1968) · doi:10.1016/S0065-2911(08)60261-1 [3] Cohn, H.: Multitype finite mean supercritical branching processes. J. Appl. Probab. 26, 398-403 (1989) · Zbl 0676.60078 · doi:10.2307/3214045 [4] Green, P. J.: Modelling yeast cell growth using stochastic branching processes. J. Appl. Probab. 18, 799-808 (1981) · Zbl 0472.60068 · doi:10.2307/3213055 [5] Gyllenberg, M.: The size and scar distributions of the yeast Saccharomyces Cerevisiae. J. Math. Biol. 24, 81-101 (1986) · Zbl 0593.92016 [6] Jagers, P.: Branching Processes with Biological Applications. London New York: Wiley 1975 · Zbl 0356.60039 [7] Jagers, P.: General branching processes as Markov fields. Stochastic Processes Appl. 32, 183-212 (1989) · Zbl 0678.92009 · doi:10.1016/0304-4149(89)90075-6 [8] Jagers, P., Nerman, O.: The growth and composition of branching populations. Adv. Appl. Probab. 16, 221-259 (1984) · Zbl 0535.60075 · doi:10.2307/1427068 [9] Jönsson, T.: Remarks on the Koch-Schaechter cell cycle model and the use of branching processes (unpublished) [10] Nerman, O.: The Growth and Composition of Supercritical Branching Processes on General Type Spaces. Dept. of Mathematics, Chalmers University of Technology and the University of Göteborg 18 (1984) · Zbl 0535.60075 [11] Shurenkov, V. M.: On the Markov renewal theory. Theory of Probab. Appl. XXIX, 247-265 (1984) · Zbl 0557.60078 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.