Statistical model of evolution of haploid organisms during simple vegetative reproduction

• Published in: Journal of theoretical biology Vol. 11; no. 3; pp. 418 - 435
• Main Authors: Drobník, Jaroslav, Dlouhá, Jarmila
• Format: Journal Article
• Language: English
• Published: England Elsevier Ltd 01.08.1966
• Subjects: Biological Evolution; Biometry; Feedback; Genetics, Population; Models, Theoretical; Molecular Biology; Mutation; Reproduction
• ISSN: 0022-5193; 1095-8541
• DOI: 10.1016/0022-5193(66)90102-0

A mathematical model has been developed to study the behaviour of one selected hereditary property in subsequent populations during cycles of asexual reproduction. The cycle is isomorphic with, e.g., the growth of a microbial culture after its transfer into a fresh broth. The suggested model is based on three random processes: the deviation of the hereditary transfer, the interaction of the property studied with the environment, and the interaction of it with other properties of the organism. Both interactions are included in a negative feedback which sets limits on the multiplicatory potency of the organism. Using these three random processes, we can follow the effect of a change in environment on the mean value of the property studied. Simultaneously the original pattern is reproduced after each cycle so that the whole system may autoreproduce. The shift of the mean value of the hereditary property has a limit which is always smaller than the shift in environment. Thus, the normalizing role of selection is expressed. Also, the standard deviation of all values of the property studied has a limit. This limit is affected neither by the change in environment nor by a reversible change of the genetic stability of the property. Thus the conservation of species is included in the model. The model shows that the population can proceed in evolution under changed environmental conditions only if the potency of the organism is greater than a certain value. This value grows exponentially with the magnitude of the environmental shift.