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Simulation of Fluctuating Populations of Microorganisms and Macroorganisms with Models Having a Normal Random Variate Term
Author(s) -
Peleg Micha,
Normand Mark D,
Tesch Ralf
Publication year - 1997
Publication title -
journal of the science of food and agriculture
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.782
H-Index - 142
eISSN - 1097-0010
pISSN - 0022-5142
DOI - 10.1002/(sici)1097-0010(199701)73:1<17::aid-jsfa705>3.0.co;2-j
Subject(s) - random variate , population , mathematics , extinction (optical mineralogy) , statistical physics , limit (mathematics) , term (time) , stability (learning theory) , constant (computer programming) , logistic function , range (aeronautics) , statistics , extinction probability , population size , physics , random variable , computer science , mathematical analysis , quantum mechanics , demography , machine learning , sociology , optics , programming language , materials science , composite material
Fluctuating populations of micro‐ and macroorganisms play a major role in the stability and safety of food and agricultural products. In recent years such populations have been described by ‘chaotic’ models, most notably the discrete logistic function. This model's major limitations, however, are that it implies determinism and that it can account for neither population explosions nor extinction. Consequently, it is suggested that in order to simulate realistic population histories, the growth rate constant, r , in the original discrete logistic function X n +1 = rX n (1‐ X n ) can be replaced by a randomly varying term, r n . The latter can be defined as r n = r 0 exp( kZ rn ) where r 0 is a characteristic constant, Z rn a normal random variate produced by a normally distributed random number generator and k its chosen standard deviation. Theoretically, the magnitude of such r n (and its corresponding X n ) can be anywhere in the range 0< X n <∞. However, the magnitude of k can be selected so that X n >1 is a very rare event. In the special case of widely fluctuating populations dominated by random factors, the model can be replaced by N n / N 0 =exp( k ′ Z rn ), where N 0 is a characteristic number. In this form the model can account for occasional aperiodic population explosions, and if a lower limit to a viable number is also set (eg N / N 0 >0·01), for extinction events as well. The flexibility of the two models is demonstrated with simulated population evolution patterns of different kinds. © 1997 SCI.