Overall population growth in periodic environment
We consider populations with an exponential growth or decay and random life time. We assume that the calendar time is subdivided into consecutive time periods of equal length. After successive completion of the nth growth period, with probability α, there will be an accumulated overall population cn, (c>1 means growth, cdecay). The time duration up to eventual termination of the growth from the start of any time period is a r.v. T, independent of the number of survived periods. M is the overall population size generated by one individuality from the start of the process until its termination. We derive the probability distribution of M and establish that it possesses the multiplicative almost lack of memory property. This appears as a kind of generalization of The Uniform distribution, when c1. We elaborate on the properties of the random variable M and discuss possible applications to environmental studies.
© 1998 John Wiley & Sons, Ltd.
Dimitrov, Boyan N.; El-Saidi, Mohammed A.; and Khalil, Zohel, "Overall population growth in periodic environment" (1998). Mathematics Publications. 48.