TY - JOUR
T1 - A three-stage discrete-time population model
T2 - Continuous versus seasonal reproduction
AU - Ackleh, Azmy S.
AU - Dib, Youssef M.
AU - Jang, Sophia R.J.
N1 - Funding Information:
The work of A.S. Ackleh is partially supported by the National Science Foundation under grant # DUE-0531915.
PY - 2007/10
Y1 - 2007/10
N2 - We consider a three-stage discrete-time population model with density-dependent survivorship and time-dependent reproduction. We provide stability analysis for two types of birth mechanisms: continuous and seasonal. We show that when birth is continuous there exists a unique globally stable interior equilibrium provided that the inherent net reproductive number is greater than unity. If it is less than unity, then extinction is the population's fate. We then analyze the case when birth is a function of period two and show that the unique two-cycle is globally attracting when the inherent net reproductive number is greater than unity, while if it is less than unity the population goes to extinction. The two birth types are then compared. It is shown that for low birth rates the adult average number over a one-year period is always higher when reproduction is continuous. Numerical simulations suggest that this remains true for high birth rates. Thus periodic birth rates of period two are deleterious for the three-stage population model. This is different from the results obtained for a two-stage model discussed by Ackleh and Jang (J. Diff. Equ. Appl., 13, 261–274, 2007), where it was shown that for low birth rates seasonal breeding results in higher adult averages.
AB - We consider a three-stage discrete-time population model with density-dependent survivorship and time-dependent reproduction. We provide stability analysis for two types of birth mechanisms: continuous and seasonal. We show that when birth is continuous there exists a unique globally stable interior equilibrium provided that the inherent net reproductive number is greater than unity. If it is less than unity, then extinction is the population's fate. We then analyze the case when birth is a function of period two and show that the unique two-cycle is globally attracting when the inherent net reproductive number is greater than unity, while if it is less than unity the population goes to extinction. The two birth types are then compared. It is shown that for low birth rates the adult average number over a one-year period is always higher when reproduction is continuous. Numerical simulations suggest that this remains true for high birth rates. Thus periodic birth rates of period two are deleterious for the three-stage population model. This is different from the results obtained for a two-stage model discussed by Ackleh and Jang (J. Diff. Equ. Appl., 13, 261–274, 2007), where it was shown that for low birth rates seasonal breeding results in higher adult averages.
KW - Continuous breeding
KW - Global stability
KW - Seasonal breeding
KW - Three-stage discrete models
UR - http://www.scopus.com/inward/record.url?scp=70350174835&partnerID=8YFLogxK
U2 - 10.1080/17513750701605440
DO - 10.1080/17513750701605440
M3 - Article
C2 - 22876818
AN - SCOPUS:70350174835
SN - 1751-3758
VL - 1
SP - 291
EP - 304
JO - Journal of Biological Dynamics
JF - Journal of Biological Dynamics
IS - 4
ER -