Biology – Quantitative Biology – Populations and Evolution
Scientific paper
2006-04-27
Biology
Quantitative Biology
Populations and Evolution
26 pages, 6 figures
Scientific paper
We develop the qualitative theory of the solutions of the McKendrick partial differential equation of population dynamics. We calculate explicitly the weak solutions of the McKendrick equation and of the Lotka renewal integral equation with time and age dependent birth rate. Mortality modulus is considered age dependent. We show the existence of demography cycles. For a population with only one reproductive age class, independently of the stability of the weak solutions and after a transient time, the temporal evolution of the number of individuals of a population is always modulated by a time periodic function. The periodicity of the cycles is equal to the age of the reproductive age class, and a population retains the memory from the initial data through the amplitude of oscillations. For a population with a continuous distribution of reproductive age classes, the amplitude of oscillation is damped. The periodicity of the damped cycles is associated with the age of the first reproductive age class. Damping increases as the dispersion of the fertility function around the age class with maximal fertility increases. In general, the period of the demography cycles is associated with the time that a species takes to reach the reproductive maturity.
Dilao Rui
Lakmeche Abdelkader
No associations
LandOfFree
On the weak solutions of the McKendrick equation: Existence of demography cycles does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the weak solutions of the McKendrick equation: Existence of demography cycles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the weak solutions of the McKendrick equation: Existence of demography cycles will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-21683