The PAT model of population dynamics

TL;DR

The paper introduces a population-age-time (PAT) model that predicts population dynamics and steady states based on birth rates, revealing robustness of distribution shapes regardless of initial conditions.

Contribution

The paper presents a novel PAT model demonstrating that population distribution dynamics are robust to birth and death rate variations and initial conditions.

Findings

Population approaches a steady state with a kink shape when birth rate equals death rate.

Total population remains constant if the average number of children per woman is 2.

Population grows or declines unbounded if the birth rate is above or below 2.

Abstract

We introduce a population-age-time (PAT) model which describes the temporal evolution of the population distribution in age. The surprising result is that the qualitative nature of the population distribution dynamics is robust with respect to the birth rate and death rate distributions in age, and initial conditions. When the number of children born per woman is 2, the population distribution approaches an asymptotically steady state of a kink shape; thus the total population approaches a constant. When the number of children born per woman is greater than 2, the total population increases without bound; and when the number of children born per woman is less than 2, the total population decreases to zero.