#### Degree Type

Thesis

#### Date of Award

2010

#### Degree Name

Master of Science

#### Department

Mathematics

#### Major

Bioinformatics and Computational Biology

#### First Advisor

Jonathan Smith

#### Second Advisor

Zhijun Wu

#### Abstract

The thesis research studies the Swedish human population with Smith's macroscopic approach. In demographic statics, a couple of plots are drawn for each time point (period) of the human populations of Sweden and five other countries namely Belgium, France, the Netherlands, the United Kingdom, and the United States. One plot is for the probability distribution of a random newborn's mother's age. Another is for the net maternity function. These plots can be used to identify past historical information from the agreement and discrepancy of related curves.

In demographic kinetics, important macroscopic parameters are tracked over time for the Swedish human population. Entropy, reproductive potential, logarithmic maternity, and generation times T and t are studied as separate parameters. From their trends of changes, important conclusions are drawn. Entropy has the overall trend to decrease. This is the response of the increasing level of human societal organization. Reproductive potential, logarithmic maternity, T, and t also reveal this kind of information. The important results from them are that many extreme points are significant in history.

More important results are obtained from the combinations of macroscopic parameters. Two relations concern the (t, u) vector, where t is the logarithmic generation time and u is a standard deviation: (a) u will decrease as t increases, and vice versa, and (b) a proper scaling factor can make the formula t+ku be constant. The first relation holds for the Swedish human population with a brief exception, but does not apply to the U.S. population. The second relation works for the Swedish human population before 1930.

Most importantly, intensive cycles are found with the (r, s) vector, where r is the Malthusian parameter, the rate of natural increase, and s is the perturbation, measuring the deviation from Lotka stability. As separate parameters, it is difficult to find patterns from their trajectories. But nearly regular cycles appear in the tracking of the (r, s) vector. Three intensive cycles are found from the Swedish human population and modeled with Kepler's second law. Further investigation shows that intensive cycles exist in most of the human populations under study. Their structures are diverse.

The intensive cycles of this kind are thought to be related to human population development. A cycle covers at least four five-year periods or twenty years. This is a relatively long time. In the Leslie matrix model, the maximum eigenvalue represents a long term growth rate. Is there some relation between these intensive cycles of the Swedish human population and their maximum eigenvalues? Explorations are made and appear to be intriguing. The maximum eigenvalue changes at similar steps in each of the terms which correspond to the three intensive cycles. Subdominant eigenvalues have a similar performance, with some exceptions.

#### Copyright Owner

Chaoliang Zhang

#### Copyright Date

2010

#### Language

en

#### Date Available

November 16, 2012

#### File Format

application/pdf

#### Recommended Citation

Zhang, Chaoliang, "A macroscopic study of the Swedish human population" (2010). *Graduate Theses and Dissertations*. 12550.

https://lib.dr.iastate.edu/etd/12550