Population Models

1
Population Models

• A Brief Introduction
• Matt Hansen
• Geography 6010

2
Overview

• Basic modeling techniques
• Population modeling techniques
• Difference and differential equations
• Conclusions

3
Evolution of Population Modeling Techniques
4
Choosing an Appropriate Model

• Know model objectives
• Simple models
• Easy to create
• Not representative of reality
• Huge models
• Universally applicable
• Complex, expensive, and quickly obsolete
• A happy medium?

5
Spatial Modeling

• Benefits of spatial analysis
• Spatial dynamics
• Spatial heterogeneity
• Spatial relationships
• Spatial Analysis Tools
• Spatial statistics
• Cellular automata
• Metapopulation modeling
• GIS

6
Basic Population Model
7
Modeling with Difference Equations

• Population in each time period is a function of
  the previous periods population
• Nt1 f (Nt)
• Linear function
• Nt1 (1r)Nt
• (N population t period of time r growth
  rate births-deaths)

8
Malthusian Growth Model

• 1798 Thomas R. Malthus
• Unchecked human populations double every 25 years
• Constant growth rate regardless of size
• 100 ? 135
• 1,000 ? 1,350
• 10,000 ? 13,500
• . . .

9
Malthusian Growth Model

• N(t) N0ert
• N0 population size at t 0
• N(t) population at given time (t)
• t time
• r growth rate per unit time

10
Logistic Difference Equations

• Nt1 r Nt (K Nt/K)
• K carrying capacity

11
Logistic Difference Equations

• Age structure dependencies
• Competition
• Lotka-Volterra predator-prey equation
• Chaos

12
Differential Equations
13
Conclusions

• Model format should be determined by desired
  level of complexity
• Geographers offer a unique spatial perspective to
  modeling
• Malthusian growth modeling forms the foundation
  of much of population modeling
• Future Geocomputation topics will add to an
  understanding of these techniques