# Population Models

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```					Population Models
A Brief Introduction

Matt Hansen
Geography 6010
Overview
Basic modeling techniques

Population modeling techniques

Difference and differential equations

Conclusions
Evolution of Population Modeling
Techniques
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?
Spatial Modeling
Benefits of spatial analysis
   Spatial dynamics
   Spatial heterogeneity
   Spatial relationships
Spatial Analysis Tools:
   Spatial statistics
   Cellular automata
   Metapopulation modeling
   GIS
Basic Population Model
Modeling with Difference Equations
Population in each time period is a
function of the previous period’s
population
Nt+1 = f (Nt)
Linear function
Nt+1 = (1+r)•Nt
(N = population; t = period of time; r = growth rate [births-deaths])
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
     ...
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
Logistic Difference Equations
Nt+1 = r •Nt (K – Nt/K)
K = carrying capacity
Logistic Difference Equations
Age structure dependencies
Competition
Lotka-Volterra predator-prey equation
Chaos
Differential Equations
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

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 views: 4 posted: 12/3/2011 language: English pages: 13
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