Lecture 5.docx

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18 Apr 2012
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Lecture 5: population ecology, models without age structure
- Defining populations and individuals with a focus on some unusual cases
Population is collection of individuals of same species restricted in some area
Pop.size N= # of individuals
Pop.density= N/area
Pop ecology: What influences N?
- Animals, straiht forward, not for plants though.
- Determining an individual is ambiguous because in the case of aspen, one
seed produces many identical connected stems. The larkspur has many
unique seeds and produces many unique plants (standard).
- Plants produce challenges for counts of themselves. Strangler fig has grafting
of roots together to make one stree with several genotypes
Coarse taxonomy of math models
NOW:
1.Continuous versus discrete generations (differential equations vs. difference
equations) (continuous reproduction vs non continuous reproduction)
2. Density dependent vs density independent models (no constraints… or effects on
density in terms of growth of pop… unrealistic)
3. Models with or without age structures (individuals within pop have different
propensity to reproduce or die based on age)
LATER:
1. Deterministic vs. stochastic models
The goals of most pop models
-can we predict how pop with grow or shrink over time
- N = size. t=time
- Nt= number of people in pop
-T+1= future in time
- Nt+1 people in pop one step later
- Nt+1 =f(Nt) general model
what are steps in time
-Differential (calculus) has time steps getting very small
Ricklefs issue
Nt=N(t)
Simple bookkeeping model: how can N change from Nt to Nt+1
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