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Jon Abbatt (10)
Lecture 5

lecture 5 notes from prof. Thomson

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Jon Abbatt

Lecture 5: Population ecology: models without age structure Continuous VS. Discrete generations Continuous-time approach  An approach to population modeling assuming that time flows continuously and that change can occur at every instant.  Differential equations are used, time steps are infinitely small: use concept of limits &calculus; growth is smooth. Discrete time approach  An approach to population modeling that uses discrete time intervals, generally corresponding to intervals between reproductive periods  Difference equations are used, time steps are discrete units (days, years, etc.): use iterated recursion equations; growth is stepwise and bumpy. Calculating population growth rates  Per capita: the rate of growth on a per-individual basis.  General bookkeeping model:  Geometric growth: Increase/decrease in a population as measured over discrete intervals in which the increment is proportional to the number of individuals at the beginning of the interval.  When we combine death, birth, emigrant and immigrant, we will have a ratio λ (factor by which population changes over one time unitnet reproductive rate).  Discrete time can be expressed as geometric growth: λ or generally: λ  Continuous time can be expressed as exponential growth. r=exponential growth rate Geometric growth Exponential growth  the geometric and exponential growth are related by λ & λ Geometric growth (λ) Exponential growth(r) Decreasing population λ Constant population size λ Increasing population λ Factor
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