Lecture 5: Population ecology: models without age structure
Continuous VS. Discrete generations
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 unitnet 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