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College aantekeningen Kwantitatieve En Theoretische Biologie (B-B1KWBI20)
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aantekeningen hoorcolleges theoretische biologie deeltentamen
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Theoretische biologie hoorcollegesH1
H2
It is important to realize that the ordinary differential equations (ODE) models we mostly work with
in this course implicitly make a number of (unrealistic) assumptions:
1. All individuals are equal, and hence can be described by a single variable.
2. The population is well mixed, and hence the spatial location of where interactions occur is
not considered.
3. The population size N is large, so we need not to worry about population sizes smaller than
one individual.
4. The parameters are constant, e.g. there is no seasonal variation in reproduction and birth
rates.
Where bN and dN represent the overall number of births and
deaths, whereas b and d represent the per capita, i.e. per individual, birth and death rates.
R0 is difined as maximum fitness. R0= b/d
In ecology the steady state is also the carrying capacity (K).
Stable Unstable
A steady state is stable if a net increase occurs for values smaller than the steady state and a net
decrease occurs for values larger than the steady state.
, H3
Systeem met 2 gekoppelde differentiele vergelijkingen
The dynamics of R and N are co-dependent
Lotka-Volterra model:
Isocline: een lijn waarvoor een waarde gelijk blijft (bijvoorbeeld x of y)
Nullcline: de lijn waarvoor het netto verschil nul is. (dN/dt = 0)
Op het punt waar de nullclines snijden is er een evenwicht. Alle pijlen wijzen naar het evenwicht
(stabiele aantrekker)
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