BIO3011 Lecture Notes - Lecture 10: Exponential Growth, Genetic Drift, Weak Interaction
31 May 2018
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9. Dynamic models
• Dynamic models - Describes how things change over time such as:
o Development rates of different body parts of a growing individual
o Patterns of genetic variability within a population
o Species diversity on islands
o Rates of movement of biochemical products across the cytoplasm of a cell
o Rate of evolutionary change in a trait under natural selection
• Forms of dynamic models:
Deterministic models
o Models where chance plays no role
o Each starting condition leads to completely predictable patterns of
future change
o All future behaviours are predictable
Stochastic models
o Include elements of chance and outcomes are probabilistic
o Eg. flipping coin = 50% tails, 50% heads
Discrete time models
o Variables are tracked across discrete steps in time
eg. each day, each year, each generation
o Depending on the interval in the model, multiple events may occur
between sequential time points
o Use if order of event is important
Continuous time models
o Variables can be tracked over any interval of time
o Focus on rates of change over small time intervals
-slow = sigmoidal -> eventually reaches a stable population
-when changes are slow you expect dynamics
-rapid = more complicated
-large n = genetic drift is relatively weak force
-small n = genetic drift is large
find more resources at oneclass.com
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Document Summary
Deterministic models: models where chance plays no role, each starting condition leads to completely predictable patterns of future change, all future behaviours are predictable. Include elements of chance and outcomes are probabilistic. Slow = sigmoidal -> eventually reaches a stable population. Large n = genetic drift is relatively weak force. (cid:374)" = o(cid:374)e step i(cid:374)to the future. If r>0 = population is growing all the time (next population will be greater) If r<0 = population is shrinking: model of negative density-dependent population growth: Since fitness cannot be negative, each parameter must take a value equal to or greater than zero (cid:894)w(cid:1005), w(cid:1006), w(cid:1007) (cid:1004)(cid:895). Is an example of a deterministic model: genetic drift: Is stochastic (includes elements of chance: makes the following assumptions: The population is composed of n diploid individuals, and population size remains stable (and constant) over time. There is a si(cid:374)gle ge(cid:374)e with two possi(cid:271)le alleles (cid:894)we"ll (cid:272)all the(cid:373) a a(cid:374)d a, as before)
