ornstein_uhlenbeck {StratPal} | R Documentation |
simulate ornstein-uhlenbeck (OU) process
Description
Simulates an Ornstein-Uhlenbeck process using the Euler-Maruyama method. The process is simulated on a scale of 0.25 * min(diff(t))
and then interpolated to the values of t
. Note that different parametrizations of OU processes are used in the literature. Here we use the parametrization common in mathematics. This translates to the parametrization used in evolutionary biology (specifically, the one in Hansen (1997)) as follows:
-
sigma
is identical -
mu
used in theStratPal
package corresponds totheta
sensu Hansen (1997) -
theta
as used in theStratPal
package corresponds toalpha
sensu Hansen (1997)
Usage
ornstein_uhlenbeck(t, mu = 0, theta = 1, sigma = 1, y0 = 0)
Arguments
t |
times at which the process is simulated. Can be heterodistant |
mu |
number, long term mean |
theta |
number, mean reversion speed |
sigma |
positive number, strength of randomness |
y0 |
number, initial value (value of process at the first entry of t) |
Value
A list with two elements: t
and y
. t
is a duplicate of the input t
, y
are the values of the OU process at these times. Output list is of S3 class timelist
(inherits from list
) and can thus be plotted directly using plot
, see ?admtools::plot.timelist
References
Hansen, Thomas F. 1997. “Stabilizing Selection and the Comparative Analysis of Adaptation.” Evolution 51 (5): 1341–51. doi:10.1111/j.1558-5646.1997.tb01457.x.
See Also
-
ornstein_uhlenbeck_sl()
for simulation on specimen level - for use in conjunction withpaleoTS
package -
random_walk()
andstasis()
to simulate other modes of evolution
Examples
library("admtools") # required for plotting of results
t = seq(0, 3, by = 0.01)
l = ornstein_uhlenbeck(t, y0 = 3) # start away from optimum (mu)
plot(l, type = "l")
l2 = ornstein_uhlenbeck(t, y0 = 0) # start in optimum
lines(l2$t, l2$y, col = "red")