simulate ornstein-uhlenbeck (OU) process (specimen level)

Simulates an Ornstein-Uhlenbeck process on specimen level (_sl). The mean trait value is simulated 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. At each sampling location there are n_per_sample specimens that are normally distributed around the mean trait value with a variance of intrapop_var. 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 the StratPal package corresponds to theta sensu Hansen (1997)

• theta as used in the StratPal package corresponds to alpha sensu Hansen (1997)

Usage

ornstein_uhlenbeck_sl(
  t,
  mu = 0,
  theta = 1,
  sigma = 1,
  y0 = 0,
  intrapop_var = 1,
  n_per_sample = 10
)

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)

intrapop_var

intrapopulation variance, determines how much specimens from the same population vary

n_per_sample

integer, number of specimens sampled per population/sampling locality

Value

an object of S3 class pre_paleoTS, inherits from timelist and list. The list has two elements: t, containing a vector of times of sampling, and vals, a list of trait values of the same length as t, with element containing trait values of individual specimens. This object can be transformed using apply_taphonomy, apply_niche or time_to_strat, and then reduced to a paleoTS object using reduce_to_paleoTS. This can then be used to test for different modes of evolution.

See also

• ornstein_uhlenbeck() to model mean trait values,

• reduce_to_paleoTS() to transform outputs into paleoTS format

• stasis_sl(), strict_stasis_sl() and random_walk_sl() to simulate other modes of evolution

Examples

library("paleoTS")
x = ornstein_uhlenbeck_sl(1:5)
y = reduce_to_paleoTS(x) # turn into paleoTS format
plot(y) # plot using the paleoTS package


# see also
#vignette("paleoTS_functionality")
#for details and advanced usage