- \code{alpha}, and \code{theta}. This may be more interesting for the
- last one to model varying phenotypic optima.
-
- By default the following formula is used:
-
- \deqn{x_{t''} = x_{t'} - \alpha l (x_{t'} - \theta) + \sigma
- l \epsilon}{x(t'') = x(t') - alpha l (x(t') - theta) + sigma
- l epsilon}
-
- where \eqn{l (= t'' - t')} is the branch length, and \eqn{\epsilon
- \sim N(0, 1)}{\epsilon ~ N(0, 1)}. If \eqn{\alpha > 1}{alpha > 1},
- this may lead to chaotic oscillations. Thus an alternative
- parameterisation is used if \code{linear = FALSE}:
-
- \deqn{x_{t''} = x_{t'} - (1 - exp(-\alpha l)) * (x_{t'} - \theta) +
- \sigma l \epsilon}{x(t'') = x(t') - (1 - exp(-alpha l)) * (x(t') -
- theta) + sigma l epsilon}}
+ \code{alpha}, and \code{theta}. This may be interesting for the last
+ one to model varying phenotypic optima. The exact updating formula
+ from Gillespie (1996) are used which are reduced to BM formula if
+ \code{alpha = 0}.}