sim_BM_budding_exp: Simulate continuous trait evolution with budding and...
In Caetanods/buddPhy: Trait Evolution and Budding Speciation

Similar to 'sim_Mk_budding_exp' function, but simulate continuous traits using a Brownian motion model instead of discrete traits.
This function adds a probability of budding speciation and allows only for a negative relationship between rates of trait evolution and lineage-age. Function also allows for cladogenetic change in the trait (a deterministic change in the state of the trait after budding speciation happens).
MOTHER LINEAGES: The user can set the 'budding_mother' parameter to control the fecundity of mother lineages. If 'budding_mother' is NA, then mother lineages will appear stochastic given the global probability of budding speciation events controlled by the 'budding_prob' argument. If 'budding_mother' is 0.0, then mother lineages will have only a single daughter lineage and the next speciation event will always be a symmetric speciation. If 'budding_mother' is set to 1.0, then once a budding speciation happens the surviving will always survive the speciation event and the descendant nodes will never represent symmetric speciation events. Intermediate values can be used to set intermediate scenarios.

sim_BM_budding_exp(
  tree,
  sigma,
  anc = 0,
  budding_prob = 0,
  budding_mother = NA,
  change_rate = 2,
  decay_fn = TRUE,
  jump_size = NA
)

`tree`	phylogeny with branch lengths.
`sigma`	the base rate for the Brownian-motion model.
`anc`	the ancestral state for the trait.
`budding_prob`	probability that the speciation event was budding.
`budding_mother`	autocorrelation of budding events. If NA, then no autocorrelation happens and the occurrence of budding speciation will always follow the same probability of 'budding_prob'. If 'budding_mother' is non-zero, then the probability that the mother lineage will generate another new lineage through a budding speciation event (and, thus, survive another speciation event) will be given by 'budding_mother' instead. The probability of the next budding event after a symmetrical speciation event will reset to 'budding_prob'.
`change_rate`	the rate for an exponential reduction of the rate of trait evolution proportional to lineage-age.
`decay_fn`	TRUE or FALSE. If TRUE, then the rate of trait evolution has a negative (exponential) relationship with lineage-age. If FALSE, then this relationship becomes positive.
`jump_size`	controls the size of the cladogenetic change associated with budding speciation. The new lineage will have an average trait value shifted by a proportion equal to 'jump_size'. For example, 'jump_size = 0.5' will cause the new lineages to start with an average trait value equal to 50% above or below the current trait value. Setting to NA (default) will turn-off the option of cladogenetic trait changes.