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This function simulates multivariate (as well as univariate) continuous traits evolving along a given phylogenetic tree or time series according to a BM/RW (Brownian Motion/Random walk), OU (Ornstein-Uhlenbeck), ACDC (Accelerating rates and Decelerating rates/Early Bursts), and SHIFT models of phenotypic evolution. The traits are simulated by random sampling from a Multivariate Normal Distribution (Paradis, 2012).

The mvSIM function allows simulating continuous trait (univariate or multivariate) evolution along a phylogeny (or a time-series) with user specified parameters or parameters estimated from a previous fit.

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The 'simulate' wrapper can also be used with a fitted object of class 'mvmorph': simulate(object, nsim=1, tree=tree). See example below.

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If parameter values are not provided, the default values are fixed to 1 (sigma, sig, alpha, beta) or to 0 for the mean at the root (ancestral state).

For the 'BMM' model were different parts of the tree have their own rate, a list with one rate (or matrix of rates) per selective regime must be provided.

For the 'OU1' and 'OUM' models, the user can specify if the ancestral state (theta0) should be computed (param$root=TRUE), assumed to be at the oldest regime state (param$root=FALSE), or if there is no root and each regimes is at the stationary point (param$root='stationary'; see also ?mvOU).

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For the 'BM1', 'BMM', and 'RWTS' models, a trend can be simulated by providing values to the 'trend' argument in the 'param' list.

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Traits names can be provided with the 'names_traits' argument in the 'param' list.For all the shift models, if the tree is not mapped the age of the shift should be directly provided (in unit of times of the tree) using the 'age' argument in the 'param' list.