Fits the SGD model with exponential growth of the metacommunity, by maximum likelihood. Notations follow Manceau et al. (2015)

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`phylo` |
an object of type 'phylo' (see ape documentation) |

`tot_time` |
the age of the phylogeny (crown age, or stem age if known). If working with crown ages, tot_time is given by max(node.age(phylo)$ages) |

`par` |
a numeric vector of initial values for the parameters (b,d,nu) to be estimated (these values are used by the optimization algorithm) |

`f` |
the fraction of extant species included in the phylogeny |

`meth` |
optimization to use to maximize the likelihood function, see |

a list with the following components

`model` |
the name of the fitted model |

`LH` |
the maximum log-likelihood value |

`aicc` |
the second order Akaike's Information Criterion |

`par` |
a numeric vector of estimated values of b (birth), b-d (growth) and nu (mutation) |

While b-d and nu can in general be well estimated, the likelihood surface is quite flat whith respect to b, such that the estimated b can vary a lot depending on the choice of the initial parameter values. Estimates of b should not be trusted.

M Manceau

Manceau, M., Lambert, A., Morlon, H. (2015) Phylogenies support out-of-equilibrium models of biodiversity Ecology Letters 18: 347-356

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