RPANDA (version 1.2)

fit_coal_cst: Maximum likelihood fit of the equilibrium model

Description

Fits the equilibrium diversity model with potentially time-varying turnover rate and potentially missing extant species to a phylogeny, by maximum likelihood. The implementation allows only exponential time variation of the turnover rate, although this could be modified using expressions in Morlon et al. PloSB 2010. Notations follow Morlon et al. PLoSB 2010.

Usage

fit_coal_cst(phylo, tau0 = 1e-2, gamma = 1, cst.rate = FALSE, meth = "Nelder-Mead", N0 = 0)

Arguments

phylo

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

tau0

initial value of the turnover rate at present (used by the optimization algorithm)

gamma

initial value of the parameter controlling the exponential variation in turnover rate (used by the optimization algorithm)

cst.rate

logical: should be set to TRUE to fit an equilibrium diversity model with time-constant turnover rate (know as the Hey model, model 1 in Morlon et al. PloSB 2010). By default, a model with expontential time-varying rate exponential is fitted (model 2 in Morlon et al. PloSB 2010).

meth

optimization to use to maximize the likelihood function, see optim for more details.

N0

Number of extant species. With default value(0), N0 is set to the number of tips in the phylogeny. That is, the phylogeny is assumed to be 100% complete.

Value

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

tau0

the estimated turnover rate at present

gamma

the estimated parameter controlling the exponential variation in turnover rate (if cst.rate is FALSE)

Details

This function fits models 1 (when cst.rate=TRUE) and 2 (when cst.rate=FALSE) from the PloSB 2010 paper. Likelihoods arising from these models are directly comparable to likelihoods from the fit_coal_var function, thus allowing to test support for equilibrium versus expanding diversity scenarios. Time runs from the present to the past. Hence, if gamma is estimated to be positive (for example), this means that the speciation rate decreases from past to present.

References

Hey, J. (1992) Using phylogenetic trees to study speciation and extinction, Evolution, 46: 627-640

Morlon, H., Potts, M.D., Plotkin, J.B. (2010) Inferring the dynamics of diversification: a coalescent approach, PLoS B, 8(9): e1000493

Morlon, H., Kemps, B., Plotkin, J.B., Brisson, D. (2012) Explosive radiation of a bacterial species group, Evolution, 66: 2577-2586

Morlon, H. (2014) Phylogenetic approaches for studying diversification, Eco Lett, 17:508-525

See Also

likelihood_coal_cst, fit_coal_var

Examples

data(Cetacea)
result <- fit_coal_cst(Cetacea, tau0=1.e-3, gamma=-1, cst.rate=FALSE, N0=89)
print(result)