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# compute.pulled.diversification <- function( v_spec0, v_ext0, delta_t ) {
#
# # compute the derivatives
# l <- head(v_spec0, n = -1) #v_spec0[-length(v_ext0)]
# l_plus_one <- tail(v_spec0, n = -1) #v_spec0[-1]
# l_derivative <- (l_plus_one - l) / delta_t
# l_derivative <- c(l_derivative[1], l_derivative)
#
# # finally, add the 1/lambda * lambda dt to the pulled diversification rate
# v_p_div <- v_spec0 - v_ext0 + (1/v_spec0) * l_derivative
#
# return (v_p_div)
# }
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