R/DAISIE_DE_logpES_max_age_coltime.R

In DAISIE: Dynamical Assembly of Islands by Speciation, Immigration and Extinction

#' @name DAISIE_DE_logpES_max_age_coltime
#' @title Function to calculate the likelihood of observing an endemic singleton
#' lineage on the island with maximum time of colonization. This is valid for
#' infinite K according to the DE equations.
#' @description This function calculates the log-likelihood of observing an
#' endemic singleton lineage on an island for which the exact colonization time
#' is unknown, but the maximum time of colonization is known. This is valid for
#' infinite K according to the DE equations.
#' @inheritParams default_params_doc
#' @return the loglikelihood
#' @examples
#'
#' # Select a dataset from a DAISIE package
#'
#' data(Macaronesia_datalist)
#'
#' datalist <- Macaronesia_datalist$Azores
#' brts = datalist[[16]]$branching_times
#' missnumspec = datalist[[16]]$missing_species
#' # Define example parameters
#' pars1 <- c(0.2, 0.1, 0.05, 0.02, 0.03)
#'
#' # choose the method to solve the system of differential equations
#' log_likelihood <- DAISIE_DE_logpES_max_age_coltime(brts = brts,
#'                                                    missnumspec = missnumspec,
#'                                                    pars1 = pars1,
#'                                                    methode = "lsodes",
#'                                                    reltolint = 1e-16,
#'                                                    abstolint = 1e-16)
#' @noRd

DAISIE_DE_logpES_max_age_coltime <- function(brts,
                                             missnumspec,
                                             pars1,
                                             methode,
                                             reltolint,
                                             abstolint) {
  t0 <- brts[1]
  t1 <- brts[2]
  tp <- 0
  parameters <- pars1

  # Define system of equations for interval [t1, tp]
  interval1 <- function(t, state, parameters) {
    with(as.list(c(state, parameters)), {
      dDE <- -(pars1[1] + pars1[2]) * DE + 2 * pars1[1] * DE * E
      dDA2 <- -pars1[4] * DA2 + pars1[4] * Dm2
      dDA3 <- -pars1[4] * DA3 + pars1[4] * Dm3
      dDm1 <- -(pars1[5] + pars1[1] + pars1[3] + pars1[4]) * Dm1 +
        (pars1[3] + pars1[5] * E + pars1[1] * E^2)* DA2 + pars1[4] * (Dm2)
      dDm2 <- -(pars1[5] + pars1[1] + pars1[3]) * Dm2 +
        (pars1[3] + pars1[5] * E + pars1[1] * E^2)* DA2 +
        (pars1[5] * DE + 2 * pars1[1] * DE * E ) * DA3
      dDm3 <- -(pars1[5] + pars1[1] + pars1[3]) * Dm3 +
        (pars1[3] + pars1[5] * E + pars1[1] * E^2) * DA3
      dE <- pars1[2] - (pars1[1] + pars1[2]) * E + pars1[1] * E^2
      list(c(dDE, dDA2, dDA3, dDm1, dDm2, dDm3, dE))
    })
  }

  # Initial conditions
  number_of_species <- length(brts) - 1
  rho <- number_of_species / (missnumspec + number_of_species)

  initial_conditions1 <- c(DE = rho, DA2 = 0, DA3 = 1, Dm1 = 0, Dm2 = 0, Dm3 = 0, E = 1 - rho)

  # Define system of equations for interval [t0, t1]
  interval2 <- function(t, state, parameters) {
    with(as.list(c(state, parameters)), {
      dDA1 <- -pars1[4] * DA1 + pars1[4] * Dm1
      dDm1 <- -(pars1[5] + pars1[1] + pars1[3]) * Dm1 + (pars1[5] * E + pars1[1] * E^2 + pars1[3]) * DA1
      dE <- pars1[2] - (pars1[1] + pars1[2]) * E + pars1[1] * E^2
      list(c(dDA1, dDm1, dE))
    })
  }

  # Time sequence for interval [t1, tp]
  time1 <- c(tp, t1)

  # Solve the system for interval [t1, tp]
  solution1 <- deSolve::ode(y = initial_conditions1,
                            times = time1,
                            func = interval1,
                            parms = parameters,
                            method = methode,
                            rtol = reltolint,
                            atol = abstolint)

  # Initial conditions
  initial_conditions2 <- c(DA1 = solution1[, "DA2"][[2]],
                           Dm1 = solution1[, "Dm1"][[2]],
                           E = solution1[, "E"][[2]])

  # Time sequence for interval [t0, t1]
  time2 <- c(t1, t0)

  # Solve the system for interval [t0, t1]
  solution2 <- deSolve::ode(y = initial_conditions2,
                            times = time2,
                            func = interval2,
                            parms = parameters,
                            method = methode,
                            rtol = reltolint,
                            atol = abstolint)

  # Extract log-likelihood
  L1 <- solution2[, "DA1"][[2]]
  logL1b <- log(L1)
  return(logL1b)
}