diff --git a/.github/workflows/R-CMD-check.yaml b/.github/workflows/R-CMD-check.yaml
index 17d90dbe..80097dc5 100644
--- a/.github/workflows/R-CMD-check.yaml
+++ b/.github/workflows/R-CMD-check.yaml
@@ -6,6 +6,8 @@ on:
 
 name: R-CMD-check
 
+permissions: read-all
+
 jobs:
   R-CMD-check:
     runs-on: ${{ matrix.config.os }}
@@ -22,13 +24,14 @@ jobs:
           - {os: windows-latest, r: 'release'}
           - {os: ubuntu-latest,   r: 'devel', http-user-agent: 'release'}
           - {os: ubuntu-latest,   r: 'release'}
+          - {os: ubuntu-latest,   r: 'oldrel-1'}
 
     env:
       GITHUB_PAT: ${{ secrets.GITHUB_TOKEN }}
       R_KEEP_PKG_SOURCE: yes
 
     steps:
-      - uses: actions/checkout@v3
+      - uses: actions/checkout@v4
 
       - uses: r-lib/actions/setup-pandoc@v2
 
@@ -46,3 +49,4 @@ jobs:
       - uses: r-lib/actions/check-r-package@v2
         with:
           upload-snapshots: true
+          build_args: 'c("--no-manual","--compact-vignettes=gs+qpdf")'
diff --git a/.github/workflows/test-coverage.yaml b/.github/workflows/test-coverage.yaml
index ddaeb214..6eea989b 100644
--- a/.github/workflows/test-coverage.yaml
+++ b/.github/workflows/test-coverage.yaml
@@ -6,16 +6,17 @@ on:
 
 name: test-coverage
 
+permissions: read-all
+
 jobs:
   test-coverage:
     runs-on: ubuntu-latest
     if: "contains(github.event.head_commit.message, '[run ci]') || (github.ref == 'refs/heads/master' || github.ref == 'refs/heads/develop') || github.event.pull_request"
-
     env:
       GITHUB_PAT: ${{ secrets.GITHUB_TOKEN }}
 
     steps:
-      - uses: actions/checkout@v3
+      - uses: actions/checkout@v4
 
       - uses: r-lib/actions/setup-r@v2
         with:
@@ -23,28 +24,37 @@ jobs:
 
       - uses: r-lib/actions/setup-r-dependencies@v2
         with:
-          extra-packages: any::covr
+          extra-packages: any::covr, any::xml2
           needs: coverage
 
       - name: Test coverage
         run: |
-          covr::codecov(
+          cov <- covr::package_coverage(
             quiet = FALSE,
             clean = FALSE,
-            install_path = file.path(Sys.getenv("RUNNER_TEMP"), "package")
+            install_path = file.path(normalizePath(Sys.getenv("RUNNER_TEMP"), winslash = "/"), "package")
           )
+          covr::to_cobertura(cov)
         shell: Rscript {0}
 
+      - uses: codecov/codecov-action@v4
+        with:
+          fail_ci_if_error: ${{ github.event_name != 'pull_request' && true || false }}
+          file: ./cobertura.xml
+          plugin: noop
+          disable_search: true
+          token: ${{ secrets.CODECOV_TOKEN }}
+
       - name: Show testthat output
         if: always()
         run: |
           ## --------------------------------------------------------------------
-          find ${{ runner.temp }}/package -name 'testthat.Rout*' -exec cat '{}' \; || true
+          find '${{ runner.temp }}/package' -name 'testthat.Rout*' -exec cat '{}' \; || true
         shell: bash
 
       - name: Upload test results
         if: failure()
-        uses: actions/upload-artifact@v3
+        uses: actions/upload-artifact@v4
         with:
           name: coverage-test-failures
           path: ${{ runner.temp }}/package
diff --git a/DESCRIPTION b/DESCRIPTION
index de450254..91cd085e 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -1,7 +1,7 @@
 Package: DAISIE
 Type: Package
 Title: Dynamical Assembly of Islands by Speciation, Immigration and Extinction
-Version: 4.4.1
+Version: 4.4.1.9000
 Date: 2023-10-20
 Depends: R (>= 4.2.0)
 biocViews:
diff --git a/NEWS.md b/NEWS.md
index 0a5047c9..5490f5bb 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -1,3 +1,5 @@
+# DAISIE (development version)
+
 # DAISIE 4.4.1
 
 * Fix bug in the calculation of shift loglikelihoods.
diff --git a/R/DAISIE_ML1.R b/R/DAISIE_ML1.R
index 2fb1edb9..4f602942 100644
--- a/R/DAISIE_ML1.R
+++ b/R/DAISIE_ML1.R
@@ -107,7 +107,8 @@ DAISIE_ML1 <- function(
   tolint = c(1E-16, 1E-10),
   island_ontogeny = NA,
   jitter = 0,
-  num_cycles = 1) {
+  num_cycles = 1,
+  function_to_optimize = 'DAISIE_exact') {
   # datalist = list of all data: branching times, status of clade, and numnber of missing species
   # datalist[[,]][1] = list of branching times (positive, from present to past)
   # - max(brts) = age of the island
@@ -156,6 +157,12 @@ DAISIE_ML1 <- function(
   #  . eqmodel = 4 : equilibrium is assumed on immigrants using deterministic equation for endemics and immigrants
   #  . eqmodel = 5 : equilibrium is assumed on endemics and immigrants using deterministic equation for endemics and immigrants
 
+  if(function_to_optimize == 'DAISIE_exact') {
+    function_to_optimize <- DAISIE_loglik_all_choosepar
+  } else
+  {
+    DAISIE_loglik_all_choosepar_approx
+  }
 
   out2err <- data.frame(
     lambda_c = NA,
@@ -288,7 +295,7 @@ DAISIE_ML1 <- function(
   )
 
   optimpars <- c(tol, maxiter)
-  initloglik <- DAISIE_loglik_all_choosepar(
+  initloglik <- function_to_optimize(
     trparsopt = trparsopt,
     trparsfix = trparsfix,
     idparsopt = idparsopt,
diff --git a/R/DAISIE_ML_CS.R b/R/DAISIE_ML_CS.R
index 18b40c7c..58dfa9a8 100644
--- a/R/DAISIE_ML_CS.R
+++ b/R/DAISIE_ML_CS.R
@@ -183,7 +183,8 @@ DAISIE_ML_CS <- DAISIE_ML <- function(
   verbose = 0,
   tolint = c(1E-16, 1E-10),
   jitter = 0,
-  num_cycles = 1) {
+  num_cycles = 1,
+  function_to_optimize = 'DAISIE_exact') {
 
   if (datatype == "single") {
     if (is.na(island_ontogeny)) {
@@ -229,7 +230,8 @@ DAISIE_ML_CS <- DAISIE_ML <- function(
                           verbose = verbose,
                           tolint = tolint,
                           jitter = jitter,
-                          num_cycles = num_cycles)
+                          num_cycles = num_cycles,
+                          function_to_optimize = function_to_optimize)
       }
     } else {
         stop(
diff --git a/R/DAISIE_ML_IW.R b/R/DAISIE_ML_IW.R
index b2c19933..e7b1d38e 100644
--- a/R/DAISIE_ML_IW.R
+++ b/R/DAISIE_ML_IW.R
@@ -104,7 +104,7 @@ DAISIE_ML_IW <- function(
   }
   np = datalist[[1]]$not_present
   if (is.null(np)) {
-    np = datalist[[1]]$not_present_type1 + datalist[[1]]$not_present_type2
+    np <- datalist[[1]]$not_present_type1 + datalist[[1]]$not_present_type2
     warning('Number of species not present is misspecified.\n')
     return(invisible(out2err))
   }
@@ -130,6 +130,18 @@ DAISIE_ML_IW <- function(
     verbose = verbose
   )
 
+  pars1 <- rep(0, 5)
+  pars1[idparsopt] <- initparsopt
+  if (length(idparsfix) != 0) {
+    pars1[idparsfix] <- parsfix
+  }
+  if (pars1[4] == 0) {
+    warning('You have chosen a zero immigration rate; an empty island will never be colonized')
+  }
+  if (pars1[2] == 0) {
+    warning('You have chosen a zero extinction rate; this might create problems in optimization; please use a number close to 0 instead')
+  }
+
   trparsopt <- initparsopt / (1 + initparsopt)
   trparsopt[which(initparsopt == Inf)] <- 1
   trparsfix <- parsfix / (1 + parsfix)
diff --git a/R/DAISIE_SR_sim_core.R b/R/DAISIE_SR_sim_core.R
index 599498bd..7b91a04a 100644
--- a/R/DAISIE_SR_sim_core.R
+++ b/R/DAISIE_SR_sim_core.R
@@ -83,8 +83,10 @@ DAISIE_SR_sim_core <- function(time,mainland_n,pars)
     immig_rate <- max(c(mainland_n * gam * (1 - length(island_spec[,1])/K),0),na.rm = T)
 
     totalrate <- ext_rate + clado_rate + ana_rate + immig_rate
-    dt <- stats::rexp(1,totalrate)
-
+    dt <- stats::rexp(1, totalrate)
+    if (is.nan(dt)) {
+      dt <- total_time - timeval
+    }
     if ( timeval < pars[11] & ((timeval + dt) >= pars[11])  )
     {
       lac <- pars[6]
@@ -98,6 +100,9 @@ DAISIE_SR_sim_core <- function(time,mainland_n,pars)
       immig_rate <- max( c(mainland_n * gam * (1 - length(island_spec[,1])/K), 0), na.rm = TRUE )
       totalrate <- ext_rate + clado_rate + ana_rate + immig_rate
       dt <- stats::rexp(1, totalrate)
+      if (is.nan(dt)) {
+        dt <- total_time - pars[11]
+      }
       timeval <- pars[11] + dt
     } else
     {
@@ -107,7 +112,7 @@ DAISIE_SR_sim_core <- function(time,mainland_n,pars)
     possible_event <- sample(1:4,1,replace = FALSE,c(immig_rate,ext_rate,ana_rate,clado_rate))
 
     ##############
-    if(timeval <= total_time)
+    if(timeval < total_time)
     {
       new_state <- DAISIE_sim_update_state_cr(timeval = timeval,
                                               total_time = total_time,
diff --git a/R/DAISIE_data.R b/R/DAISIE_data.R
index 4e4991a0..1daeb6ea 100644
--- a/R/DAISIE_data.R
+++ b/R/DAISIE_data.R
@@ -565,3 +565,43 @@ NULL
 #' }
 #' @keywords datasets
 NULL
+
+#' @name frogs_sim_datalist
+#' @title Colonization and branching times of a data set simulated with the
+#' MLE parameters of frogs_datalist
+#' @docType data
+#' @format A list with the first element containing 2 elements and the following
+#'elements containing 5 components.
+#' @description A list containing the colonization and branching times
+#' of a simulated data set using the MLE parameters of IW model for the
+#' frogs_datalist. It is an R list object with the following elements.\cr \cr
+#' The first element of the list has two components: \cr \cr
+#' \code{$island_age} - the island age \cr
+#' \code{$not_present} - the number of mainland lineages that are not present
+#' on the island \cr \cr
+#' The following elements of the list each contains
+#' information on a single colonist lineage on the island and has 5
+#' components:\cr \cr
+#' \code{$colonist_name} - the name of the species or clade
+#' that colonized the island \cr
+#' \code{$branching_times} - island age followed by stem age of the population/species
+#' in the case of Non-endemic, Non-endemic_MaxAge species and Endemic species with no close
+#' relatives on the island. For endemic clades with more than one species on the island
+#' (cladogenetic clades/ radiations) these should be island age followed by the
+#' branching times of the island clade including the stem age of the clade.\cr
+#' \code{$stac} - the status of the colonist \cr \cr
+#' * Non_endemic_MaxAge: 1 \cr
+#' * Endemic: 2 \cr
+#' * Endemic&Non_Endemic: 3 \cr
+#' * Non_endemic: 4 \cr
+#' * Endemic_MaxAge: 5 or 6 \cr \cr
+#' \code{$missing_species} - number of island species
+#' that were not sampled for particular clade (only applicable for endemic
+#' clades) \cr
+#' \code{$type1or2} - whether the colonist belongs to type 1 or
+#' type 2. In this dataset all are equal to 1. \cr
+#' @seealso \code{\link{DAISIE_ML}}, \code{\link{DAISIE_SR_ML}}
+#' @source Etienne RS, Haegeman B, Dugo-Cota A, Vila C, Gonzalez-Voyer A &
+#' Valente L. The limits to ecological limits to diversification.\cr
+#' @keywords datasets
+NULL
diff --git a/R/DAISIE_format_IW.R b/R/DAISIE_format_IW.R
index 9584c632..c26d1867 100644
--- a/R/DAISIE_format_IW.R
+++ b/R/DAISIE_format_IW.R
@@ -117,7 +117,7 @@ DAISIE_format_IW_trait <- function(island_replicates,
   return(several_islands)
 }
 
-add_brt_table <- function(island, full_table = FALSE) {
+add_brt_table_old <- function(island, full_table = FALSE) {
   island_age <- island[[1]]$island_age
   island_top <- island[[1]]
   if (length(island) == 1) {
@@ -175,7 +175,7 @@ add_brt_table <- function(island, full_table = FALSE) {
           for (k in 1:length(island[[i]]$all_colonisations)) {
             the_brts <- island[[i]]$all_colonisations[[k]]$event_times[-1]
             pos2 <- pos1 + length(the_brts)
-            ff <- matrix(ncol = 5, nrow = pos2 - pos1 + 1)
+            ff <- matrix(ncol = 5, nrow = pos2 - pos1)
             ff[1:(pos2 - pos1), 1] <- the_brts
             ff[1:(pos2 - pos1), 2] <- j
             ff[1:(pos2 - pos1), 3] <- seq(1, length(the_brts))
@@ -203,3 +203,88 @@ add_brt_table <- function(island, full_table = FALSE) {
   colnames(island[[1]]$brts_table) <- c("brt", "clade", "event", "endemic", "col")
   return(island)
 }
+
+add_brt_table <- function(island, full_table = TRUE) {
+  island_age <- island[[1]]$island_age
+  island_top <- island[[1]]
+  if (length(island) == 1) {
+    brts_table <- matrix(ncol = 5, nrow = 1)
+    brts_table[1, ] <-  c(island_age, 0, 0, NA, NA)
+    island[[1]]$brts_table <- brts_table
+  } else {
+    island_top <- island[[1]]
+    island[[1]] <- NULL
+    btimes <- list()
+    for (i in 1:length(island)) {
+      btimes[[i]] <- island[[i]]$branching_times[-1]
+    }
+    island <- island[rev(order(sapply(btimes, "[", 1)))]
+    il <- unlist(island)
+    stac1s <- which(il[which(names(il) == "stac")] == "1")
+    stac5s <- which(il[which(names(il) == "stac")] == "5")
+    stac1_5s <- sort(c(stac1s, stac5s))
+    if (length(stac1_5s) != 0) {
+      if (length(stac1_5s) == length(island)) {
+        brts_table <- matrix(ncol = 5, nrow = 1)
+        brts_table[1, ] <- c(island_age, 0, 0, NA, NA)
+        island_no_stac1or5 <- NULL
+      } else {
+        island_no_stac1or5 <- island[-stac1_5s]
+      }
+    }
+    if (length(stac1_5s) == 0) {
+      island_no_stac1or5 <- island
+    }
+    if (length(island_no_stac1or5) != 0) {
+      btimes <- list()
+      for (i in 1:length(island_no_stac1or5)) {
+        btimes[[i]] <- island_no_stac1or5[[i]]$branching_times[-1]
+      }
+      brts <- rev(sort(unlist(btimes)))
+      brts_IWK <- NULL
+      pos1 <- 0
+      for (i in 1:length(btimes)) {
+        the_stac <- island_no_stac1or5[[i]]$stac
+        if(!is.null(island[[i]]$all_colonisations) & full_table == TRUE) {
+          #if(length(island[[i]]$all_colonisations) > 0) print(i)
+          for (k in 1:length(island[[i]]$all_colonisations)) {
+            the_brts <- island[[i]]$all_colonisations[[k]]$event_times[-1]
+            pos2 <- pos1 + length(the_brts)
+            ff <- matrix(ncol = 5, nrow = pos2 - pos1)
+            ff[1:(pos2 - pos1), 1] <- the_brts
+            ff[1:(pos2 - pos1), 2] <- i
+            ff[1:(pos2 - pos1), 3] <- seq(1, length(the_brts))
+            ff[1:(pos2 - pos1), 4] <- (the_stac == 2) + (the_stac == 3)
+            ff[1:(pos2 - pos1), 5] <- k
+            brts_IWK <- rbind(brts_IWK,ff)
+            pos1 <- pos2
+          }
+        } else {
+          the_brts <- btimes[[i]]
+          pos2 <- pos1 + length(the_brts)
+          ff <- matrix(ncol = 5, nrow = pos2 - pos1)
+          ff[1:(pos2 - pos1), 1] <- the_brts
+          ff[1:(pos2 - pos1), 2] <- i
+          ff[1:(pos2 - pos1), 3] <- seq(1, length(the_brts))
+          ff[1:(pos2 - pos1), 4] <- (the_stac == 2) + (the_stac == 3)
+          ff[1:(pos2 - pos1), 5] <- 1
+          brts_IWK <- rbind(brts_IWK,ff)
+          pos1 <- pos2
+        }
+      }
+      brts_table <- brts_IWK[rev(order(brts_IWK[, 1])), ]
+      brts_table <- rbind(c(island_age, 0, 0, NA, NA), brts_table)
+    }
+    island_top$brts_table <- brts_table
+    if (length(stac1_5s) != 0) {
+      for (i in 1:length(stac1_5s)) {
+        island[[length(island) + 1]] <- island[[stac1_5s[i]]]
+        island[[stac1_5s[i]]] <- NULL
+        stac1_5s <- stac1_5s - 1
+      }
+    }
+    island <- append(list(island_top), island)
+  }
+  colnames(island[[1]]$brts_table) <- c("brt", "clade", "event", "endemic", "col")
+  return(island)
+}
diff --git a/R/DAISIE_loglik_CS.R b/R/DAISIE_loglik_CS.R
index 1bbb2993..c2a9afa6 100644
--- a/R/DAISIE_loglik_CS.R
+++ b/R/DAISIE_loglik_CS.R
@@ -545,14 +545,14 @@ DAISIE_loglik_CS_M1 <- DAISIE_loglik <- function(pars1,
           # means that any colonization that took place before this maximum
           # colonization time (including presence in the non-oceanic scenario)
           # does not count and should be followed by another colonization.
-          # To allow this we introduce a third set of equations for the
-          # probability that colonization might have happened before but
-          # recolonization has not taken place yet (Q_M,n).
+          # To allow this we introduce a third and fourth set of equations for
+          # the probability that colonization might have happened before but
+          # recolonization has not taken place yet (Q_M,n and Q^M_{M,n}).
           epss <- 1.01E-5 #We're taking the risk
           if (abs(brts[2] - brts[1]) >= epss) {
             probs[(2 * lx + 1):(4 * lx)] <- probs[1:(2 * lx)]
             probs[1:(2 * lx)] <- 0
-          } else {
+          } else { #max age equals island age
             probs[(2 * lx + 1):(4 * lx)] <- 0
           }
 
diff --git a/R/DAISIE_loglik_IW.R b/R/DAISIE_loglik_IW.R
index 6a059c48..bc8c539f 100644
--- a/R/DAISIE_loglik_IW.R
+++ b/R/DAISIE_loglik_IW.R
@@ -368,7 +368,9 @@ DAISIE_loglik_IW <- function(
   lxm <- min(lx,M + 1)
   lxe <- lx
 
-  if(M * (1 - exp((min(brts) * gam))) > 0.2 * lxm) {
+  est_num_potential_colonizers <- min(1 + ceiling(Kprime), M * (1 - exp((min(brts) * gam))))
+
+  if(est_num_potential_colonizers > lxm) {
     message('With this colonization rate and system size setting, results may not be accurate.')
   }
 
@@ -427,7 +429,12 @@ DAISIE_loglik_IW <- function(
           test_for_colonization <- TRUE
         } else
         {
-          test_for_colonization <- (max(event[which(clade == col[k + 2])]) > 1)
+          #test_for_colonization <- (max(event[which(clade == col[k + 2])]) > 1)
+          # this tests whether the original clade has diversified, but this does not need to be the case
+          # it could also be a case of anagenesis followed by colonization, so this test seems inappropriate
+          # also, one should expect that colonizations in the data are all real colonizations; a colonization
+          # which is not followed by speciation but by recolonization should only occur once (the last colonization)
+          test_for_colonization <- TRUE
         }
         if(test_for_colonization) # new colonization or recolonization after speciation
         {
diff --git a/R/DAISIE_loglik_high_lambda.R b/R/DAISIE_loglik_high_lambda.R
index ccbb2d8b..a8164503 100644
--- a/R/DAISIE_loglik_high_lambda.R
+++ b/R/DAISIE_loglik_high_lambda.R
@@ -1,27 +1,30 @@
 DAISIE_loglik_high_lambda <- function(pars1, brts, stac) {
    lbrts <- length(brts)
    if (brts[lbrts] == 0) {
-       brts <- brts[-lbrts]
-       lbrts <- length(brts)
+     brts <- brts[-lbrts]
+     lbrts <- length(brts)
    }
-   N <- lbrts - 1
-   mu <- pars1[2]
    gam <- pars1[4]
-   brtsdiff <- brts - c(brts[2:(N + 1)], 0)
    if (stac == 0) {
-      out <- -gam * brts[1]
-   }
-   if (stac == 2) {
-      out <- -gam * brtsdiff[1] +
-        log(gam) +
-        log(N) +
-        (N - 1) * log(mu) +
-        lgamma(N) +
-        - (N - 1) * log(N - 1) +
-        - mu / (N - 1) * sum((1:N) * (0:(N - 1)) * brtsdiff[2:(N + 1)])
-   }
-   if (stac == 1 | stac == 3 | stac == 4) {
-      out <- -Inf
+     out <- -gam * brts[1]
+     return(out)
    }
+   if (stac == 2 | stac == 6) {
+     N <- lbrts - 1 - (stac == 6)
+     mu <- pars1[2]
+     brtsdiff <- brts - c(brts[2:lbrts], 0)
+     out <- -gam * brtsdiff[1] +
+       log(gam) * (stac == 2) +
+       log(1 - exp(-gam * brtsdiff[2])) * (stac == 6) +
+       #log(-expm1(-gam * brtsdiff[2])) * (stac == 6) +
+       #log1p(-exp(-gam * brtsdiff[2])) * (stac == 6) +
+       log(N) +
+       (N - 1) * log(mu) +
+       lgamma(N) +
+       - (N - 1) * log(N - 1) +
+       - mu / (N - 1) * sum((1:N) * (0:(N - 1)) * brtsdiff[(2 + (stac == 6)):(N + 1 + (stac == 6))])
+     return(out)
+   } else return(-Inf) # stac == 1, 3, 4, 5, 7, 8, 9
+   #Stac 6 to be checked still
    return(out)
 }
diff --git a/R/DAISIE_rates.R b/R/DAISIE_rates.R
index ee8a574c..f4030306 100644
--- a/R/DAISIE_rates.R
+++ b/R/DAISIE_rates.R
@@ -607,7 +607,7 @@ get_trans_rate <- function(trait_pars,
 #' @keywords internal
 #'
 #' @author Joshua Lambert, Pedro Neves, Shu Xie
-calc_next_timeval <- function(max_rates, timeval) {
+calc_next_timeval <- function(max_rates, timeval, total_time) {
   # testit::assert(timeval >= 0)
 
   if (length(max_rates) == 4) {   ## no considering about two trait states
@@ -619,8 +619,12 @@ calc_next_timeval <- function(max_rates, timeval) {
       max_rates[[5]] + max_rates[[6]] + max_rates[[7]] + max_rates[[8]] +
       max_rates[[9]] + max_rates[[10]]
   }
-  dt <- stats::rexp(1, totalrate)
-  timeval <- timeval + dt
+  if (totalrate != 0) {
+      dt <- stats::rexp(1, totalrate)
+      timeval <- timeval + dt
+  } else {
+      timeval <- total_time
+  }
   return(list(timeval = timeval, dt = dt))
 }
 
@@ -639,11 +643,16 @@ calc_next_timeval <- function(max_rates, timeval) {
 #' @author Joshua Lambert, Pedro Neves, Shu Xie
 calc_next_timeval_shift <- function(max_rates,
                                     timeval,
-                                    dynamic_shift_times) {
+                                    dynamic_shift_times,
+                                    total_time) {
   # testit::assert(timeval >= 0)
   totalrate <- max_rates[[1]] + max_rates[[2]] + max_rates[[3]] + max_rates[[4]]
-  dt <- stats::rexp(1, totalrate)
-  timeval <- timeval + dt
+  if (totalrate != 0) {
+    dt <- stats::rexp(1, totalrate)
+    timeval <- timeval + dt
+  } else {
+    timeval <- total_time
+  }
   rate_shift <- FALSE
 
   if (timeval >= dynamic_shift_times[1]) {
diff --git a/R/DAISIE_sim_core_cr.R b/R/DAISIE_sim_core_cr.R
index 5da5b211..41f1c514 100644
--- a/R/DAISIE_sim_core_cr.R
+++ b/R/DAISIE_sim_core_cr.R
@@ -74,12 +74,13 @@ DAISIE_sim_core_cr <- function(
 
     timeval_and_dt <- calc_next_timeval(
       max_rates = rates,
-      timeval = timeval
+      timeval = timeval,
+      total_time = total_time
     )
 
     timeval <- timeval_and_dt$timeval
 
-  if (timeval <= total_time) {
+  if (timeval < total_time) {
       rates <- update_rates(
         timeval = timeval,
         total_time = total_time,
diff --git a/R/DAISIE_sim_core_cr_shift.R b/R/DAISIE_sim_core_cr_shift.R
index 7379db30..02510dca 100644
--- a/R/DAISIE_sim_core_cr_shift.R
+++ b/R/DAISIE_sim_core_cr_shift.R
@@ -90,7 +90,8 @@ DAISIE_sim_core_cr_shift <- function(
     timeval_shift <- calc_next_timeval_shift(
       max_rates = rates,
       timeval = timeval,
-      dynamic_shift_times = dynamic_shift_times
+      dynamic_shift_times = dynamic_shift_times,
+      total_time = total_time
     )
 
     timeval <- timeval_shift$timeval
diff --git a/R/DAISIE_sim_core_time_dep.R b/R/DAISIE_sim_core_time_dep.R
index f1388641..ad65de6f 100644
--- a/R/DAISIE_sim_core_time_dep.R
+++ b/R/DAISIE_sim_core_time_dep.R
@@ -86,7 +86,8 @@ DAISIE_sim_core_time_dep <- function(
 
     timeval_and_dt <- calc_next_timeval(
       max_rates = max_rates,
-      timeval = timeval
+      timeval = timeval,
+      total_time = total_time
     )
     timeval <- timeval_and_dt$timeval
 
diff --git a/R/DAISIE_sim_core_trait_dep.R b/R/DAISIE_sim_core_trait_dep.R
index d35e5c87..65d68b3b 100644
--- a/R/DAISIE_sim_core_trait_dep.R
+++ b/R/DAISIE_sim_core_trait_dep.R
@@ -77,7 +77,8 @@ DAISIE_sim_core_trait_dep <- function(
     )
     timeval_and_dt <- calc_next_timeval(
       max_rates = rates,
-      timeval = timeval
+      timeval = timeval,
+      total_time = total_time
     )
     timeval <- timeval_and_dt$timeval
 
diff --git a/R/DAISIE_sim_trait_dep.R b/R/DAISIE_sim_trait_dep.R
index 4f575444..03481696 100644
--- a/R/DAISIE_sim_trait_dep.R
+++ b/R/DAISIE_sim_trait_dep.R
@@ -1,6 +1,6 @@
 #' @title Simulate islands with given trait-dependent parameters.
 #' @description This function simulates islands with given cladogenesis,
-#' extinction, K, immigration and anagenesis parameters for binary states.
+#' extinction, K, immigration and anagenesis parameters for binary trait states.
 #'
 #' Returns R list object that contains the simulated islands
 #'
@@ -8,7 +8,7 @@
 #'
 #' @return
 #' A list. The highest level of the least corresponds to each individual
-#' replciate. The first element of each replicate is composed of island
+#' replicate. The first element of each replicate is composed of island
 #' information containing:
 #' \itemize{
 #'   \item{\code{$island_age}: A numeric with the island age.}
@@ -115,7 +115,7 @@ DAISIE_sim_trait_dep <- function(
       }
       while (number_present < cond) {
         if(M == 0 || is.null(trait_pars)){
-          stop("One state exist on mainland, should use constant rate DAISIE.")
+          stop("One state exists on mainland, should use constant rate DAISIE.")
         }else{
           for (m_spec in 1:M) {
             ### M1 = 1, M2 = 0
diff --git a/R/DAISIE_utils.R b/R/DAISIE_utils.R
index da83b360..f02a1aa6 100644
--- a/R/DAISIE_utils.R
+++ b/R/DAISIE_utils.R
@@ -439,10 +439,12 @@ add_column_to_dataframe <- function(df, position, column_to_insert) {
   if(is.character(position)) {
     position <- which(names(df) == position)
   }
+  rn <- row.names(df)
   df <- data.frame(df[1:position],
                    nc = column_to_insert,
                    df[(position + 1):ncol(df)])
   names(df)[names(df) == 'nc'] <- names(column_to_insert)
+  row.names(df) <- rn
   return(df)
 }
 
diff --git a/R/default_params_doc.R b/R/default_params_doc.R
index 2ebaafe5..666d9502 100644
--- a/R/default_params_doc.R
+++ b/R/default_params_doc.R
@@ -420,6 +420,10 @@
 #'   incorrect output due to parameter transformation.
 #' @param num_cycles The number of cycles the optimizer will go through.
 #'   Default is 1.
+#' @param function_to_optimize Here one can indicate to use a function
+#'   ('DAISIE_approx') that approximates the DAISIE likelihood or the default
+#'   value 'DAISIE_exact'). The approximate likelihood can for example be used
+#'   in case the exact one fails.
 #' @param trait_pars A named list containing diversification rates considering
 #'   two trait states created by \code{\link{create_trait_pars}}:
 #' \itemize{
diff --git a/README.md b/README.md
index 67b5f693..963c7765 100644
--- a/README.md
+++ b/README.md
@@ -18,7 +18,7 @@ The model can be fitted to both empirical dated phylogenies and simulated data.
 
 * For an overview of the simulation functionality see [here](https://cran.r-project.org/web/packages/DAISIE/vignettes/demo_sim.html).
 * Details and an overview of the maximum likelihood inference capabilities to estimate parameters see [here](https://cran.r-project.org/web/packages/DAISIE/vignettes/demo_optimize.html).
-* For details on comparing between two diversity depedence models see [here](https://cran.r-project.org/web/packages/DAISIE/vignettes/demo_CSvsIW.html).
+* For details on comparing between two diversity dependence models see [here](https://cran.r-project.org/web/packages/DAISIE/vignettes/demo_CSvsIW.html).
 
 ## Installing DAISIE
 
diff --git a/data/frogs_sim_datalist.RData b/data/frogs_sim_datalist.RData
new file mode 100644
index 00000000..fa197a15
Binary files /dev/null and b/data/frogs_sim_datalist.RData differ
diff --git a/man/DAISIE_ML.Rd b/man/DAISIE_ML.Rd
index 3cf746dd..8004a6cf 100644
--- a/man/DAISIE_ML.Rd
+++ b/man/DAISIE_ML.Rd
@@ -30,7 +30,8 @@ DAISIE_ML_CS(
   verbose = 0,
   tolint = c(1e-16, 1e-10),
   jitter = 0,
-  num_cycles = 1
+  num_cycles = 1,
+  function_to_optimize = "DAISIE_exact"
 )
 }
 \arguments{
@@ -201,6 +202,11 @@ incorrect output due to parameter transformation.}
 
 \item{num_cycles}{The number of cycles the optimizer will go through.
 Default is 1.}
+
+\item{function_to_optimize}{Here one can indicate to use a function
+('DAISIE_approx') that approximates the DAISIE likelihood or the default
+value 'DAISIE_exact'). The approximate likelihood can for example be used
+in case the exact one fails.}
 }
 \value{
 The output is a dataframe containing estimated parameters and
diff --git a/man/DAISIE_ML1.Rd b/man/DAISIE_ML1.Rd
index 158de7c1..2cb61361 100644
--- a/man/DAISIE_ML1.Rd
+++ b/man/DAISIE_ML1.Rd
@@ -26,7 +26,8 @@ DAISIE_ML1(
   tolint = c(1e-16, 1e-10),
   island_ontogeny = NA,
   jitter = 0,
-  num_cycles = 1
+  num_cycles = 1,
+  function_to_optimize = "DAISIE_exact"
 )
 }
 \arguments{
@@ -184,6 +185,11 @@ incorrect output due to parameter transformation.}
 
 \item{num_cycles}{The number of cycles the optimizer will go through.
 Default is 1.}
+
+\item{function_to_optimize}{Here one can indicate to use a function
+('DAISIE_approx') that approximates the DAISIE likelihood or the default
+value 'DAISIE_exact'). The approximate likelihood can for example be used
+in case the exact one fails.}
 }
 \value{
 The output is a dataframe containing estimated parameters and
diff --git a/man/DAISIE_sim_trait_dep.Rd b/man/DAISIE_sim_trait_dep.Rd
index 1a3cb8e7..94cb76c8 100644
--- a/man/DAISIE_sim_trait_dep.Rd
+++ b/man/DAISIE_sim_trait_dep.Rd
@@ -153,7 +153,7 @@ same as `2` and prints intermediate progress during likelihood computation.}
 }
 \value{
 A list. The highest level of the least corresponds to each individual
-replciate. The first element of each replicate is composed of island
+replicate. The first element of each replicate is composed of island
 information containing:
 \itemize{
   \item{\code{$island_age}: A numeric with the island age.}
@@ -184,7 +184,7 @@ not sampled for particular clade (only applicable for endemic clades)}
 }
 \description{
 This function simulates islands with given cladogenesis,
-extinction, K, immigration and anagenesis parameters for binary states.
+extinction, K, immigration and anagenesis parameters for binary trait states.
 
 Returns R list object that contains the simulated islands
 }
diff --git a/man/calc_next_timeval.Rd b/man/calc_next_timeval.Rd
index 993ad3c1..def18a12 100644
--- a/man/calc_next_timeval.Rd
+++ b/man/calc_next_timeval.Rd
@@ -4,7 +4,7 @@
 \alias{calc_next_timeval}
 \title{Calculates when the next timestep will be.}
 \usage{
-calc_next_timeval(max_rates, timeval)
+calc_next_timeval(max_rates, timeval, total_time)
 }
 \arguments{
 \item{max_rates}{named list of max rates as returned by
diff --git a/man/calc_next_timeval_shift.Rd b/man/calc_next_timeval_shift.Rd
index 3e27b462..6860ca35 100644
--- a/man/calc_next_timeval_shift.Rd
+++ b/man/calc_next_timeval_shift.Rd
@@ -4,7 +4,7 @@
 \alias{calc_next_timeval_shift}
 \title{Calculates when the next timestep will be, and if a shift has occured.}
 \usage{
-calc_next_timeval_shift(max_rates, timeval, dynamic_shift_times)
+calc_next_timeval_shift(max_rates, timeval, dynamic_shift_times, total_time)
 }
 \arguments{
 \item{max_rates}{named list of max rates as returned by
diff --git a/man/default_params_doc.Rd b/man/default_params_doc.Rd
index 5665810c..9ce49557 100644
--- a/man/default_params_doc.Rd
+++ b/man/default_params_doc.Rd
@@ -737,6 +737,11 @@ DAISIEprep. Can also be simulated data generated with DAISIE_sim function.}
 \item{sort_clade_sizes}{Default sort_clade_sizes = T outputs clade sizes
 sorted in ascending order of number of species. sort_clade_sizes=F outputs
 clade sizes in the same order as they appear in the input datalist.}
+
+\item{function_to_optimize}{Here one can indicate to use a function
+('DAISIE_approx') that approximates the DAISIE likelihood or the default
+value 'DAISIE_exact'). The approximate likelihood can for example be used
+in case the exact one fails.}
 }
 \value{
 Nothing
diff --git a/man/frogs_sim_datalist.Rd b/man/frogs_sim_datalist.Rd
new file mode 100644
index 00000000..929c8365
--- /dev/null
+++ b/man/frogs_sim_datalist.Rd
@@ -0,0 +1,49 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/DAISIE_data.R
+\docType{data}
+\name{frogs_sim_datalist}
+\alias{frogs_sim_datalist}
+\title{Colonization and branching times of a data set simulated with the
+MLE parameters of frogs_datalist}
+\format{
+A list with the first element containing 2 elements and the following
+elements containing 5 components.
+}
+\source{
+Etienne RS, Haegeman B, Dugo-Cota A, Vila C, Gonzalez-Voyer A &
+Valente L. The limits to ecological limits to diversification.\cr
+}
+\description{
+A list containing the colonization and branching times
+of a simulated data set using the MLE parameters of IW model for the
+frogs_datalist. It is an R list object with the following elements.\cr \cr
+The first element of the list has two components: \cr \cr
+\code{$island_age} - the island age \cr
+\code{$not_present} - the number of mainland lineages that are not present
+on the island \cr \cr
+The following elements of the list each contains
+information on a single colonist lineage on the island and has 5
+components:\cr \cr
+\code{$colonist_name} - the name of the species or clade
+that colonized the island \cr
+\code{$branching_times} - island age followed by stem age of the population/species
+in the case of Non-endemic, Non-endemic_MaxAge species and Endemic species with no close
+relatives on the island. For endemic clades with more than one species on the island
+(cladogenetic clades/ radiations) these should be island age followed by the
+branching times of the island clade including the stem age of the clade.\cr
+\code{$stac} - the status of the colonist \cr \cr
+* Non_endemic_MaxAge: 1 \cr
+* Endemic: 2 \cr
+* Endemic&Non_Endemic: 3 \cr
+* Non_endemic: 4 \cr
+* Endemic_MaxAge: 5 or 6 \cr \cr
+\code{$missing_species} - number of island species
+that were not sampled for particular clade (only applicable for endemic
+clades) \cr
+\code{$type1or2} - whether the colonist belongs to type 1 or
+type 2. In this dataset all are equal to 1. \cr
+}
+\seealso{
+\code{\link{DAISIE_ML}}, \code{\link{DAISIE_SR_ML}}
+}
+\keyword{datasets}
diff --git a/tests/testthat/test-DAISIE_ML1.R b/tests/testthat/test-DAISIE_ML1.R
index 291e783f..7b32743d 100644
--- a/tests/testthat/test-DAISIE_ML1.R
+++ b/tests/testthat/test-DAISIE_ML1.R
@@ -1,8 +1,9 @@
 context("DAISIE_ML1")
 
-test_that("use", {
+test_that("DAISIE_ML1 works and simplex and subplex give the same answer", {
   skip_if(Sys.getenv("CI") == "", message = "Run only on CI")
   skip_on_cran()
+  set.seed(42)
   data(Galapagos_datalist)
   datalist <- Galapagos_datalist
   initparsopt <- c(2.5, 2.7, 20, 0.009, 1.01)
@@ -10,29 +11,60 @@ test_that("use", {
   idparsopt <- c(1,2,3,4,5)
   parsfix <- c()
   idparsfix <- c()
-    tested_MLE <- DAISIE_ML1(
-      datalist = datalist,
-      initparsopt = initparsopt,
-      idparsopt = idparsopt,
-      parsfix = parsfix,
-      ddmodel = ddmodel,
-      idparsfix = idparsfix,
-      verbose = 0,
-      tol = c(0.01, 0.1, 0.001),
-      res = 15,
-      tolint = c(0.1, 0.01)
-    )
+  tested_MLE1 <- DAISIE_ML1(
+    datalist = datalist,
+    initparsopt = initparsopt,
+    idparsopt = idparsopt,
+    parsfix = parsfix,
+    ddmodel = ddmodel,
+    idparsfix = idparsfix,
+    verbose = 0,
+    methode = 'odeint::runge_kutta_cash_karp54',
+    tol = c(1e-04, 1e-05, 1e-07),
+    res = 15,
+    tolint = c(1E-16, 1E-10),
+    optimmethod = 'subplex',
+    num_cycles = 4)
+  tested_MLE2 <- DAISIE_ML1(
+    datalist = datalist,
+    initparsopt = as.numeric(tested_MLE1[1:5]),
+    idparsopt = idparsopt,
+    parsfix = parsfix,
+    ddmodel = ddmodel,
+    idparsfix = idparsfix,
+    verbose = 0,
+    methode = 'odeint::runge_kutta_cash_karp54',
+    tol = c(1e-04, 1e-05, 1e-07),
+    res = 15,
+    tolint = c(1E-16, 1E-10),
+    optimmethod = 'simplex',
+    num_cycles = 1)
+  tested_MLE3 <- DAISIE_ML1(
+    datalist = datalist,
+    initparsopt = as.numeric(tested_MLE2[1:5]),
+    idparsopt = idparsopt,
+    parsfix = parsfix,
+    ddmodel = ddmodel,
+    idparsfix = idparsfix,
+    verbose = 0,
+    methode = 'odeint::runge_kutta_cash_karp54',
+    tol = c(1e-04, 1e-05, 1e-07),
+    res = 15,
+    tolint = c(1E-16, 1E-10),
+    optimmethod = 'subplex',
+    num_cycles = 1)
+  testthat::expect_equal(tested_MLE2, tested_MLE3, tolerance = 1E-6)
   expected_MLE <- data.frame(
-    lambda_c = 3.689104200780465,
-    mu = 4.31030299415995,
-    K = 906.6501180193454,
-    gamma = 0.0173458887696076,
-    lambda_a = 3.677789527566334,
-    loglik = -64.2199684450019,
+    lambda_c = 1.8704396748021859,
+    mu = 1.9365019587293075,
+    K = Inf,
+    gamma = 0.0073959695777554,
+    lambda_a = 1.1636058561427665,
+    loglik = -76.7923936480216014,
     df = 5L,
     conv = 0L
   )
-  testthat::expect_equal(tested_MLE, expected_MLE)
+  testthat::expect_equal(tested_MLE3, expected_MLE, tolerance = 1E-6)
 })
 
 test_that("abuse", {
diff --git a/tests/testthat/test-DAISIE_ML2.R b/tests/testthat/test-DAISIE_ML2.R
index 38635aa0..c310a0cc 100644
--- a/tests/testthat/test-DAISIE_ML2.R
+++ b/tests/testthat/test-DAISIE_ML2.R
@@ -19,38 +19,27 @@ test_that("use", {
       idparsopt = c(2, 4, 5, 6, 7),
       parsfix = c(0, Inf),
       idparsfix = c(1, 3),
+      methode = 'odeint::runge_kutta_cash_karp54',
       tol = c(0.01, 0.1, 0.001),
       res = 15,
-      tolint = c(0.1, 0.01),
+      tolint = c(1E-16, 1E-10),
       verbose = 0
     )
   expected_MLE <- data.frame(
     lambda_c = c(0.0,
-                 0.315015693879739,
+                 0.1198600880941345,
                  0.0,
                  0.0),
-    mu = c(2.67928476648249,
-           2.67928476648249,
-           2.67928476648249,
-           2.67928476648249),
-    K = c(Inf,
-          Inf,
-          Inf,
-          Inf),
-    gamma = c(0.141748213992604,
-              0.338044376412124,
-              0.141748213992604,
-              0.141748213992604),
-    lambda_a = c(1.10809210249609,
-                 1.10809210249609,
-                 1.10809210249609 ,
-                 1.10809210249609),
-    loglik = c(-409.60117813893,
-               -409.60117813893,
-               -409.60117813893,
-               -409.60117813893),
-    df = c(5L, 5L, 5L, 5L),
-    conv = c(0L, 0L, 0L, 0L)
+    mu = rep(1.0604828698048443,4),
+    K = rep(Inf,4),
+    gamma = c(0.0544106971300572,
+              0.1706160417441286,
+              0.0544106971300572,
+              0.0544106971300572),
+    lambda_a = rep(0.4749396123469573,4),
+    loglik = rep(-449.6525311168169310,4),
+    df = rep(5L,4),
+    conv = rep(0L,4)
   )
   testthat::expect_equal(tested_MLE, expected_MLE)
 })
diff --git a/tests/testthat/test-DAISIE_format_IW.R b/tests/testthat/test-DAISIE_format_IW.R
index d257aa3a..fcdfab0e 100644
--- a/tests/testthat/test-DAISIE_format_IW.R
+++ b/tests/testthat/test-DAISIE_format_IW.R
@@ -94,11 +94,11 @@ test_that("silent with non-empty island with correct output", {
   brts_table <- matrix(ncol = 5, nrow = 6)
   colnames(brts_table) <- c("brt", "clade", "event", "endemic", "col")
   brts_table[1, ] <- c(1, 0, 0, NA, NA)
-  brts_table[2, ] <- c(0.9244818166871660, 1, 1, 1, NA)
-  brts_table[3, ] <- c(0.9105856673960619, 1, 2, 1, NA)
-  brts_table[4, ] <- c(0.5557734125062590, 2, 1, 0, NA)
-  brts_table[5, ] <- c(0.5288428248966160, 3, 1, 0, NA)
-  brts_table[6, ] <- c(0.3146835586399670, 1, 3, 1, NA)
+  brts_table[2, ] <- c(0.9244818166871660, 1, 1, 1, 1)
+  brts_table[3, ] <- c(0.9105856673960619, 1, 2, 1, 1)
+  brts_table[4, ] <- c(0.5557734125062590, 2, 1, 0, 1)
+  brts_table[5, ] <- c(0.5288428248966160, 3, 1, 0, 1)
+  brts_table[6, ] <- c(0.3146835586399670, 1, 3, 1, 1)
   expected_IW_format[[1]][[1]] <- list(island_age = 1,
                                        not_present = 7,
                                        stt_all = stt_all,
@@ -255,8 +255,8 @@ test_that("silent with non-empty nonoceanic island with
             brts_table <- matrix(ncol = 5, nrow = 3)
             colnames(brts_table) <- c("brt", "clade", "event", "endemic", "col")
             brts_table[1, ] <- c(1, 0, 0, NA, NA)
-            brts_table[2, ] <- c(1, 2, 1, 1, NA)
-            brts_table[3, ] <- c(1, 1, 1, 1, NA)
+            brts_table[2, ] <- c(1, 2, 1, 1, 1)
+            brts_table[3, ] <- c(1, 1, 1, 1, 1)
             expected_IW_format[[1]][[1]] <- list(island_age = 1,
                                                  not_present = 8,
                                                  stt_all = stt_all,
@@ -316,8 +316,8 @@ test_that("silent with non-empty nonoceanic island with
             brts_table <- matrix(ncol = 5, nrow = 3)
             colnames(brts_table) <- c("brt", "clade", "event", "endemic", "col")
             brts_table[1, ] <- c(1, 0, 0, NA, NA)
-            brts_table[2, ] <- c(1, 2, 1, 1, NA)
-            brts_table[3, ] <- c(1, 1, 1, 1, NA)
+            brts_table[2, ] <- c(1, 2, 1, 1, 1)
+            brts_table[3, ] <- c(1, 1, 1, 1, 1)
             expected_IW_format[[1]][[1]] <- list(island_age = 1,
                                                  not_present = 8,
                                                  stt_all = stt_all,
@@ -385,10 +385,10 @@ test_that("add_brt_table output is correct when length(island) != 1", {
   brt_table <- matrix(ncol = 5, nrow = 5)
   colnames(brt_table) <- c("brt", "clade", "event", "endemic", "col")
   brt_table[1, ] <- c(1, 0, 0, NA, NA)
-  brt_table[2, ] <- c(0.9244818, 1, 1, 1, NA)
-  brt_table[3, ] <- c(0.9105857, 1, 2, 1, NA)
-  brt_table[4, ] <- c(0.5557734, 2, 1, 0, NA)
-  brt_table[5, ] <- c(0.3146836, 1, 3, 1, NA)
+  brt_table[2, ] <- c(0.9244818, 1, 1, 1, 1)
+  brt_table[3, ] <- c(0.9105857, 1, 2, 1, 1)
+  brt_table[4, ] <- c(0.5557734, 2, 1, 0, 1)
+  brt_table[5, ] <- c(0.3146836, 1, 3, 1, 1)
   expected_brt <- list()
   expected_brt[[1]] <- list(island_age = 1,
                             not_present = 3,
@@ -540,9 +540,9 @@ test_that("silent when species with two trait states with
             brts_table <- matrix(ncol = 5, nrow = 4)
             colnames(brts_table) <- c("brt", "clade", "event", "endemic", "col")
             brts_table[1, ] <- c(5.00000000000000, 0, 0, NA, NA)
-            brts_table[2, ] <- c(3.10261367452990, 1, 1, 1, NA)
-            brts_table[3, ] <- c(1.50562999775257, 2, 1, 1, NA)
-            brts_table[4, ] <- c(1.26245655913561, 2, 2, 1, NA)
+            brts_table[2, ] <- c(3.10261367452990, 1, 1, 1, 1)
+            brts_table[3, ] <- c(1.50562999775257, 2, 1, 1, 1)
+            brts_table[4, ] <- c(1.26245655913561, 2, 2, 1, 1)
             expected_IW_format[[1]][[1]] <- list(island_age = 5,
                                                  not_present = 13,
                                                  stt_all = stt_all,
diff --git a/tests/testthat/test-DAISIE_format_IW_full_stt.R b/tests/testthat/test-DAISIE_format_IW_full_stt.R
index 6cd03312..6b5f6a31 100644
--- a/tests/testthat/test-DAISIE_format_IW_full_stt.R
+++ b/tests/testthat/test-DAISIE_format_IW_full_stt.R
@@ -67,7 +67,7 @@ test_that("complete stt, 1 type, no geodynamics, oceanic island, one trait state
     c(Time = 0.0, nI = 0.0, nA = 1.0, nC = 0.0)
   )
   expected_brts_table <- matrix(
-    c(1.0, 0.24481816687165, 0, 1, 0, 1, NA, 1, NA, NA),
+    c(1.0, 0.24481816687165, 0, 1, 0, 1, NA, 1, NA, 1),
     nrow = 2
   )
   colnames(expected_brts_table) <- c("brt", "clade", "event", "endemic", "col")
@@ -109,7 +109,7 @@ test_that("complete stt, 1 type, no geodynamics, oceanic island, one trait state
   )
 
   expected_brts_table <- matrix(
-    c(1.0, 0.741771912202239, 0, 1, 0, 1, NA, 0, NA, NA),
+    c(1.0, 0.741771912202239, 0, 1, 0, 1, NA, 0, NA, 1),
     nrow = 2
   )
   colnames(expected_brts_table) <- c("brt", "clade", "event", "endemic", "col")
@@ -245,7 +245,7 @@ test_that("complete stt, 1 type, geodynamics, oceanic island, one trait state
   )
   testthat::expect_equal(
     formatted_IW_sim[[1]][[1]]$brts_table[5, ],
-    c(brt = 0.83094531417507, clade = 4, event = 1, endemic = 1, col = NA)
+    c(brt = 0.83094531417507, clade = 4, event = 1, endemic = 1, col = 1)
   )
 
 })
diff --git a/tests/testthat/test-DAISIE_format_IW_sampled_stt.R b/tests/testthat/test-DAISIE_format_IW_sampled_stt.R
index 34ff22bf..8424f9a4 100644
--- a/tests/testthat/test-DAISIE_format_IW_sampled_stt.R
+++ b/tests/testthat/test-DAISIE_format_IW_sampled_stt.R
@@ -59,9 +59,9 @@ test_that("sampled stt, 1 type, no geodynamics, oceanic island (same arguments a
   expected_brts_table <- matrix(
     data = c(
       1.0, 0.0, 0.0, NA, NA,
-      0.244818166871655, 1, 1, 1, NA,
-      0.173128288990374, 1, 2, 1, NA,
-      0.029668240213840, 1, 3, 1, NA
+      0.244818166871655, 1, 1, 1, 1,
+      0.173128288990374, 1, 2, 1, 1,
+      0.029668240213840, 1, 3, 1, 1
     ),
     ncol = 5,
     byrow = TRUE
diff --git a/tests/testthat/test-integration_DAISIE.R b/tests/testthat/test-integration_DAISIE.R
index 857af43a..fd29255f 100644
--- a/tests/testthat/test-integration_DAISIE.R
+++ b/tests/testthat/test-integration_DAISIE.R
@@ -100,6 +100,99 @@ test_that("IW and CS loglik is same when K = Inf", {
   testthat::expect_equal(loglik_IW, loglik_CS, tol = 5E-6)
 })
 
+test_that("IW loglik is correct", {
+  skip_if(Sys.getenv("CI") == "" && !(Sys.getenv("USERNAME") == "rampa"),
+          message = "Run only on CI")
+  skip_on_cran()
+  frogs_datalist <- NULL
+  rm(frogs_datalist)
+  data(frogs_datalist, package = "DAISIE")
+  M <- 1000
+  frogs_datalist[[1]]$not_present <- frogs_datalist[[1]]$not_present + (M - 300)
+  ddmodel <- 11
+  initparsopt <- c(4.012298e-01,1.699521e-01,1.319595e+02,3.487955e-04)
+  idparsopt <- c(1,2,3,4)
+  parsfix <- 0
+  idparsfix <- 5
+  verbose <- 1
+  cond <- 1
+  res <- 200
+  methode <- 'odeint::runge_kutta_fehlberg78'
+  tolint <- c(1E-16, 1E-14)
+
+  trparsopt <- initparsopt / (1 + initparsopt)
+  trparsopt[which(initparsopt == Inf)] <- 1
+  trparsfix <- parsfix / (1 + parsfix)
+  trparsfix[which(parsfix == Inf)] <- 1
+  pars2 <- c(res, ddmodel, cond, verbose)
+  initloglik_IW <- DAISIE_loglik_IW_choosepar(trparsopt = trparsopt,
+                                              trparsfix = trparsfix,
+                                              idparsopt = idparsopt,
+                                              idparsfix = idparsfix,
+                                              M = M,
+                                              pars2 = pars2,
+                                              datalist = frogs_datalist,
+                                              methode = methode,
+                                              abstolint = tolint[1],
+                                              reltolint = tolint[2])
+
+  testthat::expect_equal(initloglik_IW, -215.097677998973, tol = 1E-6)
+})
+
+test_that("IW loglik does not error when there is recolonization", {
+  skip_if(Sys.getenv("CI") == "" && !(Sys.getenv("USERNAME") == "rampa"),
+          message = "Run only on CI")
+  skip_on_cran()
+  frogs_sim_datalist <- NULL
+  rm(frogs_sim_datalist)
+  data(frogs_sim_datalist, package = "DAISIE")
+  #This is data set 897 from the CS simulated data sets
+  M <- 1000
+  ddmodel <- 11
+  initparsopt <- c(4.012298e-01,1.699521e-01,1.319595e+02,3.487955e-04)
+  idparsopt <- c(1,2,3,4)
+  parsfix <- 0
+  idparsfix <- 5
+  verbose <- 1
+  cond <- 1
+  res <- 200
+  methode <- 'odeint::runge_kutta_fehlberg78'
+  tolint <- c(1E-16, 1E-14)
+
+  trparsopt <- initparsopt / (1 + initparsopt)
+  trparsopt[which(initparsopt == Inf)] <- 1
+  trparsfix <- parsfix / (1 + parsfix)
+  trparsfix[which(parsfix == Inf)] <- 1
+  pars2 <- c(res, ddmodel, cond, verbose)
+  initloglik_IW <- DAISIE_loglik_IW_choosepar(trparsopt = trparsopt,
+                                              trparsfix = trparsfix,
+                                              idparsopt = idparsopt,
+                                              idparsfix = idparsfix,
+                                              M = M,
+                                              pars2 = pars2,
+                                              datalist = frogs_sim_datalist,
+                                              methode = methode,
+                                              abstolint = tolint[1],
+                                              reltolint = tolint[2])
+
+  testthat::expect_equal(initloglik_IW, -244.7340301475871911, tol = 1E-6)
+
+  frogs_sim_datalist2 <- frogs_sim_datalist
+  frogs_sim_datalist2[[2]]$all_colonisations[[2]]$event_times <- c(frogs_sim_datalist2[[2]]$all_colonisations[[2]]$event_times, 5)
+  initloglik_IW <- DAISIE_loglik_IW_choosepar(trparsopt = trparsopt,
+                                              trparsfix = trparsfix,
+                                              idparsopt = idparsopt,
+                                              idparsfix = idparsfix,
+                                              M = M,
+                                              pars2 = pars2,
+                                              datalist = frogs_sim_datalist2,
+                                              methode = methode,
+                                              abstolint = tolint[1],
+                                              reltolint = tolint[2])
+
+  testthat::expect_equal(initloglik_IW, -246.8143677718335880, tol = 1E-6)
+})
+
 test_that("DAISIE_ML simple case works", {
   skip_if(Sys.getenv("CI") == "" && !(Sys.getenv("USERNAME") == "rampa"),
           message = "Run only on CI")
@@ -231,6 +324,25 @@ test_that("DAISIE_ML with nonzero probability of initial presence gives
   testthat::expect_false(isTRUE(all.equal(tested_mle_zero, tested_mle_nonzero)))
 })
 
+test_that("DAISIE_ML gives a -Inf loglikelhood when probability of initial
+          presence is nonzero and colonization rate equals 0 for Galapagos", {
+            skip_if(Sys.getenv("CI") == "" && !(Sys.getenv("USERNAME") == "rampa"),
+                    message = "Run only on CI")
+            skip_on_cran()
+
+            utils::data(Galapagos_datalist)
+            tested_mle <- DAISIE_ML(
+                datalist = Galapagos_datalist,
+                initparsopt = c(2.5, 2.7, 20, 0, 1.01, 0.001),
+                ddmodel = 11,
+                idparsopt = 1:6,
+                parsfix = NULL,
+                idparsfix = NULL
+            )
+            testthat::expect_true(is.na(tested_mle$loglik))
+          })
+
+
 test_that("DAISIE_ML simple case works with estimating probability of initial
           presence", {
             skip_if(Sys.getenv("CI") == "" && !(Sys.getenv("USERNAME") == "rampa"),
diff --git a/vignettes/demo_CSvsIW.R b/vignettes/demo_CSvsIW.R
index c09231b0..25992bf1 100644
--- a/vignettes/demo_CSvsIW.R
+++ b/vignettes/demo_CSvsIW.R
@@ -87,21 +87,21 @@ readRDS(file = system.file("extdata", "frog_M1_ML.rds", package = "DAISIE", must
 ## ----DAISIE_sim_CS, results='hide'--------------------------------------------
 set.seed(1)
 frog_sims_CS <- DAISIE_sim_cr(
-  time=30,
-  M=300,
-  pars=c(0.44,0.11,36.44,0.0007,0),
+  time = 30,
+  M = 300,
+  pars = c(0.44, 0.11, 36.44, 0.0007, 0),
   divdepmodel = "CS",
-  replicates= 100,
+  replicates = 100,
   plot_sims = FALSE)
 
 ## ----DAISIE_sim_IW, results='hide'--------------------------------------------
 set.seed(1)
 frog_sims_CS <- DAISIE_sim_cr(
-  time=30,
-  M=300,
-  pars=c(0.40,0.17,131.83,0.0012,0),
+  time = 30,
+  M = 300,
+  pars = c(0.40, 0.17, 131.83, 0.0012, 0),
   divdepmodel = "IW",
-  replicates= 100,
+  replicates = 100,
   plot_sims = FALSE)
 
 ## ---- echo=TRUE---------------------------------------------------------------