# Model biogeographic range evolution

#### Maël Doré

#### 2026-01-13

This vignette presents the different options available to model biogeographic data = range evolution = biogeographic history within deepSTRAPP.

It builds mainly upon functions from R package `[BioGeoBEARS]` to offer a simplified framework to model and visualize biogeographic range evolution on a time-calibrated phylogeny.
Please, cite also the initial R package if you are using deepSTRAPP for this purpose.

For an example with continuous data, see this vignette: `vignette("model_continuous_trait_evolution")`

For an example with categorical data, see this vignette: `vignette("model_categorical_trait_evolution")`

The R package `BioGeoBEARS` is needed for this workflow to process biogeographic data.
Please install it manually from: https://github.com/nmatzke/BioGeoBEARS.

    # ------ Step 0: Load data ------ #

    ## Load phylogeny and tip data

    library(phytools)
    data(eel.tree)
    data(eel.data)
    # Dataset of feeding mode and maximum total length from 61 species of elopomorph eels.
    # Source: Collar, D. C., P. C. Wainwright, M. E. Alfaro, L. J. Revell, and R. S. Mehta (2014)
    # Biting disrupts integration to spur skull evolution in eels. Nature Communications, 5, 5505.

    # Transform feeding mode data into biogeographic data with ranges A, B, and AB.
    # This is NOT actual biogeographic data, but data fake generated for the sake of example!
    eel_range_tip_data <- stats::setNames(eel.data$feed_mode, rownames(eel.data))
    eel_range_tip_data <- as.character(eel_range_tip_data)
    eel_range_tip_data[eel_range_tip_data == "bite"] <- "A"
    eel_range_tip_data[eel_range_tip_data == "suction"] <- "B"
    eel_range_tip_data[c(5, 6, 7, 15, 25, 32, 33, 34, 50, 52, 57, 58, 59)] <- "AB"
    eel_range_tip_data <- stats::setNames(eel_range_tip_data, rownames(eel.data))
    table(eel_range_tip_data)

    # Here, the input date is a vector of character strings with tip.label as names, and range data as values.
    # Range coding scheme must follow the coding scheme used in BioGeoBEARS:
      # Unique areas must be in CAPITAL letters (e.g., "A", "B")
      # Ranges encompassing multiple areas are formed in combining unique area letters
      # in alphabetic order (e.g., "AB", "BC", "ABC")
    eel_range_tip_data

    ## Convert into binary presence/absence matrix

    # deepSTRAPP also accept biogeographic data as binary presence/absence matrix or data.frame
    # Here is the equivalent biogeographic data converted into a valid binary presence/absence matrix

    # Extract ranges
    all_ranges <- levels(as.factor(eel_range_tip_data))
    # Order in number of areas x alphabetic order (i.e., single areas, then 2-area ranges, etc.)
    unique_areas <- all_ranges[nchar(all_ranges) == 1]
    unique_areas <- unique_areas[order(unique_areas)]
    multi_area_ranges <- setdiff(all_ranges, unique_areas)
    multi_area_ranges <- multi_area_ranges[order(multi_area_ranges)]
    all_ranges_ordered <- c(unique_areas, multi_area_ranges)
    # Create template matrix only with unique areas
    eel_range_binary_matrix <- matrix(data = 0,
                                      nrow = length(eel_range_tip_data),
                                      ncol = length(unique_areas),
                                      dimnames = list(names(eel_range_tip_data), unique_areas))
    # Fill with presence/absence data
    for (i in seq_along(eel_range_tip_data))
    {
      # i <- 1

      # Extract range for taxa i
      range_i <- eel_range_tip_data[i]
      # Decompose range in unique areas
      all_unique_areas_in_range_i <- unlist(strsplit(x = range_i, split = ""))
      # Record match in eel_range_tip_data vector
      eel_range_binary_matrix[i, all_unique_areas_in_range_i] <- 1
    }
    eel_range_binary_matrix

    # Rows are taxa. Columns are unique areas. Values are presence/absence recorded in each area with '0/1'.
    # Taxa with multi-area ranges (i.e., encompassing multiple unique areas)
    # have multiple '1' in the same row.

    ## Check that trait tip data and phylogeny are named and ordered similarly
    all(names(eel_range_tip_data) == eel.tree$tip.label)
    all(row.names(eel_range_binary_matrix) == eel.tree$tip.label)

    # Reorder tip_data as in phylogeny
    eel_range_tip_data <- eel_range_tip_data[eel.tree$tip.label]
    # Reorder eel_range_binary_matrix as in phylogeny
    eel_range_binary_matrix <- eel_range_binary_matrix[eel.tree$tip.label, ]

    ## Set colors per ranges
    colors_per_ranges <- c("dodgerblue3", "gold")
    names(colors_per_ranges) <- c("A", "B")

    # If you provide only colors for unique areas (e.g., "A", "B"), the colors of multi-area ranges
    # will be interpolated (e.g., "AB")
    # In this example, using types of blue and yellow for range "A" and "B" respectively
    # will yield a type of green for multi-area range "AB".

    # ------ Step 1: Prepare biogeographic data ------ #

    ## Goal: Map biogeographic range evolution on the time-calibrated phylogeny

    # 1.1/ Fit biogeographic evolutionary models to trait data using Maximum Likelihood.
    # 1.2/ Select the best fitting model comparing AICc.
    # 1.3/ Infer ancestral characters estimates (ACE) of ranges at nodes.
    # 1.4/ Run Biogeographic Stochastic Mapping (BSM) simulations to generate biogeographic histories
    #      compatible with the best model and inferred ACE.
    # 1.5/ Infer ancestral ranges along branches.
    #  - Compute posterior frequencies of each range to produce a `densityMap` for each range.

    library(deepSTRAPP)

    # All these actions are performed by a single function: deepSTRAPP::prepare_trait_data()
    ?deepSTRAPP::prepare_trait_data()
    # Model selection is performed internally with deepSTRAPP::select_best_model_from_geiger()
    ?deepSTRAPP::select_best_model_from_geiger()
    # Plotting of all densityMaps as a unique phylogeny is carried out
    # with deepSTRAPP::plot_densityMaps_overlay()
    ?deepSTRAPP::plot_densityMaps_overlay()

    ## The R package `BioGeoBEARS` is needed for this workflow to process biogeographic data.
    ## Please install it manually from: https://github.com/nmatzke/BioGeoBEARS.

    ## Macroevolutionary models for biogeographic data

    # For more in-depth information on the models available see the R package [BioGeoBEARS]
    # See the associated website: http://phylo.wikidot.com/biogeobears

    ## Parameters in BioGeoBEARS

    # Biogeographic models are based on a set of biogeographic events defined by a set of parameters

      ## Anagenetic events = occurring along branches
      # d = dispersal rate = anagenetic range extension. Ex: A -> AB
      # e = extinction rate = anagenetic range contraction. Ex: AB -> A

      ## Cladogenetic events = occurring at speciation
      # y = Non-transitional speciation relative weight = cladogenetic inheritance.
        # Ex: Narrow inheritance: A -> (A),(A); Wide-spread sympatric speciation: AB -> (AB),(AB)
      # v = Vicariance relative weight = cladogenetic vicariance.
        # Ex: Narrow vicariance: AB -> (A),(B); Wide-vicariance: ABCD -> (AB),(CD)
      # s = Subset speciation relative weight = cladogenetic sympatric speciation.
        # Ex: AB -> (AB),(A)
      # j = Jump-dispersal relative weight = cladogenetic founder-event.
        # Ex: A -> (A),(B)

    ## 6 models from BioGeoBEARS are available

     # "BAYAREALIKE": BAYAREALIKE is a likelihood interpretation of the Bayesian implementation
     # of BAYAREA model, and it is "like BAYAREA".
        # It is the "simpler" model, that allows the least types of biogeographic events to occur.
        # Nothing is happening during cladogenesis. Only inheritance of previous range (y = 1).
          # Allows narrow and wide-spread sympatric speciation: A -> (A),(A); AB => (AB),(AB)
        # No narrow or wide vicariance (v = 0)
        # No subset sympatric speciation (s = 0)
        # No jump dispersal (j = 0)
        # Model has 2 free parameters = d (range extension), e (range contraction).

     # "DIVALIKE": DIVALIKE is a likelihood interpretation of parsimony DIVA, and it is "like DIVA".
        # Compared to BAYAREALIKE, it allows vicariance events to occur during speciation.
        # Allows narrow sympatric speciation (y): A -> (A),(A)
          # Does NOT allow wide-spread sympatric speciation.
        # Allows and narrow AND wide-spread vicariance (v): AB -> (A),(B); ABCD -> (AB),(CD)
        # No subset sympatric speciation (s = 0)
        # No jump dispersal (j = 0)
        # Relative weights of y and v are fixed to 1.
        # Model has 2 free parameters = d (range extension), e (range contraction).

     # "DEC": Dispersal-Extinction-Cladogenesis model. This is the default model in deepSTRAPP.
        # Compared to BAYAREALIKE, it allows subset speciation (s) to occur,
        # but it does not allows wide-spread vicariance.
        # Allows narrow sympatric speciation (y): A -> (A),(A)
          # Does NOT allow wide-spread sympatric speciation.
        # Allows narrow vicariance (v): AB -> (A),(B)
          # Does NOT allow wide-spread vicariance.
        # Allows subset sympatric speciation: AB -> (AB),(A)
        # No jump dispersal (j = 0)
        # Relative weights of y, v, and s are fixed to 1.
        # Model has 2 free parameters = d (range extension), e (range contraction).

     # "...+J": All previous models can add jump-dispersal events with the parameter j.
        # Allows jump-dispersal events to occur at speciation: A -> (A),(B)
          # Depicts cladogenetic founder events where a small population disperse to a new area.
          # Isolation results in speciation of the two populations in distinct lineages
          # occurring in two different areas.
        # Relative weights of y,v,s are fixed to 1-j ("BAYAREALIKE+J"), 2-j ("DIVALIKE+J"), or 3-j ("DEC+J").
        # Models have only 3 free parameters = d (range extension), e (range contraction),
        # and j (jump dispersal).

    ## Model trait data evolution
    eel_biogeo_data <- prepare_trait_data(
         tip_data = eel_range_tip_data,
         # Alternative input using the binary presence/absence range matrix
         # tip_data = eel_range_binary_matrix,
         trait_data_type = "biogeographic",
         phylo = eel.tree,
         seed = 1234, # Set seed for reproducibility
         # All models available
         evolutionary_models = c("BAYAREALIKE", "DIVALIKE", "DEC", "BAYAREALIKE+J", "DIVALIKE+J", "DEC+J"),
         # To provide link to the directory folder where the outputs of BioGeoBEARS will be saved
         BioGeoBEARS_directory_path = "./BioGeoBEARS_directory/",
         # Whether to save BioGeoBEARS intermediate files, or remove them after the run
         keep_BioGeoBEARS_files = TRUE,
         prefix_for_files = "eel", # Prefixe used to save BioGeoBEARS intermediate files
         # To set the number of core to use for computation.
         # Parallelization over multiple cores may speed up the process.
         nb_cores = 1,
         # To define the maximum number of unique areas in ranges. Ex: "AB" = 2; "ABC" = 3.
         max_range_size = 2,
         split_multi_area_ranges = TRUE, # Set to TRUE to display the two outputs
         res = 100, # To set the resolution of the continuous mapping of ranges on the densityMaps
         colors_per_levels = colors_per_ranges,
         # Reduce the number of Stochastic Mapping simulations to save time (Default = '1000')
         nb_simulations = 100,
         # Plot the densityMaps with plot_densityMaps_overlay() to show all ranges at once.
         plot_overlay = TRUE,
         # PDF_file_path = "./eel_biogeo_evolution_mapped_on_phylo.pdf",
         # To include Ancestral Character Estimates (ACE) of ranges at nodes in the output
         return_ace = TRUE,
         # To include the lists of cladogenetic and anagenetic events produced with BioGeoBEARS::runBSM()
         return_BSM = FALSE,
         # To include the Biogeographic Stochastic Mapping simulations (simmaps) in the output
         return_simmaps = TRUE,
         # To include the best model fit in the output
         return_best_model_fit = TRUE,
         # To include the df for model selection in the output
         return_model_selection_df = TRUE,
         verbose = TRUE) # To display progress

    # ------ Step 2: Explore output ------ #

    ## Explore output
    str(eel_biogeo_data, 1)

    ## Extract the densityMaps showing posterior probabilities of ranges on the phylogeny
    ## as estimated from the model
    eel_densityMaps <- eel_biogeo_data$densityMaps

    # Because we selected 'split_multi_area_ranges = TRUE',
    # those densityMaps only record posterior probability of presence in the two unique areas "A" and "B".
    # Probability of presences in multi-area range "AB" have been equally split between "A" and "B".
    # This is useful when you wish to test for differences in rates
    # between unique areas only (e.g., "A" and "B").

    # densityMaps including all ranges are also available in the output
    eel_densityMaps_all_ranges <- eel_biogeo_data$densityMaps_all_ranges
    # If you wish to test for differences across all types of ranges (e.g., "A", "B", and "AB"),
    # you need to use these densityMaps, or set 'split_multi_area_ranges = FALSE'
    # such as no split of multi-area ranges is performed, and the densityMaps contains all ranges by default.

    ## Plot densityMap for each range
    # Grey represents absence of the range. Color represents presence of the range.
    plot(eel_densityMaps_all_ranges[[1]]) # densityMap for range n°1 ("A")
    plot(eel_densityMaps_all_ranges[[2]]) # densityMap for range n°2 ("B")
    plot(eel_densityMaps_all_ranges[[3]]) # densityMap for range n°3 ("AB")

    ## Plot all densityMaps overlaid in on a single phylogeny
    # Each color highlights presence of its associated range.

    # Plot densityMaps considering only unique areas
    plot_densityMaps_overlay(eel_densityMaps)
    # Plot densityMaps with all ranges, including multi-area ranges
    plot_densityMaps_overlay(eel_densityMaps_all_ranges)

    # The densityMaps are the main input needed to perform a deepSTRAPP run on categorical trait data.

    ## Extract the Ancestral Character Estimates (ACE) = trait values at nodes

    # Only with unique areas
    eel_ACE <- eel_biogeo_data$ace
    head(eel_ACE)

    # Including multi-area ranges (Here, "AB")
    eel_ACE_all_ranges <- eel_biogeo_data$ace_all_ranges
    head(eel_ACE_all_ranges)

    # This is a matrix of numerical values with row.names = internal node ID,
    # colnames = ancestral ranges and values = posterior probability.
    # It can be used as an optional input in deepSTRAPP run to provide
    # perfectly accurate estimates for ancestral ranges at internal nodes.

    ## Explore summary of model selection
    eel_biogeo_data$model_selection_df # Summary of model selection
    # Models are compared using the corrected Akaike's Information Criterion (AICc)
    # Akaike's weights represent the probability that a given model is the best
    # among the set of candidate models, given the data.
    # Here, the best model is the "DEC+J" model

    ## Explore best model fit (DEC+J model)
    # Summary of best model optimization by BioGeoBEARS::bears_optim_run()
    str(eel_biogeo_data$best_model_fit, 1)
    # Parameter estimates and likelihood optimization information
    eel_biogeo_data$best_model_fit$optim_result
      # p1 = d = dispersal rate = anagenetic range extension. Ex: A -> AB
      # p2 = e = extinction rate = anagenetic range contraction. Ex: AB -> A
      # p3 = j = jump-dispersal relative weight = cladogenetic founder-event. Ex: A -> (A),(B)

    ## Explore Biogeographic Stochastic Mapping outputs from BioGeoBEARS::runBSM()
    # Since we selected 'return_BSM = TRUE', lists of cladogenetic and anagenetic events produced
    # with BioGeoBEARS::runBSM() are included in the output
    ?BioGeoBEARS::runBSM()

    # This element contains two lists of data.frames summarizing cladogenetic
    # and anagenetic events occurring all BSM simulations.
    # Each simulation yields a data.frame for each list.
    str(eel_biogeo_data$BSM_output, 1)

    # Example: Cladogenetic event summary for simulation n°1
    head(eel_biogeo_data$BSM_output$RES_clado_events_tables[[1]])
    # Example: Anagenetic event summary for simulation n°1
    head(eel_biogeo_data$BSM_output$RES_ana_events_tables[[1]])

    ## Explore simmaps
    # Since we selected 'return_simmaps = TRUE',
    # Stochastic Mapping simulations (simmaps) are included in the output
    # Each simmap represents a simulated evolutionary history with final ranges
    # compatible with the tip_data and estimated ACE at nodes.
    # Each simmap also follows the transition parameters of the best fit model
    # to simulate transitions along branches.

    # Update color_per_ranges to include the color interpolated for range "AB"
    AB_color_gradient <- eel_densityMaps_all_ranges$Density_map_AB$cols
    AB_color <- AB_color_gradient[length(AB_color_gradient)]

    colors_per_all_ranges <- c(colors_per_ranges, AB_color)
    names(colors_per_all_ranges) <- c("A", "B", "AB")

    # Plot simmap n°1 using the same color scheme as in densityMaps
    plot(eel_biogeo_data$simmaps[[1]], colors = colors_per_all_ranges, fsize = 0.7)
    # Plot simmap n°10 using the same color scheme as in densityMaps
    plot(eel_biogeo_data$simmaps[[10]], colors = colors_per_all_ranges, fsize = 0.7)
    # Plot simmap n°100 using the same color scheme as in densityMaps
    plot(eel_biogeo_data$simmaps[[100]], colors = colors_per_all_ranges, fsize = 0.7)

    ## Inputs needed to run deepSTRAPP are the densityMaps (eel_densityMaps),
    ## and optionally, the tip_data (eel_tip_data), and the ACE (eel_ACE)

    #>                       model     logLk k      AIC     AICc delta_AICc
    #> BAYAREALIKE     BAYAREALIKE -80.93972 2 165.8794 165.9484  40.467618
    #> DIVALIKE           DIVALIKE -63.80815 2 131.6163 131.6853   6.204488
    #> DEC                     DEC -63.83295 2 131.6659 131.7349   6.254083
    #> BAYAREALIKE+J BAYAREALIKE+J -66.46193 3 138.9239 139.1344  13.653595
    #> DIVALIKE+J       DIVALIKE+J -60.28105 3 126.5621 126.7726   1.291847
    #> DEC+J                 DEC+J -59.63513 3 125.2703 125.4808   0.000000
    #>               Akaike_weights rank
    #> BAYAREALIKE              0.0    6
    #> DIVALIKE                 2.8    3
    #> DEC                      2.7    4
    #> BAYAREALIKE+J            0.1    5
    #> DIVALIKE+J              32.5    2
    #> DEC+J                   62.0    1