# Analyzing FBD Parameters

#### 2025-08-27

This vignette explains how to extract, plot, and statistically test for differences among BD (Birth-Death) or FBD (fossilized birth-death) parameters (e.g., net diversification, relative extinction (turnover), and relative fossilization) across the tree when using the Skyline BD or Skyline FBD tree models produced by the program Mr. Bayes or BEAST2 (SA or BDSKY packages).

Load the EvoPhylo package

    library(EvoPhylo)

## FBD Parameters Statistics and Plots (Mr. Bayes)

Below we demonstrate how to extract evolutionary rate summary statistics from each node from a Bayesian clock (time-calibrate) summary tree produced by Mr. Bayes, store them in a data frame, produce summary tables, and plots.

### 1. Import combined log file from all runs.

This is produced by using `combine_log()`.The first argument passed to `combine_log()` should be a path to the folder containing the log files to be imported and combined.

    ## Import all log (.p) files from all runs and combine them, with burn-in = 25%
    ## and downsampling to 2.5k trees in each log file
    posterior3p <- combine_log("LogFiles3p", burnin = 0.25, downsample = 1000)

Below, we use the posterior dataset `posterior3p` that accompanies `EvoPhylo`.

    data(posterior3p)

    ## Show first 5 lines of combined log file
    head(posterior3p, 5)

The posterior data must first be transformed from wide to long to be used with the functions described below; `FBD_reshape()` accomplishes this.

    ## Reshape imported combined log file from wide to long with FBD_reshape
    posterior3p_long <- FBD_reshape(posterior3p, variables = NULL, log.type = "MrBayes")

### 2. Summarize FBD parameters by time bin

Summary statistics for each FBD parameter by time bin can be quickly summarized using `FBD_summary()`:

    ## Summarize parameters by time bin and analysis
    t3.1 <- FBD_summary(posterior3p_long)
    t3.1

FBD parameters by time bin
parameter | Time_bin | n | mean | sd | min | Q1 | median | Q3 | max
--- | --- | --- | --- | --- | --- | --- | --- | --- | ---
net_speciation | 1 | 10000 | 0.04 | 0.02 | 0.00 | 0.03 | 0.04 | 0.06 | 0.17
net_speciation | 2 | 10000 | 0.03 | 0.02 | 0.00 | 0.02 | 0.03 | 0.04 | 0.12
net_speciation | 3 | 10000 | 0.02 | 0.01 | 0.00 | 0.01 | 0.02 | 0.03 | 0.12
net_speciation | 4 | 10000 | 0.05 | 0.02 | 0.00 | 0.03 | 0.05 | 0.06 | 0.12
relative_extinction | 1 | 10000 | 0.79 | 0.15 | 0.08 | 0.71 | 0.82 | 0.90 | 1.00
relative_extinction | 2 | 10000 | 0.93 | 0.05 | 0.55 | 0.90 | 0.93 | 0.96 | 1.00
relative_extinction | 3 | 10000 | 0.95 | 0.05 | 0.18 | 0.93 | 0.96 | 0.98 | 1.00
relative_extinction | 4 | 10000 | 0.03 | 0.10 | 0.00 | 0.00 | 0.00 | 0.01 | 0.97
relative_fossilization | 1 | 10000 | 0.04 | 0.05 | 0.00 | 0.01 | 0.02 | 0.05 | 0.72
relative_fossilization | 2 | 10000 | 0.07 | 0.04 | 0.00 | 0.04 | 0.06 | 0.09 | 0.36
relative_fossilization | 3 | 10000 | 0.01 | 0.02 | 0.00 | 0.00 | 0.01 | 0.02 | 0.54
relative_fossilization | 4 | 10000 | 0.04 | 0.11 | 0.00 | 0.00 | 0.00 | 0.02 | 0.99

    ## Export the table
    write.csv(t3.1, file = "FBD_summary.csv")

### 3. Plot the distribution of each FBD parameter

Each of (or all) the FBD parameter distributions can be plotted by time bin using various plotting alternatives with `FBD_dens_plot()`:

    ## Plot distribution of the desired FBD parameter by time bin with
    ## kernel density plot
    FBD_dens_plot(posterior3p_long, parameter = "net_speciation",
                  type = "density", stack = FALSE)

    ## Plot distribution of the desired FBD parameter by time bin with
    ## stacked kernel density plot
    FBD_dens_plot(posterior3p_long, parameter = "net_speciation",
                  type = "density", stack = TRUE)

    ## Plot distribution of the desired FBD parameter by time bin with
    ## a violin plot
    FBD_dens_plot(posterior3p_long, parameter = "net_speciation",
                  type = "violin", stack = FALSE, color = "red")

    ## Plot distribution of all FBD parameter by time bin with a violin plot
    p1 <- FBD_dens_plot(posterior3p_long, parameter = "net_speciation",
                        type = "violin", stack = FALSE, color = "red")
    p2 <- FBD_dens_plot(posterior3p_long, parameter = "relative_extinction",
                        type = "violin", stack = FALSE, color = "cyan3")
    p3 <- FBD_dens_plot(posterior3p_long, parameter = "relative_fossilization",
                        type = "violin", stack = FALSE, color = "green3")

    library(patchwork)
    p1 + p2 + p3 + plot_layout(nrow = 1)

    ## Save your plot to your working directory as a PDF
    ggplot2::ggsave("Plot_regs.pdf", width = 12, height = 4)

### 4. Test for assumptions

In this step, users can perform tests for normality and homoscedasticity in data distribution for each of the FBD parameters under consideration. The output will determine whether parametric or nonparametric tests will be performed subsequently.

    ##### Tests for normality and homoscedasticity for each FBD parameter for all time bins
    t3.2 <- FBD_tests1(posterior3p_long)

    ### Export the output table for all tests
    write.csv(t3.2, file = "FBD_Tests1_Assum.csv")

The results of the Shapiro-Wilk normality test for each parameter can be output as seperate tables or as a single combined table.

    # Output as separate tables
    t3.2$shapiro

Shapiro-Wilk normality test
| parameter | statistic | p-value
--- | --- | --- | ---
Time bin 1 | net_speciation | 0.9917 | 0
Time bin 2 | net_speciation | 0.9385 | 0
Time bin 3 | net_speciation | 0.9227 | 0
Time bin 4 | net_speciation | 0.9898 | 0
Overall | net_speciation | 0.9568 | 0
Residuals | net_speciation | 0.9874 | 0
| parameter | statistic | p-value
--- | --- | --- | ---
Time bin 1 | relative_extinction | 0.8927 | 0
Time bin 2 | relative_extinction | 0.9247 | 0
Time bin 3 | relative_extinction | 0.8044 | 0
Time bin 4 | relative_extinction | 0.3775 | 0
Overall | relative_extinction | 0.7036 | 0
Residuals | relative_extinction | 0.8238 | 0
| parameter | statistic | p-value
--- | --- | --- | ---
Time bin 1 | relative_fossilization | 0.5764 | 0
Time bin 2 | relative_fossilization | 0.8853 | 0
Time bin 3 | relative_fossilization | 0.6210 | 0
Time bin 4 | relative_fossilization | 0.4637 | 0
Overall | relative_fossilization | 0.5473 | 0
Residuals | relative_fossilization | 0.5531 | 0

    # OR as single merged table
    t3.2$shapiro$net_speciation$bin <- row.names(t3.2$shapiro$net_speciation)
    t3.2$shapiro$relative_extinction$bin <- row.names(t3.2$shapiro$relative_extinction)
    t3.2$shapiro$relative_fossilization$bin <- row.names(t3.2$shapiro$relative_fossilization)

    k1all <- rbind(t3.2$shapiro$net_speciation,
                   t3.2$shapiro$relative_extinction,
                   t3.2$shapiro$relative_fossilization,
                   make.row.names = FALSE)

    k1all

Shapiro-Wilk normality test
parameter | statistic | p-value | bin
--- | --- | --- | ---
net_speciation | 0.9917 | 0 | Time bin 1
net_speciation | 0.9385 | 0 | Time bin 2
net_speciation | 0.9227 | 0 | Time bin 3
net_speciation | 0.9898 | 0 | Time bin 4
net_speciation | 0.9568 | 0 | Overall
net_speciation | 0.9874 | 0 | Residuals
relative_extinction | 0.8927 | 0 | Time bin 1
relative_extinction | 0.9247 | 0 | Time bin 2
relative_extinction | 0.8044 | 0 | Time bin 3
relative_extinction | 0.3775 | 0 | Time bin 4
relative_extinction | 0.7036 | 0 | Overall
relative_extinction | 0.8238 | 0 | Residuals
relative_fossilization | 0.5764 | 0 | Time bin 1
relative_fossilization | 0.8853 | 0 | Time bin 2
relative_fossilization | 0.6210 | 0 | Time bin 3
relative_fossilization | 0.4637 | 0 | Time bin 4
relative_fossilization | 0.5473 | 0 | Overall
relative_fossilization | 0.5531 | 0 | Residuals

    ## Bartlett's test for homogeneity of variance
    t3.2$bartlett

Bartlett’s test
parameter | statistic | p-value
--- | --- | ---
net_speciation | 3815.464 | 0
relative_extinction | 18159.213 | 0
relative_fossilization | 25654.975 | 0

    ## Fligner-Killeen test for homogeneity of variance
    t3.2$fligner

Fligner-Killeen test
parameter | statistic | p-value
--- | --- | ---
net_speciation | 3748.140 | 0
relative_extinction | 12599.843 | 0
relative_fossilization | 4808.545 | 0

Deviations from normality can be displayed graphically using `FBD_normality_plot()`:

    ## Visualize deviations from normality and similarity of variances
    FBD_normality_plot(posterior3p_long)

    ## Save your plot to your working directory as a PDF
    ggplot2::ggsave("Plot_normTests.pdf", width = 8, height = 6)

### 5. Test for significant FBD shifts between time bins

Significant shifts in FBD parameters across time bins can be easily tested using parametric (Student’s t-test) and nonparametric (Mann-Whitney test) pairwise comparisons with `FBD_tests2()`. Both are automatically calculated and the preferred pairwise comparison will be chosen by the user depending on the results of the assumption tests step #4 (above).

    ##### Test for significant differences between each time bin for each FBD parameter
    t3.3 <- FBD_tests2(posterior3p_long)

    ### Export the output table for all tests
    write.csv(t3.3, file = "FBD_Tests2_Sign.csv")

    ## Pairwise t-tests
    # Output as separate tables
    t3.3$t_tests

Significant tests
parameter | Time_bin1 | Time_bin2 | n1 | n2 | p-value | p-value adj
--- | --- | --- | --- | --- | --- | ---
net_speciation | 1 | 2 | 10000 | 10000 | 0 | 0
net_speciation | 1 | 3 | 10000 | 10000 | 0 | 0
net_speciation | 1 | 4 | 10000 | 10000 | 0 | 0
net_speciation | 2 | 3 | 10000 | 10000 | 0 | 0
net_speciation | 2 | 4 | 10000 | 10000 | 0 | 0
net_speciation | 3 | 4 | 10000 | 10000 | 0 | 0
parameter | Time_bin1 | Time_bin2 | n1 | n2 | p-value | p-value adj
--- | --- | --- | --- | --- | --- | ---
relative_extinction | 1 | 2 | 10000 | 10000 | 0 | 0
relative_extinction | 1 | 3 | 10000 | 10000 | 0 | 0
relative_extinction | 1 | 4 | 10000 | 10000 | 0 | 0
relative_extinction | 2 | 3 | 10000 | 10000 | 0 | 0
relative_extinction | 2 | 4 | 10000 | 10000 | 0 | 0
relative_extinction | 3 | 4 | 10000 | 10000 | 0 | 0
parameter | Time_bin1 | Time_bin2 | n1 | n2 | p-value | p-value adj
--- | --- | --- | --- | --- | --- | ---
relative_fossilization | 1 | 2 | 10000 | 10000 | 0 | 0
relative_fossilization | 1 | 3 | 10000 | 10000 | 0 | 0
relative_fossilization | 1 | 4 | 10000 | 10000 | 0 | 0
relative_fossilization | 2 | 3 | 10000 | 10000 | 0 | 0
relative_fossilization | 2 | 4 | 10000 | 10000 | 0 | 0
relative_fossilization | 3 | 4 | 10000 | 10000 | 0 | 0

    # OR as single merged table
    k3.3a <- rbind(t3.3$t_tests$net_speciation,
                   t3.3$t_tests$relative_extinction,
                   t3.3$t_tests$relative_fossilization,
                   make.row.names = FALSE)

    k3.3a

Pairwise t-tests
parameter | Time_bin1 | Time_bin2 | n1 | n2 | p-value | p-value adj
--- | --- | --- | --- | --- | --- | ---
net_speciation | 1 | 2 | 10000 | 10000 | 0 | 0
net_speciation | 1 | 3 | 10000 | 10000 | 0 | 0
net_speciation | 1 | 4 | 10000 | 10000 | 0 | 0
net_speciation | 2 | 3 | 10000 | 10000 | 0 | 0
net_speciation | 2 | 4 | 10000 | 10000 | 0 | 0
net_speciation | 3 | 4 | 10000 | 10000 | 0 | 0
relative_extinction | 1 | 2 | 10000 | 10000 | 0 | 0
relative_extinction | 1 | 3 | 10000 | 10000 | 0 | 0
relative_extinction | 1 | 4 | 10000 | 10000 | 0 | 0
relative_extinction | 2 | 3 | 10000 | 10000 | 0 | 0
relative_extinction | 2 | 4 | 10000 | 10000 | 0 | 0
relative_extinction | 3 | 4 | 10000 | 10000 | 0 | 0
relative_fossilization | 1 | 2 | 10000 | 10000 | 0 | 0
relative_fossilization | 1 | 3 | 10000 | 10000 | 0 | 0
relative_fossilization | 1 | 4 | 10000 | 10000 | 0 | 0
relative_fossilization | 2 | 3 | 10000 | 10000 | 0 | 0
relative_fossilization | 2 | 4 | 10000 | 10000 | 0 | 0
relative_fossilization | 3 | 4 | 10000 | 10000 | 0 | 0

    ## Mann-Whitney tests (use if Tests in step #4 fail assumptions)
    # Output as separate tables
    t3.3$mwu_tests

Mann-Whitney tests
parameter | Time_bin1 | Time_bin2 | n1 | n2 | p-value | p-value adj
--- | --- | --- | --- | --- | --- | ---
net_speciation | 1 | 2 | 10000 | 10000 | 0 | 0
net_speciation | 1 | 3 | 10000 | 10000 | 0 | 0
net_speciation | 1 | 4 | 10000 | 10000 | 0 | 0
net_speciation | 2 | 3 | 10000 | 10000 | 0 | 0
net_speciation | 2 | 4 | 10000 | 10000 | 0 | 0
net_speciation | 3 | 4 | 10000 | 10000 | 0 | 0
parameter | Time_bin1 | Time_bin2 | n1 | n2 | p-value | p-value adj
--- | --- | --- | --- | --- | --- | ---
relative_extinction | 1 | 2 | 10000 | 10000 | 0 | 0
relative_extinction | 1 | 3 | 10000 | 10000 | 0 | 0
relative_extinction | 1 | 4 | 10000 | 10000 | 0 | 0
relative_extinction | 2 | 3 | 10000 | 10000 | 0 | 0
relative_extinction | 2 | 4 | 10000 | 10000 | 0 | 0
relative_extinction | 3 | 4 | 10000 | 10000 | 0 | 0
parameter | Time_bin1 | Time_bin2 | n1 | n2 | p-value | p-value adj
--- | --- | --- | --- | --- | --- | ---
relative_fossilization | 1 | 2 | 10000 | 10000 | 0 | 0
relative_fossilization | 1 | 3 | 10000 | 10000 | 0 | 0
relative_fossilization | 1 | 4 | 10000 | 10000 | 0 | 0
relative_fossilization | 2 | 3 | 10000 | 10000 | 0 | 0
relative_fossilization | 2 | 4 | 10000 | 10000 | 0 | 0
relative_fossilization | 3 | 4 | 10000 | 10000 | 0 | 0

    # OR as single merged table
    k3.3b <- rbind(t3.3$mwu_tests$net_speciation,
                   t3.3$mwu_tests$relative_extinction,
                   t3.3$mwu_tests$relative_fossilization,
                   make.row.names = FALSE)

    k3.3b

Mann-Whitney tests
parameter | Time_bin1 | Time_bin2 | n1 | n2 | p-value | p-value adj
--- | --- | --- | --- | --- | --- | ---
net_speciation | 1 | 2 | 10000 | 10000 | 0 | 0
net_speciation | 1 | 3 | 10000 | 10000 | 0 | 0
net_speciation | 1 | 4 | 10000 | 10000 | 0 | 0
net_speciation | 2 | 3 | 10000 | 10000 | 0 | 0
net_speciation | 2 | 4 | 10000 | 10000 | 0 | 0
net_speciation | 3 | 4 | 10000 | 10000 | 0 | 0
relative_extinction | 1 | 2 | 10000 | 10000 | 0 | 0
relative_extinction | 1 | 3 | 10000 | 10000 | 0 | 0
relative_extinction | 1 | 4 | 10000 | 10000 | 0 | 0
relative_extinction | 2 | 3 | 10000 | 10000 | 0 | 0
relative_extinction | 2 | 4 | 10000 | 10000 | 0 | 0
relative_extinction | 3 | 4 | 10000 | 10000 | 0 | 0
relative_fossilization | 1 | 2 | 10000 | 10000 | 0 | 0
relative_fossilization | 1 | 3 | 10000 | 10000 | 0 | 0
relative_fossilization | 1 | 4 | 10000 | 10000 | 0 | 0
relative_fossilization | 2 | 3 | 10000 | 10000 | 0 | 0
relative_fossilization | 2 | 4 | 10000 | 10000 | 0 | 0
relative_fossilization | 3 | 4 | 10000 | 10000 | 0 | 0

## FBD Parameters Statistics and Plots (BEAST2)

### 1. Import combined log file from all runs.

The combined posterior log file from BEAST2 is outputted by LogCombiner from their software package. Our own function to combined log files `combine_log` is intended to work with Mr. Bayes posterior files only.

Below, we use the posterior dataset “Penguins_log.log” that accompanies `EvoPhylo`.

    posterior <- system.file("extdata", "Penguins_log.log", package = "EvoPhylo")
    posterior <- read.table(posterior, header = TRUE)

    ## Show first 10 lines of combined log file
    head(posterior, 5)

The posterior data must first be transformed from wide to long to be used with the functions described below; `FBD_reshape()` accomplishes this.

    ## Reshape imported combined log file from wide to long with FBD_reshape
    posterior_long <- FBD_reshape(posterior, variables = NULL, log.type = "BEAST2")

### 2. Summarize FBD parameters by time bin

Summary statistics for each FBD parameter by time bin can be quickly summarized using `FBD_summary()`:

    ## Summarize parameters by time bin and analysis
    t3.1 <- FBD_summary(posterior_long)
    t3.1

FBD parameters by time bin
parameter | Time_bin | n | mean | sd | min | Q1 | median | Q3 | max
--- | --- | --- | --- | --- | --- | --- | --- | --- | ---
diversificationRateFBD | 1 | 556 | 0.04 | 0.03 | 0.00 | 0.02 | 0.04 | 0.06 | 0.17
turnoverFBD | 1 | 556 | 0.86 | 0.10 | 0.45 | 0.81 | 0.89 | 0.94 | 1.00
samplingProportionFBD | 1 | 556 | 0.27 | 0.12 | 0.06 | 0.19 | 0.25 | 0.34 | 0.74

    ## Export the table
    write.csv(t3.1, file = "FBD_summary_BEAST2.csv")

### 3. Plot the distribution of each FBD parameter

Each of (or all) the FBD parameter distributions can be plotted by time bin using various plotting alternatives with `FBD_dens_plot()`:

    ## Plot distribution of the desired FBD parameter by time bin with
    ## kernel density plot
    FBD_dens_plot(posterior_long, parameter = "diversificationRateFBD",
                  type = "density", stack = FALSE)

    ## Plot distribution of the desired FBD parameter by time bin with
    ## a violin plot
    FBD_dens_plot(posterior_long, parameter = "diversificationRateFBD",
                  type = "violin", stack = FALSE, color = "red")

    ## Plot distribution of all FBD parameter by time bin with a violin plot
    p1 <- FBD_dens_plot(posterior_long, parameter = "diversificationRateFBD",
                        type = "violin", stack = FALSE, color = "red")
    p2 <- FBD_dens_plot(posterior_long, parameter = "turnoverFBD",
                        type = "violin", stack = FALSE, color = "cyan3")
    p3 <- FBD_dens_plot(posterior_long, parameter = "samplingProportionFBD",
                        type = "violin", stack = FALSE, color = "green3")

    library(patchwork)
    p1 + p2 + p3 + plot_layout(nrow = 1)

    ## Save your plot to your working directory as a PDF
    ggplot2::ggsave("Plot_regs.pdf", width = 12, height = 4)

## References