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) since EvoPhylo v. 0.2.0.
FBD Parameters Statistics and Plots
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.
Load the EvoPhylo package
1. Import combined log file from all runs.
This is produced by using combine_log()
. Alternatively, users can also use LogCombiner from the BEAST2 software package. 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
.
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")
## Show first 5 lines of combined log file
head(posterior3p_long, 5)
## Gen LnL LnPr TH.all. TL.all. prop_ancfossil.all. sigma.1.
## 1 8750000 -1449.425 -143.1907 5.271118 11.969460 0 0.07660715
## 2 8761000 -1458.367 -174.9627 4.775064 11.070210 0 0.05850396
## 3 8771000 -1449.445 -163.9216 5.927716 12.628460 0 0.05182430
## 4 8782000 -1453.218 -153.2030 4.451376 9.931809 0 0.14644520
## 5 8792000 -1461.906 -132.1172 5.095504 11.083810 0 0.14143120
## sigma.2. sigma.3. m.1. m.2. m.3. tk02var.1. tk02var.2.
## 1 1.33351500 0.8523453 0.3695799 1.544579 1.362332 0.3197728 0.3848931
## 2 0.06463618 0.1380557 0.5083868 1.495777 1.108471 0.2710006 0.3609312
## 3 0.67980130 0.7776142 0.4275609 1.569911 1.144364 0.2853423 0.1831945
## 4 0.65005980 0.2999867 0.6445027 1.329942 1.148377 0.4670378 0.3483061
## 5 0.52745340 1.3928490 0.4993570 1.368074 1.445410 0.2115789 0.2723863
## tk02var.3. clockrate.all. Time_bin net_speciation relative_extinction
## 1 0.2075079 0.01192715 1 0.04987983 0.6785586
## 2 0.3622265 0.01086355 1 0.04675159 0.9174022
## 3 0.6146289 0.01349259 1 0.01064803 0.9677827
## 4 0.4949015 0.01016002 1 0.07373453 0.8976315
## 5 0.3463915 0.01160514 1 0.04990040 0.7887825
## relative_fossilization
## 1 0.055629950
## 2 0.006523517
## 3 0.010535440
## 4 0.001264865
## 5 0.036796000
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)
![](data:image/png;base64,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)
## 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)
![](data:image/png;base64,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)
## 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")
![](data:image/png;base64,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)
## 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)
![](data:image/png;base64,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)
## 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)
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)
![](data:image/png;base64,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)
## 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$relative_fossilization,
make.row.names = FALSE)
Pairwise t-tests
parameter
|
Time_bin1
|
Time_bin2
|
n1
|
n2
|
p-value
|
p-value adj
|
net_speciation
|
1
|
2
|
10000
|
10000
|
0
|
0
|
net_speciation
|
1
|
3
|
10000
|
10000
|
0
|
0
|
net_speciation
|
1
|
4
|
10000
|
10000
|
0
|
0
|
net_speciation
|
2
|
3
|
10000
|
10000
|
0
|
0
|
net_speciation
|
2
|
4
|
10000
|
10000
|
0
|
0
|
net_speciation
|
3
|
4
|
10000
|
10000
|
0
|
0
|
relative_extinction
|
1
|
2
|
10000
|
10000
|
0
|
0
|
relative_extinction
|
1
|
3
|
10000
|
10000
|
0
|
0
|
relative_extinction
|
1
|
4
|
10000
|
10000
|
0
|
0
|
relative_extinction
|
2
|
3
|
10000
|
10000
|
0
|
0
|
relative_extinction
|
2
|
4
|
10000
|
10000
|
0
|
0
|
relative_extinction
|
3
|
4
|
10000
|
10000
|
0
|
0
|
relative_fossilization
|
1
|
2
|
10000
|
10000
|
0
|
0
|
relative_fossilization
|
1
|
3
|
10000
|
10000
|
0
|
0
|
relative_fossilization
|
1
|
4
|
10000
|
10000
|
0
|
0
|
relative_fossilization
|
2
|
3
|
10000
|
10000
|
0
|
0
|
relative_fossilization
|
2
|
4
|
10000
|
10000
|
0
|
0
|
relative_fossilization
|
3
|
4
|
10000
|
10000
|
0
|
0
|
## Mann-Whitney tests (use if Tests in step #4 fail assumptions)
# Output as separate tables
t3.3$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)
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
|