---
title: "Benchmarking phyloregion"
author: "Barnabas H. Daru, Piyal Karunarathne & Klaus Schliep"
date: "November 15, 2022"
output: rmarkdown::html_vignette
bibliography: phyloregion.bib
vignette: >
   %\VignetteIndexEntry{Benchmarking phyloregion}
   %\VignetteEngine{knitr::rmarkdown}
   %\usepackage[utf8]{inputenc}
---



## Benchmarking `phyloregion` with comparable packages

In this vignette, we benchmark `phyloregion` against other similar `R`
packages in analyses of standard alpha diversity metrics commonly
used in conservation, such as phylogenetic diversity and phylogenetic
endemism as well as metrics for analyzing compositional turnover (e.g.,
beta diversity and phylogenetic beta diversity). Specifically, we
compare `phyloregion`'s functions with available packages for efficiency
in memory allocation and computation speed in various biogeographic analyses.

First, load the packages for the benchmarking:


```r
library(ape)
library(Matrix)
library(bench)
library(ggplot2)
# packages we benchmark
library(phyloregion)
library(betapart)
library(picante)
library(vegan)
library(hilldiv)
library(BAT)
library(pez)
```
We will use a small data set which comes with `phyloregion`. This dataset
consists of a dated phylogeny of the woody plant species of southern
Africa along with their geographical distributions. The dataset comes from a study that maps tree diversity hotspots in southern Africa [@Daru2015ddi].


```r
data(africa)
# subset matrix
X_sparse <- africa$comm[1:30, ]
X_sparse <- X_sparse[, colSums(X_sparse)>0]
X_dense <- as.matrix(X_sparse)
Xt_dense <- t(X_dense)

object.size(X_sparse)
```

```
## 76504 bytes
```

```r
object.size(X_dense)
```

```
## 134752 bytes
```

```r
dim(X_sparse)
```

```
## [1]  30 401
```
To make results comparable, it is often desirable to make sure
that the taxa in different datasets match each other [@Kembel2010].
For example, the community matrix in the `hilldiv` package [@hilldiv]
needs to be transposed. These transformations can influence the execution
times of the function, often only marginally.
Thus, to benchmark `phyloregion` against other packages, we here use the
package `bench` [@bench2020] because it returns execution times and
provides estimates of memory allocations for each computation.

## 1. Analysis of alpha diversity
#### 1.1. Benchmarking `phyloregion` for analysis of phylogenetic diversity

For analysis of alpha diversity commonly used in conservation such as phylogenetic
diversity - the sum of all phylogenetic branch lengths within an area [@Faith1992]
- `phyloregion` is 31 to 284 times faster and 67 to 192 times
memory efficient, compared to other packages!

```r
tree <- africa$phylo
tree <- keep.tip(tree, colnames(X_sparse))

pd_picante <- function(x, tree){
    res <- picante::pd(x, tree)[,1]
    names(res) <- row.names(x)
    res
}

pd_pez <- function(x, tree){
    dat <- pez::comparative.comm(tree, x)
    res <- pez::.pd(dat)[,1]
    names(res) <- row.names(x)
    res
}

pd_hilldiv <- function(x, tree) hilldiv::index_div(x, tree, index="faith")
pd_phyloregion <- function(x, tree) phyloregion::PD(x, tree)

res1 <- bench::mark(picante=pd_picante(X_dense, tree),
          hilldiv=pd_hilldiv(Xt_dense,tree=tree),
          pez=pd_pez(X_dense, tree),
          phyloregion=pd_phyloregion(X_sparse, tree))
summary(res1)
```

```
## # A tibble: 4 × 6
##   expression       min   median `itr/sec` mem_alloc `gc/sec`
##   <bch:expr>  <bch:tm> <bch:tm>     <dbl> <bch:byt>    <dbl>
## 1 picante      97.85ms 112.45ms      8.22    59.6MB     9.87
## 2 hilldiv     762.42ms 762.42ms      1.31   170.1MB     3.93
## 3 pez         108.59ms 122.83ms      8.16    60.4MB     8.16
## 4 phyloregion   2.82ms   3.23ms    268.     909.8KB     5.99
```

```r
autoplot(res1)
```

![plot of chunk phylo_diversity](benchmark-phylo_diversity-1.png)

#### 1.2. Benchmarking `phyloregion` for analysis of phylogenetic endemism

Another benchmark for `phyloregion` is in the analysis of phylogenetic
endemism, the degree to which phylogenetic diversity is restricted to
any given area [@Rosauer2009]. Here, we found that `phyloregion` is
160 times faster and 489 times efficient in memory allocation.


```r
tree <- africa$phylo
tree <- keep.tip(tree, colnames(X_sparse))

pe_pez <- function(x, tree){
    dat <- pez::comparative.comm(tree, x)
    res <- pez::pez.endemism(dat)[,1]
    names(res) <- row.names(x)
    res
}

pe_phyloregion <- function(x, tree) phyloregion::phylo_endemism(x, tree)

res2 <- bench::mark(pez=pe_pez(X_dense, tree),
          phyloregion=pe_phyloregion(X_sparse, tree))
summary(res2)
```

```
## # A tibble: 2 × 6
##   expression       min   median `itr/sec` mem_alloc `gc/sec`
##   <bch:expr>  <bch:tm> <bch:tm>     <dbl> <bch:byt>    <dbl>
## 1 pez         630.38ms 630.38ms      1.59  493.88MB     9.52
## 2 phyloregion   2.94ms   3.19ms    280.      1.06MB     3.98
```

```r
autoplot(res2)
```

![plot of chunk phylo_endemism](benchmark-phylo_endemism-1.png)

## 2. Analysis of compositional turnover (beta diversity)
#### 2.1. Benchmarking `phyloregion` for analysis of taxonomic beta diversity

For analysis of taxonomic beta diversity, which compares diversity between
communities [@Koleff2003], `phyloregion` has marginal advantage
over other packages. Nonetheless, it is 1-39 times faster and allocates 2 to 110
times less memory than other packages.

```r
chk_fun <- function(target, current)
    all.equal(target, current, check.attributes = FALSE)

fun_phyloregion <- function(x) as.matrix(phyloregion::beta_diss(x)[[3]])
fun_betapart <- function(x) as.matrix(betapart::beta.pair(x)[[3]])
fun_vegan  <- function(x) as.matrix(vegan::vegdist(x, binary=TRUE))
fun_BAT <- function(x) as.matrix(BAT::beta(x, func = "Soerensen")[[1]])
res3 <- bench::mark(phyloregion=fun_phyloregion(X_sparse),
                    betapart=fun_betapart(X_dense),
                    vegan=fun_vegan(X_dense),
                    BAT=fun_BAT(X_dense), check=chk_fun)
summary(res3)
```

```
## # A tibble: 4 × 6
##   expression       min   median `itr/sec` mem_alloc `gc/sec`
##   <bch:expr>  <bch:tm> <bch:tm>     <dbl> <bch:byt>    <dbl>
## 1 phyloregion  598.5µs    689µs    1210.    428.2KB     4.39
## 2 betapart     849.4µs    909µs    1024.    594.1KB    10.3 
## 3 vegan        946.8µs    992µs     958.   1016.1KB     7.01
## 4 BAT           44.5ms     47ms      20.9    31.8MB     8.95
```

```r
autoplot(res3)
```

![plot of chunk beta_diversity](benchmark-beta_diversity-1.png)

#### 2.2. Benchmarking `phyloregion` for analysis of phylogenetic beta diversity
For analysis of phylogenetic turnover (beta-diversity) among communities - the
proportion of shared phylogenetic branch lengths between communities [@Graham2008] - `phyloregion` is 300-400 times faster and allocates 100-600 times less memory!

```r
fun_phyloregion <- function(x, tree) phyloregion::phylobeta(x, tree)[[3]]
fun_betapart <- function(x, tree) betapart::phylo.beta.pair(x, tree)[[3]]
fun_picante <- function(x, tree) 1 - picante::phylosor(x, tree)
fun_BAT <- function(x, tree) BAT::beta(x, tree, func = "Soerensen")[[1]]

chk_fun <- function(target, current)
    all.equal(target, current, check.attributes = FALSE)

res4 <- bench::mark(picante=fun_picante(X_dense, tree),
                       betapart=fun_betapart(X_dense, tree),
                       BAT=fun_BAT(X_dense, tree),
                       phyloregion=fun_phyloregion(X_sparse, tree), check=chk_fun)
summary(res4)
```

```
## # A tibble: 4 × 6
##   expression       min   median `itr/sec` mem_alloc `gc/sec`
##   <bch:expr>  <bch:tm> <bch:tm>     <dbl> <bch:byt>    <dbl>
## 1 picante        2.25s    2.25s     0.444    1.24GB    2.66 
## 2 betapart       2.05s    2.05s     0.489    1.24GB    2.93 
## 3 BAT            1.41s    1.41s     0.712  293.64MB    0.712
## 4 phyloregion   4.21ms   4.49ms   175.       1.12MB    1.99
```

```r
autoplot(res4)
```

![plot of chunk phylobeta](benchmark-phylobeta-1.png)

Note that for this test, `picante` returns a similarity matrix while
`betapart`, and `phyloregion` return a dissimilarity matrix.

## Session Information

```r
sessionInfo()
```

```
## R version 4.2.1 (2022-06-23)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Monterey 12.6
## 
## Matrix products: default
## LAPACK: /Library/Frameworks/R.framework/Versions/4.2/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] pez_1.2-4         BAT_2.9.2         hilldiv_1.5.1     picante_1.8.2    
##  [5] nlme_3.1-157      vegan_2.6-2       lattice_0.20-45   permute_0.9-7    
##  [9] betapart_1.5.6    phyloregion_1.0.7 bench_1.1.2       Matrix_1.5-3     
## [13] ape_5.6-2         knitr_1.39        ggplot2_3.3.6    
## 
## loaded via a namespace (and not attached):
##   [1] utf8_1.2.2              proto_1.0.0             ks_1.13.5              
##   [4] tidyselect_1.2.0        htmlwidgets_1.5.4       grid_4.2.1             
##   [7] combinat_0.0-8          pROC_1.18.0             animation_2.7          
##  [10] munsell_0.5.0           codetools_0.2-18        clustMixType_0.2-15    
##  [13] interp_1.1-3            future_1.29.0           withr_2.5.0            
##  [16] profmem_0.6.0           colorspace_2.0-3        highr_0.9              
##  [19] rstudioapi_0.13         geometry_0.4.6.1        stats4_4.2.1           
##  [22] ggsignif_0.6.4          listenv_0.8.0           slam_0.1-50            
##  [25] FD_1.0-12.1             nls2_0.3-3              mnormt_2.1.0           
##  [28] farver_2.1.1            coda_0.19-4             parallelly_1.32.1      
##  [31] vctrs_0.5.0             generics_0.1.3          clusterGeneration_1.3.7
##  [34] ipred_0.9-13            xfun_0.31               itertools_0.1-3        
##  [37] fastcluster_1.2.3       R6_2.5.1                doParallel_1.0.17      
##  [40] ggbeeswarm_0.6.0        pdist_1.2.1             assertthat_0.2.1       
##  [43] scales_1.2.0            nnet_7.3-17             beeswarm_0.4.0         
##  [46] rgeos_0.5-9             gtable_0.3.0            globals_0.16.1         
##  [49] caper_1.0.1             phangorn_2.9.0          MatrixModels_0.5-1     
##  [52] timeDate_4021.106       rlang_1.0.6             FSA_0.9.3              
##  [55] scatterplot3d_0.3-41    splines_4.2.1           rstatix_0.7.1          
##  [58] rgdal_1.5-30            ModelMetrics_1.2.2.2    broom_1.0.1            
##  [61] checkmate_2.1.0         reshape2_1.4.4          abind_1.4-5            
##  [64] backports_1.4.1         Hmisc_4.7-1             caret_6.0-93           
##  [67] tools_4.2.1             lava_1.7.0              psych_2.2.9            
##  [70] lavaan_0.6-12           ellipsis_0.3.2          raster_3.5-21          
##  [73] RColorBrewer_1.1-3      proxy_0.4-27            Rcpp_1.0.9             
##  [76] plyr_1.8.7              base64enc_0.1-3         progress_1.2.2         
##  [79] purrr_0.3.4             prettyunits_1.1.1       ggpubr_0.4.0           
##  [82] rpart_4.1.16            deldir_1.0-6            pbapply_1.5-0          
##  [85] deSolve_1.34            qgraph_1.9.2            cluster_2.1.3          
##  [88] magrittr_2.0.3          data.table_1.14.2       SparseM_1.81           
##  [91] mvtnorm_1.1-3           smoothr_0.2.2           hms_1.1.1              
##  [94] evaluate_0.15           jpeg_0.1-9              mclust_6.0.0           
##  [97] gridExtra_2.3           compiler_4.2.1          tibble_3.1.8           
## [100] maps_3.4.0              KernSmooth_2.23-20      crayon_1.5.1           
## [103] hypervolume_3.0.4       htmltools_0.5.3         mgcv_1.8-40            
## [106] corpcor_1.6.10          Formula_1.2-4           snow_0.4-4             
## [109] tidyr_1.2.0             expm_0.999-6            lubridate_1.8.0        
## [112] DBI_1.1.3               magic_1.6-0             subplex_1.8            
## [115] MASS_7.3-57             ade4_1.7-19             car_3.1-1              
## [118] cli_3.4.1               quadprog_1.5-8          parallel_4.2.1         
## [121] gower_1.0.0             igraph_1.3.4            pkgconfig_2.0.3        
## [124] numDeriv_2016.8-1.1     foreign_0.8-82          sp_1.5-0               
## [127] terra_1.5-21            recipes_1.0.3           foreach_1.5.2          
## [130] pbivnorm_0.6.0          predicts_0.1-3          vipor_0.4.5            
## [133] hardhat_1.2.0           prodlim_2019.11.13      stringr_1.4.0          
## [136] digest_0.6.29           pracma_2.4.2            phytools_1.0-3         
## [139] rcdd_1.5                fastmatch_1.1-3         htmlTable_2.4.1        
## [142] quantreg_5.94           gtools_3.9.3            geiger_2.0.10          
## [145] lifecycle_1.0.3         glasso_1.11             carData_3.0-5          
## [148] maptpx_1.9-7            fansi_1.0.3             pillar_1.8.0           
## [151] fastmap_1.1.0           plotrix_3.8-2           survival_3.3-1         
## [154] glue_1.6.2              fdrtool_1.2.17          png_0.1-7              
## [157] iterators_1.0.14        class_7.3-20            stringi_1.7.8          
## [160] palmerpenguins_0.1.1    doSNOW_1.0.20           latticeExtra_0.6-30    
## [163] dplyr_1.0.9             e1071_1.7-11            future.apply_1.10.0
```

## REFERENCES
