Author: Barnabas H. Daru, Piyal Karunarathne & Klaus Schliep
Date: 2022-11-15

# Benchmarking phyloregion

#### Barnabas H. Daru, Piyal Karunarathne & Klaus Schliep

#### November 15, 2022

## 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:

    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 (Daru, Bank, and Davies 2015).

    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

    object.size(X_dense)

    ## 134752 bytes

    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 (Kembel et al. 2010). For example, the community matrix in the `hilldiv` package (Alberdi 2019) 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` (Hester 2020) 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 (Faith 1992) - `phyloregion` is 31 to 284 times faster and 67 to 192 times memory efficient, compared to other packages!

    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

    autoplot(res1)

plot of chunk phylo_diversity

#### 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 (Rosauer et al. 2009). Here, we found that `phyloregion` is 160 times faster and 489 times efficient in memory allocation.

    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

    autoplot(res2)

plot of chunk phylo_endemism

## 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 (Koleff, Gaston, and Lennon 2003), `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.

    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

    autoplot(res3)

plot of chunk beta_diversity

#### 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 (Graham and Fine 2008) - `phyloregion` is 300-400 times faster and allocates 100-600 times less memory!

    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

    autoplot(res4)

plot of chunk phylobeta

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

## Session Information

    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

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Alberdi, Antton. 2019. “Hilldiv: An r Package for the Integral Analysis of Diversity Based on Hill Numbers.” bioRxiv. https://www.biorxiv.org/content/10.1101/545665v1.
Daru, Barnabas H., Michelle van der Bank, and T. Jonathan Davies. 2015. “Spatial Incongruence Among Hotspots and Complementary Areas of Tree Diversity in Southern Africa.” Diversity and Distributions 21 (7): 769–80. https://doi.org/10.1111/ddi.12290.
Faith, Daniel P. 1992. “Conservation Evaluation and Phylogenetic Diversity.” Biological Conservation 61 (1): 1–10. https://doi.org/10.1016/0006-3207(92)91201-3.
Graham, Catherine H., and Paul V. A. Fine. 2008. “Phylogenetic Beta Diversity: Linking Ecological and Evolutionary Processes Across Space in Time.” Ecology Letters 11 (12): 1265–77. https://doi.org/10.1111/j.1461-0248.2008.01256.x.
Hester, Jim. 2020. Bench: High Precision Timing of r Expressions. https://CRAN.R-project.org/package=bench.
Kembel, S. W., P. D. Cowan, M. R. Helmus, W. K. Cornwell, H. Morlon, D. D. Ackerly, S. P. Blomberg, and C. O. Webb. 2010. “Picante: R Tools for Integrating Phylogenies and Ecology.” Bioinformatics 26: 1463–64.
Koleff, Patricia, Kevin J. Gaston, and Jack J. Lennon. 2003. “Measuring Beta Diversity for Presence–Absence Data.” Journal of Animal Ecology 72 (3): 367–82. https://doi.org/10.1046/j.1365-2656.2003.00710.x.
Rosauer, Dan, Shawn W. Laffan, Michael D. Crisp, Stephen C. Donnellan, and Lyn G. Cook. 2009. “Phylogenetic Endemism: A New Approach for Identifying Geographical Concentrations of Evolutionary History.” Molecular Ecology 18 (19): 4061–72. https://doi.org/10.1111/j.1365-294X.2009.04311.x.