This vignette presents some performance tests ran between fundiversity and other functional diversity packages. Note that to avoid the dependency on other packages, this vignette is pre-computed.

Other packages to compute FD indices

Main functions

Here is a table that summarizes the comparable functions (and their arguments) for functions included in fundiversity. Note that the package name is indicated before :: followed by the function name.

Index Type	Index Name	Source	`fundiversity` function	Equivalent Functions
α-diversity	Functional Dispersion (FDis)	Laliberté and Legendre (2010)	`fd_fdis()`	~~`BAT::dispersion()`~~ (doesn’t compute FDis) `FD::fdisp()` ~~`hillR::hill_func()`~~ (actually rely on `FD` for FDis computations and standardize the traits without telling the user) `mFD::alpha.fd.multidim(..., ind_vect = "fdis")`
α-diversity	Functional Divergence (FDiv)	Villéger et al. (2008)	`fd_fdiv()`	`mFD::alpha.fd.multidim(..., ind_vect = "fdiv")`
α-diversity	Functional Evenness (FEve)	Villéger et al. (2008)	`fd_feve()`	`mFD::alpha.fd.multidim(..., ind_vect = "feve")`
α-diversity	Functional Richness (FRic)	Villéger et al. (2008)	`fd_fric()`	`BAT::alpha()` (tree, not strictly equal) `BAT::hull.alpha()` (hull) `mFD::alpha.fd.multidim(..., ind_vect = "fric")`
α-diversity	Rao’s Quadratic Entropy (Q)	Villéger et al. (2013)	`fd_raoq()`	`adiv::QE()` `BAT::rao()` `hillR::hill_func()` (standardize traits without warning) `mFD::alpha.fd.hill(..., q = 2, tau = "max")` (returns a slightly modified version of Q according to Ricotta and Szeidl (2009))
β-diversity	Functional Richness Intersection (FRic_intersect)	Rao (1982)	`fd_fric_intersect()`	`betapart::functional.beta.pair()` `hillR::hill_func_parti_pairwise()`

The other packages are thus: adiv (Pavoine 2020), BAT (Cardoso et al. 2015), betapart (Baselga and Orme 2012), FD (Laliberté et al. 2014), hillR (Li 2018), and mFD (Magneville et al. 2022). For fairness of comparison, even if FD::dbFD() contains most indices we’re not considering it as it computes all indices together for each call, and would necessarily be slower.

Benchmark between packages

We will now benchmark the functions included in fundiversity with the corresponding function in other packages using the microbenchmark::microbenchmark() function. We will use the fairly small (~220 species, 8 sites, 4 traits) provided dataset in fundiversity.

tictoc::tic()  # Time execution of vignette
library(fundiversity)
data("traits_birds", package = "fundiversity")
data("site_sp_birds", package = "fundiversity")

dist_traits_birds <- dist(traits_birds)

Functional Dispersion (FDis)

fdis_bench <- microbenchmark::microbenchmark(
  fundiversity = {
    fundiversity::fd_fdis(traits_birds, site_sp_birds)
  },
  FD = {
    FD::fdisp(dist_traits_birds, site_sp_birds)
  },
  mFD = {
    mFD::alpha.fd.multidim(
    traits_birds, site_sp_birds, ind_vect = "fdis",
    scaling = FALSE, verbose = FALSE, details_returned = FALSE
  )
  },
  times = 30
)

ggplot2::autoplot(fdis_bench) +
  labs(title = "Functional Dispersion (FDis)")

plot of chunk bench-fdis

Functional Divergence (FDiv)

fdiv_bench <- microbenchmark::microbenchmark(
  fundiversity = fd_fdiv(traits_birds, site_sp_birds),
  mFD = mFD::alpha.fd.multidim(
    traits_birds, site_sp_birds, ind_vect = "fdiv",
    scaling = FALSE, verbose = FALSE
  ),
  times = 30
)

ggplot2::autoplot(fdiv_bench) +
  labs(title = "Functional Divergence (FDiv)")

plot of chunk bench-fdiv

Functional Evenness (FEve)

feve_bench <- microbenchmark::microbenchmark(
  fundiversity = fd_feve(traits_birds, site_sp_birds),
  mFD = mFD::alpha.fd.multidim(
    traits_birds, site_sp_birds, ind_vect = "feve",
    scaling = FALSE, verbose = FALSE
  ),
  times = 30
)

ggplot2::autoplot(feve_bench) +
  labs(title = "Functional Evenness (FEve)")

plot of chunk bench-feve

Functional Richness (FRic)

fric_bench <- microbenchmark::microbenchmark(
  fundiversity = fd_fric(traits_birds, site_sp_birds),
  BAT_tree = BAT::alpha(
    site_sp_birds, traits_birds
  ),
  BAT_alpha_hull = BAT::hull.alpha(
    BAT::hull.build(site_sp_birds, traits_birds)
  ),
  mFD = mFD::alpha.fd.multidim(
    traits_birds, site_sp_birds, ind_vect = "fric",
    scaling = FALSE, verbose = FALSE
  ),
  times = 30
)

ggplot2::autoplot(fric_bench) +
  labs(title = "Functional Richness (FRic)")

plot of chunk bench-fric

Functional Richness Intersection (FRic_intersect)

fric_bench <- microbenchmark::microbenchmark(
  fundiversity  = fd_fric_intersect(traits_birds, site_sp_birds) ,
  betapart = betapart::functional.beta.pair(
    site_sp_birds, traits_birds
  ),
  hillR = hillR::hill_func_parti_pairwise(
    site_sp_birds, traits_birds, .progress = FALSE
  ),
  times = 30
)

ggplot2::autoplot(fric_bench) +
  labs(title = "Functional Richness Intersection (FRic)")

plot of chunk bench-fric-intersect

Rao’s Quadratic Entropy (Q)

raoq_bench <- fric_bench <- microbenchmark::microbenchmark(
  fundiversity = fd_raoq(traits_birds, site_sp_birds),
  adiv= adiv::QE(
    site_sp_birds, dist_traits_birds
  ),
  BAT_rao           = BAT::rao(
    site_sp_birds, distance = traits_birds
  ),
  hillR_hill_func   = hillR::hill_func(
    site_sp_birds, traits_birds, fdis = FALSE
  ),
  mFD_alpha_fd_hill = mFD::alpha.fd.hill(
    site_sp_birds, dist_traits_birds, q = 2,
    tau = "max"
  ),
  times = 30
)

ggplot2::autoplot(raoq_bench) +
  labs(title = "Rao's Quadatric Entropy (Q)")

plot of chunk bench-raoq

Benchmark within `fundiversity`

We now proceed to the performance evaluation of functions within fundiversity with datasets of increasing sizes.

Increasing the number of species

make_more_sp <- function(n) {
  traits <- do.call(rbind, replicate(n, traits_birds, simplify = FALSE))
  row.names(traits) <- paste0("sp", seq_len(nrow(traits)))

  site_sp <- do.call(cbind, replicate(n, site_sp_birds, simplify = FALSE))
  colnames(site_sp) <- paste0("sp", seq_len(ncol(site_sp)))

  list(tr = traits, si = site_sp)
}

null_sp_1000   <- make_more_sp(5)
null_sp_10000  <- make_more_sp(50)
null_sp_100000 <- make_more_sp(500)

Functional Richness

bench_sp_fric <- microbenchmark::microbenchmark(
  species_200    = fd_fric(     traits_birds, site_sp_birds),
  species_1000   = fd_fric(  null_sp_1000$tr, null_sp_1000$si),
  species_10000  = fd_fric( null_sp_10000$tr, null_sp_10000$si),
  species_100000 = fd_fric(null_sp_100000$tr, null_sp_100000$si),
  times = 30
)

ggplot2::autoplot(bench_sp_fric)

Performance comparison of fd_fric() with increasing number of species.

bench_sp_fric
#> Unit: milliseconds
#>            expr       min        lq      mean    median        uq        max neval
#>     species_200  64.13693  77.22506  86.41686  87.48392  95.01912  101.53571    30
#>    species_1000  19.91788  48.31584  62.22163  67.09528  78.68881   90.86103    30
#>   species_10000  54.59200  80.25405 106.29215 113.69053 123.96300  166.99047    30
#>  species_100000 705.44201 805.23353 895.93754 872.40737 950.08097 1357.15555    30

Functional Divergence

bench_sp_fdiv <- microbenchmark::microbenchmark(
  species_200    = fd_fdiv(     traits_birds, site_sp_birds),
  species_1000   = fd_fdiv(  null_sp_1000$tr, null_sp_1000$si),
  species_10000  = fd_fdiv( null_sp_10000$tr, null_sp_10000$si),
  species_100000 = fd_fdiv(null_sp_100000$tr, null_sp_100000$si),
  times = 30
)

ggplot2::autoplot(bench_sp_fdiv)

Performance comparison of fd_fdiv() with increasing number of species.

bench_sp_fdiv
#> Unit: milliseconds
#>            expr       min        lq      mean    median        uq       max neval
#>     species_200  65.75675  82.74022  92.22989  95.55403  98.83634  113.6111    30
#>    species_1000  24.31990  71.34581  85.56509  82.23807  93.26562  258.7621    30
#>   species_10000  77.21861 100.54385 119.36332 125.36045 135.46570  150.1822    30
#>  species_100000 694.82638 789.91390 853.43494 836.83280 919.55921 1033.8374    30

Rao’s Quadratic Entropy

bench_sp_raoq <- microbenchmark::microbenchmark(
  species_200    = fd_raoq(     traits_birds, site_sp_birds),
  species_1000   = fd_raoq(  null_sp_1000$tr, null_sp_1000$si),
  species_10000  = fd_raoq( null_sp_10000$tr, null_sp_10000$si),
  times = 30
)

ggplot2::autoplot(bench_sp_raoq)

Performance comparison of fd_raoq() with increasing number of species.

bench_sp_raoq
#> Unit: microseconds
#>           expr         min          lq         mean      median          uq         max
#>    species_200     617.236     645.822     914.5668     737.549     897.623    3043.669
#>   species_1000    9534.446    9652.328   10449.2975    9774.182   10267.441   20289.876
#>  species_10000 2212780.688 2227410.464 2396306.9486 2234898.178 2507233.705 3239781.685
#>  neval
#>     30
#>     30
#>     30

Functional Evenness

bench_sp_feve <- microbenchmark::microbenchmark(
  species_200    = fd_feve(     traits_birds, site_sp_birds),
  species_1000   = fd_feve(  null_sp_1000$tr, null_sp_1000$si),
  species_10000  = fd_feve( null_sp_10000$tr, null_sp_10000$si),
  times = 15
)

ggplot2::autoplot(bench_sp_feve)

Performance comparison of fd_feve() with increasing number of species.

bench_sp_feve
#> Unit: milliseconds
#>           expr        min         lq       mean     median         uq       max neval
#>    species_200   19.45845   61.86210   66.13876   70.94195   75.60393   92.3494    15
#>   species_1000   61.28659   96.18897  103.89838  111.66572  118.36332  137.2943    15
#>  species_10000 7974.82839 8187.74411 8294.13681 8273.52413 8376.39503 8759.0515    15

Comparing between indices

all_bench_sp <- list(fric = bench_sp_fric,
                     fdiv = bench_sp_fdiv,
                     raoq = bench_sp_raoq,
                     feve = bench_sp_feve) %>%
  bind_rows(.id = "fd_index") %>%
  mutate(n_sp = gsub("species_", "", expr) %>%
           as.numeric())

all_bench_sp %>%
  ggplot(aes(n_sp, time * 1e-9, color = fd_index)) +
  geom_point(alpha = 1/3) +
  geom_smooth() +
  scale_x_log10() +
  scale_y_log10() +
  scale_color_brewer(type = "qual",
                     labels = c(fric = "FRic", fdiv = "FDiv", raoq = "Rao's Q",
                                feve = "FEve")) +
  labs(title = "Performance comparison between indices",
       x = "# of species", y = "Time (in seconds)",
       color = "FD index") +
  theme_bw() +
  theme(aspect.ratio = 1)

Performance comparison between functions for distinct indices in fundiversity with increasing number of species. Smoothed trend lines and standard error envelopes ares shown.

Increasing the number of sites

make_more_sites <- function(n) {
  site_sp <- do.call(rbind, replicate(n, site_sp_birds, simplify = FALSE))
  rownames(site_sp) <- paste0("s", seq_len(nrow(site_sp)))

  site_sp
}

site_sp_100   <- make_more_sites(12)
site_sp_1000  <- make_more_sites(120)
site_sp_10000 <- make_more_sites(1200)

Functional Richness

bench_sites_fric <- microbenchmark::microbenchmark(
  sites_10    = fd_fric(traits_birds, site_sp_birds),
  sites_100   = fd_fric(traits_birds, site_sp_100),
  sites_1000  = fd_fric(traits_birds, site_sp_1000),
  sites_10000 = fd_fric(traits_birds, site_sp_10000),
  times = 15
)

ggplot2::autoplot(bench_sites_fric)

Performance comparison of fd_fric() with increasing number of sites.

bench_sites_fric
#> Unit: milliseconds
#>         expr        min         lq       mean     median         uq       max neval
#>     sites_10   71.68416   74.57767   86.00700   86.54204   89.98176  133.8206    15
#>    sites_100   38.16260   61.20081   75.49481   68.14976   89.16593  141.3453    15
#>   sites_1000  217.49465  259.31534  284.66718  280.32306  315.58773  339.4681    15
#>  sites_10000 2178.74594 2241.01618 2287.08006 2262.96084 2341.91784 2396.5195    15

Functional Divergence

bench_sites_fdiv <- microbenchmark::microbenchmark(
  sites_10    = fd_fdiv(traits_birds, site_sp_birds),
  sites_100   = fd_fdiv(traits_birds, site_sp_100),
  sites_1000  = fd_fdiv(traits_birds, site_sp_1000),
  sites_10000 = fd_fdiv(traits_birds, site_sp_10000),
  times = 15
)

ggplot2::autoplot(bench_sites_fdiv)

Performance comparison of fd_fdiv() with increasing number of sites.

bench_sites_fdiv
#> Unit: milliseconds
#>         expr        min         lq       mean     median        uq       max neval
#>     sites_10   71.26430   81.32178   93.05191   92.95528  102.5015  115.5599    15
#>    sites_100   49.15161   78.18654   87.77382   98.11574  102.1231  108.4241    15
#>   sites_1000  255.95116  314.93415  334.68212  340.96382  365.8025  410.0258    15
#>  sites_10000 2442.80506 2489.52070 2563.07758 2563.32031 2603.2711 2742.8240    15

Rao’s Quadratic Entropy

bench_sites_raoq = microbenchmark::microbenchmark(
  sites_10    = fd_raoq(traits = NULL, site_sp_birds, dist_traits_birds),
  sites_100   = fd_raoq(traits = NULL, site_sp_100,   dist_traits_birds),
  sites_1000  = fd_raoq(traits = NULL, site_sp_1000,  dist_traits_birds),
  sites_10000 = fd_raoq(traits = NULL, site_sp_10000, dist_traits_birds),
  times = 15
)

ggplot2::autoplot(bench_sites_raoq)

Performance comparison of fd_raoq() with increasing number of sites.

bench_sites_raoq
#> Unit: microseconds
#>         expr        min          lq        mean     median         uq        max neval
#>     sites_10    489.460    528.4935    815.2409    544.496    634.829   3576.162    15
#>    sites_100    834.088    870.0800   1523.9049    968.512   1349.571   4322.532    15
#>   sites_1000   5510.532   5648.2775   6217.1693   5722.048   6303.896   8682.980    15
#>  sites_10000 364585.747 387482.0435 446235.0449 391929.816 401485.191 979961.408    15

Functional Evenness

bench_sites_feve <- microbenchmark::microbenchmark(
  sites_10    = fd_feve(traits = NULL, site_sp_birds, dist_traits_birds),
  sites_100   = fd_feve(traits = NULL, site_sp_100,   dist_traits_birds),
  sites_1000  = fd_feve(traits = NULL, site_sp_1000,  dist_traits_birds),
  sites_10000 = fd_feve(traits = NULL, site_sp_10000, dist_traits_birds),
  times = 15
)

ggplot2::autoplot(bench_sites_feve)

Performance comparison of fd_feve() with increasing number of sites

bench_sites_feve
#> Unit: milliseconds
#>         expr        min         lq       mean     median         uq       max neval
#>     sites_10   34.80425   65.51428   75.59681   75.20675   80.92903  123.1772    15
#>    sites_100   36.21243   52.06759   67.81010   70.84707   79.89431  113.9671    15
#>   sites_1000  228.73873  272.52938  294.80104  305.90444  318.44339  343.6069    15
#>  sites_10000 2030.46418 2056.30757 2150.92871 2105.95845 2203.93375 2441.4576    15

Comparing between indices

all_bench_sites <- list(fric = bench_sites_fric,
                        fdiv = bench_sites_fdiv,
                        raoq = bench_sites_raoq,
                        feve = bench_sites_feve) %>%
  bind_rows(.id = "fd_index") %>%
  mutate(n_sites = as.numeric(gsub("sites", "", expr, fixed = TRUE)))

all_bench_sites %>%
  ggplot(aes(n_sites, time * 1e-9, color = fd_index)) +
  geom_point(alpha = 1/3) +
  geom_smooth() +
  scale_x_log10() +
  scale_y_log10() +
  scale_color_brewer(type = "qual",
                     labels = c(fric = "FRic", fdiv = "FDiv", raoq = "Rao's Q",
                                feve = "FEve")) +
  labs(title = "Performance comparison between indices",
       x = "# of sites", y = "Time (in seconds)",
       color = "FD index") +
  theme_bw() +
  theme(aspect.ratio = 1)

Performance comparison between functions for distinct indices in fundiversity with increasing number of sites. Smoothed trend lines and standard error envelopes ares shown.

Session info of the machine on which the benchmark was ran and time it took to run

#>  seconds needed to generate this document: 600.353 sec elapsed
#> ─ Session info ────────────────────────────────────────────────────────────────────────
#>  setting  value
#>  version  R version 4.5.3 (2026-03-11)
#>  os       Ubuntu 24.04.4 LTS
#>  system   x86_64, linux-gnu
#>  ui       Positron
#>  language (EN)
#>  collate  en_GB.UTF-8
#>  ctype    en_GB.UTF-8
#>  tz       Europe/Berlin
#>  date     2026-03-30
#>  pandoc   3.1.3 @ /bin/pandoc
#>  quarto   1.9.12 @ /opt/quarto/bin/quarto
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References

Baselga, Andrés, and C. David L. Orme. 2012. “Betapart: An R Package for the Study of Beta Diversity.” Methods in Ecology and Evolution 3 (5): 808–12. https://doi.org/10.1111/j.2041-210X.2012.00224.x.

Cardoso, Pedro, François Rigal, and José C. Carvalho. 2015. “BAT Biodiversity Assessment Tools, an R Package for the Measurement and Estimation of Alpha and Beta Taxon, Phylogenetic and Functional Diversity.” Methods in Ecology and Evolution 6 (2): 232–36. https://doi.org/10.1111/2041-210X.12310.

Laliberté, Etienne, and Pierre Legendre. 2010. “A Distance-Based Framework for Measuring Functional Diversity from Multiple Traits.” Ecology 91 (1): 299–305. https://doi.org/10.1890/08-2244.1.

Laliberté, Etienne, Pierre Legendre, and Bill Shipley. 2014. FD: Measuring Functional Diversity from Multiple Traits, and Other Tools for Functional Ecology.

Li, Daijiang. 2018. “hillR: Taxonomic, Functional, and Phylogenetic Diversity and Similarity Through Hill Numbers.” Journal of Open Source Software 3 (31): 1041. https://doi.org/10.21105/joss.01041.

Magneville, Camille, Nicolas Loiseau, Camille Albouy, et al. 2022. “mFD: An R Package to Compute and Illustrate the Multiple Facets of Functional Diversity.” Ecography 2022 (1). https://doi.org/10.1111/ecog.05904.

Pavoine, Sandrine. 2020. “adiv: An r Package to Analyse Biodiversity in Ecology.” Methods in Ecology and Evolution 11 (9): 1106–12. https://doi.org/10.1111/2041-210X.13430.

Rao, C. Radhakrishna. 1982. “Diversity and Dissimilarity Coefficients: A Unified Approach.” Theoretical Population Biology 21 (1): 24–43. https://doi.org/10.1016/0040-5809(82)90004-1.

Ricotta, Carlo, and Laszlo Szeidl. 2009. “Diversity Partitioning of Rao’s Quadratic Entropy.” Theoretical Population Biology 76 (4): 299–302. https://doi.org/10.1016/j.tpb.2009.10.001.

Villéger, Sébastien, Gaël Grenouillet, and Sébastien Brosse. 2013. “Decomposing Functional \(\beta\)-Diversity Reveals That Low Functional \(\beta\)-Diversity Is Driven by Low Functional Turnover in European Fish Assemblages.” Global Ecology and Biogeography 22 (6): 671–81. https://doi.org/10.1111/geb.12021.

Villéger, Sébastien, Norman W. H. Mason, and David Mouillot. 2008. “New Multidimensional Functional Diversity Indices for a Multifaceted Framework in Functional Ecology.” Ecology 89 (8): 2290–301. https://doi.org/10.1890/07-1206.1.

3. Performance Benchmark with other packages

Other packages to compute FD indices

Main functions

Benchmark between packages

Functional Dispersion (FDis)

Functional Divergence (FDiv)

Functional Evenness (FEve)

Functional Richness (FRic)

Functional Richness Intersection (FRic_intersect)

Rao’s Quadratic Entropy (Q)

Benchmark within fundiversity

Increasing the number of species

Functional Richness

Functional Divergence

Rao’s Quadratic Entropy

Functional Evenness

Comparing between indices

Increasing the number of sites

Functional Richness

Functional Divergence

Rao’s Quadratic Entropy

Functional Evenness

Comparing between indices

References

Benchmark within `fundiversity`