How to Deal With Functional Entities

Camille Magneville

2021-12-16


1. Why Functional Entities (FEs)?


mFD allows gathering species into functional entities (FEs) i.e. groups of species with same trait values when many species are described with a few categorical or ordinal traits. It is particularly useful when using large datasets with “functionally similar” species. FEs also allow to understand the links between functional diversity and ecological processes as redundant species that are supposed to have similar ecological roles are clustered in this method.


2. Tutorial’s data


DATA The dataset used to illustrate this tutorial is a fruits dataset based on 25 types of fruits (i.e. species) distributed in 10 fruit baskets (i.e. assemblages). Each fruit is characterized by six trait values summarized in the following table:


Trait name Trait measurement Trait type Number of classes Classes code Unit
Size Maximal diameter Ordinal 5 small ; medium ; large cm
Plant Growth form Categorical 4 tree ; not tree NA
Climate Climatic niche Ordinal 3 temperate ; tropical NA
Seed Seed type Ordinal 3 none ; pip ; pit NA


NOTE We reduced the dataset used in mFD General Workflow to only keep ordinal and categorical traits. Categorical traits are restrained to 2 or 3 modalities per traits to limit the number of unique combinations.


The following data frame and matrix are needed:


data("fruits_traits", package = "mFD")

fruits_traits <- fruits_traits[ , 1:4]      # only keep the first 4 traits to illustrate FEs

# Decrease the number of modalities per trait for convenience ...
# ... (to have less unique combinations of trait values):

# Size grouped into only 3 categories:
fruits_traits[ , "Size"] <- as.character(fruits_traits[ , "Size"])

fruits_traits[which(fruits_traits[ , "Size"] %in% c("0-1cm", "1-3cm", "3-5cm")), "Size"] <- "small"
fruits_traits[which(fruits_traits[ , "Size"] == "5-10cm"), "Size"]  <- "medium"
fruits_traits[which(fruits_traits[ , "Size"] == "10-20cm"), "Size"] <- "large"

fruits_traits[ , "Size"] <- factor(fruits_traits[, "Size"], levels = c("small", "medium", "large"), ordered = TRUE)

# Plant type grouped into only 2 categories:
fruits_traits[ , "Plant"] <- as.character(fruits_traits[, "Plant"])

fruits_traits[which(fruits_traits[ , "Plant"] != "tree"), "Plant"] <- "Not_tree"
fruits_traits[ , "Plant"] <- factor(fruits_traits[ , "Plant"], levels = c("Not_tree", "tree"), ordered = TRUE)

# Plant Origin grouped into only 2 categories:
fruits_traits[ , "Climate"] <- as.character(fruits_traits[ , "Climate"])

fruits_traits[which(fruits_traits[ , "Climate"] != "temperate"), "Climate"] <- "tropical"
fruits_traits[ , "Climate"] <- factor(fruits_traits[, "Climate"], levels = c("temperate", "tropical"), ordered = TRUE)

# Display the table:
knitr::kable(head(fruits_traits), caption = "Species x traits dataframe based on *fruits* dataset")
Species x traits dataframe based on fruits dataset
Size Plant Climate Seed
apple medium tree temperate pip
apricot small tree temperate pit
banana large tree tropical none
currant small Not_tree temperate pip
blackberry small Not_tree temperate pip
blueberry small Not_tree temperate pip



data("baskets_fruits_weights", package = "mFD")

knitr::kable(as.data.frame(baskets_fruits_weights[1:6, 1:6]), 
             caption = "Species x assemblages dataframe based on *fruits* dataset")
Species x assemblages dataframe based on fruits dataset
apple apricot banana currant blackberry blueberry
basket_1 400 0 100 0 0 0
basket_2 200 0 400 0 0 0
basket_3 200 0 500 0 0 0
basket_4 300 0 0 0 0 0
basket_5 200 0 0 0 0 0
basket_6 100 0 200 0 0 0



Traits types based on fruits & baskets dataset
trait_name trait_type fuzzy_name
Size O NA
Plant N NA
Climate O NA
Seed O NA


Using the mFD::asb.sp.summary() function, we can sum up the assemblages data and retrieve species occurrence data:


# summarize species assemblages: 
asb_sp_fruits_summ <- mFD::asb.sp.summary(baskets_fruits_weights)

# retrieve species occurrences for the first 3 assemblages (fruits baskets):
head(asb_sp_fruits_summ$asb_sp_occ, 3)
##          apple apricot banana currant blackberry blueberry cherry grape
## basket_1     1       0      1       0          0         0      1     0
## basket_2     1       0      1       0          0         0      1     0
## basket_3     1       0      1       0          0         0      1     0
##          grapefruit kiwifruit lemon lime litchi mango melon orange
## basket_1          0         0     1    0      0     0     1      0
## basket_2          0         0     1    0      0     0     1      0
## basket_3          0         0     1    0      0     0     1      0
##          passion_fruit peach pear pineapple plum raspberry strawberry tangerine
## basket_1             1     0    1         0    0         0          1         0
## basket_2             1     0    1         0    0         0          1         0
## basket_3             1     0    1         0    0         0          1         0
##          water_melon
## basket_1           0
## basket_2           0
## basket_3           0
asb_sp_fruits_occ <- asb_sp_fruits_summ$"asb_sp_occ"


3. Gather species into FEs


mFD allows you to gather species into FEs using the mFD::sp.to.fe() function. It uses the following arguments:


USAGE

mFD::sp.to.fe(
  sp_tr       = fruits_traits, 
  tr_cat      = fruits_traits_cat, 
  fe_nm_type  = "fe_rank", 
  check_input = TRUE) 


Let’s use this function with the fruits dataset:


sp_to_fe_fruits <- mFD::sp.to.fe(
  sp_tr       = fruits_traits, 
  tr_cat      = fruits_traits_cat, 
  fe_nm_type  = "fe_rank", 
  check_input = TRUE) 


mFD::sp.to.fe() returns:

sp_to_fe_fruits$"fe_nm"
##  [1] "fe_1"  "fe_2"  "fe_3"  "fe_4"  "fe_5"  "fe_6"  "fe_7"  "fe_8"  "fe_9" 
## [10] "fe_10" "fe_11" "fe_12" "fe_13" "fe_14"


sp_fe <- sp_to_fe_fruits$"sp_fe"
sp_fe
##         apple       apricot        banana       currant    blackberry 
##        "fe_3"        "fe_2"        "fe_7"        "fe_1"        "fe_1" 
##     blueberry        cherry         grape    grapefruit     kiwifruit 
##        "fe_1"        "fe_2"        "fe_1"        "fe_8"        "fe_9" 
##         lemon          lime        litchi         mango         melon 
##        "fe_4"        "fe_5"       "fe_10"       "fe_11"        "fe_6" 
##        orange passion_fruit         peach          pear     pineapple 
##        "fe_4"       "fe_12"       "fe_13"        "fe_3"       "fe_14" 
##          plum     raspberry    strawberry     tangerine   water_melon 
##        "fe_2"        "fe_1"        "fe_1"        "fe_5"        "fe_6"



fe_tr <- sp_to_fe_fruits$"fe_tr"
fe_tr
##         Size    Plant   Climate Seed
## fe_1   small Not_tree temperate  pip
## fe_2   small     tree temperate  pit
## fe_3  medium     tree temperate  pip
## fe_4  medium     tree  tropical  pip
## fe_5   small     tree  tropical  pip
## fe_6   large Not_tree temperate  pip
## fe_7   large     tree  tropical none
## fe_8   large     tree  tropical  pip
## fe_9  medium Not_tree temperate  pip
## fe_10  small     tree  tropical  pit
## fe_11  large     tree  tropical  pit
## fe_12  small Not_tree  tropical  pip
## fe_13 medium     tree temperate  pit
## fe_14  large Not_tree  tropical none



fe_nb_sp <- sp_to_fe_fruits$"fe_nb_sp"
fe_nb_sp
##  fe_1  fe_2  fe_3  fe_4  fe_5  fe_6  fe_7  fe_8  fe_9 fe_10 fe_11 fe_12 fe_13 
##     6     3     2     2     2     2     1     1     1     1     1     1     1 
## fe_14 
##     1



sp_to_fe_fruits$"details_fe"
## $fe_codes
##                                                fe_1 
##  "SIZEsmall_PLANTnot_tree_CLIMATEtemperate_SEEDpip" 
##                                                fe_2 
##      "SIZEsmall_PLANTtree_CLIMATEtemperate_SEEDpit" 
##                                                fe_3 
##     "SIZEmedium_PLANTtree_CLIMATEtemperate_SEEDpip" 
##                                                fe_4 
##      "SIZEmedium_PLANTtree_CLIMATEtropical_SEEDpip" 
##                                                fe_5 
##       "SIZEsmall_PLANTtree_CLIMATEtropical_SEEDpip" 
##                                                fe_6 
##  "SIZElarge_PLANTnot_tree_CLIMATEtemperate_SEEDpip" 
##                                                fe_7 
##      "SIZElarge_PLANTtree_CLIMATEtropical_SEEDnone" 
##                                                fe_8 
##       "SIZElarge_PLANTtree_CLIMATEtropical_SEEDpip" 
##                                                fe_9 
## "SIZEmedium_PLANTnot_tree_CLIMATEtemperate_SEEDpip" 
##                                               fe_10 
##       "SIZEsmall_PLANTtree_CLIMATEtropical_SEEDpit" 
##                                               fe_11 
##       "SIZElarge_PLANTtree_CLIMATEtropical_SEEDpit" 
##                                               fe_12 
##   "SIZEsmall_PLANTnot_tree_CLIMATEtropical_SEEDpip" 
##                                               fe_13 
##     "SIZEmedium_PLANTtree_CLIMATEtemperate_SEEDpit" 
##                                               fe_14 
##  "SIZElarge_PLANTnot_tree_CLIMATEtropical_SEEDnone" 
## 
## $tr_uval
## $tr_uval$Size
## [1] "medium" "small"  "large" 
## 
## $tr_uval$Plant
## [1] "tree"     "Not_tree"
## 
## $tr_uval$Climate
## [1] "temperate" "tropical" 
## 
## $tr_uval$Seed
## [1] "pip"  "pit"  "none"
## 
## 
## $tr_nb_uval
##    Size   Plant Climate    Seed 
##       3       2       2       3 
## 
## $max_nb_fe
## [1] 36


4. Compute alpha and beta functional indices


Then based on the data frame containing the value of traits for each FE, the workflow is the same as the one listed in mFD General Workflow to compute functional trait based distance, multidimensional functional space and associated plots and compute alpha and beta functional indices (step 3 till the end). It will thus not be summed up in this tutorial.


mFD also allows to compute functional indices based on FEs following the framework proposed in Mouillot et al. 2014) using the mFD::alpha.fd.fe() function. It computes:


mFD::alpha.fd.fe() function is used as follows:


USAGE

mFD::alpha.fd.fe(
  asb_sp_occ       = asb_sp_fruits_occ, 
  sp_to_fe         = sp_to_fe_fruits,
  ind_nm           = c("fred", "fored", "fvuln"),
  check_input      = TRUE,
  details_returned = TRUE) 


It takes as inputs:


Let’s apply this function with the fruits dataset:


alpha_fd_fe_fruits <- mFD::alpha.fd.fe(
  asb_sp_occ       = asb_sp_fruits_occ, 
  sp_to_fe         = sp_to_fe_fruits,
  ind_nm           = c("fred", "fored", "fvuln"),
  check_input      = TRUE,
  details_returned = TRUE) 


This function returns a dataframe of indices values for each assemblage and a detailed list containing a matrix gathering the number of species per FE in each assemblage:


# dataframe with indices values for each assemblage:
alpha_fd_fe_fruits$"asb_fdfe"
##           nb_sp nb_fe     fred     fored     fvuln
## basket_1      8     7 1.142857 0.1071429 0.8571429
## basket_2      8     7 1.142857 0.1071429 0.8571429
## basket_3      8     7 1.142857 0.1071429 0.8571429
## basket_4      8     6 1.333333 0.1666667 0.6666667
## basket_5      8     6 1.333333 0.1666667 0.6666667
## basket_6      8     8 1.000000 0.0000000 1.0000000
## basket_7      8     8 1.000000 0.0000000 1.0000000
## basket_8      8     3 2.666667 0.4166667 0.6666667
## basket_9      8     3 2.666667 0.4166667 0.6666667
## basket_10     8     5 1.600000 0.1500000 0.4000000
# a matrix gathering the number of species per FE in each assemblage
alpha_fd_fe_fruits$"details_fdfe"
## $asb_fe_nbsp
##           fe_3 fe_2 fe_7 fe_1 fe_8 fe_9 fe_4 fe_5 fe_10 fe_11 fe_6 fe_12 fe_13
## basket_1     2    1    1    1    0    0    1    0     0     0    1     1     0
## basket_2     2    1    1    1    0    0    1    0     0     0    1     1     0
## basket_3     2    1    1    1    0    0    1    0     0     0    1     1     0
## basket_4     2    1    0    0    0    1    2    1     0     0    0     0     1
## basket_5     2    1    0    0    0    1    2    1     0     0    0     0     1
## basket_6     1    0    1    0    0    0    1    1     1     1    1     0     0
## basket_7     1    0    1    0    0    0    1    1     1     1    1     0     0
## basket_8     0    1    0    6    0    0    1    0     0     0    0     0     0
## basket_9     0    1    0    6    0    0    1    0     0     0    0     0     0
## basket_10    2    2    0    2    1    0    0    0     0     0    1     0     0
##           fe_14
## basket_1      0
## basket_2      0
## basket_3      0
## basket_4      0
## basket_5      0
## basket_6      1
## basket_7      1
## basket_8      0
## basket_9      0
## basket_10     0


5. Plot functional indices based on FEs


Then, it is possible to have a graphical representation of FE-based indices for a given assemblage using the mFD::alpha.fe.fd.plot() function:


USAGE

mFD::alpha.fd.fe.plot(
  alpha_fd_fe       = alpha_fd_fe_fruits,
  plot_asb_nm       = c("basket_1"),
  plot_ind_nm       = c("fred", "fored", "fvuln"),
  name_file         = NULL,
  color_fill_fored  = "darkolivegreen2",
  color_line_fred   = "darkolivegreen4",
  color_fill_bar    = "grey80",
  color_fill_fvuln  = "lightcoral",
  color_arrow_fvuln = "indianred4",
  size_line_fred    = 1.5,
  size_arrow_fvuln  = 1,
  check_input       = TRUE)


This function takes as inputs:


For the studied example, the plot looks as follows:


mFD::alpha.fd.fe.plot(
  alpha_fd_fe       = alpha_fd_fe_fruits,
  plot_asb_nm       = c("basket_1"),
  plot_ind_nm       = c("fred", "fored", "fvuln"),
  name_file         = NULL,
  color_fill_fored  = "darkolivegreen2",
  color_line_fred   = "darkolivegreen4",
  color_fill_bar    = "grey80",
  color_fill_fvuln  = "lightcoral",
  color_arrow_fvuln = "indianred4",
  size_line_fred    = 1.5,
  size_arrow_fvuln  = 1,
  check_input       = TRUE)


All FE except “fe_3” contain only one species thus FRed and FVuln are close to 1. Only “fe_3” has more species than the average number of species thus the proportion of species in excess in FE richer than average is quite low (FRed = 0.107).


References