Compute functional alpha diversity applied to distance between species following the framework from Chao et al.(2019).

alpha.fd.hill(
asb_sp_w,
sp_dist,
q = c(0, 1, 2),
tau = "mean",
check_input = TRUE,
details_returned = TRUE
)

## Arguments

asb_sp_w

a matrix with weight of species (columns) in a set of assemblages (rows). Rows and columns should have names. NA are not allowed.

sp_dist

a matrix or dist object with distance between species. Species names should be provided and match those in 'asb_sp_w'. NA are not allowed.

q

a vector containing values referring to the order of diversity to consider, could be 0, 1 and/or 2.

tau

a character string with name of function to apply to distance matrix (i.e. among all pairs of species) to get the threshold used to define 'functionally indistinct set of species'. Could be 'mean' (default), 'min' or 'max'. If tau = 'min' and there are null values in sp_dist, the threshold is the lowest strictly positive value and a warning message is displayed.

check_input

a logical value indicating whether key features the inputs are checked (e.g. class and/or mode of objects, names of rows and/or columns, missing values). If an error is detected, a detailed message is returned. Default: check.input = TRUE.

details_returned

a logical value indicating whether the user want to store values used for computing indices (see list below)

## Value

A list with:

• asb_FD_Hill a matrix containing indices values for each level of q (columns, named as 'FD_qx') for each assemblage (rows, named as in asb_sp_w)

• tau_dist the threshold value applied to distance between species to compute diversity according to function provided in tau

• if details_returned turned to TRUE a list details with

• asb_totw a vector with total weight of each assemblage

• asb_sp_relw a matrix with relative weight of species in assemblages

## Note

FD is computed applying the special case where function 'f' in equation 3c is linear:f(dij(tau)) = dij(tau)/tau, hence f(0) = 0 and f(tau) = 1. FD computed with q=2 and tau = 'max' is equivalent to the Rao's quadratic entropy from Ricotta & Szeidl (2009, J Theor Biol). FD computed with tau = 'min' is equivalent to Hill number taxonomic diversity, thus with q=0 it is species richness (S), with q = 1 it is exponential of Shannon entropy (H) and with q = 2 it is 1/(1-D) where D is Simpson diversity. Note that even when q=0, weights of species are accounted for in FD. Hence to compute FD based only on distance between species present in an assemblage (i.e. a richness-like index) , asb_sp_w has to contain only species presence/absence coded as 0/1 with q=0 and tau = 'mean'. If asb_sp_w contains only 0/1 and q>0, it means that all species have the same contribution to FD.

## References

Chao et al. (2019) An attribute diversity approach to functional diversity, functional beta diversity, and related (dis)similarity measures. Ecological Monographs, 89, e01343.

## Author

Sebastien Villeger and Camille Magneville

## Examples

# Load Species*Traits dataframe:
data('fruits_traits', package = 'mFD')

# Compute functional distance
sp_dist_fruits <- mFD::funct.dist(sp_tr         = fruits_traits,
tr_cat        = fruits_traits_cat,
metric        = "gower",
scale_euclid  = "scale_center",
ordinal_var   = "classic",
weight_type   = "equal",
stop_if_NA    = TRUE)
#> [1] "Running w.type=equal on groups=c(Size)"
#> [1] "Running w.type=equal on groups=c(Plant)"
#> [1] "Running w.type=equal on groups=c(Climate)"
#> [1] "Running w.type=equal on groups=c(Seed)"
#> [1] "Running w.type=equal on groups=c(Sugar)"
#> [1] "Running w.type=equal on groups=c(Use,Use,Use)"

# Compute alpha fd hill indices:
alpha.fd.hill(
sp_dist          = sp_dist_fruits,
q                = c(0, 1, 2),
tau              = 'mean',
check_input      = TRUE,
details_returned = TRUE)
#> $asb_FD_Hill #> FD_q0 FD_q1 FD_q2 #> basket_1 3.912219 3.082878 2.615626 #> basket_2 4.495517 4.198786 3.972157 #> basket_3 4.493944 4.266210 4.101477 #> basket_4 1.758038 1.740013 1.722964 #> basket_5 1.891440 1.872348 1.853837 #> basket_6 4.513411 4.049255 3.730993 #> basket_7 4.474346 4.175529 3.944302 #> basket_8 3.367259 2.516060 2.156245 #> basket_9 3.393249 3.039767 2.749451 #> basket_10 3.378281 3.168822 3.006560 #> #>$tau_dist
#> [1] 0.3593121
#>
#> $details #>$details$asb_totw #> basket_1 basket_2 basket_3 basket_4 basket_5 basket_6 basket_7 basket_8 #> 2000 2000 2000 2000 2000 2000 2000 2000 #> basket_9 basket_10 #> 2000 2000 #> #>$details\$asb_sp_relw
#>           apple apricot banana currant blackberry blueberry cherry grape
#> basket_1  0.200     0.0   0.05    0.00       0.00      0.00  0.075  0.00
#> basket_2  0.100     0.0   0.20    0.00       0.00      0.00  0.125  0.00
#> basket_3  0.100     0.0   0.25    0.00       0.00      0.00  0.125  0.00
#> basket_4  0.150     0.0   0.00    0.00       0.00      0.00  0.000  0.00
#> basket_5  0.100     0.0   0.00    0.00       0.00      0.00  0.000  0.00
#> basket_6  0.050     0.0   0.10    0.00       0.00      0.00  0.000  0.00
#> basket_7  0.050     0.0   0.10    0.00       0.00      0.00  0.000  0.00
#> basket_8  0.000     0.0   0.00    0.10       0.15      0.10  0.100  0.10
#> basket_9  0.000     0.0   0.00    0.05       0.05      0.05  0.050  0.20
#> basket_10 0.175     0.1   0.00    0.00       0.00      0.00  0.000  0.15
#>           grapefruit kiwifruit lemon lime litchi mango melon orange
#> basket_1        0.00      0.00  0.10  0.0   0.00  0.00  0.10   0.00
#> basket_2        0.00      0.00  0.05  0.0   0.00  0.00  0.25   0.00
#> basket_3        0.00      0.00  0.05  0.0   0.00  0.00  0.20   0.00
#> basket_4        0.00      0.05  0.05  0.0   0.00  0.00  0.00   0.20
#> basket_5        0.00      0.15  0.15  0.0   0.00  0.00  0.00   0.15
#> basket_6        0.00      0.00  0.00  0.1   0.10  0.25  0.00   0.05
#> basket_7        0.00      0.00  0.00  0.1   0.05  0.10  0.00   0.05
#> basket_8        0.00      0.00  0.05  0.0   0.00  0.00  0.00   0.00
#> basket_9        0.00      0.00  0.15  0.0   0.00  0.00  0.00   0.00
#> basket_10       0.15      0.00  0.00  0.0   0.00  0.00  0.20   0.00
#>           passion_fruit peach pear pineapple  plum raspberry strawberry
#> basket_1           0.05  0.00 0.30      0.00 0.000      0.00      0.125
#> basket_2           0.05  0.00 0.10      0.00 0.000      0.00      0.125
#> basket_3           0.05  0.00 0.10      0.00 0.000      0.00      0.125
#> basket_4           0.00  0.15 0.20      0.00 0.100      0.00      0.000
#> basket_5           0.00  0.15 0.15      0.00 0.100      0.00      0.000
#> basket_6           0.00  0.00 0.00      0.25 0.000      0.00      0.000
#> basket_7           0.00  0.00 0.00      0.25 0.000      0.00      0.000
#> basket_8           0.00  0.00 0.00      0.00 0.000      0.20      0.200
#> basket_9           0.00  0.00 0.00      0.00 0.000      0.25      0.200
#> basket_10          0.00  0.00 0.10      0.00 0.075      0.00      0.050
#>           tangerine water_melon