f_rich: f_rich

In alexology/biomonitoR: biomonitoring indices and metrics

f_rich

Description

\Sexpr[results=rd, stage=render]{ lifecycle::badge("maturing") }

Functional richness calculated as the hypervolume enclosing the functional space.

Usage

f_rich(
  x,
  trait_db = NULL,
  tax_lev = "Taxa",
  type = NULL,
  traitSel = FALSE,
  col_blocks = NULL,
  nbdim = 2,
  distance = "gower",
  zerodist_rm = FALSE,
  correction = "none",
  traceB = FALSE,
  set_param = NULL
)

Arguments

x	Result of aggregate_taxa().
trait_db	A trait dataset. Can be a data.frame ot a dist object. Taxonomic level of the traits dataset must match those of the taxonomic database. No automatic check is done.
tax_lev	Character string giving the taxonomic level used to retrieve trait information. Possible levels are Taxa, Species, Genus, Family as returned by aggregate_taxa().
type	The type of variables specified in trait_db. Must be one of F, fuzzy, or C, continuous. If more control is needed please consider to provide trait_db as a dist object. It works only when trait_db is a data.frame, otherwise ignored.
traitSel	Interactively select traits.
col_blocks	A vector that contains the number of modalities for each trait. Not needed when euclidean distance is used.
nbdim	number of dimensions for the multidimensional functional spaces. We suggest to keep nbdim as low as possible. By default biomonitoR set the number of dimensions to 2. Select auto if you want the automated selection approach according to Maire et al. (2015).
distance	To be used to compute functional distances, euclidean or gower. Default to gower. See details.
zerodist_rm	If TRUE aggregates taxa with the same traits.
correction	Correction methods for negative eigenvalues, can be one of none, lingoes, cailliez, sqrt and quasi. Ignored when type is set to C.
traceB	If TRUE ffrich will return a list as specified in details.
set_param	A list of parameters for fine tuning the calculations. max_nbdim set the maximum number of dimension for evaluating the quality of the functional space. prec can be Qt or QJ, please refere to the convhulln documentation for more information. Deafault to QJ, less accurate but less prone to errors. tol a tolerance threshold for zero, see the function is.euclid, lingoes and cailliez from the ade4 for more details. Default to 1e-07. If cor.zero is TRUE, zero distances are not modified. see the function is.euclid, lingoes and cailliez from the ade4 for more details. Default to TRUE.

Details

Functional richness (FRic) represents the amount of functional space filled by the community (Villeger et al., 2008) and it is related to the community use of resources and productivity (Mason et al., 2005). FRic is defined by the trait extremes and thus reflects the potential maximum functional dissimilarity. FRic is calculated as the hypervolume enclosing the functional space filled by the community. For this the convex hull approach is applied (Cornwell et al., 2006) using the Quickhull algorithm (Barber et al., 1996) that estimates the minimum convex hull which includes all the species considered in the previously defined functional space. Basically, this algorithm determines the taxa in the most extreme points of the functional space, links them to build the convex hull in order to calculate the volume inside it. In particular, the convex hull of a set of points S in n dimensions is the intersection of all convex sets containing S. For N points the convex hull C is then given by the expression:

C = \sum_{j=1}^{N} \lambda_j \ p_j : \ \lambda_j \geq \ for \ all \ j \ and \ \sum_{j=1}^{N} \lambda_j = 1

The functional T dimensional space is built using a certain number of dimensions (T) determined by the axes of a principal component analysis based on the trait dissimilarity matrix. Using a poor quality functional space could led to a biased assessment of FRic and false ecological conclusions so the number of axes retained for its estimation is case-specific and decided following the method proposed in Maire et al., (2015): a pragmatic approach consisting of computing all the possible functional spaces and selecting the most parsimonious one. This method uses the mSD index (mean squared deviation between the initial functional distance and the scaled distance in the functional space), which accounts explicitly for the deviation between the initial and final distance and penalizes the strong deviation. The mSD index has been widely used in statistics to assess errors and it has been demonstrated to work in different contexts and situations (Maire et al., 2015). In addition, when using Gower's distance the mSD ranges from 0 and 1, which helps to interpret quality. Finally, the resulting FRic variable is standardized by its maximum, ranging from 0 to 1. In addition, it must be considered that the number of taxa must be higher than the number of traits to have reliable FRic values (Villeger et al., 2008).

The gower distance refers to the mixed-variables coefficient of distance of Pavoine et al. (2009) as implemented in the ade4 package. This distance is meant to be used with fuzzy data.

Value

a vector with fuzzy functional richness results.

1. results Results of the f_rich() function.

2. traits A data.frame containing the traits used for the calculations.

3. taxa A data.frame conaining the taxa used for the calculations.

4. nbdim Number of dimensions used after calculatin the quality of functional spaces according to Maire et al. (2015).

5. correction The type of correction used.

6. NA_detection A data.frame containing taxa on the first column and the corresponding trais with NAs on the second column.

7. duplicated_traits If present, list the taxa with the same traits.

8. parent_child_pairs For instance in Spanish aspt both Ferrissia and Planorbidae receive a score. Abundances of the higher taxonomic level need therefore to be adjusted by subtracting the abundances of the lower taxonomic level.

References

Barber, C. B., Dobkin, D. P., & Huhdanpaa, H. (1996). The quickhull algorithm for convex hulls. ACM Transactions on Mathematical Software (TOMS), 22(4), 469-483.

Cornwell, W. K., Schwilk, D. W., & Ackerly, D. D. (2006). A trait-based test for habitat filtering: convex hull volume. Ecology, 87(6), 1465-1471

Maire, E., Grenouillet, G., Brosse, S., & Villeger, S. (2015). How many dimensions are needed to accurately assess functional diversity? A pragmatic approach for assessing the quality of functional spaces. Global Ecology and Biogeography, 24(6), 728-740.

Mason, N. W., Mouillot, D., Lee, W. G., and Wilson, J. B. (2005). Functional richness, functional evenness and functional divergence: the primary components of functional diversity. Oikos, 111(1), 112-118.

Pavoine, S., Vallet, J., Dufour, A. B., Gachet, S., & Daniel, H. (2009). On the challenge of treating various types of variables: application for improving the measurement of functional diversity. Oikos, 118(3), 391-402.

Villeger, S., Mason, N. W., & Mouillot, D. (2008). New multidimensional functional diversity indices for a multifaceted framework in functional ecology. Ecology, 89(8), 2290-2301.

See Also

aggregate_taxa

Examples

data(macro_ex)

data_bio <- as_biomonitor(macro_ex)
data_agr <- aggregate_taxa(data_bio)
data_ts <- assign_traits(data_agr)
# averaging
data_ts_av <- average_traits(data_ts)

col_blocks <- c(8, 7, 3, 9, 4, 3, 6, 2, 5, 3, 9, 8, 8, 5, 7, 5, 4, 4, 2, 3, 8)

f_rich(data_agr, trait_db = data_ts_av, type = "F", col_blocks = col_blocks)
f_rich(data_agr,
  trait_db = data_ts_av, type = "F", col_blocks = col_blocks,
  nbdim = 10, correction = "cailliez"
)

library(ade4)

rownames(data_ts_av) <- data_ts_av$Taxa
traits_prep <- prep.fuzzy(data_ts_av[, -1], col.blocks = col_blocks)

traits_dist <- ktab.list.df(list(traits_prep))
traits_dist <- dist.ktab(traits_dist, type = "F")

f_rich(data_agr, trait_db = traits_dist)

alexology/biomonitoR documentation built on Oct. 10, 2024, 12:02 a.m.