f_red: Functional redundancy
In alexology/biomonitoR: biomonitoring indices and metrics
f_red R Documentation
Functional redundancy
Description
\Sexpr[results=rd, stage=render]{ lifecycle::badge("maturing") }
This function calculates the functional redundancy based on trait categories.
Usage
f_red(
x,
trait_db = NULL,
tax_lev = "Taxa",
type = NULL,
traitSel = FALSE,
col_blocks = NULL,
distance = "gower",
zerodist_rm = FALSE,
traceB = FALSE,
correction = "none",
set_param = NULL
)
Arguments
x
Results 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 speciefied 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 ingored.
traitSel
Interactively select traits.
col_blocks
A vector that contains the number of modalities for each trait.
Not needed when euclidean distance is used.
By default biomonitoR select the optimal number of dimensions with the quality of the functional space approach.
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.
traceB
if TRUE returns a list as specified in details.
correction
Correction methods for negative eigenvalues, can be one of none, lingoes , cailliez, sqrt and quasi.
Ignored when type is set to C.
set_param
A list of parameters for fine tuning the calculations.
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 redundancy (FR) is measured as the difference between taxonomic
diversity and functional diversity (de Bello et al., 2007). It relates positively
to ecosystem stability, resistance and resilience (Hooper et al. 2005; Guillemot
et al., 2011).
FR = D - Q
The Gini-Simpson index is used to quantify Taxonomic Diversity (D, which ranges
from 0 to 1) where pi is the proportion of the abundance of taxa i in a
biological community.
D = 1 - \sum_{i=1}^{S} p_i^{2}
Rao quadratic entropy (Q; Rao, 1982) was used to estimate Functional Diversity
because it has been considered more appropriate than other indices (Botta-Dukat,
2005; Ricotta, 2005). In this formula (Q) dij is the dissimilarity (ranging
from 0 to 1), between species i and j based on a set of specified functional
traits (i.e. effect traits, see below). This index is standardized by the maximum value to constrain the values
within the range of 0-1. Rao index is estimated using presence or abundance data
and the Euclidean transformed version of the traits-based Gower dissimilarity
matrix. For this, Gower's dissimilarity index (which ranges from 0 to 1) is used
because it can deal with traits of different nature and measuring scales
(continuous, nominal, binary, ordinal, etc.; see Podani 1999 for more information)
Q = \sum_{i=1}^{S} \sum_{j=1}^{S} d_{ij} \ p_i \ p_j
Given that the concept of FR was originally developed to represent the number
of taxa contributing similarly to an ecosystem function (Walker 1992; Lawton and
Brown 1993; Rosenfeld, 2002), FR and therefore functional diversity should be
calculated using only effect traits. Effect traits are those biological
features that directly influence a specific function of the ecosystem
(e.g. productivity, nutrient cycling). See Schmera et al. (2017) and Hevia et al (2017) for more
information about effect traits in aquatic invertebrate communities. Regarding
the interpretation of the results, when taxa within a community differ
completely in their functional traits, then Q = D and thus FR = 0. On the
other hand, when all taxa have identical functional traits, then Q = 0 and
FR = D, and when in addition the number of taxa is very large and they are
equally abundant, then D (and in this case FR) approaches 1 (Pillar et al., 2013).
Although the concept of FR could suggest that functionally similar species may
compensate for the loss or failure of others, there is evidence that ecosystems
need such redundancy to perform their functions efficiently and stably over time
(Rosenfeld 2002; Biggs et al. 2012). In fact, a decrease in FR could be dramatic
in non-redundant communities since the loss or replacement of one species could
lead to loss of unique traits or functions (Hooper et al. 2005), increasing
ecosystem vulnerability (Elmqvist et al. 2003).
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.
Taxa without traits assigned in the trait database are removed from both the trait and abundance databases.
Value
a vector with fuzzy functional richness results.
-
results Results of f_red().
-
traits A data.frame containing the traits used for the calculations.
-
taxa A data.frame conaining the taxa used for the calculations.
-
nbdim Number of dimensions used after calculatin the quality of functional spaces according to Maire et al. (2015).
-
correction The type of correction used.
-
NA_detection A data.frame containing taxa on the first column and the corresponding trais with NAs on the second column.
-
duplicated_traits If present, list the taxa with the same traits.
References
Biggs, R., Schluter, M., Biggs, D., Bohensky, E. L., BurnSilver, S.,
Cundill, G., ... & Leitch, A. M. (2012). Toward principles for enhancing the
resilience of ecosystem services. Annual Review of Environment and Resources,
37, 421-448.
Botta-Dukat, Z. (2005). Rao's quadratic entropy as a measure of
functional diversity based on multiple traits. Journal of Vegetation Science,
16(5), 533-540.
de Bello, F., Leps, J., Lavorel, S., & Moretti, M. (2007).
Importance of species abundance for assessment of trait composition:
an example based on pollinator communities. Community Ecology, 8(2), 163-170.
Elmqvist, T., Folke, C., Nystrom, M., Peterson, G.,
Bengtsson, J., Walker, B., & Norberg, J. (2003). Response diversity, ecosystem
change, and resilience. Frontiers in Ecology and the Environment, 1(9), 488-494.
Guillemot, N., Kulbicki, M., Chabanet, P., & Vigliola, L. (2011).
Functional redundancy patterns reveal non-random assembly rules in a
species-rich marine assemblage. PLoS One, 6(10), e26735.
Hevia, V., Martin-Lopez, B., Palomo, S., Garcia-Llorente, M., de Bello, F.,
& Gonzalez, J. A. (2017). Trait-based approaches to analyze links between the drivers
of change and ecosystem services: Synthesizing existing evidence and future challenges.
Ecology and evolution, 7(3), 831-844.
Hooper, D. U., Chapin, F. S., Ewel, J. J., Hector, A., Inchausti,
P., Lavorel, S., et al. (2005). Effects of biodiversity on ecosystem
functioning: a consensus of current knowledge. Ecological Monographs,
75(1), 3-35.
Lawton, J.H. & Brown, V.K. (1993) Redundancy in ecosystems.
Biodiversity and Ecosystem Function (eds E.-D. Schulze & H.A. Mooney),
pp. 255-270. Springer-Verlag, Berlin.
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.
Pillar, V. D., Blanco, C. C., Muller, S. C., Sosinski, E. E.,
Joner, F., & Duarte, L. D. (2013). Functional redundancy and stability
in plant communities. Journal of Vegetation Science, 24(5), 963-974.
Podani, J. (1999). Extending Gower's general coefficient of
similarity to ordinal characters. Taxon, 331-340.
Rao, C. R. (1982). Diversity and dissimilarity coefficients:
a unified approach. Theoretical population biology, 21(1), 24-43.
Ricotta, C. (2005). A note on functional diversity measures.
Basic and Applied Ecology, 6(5), 479-486.
Rosenfeld, J. S. (2002). Functional redundancy in ecology
and conservation. Oikos, 98(1), 156-162.
Schmera, D., Heino, J., Podani, J., Eros, T., & Doledec, S. (2017).
Functional diversity: a review of methodology and current knowledge in
freshwater macroinvertebrate research. Hydrobiologia, 787(1), 27-44.
Walker, B. H. (1992). Biodiversity and ecological redundancy.
Conservation biology, 6(1), 18-23.
See Also
aggregatoR
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_red(data_agr, trait_db = data_ts_av, type = "F", col_blocks = col_blocks)
f_red(data_agr,
trait_db = data_ts_av, type = "F", col_blocks = col_blocks,
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_red(data_agr, trait_db = traits_dist)
alexology/biomonitoR documentation built on April 7, 2024, 10:15 a.m.
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| f_red | R Documentation |
Functional redundancy
Description
\Sexpr[results=rd, stage=render]{ lifecycle::badge("maturing") }This function calculates the functional redundancy based on trait categories.
Usage
f_red(
x,
trait_db = NULL,
tax_lev = "Taxa",
type = NULL,
traitSel = FALSE,
col_blocks = NULL,
distance = "gower",
zerodist_rm = FALSE,
traceB = FALSE,
correction = "none",
set_param = NULL
)
Arguments
x |
Results of |
trait_db |
A trait dataset. Can be a |
tax_lev |
Character string giving the taxonomic level used to retrieve
trait information. Possible levels are |
type |
The type of variables speciefied in |
traitSel |
Interactively select traits. |
col_blocks |
A vector that contains the number of modalities for each trait.
Not needed when |
distance |
To be used to compute functional distances, |
zerodist_rm |
If |
traceB |
if |
correction |
Correction methods for negative eigenvalues, can be one of |
set_param |
A list of parameters for fine tuning the calculations.
|
Details
Functional redundancy (FR) is measured as the difference between taxonomic diversity and functional diversity (de Bello et al., 2007). It relates positively to ecosystem stability, resistance and resilience (Hooper et al. 2005; Guillemot et al., 2011).
FR = D - Q
The Gini-Simpson index is used to quantify Taxonomic Diversity (D, which ranges from 0 to 1) where pi is the proportion of the abundance of taxa i in a biological community.
D = 1 - \sum_{i=1}^{S} p_i^{2}
Rao quadratic entropy (Q; Rao, 1982) was used to estimate Functional Diversity because it has been considered more appropriate than other indices (Botta-Dukat, 2005; Ricotta, 2005). In this formula (Q) dij is the dissimilarity (ranging from 0 to 1), between species i and j based on a set of specified functional traits (i.e. effect traits, see below). This index is standardized by the maximum value to constrain the values within the range of 0-1. Rao index is estimated using presence or abundance data and the Euclidean transformed version of the traits-based Gower dissimilarity matrix. For this, Gower's dissimilarity index (which ranges from 0 to 1) is used because it can deal with traits of different nature and measuring scales (continuous, nominal, binary, ordinal, etc.; see Podani 1999 for more information)
Q = \sum_{i=1}^{S} \sum_{j=1}^{S} d_{ij} \ p_i \ p_j
Given that the concept of FR was originally developed to represent the number of taxa contributing similarly to an ecosystem function (Walker 1992; Lawton and Brown 1993; Rosenfeld, 2002), FR and therefore functional diversity should be calculated using only effect traits. Effect traits are those biological features that directly influence a specific function of the ecosystem (e.g. productivity, nutrient cycling). See Schmera et al. (2017) and Hevia et al (2017) for more information about effect traits in aquatic invertebrate communities. Regarding the interpretation of the results, when taxa within a community differ completely in their functional traits, then Q = D and thus FR = 0. On the other hand, when all taxa have identical functional traits, then Q = 0 and FR = D, and when in addition the number of taxa is very large and they are equally abundant, then D (and in this case FR) approaches 1 (Pillar et al., 2013). Although the concept of FR could suggest that functionally similar species may compensate for the loss or failure of others, there is evidence that ecosystems need such redundancy to perform their functions efficiently and stably over time (Rosenfeld 2002; Biggs et al. 2012). In fact, a decrease in FR could be dramatic in non-redundant communities since the loss or replacement of one species could lead to loss of unique traits or functions (Hooper et al. 2005), increasing ecosystem vulnerability (Elmqvist et al. 2003).
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.
Taxa without traits assigned in the trait database are removed from both the trait and abundance databases.
Value
a vector with fuzzy functional richness results.
-
resultsResults off_red(). -
traitsAdata.framecontaining the traits used for the calculations. -
taxaAdata.frameconaining the taxa used for the calculations. -
nbdimNumber of dimensions used after calculatin the quality of functional spaces according to Maire et al. (2015). -
correctionThe type of correction used. -
NA_detectionAdata.framecontaining taxa on the first column and the corresponding trais with NAs on the second column. -
duplicated_traitsIf present, list the taxa with the same traits.
References
Biggs, R., Schluter, M., Biggs, D., Bohensky, E. L., BurnSilver, S., Cundill, G., ... & Leitch, A. M. (2012). Toward principles for enhancing the resilience of ecosystem services. Annual Review of Environment and Resources, 37, 421-448.
Botta-Dukat, Z. (2005). Rao's quadratic entropy as a measure of functional diversity based on multiple traits. Journal of Vegetation Science, 16(5), 533-540.
de Bello, F., Leps, J., Lavorel, S., & Moretti, M. (2007). Importance of species abundance for assessment of trait composition: an example based on pollinator communities. Community Ecology, 8(2), 163-170.
Elmqvist, T., Folke, C., Nystrom, M., Peterson, G., Bengtsson, J., Walker, B., & Norberg, J. (2003). Response diversity, ecosystem change, and resilience. Frontiers in Ecology and the Environment, 1(9), 488-494.
Guillemot, N., Kulbicki, M., Chabanet, P., & Vigliola, L. (2011). Functional redundancy patterns reveal non-random assembly rules in a species-rich marine assemblage. PLoS One, 6(10), e26735.
Hevia, V., Martin-Lopez, B., Palomo, S., Garcia-Llorente, M., de Bello, F., & Gonzalez, J. A. (2017). Trait-based approaches to analyze links between the drivers of change and ecosystem services: Synthesizing existing evidence and future challenges. Ecology and evolution, 7(3), 831-844.
Hooper, D. U., Chapin, F. S., Ewel, J. J., Hector, A., Inchausti, P., Lavorel, S., et al. (2005). Effects of biodiversity on ecosystem functioning: a consensus of current knowledge. Ecological Monographs, 75(1), 3-35.
Lawton, J.H. & Brown, V.K. (1993) Redundancy in ecosystems. Biodiversity and Ecosystem Function (eds E.-D. Schulze & H.A. Mooney), pp. 255-270. Springer-Verlag, Berlin.
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.
Pillar, V. D., Blanco, C. C., Muller, S. C., Sosinski, E. E., Joner, F., & Duarte, L. D. (2013). Functional redundancy and stability in plant communities. Journal of Vegetation Science, 24(5), 963-974.
Podani, J. (1999). Extending Gower's general coefficient of similarity to ordinal characters. Taxon, 331-340.
Rao, C. R. (1982). Diversity and dissimilarity coefficients: a unified approach. Theoretical population biology, 21(1), 24-43.
Ricotta, C. (2005). A note on functional diversity measures. Basic and Applied Ecology, 6(5), 479-486.
Rosenfeld, J. S. (2002). Functional redundancy in ecology and conservation. Oikos, 98(1), 156-162.
Schmera, D., Heino, J., Podani, J., Eros, T., & Doledec, S. (2017). Functional diversity: a review of methodology and current knowledge in freshwater macroinvertebrate research. Hydrobiologia, 787(1), 27-44.
Walker, B. H. (1992). Biodiversity and ecological redundancy. Conservation biology, 6(1), 18-23.
See Also
aggregatoR
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_red(data_agr, trait_db = data_ts_av, type = "F", col_blocks = col_blocks)
f_red(data_agr,
trait_db = data_ts_av, type = "F", col_blocks = col_blocks,
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_red(data_agr, trait_db = traits_dist)
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