Package 'TraitEnvMLMWA' reference manual

Title:	Weighted Averaging (WA) and Multi-Level Methods (MLM) for Trait-Environment Association in Functional and Community Ecology
Description:	This package grew out of the paper New robust weighted averaging- and model-based methods for assessing trait-environment relationships (Methods in Ecology and Evolution). The model-based methods are GLMMs, here called multi-level models (MLM), of which the novel MLM3 outperforms all existing methods. MLM3 has up to 30% more power, but the WA-methods are 500 times faster than MLM3. The main function for WA-methods is CWMSNC_regressions. The main functions for MLM3 are make_obj_for_traitenv, expand4glmm and MLM3_p_max.
Authors:	Cajo ter Braak [aut, cre]
Maintainer:	Cajo ter Braak <[email protected]>
License:	GPL-3 \| file LICENSE
Version:	0.9001
Built:	2025-02-15 04:55:24 UTC
Source:	https://github.com/CajoterBraak/TraitEnvMLMWA

Parametric bootstrap test of trait-environment assocation using the MLM models

Description

Bootstrap_test_prmtrc performs a parametric bootstrap test on trait-environment interaction, starting from a fitted MLM3 object (or any other MLM object with the trait:env term as last fixed parameter).

Usage

Bootstrap_test_prmtrc(
  MLM3,
  test_stat = "Wald",
  nrepet = 19,
  Binomial_total = 0,
  nAGQ = 0
)
Bootstrap_test_prmtrc(
  MLM3,
  test_stat = "Wald",
  nrepet = 19,
  Binomial_total = 0,
  nAGQ = 0
)

Arguments

`MLM3`	the fitted MLM3 object, created by glmer (lme4) or glmmTMB.
`test_stat`	choice of test statistic; 'Wald' (default), 'LRT' or 'both'. The default is quicker.
`nrepet`	number of bootstraps
`Binomial_total`	scalar, 0 for count-like data and the binomial total for logit models (1 for presence-absence).
`nAGQ`	integer scalar (default 0), used only for an object created by glmer

Details

The code assumes that the parameter for trait-environment interaction (trait:env) is the last fixed parameter in summary(MLM3). First, the formula of the null model is created by deleting the trait:env term from the formula of object MLM3 (the non-null model). Second, the null model (MLM0) is fitted. Three, sampling is from this null model. For each simulated data set, the model is refitted using the formula of the MLM3 object. The code works therefore also for MLM1 and MLM2, although their use is not recommended. See also Box A2 in Appendix A4 and Appendix A1.

Value

A named list,

`p_values`	the parametric and bootstrap p-values
`MLM0`	the fitted null model
`obs`	value of the test statistic(s)
`nrepet`	number of bootstraps
`sim.boot`	values of the test statistic(s) for the nrepet bootstrapped data
`test_stat`	the chosen test statistic(s)

References

ter Braak (2019) New robust weighted averaging- and model-based methods for assessing trait-environment relationships. Methods in Ecology and Evolution (https://doi.org/10.1111/2041-210X.13278)

Examples

## Not run: 
#use a precomputed MLM3 model, e.g. from the Revisit data
data("MLM3")
## or compute the MLM3 model from the data
# data("Revisit")
# formula.MLM3 <- y ~ poly(env,2) + poly(trait,2) +
 env : trait  + (1 + env|species) + (1 + trait| site)
# MLM3 <- glmmTMB(formula.MLM3, family = betabinomial,  data=Revisit)
summary(MLM3)
res_boot <- Bootstrap_test_prmtrc(MLM3, test_stat = "Wald", nrepet = nrepet, Binomial_total = 100)
names(res_boot)
round(res_boot$p_values,3)

## End(Not run)
## Not run: 
#use a precomputed MLM3 model, e.g. from the Revisit data
data("MLM3")
## or compute the MLM3 model from the data
# data("Revisit")
# formula.MLM3 <- y ~ poly(env,2) + poly(trait,2) +
 env : trait  + (1 + env|species) + (1 + trait| site)
# MLM3 <- glmmTMB(formula.MLM3, family = betabinomial,  data=Revisit)
summary(MLM3)
res_boot <- Bootstrap_test_prmtrc(MLM3, test_stat = "Wald", nrepet = nrepet, Binomial_total = 100)
names(res_boot)
round(res_boot$p_values,3)

## End(Not run)

Weigthed averaging methods for pairwise trait-environment associations

Description

CWMSNC_regressions carries out weighted or unweighted CWM/SNC regression for each combition of trait and environmental variable with permutation testing via the max test and computation of the (un)weighted fourth-corner correlations. The output can be summarized and plotted using summary and plot.

Usage

CWMSNC_regressions(
  E,
  L,
  T,
  weighing = "N2",
  cutoff = 0,
  nrepet = 499,
  how_to_permute = list(sites = how(), species = how())
)
CWMSNC_regressions(
  E,
  L,
  T,
  weighing = "N2",
  cutoff = 0,
  nrepet = 499,
  how_to_permute = list(sites = how(), species = how())
)

Arguments

`E`	a data frame, numeric n-vector, factor or n-by-p matrix, containing the values of the environmentalvariables in n sites, or a TE_obj object containing the trait, environment and abundance data,
`L`	a n by m matrix or data frame of abundance values of m species in n sites
`T`	a data frame, numeric m-vector, factor or m-by-q matrix, containing the values of the trait(s) for m species
`weighing`	type of weights used in the regression of CWM on E and SNC on T; "unw", "FC" or "N2" (default)
`cutoff`	minimal number of occurrences of species
`nrepet`	number of permutations
`how_to_permute`	a list for two `how` calls from the permute package, the first for site permutation, the second for species permutation. Default: completely random permuation.

Details

CWMSNC_regressions is for pairwise association between traits and environmental variables. Factors in E and T data frames are expanded in to dummy variable format. For p-values of an entire factor, use WA_p_max. Entering E and T as matrices or data frames has the advantage the variable names are retained.

The permutation test(s) are carried out by the max test. This test takes the maximum of the p-values of the CWM-E regression(s) and the SNC-T regression(s). Both p-values are obtained by permutation. In the former, the rows of E are permuted (i.e. the sites), in the latter the rows of T are permuted (i.e. the species).

Details of the weighing options: "FC" give the results of the unembellished fourth-corner correlation (which uses weighting by site and species totals); "unw" gives each site and species equal weight in the regression; "N2" weighs each site and species in proportion to its Hill number of order 2 (N2); i.e. the effective richness of the site and effective number of occurrences of the species. All weighing variants use the same CWM and SNC values (the weights in calculating CWM and SNC being the abundances in L).

The option nperm in how is overruled by nrepet.

Value

An object of class CWMSNCr which is a named list, among which,

`p_values`	three permutational p-values: site-based and species-based and the maximum of these two values
`p_parametric`	parametric p-values: site-based and species-based and the maximum of these two values (can be trusted only for weighing =='unw'). NA for more than one trait or one environmental variable.
`wFC`	(weighted) fourth-corner correlations for sites and species and its signed minimum.
`lm_CWMe`	lm-object of the (possibly multiple!) regression of CWM on E. This item is pairwise only for a single environmental variable.
`lm_SNCt`	lm-object of the (possibly multiple!) regression of SNC on T. This item is pairwise only for a single trait.

References

ter Braak (2019) New robust weighted averaging- and model-based methods for assessing trait-environment relationships. Methods in Ecology and Evolution (https://doi.org/10.1111/2041-210X.13278)

ter Braak, C.J.F., Peres-Neto, P.R. & Dray, S. (2018) Simple parametric tests for trait–environment association. Journal of Vegetation Science, 29, 801-811. https://doi.org//10.1111/jvs.12666

Peres-Neto, P.R., Dray, S. & ter Braak, C.J.F. (2017) Linking trait variation to the environment: critical issues with community-weighted mean correlation resolved by the fourth-corner approach. Ecography, 40, 806-816. https://doi.org/10.1111/ecog.02302

Examples

# Aravo data set ----------------------------------------------------------
data("aravo",  package = "ade4")
Y <- aravo$spe
SLA <- aravo$traits$SLA
Snow <- aravo$env$Snow
nrepet <- 19 # change to e.g. 499 or 999
result <- CWMSNC_regressions(Snow, Y, SLA, weighing = "N2", nrepet = nrepet)
result$p_values
summary(result)
plot(result)

# untransformed analysis of all pairs. See TutorialWA_Aravo_Multi.r
#                                      for transformations that appear useful
#  data frames E,L,T
result <- CWMSNC_regressions(aravo$env, aravo$spe, aravo$traits, weighing = "N2", nrepet = nrepet)
#result$p_values # contains all pairwise p-values
#                  for site-based, species-based and max-based permutations
#result$wFC      # contains all pairwise weighted fourth-corner correlations
# (site-based, species-based, and signed min-based)
summary(result, type = "max", p_value_adjust_method = "fdr", significance_level = 0.05)
# in the  E or T matrix or data frame case, you cannot choose your own labels;
# names shoud refer to names of variables or labels of factors
(nam.list <- plot(result, trait = "", env = "" ))
plot(result, trait = "Spread", env = "Snow" )
## All plots
# for (trait in nam.list$trait.names){
#   for (env in nam.list$env.names){
#     print(plot(result, trait = trait, env = env ))
#   }
# }

# get Revisit data ---------------------------------------------------
data("Revisit")
## adapt dataframe dat for WA-based analyses
n_sites <- with(Revisit, nlevels(factor(site)))
n_species <- with(Revisit, nlevels(factor(species)))
species <- Revisit$species[seq(from  = 1, by = n_sites, length.out = n_species)]
sites <- Revisit$site[1:n_sites]
trait <- Revisit$trait[seq(from  = 1, by = n_sites, length.out = n_species)]
env <- Revisit$env[1:n_sites]
Y <- matrix(Revisit$value, nrow = n_sites,ncol = n_species,
            dimnames = list(sites= sites,species=species))
# #Alternative using the function dat4MLM2TE_obj
# TE_obj <- dat4MLM2TE_obj(Revisit)
# trait <- TE_obj$T; env <- TE_obj$E; Y <- TE_obj$L
#  CWM/SNC regressions ------------------------------------------
set.seed(1231)
result <- CWMSNC_regressions(env, Y, trait, weighing = "N2", nrepet = nrepet)
summary(result)
plot(result)



# Comparison of two versions of the max test------------------------------------
obj <- make_obj_for_traitenv(env,Y, trait, cutoff=0)
set.seed(1231)
# slow
system.time(aa<- WA_p_max(obj, nrepet = nrepet, fast = FALSE))
round(aa$p_values,4)

set.seed(1231)
# default
system.time(bb<- WA_p_max(obj, nrepet = nrepet, fast = TRUE))
round(bb$p_values,4)
# illustrating their equality
or1<- order(aa$sim.row)
or2<- order(bb$sim.row)
all.equal(or1,or2)
or1<- order(aa$sim.col)
or2<- order(bb$sim.col)
all.equal(or1,or2)


# fast, all three weighings   --------------------------------------------------

system.time(bb<- WA_p_max(obj, weighing = "N2", nrepet = nrepet))
round(bb$p_values,5)

system.time(FC<- WA_p_max(obj, weighing = "FC", nrepet = nrepet))
round(FC$p_values,5)

system.time(cc<- WA_p_max(obj, weighing = "unw", nrepet = nrepet))
round(cc$p_values,5)

# comparion with fourtcorner in ade4  ---------------------------------------

ade4::fourthcorner(data.frame(env),as.data.frame(Y),data.frame(trait), nrepet = nrepet)
result <- CWMSNC_regressions(env, Y, trait, weighing = "FC", nrepet = nrepet)
summary(result,digits = 4)



# Aravo data set ----------------------------------------------------------
data("aravo",  package = "ade4")
Y <- aravo$spe
SLA <- aravo$traits$SLA
Snow <- aravo$env$Snow
nrepet <- 19 # change to e.g. 499 or 999
result <- CWMSNC_regressions(Snow, Y, SLA, weighing = "N2", nrepet = nrepet)
result$p_values
summary(result)
plot(result)

# untransformed analysis of all pairs. See TutorialWA_Aravo_Multi.r
#                                      for transformations that appear useful
#  data frames E,L,T
result <- CWMSNC_regressions(aravo$env, aravo$spe, aravo$traits, weighing = "N2", nrepet = nrepet)
#result$p_values # contains all pairwise p-values
#                  for site-based, species-based and max-based permutations
#result$wFC      # contains all pairwise weighted fourth-corner correlations
# (site-based, species-based, and signed min-based)
summary(result, type = "max", p_value_adjust_method = "fdr", significance_level = 0.05)
# in the  E or T matrix or data frame case, you cannot choose your own labels;
# names shoud refer to names of variables or labels of factors
(nam.list <- plot(result, trait = "", env = "" ))
plot(result, trait = "Spread", env = "Snow" )
## All plots
# for (trait in nam.list$trait.names){
#   for (env in nam.list$env.names){
#     print(plot(result, trait = trait, env = env ))
#   }
# }

# get Revisit data ---------------------------------------------------
data("Revisit")
## adapt dataframe dat for WA-based analyses
n_sites <- with(Revisit, nlevels(factor(site)))
n_species <- with(Revisit, nlevels(factor(species)))
species <- Revisit$species[seq(from  = 1, by = n_sites, length.out = n_species)]
sites <- Revisit$site[1:n_sites]
trait <- Revisit$trait[seq(from  = 1, by = n_sites, length.out = n_species)]
env <- Revisit$env[1:n_sites]
Y <- matrix(Revisit$value, nrow = n_sites,ncol = n_species,
            dimnames = list(sites= sites,species=species))
# #Alternative using the function dat4MLM2TE_obj
# TE_obj <- dat4MLM2TE_obj(Revisit)
# trait <- TE_obj$T; env <- TE_obj$E; Y <- TE_obj$L
#  CWM/SNC regressions ------------------------------------------
set.seed(1231)
result <- CWMSNC_regressions(env, Y, trait, weighing = "N2", nrepet = nrepet)
summary(result)
plot(result)



# Comparison of two versions of the max test------------------------------------
obj <- make_obj_for_traitenv(env,Y, trait, cutoff=0)
set.seed(1231)
# slow
system.time(aa<- WA_p_max(obj, nrepet = nrepet, fast = FALSE))
round(aa$p_values,4)

set.seed(1231)
# default
system.time(bb<- WA_p_max(obj, nrepet = nrepet, fast = TRUE))
round(bb$p_values,4)
# illustrating their equality
or1<- order(aa$sim.row)
or2<- order(bb$sim.row)
all.equal(or1,or2)
or1<- order(aa$sim.col)
or2<- order(bb$sim.col)
all.equal(or1,or2)


# fast, all three weighings   --------------------------------------------------

system.time(bb<- WA_p_max(obj, weighing = "N2", nrepet = nrepet))
round(bb$p_values,5)

system.time(FC<- WA_p_max(obj, weighing = "FC", nrepet = nrepet))
round(FC$p_values,5)

system.time(cc<- WA_p_max(obj, weighing = "unw", nrepet = nrepet))
round(cc$p_values,5)

# comparion with fourtcorner in ade4  ---------------------------------------

ade4::fourthcorner(data.frame(env),as.data.frame(Y),data.frame(trait), nrepet = nrepet)
result <- CWMSNC_regressions(env, Y, trait, weighing = "FC", nrepet = nrepet)
summary(result,digits = 4)

Utility function dat4MLM2TE_obj

Description

dat4MLM2TE_obj creates from data in a format for glm(m)/MLM a TE_obj object (see make_obj_for_traitenv), which consists of trait, environment and abundance data. The argument dat is usually created using expand4glmm. The function is used repeatedly in MLM3_p_max.

Usage

dat4MLM2TE_obj(dat, cutoff = 0)
dat4MLM2TE_obj(dat, cutoff = 0)

Arguments

`dat`	dataframe with names y, site, species, trait and env for values of abundance, identity of site and of species and the trait value and environmental value, respectively.
`cutoff`	minimal number of occurrences of species

Details

The order of data in dat should be in standard order, that is, first all data on species 1, then species 2, with all sites listed in identical order for each species (including zero abundances). BEWARE: The function currently works for a single trait and environmental variable only!!!!

Value

An object of class TE_obj

References

ter Braak (2019) New robust weighted averaging- and model-based methods for assessing trait-environment relationships. Methods in Ecology and Evolution (https://doi.org/10.1111/2041-210X.13278)

Examples

## Not run: 
data("Revisit")
str(Revisit)
TE_obj <- dat4MLM2TE_obj(Revisit)
str(TE_obj)

## End(Not run)
## Not run: 
data("Revisit")
str(Revisit)
TE_obj <- dat4MLM2TE_obj(Revisit)
str(TE_obj)

## End(Not run)

Utility function expand4glmm

Description

expand4glmm inflates a TE_obj object (see make_obj_for_traitenv), which consists of trait, environment and abundance data, into a format for glm, glmer and glmmTMB.

Usage

expand4glmm(obj, K = 0)
expand4glmm(obj, K = 0)

Arguments

`obj`	an object of class TE_obj, usually the output of function `make_obj_for_traitenv`.
`K`	scalar, 0 for count-like data and the binomial total for data that you like to analyse using logit models (1 for presence-absence).

Details

With single trait and single environment variable data (ncol(obj$T)== ncol(obj$E)==1), the names of the trait and environmental variables are changed to trait and env (to allow identical MLM formulas for different data and variables ). In the multi-variable case, the original names are kept and all interactions are added. expand4glmm is used repeatedly in the model-based permutational max test using function MLM3_p_max. In this function, obj is extended with list elements trait0 and env0 to allow for the detail needed in the model-based permutational max test. If used in this way, the internal logical inPermut_r_c is set to TRUE.

Value

A data frame. For single trat and enviornmental variable data:

`y`	the response; the abuncance values in obj$L
`site`	a factor indicating the site corresponding to each value of y
`species`	a factor indicating the species corresponding to each value of y
`obs`	integer 1 to N, the length of y
`trait`	trait
`env`	environmental variable
`trait.env`	the product

In the multi-trait environment case: all traits and environmental variables and all pairwise interactions

References

ter Braak (2019) New robust weighted averaging- and model-based methods for assessing trait-environment relationships. Methods in Ecology and Evolution (https://doi.org/10.1111/2041-210X.13278 )

ter Braak, C.J.F., Peres-Neto, P. & Dray, S. (2017) A critical issue in model-based inference for studying trait-based community assembly and a solution. PeerJ, 5, e2885. https://doi.org/10.7717/peerj.2885

Examples

## Not run: 
data("aravo",  package = "ade4")
Y <-aravo$spe
trait <- scale(aravo$traits$SLA)
env <- scale(aravo$env$Snow)
obj <- make_obj_for_traitenv(env,Y, trait, cutoff=0)
K  = 0 # 0 for non-binomial models
dat <- expand4glmm(obj, K = K)
names(dat)
library(glmmTMB)
formula.MLM3 <- y ~ poly(env,2) + poly(trait,2) +
 env : trait  + (1 + env|species) + (1 + trait| site)
MLM3 <- glmmTMB(formula.MLM3, family = betabinomial,  data=dat)
summary(MLM3)
plot_MLM3(MLM3)

## End(Not run)
## Not run: 
data("aravo",  package = "ade4")
Y <-aravo$spe
trait <- scale(aravo$traits$SLA)
env <- scale(aravo$env$Snow)
obj <- make_obj_for_traitenv(env,Y, trait, cutoff=0)
K  = 0 # 0 for non-binomial models
dat <- expand4glmm(obj, K = K)
names(dat)
library(glmmTMB)
formula.MLM3 <- y ~ poly(env,2) + poly(trait,2) +
 env : trait  + (1 + env|species) + (1 + trait| site)
MLM3 <- glmmTMB(formula.MLM3, family = betabinomial,  data=dat)
summary(MLM3)
plot_MLM3(MLM3)

## End(Not run)

Utility function make_obj_for_traitenv

Description

make_obj_for_traitenv combines the three data items needed for analyzing trait-environment association into a single object of class TE_obj. In the process, empty sites and non-occurring species are deleted. There is an option for stronger deleting criteria.

Usage

make_obj_for_traitenv(E, L, T, cutoff = 0)
make_obj_for_traitenv(E, L, T, cutoff = 0)

Arguments

`E`	a numeric n-vector or n by p matrix containing p environmental variable(s) of n sites
`L`	a n by m matrix or data frame of abundance values of m species in n sites
`T`	a numeric m-vector or m by q matrix containing q traits of m species
`cutoff`	minimal number of occurrences of species

Details

If E or T is a matrix, the column names are retained. If E or T is a vector, E gets name "env" and T gets name "trait". If you wish to retain the original name, enter E and T as data frames or single column matrices with a column name.

Value

A named list,

`L`	a sites by species matrix of abundances, after removal of species and sites, based on cutoff
`E`	a matrix of environmental values (rows are the same sites as the rows of L)
`T`	a matrix of trait values (rows are the same as the column of L)

References

ter Braak (2019) New robust weighted averaging- and model-based methods for assessing trait-environment relationships. Methods in Ecology and Evolution (https://doi.org/10.1111/2041-210X.13278)

Examples

## Not run: 
data("aravo",  package = "ade4")
Y <-aravo$spe
trait <- scale(aravo$traits$SLA)
env <- scale(aravo$env$Snow)
obj <- make_obj_for_traitenv(env,Y, trait, cutoff=0)
str(obj)

## End(Not run)
## Not run: 
data("aravo",  package = "ade4")
Y <-aravo$spe
trait <- scale(aravo$traits$SLA)
env <- scale(aravo$env$Snow)
obj <- make_obj_for_traitenv(env,Y, trait, cutoff=0)
str(obj)

## End(Not run)

MLM3-fit to Revisit data using trait C:N ratio and environmental variable TMG

Description

MLM3 is a glmmTMB object consisting of the fit of the MLM3 model to the Revisit data using the code

formula.MLM3 <- y ~ trait*env +(1+trait|site)+(1+env|species)

MLM3 <- glmmTMB(formula.MLM3, family = betabinomial, data= Revisit)

References

ter Braak (2019) New robust weighted averaging- and model-based methods for assessing trait-environment relationships. Methods in Ecology and Evolution (https://doi.org/10.1111/2041-210X.13278)

quadratic MLM3-fit to Aravo data using SLA and Snow

Description

MLM3_Aravo is a glmerMod object from the lme4 package consisting of the quadratic fit of the MLM3 model to the Aravo data from the ade4 package using the trait SLA and the environmental variable Snow with code

formula.MLM3.quad <- y ~ poly(trait,2) + poly(env,2) +trait:env +

(1+trait|site)+(1+env|species)

MLM3_Aravo <- glmer(formula.MLM3.quad, data=Aravo_in_glmmformat,

family= poisson, nAGQ=0, control = glmerControl(calc.derivs=F))

To get the data in Aravo_in_glmmformat use expand4glmm.

References

ter Braak (2019) New robust weighted averaging- and model-based methods for assessing trait-environment relationships. Methods in Ecology and Evolution, Appendix A7 (https://doi.org/10.1111/2041-210X.13278)

Permutational max test of trait-environment assocation for MLM models

Description

MLM3_p_max performs the permutational max test of trait-environment interaction for MLM models, starting from a fitted MLM3 object.

Usage

MLM3_p_max(
  MLM3,
  nrepet = 19,
  Binomial_total = 0,
  test_stat = "Wald",
  how_to_permute = list(sites = how(), species = how()),
  print = 1,
  nAGQ = 0
)
MLM3_p_max(
  MLM3,
  nrepet = 19,
  Binomial_total = 0,
  test_stat = "Wald",
  how_to_permute = list(sites = how(), species = how()),
  print = 1,
  nAGQ = 0
)

Arguments

`MLM3`	the fitted MLM3 object, created by glmer (lme4) or glmmTMB.
`nrepet`	number of bootstraps
`Binomial_total`	scalar, 0 for count-like data and the binomial total for logit models (1 for presence-absence).
`test_stat`	choice of test statistic; 'Wald' (default) or 'LRT'.
`how_to_permute`	a list for two `how` calls, the first for site permutation, the second for species permutation.
`print`	integer; print progress every `print` iterations
`nAGQ`	integer scalar (default 0), used only for an object created by glmer

Details

The code assumes that the interaction parameter is the last fixed parameter in summary(MLM3). The data used in the max test is extracted using dat4MLM2TE_obj. This generates an object of class TE_obj (see make_obj_for_traitenv). dat4MLM2TE_obj is limitted for use with a single trait and single environmental variable, and so is therefore MLM3_p_max. In the model-based permutation tests, either the trait values or the environmental values in the interaction term T*E of the model are permuted to yield a species- and site-level test, respectively. Main effects for the permuted trait and environmental variable are added to ensure that the interaction after permutation has a corresponding main effect. For further details, see Appendices A4 and A5 of ter Braak (2019).

Value

A named list, among which,

`p_values`	four p-values: one parametric p-value (Wald test) and three permutational p-values: site-based and species-based and the maximum of these two values
`obs`	values of the test statistic for sites (first row) and species (second row)
`sim.row`	values of the test statistic for the nrepet data in which the rows of E are permuted
`sim.col`	values of the test statistic for the nrepet data in which the rows of T are permuted
`nrepet`	number of permutations

References

ter Braak (2019) New robust weighted averaging- and model-based methods for assessing trait-environment relationships. Methods in Ecology and Evolution (https://doi.org/10.1111/2041-210X.13278)

Examples

## Not run: 
#use a precomputed MLM3 model for the Revisit data
data("MLM3")
## or compute an MLM3 model from the data
# data("Revisit")
# formula.MLM3 <- y ~ poly(env,2) + poly(trait,2) +
  env : trait  + (1 + env|species) + (1 + trait| site)
# MLM3 <- glmmTMB(formula.MLM3, family = betabinomial,  data=Revisit)
summary(MLM3)
res_perm <- MLM3_p_max(MLM3, test_stat = "Wald", nrepet = nrepet, Binomial_total = 100)
names(res_perm)
round(res_perm$p_values,3)

## End(Not run)
## Not run: 
#use a precomputed MLM3 model for the Revisit data
data("MLM3")
## or compute an MLM3 model from the data
# data("Revisit")
# formula.MLM3 <- y ~ poly(env,2) + poly(trait,2) +
  env : trait  + (1 + env|species) + (1 + trait| site)
# MLM3 <- glmmTMB(formula.MLM3, family = betabinomial,  data=Revisit)
summary(MLM3)
res_perm <- MLM3_p_max(MLM3, test_stat = "Wald", nrepet = nrepet, Binomial_total = 100)
names(res_perm)
round(res_perm$p_values,3)

## End(Not run)

Plotting the interaction of a MLM3 model

Description

plot_MLM3 plots the trait-environment interaction of a fitted MLM3 object.

Usage

plot_MLM3(
  MLM3,
  verbose = FALSE,
  title = paste("site and species effects (fixed + random) against env and trait")
)
plot_MLM3(
  MLM3,
  verbose = FALSE,
  title = paste("site and species effects (fixed + random) against env and trait")
)

Arguments

`MLM3`	the fitted MLM3 object, created by glmer (lme4) or glmmTMB.
`verbose`	logical; default FALSE. If TRUE, a summary of the MLM3 object is printed.
`title`	character text to adapt the main title.

Details

The code uses libraries ggplot2 and dplyr. The trait and environment variable names in the MLM3 model must be 'trait' and 'env' as in the example (as they are hard coded)

Value

A list of printable and modifiable objects of class ggplot2.

References

ter Braak (2019) New robust weighted averaging- and model-based methods for assessing trait-environment relationships. Methods in Ecology and Evolution (https://doi.org/10.1111/2041-210X.13278)

Examples

## Not run: 
data("Revisit")
formula.MLM3 <- y ~  env*trait  + (1 + env|species) + (1 + trait| site)
MLM3 <- glmmTMB(formula.MLM3, family = betabinomial,  data=Revisit)
plot_MLM3(MLM3)

## End(Not run)
## Not run: 
data("Revisit")
formula.MLM3 <- y ~  env*trait  + (1 + env|species) + (1 + trait| site)
MLM3 <- glmmTMB(formula.MLM3, family = betabinomial,  data=Revisit)
plot_MLM3(MLM3)

## End(Not run)

Plotting the results of a weigthed averaging-based analysis of pairwise trait-environment association(s)

Description

plot.CWMSNCr plots the results of CWMSNC_regressions for the single quantitative trait and the single quantitative environmental variable, specified by the arguments trait and env. Both main effects (site totals vs E and species totals vs T) and the associations (CWM vs E and SNC vs T) are plotted.

Usage

## S3 method for class 'CWMSNCr'
plot(x, ..., title = NA, trait = 1, env = 1)
## S3 method for class 'CWMSNCr'
plot(x, ..., title = NA, trait = 1, env = 1)

Arguments

`x`	an object of class CWMSNCr, created by `CWMSNC_regressions`.
`...`	other optional arguments
`title`	character text for the main title of the association graph (optional)
`trait`	trait name or level of a nominal tait to be plotted.
`env`	environmental variable name or level of a nominal environmental variable to be plotted

Details

In the one E vector - one T vector case, you can choose your own labels for trait and env. In the E or T matrix or data frame case, names shoud refer to names of variables or labels of factors. If in error, a list of names is returned. The arguments trait and env can be numbers referring to the columns numbers in x$E and x$T; these numbers do not reflect the orginal E and T if any variable in them is a factor (nominal).

The code uses the libraries ggplot2 and dplyr.

Value

A list of two printable and modifiable objects of class ggplot2. The first plots the main effects, the second the association. The y-coordinate of the points in the first plot is the logarithm of the site total (left) and the species total (right). The y-coordinate of the points in the second plot is weighted trait mean (CWM, left) and weighted environmental mean (SNC, right). The long-dash line is at the weighted mean of the y-coordinate of the points in plots. The dotted line is at the unweighted mean of the trait (left) and of the environmental variable (right). If, in the second-left plot, the dashed line is above the dotted line, the trait main effect is positive (check in first plot, right diagram). If, in the second-right plot, the dashed line is above the dotted line, the environmental main effect is positive (check in first plot, left diagram). In this sense, the second plot shows not only the assocation (interaction) but also the sign of the main effects, shown more explicitly in the first plot.

References

ter Braak (2019) New robust weighted averaging- and model-based methods for assessing trait-environment relationships. Methods in Ecology and Evolution (https://doi.org/10.1111/2041-210X.13278)

Examples

# get Aravo data set ----------------------------------------------------------
data("aravo",  package = "ade4")
Y <- aravo$spe
SLA <- aravo$traits$SLA
Snow <- aravo$env$Snow
nrepet <- 19 # change to e.g. 499 or 999
result <- CWMSNC_regressions(Snow, Y, SLA, weighing = "N2", nrepet = nrepet)
names(result)
result$p_values
summary(result)
plot(result)


Snow <- aravo$env$Snow
Spread <- log(aravo$traits$Spread)
result <- CWMSNC_regressions(Snow, Y, Spread, weighing = "N2", nrepet = nrepet)
result$p_values
summary(result)
# in the one E vector - one T vector case, you can choose your own labels
plot(result, trait = "log Spread", env = "Snow")

# untransformed analysis of all pairs. See TutorialWA_Aravo_Multi.r
#                                      for transformations that appear useful
#  data frames E,L,T
result <- CWMSNC_regressions(aravo$env, aravo$spe, aravo$traits, weighing = "N2", nrepet = nrepet)
#result$p_values # contains all pairwise p-values
#                  for site-based, species-based and max-based permutations
#result$wFC      # contains all pairwise weighted fourth-corner correlations
# (site-based, species-based, and signed min-based)
summary(result, type = "max", p_value_adjust_method = "fdr", significance_level = 0.05)
# in the  E or T matrix or data frame case,
# names shoud refer to names of variables or labels of factors
# The next statement generates the available valid names.
(nam.list <- plot(result, trait = "", env = "" ))
plot(result, trait = "Spread", env = "Snow" )
## All plots
# for (trait in nam.list$trait.names){
#   for (env in nam.list$env.names){
#     print(plot(result, trait = trait, env = env ))
#   }
# }

# get Aravo data set ----------------------------------------------------------
data("aravo",  package = "ade4")
Y <- aravo$spe
SLA <- aravo$traits$SLA
Snow <- aravo$env$Snow
nrepet <- 19 # change to e.g. 499 or 999
result <- CWMSNC_regressions(Snow, Y, SLA, weighing = "N2", nrepet = nrepet)
names(result)
result$p_values
summary(result)
plot(result)


Snow <- aravo$env$Snow
Spread <- log(aravo$traits$Spread)
result <- CWMSNC_regressions(Snow, Y, Spread, weighing = "N2", nrepet = nrepet)
result$p_values
summary(result)
# in the one E vector - one T vector case, you can choose your own labels
plot(result, trait = "log Spread", env = "Snow")

# untransformed analysis of all pairs. See TutorialWA_Aravo_Multi.r
#                                      for transformations that appear useful
#  data frames E,L,T
result <- CWMSNC_regressions(aravo$env, aravo$spe, aravo$traits, weighing = "N2", nrepet = nrepet)
#result$p_values # contains all pairwise p-values
#                  for site-based, species-based and max-based permutations
#result$wFC      # contains all pairwise weighted fourth-corner correlations
# (site-based, species-based, and signed min-based)
summary(result, type = "max", p_value_adjust_method = "fdr", significance_level = 0.05)
# in the  E or T matrix or data frame case,
# names shoud refer to names of variables or labels of factors
# The next statement generates the available valid names.
(nam.list <- plot(result, trait = "", env = "" ))
plot(result, trait = "Spread", env = "Snow" )
## All plots
# for (trait in nam.list$trait.names){
#   for (env in nam.list$env.names){
#     print(plot(result, trait = trait, env = env ))
#   }
# }

Revisit data

Description

The data is from the revisit to the low-elevation, non-serpentine sites of Robert Whittaker’s historic plant community study sites in the Siskiyou Mountains of Southwest Oregon (Damschen, Harrison & Grace 2010). Briefly, the data consists of the abundance of 75 species in 52 sites, calculated from the number of 100 quadrat corners per site that each species intersected (Miller et al. 2018, 2019). The environmental variable and functional trait are standardized versions of the original topographic moisture gradient (TMG) and the leaf carbon-to-nitrogen ratio (C:N), respectively (Miller et al. 2019). The dataframe Revisit has been derived from the whittaker_revisit_data.csv file from Miller et al. (2018), who describe the variables as follows

site study site ID (integer, one study plot per site)
species name of species
trait functional trait: leaf tissue carbon to nitrogen ratio
env environmental variable: site position on the topographic moisture gradient (higher numbers are topographically drier sites)
value plant abundance (see Description for details)
y matrix with two columns with, as successes and failures, value and 100 - value, respectively.

References

Damschen, E.I., Harrison, S. & Grace, J.B. (2010) Climate change effects on an endemic-rich edaphic flora: resurveying Robert H. Whittaker's Siskiyou sites (Oregon, USA). Ecology, 91, 3609-3619. https://doi.org/10.1890/09-1057.1

Miller JED, Damschen EI, Ives AR (2018) Data from: Functional traits and community composition: a comparison among community-weighted means, weighted correlations, and multilevel models. Dryad Digital Repository. https://doi.org/10.5061/dryad.7gj0s3b

Miller JED, Damschen EI, Ives AR (2019) Functional traits and community composition: a comparison among community-weighted means, weighted correlations, and multilevel models. Methods in Ecology and Evolution. https://doi.org/10.1111/2041-210x.13119

ter Braak (2019) New robust weighted averaging- and model-based methods for assessing trait-environment relationships. Methods in Ecology and Evolution (https://doi.org/10.1111/2041-210X.13278)

Summary of a weigthed averaging-based analysis of trait-environment association

Description

summary.CWMSNCr summarizes the results of CWMSNC_regressions. For a single quantitative trait and a single quantitative environmental variable three types of correlations and p-values are given (sites, species, min/max). For nominal and multipe trait and environment data, one set of such correlations and p-values is printed (by default, the max p-values and signed minimum fourth-corner correlations) with an associated heatmap of the significant associations. The p-values can be adjusted for multiple testing.

Usage

## S3 method for class 'CWMSNCr'
summary(
  object,
  ...,
  digits = 3,
  type = "max",
  p_value_adjust_method = "fdr",
  significance_level = 0.05,
  silent = FALSE
)
## S3 method for class 'CWMSNCr'
summary(
  object,
  ...,
  digits = 3,
  type = "max",
  p_value_adjust_method = "fdr",
  significance_level = 0.05,
  silent = FALSE
)

Arguments

`object`	an object of class CWMSNCr, created by `CWMSNC_regressions`.
`...`	other optional arguments
`digits`	number of digits to print
`type`	"sites", "species" or "max" (default, which combines sites and species). Used only for multiple or nominal trait and environmental data
`p_value_adjust_method`	method for adjustment of the p-values for multiple comparison. "fdr" (default), "holm", "hochberg", "hommel", "bonferroni", "BH", "BY", or "none". Used only for multiple or nominal trait and environmental data
`significance_level`	threshold for plotting a heatmap of the signed p-values
`silent`	no printed output when TRUE (default FALSE)

Details

p_value_adjust_method uses p.adjust on P-values of all pxq trait-environment combinations of the site-level and the species-level tests, which, for type == 'max' are subsequently combined by taking the maximum of the adjusted site P-value of the CWM regression and adjusted species P-value for the SNC regression for each combination. This adjustment method is the same as used in fourthcorner and is less conservative than applying p.adjust on the max P-values directly.

Value

For quantitative single trait-single environmental variable data: a numeric matrix with trait-environment correlations (first row) and p-values (second row) for sites, species and their min/max combination (columns). Correlations in the min/max column are signed minima of sites and species, being 0 if the correlations for sites and species differ in sign. p-values in the min/max column are the maximum of the p-values for sites and species.

For nominal or multiple trait/environment data: a list of

`p_val_adj`	the adjusted p-values
`FCcorrelations`	the (weighted) fourth corner correlations
`heatmap`	a gglot object containing the basis heatmap on the basis of argument `significance_level`

References

ter Braak (2019) New robust weighted averaging- and model-based methods for assessing trait-environment relationships. Methods in Ecology and Evolution (https://doi.org/10.1111/2041-210X.13278)

Examples

# get Aravo data set ----------------------------------------------------------
data("aravo",  package = "ade4")
Y <- aravo$spe
SLA <- aravo$traits$SLA
Snow <- aravo$env$Snow
nrepet <- 19 # change to e.g. 499 or 999
result <- CWMSNC_regressions(Snow, Y, SLA, weighing = "N2", nrepet = nrepet)
names(result)
result$p_values
summary(result)
plot(result)


Snow <- aravo$env$Snow
Spread <- log(aravo$traits$Spread)
result <- CWMSNC_regressions(Snow, Y, Spread, weighing = "N2", nrepet = nrepet)
result$p_values
summary(result)
# in the one E vector - one T vector case, you can choose your own labels
plot(result, trait = "log Spread", env = "Snow")

# untransformed analysis of all pairs. See TutorialWA_Aravo_Multi.r
#                                      for transformations that appear useful
#  data frames E,L,T
result <- CWMSNC_regressions(aravo$env, aravo$spe, aravo$traits, weighing = "N2", nrepet = nrepet)
#result$p_values # contains all pairwise p-values
#                  for site-based, species-based and max-based permutations
#result$wFC      # contains all pairwise weighted fourth-corner correlations
# (site-based, species-based, and signed min-based)
summary(result, type = "max", p_value_adjust_method = "fdr", significance_level = 0.05)
# in the  E or T matrix or data frame case,
# names shoud refer to names of variables or labels of factors
# The next statement generates the available valid names.
(nam.list <- plot(result, trait = "", env = "" ))
plot(result, trait = "Spread", env = "Snow" )
## All plots
# for (trait in nam.list$trait.names){
#   for (env in nam.list$env.names){
#     print(plot(result, trait = trait, env = env ))
#   }
# }

# get Aravo data set ----------------------------------------------------------
data("aravo",  package = "ade4")
Y <- aravo$spe
SLA <- aravo$traits$SLA
Snow <- aravo$env$Snow
nrepet <- 19 # change to e.g. 499 or 999
result <- CWMSNC_regressions(Snow, Y, SLA, weighing = "N2", nrepet = nrepet)
names(result)
result$p_values
summary(result)
plot(result)


Snow <- aravo$env$Snow
Spread <- log(aravo$traits$Spread)
result <- CWMSNC_regressions(Snow, Y, Spread, weighing = "N2", nrepet = nrepet)
result$p_values
summary(result)
# in the one E vector - one T vector case, you can choose your own labels
plot(result, trait = "log Spread", env = "Snow")

# untransformed analysis of all pairs. See TutorialWA_Aravo_Multi.r
#                                      for transformations that appear useful
#  data frames E,L,T
result <- CWMSNC_regressions(aravo$env, aravo$spe, aravo$traits, weighing = "N2", nrepet = nrepet)
#result$p_values # contains all pairwise p-values
#                  for site-based, species-based and max-based permutations
#result$wFC      # contains all pairwise weighted fourth-corner correlations
# (site-based, species-based, and signed min-based)
summary(result, type = "max", p_value_adjust_method = "fdr", significance_level = 0.05)
# in the  E or T matrix or data frame case,
# names shoud refer to names of variables or labels of factors
# The next statement generates the available valid names.
(nam.list <- plot(result, trait = "", env = "" ))
plot(result, trait = "Spread", env = "Snow" )
## All plots
# for (trait in nam.list$trait.names){
#   for (env in nam.list$env.names){
#     print(plot(result, trait = trait, env = env ))
#   }
# }

Max test for the joint association between multiple traits and environmental variables (incl. nominal variables) using weighted averaging methods (CWM/SNC regression)

Description

For the test on multi-trait multi-environment association, two test statistics are available, one which accounts for correlations among the traits and among the environmental variables (score_test == TRUE) and one which does not. The former is related to double constrained correspondence analysis (ter Braak et al. 2018) and the latter to RLQ (Dray et al. 2014). created using make_obj_for_traitenv. If E is a TE_obj, the arguments L and T are ignored.

Usage

WA_p_max(
  E,
  L = 0,
  T = 0,
  nrepet = 19,
  weighing = "N2",
  type = "joint",
  score_test = TRUE,
  cutoff = 0,
  fast = TRUE
)
WA_p_max(
  E,
  L = 0,
  T = 0,
  nrepet = 19,
  weighing = "N2",
  type = "joint",
  score_test = TRUE,
  cutoff = 0,
  fast = TRUE
)

Arguments

`E`	a data frame, numeric n-vector, factor or n-by-p matrix, containing the values of the environmentalvariables in n sites, or a TE_obj object containing the trait, environment and abundance data,
`L`	a n by m matrix or data frame of abundance values of m species in n sites
`T`	a data frame, numeric m-vector, factor or m-by-q matrix, containing the values of the trait(s) for m species
`nrepet`	number of permutations
`weighing`	type of weights used in the regression of CWM on E and SNC on T; "unw", "FC" or "N2" (default)
`type`	'joint' testing of the association between a set of traits and a set environmental variables (default) or 'onebyone' 1-1 tests for each pair of trait and environmental variable
`score_test`	logical. TRUE for the score test statistic, which accounts for correlations (default) and FALSE without accounting for correlations among traits and among environmental variables
`cutoff`	minimal number of occurrences of species
`fast`	logical, whether the fast version is used or the slow version (default TRUE). For multi-trait-environment data, fast is set to TRUE.

Details

Nomimal traits and environmental variables (factors) are expanded into dummy variables if E and/or T are data frames. Set E or T to a data frame with a single factor to obtain test of association with the factor. For multi-trait, multi-environment data and score_test==TRUE, the trait and environment data are internally transformed to normalized singular vectors. If score_test== FALSE, the variables are standardized internally to weighted mean 0 and variance 1. The permutation tests is carried out by the max test. This test takes the maximum of the p-values of the CWM-E regression and the SNC-T regression. Both p-values are obtained by permutation. In the former, the rows of E are permuted, in the latter the rows of T are permuted. The slow version recomputes the CWM and SNC and the associated regression from scratch for each permutation and is available only with single numberic trait and environmental variable. The fast version precomputes the CWM and SNC and computes the test statistic by a matrix product in which the permuted traits or environmental variables are rescaled to weigthed mean 0 and variance 1 using the precomputed weights (determined by the weighing option).

Value

A named list, among which,

`p_values`	five p-values: permutational, site-based and species-based and its maximum, and the parametric ones
`obs`	values of the test statistic for sites (first row) and species (second row)
`sim.row`	values of the test statistic for the nrepet data in which the rows of E are permuted
`sim.col`	values of the test statistic for the nrepet data in which the rows of T are permuted
`nrepet`	number of permutations

References

ter Braak (2019) New robust weighted averaging- and model-based methods for assessing trait-environment relationships. Methods in Ecology and Evolution (https://doi.org/10.1111/2041-210X.13278)

ter Braak, C.J.F., Šmilauer, P. & Dray, S. (2018) Algorithms and biplots for double constrained correspondence analysis. Environmental and Ecological Statistics, 25, 171-197. https://doi.org/10.1007/s10651-017-0395-x

Dray, S., Choler, P., Dolédec, S., Peres-Neto, P.R., Thuiller, W., Pavoine, S. & ter Braak, C.J.F. (2014) Combining the fourth-corner and the RLQ methods for assessing trait responses to environmental variation. Ecology, 95, 14-21. http://dx.doi.org/10.1890/13-0196.1

Examples

# get Aravo data set ----------------------------------------------------------
data("aravo",  package = "ade4")
Y <- aravo$spe
# Aravo data set: multi-trait multi-env test -----------------------------------
summary(aravo$env)
#E <- aravo$env[,-c(5,6)] # without Snow, without ZoogD
E <- aravo$env[,-c(5)] # without Snow, without ZoogD
# Slope is positive and very skew; therefore we logtransform, but there are zeroes
# add minimum non-zero value before taking logs
a <- min(E[E[,"Slope"]>0, "Slope"])
E[,"Slope"] <- log(E[,"Slope"]+ a)
summary(E)
T <- aravo$traits #[, -6 ] # without SLA
# all traits are skew; therefore we logtransform
T[,c(1,3)] <- log(T[,c(1,3)]+ 1) # traits with zeroes
T[,-c(1,3)] <- log(T[,-c(1,3)]) # traits without zeroes
summary(T)

set.seed(1231)
# score_test = TRUE gives the score test which
# takes intra-trait and intra-env correlations into account
#          If weighing == "FC", it give the test used
#              in double constrained correspondence analysis  )
# score_test = FALSE ignores such correlations.
#              If weighing == "FC", it give the gives the test used in RLQ

E<- aravo$env[,c(1,6,2)]
T <- aravo$traits[,c(2,6)]
nrepet <- 99 # change to e.g. 499 or 999
cc<- WA_p_max(E, Y, T, nrepet =nrepet, weighing = "N2", type = "onebyone")
cc$p_values



dd<- CWMSNC_regressions(E, Y, T, nrepet =nrepet, weighing = "N2")


aa<- WA_p_max(E, Y, T, nrepet =nrepet, weighing = "N2", score_test = TRUE)
aa$p_values

# Explicit conversion to dummy variables as performed in WA_p_max  -------
# convert any factor into dummy variables
E <-  model.matrix(as.formula(paste("~ 0", paste(names(E),  collapse= "+"), sep= "+")), data = E)
summary(E)
# convert any factor into dummy variables
T <-  model.matrix(as.formula(paste("~ 0", paste(names(T),  collapse= "+"), sep= "+")), data = T)
summary(T)
obj <- make_obj_for_traitenv(E,Y, T, cutoff=0)
set.seed(1231)

bb<- WA_p_max(obj, nrepet =nrepet, weighing = "N2", score_test = TRUE)
bb$p_values









# get Aravo data set ----------------------------------------------------------
data("aravo",  package = "ade4")
Y <- aravo$spe
# Aravo data set: multi-trait multi-env test -----------------------------------
summary(aravo$env)
#E <- aravo$env[,-c(5,6)] # without Snow, without ZoogD
E <- aravo$env[,-c(5)] # without Snow, without ZoogD
# Slope is positive and very skew; therefore we logtransform, but there are zeroes
# add minimum non-zero value before taking logs
a <- min(E[E[,"Slope"]>0, "Slope"])
E[,"Slope"] <- log(E[,"Slope"]+ a)
summary(E)
T <- aravo$traits #[, -6 ] # without SLA
# all traits are skew; therefore we logtransform
T[,c(1,3)] <- log(T[,c(1,3)]+ 1) # traits with zeroes
T[,-c(1,3)] <- log(T[,-c(1,3)]) # traits without zeroes
summary(T)

set.seed(1231)
# score_test = TRUE gives the score test which
# takes intra-trait and intra-env correlations into account
#          If weighing == "FC", it give the test used
#              in double constrained correspondence analysis  )
# score_test = FALSE ignores such correlations.
#              If weighing == "FC", it give the gives the test used in RLQ

E<- aravo$env[,c(1,6,2)]
T <- aravo$traits[,c(2,6)]
nrepet <- 99 # change to e.g. 499 or 999
cc<- WA_p_max(E, Y, T, nrepet =nrepet, weighing = "N2", type = "onebyone")
cc$p_values



dd<- CWMSNC_regressions(E, Y, T, nrepet =nrepet, weighing = "N2")


aa<- WA_p_max(E, Y, T, nrepet =nrepet, weighing = "N2", score_test = TRUE)
aa$p_values

# Explicit conversion to dummy variables as performed in WA_p_max  -------
# convert any factor into dummy variables
E <-  model.matrix(as.formula(paste("~ 0", paste(names(E),  collapse= "+"), sep= "+")), data = E)
summary(E)
# convert any factor into dummy variables
T <-  model.matrix(as.formula(paste("~ 0", paste(names(T),  collapse= "+"), sep= "+")), data = T)
summary(T)
obj <- make_obj_for_traitenv(E,Y, T, cutoff=0)
set.seed(1231)

bb<- WA_p_max(obj, nrepet =nrepet, weighing = "N2", score_test = TRUE)
bb$p_values

Package 'TraitEnvMLMWA'

Help Index

Parametric bootstrap test of trait-environment assocation using the MLM models

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Weigthed averaging methods for pairwise trait-environment associations

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Utility function dat4MLM2TE_obj

Description

Usage

Arguments

Details

Value

References

Examples

Utility function expand4glmm

Description

Usage

Arguments

Details

Value

References

Examples

Utility function make_obj_for_traitenv

Description

Usage

Arguments

Details

Value

References

See Also

Examples

MLM3-fit to Revisit data using trait C:N ratio and environmental variable TMG

Description

References

See Also

quadratic MLM3-fit to Aravo data using SLA and Snow

Description

References

Permutational max test of trait-environment assocation for MLM models

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Plotting the interaction of a MLM3 model

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Plotting the results of a weigthed averaging-based analysis of pairwise trait-environment association(s)

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Revisit data