# sensiPhy: R-package for sensitivity analysis in phylogenetic comparative methods.

#### Gustavo Paterno, Caterina Penone, Gijsbert Werner

#### 2020-04-02

##Introduction to sensiPhy The sensiPhy package provides simple functions to perform sensitivity analyses in phylogenetic comparative methods. It uses several simulation methods to estimate the impact of different types of uncertainty on Phylogenetic comparative methods:

1. Species Sampling uncertainty (sample size; influential species and clades)
2. Phylogenetic uncertainty
3. Data uncertainty (intraspecific variation and measurement error)

Functions for sensitivity analysis

sensiPhy functions use a common syntax that combines the type of uncertainty and the type of analysis:

- xxx_phylm (for linear regressions)
- xxx_phyglm (for logistic regressions)
- xxx_physig (for phylogenetic signal)
- xxx_continuous (for continuous trait evolution)
- xxx_discrete (for discrete trait evolution)

where “xxx” can be one of the 5 sensiPhy methods (see Figure below):

- Species sampling uncertainty: influ; clade; samp;
- Phylogenetic uncertainty: tree
- Data uncertainty: intra

sensiPhy workflow & functions

Additional functions

- match_dataPhy: Match data and phylogeny based on model formula
- miss.phylo.d: Calculate the phylogenetic signal for missing data
- tree.bd: Tree diversification and speciation with phylogenetic uncertainty

## 1. Sampling uncertainty

### 1.1 Sensitivity analysis for influential species

The `influ` method performs leave-one-out deletion analysis and detects influential species on parameter estimates.

##### 1.1.1 influ_phylm(): Phylogenetic linear regression

    library(sensiPhy)
    # run analysis:
    influ <- influ_phylm(log(gestaLen) ~ log(adultMass), phy = alien$phy[[1]],
                         data = alien$data, track=FALSE)

Note that `track = TRUE` shows the progress of the analysis

    # To check summary results:
    summary(influ)

    # Most influential species
    influ$influential.species

    # Visual diagnostics
    sensi_plot(influ)

    # Check most influential species on the original regression plot:
    sensi_plot(influ, graphs = 2)

##### 1.1.2. influ_physig(): Phylogenetic signal

    # Logtransform data
    alien.data$logMass <- log(alien.data$adultMass)
    # Run sensitivity analysis:
    influ <- influ_physig("logMass", data = alien.data, phy = alien.phy[[1]], track=FALSE)
    # You can change the method used to estimate signal:
    influ2 <- influ_physig("logMass", data = alien.data, phy = alien.phy[[1]], method = "lambda", track=FALSE)

    # To check summary results:
    summary(influ)
    # Most influential speciesL
    influ$influential.species
    # Visual diagnostics
    sensi_plot(influ)
    sensi_plot(influ2)

    # You can specify which graph to print:
    sensi_plot(influ, graphs = 1)
    sensi_plot(influ2, graphs = 1)

##### 1.1.3 influ_continuous() and influ_discrete: Trait Evolution Continuous and Discrete Characters

Continuous characters

    # Load data:
    data("primates")
    # Model trait evolution accounting for influential species
    adultMass<-primates$data$adultMass
    names(adultMass)<-rownames(primates$data)
    # Model trait evolution accounting for influential species
    influ_cont<-influ_continuous(data = adultMass,phy = primates$phy[[1]],
    model = "OU",cutoff = 2,n.cores = 2,track = FALSE)
    # Print summary statistics for the transitions rates, aic-values and (if applicable)
    # optimisation parameter
    summary(influ_cont)
    # Visual diagnostics
    sensi_plot(influ_cont)

Different evolutionary models from `fitContinuous` can be used: `BM`,`OU`, `EB`, `trend`, `lambda`, `kappa`, `delta` and `drift`.

Discrete characters

    # Load data:
    data("primates")

    # Create a binary trait factor
    adultMass_binary<-ifelse(primates$data$adultMass > 7350, "big", "small")
    adultMass_binary<-as.factor(as.factor(adultMass_binary))
    names(adultMass_binary)<-rownames(primates$data)

    # Model trait evolution accounting for influential species - symmetric model
    influ_binary <- influ_discrete(data = adultMass_binary, phy = primates$phy[[1]],
    model = "SYM", transform = "none", cutoff = 2, n.cores = 2, track = FALSE)

    # Print summary statistics for the transition rates, aic-values and
    # (if applicable) optimisation parameter
    summary(influ_binary)

    # Visual diagnostics - in symmetrical model q12 and q21 are, as expected,
    # exactly the same
    sensi_plot(influ_binary)

Different character models from `fitDiscrete` can be fit by changing the `model` argument. These include `ER` (equal-rates), `SYM` (symmetric), `ARD` (all-rates-different) and `meristic` (stepwise fashion). Similarly, all transformations to the phylogenetic tree from `fitDiscrete` can be used: `none`, `EB`, `lambda`, `kappa` and `delta`.

### 1.2. Sensitivity analysis for influential clades

The `clade` method can be used to estimate and test the influence of specific clades on parameter estimates.

##### 1.2.1 clade_phylm(): Phylogenetic linear regression

Additional arguments: clade.col: The name of a column in the provided data frame with clades specification (a character vector with clade names). n.species: Minimum number of species in the clade in order to include this clade in the leave-one-out deletion analysis. Default is 5. n.sim: The number of repetitions for the randomization test

    data(primates)
    # run analysis:
    clade <- clade_phylm(log(sexMaturity) ~ log(adultMass), phy = primates$phy[[1]],
                         data = primates$data, clade.col = "family", track=FALSE)
    # To check summary results and most influential clades:
    summary(clade)

    # Visual diagnostics for clade removal:
    sensi_plot(clade, "Cercopithecidae")

    sensi_plot(clade, "Cebidae")

##### 1.2.2 clade_physig(): Phylogenetic signal

    # Logtransform data
    alien.data$logMass <- log(alien.data$adultMass)
    # Run sensitivity analysis:
    clade <- clade_physig(trait.col = "logMass", data = alien.data, n.sim = 100,
                          phy = alien.phy[[1]], clade.col = "family", method = "K", track=FALSE)
    summary(clade)
    sensi_plot(clade, "Bovidae")
    sensi_plot(clade, "Sciuridae")

##### 1.2.3 clade_continuous() and clade_discrete: Trait Evolution Continuous and Discrete Characters

Continuous characters

    # Load data:
    data("primates")
    # Model trait evolution accounting for influential clades
    clade_cont <- clade_continuous(data=primates$data, phy = primates$phy[[1]],
    model="OU", trait.col = "adultMass", clade.col="family", n.sim=30, n.species=10,
    n.cores = 2, track=TRUE)

    # Check summary statistics for the transitions rates, aic-values and (if applicable) optimisation parameter
    summary(clade_cont)
    # Visual diagnostics
    sensi_plot(clade_cont,graph="all")
    # Plot only one clade and one parameter
    sensi_plot(clade_cont,clade="Cebidae",graph = "optpar")

Discrete characters

    # Load data:
    data("primates")

    # Create a binary trait factor
    primates$data$adultMass_binary<-ifelse(primates$data$adultMass > 7350, "big", "small")
    # Model trait evolution accounting for influential clades
    clade_disc <- clade_discrete(data=primates$data,phy = primates$phy[[1]],
                                 model="ARD",transform="kappa",
                                 trait.col = "adultMass_binary", clade.col = "family",
                                 n.sim = 30, n.species=8,n.cores = 2)
    # Check summary statistics:
    summary(clade_disc)
    # Visual diagnostics
    sensi_plot(clade_disc)

### 1.3. Sensitivity analysis for sample size

The `samp` method performs analyses of sensitivity to species sampling by randomly removing species from the dataset and detecting the effects on parameter estimates.

### 1.3.1 samp_phylm: Phylogenetic Linear regression

- Additional arguments:
  breaks: A vector containing the percentages of species to remove
  n.sim: The number of times species are randomly deleted for each break

    # run analysis:
    samp <- samp_phylm(log(gestaLen) ~ log(adultMass), phy = alien$phy[[1]],
                       data = alien$data, n.sim = 50, track=FALSE)

    # You can change the number of repetitions and break intervals:
    samp2 <- samp_phylm(log(gestaLen) ~ log(adultMass), phy = alien$phy[[1]],
                        data = alien$data, n.sim = 100, breaks = c(0.1, 0.2, 0.3, 0.4), track=FALSE)
    # You can change the phylogenetic model:
    samp3 <- samp_phylm(log(gestaLen) ~ log(adultMass), phy = alien$phy[[1]],
                       data = alien$data, model = "kappa", track=FALSE)
    # Check results:
    summary(samp)

    # Visual diagnostics
    sensi_plot(samp)
    sensi_plot(samp2)
    sensi_plot(samp3)

    # You can specify which graph and parameter ("slope" or "intercept") to print:
    sensi_plot(samp2, graphs = 1)
    sensi_plot(samp2, param = "intercept")
    sensi_plot(samp2, graphs = 2, param = "estimate")
    sensi_plot(samp)
    sensi_plot(samp2, graphs = 1)

    sensi_plot(samp)

### 1.3.2 samp_physig: Phylogenetic signal (k or lambda)

- Additional arguments:
  trait.col: The name of a column in the provided data frame with trait to be analyzed (e.g. “Body_mass”).
  method: Method to compute phylogenetic signal: can be “K” or “lambda”.

    # Logtransform data
    alien.data$logMass <- log(alien.data$adultMass)

    # Run sensitivity analysis:
    samp <- samp_physig(trait.col = "logMass", data = alien.data, n.sim = 30, phy = alien.phy[[1]], track=FALSE)
    # You can change the method used to estimate signal:
    samp2 <- samp_physig(trait.col = "logMass", data = alien.data, n.sim = 30,
                        phy = alien.phy[[1]], method = "lambda", track=FALSE)
    # Check results:
    summary(samp)
    # Visual diagnostics
    sensi_plot(samp)

    # More visual diagnostics
    sensi_plot(samp2)
    sensi_plot(samp, graphs = 1)

### 1.3.3 samp_continuous() and samp_discrete: Trait Evolution Continuous and Discrete Characters

Continuous characters

    # Load data:
    data("primates")

    # Model trait evolution
    adultMass<-primates$data$adultMass
    names(adultMass)<-rownames(primates$data)
    samp_cont<-samp_continuous(data = adultMass,phy = primates$phy[[1]],
    model = "OU",n.sim=25,breaks=seq(.05,.2,.05),n.cores = 2, track = FALSE)
    # Print summary statistics for the transitions rates, aic-values and (if applicable)
    # optimisation parameter
    summary(samp_cont)
    # Visual diagnostics
    sensi_plot(samp_cont)

Discrete characters

    # Load data:
    data("primates")
    # Create a binary trait factor
    adultMass_binary<-ifelse(primates$data$adultMass > 7350, "big", "small")
    adultMass_binary<-as.factor(as.factor(adultMass_binary))
    names(adultMass_binary)<-rownames(primates$data)
    # Model trait evolution
    samp_binary <- samp_discrete(data = adultMass_binary,phy = primates$phy[[1]], n.sim=25,
        breaks = seq(.1,.3,.1),model = "ARD", transform = "lambda", n.cores = 2,
        track = TRUE)
    # Print summary statistics for the transitions rates, aic-values and (if applicable)
    # optimisation parameter
    summary(samp_binary)
    # Visual diagnostics
    sensi_plot(samp_binary)

## 2. Phylogenetic uncertainty

The `tree` method performs sensitivity analysis to estimate the influence of phylogenetic uncertainty on parameter estimates.

Additional arguments:
n.tree: Number of times to repeat the analysis with n different trees picked randomly in the multiPhylo file.

### 2.1 tree_phylm: `tree` method for phylogenetic linear regression

    # Load data
    data(alien)
    # This analysis needs a multiphylo file:
    class(alien$phy)
    alien$phy
    # run PGLS accounting for phylogenetic uncertainty:
    tree <- tree_phylm(log(gestaLen) ~ log(adultMass), phy = alien$phy,
                       data = alien$data, n.tree = 30, track=FALSE)
    # To check summary results:
    summary(tree)
    # Visual diagnostics
    sensi_plot(tree)

### 2.2 tree_physig(): `tree` method for phylogenetic signal

    # Load data:
    data(alien)
    # Logtransform data
    alien.data$logMass <- log(alien.data$adultMass)
    # Run sensitivity analysis:
    tree <- tree_physig(trait.col = "logMass", data = alien.data, phy = alien.phy, track=FALSE)
    summary(tree)

    sensi_plot(tree, graphs = 1)
    sensi_plot(tree, graphs = 2)

    sensi_plot(tree)

### 2.3 tree_continuous() and tree_discrete: `tree` method for trait evolution of continuous and discrete characters

Continuous characters

    # Load data:
    data("primates")
    # Model trait evolution accounting for phylogenetic uncertainty
    adultMass<-primates$data$adultMass
    names(adultMass)<-rownames(primates$data)
    tree_cont<-tree_continuous(data = adultMass,phy = primates$phy,
    model = "OU",n.tree=30,n.cores = 2,track = FALSE)
    # Print summary statistics for the transitions rates, aic-values and (if applicable)
    # optimisation parameter
    summary(tree_cont)

    # Plot only some parameters
    sensi_plot(tree_cont,graphs="sigsq")
    sensi_plot(tree_cont,graphs="optpar")

    ## Visual diagnostics
    sensi_plot(tree_cont)

Discrete characters

    # Load data:
    data("primates")
    # Create a binary trait factor
    adultMass_binary<-ifelse(primates$data$adultMass > 7350, "big", "small")
    adultMass_binary<-as.factor(as.factor(adultMass_binary))
    names(adultMass_binary)<-rownames(primates$data)
    # Model trait evolution accounting for phylogenetic uncertainty
    tree_binary<-tree_discrete(data = adultMass_binary,phy = primates$phy,
    model = "ARD",transform = "none",n.tree = 30,n.cores = 2,track = FALSE)
    # Print summary statistics for the transitions rates, aic-values and (if applicable)
    # optimisation parameter
    summary(tree_binary)

    ## Visual diagnostics
    sensi_plot(tree_binary,graphs="q12")
    sensi_plot(tree_binary,graphs="q21")

    sensi_plot(tree_binary)

## 3. Data uncertainty

The `intra` method performs Sensitivity analysis for intraspecific variation and measurement error

### 3.1 intra_phylm(): `intra` method for phylogenetic linear regression

Additional arguments:
Vy: Name of the column containing the standard deviation or the standard error of the response variable. When information is not available for one taxon, the value can be 0 or NA.
Vx: Name of the column containing the standard deviation or the standard error of the predictor variable. When information is not available for one taxon, the value can be 0 or NA
x.transf: Transformation for the response variable (e.g. log or sqrt). Please use this argument instead of transforming data in the formula directly.
y.transf: Transformation for the predictor variable (e.g. log or sqrt). Please use this argument instead of transforming data in the formula directly.
distrib: A character string indicating which distribution to use to generate a random value for the response and/or predictor variables. Default is normal distribution: “normal” (function rnorm). Uniform distribution: “uniform” (runif) Warning: we recommend to use normal distribution with Vx or Vy = standard deviation of the mean.
n.intra: Number of times to repeat the analysis with n different trees picked randomly in the multiPhylo file. If NULL, times = 2

    # run PGLS accounting for intraspecific variation:
    intra <- intra_phylm(gestaLen ~ adultMass, phy = alien$phy[[1]],
                         data = alien$data, Vy = "SD_gesta", Vx = "SD_mass",
                         n.intra = 100, x.transf = log, y.transf = log, track=FALSE)
    # To check summary results:
    summary(intra)
    # Visual diagnostics
    sensi_plot(intra)

### 3.2 intra_physig(): `intra` method for phylogenetic signal

Additional arguments:
V: Name of the column containing the standard deviation or the standard error of the trait variable. When information is not available for one taxon, the value can be 0 or NA.

    data(alien)
    # Run sensitivity analysis:
    intra <- intra_physig(trait.col = "gestaLen", V = "SD_gesta" , data = alien.data,
                          phy = alien.phy[[1]], n.intra = 100, track=FALSE)
    summary(intra)

    sensi_plot(intra, graphs = 1)
    sensi_plot(intra, graphs = 2)

    sensi_plot(intra)

## 4. Interacting uncertainties

The ‘sensiPhy’ package can perform sensitivity analysis by interacting multiple types of uncertainty (described above).

‘sensiPhy’ implements functions to study interactions of both phylogenetic uncertainty (tree-functions) and data uncertainty (intra-functions) with sampling uncertainty (`clade`, `influ`, and `samp`), as well as interactions between data and phylogenetic uncertainty (`tree_intra`).

Both `intra` and `tree` methods can be used together with all other uncertainties to evaluate the interaction between two types of uncertainty at the same time.

### Examples:

#### 4.1 tree_influ_phylm(): `tree_influ` method for phylogenetic linear regression

    data(alien)
    # run analysis:
    tree_influ <- tree_influ_phylm(log(gestaLen) ~ log(adultMass), phy = alien$phy,
                                   data = alien$data, n.tree = 5, track=FALSE)
    # To check summary results:
    summary(tree_influ)

    # Visual diagnostics
    sensi_plot(tree_influ, graphs = 1)
    sensi_plot(tree_influ, graphs = 2)

    sensi_plot(tree_influ)

#### 4.2 tree_clade_phylm(): `tree_clade` method for phylogenetic linear regression

    data(primates)
    # run analysis:
    clade_tree <- tree_clade_phylm(log(sexMaturity) ~ log(adultMass),
                                   phy = primates$phy, data = primates$data,
                                   clade.col = "family",
                                   n.sim = 50, n.tree = 5, track=F)
    # To check summary results and most influential clades:
    summary(clade_tree)

    # Visual diagnostics for clade removal:
    sensi_plot(clade_tree)

    # Specify which clade removal to plot:
    sensi_plot(clade_tree, "Cercopithecidae")
    sensi_plot(clade_tree, clade = "Cebidae")

#### 4.3 tree_samp_phylm(): `tree_samp` method for phylogenetic linear regression

    # Load data:
    data(alien)
    # Run analysis:
    samp <- tree_samp_phylm(log(gestaLen) ~ log(adultMass), phy = alien$phy,
                            data = alien$data, n.tree = 5, n.sim=30, track=FALSE)
    summary(samp)
    head(samp$sensi.estimates)
    # Visual diagnostics
    sensi_plot(samp)

    sensi_plot(samp, graphs = 1)
    sensi_plot(samp, graphs = 2)

#### 4.4 tree_intra_phylm(): `tree_intra` method for phylogenetic linear regression

    # Load data:
    data(alien)
    # run PGLS accounting for intraspecific and phylogenetic variation:
    intra.tree <- tree_intra_phylm(gestaLen ~ adultMass, data = alien$data, phy = alien$phy,
                                   Vy = "SD_gesta", n.intra = 10, n.tree = 30,
                                   y.transf = log, x.transf = log, track=FALSE)
    # To check summary results:
    summary(intra.tree)
    # Visual diagnostics
    sensi_plot(intra.tree, uncer.type = "all") #or uncer.type = "tree", uncer.type = "intra"

## 5. Additional functions

### 5.1 Combine data and phylogeny

The function `match_dataphy` combines phylogeny and data to ensure that tips in phylogeny match data and that observations with missing values are removed.

> This function uses all variables provided in the ‘formula’ to match data and phylogeny. To avoid cropping the full dataset, ‘match_dataphy’ searches for NA values only on variables provided by formula. Missing values on other variables, not included in ‘formula’, will not be removed from data.

    library(sensiPhy)
    # Load data:
    data(alien)
    # Match data and phy based on model formula:
    comp.data <- match_dataphy(gestaLen ~ homeRange, data = alien$data, alien$phy[[1]], track=FALSE)
    # With a `multiphylo` tree:
    comp.data2 <- match_dataphy(homeRange ~ homeRange, data = alien$data, alien$phy, track=FALSE)
    # Check combined data:
    knitr::kable(head(comp.data$data))

    # Check phy:
    plot(comp.data$phy)

    # See species dropped from phy or data:
    comp.data$dropped

### 5.2 Phylogenetic signal for missing data

#### Background

The supplementary function `miss.phylo.d` tests if there is a phylogenetic signal in missing data, using the D framework developed in Fritz & Purvis (2010). A phylogenetic signal in missing data can bias comparative analyses, because it means that absence of data points is not independent of the phylogeny. This function can help alert users to this problem, suggesting that more balanced data collection would be required.

The function calculates D statistic for missing data. Missingness is recoded into a binary variable (1 = missing, 0 = non missing).

#### Example:

    library(sensiPhy)
    # Load caper:
    library(caper)
    # Load data
    data(alien)
    knitr::kable(head(alien.data))

    data <- alien.data
    phy = alien.phy[[1]]

    # Test phylogenetic signal for missing data:
    homeNAsig <- miss.phylo.d(data, phy, binvar = homeRange)
    print(homeNAsig)
    plot(homeNAsig)

    massNAsig <- miss.phylo.d(data, phy, binvar = adultMass)
    print(massNAsig)
    plot(massNAsig)

### 5.3 Diversification and speciation rates

#### Background

The funcion `tree_bd`estimates diversification and speciation rates evaluating uncertainty in tree topology. It estimates net diversification rate using `geiger::bd.ms` Magallon and Sanderson (2000) method or speciation rate using `geiger::bd.km` Kendall-Moran method for `n` trees, randomly picked from a `multiPhylo` file.

#### Examples:

To estimate diversification rate with Magallon and Sanderson method

    library(sensiPhy)
    # Load data:
    data("primates")
    # Run analysis
    fit.ms <- tree_bd(phy = primates.phy, n.tree = 30, method = "ms")
    # Check results
    summary(fit.ms)
    # Plot data
    sensi_plot(fit.ms)

To estimate speciation rate Kendall-Moran method

    # Load data:
    data("primates")
    # Run analysis
    fit.km <- tree_bd(phy = primates.phy, n.tree = 30, method = "km")
    # Check results
    summary(fit.km)
    # Plot data
    sensi_plot(fit.km)

### 6. Using sensiPhy with other packages (caper, phytools, gls)

sensiPhy leverages comparative methods implemented in specific R packages:
1. `phylolm` for pgls regressions
2. `phytools` for phylogenetic signal estimates
3. `geiger` for macroevolutionary models (continuous and discrete trait evolution)

Nevertheless, users can still use sensiPhy to perform sensitivity analysis when they had performed their initial comparative analyses in another package.

For instance, if you have used `caper`, `phytools` or `gls` to fit your full models, you can still use `sensiPhy` to test the sensitivity of those models to multiple types of uncertainty. In order to do this, users will need to set arguments that mirror the specific parameters from their full analysis. For example, to compare results one needs to use the same evolutionary model in pgls (e.g “lambda”, “BM”, etc), or the same metric for phylogenetic signal tests (K or lambda). See below for some examples:

#### 6.1 PGLS regression

    ### prepare dataset for caper pgls:
    library(caper)
    library(phytools)
    library(phylolm)
    library(sensiPhy)
    # selected variables from dataset:
    alien.data <- alien.data[c("gestaLen", "adultMass")]

    # create variable with species names:
    alien.data$sp <- rownames(alien.data)

    # caper
    # prepare comparative dataset:
    comp.dat <- comparative.data(data = alien.data, phy = alien.phy[[1]],
                                 names.col = "sp")
    # check comparative dataset:
    print(comp.dat)

    ### Run PGLS analysis (full model)
    # using caper (lambda)
    fit.caper.lam <- pgls(log(gestaLen)~ log(adultMass), comp.dat, lambda="ML")
    coef(fit.caper.lam)

    # using caper (delta)
    fit.caper.del <- pgls(log(gestaLen)~ log(adultMass), comp.dat, delta="ML")
    coef(fit.caper.del)

    # using phylolm (lambda)
    fit.phylo.lam <- phylolm(log(gestaLen)~ log(adultMass), comp.dat$data, comp.dat$phy,
                     model = "lambda")
    coef(fit.phylo.lam)

    # using phylolm (del)
    fit.phylo.del <- phylolm(log(gestaLen)~ log(adultMass), comp.dat$data, comp.dat$phy,
                             model = "delta")
    coef(fit.phylo.del)

    ### run sensitivity analysis with sensiPhy (influential species):
    library(sensiPhy)
    # run analysis (lambda):
    lam <- influ_phylm(log(gestaLen) ~ log(adultMass), phy = comp.dat$phy,
                         data = comp.dat$data, model = "lambda")
    # check full model estimates and compare to initial estimates:
    lam$full.model.estimates
    # test for influential species:
    summary(lam)

    # run analysis (delta):
    del <- influ_phylm(log(gestaLen) ~ log(adultMass), phy = comp.dat$phy,
                         data = comp.dat$data, model = "delta")
    # check full model estimates and compare to initial estimates:
    del$full.model.estimates
    # test for influential species:
    summary(del)

#### 6.2 phylogenetic signal

    # 2. phylogenetic signal:-------------------------------------------------------
    library(picante)
    library(phytools)
    library(sensiPhy)

    ### Estimate phylogenetic signal:
    # using picante (K)
    phylosignal(log(comp.dat$data$adultMass), comp.dat$phy, reps = 1000)

    # using phytools (K):
    phytools::phylosig(x = log(comp.dat$data$adultMass), tree = comp.dat$phy,
                       nsim = 1000,
                       method = "K", test = T)

    # using phytools (lambda):
    phytools::phylosig(x = log(comp.dat$data$adultMass), tree = comp.dat$phy,
                       nsim = 1000,
                       method = "lambda", test = T)

    ### run sensitivity analysis with sensiPhy (influential species):
    library(sensiPhy)
    # Load data:
    data(alien)
    # Logtransform data
    comp.dat$data$logMass <- log(comp.dat$data$adultMass)

    # Run sensitivity analysis (K):
    influ.k <- influ_physig("logMass", data = comp.dat$data, phy = comp.dat$phy,
                          method = "K")
    # check full model estimates and compare to initial estimates:
    influ.k$full.data.estimates
    # check for influential species:
    summary(influ.k)

    # Run sensitivity analysis (lambda):
    influ.lam <- influ_physig("logMass", data = comp.dat$data, phy = comp.dat$phy,
                          method = "lambda")
    # check full model estimates and compare to initial estimates:
    influ.lam$full.data.estimates
    # check for influential species:
    summary(influ.lam)

### 7. How long does it take?

Although most functions implemented in sensiPhy are reasonably fast (runtime less them 1 min), it is important to be aware that some functions might take a long time to run. This is more likely when analyzing models with a high number of species (>1000) or number of repetitions, and also when interacting two types of uncertainties (e.g. functions: `tree_clade` and `tree_samp`). To keep track of the time while running functions, we recommend users to set the argument `“track = TRUE”` which prints a progress bar and gives a good idea of how long the analysis will take before it finishes. As an indication, some examples of elapsed time on a standard desktop computer [Linux, Intel i7, 2.7GHz, 12GB ram] are presented below:

Analyses with single uncertainty: `tree_phylm`

function | N species | N trees | time
--- | --- | --- | ---
tree_phylm | 100 | 30 | ~ 2 sec
tree_phylm | 100 | 100 | ~ 5 sec

Analyses with single uncertainty: `clade_phylm`

function | N species | N sim | time
--- | --- | --- | ---
clade_phylm | 100 | 100 | ~ 7 sec
clade_phylm | 100 | 300 | ~ 31 sec
clade_phylm | 100 | 500 | ~ 61 sec

Analyses with single uncertainty: `samp_phylm`

function | N species | N sim | time
--- | --- | --- | ---
samp_phylm | 100 | 100 | ~ 11 sec
samp_phylm | 100 | 300 | ~ 25 sec
samp_phylm | 100 | 500 | ~ 43 sec
samp_phylm | 500 | 100 | ~ 22 sec
samp_phylm | 1000 | 100 | ~ 35 sec

Analyses with single uncertainty: `influ_phylm`

function | N species | time
--- | --- | ---
influ_phylm | 100 | ~ 4 sec
influ_phylm | 500 | ~ 43 sec
influ_phylm | 1000 | ~ 148 sec

## 8. How to support sensiPhy

Thanks for you interest in contributing with `sensiPhy`. First you need to register at Github. You can help developing `sensiPhy` in different ways:

### 8.1 Report bugs or errors

If you have any problem running `sensiPhy` functions, please report the problem as a new issue. To do this, follow the steps below:

- Create a new issue
- Name this issue as "BUG: function_name
- Write a small description about your problem/error
- If possible, include a reproducible example using the R package reprex

### 8.2 Small changes in `sensiPhy` documentation

If you find a typo on `sensiPhy` documentation or if you want to make a small change on any file, you can do it online. Search for the file you want to change at the master branch, then:

- Edit the file online
- Save your change
- Describe the changes you have made
- Click `send a pull request`

### 8.3 Contribute with code

If you want to make a bigger contribution and help us with `sensiPhy` code:

1. Fork it (https://github.com/paternogbc/sensiPhy/fork)
2. Create your feature branch (`git checkout -b my-new-feature`)
3. Commit your changes (`git commit -am 'Add some feature'`)
4. Push to the branch (`git push origin my-new-feature`)
5. Create a new Pull Request

### 8.4 New ideas or suggestions?

If you need to ask something via email, send to paternogbc@gmail.com

### 8.5 Code of Conduct

Please note that this project is released with a Contributor Code of Conduct. By participating in this project you agree to abide by its terms.