Package 'CoDaLoMic'

Description

This package contain functions to model compositional and longitudinal microbiome datasets. This package contains the functions needed to execute the models published in the articles:

• Creus-Martí, I., Moya, A., Santonja, F. J. (2018), A Statistical Model with a Lotka-Volterra Structure for Microbiota Data, Lucas Jodar, Juan Carlos Cortes and Luis Acedo, Modelling for engineering and human behavior 2018, Instituto Universitario de Matematica Multidisciplinar, ISBN: 978-84-09-07541-6.

• Creus-Martí, I., Moya, A., Santonja, F. J. (2021). A Dirichlet autoregressive model for the analysis of microbiota time-series data. Complexity, 2021, 1-16.

• Creus-Martí, I., Moya, A., Santonja, F. J. (2022). Bayesian hierarchical compositional models for analysing longitudinal abundance data from microbiome studies. Complexity, 2022.

In addition, the package contains one real dataset extracted from:

• Marín-Miret, J., Pérez-Cobas, A. E., Domínguez-Santos, R., Pérez-Rocher, B., Latorre, A., & Moya, A. (2024). Adaptability of the gut microbiota of the German cockroach Blattella germanica to a periodic antibiotic treatment. Microbiological Research, 287, 127863.

Details

We refer to the model described in Creus-Martí (2018) as Dirich-gLV, we refer to the model described in Creus-Martí (2021) as FBM and we refer to the model described in Creus-Martí (2022) as BPBM.

Access to Additional Files

This package includes files in the directory 'inst/extdata'. Users can access these files using 'system.file()'. The following files are available:

• README.pdf, README.Rmd, README.R: Basic instructions for using the package.

• 1-s2.0-S0944501324002647-mmc6.xlsx: Original cockroach dataset extracted from Marín-Miret et al (2024).

• Simulated.R: Code use to obtain the Simulated dataset.

• cockroach.R: Code use to obtain the cockroach dataset.

To access these files, use: base::system.file("extdata", "filename", package = "CoDaLoMic")

For instance: base::system.file("extdata", "README.pdf", package = "CoDaLoMic")

On Windows, the PDF can be opened as follows: base::shell.exec(system.file("extdata", "README.pdf", package = "CoDaLoMic"))

Author(s)

Maintainer: Irene Creus Martí [email protected] (ORCID)

Description

Defining the part of the ridge regression matrix that carries the information of the bacteria especieII.

Usage

B1MODImatrizP(Tt, especieII, especie, E, EspecieMaxima)

Arguments

Value

Returns a matrix. The first column contain the number 1 repeated Tt times. The second column contains the alr transformation of the especieII in all time points. The third column contains the balance (whose numerator has all the bacteria except especieII and EspecieMaxima and the denominator contains the EspecieMaxima) in all time points.

Examples

Tt=2
especie1=cbind(c(0.5,0.3,0.2), c(0.1,0.3,0.6))
especieII=1
E=3
EspecieMaxima=3

B1MODImatrizP(Tt, especieII,especie1, E, EspecieMaxima)

Description

This function calculates the value of the FBM regression, defined by:

$\mu_{it}=a_{i1}+a_{i2}\cdot\text{alr}(x_{i,(t-1)})+a_{i3}\cdot\text{Balance}(x_{i,(t-1)})\text{ for }i=1,\dots, D-1\text{ where } D \text{ is the number of bacteria}$

Usage

B1MODImodel(A, especie, E, EspecieMaxima, Tt)

Arguments

Value

Returns a matrix. The row i contains the regression values of the bacteria i at all time points.

References

Creus-Martí, I., Moya, A., Santonja, F. J. (2021). A Dirichlet autoregressive model for the analysis of microbiota time-series data. Complexity, 2021, 1-16.

Examples

df<-data.frame(cbind(c(0.1,0.1,0.8),c(0.2,0.1,0.7)))
E=3
EspecieMaxima=3
set.seed(724)
A=matrix(c(-2:3),2,3)
Tt=2

B1MODImodel(A,df, E, EspecieMaxima,Tt)

Description

Defining a balance where we compare all the bacteria (except the one chosen as reference and the especieI) with the one chosen as reference.

Usage

Balance(A, especieI, especie, E, EspecieMaxima)

Arguments

Value

Returns a vector with the value of the balance for all the time points indicated.

Examples

Balance(2,2,cbind(c(0.1,0.1,0.8),c(0.2,0.1,0.7)),3,3)

Description

This function writes the matrix of covariates of the BPBM.

Usage

BPBM_Matrix(rows.position, PB, Tt)

Arguments

Details

In an example with two SPBal and three time points, the covariates are written in the following order:

Value

Returns a matrix with the covariates of the model.

References

Creus-Martí, I., Moya, A., Santonja, F. J. (2022). Bayesian hierarchical compositional models for analysing longitudinal abundance data from microbiome studies. Complexity, 2022.

Examples

matt=matrix(c(1:12),3,4)
rows.position=c(2,3)
BPBM_Matrix(rows.position,matt,4)

Description

Gut microbiome dataset of a Blatella germanica cockroach treated by kanamycin during three periods of time (days: 1–10, 36–45, 71–80). The data is extracted from Marín-Miret et al (2024), more specifically, the data is the information of the K3 cockroach in the article. The dataset contains 105 time points and 210 genera.

Usage

data(cockroach)

Format

A data frame with 105 rows and 211 columns.

References

Marín-Miret, J., Pérez-Cobas, A. E., Domínguez-Santos, R., Pérez-Rocher, B., Latorre, A., & Moya, A. (2024). Adaptability of the gut microbiota of the German cockroach Blattella germanica to a periodic antibiotic treatment. Microbiological Research, 287, 127863.

Description

This function calculates the estimated parameters of the Dirich-gLV model.

Usage

Estimate_Param_EstParmFunc(Iter.EstParmFunc, paramini, especie, seed = NULL)

Arguments

Details

Maximum likelihood estimation is used. This function makes an iterative process, it obtains the value of the parameter that maximize the Dirichlet loglikelihood (defined in EstParmFunc) using the Nelder-Mead method and some initial parameters. Then it uses this value as initial parameters and repeats the process Iter.EstParmFunc times.

Value

Returns a list with:

• All.iter: Matrix. Each row has the parameters obtained in each iteration. The parameters are in the columns written in the same order that they are written in paramini. In this matrix we must observe that in the last iterations the values has really similar or equal values, it not, we need to increase the value of Iter.EstParmFunc.

• Param.Estimates: The estimated parameters. The parameters are in the columns written in the same order that they are written in paramini.

References

Creus-Martí, I. and Moya, A. and Santonja, F. J. (2018). A Statistical Model with a Lotka-Volterra Structure for Microbiota Data. Lucas Jodar, Juan Carlos Cortes and Luis Acedo, Modelling for engineering and human behavior 2018, Instituto Universitario de Matematica Multidisciplinar. ISBN: 978-84-09-07541-6

Examples

especie=cbind(c(0.5,0.3,0.2),c(0.1,0.3,0.6))
paramini=c(100,2,3,4,5,6,7)
Estimate_Param_EstParmFunc(5, paramini , especie,714)

Description

This function estimates the parameters of the FBM model.

Usage

Estimate_Param_FBM(
  tau,
  ridge.final,
  Iter.EstParmFunc = 80,
  especie,
  EspecieMaxima,
  Tt,
  E,
  seed = NULL
)

Arguments

Details

Maximum likelihood estimation is used. This function makes an iterative process, for a given value of tau, it obtains the value of the rest of the parameters that maximize the dirichlet loglikelihood (defined in EstParmFunc_FBM) using the Nelder-Mead method and the values obtained in the ridge regression as initial parameters. Then it uses the values obtained as initial parameters and repeats the process Iter.EstParmFunc times.

The regression of this model is defined by

$\mu_{it}=a_{i1}+a_{i2}\cdot\text{alr}(x_{i,(t-1)})+a_{i3}\cdot\text{Balance}(x_{i,(t-1)})\text{ for }i=1,\dots, D-1\text{ where } D \text{ is the number of bacteria}$

Value

Returns a list with:

• All.iter: Matrix. Each row has the parameters obtained in each iteration. The parameters are in the columns written in following order: a11,a12,a13, a21, a22,a23, ...a(D-1)1,a(D-1)2,a(D-1)3,tau. Where D is the number of bacterial species present in the matrix especie. In this matrix we must observe that in the last iterations the values has really similar or equal values, it not, we need to increase the value of Iter.EstParmFunc.

• Param.Estimates: Vector with the estimated parameters, in the following order: a11,a12,a13, a21, a22,a23, ...a(D-1)1,a(D-1)2,a(D-1)3,tau. Where D is the number of bacterial species present in the matrix especie.

• AIC Number: Value of the AIC.

References

Creus-Martí, I., Moya, A., Santonja, F. J. (2021). A Dirichlet autoregressive model for the analysis of microbiota time-series data. Complexity, 2021, 1-16.

Examples

set.seed(123)
especie=t(gtools::rdirichlet(5,c(1,3,1)))
Tt=5
E=3
EspecieMaxima=3
ridge.final=ridgeregression(Tt,especie, E, EspecieMaxima)
tau=20
Iter.EstParmFunc=40

Estimate_Param_FBM(tau,ridge.final,Iter.EstParmFunc, especie,EspecieMaxima,Tt,E, 714)

Description

The estimation of the BPBM model is carried out using MCMC. To execute this function it is necessary to have the program Just Another Gibbs Sampler (JAGS) (Plummer, 2003) program installed.

Usage

Estimating_BPBM(
  especie,
  Tt,
  E,
  MatrizPBmodelo,
  nn.chain = 3,
  nn.burnin = 5000,
  nn.sample = 20000,
  nn.thin = 10,
  seed = NULL
)

Arguments

Value

Returns a list with:

• List with:

  • R2jagsOutput: R2jags object with the information of the estimation.

  • SamplesAllChains: Matrix. Matrix that has the iterations of all the Markov chains joined.

References

• Creus-Martí, I., Moya, A., Santonja, F. J. (2022). Bayesian hierarchical compositional models for analysing longitudinal abundance data from microbiome studies. Complexity, 2022.

• Plummer, M. (2003, March). JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling. In Proceedings of the 3rd international workshop on distributed statistical computing (Vol. 124, No. 125.10, pp. 1-10).

Examples

set.seed(314)
especie=t(gtools::rdirichlet(n=6, c(6,6,1,6,6)))
E=5
Tt=6
MatrizPBmodelo=rbind(c(1,1,1,1,1,1),c(-0.3,0.4,0.3,-0.7,-0.4,-0.6),c(0.3,0.5,-0.3,0.1,0.4,0.1))



Estimating_BPBM(especie,
               Tt,
               E,
               MatrizPBmodelo,
               nn.chain=3,
               nn.burnin=1000,
               nn.sample=2000,
               nn.thin=10,
               714)

Description

This function calculates the loglikelihood of the dirichlet for the Dirich-gLV model.

Usage

EstParmFunc(parms.vector, especie)

Arguments

Details

In an example with three bacteria, the regression of this model is defined by

$r_{1}\cdot log(x_{1}(t)/x_{3}(t))+log(x_{1}(t)/x_{3}(t))\cdot [a_{11}\cdot log(x_{1}(t)/x_{3}(t))(t)+a_{12}\cdot log(x_{2}(t)/x_{3}(t))]$

$r_{2}\cdot log(x_{2}(t)/x_{3}(t))+log(x_{2}(t)/x_{3}(t))\cdot [a_{21}\cdot log(x_{1}(t)/x_{3}(t))(t)+a_{22}\cdot log(x_{2}(t)/x_{3}(t))]$

Value

Returns a number with the value of the dirichlet loglikelihood.

References

Creus-Martí, I. and Moya, A. and Santonja, F. J. (2018). A Statistical Model with a Lotka-Volterra Structure for Microbiota Data. Lucas Jodar, Juan Carlos Cortes and Luis Acedo, Modelling or engineering and human behavior 2018, Instituto Universitario de Matematica Multidisciplinar. ISBN: 978-84-09-07541-6

Examples

especie1=cbind(c(0.5,0.3,0.2), c(0.1,0.3,0.6))
tau1=0.4
parms1= cbind(c(0.1,0.2),c(-0.2,0.1),c(0.3,0.2))
parms11=c(tau1,as.vector( parms1))

EstParmFunc(parms11,especie1)

Description

This function calculates the loglikelihood of the dirichlet for the FBM model.

Usage

EstParmFunc_FBM(param, especie, E, EspecieMaxima, Tt, especiemodi)

Arguments

Details

The regression of this model is defined by

$\mu_{it}=a_{i1}+a_{i2}\cdot\text{alr}(x_{i,(t-1)})+a_{i3}\cdot\text{Balance}(x_{i,(t-1)})\text{ for }i=1,\dots, D-1\text{ where } D \text{ is the number of bacteria}$

Value

Returns a number with the value of the dirichlet loglikelihood.

References

Creus-Martí, I., Moya, A., Santonja, F. J. (2021). A Dirichlet autoregressive model for the analysis of microbiota time-series data. Complexity, 2021, 1-16.

Examples

especie1=cbind(c(0.5,0.3,0.2), c(0.1,0.3,0.6))
especiemodi=especie1[,-1]
tau1=0.4
parms1= cbind(c(0.1,0.2),c(-0.2,0.1),c(0.3,0.2))
parms11=c(as.vector( t(parms1)),tau1)

EstParmFunc_FBM(parms11,especie1,3 ,3  , 2,especiemodi)

Description

This function calculates the value of the Dirichlet parameters, the expected value and the variance for the Dirich-gLV model.

Usage

ExpectedValue_EstParmFunc(Param.Estimates, especie)

Arguments

Value

Returns a list with:

• Dirichlet.Param: Matrix. Matrix that contains at row i the Dirichlet parameter of the bacteria i at all time points.

• Expected.Value: Matrix. Matrix that contains at row i the expected value of the bacteria i at all time points. The bacterias are placed at the same orden than in especies.

• Variance.Value: Matrix. Matrix that contains at row i the variance of the bacteria i at all time points. The bacterias are placed at the same orden than in especies.

References

Creus-Martí, I. and Moya, A. and Santonja, F. J. (2018). A Statistical Model with a Lotka-Volterra Structure for Microbiota Data. Lucas Jodar, Juan Carlos Cortes and Luis Acedo, Modelling or engineering and human behavior 2018, Instituto Universitario de Matematica Multidisciplinar. ISBN: 978-84-09-07541-6

Examples

especie1=cbind(c(0.5,0.3,0.2), c(0.1,0.3,0.6))
tau1=0.4
parms1= cbind(c(0.1,0.2),c(-0.2,0.1),c(0.3,0.2))
parms11=c(tau1,as.vector( parms1))

ExpectedValue_EstParmFunc(parms11,especie1)

Description

This function calculates the value of the dirichlet parameters, the expected value and the variance for the FBM model.

Usage

ExpectedValues_EstParmFunc_FBM(
  paramEstimadosFinal,
  especie,
  E,
  EspecieMaxima,
  Tt
)

Arguments

Details

The regression of this model is defined by

$\mu_{it}=a_{i1}+a_{i2}\cdot\text{alr}(x_{i,(t-1)})+a_{i3}\cdot\text{Balance}(x_{i,(t-1)})\text{ for }i=1,\dots, D-1\text{ where } D \text{ is the number of bacteria}$

Value

Returns a list with:

• Dirichlet.Param: Matrix. Matrix that contains at row i the dirichlet parameter of the bacteria i at all time points.

• Expected.Value: Matrix. Matrix that contains at row i the expected value of the bacteria i at all time points. The bacterias are placed at the same orden than in especies.

• Variance.Value: Matrix. Matrix that contains at row i the variance of the bacteria i at all time points. The bacterias are placed at the same orden than in especies.

References

Creus-Martí, I., Moya, A., Santonja, F. J. (2021). A Dirichlet autoregressive model for the analysis of microbiota time-series data. Complexity, 2021, 1-16.

Examples

set.seed(123)
especie=t(gtools::rdirichlet(2,c(1,1,3)))
Tt=2
E=3
tau=5
EspecieMaxima=3
Iter.EstParmFunc=5
parms11=c(0.1,0.2,0.3,0.4,0.5,0.6,tau)

ExpectedValues_EstParmFunc_FBM(parms11 , especie,E,EspecieMaxima,Tt)

Description

This function calculates the value of the dirichlet parameters, the expected value and the variance for the BPBM model.

Usage

ExpectedValuess_BPBM(Estimated.Param, MatrizPBmodelo, E, Tt)

Arguments

Details

The regression of this model is defined by:

$\mu_{it}=a_{i0}+a_{i1}\cdot\text{SPBal}_{1,t-1}+\cdots+a_{iM}\cdot\text{SPBal}_{M,t-1}$

Value

Returns a list with:

• Dirichlet.Param: Matrix. Matrix that contains at row i the dirichlet parameter of the bacteria i at all time points.

• Expected.Value: Matrix. Matrix that contains at row i the expected value of the bacteria i at all time points. The bacterias are placed at the same orden than in especies.

• Variance.Value: Matrix. Matrix that contains at row i the variance of the bacteria i at all time points. The bacterias are placed at the same orden than in especies.

References

Creus-Martí, I., Moya, A., Santonja, F. J. (2022). Bayesian hierarchical compositional models for analysing longitudinal abundance data from microbiome studies. Complexity, 2022.

Examples

Tt=3
E=3
Estimated.Param=c(0.1 ,0.4, 0.7, 0.2 ,0.5, 0.8 ,0.3, 0.6, 0.9,
                 0.1, 0.4 ,0.7, 0.2, 0.5, 0.8, 0.3 ,0.6, 0.9)
MatrizPBmodelo=rbind(c(1,1,1),c(0.3,0.6,-0.1),c(0.2,-0.4,0.3))
ExpectedValuess_BPBM(Estimated.Param,MatrizPBmodelo,E,Tt)

Description

StudyingParam returns a matrix where the value of the parameters is in the column "mean". This function inputs this columns and outputs the parameters in the matrix form required by the BPBM model.

Usage

FromVectorToMatrix_BPBM(param, MatrizPBmodelo, E)

Arguments

Value

Returns a matrix with the parameters in the order required by the BPBM model.

References

Creus-Martí, I., Moya, A., Santonja, F. J. (2022). Bayesian hierarchical compositional models for analysing longitudinal abundance data from microbiome studies. Complexity, 2022.

Examples

set.seed(314)
especie=t(gtools::rdirichlet(n=6, c(6,6,1,6,6)))
E=5
Tt=6
MatrizPBmodelo=rbind(c(1,1,1,1,1,1),
                   c(-0.3,0.4,0.3,-0.7,-0.4,-0.6),
                   c(0.3,0.5,-0.3,0.1,0.4,0.1))

est=Estimating_BPBM(especie,
                   Tt,
                   E,
                   MatrizPBmodelo,
                   nn.chain=3,
                   nn.burnin=1000,
                   nn.sample=5000,
                   nn.thin=10)

mm=StudyingParam(est$R2jagsOutput$BUGSoutput$summary,est$SamplesAllChains)
FromVectorToMatrix_BPBM(mm$Param.Summary[,"mean"],MatrizPBmodelo,5)

Description

Calculates a vector with the covariates of the BPBM model in one time point.

Usage

FVectorPBmodeloPredi(NumSPBal, DemSPBal, v, MatrizPBmodelo)

Arguments

Value

Returns a vector where the first component is a 1 and the following components have the values of the SPBal. The SPBal in the component i+1 has at its numerator the bacteria placed in the rows Num[[i]] of the especie. The SPBal of the component i+1 has at its denominator the bacteria placed in the rows Dem[[i]] of the especie.

References

Creus-Martí, I., Moya, A., Santonja, F. J. (2022). Bayesian hierarchical compositional models for analysing longitudinal abundance data from microbiome studies. Complexity, 2022.

Examples

v=c(0.1,0.1,0.2,0.3,0.3)
Num2<-list(3,c(3,5),1,c(3,5,4))
Dem2<-list(5,4,2,c(1,2))
MatrizPBmodelo=rbind(c(1,1,1,1),
                    c(-0.3,0.2,0.5,0.6),
                    c(-0.4,0.3,0.5,0.6),
                    c(0.5,0.3,0.2,0.7),
                    c(-0.2,0.9,0.2,0.1)   )

FVectorPBmodeloPredi(Num2,Dem2,v,MatrizPBmodelo)

Description

Plots the time series

Usage

Graphics(especie, names.especie, esperanza, Variance, Plot.Tipe, Detail)

Arguments

Value

Returns the indicated plots.

Examples

names.especie=c("Bact1", "Bact2", "Bact3")
especie=cbind(c(0.5,0.3,0.2), c(0.6,0.3,0.1),c(0.4,0.1,0.5),c(0.4,0.1,0.5))
esperanza=especie[,c(1:3)]+0.1
Variance=matrix(c(runif(9,0.001,0.004)), 3,3)

Graphics(especie, names.especie, esperanza, Variance,"Data","no")
Graphics(especie, names.especie, esperanza, Variance,"DataExpected","no")
Graphics(especie, names.especie, esperanza, Variance,"All","no")

Description

This function takes into account the data used to estimate and the data used to predict.

Usage

GraphicsPrediction(
  especie.All,
  names.especie,
  ExpectedValue.All,
  VarianceValue.All,
  Pred,
  Plot.Tipe,
  Detail
)

Arguments

Value

Returns the indicated plots with a vertical line when the time point is equal to Pred-1, in Pred the prediction has started.

Examples

names.especie=c("Bact1", "Bact2", "Bact3")
especie.All=cbind(c(0.5,0.3,0.2),
                c(0.6,0.3,0.1),
                c(0.4,0.1,0.5),
                c(0.4,0.1,0.5),
                c(0.4,0.1,0.5),
                c(0.4,0.1,0.5))
ExpectedValue.All=especie.All[,-1]+0.1
VarianceValue.All=matrix(c(runif(15,0.001,0.004)), 3,5)
Pred=4

GraphicsPrediction(especie.All,
                  names.especie,
                  ExpectedValue.All,
                  VarianceValue.All ,
                  Pred,
                  "Data",
                  "no")

GraphicsPrediction(especie.All,
                 names.especie,
                 ExpectedValue.All,
                 VarianceValue.All ,
                 Pred,
                 "DataExpected",
                 "no")

GraphicsPrediction(especie.All,
                 names.especie,
                 ExpectedValue.All,
                 VarianceValue.All ,
                 Pred,
                 "All",
                 "no")

GraphicsPrediction(especie.All,
                 names.especie,
                 ExpectedValue.All,
                 VarianceValue.All ,
                 Pred,
                 "Var",
                 "no")

GraphicsPrediction(especie.All,
                 names.especie,
                 ExpectedValue.All,
                 VarianceValue.All ,
                 Pred,
                 "OnlyVar",
                 "no")

Description

This function takes into account the data used to estimate and the data used to predict. We use this function when we want to observe the results obtained with the BPBM model.

Usage

GraphicsPredictionBPBM(
  especie.All,
  names.especie,
  ExpectedValue.All,
  VarianceValue.All,
  Pred,
  Plot.Tipe,
  Varmas,
  Varmenos,
  Detail
)

Arguments

Value

Returns the indicated plots with a vertical line when the time point is equal to Tt=Pred-1, in Pred=Tt+1 the predicction has started.

References

Creus-Martí, I., Moya, A., Santonja, F. J. (2022). Bayesian hierarchical compositional models for analysing longitudinal abundance data from microbiome studies. Complexity, 2022.

Examples

names.especie=c("Bact1", "Bact2", "Bact3")
especie.All=cbind(c(0.5,0.3,0.2),
                 c(0.6,0.3,0.1),
                 c(0.4,0.1,0.5),
                 c(0.4,0.1,0.5),
                 c(0.4,0.1,0.5),
                 c(0.4,0.1,0.5))
ExpectedValue.All=especie.All[,-1]+0.1
VarianceValue.All=matrix(c(runif(15,0.001,0.004)), 3,5)
Pred=4
Varmas=cbind(matrix(0,3,2),matrix(c(runif(9,0.001,0.004)) ,3 ,3 ))
Varmenos=cbind(matrix(0,3,2),matrix(c(runif(9,0.001,0.004)) ,3 ,3 ))

GraphicsPredictionBPBM(especie.All,
                      names.especie,
                      ExpectedValue.All,
                      VarianceValue.All ,
                      Pred ,
                      "Data",
                      Varmas,
                      Varmenos,
                      "no")

GraphicsPredictionBPBM(especie.All,
                      names.especie,
                      ExpectedValue.All,
                      VarianceValue.All ,
                      Pred ,
                      "DataExpected",
                      Varmas,
                      Varmenos,
                      "no")

GraphicsPredictionBPBM(especie.All,
                      names.especie,
                      ExpectedValue.All,
                      VarianceValue.All,
                      Pred ,
                      "All",
                      Varmas,
                      Varmenos,
                      "no")

GraphicsPredictionBPBM(especie.All,
                      names.especie,
                      ExpectedValue.All,
                      VarianceValue.All ,
                      Pred ,
                      "Var",
                      Varmas,
                      Varmenos,
                      "no")

GraphicsPredictionBPBM(especie.All,
                      names.especie,
                      ExpectedValue.All,
                      VarianceValue.All ,
                      Pred ,
                      "OnlyVar",
                      Varmas,
                      Varmenos,
                      "no")

Description

The SPBal (of BPBM model) are ordered from highest to lowest variance percentage. The zero is highlight because the closer the value of the balance is to zero, the more similar (in terms of relative abundance) the numerator and denominator groups will be. The farther away from zero, the more different.

Usage

GraphicsSPBal(MatrizPBmodelo)

Arguments

Value

Returns a graphic.

References

Creus-Martí, I., Moya, A., Santonja, F. J. (2022). Bayesian hierarchical compositional models for analysing longitudinal abundance data from microbiome studies. Complexity, 2022.

Examples

MatrizPBmodelo=rbind(c(1,1,1,1,1,1),c(-0.3,0.4,0.3,-0.7,-0.4,-0.6),c(0.3,0.5,-0.3,0.1,0.4,0.1))
GraphicsSPBal(MatrizPBmodelo)

Description

This function calculates the loglikelihood of the dirichlet for the BPBM model.

Usage

LogVeroFuncBUENA(param, MatrizPBmodelo, E, Tt, especiemodi)

Arguments

Value

Returns a number with the value of the dirichlet loglikelihood.

References

Creus-Martí, I., Moya, A., Santonja, F. J. (2022). Bayesian hierarchical compositional models for analysing longitudinal abundance data from microbiome studies. Complexity, 2022.

Examples

set.seed(314)
especie=t(gtools::rdirichlet(n=2, c(1,2,3)))
E=3
Tt=2
MatrizPBmodelo=rbind(c(1,1),c(-0.3,0.4),c(0.3,0.5))
set.seed(314)
est=Estimating_BPBM(especie,
                   Tt,
                   E,
                   MatrizPBmodelo,
                   nn.chain=3,
                   nn.burnin=1000,
                   nn.sample=5000,
                   nn.thin=10)

param=est$SamplesAllChains

especiemodi=especie[,-1]


LogVeroFuncBUENA(param,MatrizPBmodelo,E,Tt,especiemodi)

Description

This function calculates the mean abundance of each bacteria. Then, it creates a matrix where each row contains the abundance of one bacteria at all time points but the bacteria with maximum (or minimum or a bacteria indicated by the user) mean abundance is placed at the last row

Usage

MaxBacteria(nombresOriginal, especieOriginal, E, Tt, which.esp)

Arguments

Value

Returns a list with

• especie - Matrix that contains at row i the bacterial taxa of bacteria i at all time points but the bacteria with maximum (or minimum) mean abundance (or the bacteria indicated by the user) is placed at the last row.

• especiemodi - Matrix that contains at row i the bacterial taxa of bacteria i at time points t=2,...,Tt but the bacteria with maximum (or minimum) mean abundance (or the bacteria indicated by the user) is placed at the last row.

• nombres - Vector with the bacteria's names placed in the order in which appear in the rows of the matrices especie and especiemodi

• EE - Row in which the bacterial with maximum (or minimum) mean abundance was (or the value of "which" if which is numerical).

• EspecieMaxima - Row in which the bacterial with maximum (or minimum) mean abundance (or the bacteria indicated by the user) is in especie.) #'

Examples

names1=c("Bact1","Bact2","Bact3")
set.seed(314)
esp1=t(gtools::rdirichlet(n=4, c(1,3,1)))
e1=3
t1=4

MaxBacteria(names1,esp1,e1,t1,"Max")


names3=c("Bact1","Bact2","Bact3","Bact4","Bact5")
set.seed(314)
esp3=t(gtools::rdirichlet(n=6, c(6,6,1,6,6)))
e3=5
t3=6
MaxBacteria(names3,esp3,e3,t3,"Min")

Description

This function calculates the mean abundance of each bacteria taking into account the time points used to estimate the model (t=1,2,...,Tt). Then, it creates a matrix where each row contains the abundance of one bacteria at all time points but the bacteria with maximum (or minimum) mean abundance (or the bacterial indicated by the user) is placed at the last row

Usage

MaxBacteriaPred(
  nombresOriginal,
  especieOriginal,
  E,
  Tt,
  Pred,
  K,
  especieOriginal.All,
  which.esp
)

Arguments

Value

Returns a list with

• especie - Matrix that contains at row i the bacterial taxa of bacteria i at time points t=1,2,...,Tt but the bacteria with with maximum (or minimum) mean abundance (or the bacteria indicated by the user) is placed at the last row.

• especiemodi - Matrix that contains at row i the bacterial taxa of bacteria i at time points t=2,...,Tt but the bacteria with with maximum (or minimum) mean abundance (or the bacteria indicated by the user) is placed at the last row.

• nombres - Vector with the bacteria's names placed in the order in which appear in the rows of the matrices especie and especiemodi

• EE - Row in which the bacterial with maximum (or minimum) mean abundance was (or the value of "which" if which is numerical).

• EspecieMaxima - Row in which the bacterial with with maximum (or minimum) mean abundance (or the bacteria indicated by the user) is in especie.) #' #'

• especie.all - Matrix that contains at row i the bacterial taxa of bacteria i at all time points (t=1,2,...,K) but the bacteria with with maximum (or minimum) mean abundance (or the bacteria indicated by the user) is placed at the last row.

• especiemodi.all - Matrix that contains at row i the bacterial taxa of bacteria i at all time points (t=2,...,K) but the bacteria with with maximum (or minimum) mean abundance (or the bacteria indicated by the user) is placed at the last row.

Examples

names2=c("Bact1","Bact2","Bact3","Bact4","Bact5")
set.seed(314)
esp2=t(gtools::rdirichlet(n=6, c(1,1,5,1,1)))
e2=5

MaxBacteriaPred(names2,esp2[,-c(4,5,6)],e2,3,Pred=4, 6,esp2, "Max")

Description

Calculates the value of the principal balances (Martín-Fernández et al, 2018) at all time points.

Usage

ObtainigValuePB(Num, Dem, especie, Tt)

Arguments

Value

Returns a matrix where the row i has the value of the principal balance at all time points. The principal balance of the row i has at its numerator the bacteria placed in the rows Num[[i]] of the especie. The principal balance of the row i has at its denominator the bacteria placed in the rows Dem[[i]] of the especie.

References

• Creus-Martí, I., Moya, A., Santonja, F. J. (2022). Bayesian hierarchical compositional models for analysing longitudinal abundance data from microbiome studies. Complexity, 2022.

• Martín-Fernández, J. A., Pawlowsky-Glahn, V., Egozcue, J. J., & Tolosona-Delgado, R. (2018). Advances in principal balances for compositional data. Mathematical Geosciences, 50, 273-298.

Examples

set.seed(314)
esp2=t(gtools::rdirichlet(n=6, c(1,1,5,1,1)))

Num2<-list(3,c(3,5),1,c(3,5,4))
Dem2<-list(5,4,2,c(1,2))

ObtainigValuePB(Num2,Dem2,esp2,6)

Description

Calculates the value of the selected principal balances (SPBal) of the BPBM model at all time points.

Usage

ObtainigValueSPBal(Num, Dem, especie, Tt)

Arguments

Value

Returns a list with:

• NumSPBal: List. The component i of the list has the number of the row of the matrix especie where the bacteria in the numerator of the selected principal balance i are placed.

• DemSPBal: List. The component i of the list has the number of the row of the matrix especie where the bacteria in the denominator of the selected principal balance i are placed.

• MatrixSPBal: MatrixSPBal is the matrix that contains the covariates of the model. The first line es equal to 1 for all columns. The other rows contain the value of one SPBal at all time points. The selected principal balance of the row i+1 has at its numerator the bacteria placed in the rows NumSPBal[[i]] of the "especie". The selected principal balance of the row i+1 has at its denominator the bacteria placed in the rows DemSPBal[[i]] of the "especie".

• PercenVarianceSPBal: Vector. The component of the vector i contains the percentage of variance of the SPBal with numerator NumSPBal[[i]] and denominator DemSPBal[[i]].

References

Creus-Martí, I., Moya, A., Santonja, F. J. (2022). Bayesian hierarchical compositional models for analysing longitudinal abundance data from microbiome studies. Complexity, 2022.

Examples

set.seed(314)
esp2=t(gtools::rdirichlet(n=6, c(1,1,5,1,1)))

Num2<-list(3,c(3,5),1,c(3,5,4))
Dem2<-list(5,4,2,c(1,2))

ObtainigValueSPBal(Num2,Dem2,esp2,6)

Description

This function calculates the loglikelihood of the dirichlet for the BPBM model. Then, it calculates the loglikelihood with the parameters of each iteration of the MCMC chains and introduces the values in a vector called vectorD. DIC=(1/2)*var(vectorD)+mean(VectorD)

Usage

ObtainingDIC(cadenas, MatrizPBmodelo, E, Tt, especiemodi)

Arguments

Value

Returns a data.frame with the DIC value (using the rule, pD = var/2).

References

Creus-Martí, I., Moya, A., Santonja, F. J. (2022). Bayesian hierarchical compositional models for analysing longitudinal abundance data from microbiome studies. Complexity, 2022.

Examples

set.seed(314)
especie=t(gtools::rdirichlet(n=2, c(1,2,3)))
E=3
Tt=2
MatrizPBmodelo=rbind(c(1,1),c(-0.3,0.4),c(0.3,0.5))
set.seed(314)
est=Estimating_BPBM(especie,
                   Tt,
                   E,
                   MatrizPBmodelo,
                   nn.chain=3,
                   nn.burnin=1000,
                   nn.sample=5000,
                   nn.thin=10)
SumFinal=StudyingParam(est$R2jagsOutput$BUGSoutput$summary   ,est$SamplesAllChains)
cadenas=SumFinal$AllChainsJoined
especiemodi=especie[,-1]

ObtainingDIC(cadenas,MatrizPBmodelo,E,Tt,especiemodi)

Description

This function calculates the balance that has at the numerator the bacteria placed at Num and has at the denominator the bacteria placed at Dem

Usage

PBalance(A, Num, Dem, especie)

Arguments

Value

Returns a vector with the value of the balance in each time point.

Examples

especie1=cbind(c(0.5,0.3,0.1,0.1), c(0.1,0.3,0.6,0.1))
Num=c(1,2)
Dem=c(3,4)
A=2
PBalance(A,Num,Dem,especie1)

Description

This function calculates the balance that has at the numerator de bacteria placed at Num and has at the denominator the bacteria placed at Dem

Usage

PBalancePredi(Num, Dem, DatosEsperanzas)

Arguments

Value

Returns the value of the balance

Examples

Num=c(1,2)
Dem=c(3,4)
DatosEsperanzas=c(0.1,0.3,0.4,0.2)

PBalancePredi(Num,Dem,DatosEsperanzas)

Description

This function calculates the value of the BPBM regression, defined by:

$\mu_{it}=a_{i0}+a_{i1}\cdot\text{SPBal}_{1,t-1}+\cdots+a_{iM}\cdot\text{SPBal}_{M,t-1}$

Usage

PBmodel(A, MatrizPBmodelo, E, Tt)

Arguments

Value

Returns a matrix. The row i contains the regression values of the bacteria i at all time points.

References

Creus-Martí, I., Moya, A., Santonja, F. J. (2022). Bayesian hierarchical compositional models for analysing longitudinal abundance data from microbiome studies. Complexity, 2022.

Examples

A=rbind(c(1,2,3),c(4,5,6),c(7,8,9))
MatrizPBmodelo=cbind(c(1,2,3),c(4,5,6),c(7,8,9))
E=3
Tt=3


PBmodel(A,MatrizPBmodelo, E,Tt)

Description

This function applys a PCA to the estimate parameters (using function "prcomp" with center = TRUE and scale. = TRUE). Then uses the ggbiplot function to plot the biplot.

Usage

PCAbiplot(paramEstimadosFinal, names, E)

Arguments

Value

Returns a list with the PCA biplot, the variance explained of each Principal Component and an object of class "prcomp" with the PCA. In the biplot, "a" denotes the intercept, "b" denotes the parameter that give information about the importance of the bacteria in defining herself in the next time point and "c" denotes denotes the parameter that give information about the importance of the rest of the community in defining the bacteria in the next time point.

Examples

set.seed(123)
especie=t(gtools::rdirichlet(10,c(1,3,1,2,4)))
names=c("Bact1","Bact2","Bact3","Bact4","Bact5")
tau1=0.4
parms1= cbind(c(0.1,0.2,0.4,0.6),c(-0.2,0.1,0.1,0.3),c(0.3,0.2,0.3,0.5))
paramEstimadosFinal=c(as.vector( t(parms1)),tau1)

PCAbiplot(paramEstimadosFinal,names,5)

Description

This function calculates the variance of each row of the matrix PB. Returns the percentage of variance of each row of the matrix PB.

Usage

Percen_Variance(PB)

Arguments

Value

Returns a vector with percentage of variance of each row of the matrix PB.

Examples

matt=matrix(c(1:4),2,2)


Percen_Variance(matt)

Description

Plots the dendogram obtained using the Ward’s method for obtaining the principal balances. The process follow in this function is explained in Section 3.1 of (Creus-Martí et al, 2022)

Usage

PlotDendogram(especie, names)

Arguments

Value

Returns a list with: the dendogram.

• Num: List. The component i of the list has the number of the row of the matrix especie where the bacteria in the numerator of the principal balance i are placed.

• Dem: List. The component i of the list has the number of the row of the matrix especie where the bacteria in the denominator of the principal balance i are placed.

• dendogram: Plots the dendogram.

References

Creus-Martí, I., Moya, A., Santonja, F. J. (2022). Bayesian hierarchical compositional models for analysing longitudinal abundance data from microbiome studies. Complexity, 2022.

Examples

names2=c("Bact1","Bact2","Bact3","Bact4","Bact5")
set.seed(314)
esp2=t(gtools::rdirichlet(n=6, c(1,1,5,1,1)))


PlotDendogram(esp2,names2)

Description

This function calculates the expected value and variance of the bacteria at time point Tt. Then, this function calculates the expected value and variance of the bacteria at time point t=(Tt+1),...,K. It calculates the expected value at each time point for each markov chain iteration. The expected value for each time point is the mean of the expected values of all iterations.mAnalogous with the variance, the dirichlet parameters and the expected valur plus(and minus) two times the sqrt of the variance.

Usage

PredictionBPBM(
  NumSPBal,
  DemSPBal,
  MCMC.CHAINS,
  alpha,
  K,
  esperanza,
  Var,
  E,
  Tt,
  MatrizPBmodelo
)

Arguments

Value

Returns a list with:

• ExpectedValue.All: Matrix. Matrix that contains at row i the expected value of the bacteria i at all time points t=1,2,...,K. The bacterias are placed at the same order than in especies.

• VarianceValue.All: Matrix. Matrix that contains at row i the variance of the bacteria i at all time points t=1,2,...,K. The bacterias are placed at the same order than in especies.

• DirichlerParam.All: Matrix. Matrix that contains at row i the dirichlet parameter of the bacteria i at all time points t=1,2,...,K. The bacterias are placed at the same order than in especies.

• ExpVarmas: Matrix. Matrix that contains at row i the expected value plus two times the sqrt(variance) of the bacteria i at all time points t=Tt,...,K, the rest of the time points has 0 values. The bacterias are placed at the same order than in especies.

• ExpVarmenos: Matrix. Matrix that contains at row i the expected value plus two times the sqrt(variance) of the bacteria i at all time points t=Tt,...,K,the rest of the time points has 0 values. The bacterias are placed at the same order than in especies.

References

Creus-Martí, I., Moya, A., Santonja, F. J. (2022). Bayesian hierarchical compositional models for analysing longitudinal abundance data from microbiome studies. Complexity, 2022.

Examples

NumSPBal=list(1,c(1,2))
DemSPBal=list(2,3)
MCMC.CHAINS=cbind(c(0.1,0.11),
                 c(0.2,0.21),
                 c(0.3,0.31),
                 c(-0.1,-0.11),
                 c(0.15,0.105),
                 c(0.44,0.41),
                 c(0.3,0.31),
                 c(0.201,0.221),
                 c(0.13,0.113) )
alpha=cbind(c(0.1,0.2,0.1),c(0.1,0.5,0.3))
K=3
esperanza=cbind(c(0.2,0.2,0.6))
Var=cbind(c(0.1,0.01,0.11))
E=3
Tt=2
MatrizPBmodelo=cbind(c(1,0.3,0.2))

PredictionBPBM(NumSPBal,DemSPBal,MCMC.CHAINS, alpha,K,esperanza,Var,E,Tt,MatrizPBmodelo )

Description

This function calculates the expected value and variance of the bacteria at time point Tt. Then, this function calculates the expected value and variance of the bacteria at time point t=(Tt+1),...,K

Usage

PredictionEstParmFunc(
  paramEstimadosFinal,
  EspecieMaxima,
  alpha,
  K,
  esperanza,
  Var,
  E,
  Tt
)

Arguments

Details

The regression of this model, in an example with three bacteria, is defined by

$r_{1}\cdot log(x_{1}(t)/x_{3}(t))+log(x_{1}(t)/x_{3}(t))\cdot [a_{11}\cdot log(x_{1}(t)/x_{3}(t))(t)+a_{12}\cdot log(x_{2}(t)/x_{3}(t))]$

$r_{2}\cdot log(x_{2}(t)/x_{3}(t))+log(x_{2}(t)/x_{3}(t))\cdot [a_{21}\cdot log(x_{1}(t)/x_{3}(t))(t)+a_{22}\cdot log(x_{2}(t)/x_{3}(t))]$

Value

Returns a list with:

• ExpectedValue.All: Matrix. Matrix that contains at row i the expected value of the bacteria i at all time points t=2,...,K. The bacteria are placed at the same order than in especies.

• VarianceValue.All: Matrix. Matrix that contains at row i the variance of the bacteria i at all time points t=2,...,K. The bacteria are placed at the same order than in especies.

• DirichlerParam.All: Matrix. Matrix that contains at row i the dirichlet parameter of the bacteria i at all time points t=2,...,K. The bacteria are placed at the same order than in especies.

References

Creus-Martí, I. and Moya, A. and Santonja, F. J. (2018). A Statistical Model with a Lotka-Volterra Structure for Microbiota Data. Lucas Jodar, Juan Carlos Cortes and Luis Acedo, Modelling or engineering and human behavior 2018, Instituto Universitario de Matematica Multidisciplinar. ISBN: 978-84-09-07541-6

Examples

pam.ini=rbind(c(0.1,0.2,0.3),c(0.4,0.5,0.6))
paramEstimadosFinal=c(5, as.vector(pam.ini))
EspecieMaxima=3
alpha=cbind(c(2,2,3),c(1,1,3))
K=3
esperanza=cbind(c(0.2,0.3,0.5))
Var=cbind(c(0.2,0.3,0.5))
E=3
Tt=2

PredictionEstParmFunc(paramEstimadosFinal,EspecieMaxima, alpha,K,esperanza,Var,E,Tt )

Description

This function calculates the expected value and variance of the bacteria at time point Tt. Then, this function calculates the expected value and variance of the bacteria at time point t=(Tt+1),...,K

Usage

PredictionFBM(
  paramEstimadosFinal,
  EspecieMaxima,
  alpha,
  K,
  esperanza,
  Var,
  E,
  Tt
)

Arguments

Details

The regression of this model is defined by

$\mu_{it}=a_{i1}+a_{i2}\cdot\text{alr}(x_{i,(t-1)})+a_{i3}\cdot\text{Balance}(x_{i,(t-1)})\text{ for }i=1,\dots, D-1\text{ where } D \text{ is the number of bacteria}$

Value

Returns a list with:

• ExpectedValue.All: Matrix. Matrix that contains at row i the expected value of the bacteria i at all time points t=1,2,...,K. The bacteria are placed at the same order than in especies.

• VarianceValue.All: Matrix. Matrix that contains at row i the variance of the bacteria i at all time points t=1,2,...,K. The bacteria are placed at the same order than in especies.

• DirichlerParam.All: Matrix. Matrix that contains at row i the dirichlet parameter of the bacteria i at all time points t=1,2,...,K. The bacteria are placed at the same order than in especies.

References

Creus-Martí, I., Moya, A., Santonja, F. J. (2021). A Dirichlet autoregressive model for the analysis of microbiota time-series data. Complexity, 2021, 1-16.

Examples

Tt=2
E=3
tau=5
EspecieMaxima=3
K=3
parms11=c(0.1,0.2,0.3,0.4,0.5,0.6,tau)
alpha=cbind(c(1.726793,1.892901,1.380306),
           c(1,1,3))
Expected=cbind(c(alpha[1,1]/tau, alpha[2,1]/tau, alpha[3,1]/tau  ),
              c(alpha[1,2]/tau,alpha[2,2]/tau,alpha[3,2]/tau))
Variance=cbind(c(0.03768101, 0.03920954, 0.03330857 ),
              c( 0.03683242,0.02784883, 0.0413761 ))
Expected.final=Expected[,-2]
Variance.final=Variance[,-2]

PredictionFBM(parms11,EspecieMaxima, alpha,K,Expected.final,Variance.final,E,Tt )

Description

Preparing the dataset to be introduce in the models' functions. In order to introduce the usage of the package there is a README file. You can find the link to the file using base::system.file("extdata", "README.pdf", package = "CoDaLoMic"). On windows you can open the file with base::shell.exec(system.file("extdata", "README.pdf", package = "CoDaLoMic")).

Usage

PreparingTheData(DaTa, Pred)

Arguments

Value

If Pred==0 returns a list with

• Tt - The number of time points available.

• E - Number of bacteria available

• especieOriginal - Matrix that contains at row i the bacterial taxa of bacteria i at all time points.

• especiemodiOriginal - Matrix that contains at row i the bacterial taxa of bacteria i at time points t=2,...,Tt.

If Pred!=0 returns a list with

• Tt - The number of time points available used to estimate the model (Tt=Pred-1).

• E - Number of bacteria available

• especieOriginal - Matrix that contains at row i the bacterial taxa of bacteria i at the time points t=1,2,...,Pred-1.

• especiemodiOriginal - Matrix that contains at row i the bacterial taxa of bacteria i at time points t=2,...,Pred-1.

• especieOriginal.All - Matrix that contains at row i the bacterial taxa of bacteria i at the time points.

• especiemodiOriginal.All - Matrix that contains at row i the bacterial taxa of bacteria i at time points.

• K - Number of time points available at the dataset.

Examples

df<-data.frame(cbind(c(1,2,3),
                     c(0.5,0.2,0.3),
                     c(0.2,0.1,0.6),
                     c(0.1,0.1,0.8),
                     c(0.3,0.3,0.4)))
PreparingTheData(df,Pred=0)

df2<-data.frame(cbind(c(1,2,3,4,5),
                      c(0.1,0.1,0.1,0.2,0.5),
                      c(0.2,0.2,0.2,0.2,0.2),
                      c(0.2,0.3,0.1,0.2,0.2)))
PreparingTheData(df2,Pred=4)

Description

This function calculates the root-mean-square deviation (RMSD), the Nash Sutchiffe Coefficient, the residual sum of squares (RSS) and the mean absolute percentage error (MAPE) for the matrices introduces. This function also calculates the mean of the RMSD, the mean of the Nash Sutchiffe Coefficient and the mean of the RSS.

Usage

QualityControl(matrixData, matrixExpected, names.especie)

Arguments

Value

Returns a data.frame.

Examples

names.especie=c("Bact1", "Bact2", "Bact3")
matrixExpected=matrix(c(1:9),3,3)
matrixData=matrixExpected+0.1

QualityControl(matrixData, matrixExpected,names.especie)

Description

Ridge regression

Usage

ridgeregression(Tt, especie, E, EspecieMaxima, seed = NULL)

Arguments

Value

Returns the result of the ridge regression, object of class "ridgelm".

Examples

set.seed(123)
especie=t(gtools::rdirichlet(10,c(1,3,1,2,4)))
Tt=10
E=5
EspecieMaxima=5

ridgeregression(Tt,especie, E, EspecieMaxima, 558562316)

Description

This function calculates the right side of the gLV equation.

Usage

rxnrate(State, parms)

Arguments

Details

For instance, if we want to solve the following gLV equations:

$\frac{dx_{1}(t)}{dt}=r_{1}\cdot x_{1}(t)+x_{1}(t)\cdot[a_{11}\cdot x_{1}(t)+a_{12}\cdot x_{2}(t)+a_{13}\cdot x_{3}(t)]$

$\frac{dx_{2}(t)}{dt}=r_{2}\cdot x_{2}(t)+x_{2}(t)\cdot[a_{21}\cdot x_{1}(t)+a_{22}\cdot x_{2}(t)+a_{23}\cdot x_{3}(t)]$

$\frac{dx_{3}(t)}{dt}=r_{3}\cdot x_{3}(t)+x_{3}(t)\cdot[a_{31}\cdot x_{1}(t)+a_{32}\cdot x_{2}(t)+a_{33}\cdot x_{3}(t)]$

This function returns a vector with the value of:

$r_{1}\cdot x_{1}(t)+x_{1}(t)\cdot[a_{11}\cdot x_{1}(t)+a_{12}\cdot x_{2}(t)+a_{13}\cdot x_{3}(t)]$

$r_{2}\cdot x_{2}(t)+x_{2}(t)\cdot[a_{21}\cdot x_{1}(t)+a_{22}\cdot x_{2}(t)+a_{23}\cdot x_{3}(t)]$

$r_{3}\cdot x_{3}(t)+x_{3}(t)\cdot[a_{31}\cdot x_{1}(t)+a_{32}\cdot x_{2}(t)+a_{33}\cdot x_{3}(t)]$

Value

Returns a vector with the value of the right side of the gLV equations.

Examples

cinit1<-c(x1<-0.7,x2<-0.2,x3<-0.1)
parms1= cbind(c(0.1,0.2,-0.1),c(-0.2,0.1,-0.1),c(0.3,0.2,0.3),c(0.1,0.22,0.2))
rxnrate(cinit1,parms1)

Description

Simulated dataset with 5 microbial taxa and 10 time points. Following the scheme given by Faust et al (2018), we generated the interaction matrix using the algorithm proposed by Klemm and Eguíluz (2002), and we generated the initial abundances using the Poisson distribution. With these two tools, we simulated the data using the generalized Lotka-Volterra structure. We carried out the simulation using the R package seqtime (Faust et al, 2018). Focusing on technical details, to generate the interaction matrix we set the clique size at 4, the diagonal values at -1, the interaction connectance at 0.04, the positive edge percentage at 64

Usage

data(Simulated)

Format

A data frame with 10 rows and 6 columns.

References

• K. Faust, F. Bauchinger, B. Laroche et al., “Signatures ofecological processes in microbial community time series”. Microbiome, vol. 6, no. 1, p. 120, 2018

• K. Klemm and V. M. Eguíluz, “Growing scale-free networkswith small-world behavior”. Physical Review, vol. 65, no. 5,Article ID 057102, 2002.

Description

This function controls that the value of the Rhat is between 0.9 and 1.1. In addition, it controls that the effective sample size is bigger than 100 and that the zero is not at the center of the credible interval (the interval between 2.5 and 97.5). We consider that the zero is in the center of the credible interval when the zero is between the 25 and the 75 quantile of the distribution formed by the limits if the credible interval.

Usage

StudyingParam(Sum, MCMC.CHAINS)

Arguments

Value

Returns a list with:

• Param.Summary: Matrix. The matrix Sum with a zero in the column Sum[,"mean"] when a parameter has the zero in the center of its credible interval.

• AllChainsJoined: Matrix. The matrix MCMC.CHAINS with a zero in all the iterations of the chain when a parameter has the zero in the center of its credible interval.

Examples

set.seed(314)
especie=t(gtools::rdirichlet(n=6, c(6,6,1,6,6)))
E=5
Tt=6
MatrizPBmodelo=rbind(c(1,1,1,1,1,1),c(-0.3,0.4,0.3,-0.7,-0.4,-0.6),c(0.3,0.5,-0.3,0.1,0.4,0.1))

est=Estimating_BPBM(especie,
                   Tt,
                   E,
                   MatrizPBmodelo,
                   nn.chain=3,
                   nn.burnin=1000,
                   nn.sample=5000,
                   nn.thin=10)

StudyingParam(est$R2jagsOutput$BUGSoutput$summary,est$SamplesAllChains)

Description

This function returns a table with the interpretable parameters of the Dirich-gLV model.

Usage

Table_alr_Dirich_glv(Param.Estimates, especie, names, E)

Arguments

Details

In an example with three bacteria, the regression of this model is defined by

$r_{1}\cdot log(x_{1}(t)/x_{3}(t))+log(x_{1}(t)/x_{3}(t))\cdot [a_{11}\cdot log(x_{1}(t)/x_{3}(t))(t)+a_{12}\cdot log(x_{2}(t)/x_{3}(t))]$

$r_{2}\cdot log(x_{2}(t)/x_{3}(t))+log(x_{2}(t)/x_{3}(t))\cdot [a_{21}\cdot log(x_{1}(t)/x_{3}(t))(t)+a_{22}\cdot log(x_{2}(t)/x_{3}(t))]$

Value

Returns a table written in latex format with the matrix pam.

References

Creus-Martí, I. and Moya, A. and Santonja, F. J. (2018). A Statistical Model with a Lotka-Volterra Structure for Microbiota Data. Lucas Jodar, Juan Carlos Cortes and Luis Acedo, Modelling or engineering and human behavior 2018, Instituto Universitario de Matematica Multidisciplinar. ISBN: 978-84-09-07541-6

Examples

pam.ini=rbind(c(0.1,0.2,0.3),c(0.4,0.5,0.6))
paramEstimadosFinal=c(5, as.vector(pam.ini))
E=3
especie=cbind(c(0.2,0.4,0.4),c(0.1,0.1,0.8),c(0.5,0.1,0.4))
names=c("a","b","c")

Table_alr_Dirich_glv(paramEstimadosFinal,especie,names,E)

Description

Returns a table with the percentage of variance that each SPBal has, the bacteria that goes in the numerator and denominator of the balance, the relationship between the group in the numerator and the denominator and the bacteria most influenced by this SPBal.

Usage

TableBPBM(
  NumSPBal,
  DemSPBal,
  PerVar,
  MatrizPBmodelo,
  Estimated.Param,
  BB = 0.55,
  names,
  E
)

Arguments

Value

Returns the table written in latex

Examples

NumSPBal=list(c(3,4),3,2)
DemSPBal=list(1,5,4)
PerVar=c(41.37487, 21.08270, 19.16870)
MatrizPBmodelo=rbind(c(1.00000000,  1.0000000,  1.0000000,  1.0000000 , 1.0000000),
                    c(1.84449081, -1.3569851, -0.1388348, -0.5269079, -1.3288684),
                    c(0.27531685,  0.4741394, -1.9045554, -0.3581268, -0.4768543),
                    c( 0.07782991,  0.3492473, -0.7138882,  1.4332828, -0.7203295))
namesOr=c("Bact1", "Bact2","Bact3","Bact4","Bact5")
Estimated.Param=c(0.5, 0.3, -0.2,0.1)
E=5

TableBPBM(NumSPBal,
         DemSPBal,
         PerVar,
         MatrizPBmodelo,
         Estimated.Param,
         BB=0.55,
         namesOr,
         E)

Description

This function returns a table with the interpretable parameters of the FBM model.

Usage

TableFBM(paramEstimadosFinal, names, E)

Arguments

Details

$\mu_{it}=a_{i1}+a_{i2}\cdot\text{alr}(x_{i,(t-1)})+a_{i3}\cdot\text{Balance}(x_{i,(t-1)})\text{ for }i=1,\dots, D-1\text{ where } D \text{ is the number of bacteria}$

Value

Returns a table written in latex format.

References

Creus-Martí, I., Moya, A., Santonja, F. J. (2021). A Dirichlet autoregressive model for the analysis of microbiota time-series data. Complexity, 2021, 1-16.

Examples

paramEstimadosFinal=c(1,2,3,1,2,3,1,2,3)
names=c("Bact1", "Bact2","Bact3")
E=3

TableFBM(paramEstimadosFinal,names,E)

Description

This function estimates the parameters of the FBM model.

Usage

TauAndParameters_EstParmFunc_FBM(
  ttau = 30,
  ridge.final,
  Iter.EstParmFunc = 80,
  especie,
  EspecieMaxima,
  Tt,
  E,
  seed = NULL
)

Arguments

Details

We give to the parameter tau the value 1,2,...,ttau. We estimate the FBM model for all this values (using the function "Estimate_param_FBM") and we select the value of tau that minimizes the AIC. The regression of this model is defined by

$\mu_{it}=a_{i1}+a_{i2}\cdot\text{alr}(x_{i,(t-1)})+a_{i3}\cdot\text{Balance}(x_{i,(t-1)})\text{ for }i=1,\dots, D-1\text{ where } D \text{ is the number of bacteria}$

Value