| Title: | Modeling the Kinetics of Carbon Dioxide Production in Alcoholic Fermentation |
|---|---|
| Description: | Developed to help researchers who need to model the kinetics of carbon dioxide (CO2) production in alcoholic fermentation of wines, beers and other fermented products. The following models are available for modeling the carbon dioxide production curve as a function of time: 5PL, Gompertz and 4PL. This package has different functions, which applied can: perform the modeling of the data obtained in the fermentation and return the coefficients, analyze the model fit and return different statistical metrics, and calculate the kinetic parameters: Maximum production of carbon dioxide; Maximum rate of production of carbon dioxide; Moment in which maximum fermentation rate occurs; Duration of the latency phase for carbon dioxide production; Carbon dioxide produced until maximum fermentation rate occurs. In addition, a function that generates graphs with the observed and predicted data from the models, isolated and combined, is available. Gava, A., Borsato, D., & Ficagna, E. (2020)."Effect of mixture of fining agents on the fermentation kinetics of base wine for sparkling wine production: Use of methodology for modeling". <doi:10.1016/j.lwt.2020.109660>. |
| Authors: | Angelo Gava [aut, cre]
|
| Maintainer: | Angelo Gava <[email protected]> |
| License: | GPL-3 |
| Version: | 2.4.1 |
| Built: | 2025-03-31 06:57:22 UTC |
| Source: | https://github.com/cran/OenoKPM |
A function that, based on the observed data, the independent variable (e.g. time in h) and the dependent variable (e.g. CO2 production in g L-1), performs the modeling of the fermentation curve based on the chosen model (5PL, Gompertz, or 4PL).
Next, the coefficients are used in mathematical formulas to obtain the following kinetic parameters:
tLag - Duration of the latency phase for CO2 production;
Vmax - Maximum rate of production of CO2;
tVmax - Moment in which maximum fermentation rate occurs;
CO2Vmax - CO2 Produced until Maximum fermentation rate occurs;
Ymax - Maximum production of carbon dioxide (CO2);
kp( data, model, save.xls = FALSE, dir.save, xls.name, startA, startB, startC, startD, startG )kp( data, model, save.xls = FALSE, dir.save, xls.name, startA, startB, startC, startD, startG )
data |
Data frame to be analyzed. The data frame must be in the following order:
|
model |
Model to be adjusted. Argument for model:
|
save.xls |
If TRUE, an xlsx file containing the coefficients and kinetic parameters will be saved in the working directory. If FALSE, the xlsx file will not be saved. |
dir.save |
Directory path where the xlsx file is to be saved. |
xls.name |
File name. Must contain the format. For example, "Parameters.xlsx". |
startA |
Starting estimate of the value of A for model. |
startB |
Starting estimate of the value of B for model. |
startC |
Starting estimate of the value of C for model. |
startD |
Starting estimate of the value of D for model. |
startG |
Starting estimate of the value of G for model. |
Curve fitting from the observed data is performed by the nlsLM() function in the 'minpack.lm' package.
You can see our article for more details on the mathematical formulas used to obtain each kinetic parameter (Gava et al., 2020). In addition, feel free to use it as a reference in your works.
The analyzed model coefficients and the calculated kinetic parameters are returned in a data.frame. In addition, a "Parameters.xlsx" file can be generated, containing the coefficients and kinetic parameters of each studied fermentation curve.
Angelo Gava
Gava, A., Borsato, D., & Ficagna, E. (2020). Effect of mixture of fining agents on the fermentation kinetics of base wine for sparkling wine production: Use of methodology for modeling. LWT, 131, 109660. doi:10.1016/j.lwt.2020.109660
Zwietering, M. H., Jongenburger, I., Rombouts, F. M., & Van't Riet, K. J. A. E. M. (1990). Modeling of the bacterial growth curve. Applied and environmental microbiology, 56(6), 1875-1881. doi:10.1128/aem.56.6.1875-1881.1990
#Creating a data.frame. #First, columns containing independent variable. #Second, columns containing dependent variable. #The data frame created presents two #fermentation curves for two yeasts with #different times and carbon dioxide production. df <- data.frame('Time_Yeast_A' = seq(0,280, by=6.23), 'Time_Yeast_B' = seq(0,170, by=3.7777778), 'CO2_Production_Yeast_A' = c(0,0.97,4.04,9.62,13.44,17.50, 24.03,27.46,33.75,36.40,40.80, 44.24,48.01,50.85,54.85,57.51, 61.73,65.43,66.50,72.41,75.47, 77.22,78.49,79.26,80.31,81.04, 81.89,82.28,82.56,83.13,83.62, 84.11,84.47,85.02,85.31,85.61, 86.05,86.27,85.29,86.81,86.94, 87.13,87.33,87.45,87.85), 'CO2_Production_Yeast_B' = c(0,0.41,0.70,3.05,15.61,18.41, 21.37,23.23,28.28,41.28,43.98, 49.54,54.43,60.40,63.75,69.29, 76.54,78.38,80.91,83.72,84.66, 85.39,85.81,86.92,87.38,87.61, 88.38,88.57,88.72,88.82,89.22, 89.32,89.52,89.71,89.92,90.11, 90.31,90.50,90.70,90.90,91.09, 91.29,91.49,91.68,91.88)) #Using the kp() function to find the #coefficients and kinetic parameters #according to the adopted model. kp(data = df, model = 1, startA = 0, startB = 1.5, startC = 500, startD = 92, startG = 1500, save.xls = FALSE) #5PL Model adopted kp(data = df,model = 2, startA = 92, startB = 1.5, startC = 0, startD = NA, startG = NA, save.xls = FALSE) #Gompertz Model adopted kp(data = df, startA = 0, startB = 2.5, startC = 10, startD = 92, startG = NA, model = 3, save.xls = FALSE) #4PL Model adopted #Saving an xlsx file. In this example, #we will use saving a temporary file in #the temporary file directories.#Creating a data.frame. #First, columns containing independent variable. #Second, columns containing dependent variable. #The data frame created presents two #fermentation curves for two yeasts with #different times and carbon dioxide production. df <- data.frame('Time_Yeast_A' = seq(0,280, by=6.23), 'Time_Yeast_B' = seq(0,170, by=3.7777778), 'CO2_Production_Yeast_A' = c(0,0.97,4.04,9.62,13.44,17.50, 24.03,27.46,33.75,36.40,40.80, 44.24,48.01,50.85,54.85,57.51, 61.73,65.43,66.50,72.41,75.47, 77.22,78.49,79.26,80.31,81.04, 81.89,82.28,82.56,83.13,83.62, 84.11,84.47,85.02,85.31,85.61, 86.05,86.27,85.29,86.81,86.94, 87.13,87.33,87.45,87.85), 'CO2_Production_Yeast_B' = c(0,0.41,0.70,3.05,15.61,18.41, 21.37,23.23,28.28,41.28,43.98, 49.54,54.43,60.40,63.75,69.29, 76.54,78.38,80.91,83.72,84.66, 85.39,85.81,86.92,87.38,87.61, 88.38,88.57,88.72,88.82,89.22, 89.32,89.52,89.71,89.92,90.11, 90.31,90.50,90.70,90.90,91.09, 91.29,91.49,91.68,91.88)) #Using the kp() function to find the #coefficients and kinetic parameters #according to the adopted model. kp(data = df, model = 1, startA = 0, startB = 1.5, startC = 500, startD = 92, startG = 1500, save.xls = FALSE) #5PL Model adopted kp(data = df,model = 2, startA = 92, startB = 1.5, startC = 0, startD = NA, startG = NA, save.xls = FALSE) #Gompertz Model adopted kp(data = df, startA = 0, startB = 2.5, startC = 10, startD = 92, startG = NA, model = 3, save.xls = FALSE) #4PL Model adopted #Saving an xlsx file. In this example, #we will use saving a temporary file in #the temporary file directories.
A function that, based on the observed data, the independent variable (e.g. time in h) and the dependent variable (e.g. CO2 production in g L-1), performs the modeling of the fermentation curve based on the chosen model (5PL, Gompertz, or 4PL) and returns the model fit metrics.
As a result, the fit metrics for the chosen model are returned in the form of data.frame: Correlation, R2,Residual sum of squares (RSSmin) and Residual standard error.
metrics( data, model, save.xls = FALSE, dir.save, xls.name, startA, startB, startC, startD, startG )metrics( data, model, save.xls = FALSE, dir.save, xls.name, startA, startB, startC, startD, startG )
data |
Data frame to be analyzed. The data frame must be in the following order:
|
model |
Model to be adjusted. Argument for model:
|
save.xls |
If TRUE, an xlsx file containing the metrics will be saved in the working directory. If FALSE, the xlsx file will not be saved. |
dir.save |
Directory path where the xlsx file is to be saved. |
xls.name |
File name. Must contain the format. For example, "Metrics.xlsx". |
startA |
Starting estimate of the value of A for model. |
startB |
Starting estimate of the value of B for model. |
startC |
Starting estimate of the value of C for model. |
startD |
Starting estimate of the value of D for model. |
startG |
Starting estimate of the value of G for model. |
Curve fitting from the observed data is performed by the nlsLM() function in the 'minpack.lm' package.
The metrics from the analyzed model are returned in a data.frame. In addition, a "Metrics.xlsx" file can be generated, containing the model fit metrics for each fermentation curve studied: Correlation; R2; Residual standard error; Residual sum of squares (RSSmin).
Angelo Gava
#Creating a data.frame. #First, columns containing independent variable. #Second, columns containing dependent variable. #The data frame created presents two #fermentation curves for two yeasts with #different times and carbon dioxide production. df <- data.frame('Time_Yeast_A' = seq(0,280, by=6.23), 'Time_Yeast_B' = seq(0,170, by=3.7777778), 'CO2_Production_Yeast_A' = c(0,0.97,4.04,9.62,13.44,17.50, 24.03,27.46,33.75,36.40,40.80, 44.24,48.01,50.85,54.85,57.51, 61.73,65.43,66.50,72.41,75.47, 77.22,78.49,79.26,80.31,81.04, 81.89,82.28,82.56,83.13,83.62, 84.11,84.47,85.02,85.31,85.61, 86.05,86.27,85.29,86.81,86.94, 87.13,87.33,87.45,87.85), 'CO2_Production_Yeast_B' = c(0,0.41,0.70,3.05,15.61,18.41, 21.37,23.23,28.28,41.28,43.98, 49.54,54.43,60.40,63.75,69.29, 76.54,78.38,80.91,83.72,84.66, 85.39,85.81,86.92,87.38,87.61, 88.38,88.57,88.72,88.82,89.22, 89.32,89.52,89.71,89.92,90.11, 90.31,90.50,90.70,90.90,91.09, 91.29,91.49,91.68,91.88)) #Using the metrics() function to find the #model fit metrics metrics(data = df, model = 1, startA = 0, startB = 1.5, startC = 500, startD = 92, startG = 1500, save.xls = FALSE) #5PL Model adopted metrics(data = df, model = 2, startA = 92, startB = 1.5, startC = 0, startD = NA, startG = NA, save.xls = FALSE) #Gompertz Model adopted metrics(data = df, model = 3, startA = 0, startB = 2.5, startC = 10, startD = 92, startG = NA, save.xls = FALSE) #4PL Model adopted #Saving an xlsx file. In this example, #we will use saving a temporary file in #the temporary file directories.#Creating a data.frame. #First, columns containing independent variable. #Second, columns containing dependent variable. #The data frame created presents two #fermentation curves for two yeasts with #different times and carbon dioxide production. df <- data.frame('Time_Yeast_A' = seq(0,280, by=6.23), 'Time_Yeast_B' = seq(0,170, by=3.7777778), 'CO2_Production_Yeast_A' = c(0,0.97,4.04,9.62,13.44,17.50, 24.03,27.46,33.75,36.40,40.80, 44.24,48.01,50.85,54.85,57.51, 61.73,65.43,66.50,72.41,75.47, 77.22,78.49,79.26,80.31,81.04, 81.89,82.28,82.56,83.13,83.62, 84.11,84.47,85.02,85.31,85.61, 86.05,86.27,85.29,86.81,86.94, 87.13,87.33,87.45,87.85), 'CO2_Production_Yeast_B' = c(0,0.41,0.70,3.05,15.61,18.41, 21.37,23.23,28.28,41.28,43.98, 49.54,54.43,60.40,63.75,69.29, 76.54,78.38,80.91,83.72,84.66, 85.39,85.81,86.92,87.38,87.61, 88.38,88.57,88.72,88.82,89.22, 89.32,89.52,89.71,89.92,90.11, 90.31,90.50,90.70,90.90,91.09, 91.29,91.49,91.68,91.88)) #Using the metrics() function to find the #model fit metrics metrics(data = df, model = 1, startA = 0, startB = 1.5, startC = 500, startD = 92, startG = 1500, save.xls = FALSE) #5PL Model adopted metrics(data = df, model = 2, startA = 92, startB = 1.5, startC = 0, startD = NA, startG = NA, save.xls = FALSE) #Gompertz Model adopted metrics(data = df, model = 3, startA = 0, startB = 2.5, startC = 10, startD = 92, startG = NA, save.xls = FALSE) #4PL Model adopted #Saving an xlsx file. In this example, #we will use saving a temporary file in #the temporary file directories.
A function that, based on the observed data, the independent variable (e.g. time in h) and the dependent variable (e.g. CO2 production in g L-1), performs the modeling of the fermentation curve based on the chosen model(s) (5PL, Gompertz, or/and 4PL).
From the observed data and predicted data, whether from one or all of the available models, this function will plot a graph for each fermentation curve evaluated. The chart will have the following basic structure:
X axis: fermentation time
Y axis: CO2 production
Observed data: Scatterplot with dots. Plot with geom_point function from ggplot2 package.
Predicted data: Smoothed line. Plot with the stat_smooth function from the ggplot2 package.
plot_fit( data, models, startA, startB, startC, startD, startG, col = "black", col1 = "red", col2 = "cornflowerblue", col3 = "forestgreen", axisX = "Time (hours)", axisY = expression(paste("CO"["2"] * " Production (g L"^{ "-1" } * ")")), breaksX = waiver(), limitsX = NULL, breaksY = waiver(), limitsY = NULL, font = "serif", font.size = 14, legend.position = "top", show.R2 = FALSE, save.PDF = FALSE, dir.save, dir.name = "Graphics", width.PDF = 15, height.PDF = 12, width.PDF2 = 25, height.PDF2 = 18 )plot_fit( data, models, startA, startB, startC, startD, startG, col = "black", col1 = "red", col2 = "cornflowerblue", col3 = "forestgreen", axisX = "Time (hours)", axisY = expression(paste("CO"["2"] * " Production (g L"^{ "-1" } * ")")), breaksX = waiver(), limitsX = NULL, breaksY = waiver(), limitsY = NULL, font = "serif", font.size = 14, legend.position = "top", show.R2 = FALSE, save.PDF = FALSE, dir.save, dir.name = "Graphics", width.PDF = 15, height.PDF = 12, width.PDF2 = 25, height.PDF2 = 18 )
data |
Data frame to be analyzed. The data frame must be in the following order:
|
models |
Model or models to be adjusted:
|
startA |
Starting estimate of the value of A for model. |
startB |
Starting estimate of the value of B for model. |
startC |
Starting estimate of the value of C for model. |
startD |
Starting estimate of the value of D for model. |
startG |
Starting estimate of the value of G for model. |
col |
Plot color of observed data in points. For example, "black". |
col1 |
Plot color of predicted data from model 1 (5PL Model). For example, "red". |
col2 |
Plot color of predicted data from model 2 (Gompertz Model). For example, "blue". |
col3 |
Plot color of predicted data from model 3 (4PL Model). For example, "green". |
axisX |
X Axis Title. Character vector (or expression). |
axisY |
Y Axis Title. Character vector (or expression). |
breaksX |
One of:
|
limitsX |
One of:
|
breaksY |
One of:
|
limitsY |
One of:
|
font |
Base font family |
font.size |
Base font size, given in pts. |
legend.position |
The position of the caption ("none", "left", "right", "bottom", "top", or a numeric vector of two elements (X,Y). |
show.R2 |
If TRUE, plots the R2 of the plotted predicted models on the graph. If FALSE, do not plot the R2 of the plotted predicted models. |
save.PDF |
If TRUE, create a folder (directory) and save each graphic in PDF format. If FALSE, it does not create a directory or save the graphics in PDF. |
dir.save |
Path of the directory in which a new folder (directory) will be created for saving graphics in PDF format. |
dir.name |
Folder name (directory name) to be created within the working directory for saving PDF graphics. Character vector. |
width.PDF |
Width, in cm, of the graphic to be saved in a PDF file. |
height.PDF |
Height, in cm, of the graphic to be saved in a PDF |
width.PDF2 |
Width, in cm, of the multiplot graphic to be saved in a PDF file. |
height.PDF2 |
Height, in cm, of the multiplot graphic to be saved in a PDF |
Curve fitting from the observed data is performed by the nlsLM() function in the 'minpack.lm' package.
Graphs are plotted using the various functions in the 'ggplot2' package.
Elegant graphics plotted according to observed and predicted data. In addition, a folder (directory) can be created, in which the PDF graphics will be saved, if desired. In this folder, the graph of each analyzed fermentation curve is saved in PDF format, with the dimensions stipulated in the width.PDF and height.PDF arguments. The name of each PDF file will be extracted from the header of the dependent variable used for the graph. See more in the examples.
Angelo Gava
#################Example 1################# #Using only required arguments #Creating a data.frame. #First, columns containing independent variable. #Second, columns containing dependent variable. #The data frame created presents two #fermentation curves for two yeasts with #different times and carbon dioxide production. df <- data.frame('Time_Yeast_A' = seq(0,280, by=6.23), 'Time_Yeast_B' = seq(0,170, by=3.7777778), 'CO2_Production_Yeast_A' = c(0,0.97,4.04,9.62,13.44,17.50, 24.03,27.46,33.75,36.40,40.80, 44.24,48.01,50.85,54.85,57.51, 61.73,65.43,66.50,72.41,75.47, 77.22,78.49,79.26,80.31,81.04, 81.89,82.28,82.56,83.13,83.62, 84.11,84.47,85.02,85.31,85.61, 86.05,86.27,85.29,86.81,86.94, 87.13,87.33,87.45,87.85), 'CO2_Production_Yeast_B' = c(0,0.41,0.70,3.05,15.61,18.41, 21.37,23.23,28.28,41.28,43.98, 49.54,54.43,60.40,63.75,69.29, 76.54,78.38,80.91,83.72,84.66, 85.39,85.81,86.92,87.38,87.61, 88.38,88.57,88.72,88.82,89.22, 89.32,89.52,89.71,89.92,90.11, 90.31,90.50,90.70,90.90,91.09, 91.29,91.49,91.68,91.88)) #Using the plot_fit function to #generate elegants graphs PDF files #containing both observed data and #predicted data. #Graph plotted only with Model 5PL #fit (models = 1) plot_fit(data = df, models = 1, startA = 0, startB = 1.5, startC = 500, startD = 92, startG = 1500) #Graph plotted with 5PL and Gompertz #model fits (models = 4) plot_fit(data = df, models = 4, startA = 0, startB = 1.5, startC = 500, startD = 92, startG = 1500) #################Example 2################# #Using the various function arguments to #customize the graph. #Creating a data.frame. #First, columns containing independent variable. #Second, columns containing dependent variable. #The data frame created presents two #fermentation curves for two yeasts with #different times and carbon dioxide production. df <- data.frame('Time_Treatment_A' = seq(0,200, by=6.45), 'Time_Treatment_B' = seq(0,200, by=6.45), 'CO2_Production_Treatment_A' = c(0,0.47,0.78,3.23,19.15,22.86, 26.81,29.36,36.14,52.61,55.58, 61.38,66.25,71.83,74.8,78.88, 83.47,84.48,85.94,87.45,87.98, 88.42,88.68,89.40,89.72,89.87, 90.41,90.51,90.62,90.70,91.05, 91.185), 'CO2_Production_Treatment_B' = c(0,0.19,0.39,1.36,9.23,11.29, 13.58,15.06,19.34,30.92,33.28, 37.98,42.14,47.17,50.00,54.28, 60.92,62.80,65.54,69.74,71.52, 73.07,73.98,76.75,77.79,78.70, 80.65,81.48,82.07,82.47,84.04, 84.60)) #Using the plot_fit function to #generate elegants graphs PDF files #containing both observed data and #predicted data. #Graph plotted only with Model 5PL #fit (models = 1) #Do not show R^2 plot_fit(data = df, startA = 0, startB = 1.5, startC = 500, startD = 92, startG = 1500, models = 1, col = "red", #Color of observed data (points) col1 = "blue", #Predicted data color from model 1 (line). Model = 1 <- 5PL Model axisX = "Fermentation time (h)", #Title X-Axis axisY = "Carbon dioxide production (g/L)", #Title Y-Axis breaksX = seq(0,200,20), #X-Axis scale (positions). 0,20,40,60,80,... limitsX = c(0,200), #X-Axis Limits breaksY = seq(0,90,5),#Y-Axis scale (positions). 0,5,10,15,20,... limitsY = c(0,95), #Y-Axis Limits font = "serif", font.size = 12, legend.position = "right", show.R2 = FALSE) #Do not show R^2 #Graph plotted with 5PL and 4PL #model fits (models = 5) #Show R^2 ## Not run: plot_fit(data = df, models = 5, startA = 0, startB = 1.5, startC = 500, startD = 92, startG = 1500, col = "#000000", #Color of observed data (points) col1 = "#FF0000", #Predicted data color from model 1 (line). Model = 1 <- 5PL Model col3 = "#0B6121",#Predicted data color from model 3 (line). Model = 3 <- 4PL Model axisX = "Time (h)", #Title X-Axis axisY = "CO2 production (g/L)", #Title Y-Axis breaksX = seq(0,200,20), #X-Axis scale (positions). 0,20,40,60,80,... limitsX = c(0,200), #X-Axis Limits breaksY = seq(0,90,10),#Y-Axis scale (positions). 0,10,20,30,40,... limitsY = c(0,95), #Y-Axis Limits font = "serif", font.size = 14, legend.position = "bottom", show.R2 = TRUE) #Show R^2 ## End(Not run) #Graph plotted with 5PL, Gompertz and 4PL #model fits (models = 7) #Do not show R^2 ## Not run: plot_fit(data = df, models = 7, startA = 0, startB = 1.5, startC = 500, startD = 92, startG = 1500, col = "#FF0000", #Color of observed data (points) col1 = "#FF00FF", #Predicted data color from model 1 (line). Model = 1 <- 5PL Model col2 = "#0101DF",#Predicted data color from model 2 (line). Model = 2 <- Gompertz Model col3 = "#088A08",#Predicted data color from model 3 (line). Model = 3 <- 4PL Model axisX = "Time (h)", #Title X-Axis axisY = "Carbon dioxide production (g/L)", #Title Y-Axis breaksX = seq(0,200,20), #X-Axis scale (positions). 0,20,40,60,80,... limitsX = c(0,200), #X-Axis Limits breaksY = seq(0,90,10),#Y-Axis scale (positions). 0,10,20,30,40,... limitsY = c(0,95), #Y-Axis Limits font = "serif", font.size = 14, legend.position = "top", show.R2 = FALSE) #Do not show R^2 ## End(Not run)#################Example 1################# #Using only required arguments #Creating a data.frame. #First, columns containing independent variable. #Second, columns containing dependent variable. #The data frame created presents two #fermentation curves for two yeasts with #different times and carbon dioxide production. df <- data.frame('Time_Yeast_A' = seq(0,280, by=6.23), 'Time_Yeast_B' = seq(0,170, by=3.7777778), 'CO2_Production_Yeast_A' = c(0,0.97,4.04,9.62,13.44,17.50, 24.03,27.46,33.75,36.40,40.80, 44.24,48.01,50.85,54.85,57.51, 61.73,65.43,66.50,72.41,75.47, 77.22,78.49,79.26,80.31,81.04, 81.89,82.28,82.56,83.13,83.62, 84.11,84.47,85.02,85.31,85.61, 86.05,86.27,85.29,86.81,86.94, 87.13,87.33,87.45,87.85), 'CO2_Production_Yeast_B' = c(0,0.41,0.70,3.05,15.61,18.41, 21.37,23.23,28.28,41.28,43.98, 49.54,54.43,60.40,63.75,69.29, 76.54,78.38,80.91,83.72,84.66, 85.39,85.81,86.92,87.38,87.61, 88.38,88.57,88.72,88.82,89.22, 89.32,89.52,89.71,89.92,90.11, 90.31,90.50,90.70,90.90,91.09, 91.29,91.49,91.68,91.88)) #Using the plot_fit function to #generate elegants graphs PDF files #containing both observed data and #predicted data. #Graph plotted only with Model 5PL #fit (models = 1) plot_fit(data = df, models = 1, startA = 0, startB = 1.5, startC = 500, startD = 92, startG = 1500) #Graph plotted with 5PL and Gompertz #model fits (models = 4) plot_fit(data = df, models = 4, startA = 0, startB = 1.5, startC = 500, startD = 92, startG = 1500) #################Example 2################# #Using the various function arguments to #customize the graph. #Creating a data.frame. #First, columns containing independent variable. #Second, columns containing dependent variable. #The data frame created presents two #fermentation curves for two yeasts with #different times and carbon dioxide production. df <- data.frame('Time_Treatment_A' = seq(0,200, by=6.45), 'Time_Treatment_B' = seq(0,200, by=6.45), 'CO2_Production_Treatment_A' = c(0,0.47,0.78,3.23,19.15,22.86, 26.81,29.36,36.14,52.61,55.58, 61.38,66.25,71.83,74.8,78.88, 83.47,84.48,85.94,87.45,87.98, 88.42,88.68,89.40,89.72,89.87, 90.41,90.51,90.62,90.70,91.05, 91.185), 'CO2_Production_Treatment_B' = c(0,0.19,0.39,1.36,9.23,11.29, 13.58,15.06,19.34,30.92,33.28, 37.98,42.14,47.17,50.00,54.28, 60.92,62.80,65.54,69.74,71.52, 73.07,73.98,76.75,77.79,78.70, 80.65,81.48,82.07,82.47,84.04, 84.60)) #Using the plot_fit function to #generate elegants graphs PDF files #containing both observed data and #predicted data. #Graph plotted only with Model 5PL #fit (models = 1) #Do not show R^2 plot_fit(data = df, startA = 0, startB = 1.5, startC = 500, startD = 92, startG = 1500, models = 1, col = "red", #Color of observed data (points) col1 = "blue", #Predicted data color from model 1 (line). Model = 1 <- 5PL Model axisX = "Fermentation time (h)", #Title X-Axis axisY = "Carbon dioxide production (g/L)", #Title Y-Axis breaksX = seq(0,200,20), #X-Axis scale (positions). 0,20,40,60,80,... limitsX = c(0,200), #X-Axis Limits breaksY = seq(0,90,5),#Y-Axis scale (positions). 0,5,10,15,20,... limitsY = c(0,95), #Y-Axis Limits font = "serif", font.size = 12, legend.position = "right", show.R2 = FALSE) #Do not show R^2 #Graph plotted with 5PL and 4PL #model fits (models = 5) #Show R^2 ## Not run: plot_fit(data = df, models = 5, startA = 0, startB = 1.5, startC = 500, startD = 92, startG = 1500, col = "#000000", #Color of observed data (points) col1 = "#FF0000", #Predicted data color from model 1 (line). Model = 1 <- 5PL Model col3 = "#0B6121",#Predicted data color from model 3 (line). Model = 3 <- 4PL Model axisX = "Time (h)", #Title X-Axis axisY = "CO2 production (g/L)", #Title Y-Axis breaksX = seq(0,200,20), #X-Axis scale (positions). 0,20,40,60,80,... limitsX = c(0,200), #X-Axis Limits breaksY = seq(0,90,10),#Y-Axis scale (positions). 0,10,20,30,40,... limitsY = c(0,95), #Y-Axis Limits font = "serif", font.size = 14, legend.position = "bottom", show.R2 = TRUE) #Show R^2 ## End(Not run) #Graph plotted with 5PL, Gompertz and 4PL #model fits (models = 7) #Do not show R^2 ## Not run: plot_fit(data = df, models = 7, startA = 0, startB = 1.5, startC = 500, startD = 92, startG = 1500, col = "#FF0000", #Color of observed data (points) col1 = "#FF00FF", #Predicted data color from model 1 (line). Model = 1 <- 5PL Model col2 = "#0101DF",#Predicted data color from model 2 (line). Model = 2 <- Gompertz Model col3 = "#088A08",#Predicted data color from model 3 (line). Model = 3 <- 4PL Model axisX = "Time (h)", #Title X-Axis axisY = "Carbon dioxide production (g/L)", #Title Y-Axis breaksX = seq(0,200,20), #X-Axis scale (positions). 0,20,40,60,80,... limitsX = c(0,200), #X-Axis Limits breaksY = seq(0,90,10),#Y-Axis scale (positions). 0,10,20,30,40,... limitsY = c(0,95), #Y-Axis Limits font = "serif", font.size = 14, legend.position = "top", show.R2 = FALSE) #Do not show R^2 ## End(Not run)
A function that, based on the observed data, the independent variable (e.g. time in h) and the dependent variable (e.g. CO2 production in g L-1), performs the modeling of the fermentation curve based on the chosen model(s) (5PL, Gompertz, or/and 4PL).
From the analyzed data, this function will provide the predicted data for each evaluated fermentation curve.
pred( data, model, startA, startB, startC, startD, startG, save.xls = FALSE, dir.save, xls.name )pred( data, model, startA, startB, startC, startD, startG, save.xls = FALSE, dir.save, xls.name )
data |
Data frame to be analyzed. The data frame must be in the following order:
|
model |
Model or models to be adjusted:
|
startA |
Starting estimate of the value of A for model. |
startB |
Starting estimate of the value of B for model. |
startC |
Starting estimate of the value of C for model. |
startD |
Starting estimate of the value of D for model. |
startG |
Starting estimate of the value of G for model. |
save.xls |
If TRUE, an xlsx file containing the predicted values of each curve will be saved in the working directory. If it is FALSE, the xlsx file will not be saved. |
dir.save |
Directory path where the xlsx file is to be saved. |
xls.name |
File name. Must contain the format. For example, "Predicted Values.xlsx". |
Curve fitting from the observed data is performed by the nlsLM() function in the 'minpack.lm' package.
The predicted values of each analyzed curve will be returned in a data.frame. In addition, a file "Predicted Values.xlsx" can be generated, containing the predicted values of each fermentation curve studied.
Angelo Gava
#Creating a data.frame. #First, columns containing independent variable. #Second, columns containing dependent variable. #The data frame created presents two #fermentation curves for two yeasts with #different times and carbon dioxide production. df <- data.frame('Time_Yeast_A' = seq(0,280, by=6.23), 'Time_Yeast_B' = seq(0,170, by=3.7777778), 'CO2_Production_Yeast_A' = c(0,0.97,4.04,9.62,13.44,17.50, 24.03,27.46,33.75,36.40,40.80, 44.24,48.01,50.85,54.85,57.51, 61.73,65.43,66.50,72.41,75.47, 77.22,78.49,79.26,80.31,81.04, 81.89,82.28,82.56,83.13,83.62, 84.11,84.47,85.02,85.31,85.61, 86.05,86.27,85.29,86.81,86.94, 87.13,87.33,87.45,87.85), 'CO2_Production_Yeast_B' = c(0,0.41,0.70,3.05,15.61,18.41, 21.37,23.23,28.28,41.28,43.98, 49.54,54.43,60.40,63.75,69.29, 76.54,78.38,80.91,83.72,84.66, 85.39,85.81,86.92,87.38,87.61, 88.38,88.57,88.72,88.82,89.22, 89.32,89.52,89.71,89.92,90.11, 90.31,90.50,90.70,90.90,91.09, 91.29,91.49,91.68,91.88)) #Using the pred() function to find the #predicted valuesaccording to the adopted model. pred(data = df, model = 1, startA = 0, startB = 1.5, startC = 500, startD = 92, startG = 1500, save.xls = FALSE) #5PL Model adopted pred(data = df, model = 2, startA = 92, startB = 1.5, startC = 0, startD = NA, startG = NA, save.xls = FALSE) #Gompertz Model adopted pred(data = df, startA = 0, startB = 2.5, startC = 10, startD = 92, startG = NA, model = 3, save.xls = FALSE) #4PL Model adopted #Saving an xlsx file. In this example, #we will use saving a temporary file in #the temporary file directories.#Creating a data.frame. #First, columns containing independent variable. #Second, columns containing dependent variable. #The data frame created presents two #fermentation curves for two yeasts with #different times and carbon dioxide production. df <- data.frame('Time_Yeast_A' = seq(0,280, by=6.23), 'Time_Yeast_B' = seq(0,170, by=3.7777778), 'CO2_Production_Yeast_A' = c(0,0.97,4.04,9.62,13.44,17.50, 24.03,27.46,33.75,36.40,40.80, 44.24,48.01,50.85,54.85,57.51, 61.73,65.43,66.50,72.41,75.47, 77.22,78.49,79.26,80.31,81.04, 81.89,82.28,82.56,83.13,83.62, 84.11,84.47,85.02,85.31,85.61, 86.05,86.27,85.29,86.81,86.94, 87.13,87.33,87.45,87.85), 'CO2_Production_Yeast_B' = c(0,0.41,0.70,3.05,15.61,18.41, 21.37,23.23,28.28,41.28,43.98, 49.54,54.43,60.40,63.75,69.29, 76.54,78.38,80.91,83.72,84.66, 85.39,85.81,86.92,87.38,87.61, 88.38,88.57,88.72,88.82,89.22, 89.32,89.52,89.71,89.92,90.11, 90.31,90.50,90.70,90.90,91.09, 91.29,91.49,91.68,91.88)) #Using the pred() function to find the #predicted valuesaccording to the adopted model. pred(data = df, model = 1, startA = 0, startB = 1.5, startC = 500, startD = 92, startG = 1500, save.xls = FALSE) #5PL Model adopted pred(data = df, model = 2, startA = 92, startB = 1.5, startC = 0, startD = NA, startG = NA, save.xls = FALSE) #Gompertz Model adopted pred(data = df, startA = 0, startB = 2.5, startC = 10, startD = 92, startG = NA, model = 3, save.xls = FALSE) #4PL Model adopted #Saving an xlsx file. In this example, #we will use saving a temporary file in #the temporary file directories.