Type:	Package
Title:	Modelling of Population Growth
Version:	1.0.6
Description:	Modelling of population growth under static and dynamic environmental conditions. Includes functions for model fitting and making prediction under isothermal and dynamic conditions. The methods (algorithms & models) are based on predictive microbiology (See Perez-Rodriguez and Valero (2012, ISBN:978-1-4614-5519-6)).
License:	GPL-3
Encoding:	UTF-8
LazyData:	true
RoxygenNote:	7.2.3
Imports:	deSolve (≥ 1.28), tibble (≥ 3.0.3), dplyr (≥ 0.8.5), FME (≥ 1.3.6), MASS (≥ 7.3), rlang (≥ 0.4.7), purrr (≥ 0.3.4), ggplot2 (≥ 3.3.2), cowplot (≥ 1.0.0), lamW (≥ 1.3.0), tidyr (≥ 1.0.2), formula.tools (≥ 1.7.1), lifecycle
Suggests:	knitr, rmarkdown, tidyverse (≥ 1.3.0)
VignetteBuilder:	knitr
Depends:	R (≥ 2.10)
NeedsCompilation:	no
Packaged:	2025-03-17 16:28:11 UTC; alber
Author:	Alberto Garre [aut, cre], Jeroen Koomen [aut], Heidy den Besten [aut], Marcel Zwietering [aut]
Maintainer:	Alberto Garre <garre.alberto@gmail.com>
Repository:	CRAN
Date/Publication:	2025-03-17 16:50:02 UTC

biogrowth: Modelling of Population Growth

Description

Modelling of population growth under static and dynamic environmental conditions. Includes functions for model fitting and making prediction under isothermal and dynamic conditions. The methods (algorithms & models) are based on predictive microbiology (See Perez-Rodriguez and Valero (2012, ISBN:978-1-4614-5519-6)).

Author(s)

Maintainer: Alberto Garre garre.alberto@gmail.com (ORCID)

Authors:

• Jeroen Koomen jeroen.koomen@wur.nl

• Heidy den Besten heidy.denbesten@wur.nl

• Marcel Zwietering marcel.zwietering@wur.nl

Secondary Aryani model

Description

Secondary model as defined by Aryani et al. (2015).

Usage

Aryani_model(x, xmin, xhalf)

Arguments

Value

The corresponding gamma factor.

Secondary Cardinal Parameter (CPM) model

Description

Secondary cardinal parameter model as defined by Rosso et al. (1995).

Usage

CPM_model(x, xmin, xopt, xmax, n)

Arguments

Value

The corresponding gamma factor.

DynamicGrowth class

Description

The class DynamicGrowth has been superseded by the top-level class GrowthPrediction, which provides a unified approach for growth modelling.

Still, it is returned if the superseded predict_dynamic_growth() is called.

A subclass of list with items:

• simulation: A tibble with the model prediction

• gammas: A tibble with the value of each gamma factor for each value of times.

• env_conditions: A list of functions interpolating the environmental conditions.

• primary_pars: A list with the model parameters of the primary model.

• sec_models: A nested list defining the secondary models.

Usage

## S3 method for class 'DynamicGrowth'
print(x, ...)

## S3 method for class 'DynamicGrowth'
plot(
  x,
  y = NULL,
  ...,
  add_factor = NULL,
  ylims = NULL,
  label_y1 = "logN",
  label_y2 = add_factor,
  line_col = "black",
  line_size = 1,
  line_type = "solid",
  line_col2 = "black",
  line_size2 = 1,
  line_type2 = "dashed",
  label_x = "time"
)

## S3 method for class 'DynamicGrowth'
coef(object, ...)

Arguments

Methods (by generic)

• print(DynamicGrowth): print of the model

• plot(DynamicGrowth): predicted growth curve under dynamic conditions.

• coef(DynamicGrowth): coefficients of the model

FitCoupledGrowth class

Description

The FitCoupledGrowth class contains a Baranyi model fitted to experimental data considering the coupling between the primary and secondary models. Its constructor is fit_coupled_growth().

It is a subclass of list with the items:

• fit: object returned by FME::modFit().

• mode: fitting approach.

• weight: type of weights for the two-steps approach.

• logbase_mu: base of the logarithm used for the calculation of mu.

• data: data used for the model fitting.

Usage

## S3 method for class 'FitCoupledGrowth'
print(x, ...)

## S3 method for class 'FitCoupledGrowth'
coef(object, ...)

## S3 method for class 'FitCoupledGrowth'
summary(object, ...)

## S3 method for class 'FitCoupledGrowth'
predict(object, newdata = NULL, ...)

## S3 method for class 'FitCoupledGrowth'
residuals(object, ...)

## S3 method for class 'FitCoupledGrowth'
vcov(object, ...)

## S3 method for class 'FitCoupledGrowth'
deviance(object, ...)

## S3 method for class 'FitCoupledGrowth'
fitted(object, ...)

## S3 method for class 'FitCoupledGrowth'
logLik(object, ...)

## S3 method for class 'FitCoupledGrowth'
AIC(object, ..., k = 2)

## S3 method for class 'FitCoupledGrowth'
plot(
  x,
  y = NULL,
  ...,
  line_col = "black",
  line_size = 1,
  line_type = 1,
  point_col = "black",
  point_size = 3,
  point_shape = 16,
  label_y = NULL,
  label_x = NULL
)

Arguments

Methods (by generic)

• print(FitCoupledGrowth): print of the model

• coef(FitCoupledGrowth): vector of fitted model parameters.

• summary(FitCoupledGrowth): statistical summary of the fit.

• predict(FitCoupledGrowth): vector of model predictions.

• residuals(FitCoupledGrowth): vector of model residuals.

• vcov(FitCoupledGrowth): variance-covariance matrix of the model, estimated as 1/(0.5*Hessian) for regression

• deviance(FitCoupledGrowth): deviance of the model.

• fitted(FitCoupledGrowth): vector of fitted values.

• logLik(FitCoupledGrowth): loglikelihood of the model

• AIC(FitCoupledGrowth): Akaike Information Criterion

• plot(FitCoupledGrowth): compares the fitted model against the data.

FitDynamicGrowth class

Description

The class FitDynamicGrowth has been superseded by the top-level class GrowthFit, which provides a unified approach for growth modelling.

Still, it is still returned if the superseded fit_dynamic_growth() is called.

It is a subclass of list with the items:

• fit_results: the object returned by modFit.

• best_prediction: the model prediction for the fitted parameters.

• env_conditions: environmental conditions for the fit.

• data: data used for the fit.

• starting: starting values for model fitting

• known: parameter values set as known.

• sec_models: a named vector with the secondary model for each environmental factor

Usage

## S3 method for class 'FitDynamicGrowth'
print(x, ...)

## S3 method for class 'FitDynamicGrowth'
plot(
  x,
  y = NULL,
  ...,
  add_factor = NULL,
  ylims = NULL,
  label_y1 = "logN",
  label_y2 = add_factor,
  line_col = "black",
  line_size = 1,
  line_type = 1,
  point_col = "black",
  point_size = 3,
  point_shape = 16,
  line_col2 = "black",
  line_size2 = 1,
  line_type2 = "dashed"
)

## S3 method for class 'FitDynamicGrowth'
summary(object, ...)

## S3 method for class 'FitDynamicGrowth'
residuals(object, ...)

## S3 method for class 'FitDynamicGrowth'
coef(object, ...)

## S3 method for class 'FitDynamicGrowth'
vcov(object, ...)

## S3 method for class 'FitDynamicGrowth'
deviance(object, ...)

## S3 method for class 'FitDynamicGrowth'
fitted(object, ...)

## S3 method for class 'FitDynamicGrowth'
predict(object, times = NULL, newdata = NULL, ...)

## S3 method for class 'FitDynamicGrowth'
logLik(object, ...)

## S3 method for class 'FitDynamicGrowth'
AIC(object, ..., k = 2)

Arguments

Methods (by generic)

• print(FitDynamicGrowth): comparison between the fitted model and the data.

• plot(FitDynamicGrowth): comparison between the fitted model and the data.

• summary(FitDynamicGrowth): statistical summary of the fit.

• residuals(FitDynamicGrowth): residuals of the model.

• coef(FitDynamicGrowth): vector of fitted parameters.

• vcov(FitDynamicGrowth): (unscaled) variance-covariance matrix of the model, calculated as 1/(0.5*Hessian)

• deviance(FitDynamicGrowth): deviance of the model.

• fitted(FitDynamicGrowth): fitted values.

• predict(FitDynamicGrowth): model predictions.

• logLik(FitDynamicGrowth): loglikelihood of the model

• AIC(FitDynamicGrowth): Akaike Information Criterion

FitDynamicGrowthMCMC class

Description

The class FitDynamicGrowthMCMC has been superseded by the top-level class GrowthFit, which provides a unified approach for growth modelling.

Still, it is returned if the superseded fit_MCMC_growth() is called.

It is a subclass of list with the items:

• fit_results: the object returned by modMCMC.

• best_prediction: the model prediction for the fitted parameters.

• env_conditions: environmental conditions for the fit.

• data: data used for the fit.

• starting: starting values for model fitting

• known: parameter values set as known.

• sec_models: a named vector with the secondary model for each environmental factor

Usage

## S3 method for class 'FitDynamicGrowthMCMC'
print(x, ...)

## S3 method for class 'FitDynamicGrowthMCMC'
plot(
  x,
  y = NULL,
  ...,
  add_factor = NULL,
  ylims = NULL,
  label_y1 = "logN",
  label_y2 = add_factor,
  line_col = "black",
  line_size = 1,
  line_type = 1,
  point_col = "black",
  point_size = 3,
  point_shape = 16,
  line_col2 = "black",
  line_size2 = 1,
  line_type2 = "dashed"
)

## S3 method for class 'FitDynamicGrowthMCMC'
summary(object, ...)

## S3 method for class 'FitDynamicGrowthMCMC'
residuals(object, ...)

## S3 method for class 'FitDynamicGrowthMCMC'
coef(object, ...)

## S3 method for class 'FitDynamicGrowthMCMC'
vcov(object, ...)

## S3 method for class 'FitDynamicGrowthMCMC'
deviance(object, ...)

## S3 method for class 'FitDynamicGrowthMCMC'
fitted(object, ...)

## S3 method for class 'FitDynamicGrowthMCMC'
predict(object, times = NULL, newdata = NULL, ...)

## S3 method for class 'FitDynamicGrowthMCMC'
logLik(object, ...)

## S3 method for class 'FitDynamicGrowthMCMC'
AIC(object, ..., k = 2)

## S3 method for class 'FitDynamicGrowthMCMC'
predictMCMC(
  model,
  times,
  env_conditions,
  niter,
  newpars = NULL,
  formula = . ~ time
)

Arguments

Value

An instance of MCMCgrowth().

Methods (by generic)

• print(FitDynamicGrowthMCMC): print of the model

• plot(FitDynamicGrowthMCMC): compares the model fitted against the data.

• summary(FitDynamicGrowthMCMC): statistical summary of the fit.

• residuals(FitDynamicGrowthMCMC): model residuals.

• coef(FitDynamicGrowthMCMC): vector of fitted model parameters.

• vcov(FitDynamicGrowthMCMC): variance-covariance matrix of the model, estimated as the variance of the samples from the Markov chain.

• deviance(FitDynamicGrowthMCMC): deviance of the model, calculated as the sum of squared residuals for the parameter values resulting in the best fit.

• fitted(FitDynamicGrowthMCMC): vector of fitted values.

• predict(FitDynamicGrowthMCMC): vector of model predictions.

• logLik(FitDynamicGrowthMCMC): loglikelihood of the model

• AIC(FitDynamicGrowthMCMC): Akaike Information Criterion

• predictMCMC(FitDynamicGrowthMCMC): prediction including parameter uncertainty

FitIsoGrowth class

Description

The class FitIsoGrowth has been superseded by the top-level class GrowthFit, which provides a unified approach for growth modelling.

Still, it is still returned if the superseded fit_isothermal_growth() is called.

It is a subclass of list with the items:

• data: data used for model fitting

• model: name of the primary inactivation model

• starting_point: initial value of the model parameters

• known: fixed model parameters

• fit: object returned by FME::modFit()

• best_prediction: model prediction for the model fitted.

Usage

## S3 method for class 'FitIsoGrowth'
print(x, ...)

## S3 method for class 'FitIsoGrowth'
plot(
  x,
  y = NULL,
  ...,
  line_col = "black",
  line_size = 1,
  line_type = 1,
  point_col = "black",
  point_size = 3,
  point_shape = 16
)

## S3 method for class 'FitIsoGrowth'
summary(object, ...)

## S3 method for class 'FitIsoGrowth'
residuals(object, ...)

## S3 method for class 'FitIsoGrowth'
coef(object, ...)

## S3 method for class 'FitIsoGrowth'
vcov(object, ...)

## S3 method for class 'FitIsoGrowth'
deviance(object, ...)

## S3 method for class 'FitIsoGrowth'
fitted(object, ...)

## S3 method for class 'FitIsoGrowth'
predict(object, times = NULL, ...)

## S3 method for class 'FitIsoGrowth'
logLik(object, ...)

## S3 method for class 'FitIsoGrowth'
AIC(object, ..., k = 2)

Arguments

Methods (by generic)

• print(FitIsoGrowth): print of the model

• plot(FitIsoGrowth): compares the fitted model against the data.

• summary(FitIsoGrowth): statistical summary of the fit.

• residuals(FitIsoGrowth): vector of model residuals.

• coef(FitIsoGrowth): vector of fitted model parameters.

• vcov(FitIsoGrowth): variance-covariance matrix of the model, estimated as 1/(0.5*Hessian)

• deviance(FitIsoGrowth): deviance of the model.

• fitted(FitIsoGrowth): vector of fitted values.

• predict(FitIsoGrowth): vector of model predictions.

• logLik(FitIsoGrowth): loglikelihood of the model

• AIC(FitIsoGrowth): Akaike Information Criterion

FitMultipleDynamicGrowth class

Description

The class FitMultipleDynamicGrowth has been superseded by the top-level class GlobalGrowthFit, which provides a unified approach for growth modelling.

Still, it is still returned if the superseded fit_multiple_growth() is called.

It is a subclass of list with the items:

• fit_results: the object returned by modFit.

• best_prediction: a list with the models predictions for each condition.

• data: a list with the data used for the fit.

• starting: starting values for model fitting

• known: parameter values set as known.

• sec_models: a named vector with the secondary model for each environmental factor.

Usage

## S3 method for class 'FitMultipleDynamicGrowth'
print(x, ...)

## S3 method for class 'FitMultipleDynamicGrowth'
plot(
  x,
  y = NULL,
  ...,
  add_factor = NULL,
  ylims = NULL,
  label_x = "time",
  label_y1 = "logN",
  label_y2 = add_factor,
  line_col = "black",
  line_size = 1,
  line_type = "solid",
  line_col2 = "black",
  line_size2 = 1,
  line_type2 = "dashed",
  point_size = 3,
  point_shape = 16,
  subplot_labels = "AUTO"
)

## S3 method for class 'FitMultipleDynamicGrowth'
summary(object, ...)

## S3 method for class 'FitMultipleDynamicGrowth'
residuals(object, ...)

## S3 method for class 'FitMultipleDynamicGrowth'
coef(object, ...)

## S3 method for class 'FitMultipleDynamicGrowth'
vcov(object, ...)

## S3 method for class 'FitMultipleDynamicGrowth'
deviance(object, ...)

## S3 method for class 'FitMultipleDynamicGrowth'
fitted(object, ...)

## S3 method for class 'FitMultipleDynamicGrowth'
predict(object, env_conditions, times = NULL, ...)

## S3 method for class 'FitMultipleDynamicGrowth'
logLik(object, ...)

## S3 method for class 'FitMultipleDynamicGrowth'
AIC(object, ..., k = 2)

Arguments

Methods (by generic)

• print(FitMultipleDynamicGrowth): print of the model

• plot(FitMultipleDynamicGrowth): comparison between the fitted model and the experimental data.

• summary(FitMultipleDynamicGrowth): statistical summary of the fit.

• residuals(FitMultipleDynamicGrowth): calculates the model residuals. Returns a tibble with 4 columns: time (storage time), logN (observed count), exp (name of the experiment) and res (residual).

• coef(FitMultipleDynamicGrowth): vector of fitted parameters.

• vcov(FitMultipleDynamicGrowth): (unscaled) variance-covariance matrix, estimated as 1/(0.5*Hessian).

• deviance(FitMultipleDynamicGrowth): deviance of the model.

• fitted(FitMultipleDynamicGrowth): fitted values. They are returned as a tibble with 3 columns: time (storage time), exp (experiment identifier) and fitted (fitted value).

• predict(FitMultipleDynamicGrowth): vector of model predictions

• logLik(FitMultipleDynamicGrowth): loglikelihood of the model

• AIC(FitMultipleDynamicGrowth): Akaike Information Criterion

FitMultipleGrowthMCMC class

Description

The class FitMultipleGrowthMCMC has been superseded by the top-level class GlobalGrowthFit, which provides a unified approach for growth modelling.

Still, it is still returned if the superseded fit_multiple_growth_MCMC() is called.

It is a subclass of list with the items:

• fit_results: the object returned by modFit.

• best_prediction: a list with the models predictions for each condition.

• data: a list with the data used for the fit.

• starting: starting values for model fitting

• known: parameter values set as known.

• sec_models: a named vector with the secondary model for each environmental factor.

Usage

## S3 method for class 'FitMultipleGrowthMCMC'
print(x, ...)

## S3 method for class 'FitMultipleGrowthMCMC'
plot(
  x,
  y = NULL,
  ...,
  add_factor = NULL,
  ylims = NULL,
  label_x = "time",
  label_y1 = "logN",
  label_y2 = add_factor,
  line_col = "black",
  line_size = 1,
  line_type = "solid",
  line_col2 = "black",
  line_size2 = 1,
  line_type2 = "dashed",
  point_size = 3,
  point_shape = 16,
  subplot_labels = "AUTO"
)

## S3 method for class 'FitMultipleGrowthMCMC'
summary(object, ...)

## S3 method for class 'FitMultipleGrowthMCMC'
residuals(object, ...)

## S3 method for class 'FitMultipleGrowthMCMC'
coef(object, ...)

## S3 method for class 'FitMultipleGrowthMCMC'
vcov(object, ...)

## S3 method for class 'FitMultipleGrowthMCMC'
deviance(object, ...)

## S3 method for class 'FitMultipleGrowthMCMC'
fitted(object, ...)

## S3 method for class 'FitMultipleGrowthMCMC'
predict(object, env_conditions, times = NULL, ...)

## S3 method for class 'FitMultipleGrowthMCMC'
logLik(object, ...)

## S3 method for class 'FitMultipleGrowthMCMC'
AIC(object, ..., k = 2)

## S3 method for class 'FitMultipleGrowthMCMC'
predictMCMC(
  model,
  times,
  env_conditions,
  niter,
  newpars = NULL,
  formula = . ~ time
)

Arguments

Value

An instance of MCMCgrowth().

Methods (by generic)

• print(FitMultipleGrowthMCMC): print of the model

• plot(FitMultipleGrowthMCMC): comparison between the model fitted and the data.

• summary(FitMultipleGrowthMCMC): statistical summary of the fit.

• residuals(FitMultipleGrowthMCMC): model residuals. They are returned as a tibble with 4 columns: time (storage time), logN (observed count), exp (name of the experiment) and res (residual).

• coef(FitMultipleGrowthMCMC): vector of fitted model parameters.

• vcov(FitMultipleGrowthMCMC): variance-covariance matrix of the model, estimated as the variance of the samples from the Markov chain.

• deviance(FitMultipleGrowthMCMC): deviance of the model, calculated as the sum of squared residuals of the prediction with the lowest standard error.

• fitted(FitMultipleGrowthMCMC): fitted values of the model. They are returned as a tibble with 3 columns: time (storage time), exp (experiment identifier) and fitted (fitted value).

• predict(FitMultipleGrowthMCMC): model predictions. They are returned as a tibble with 3 columns: time (storage time), logN (observed count), and exp (name of the experiment).

• logLik(FitMultipleGrowthMCMC): loglikelihood of the model

• AIC(FitMultipleGrowthMCMC): Akaike Information Criterion

• predictMCMC(FitMultipleGrowthMCMC): prediction including parameter uncertainty

FitSecondaryGrowth class

Description

The FitSecondaryGrowth class contains a model fitted to a set of growth rates gathered under a variety of static conditions. Its constructor is fit_secondary_growth().

It is a subclass of list with the items:

• fit_results: object returned by FME::modFit().

• secondary_model: secondary model fitted to the data.

• mu_opt_fit: estimated growth rate under optimum conditions.

• data: data used for the fit.

• transformation: type of transformation of mu for the fit.

Usage

## S3 method for class 'FitSecondaryGrowth'
print(x, ...)

## S3 method for class 'FitSecondaryGrowth'
plot(x, y = NULL, ..., which = 1, add_trend = FALSE, add_segment = FALSE)

## S3 method for class 'FitSecondaryGrowth'
summary(object, ...)

## S3 method for class 'FitSecondaryGrowth'
residuals(object, ...)

## S3 method for class 'FitSecondaryGrowth'
coef(object, ...)

## S3 method for class 'FitSecondaryGrowth'
vcov(object, ...)

## S3 method for class 'FitSecondaryGrowth'
deviance(object, ...)

## S3 method for class 'FitSecondaryGrowth'
fitted(object, ...)

## S3 method for class 'FitSecondaryGrowth'
predict(object, newdata = NULL, ...)

## S3 method for class 'FitSecondaryGrowth'
logLik(object, ...)

## S3 method for class 'FitSecondaryGrowth'
AIC(object, ..., k = 2)

Arguments

Methods (by generic)

• print(FitSecondaryGrowth): print of the model

• plot(FitSecondaryGrowth): plots to evaluate the goodness of the fit.

• summary(FitSecondaryGrowth): statistical summary of the fit.

• residuals(FitSecondaryGrowth): vector of model residuals.

• coef(FitSecondaryGrowth): vector of fitted model parameters.

• vcov(FitSecondaryGrowth): variance-covariance matrix of the model, estimated as 1/(0.5*Hessian)

• deviance(FitSecondaryGrowth): deviance of the model.

• fitted(FitSecondaryGrowth): vector of fitted values.

  The fitted values are returned in the same scale as the one used for the fitting (sqrt, log or none).

• predict(FitSecondaryGrowth): vector of model predictions.

• logLik(FitSecondaryGrowth): loglikelihood of the model

• AIC(FitSecondaryGrowth): Akaike Information Criterion

GlobalGrowthComparison class

Description

The GlobalGrowthComparison class contains several functions for model comparison and model selection of growth models. It should not be instanced directly. Instead, it should be constructed using compare_growth_fits(). It is similar to GrowthComparison, although with specific tools to deal with several experiments.

It includes two type of tools for model selection and comparison: statistical indexes and visual analyses. Please check the sections below for details.

Note that all these tools use the names defined in compare_growth_fits(), so we recommend passing a named list to that function.

Usage

## S3 method for class 'GlobalGrowthComparison'
coef(object, ...)

## S3 method for class 'GlobalGrowthComparison'
summary(object, ...)

## S3 method for class 'GlobalGrowthComparison'
print(x, ...)

## S3 method for class 'GlobalGrowthComparison'
plot(x, y, ..., type = 1, add_trend = TRUE)

Arguments

Methods (by generic)

• coef(GlobalGrowthComparison): table of parameter estimates

• summary(GlobalGrowthComparison): summary table for the comparison

• print(GlobalGrowthComparison): print of the model comparison

• plot(GlobalGrowthComparison): illustrations comparing the fitted models

Statistical indexes

GlobalGrowthComparison implements two S3 methods to obtain numerical values to facilitate model comparison and selection.

• the coef method returns a tibble with the values of the parameter estimates and their corresponding standard errors for each model.

• the summary returns a tibble with the AIC, number of degrees of freedom, mean error and root mean squared error for each model.

Visual analyses

The S3 plot method can generate three types of plots:

• when type = 1, the plot compares the fitted growth curves against the experimental data used to fit the model.

• when type = 2, the plot compares the parameter estimates using error bars, where the limits of the error bars are the expected value +/- one standard error. In case one model does not has some model parameter (i.e. either because it is not defined or because it was fixed), the parameter is not included in the plot.

• when type=3, the plot shows the tendency of the residuals for each model. This plot can be used to detect deviations from independence.

These plots are divided by facets for each experiment.

GlobalGrowthFit class

Description

The GlobalGrowthFit class contains a growth model fitted to data using a global approach. Its constructor is fit_growth().

It is a subclass of list with the items:

• algorithm: type of algorithm as in fit_growth()

• data: data used for model fitting

• start: initial guess of the model parameters

• known: fixed model parameters

• primary_model: a character describing the primary model

• fit_results: an instance of modFit or modMCMC with the results of the fit

• best_prediction: Instance of GrowthPrediction with the best growth fit

• sec_models: a named vector with the secondary models assigned for each environmental factor. NULL for environment="constant"

• env_conditions: a list with the environmental conditions used for model fitting. NULL for environment="constant"

• niter: number of iterations of the Markov chain. NULL if algorithm != "MCMC"

• logbase_mu: base of the logarithm for the definition of parameter mu (check the relevant vignette)

• logbase_logN: base of the logarithm for the definition of the population size (check the relevant vignette)

• environment: "dynamic". Always

Usage

## S3 method for class 'GlobalGrowthFit'
print(x, ...)

## S3 method for class 'GlobalGrowthFit'
coef(object, ...)

## S3 method for class 'GlobalGrowthFit'
summary(object, ...)

## S3 method for class 'GlobalGrowthFit'
predict(object, env_conditions, times = NULL, ...)

## S3 method for class 'GlobalGrowthFit'
residuals(object, ...)

## S3 method for class 'GlobalGrowthFit'
vcov(object, ...)

## S3 method for class 'GlobalGrowthFit'
deviance(object, ...)

## S3 method for class 'GlobalGrowthFit'
fitted(object, ...)

## S3 method for class 'GlobalGrowthFit'
logLik(object, ...)

## S3 method for class 'GlobalGrowthFit'
AIC(object, ..., k = 2)

## S3 method for class 'GlobalGrowthFit'
plot(
  x,
  y = NULL,
  ...,
  add_factor = NULL,
  ylims = NULL,
  label_x = "time",
  label_y1 = NULL,
  label_y2 = add_factor,
  line_col = "black",
  line_size = 1,
  line_type = "solid",
  line_col2 = "black",
  line_size2 = 1,
  line_type2 = "dashed",
  point_size = 3,
  point_shape = 16,
  subplot_labels = "AUTO"
)

## S3 method for class 'GlobalGrowthFit'
predictMCMC(
  model,
  times,
  env_conditions,
  niter,
  newpars = NULL,
  formula = . ~ time
)

Arguments

Value

An instance of MCMCgrowth.

Methods (by generic)

• print(GlobalGrowthFit): print of the model

• coef(GlobalGrowthFit): vector of fitted model parameters.

• summary(GlobalGrowthFit): statistical summary of the fit.

• predict(GlobalGrowthFit): vector of model predictions

• residuals(GlobalGrowthFit): model residuals. They are returned as a tibble with 4 columns: time (storage time), logN (observed count), exp (name of the experiment) and res (residual).

• vcov(GlobalGrowthFit): variance-covariance matrix of the model, estimated as 1/(0.5*Hessian) for regression and as the variance-covariance of the draws for MCMC

• deviance(GlobalGrowthFit): deviance of the model.

• fitted(GlobalGrowthFit): fitted values. They are returned as a tibble with 3 columns: time (storage time), exp (experiment identifier) and fitted (fitted value).

• logLik(GlobalGrowthFit): loglikelihood of the model

• AIC(GlobalGrowthFit): Akaike Information Criterion

• plot(GlobalGrowthFit): comparison between the fitted model and the experimental data.

• predictMCMC(GlobalGrowthFit): prediction including parameter uncertainty

GrowthComparison class

Description

The GrowthComparison class contains several functions for model comparison and model selection of growth models. It should not be instanced directly. Instead, it should be constructed using compare_growth_fits().

It includes two type of tools for model selection and comparison: statistical indexes and visual analyses. Please check the sections below for details.

Note that all these tools use the names defined in compare_growth_fits(), so we recommend passing a named list to that function.

Usage

## S3 method for class 'GrowthComparison'
plot(x, y, ..., type = 1, add_trend = TRUE)

## S3 method for class 'GrowthComparison'
coef(object, ...)

## S3 method for class 'GrowthComparison'
print(x, ...)

## S3 method for class 'GrowthComparison'
summary(object, ...)

Arguments

Methods (by generic)

• plot(GrowthComparison): illustrations comparing the fitted models

• coef(GrowthComparison): table of parameter estimates

• print(GrowthComparison): print of the model comparison

• summary(GrowthComparison): summary table for the comparison

Statistical indexes

GrowthComparison implements two S3 methods to obtain numerical values to facilitate model comparison and selection.

• the coef method returns a tibble with the values of the parameter estimates and their corresponding standard errors for each model.

• the summary returns a tibble with the AIC, number of degrees of freedom, mean error and root mean squared error for each model.

Visual analyses

The S3 plot method can generate three types of plots:

• when type = 1, the plot compares the fitted growth curves against the experimental data used to fit the model.

• when type = 2, the plot compares the parameter estimates using error bars, where the limits of the error bars are the expected value +/- one standard error. In case one model does not have some model parameter (i.e. either because it is not defined or because it was fixed), the parameter is not included in the plot.

• when type=3, the plot shows the tendency of the residuals for each model. This plot can be used to detect deviations from independence.

GrowthFit class

Description

The GrowthFit class contains a growth model fitted to data under static or dynamic conditions. Its constructor is fit_growth().

It is a subclass of list with the items:

• environment: type of environment as in fit_growth()

• algorithm: type of algorithm as in fit_growth()

• data: data used for model fitting

• start: initial guess of the model parameters

• known: fixed model parameters

• primary_model: a character describing the primary model

• fit_results: an instance of modFit or modMCMC with the results of the fit

• best_prediction: Instance of GrowthPrediction with the best growth fit

• sec_models: a named vector with the secondary models assigned for each environmental factor. NULL for environment="constant"

• env_conditions: a tibble with the environmental conditions used for model fitting. NULL for environment="constant"

• niter: number of iterations of the Markov chain. NULL if algorithm != "MCMC"

• logbase_mu: base of the logarithm for the definition of parameter mu (check the relevant vignette)

• logbase_logN: base of the logarithm for the definition of the population size (check the relevant vignette)

Usage

## S3 method for class 'GrowthFit'
print(x, ...)

## S3 method for class 'GrowthFit'
coef(object, ...)

## S3 method for class 'GrowthFit'
summary(object, ...)

## S3 method for class 'GrowthFit'
predict(object, times = NULL, env_conditions = NULL, ...)

## S3 method for class 'GrowthFit'
residuals(object, ...)

## S3 method for class 'GrowthFit'
vcov(object, ...)

## S3 method for class 'GrowthFit'
deviance(object, ...)

## S3 method for class 'GrowthFit'
fitted(object, ...)

## S3 method for class 'GrowthFit'
logLik(object, ...)

## S3 method for class 'GrowthFit'
AIC(object, ..., k = 2)

## S3 method for class 'GrowthFit'
plot(
  x,
  y = NULL,
  ...,
  add_factor = NULL,
  line_col = "black",
  line_size = 1,
  line_type = 1,
  point_col = "black",
  point_size = 3,
  point_shape = 16,
  ylims = NULL,
  label_y1 = NULL,
  label_y2 = add_factor,
  label_x = "time",
  line_col2 = "black",
  line_size2 = 1,
  line_type2 = "dashed"
)

## S3 method for class 'GrowthFit'
predictMCMC(
  model,
  times,
  env_conditions,
  niter,
  newpars = NULL,
  formula = . ~ time
)

Arguments

Value

An instance of MCMCgrowth.

Methods (by generic)

• print(GrowthFit): print of the model

• coef(GrowthFit): vector of fitted model parameters.

• summary(GrowthFit): statistical summary of the fit.

• predict(GrowthFit): vector of model predictions.

• residuals(GrowthFit): vector of model residuals.

• vcov(GrowthFit): variance-covariance matrix of the model, estimated as 1/(0.5*Hessian) for regression and as the variance-covariance of the draws for MCMC

• deviance(GrowthFit): deviance of the model.

• fitted(GrowthFit): vector of fitted values.

• logLik(GrowthFit): loglikelihood of the model

• AIC(GrowthFit): Akaike Information Criterion

• plot(GrowthFit): compares the fitted model against the data.

• predictMCMC(GrowthFit): prediction including parameter uncertainty

GrowthPrediction class

Description

The GrowthPrediction class contains the results of a growth prediction. Its constructor is predict_growth().

It is a subclass of list with the items:

• simulation: a tibble with the model simulation

• primary model: a list describing the primary model as in predict_growth()

• environment: a character describing the type of environmental conditions as in predict_growth()

• env_conditions: a named list with the functions used to approximate the (dynamic) environmental conditions. NULL if environment="constant".

• sec_models: a named list describing the secondary models as in predict_growth(). NULL if environment="constant".

• gammas: a tibble describing the variation of the gamma factors through the experiment. NUll if environment="constant".

• logbase_mu: the log-base for the definition of parameter mu (see the relevant vignette)

• logbase_logN: the log-base for the definition of the logarithm of the population size

Usage

## S3 method for class 'GrowthPrediction'
print(x, ...)

## S3 method for class 'GrowthPrediction'
summary(object, ...)

## S3 method for class 'GrowthPrediction'
plot(
  x,
  y = NULL,
  ...,
  add_factor = NULL,
  ylims = NULL,
  label_y1 = NULL,
  label_y2 = add_factor,
  line_col = "black",
  line_size = 1,
  line_type = "solid",
  line_col2 = "black",
  line_size2 = 1,
  line_type2 = "dashed",
  label_x = "time"
)

## S3 method for class 'GrowthPrediction'
coef(object, ...)

Arguments

Methods (by generic)

• print(GrowthPrediction): print of the model

• summary(GrowthPrediction): summary of the model

• plot(GrowthPrediction): predicted growth curve.

• coef(GrowthPrediction): coefficients of the model

GrowthUncertainty class

Description

The GrowthUncertainty class contains the results of a growth prediction under isothermal conditions considering parameter uncertainty. Its constructor is predict_growth_uncertainty().

It is a subclass of list with the items:

• sample: parameter sample used for the calculations.

• simulations: growth curves predicted for each parameter.

• quantiles: limits of the credible intervals (5%, 10%, 50%, 90%, 95%) for each time point.

• model: Model used for the calculations.

• mus: Mean parameter values used for the simulations.

• sigma: Variance-covariance matrix used for the simulations.

• logbase_mu: base of the logarithm for the definition of parameter mu (check the relevant vignette)

• logbase_logN: base of the logarithm for the definition of the population size (check the relevant vignette)

Usage

## S3 method for class 'GrowthUncertainty'
print(x, ...)

## S3 method for class 'GrowthUncertainty'
plot(
  x,
  y = NULL,
  ...,
  line_col = "black",
  line_size = 0.5,
  line_type = "solid",
  ribbon80_fill = "grey",
  ribbon90_fill = "grey",
  alpha80 = 0.5,
  alpha90 = 0.4
)

Arguments

Methods (by generic)

• print(GrowthUncertainty): print of the model

• plot(GrowthUncertainty): Growth prediction (prediction band) considering parameter uncertainty.

IsothermalGrowth class

Description

The class IsothermalGrowth has been superseded by the top-level class GrowthPrediction, which provides a unified approach for growth modelling.

Still, it is still returned if the superseded predict_isothermal_growth() is called.

It is a subclass of list with the items:

• simulation: A tibble with the model simulation.

• model: The name of the model used for the predictions.

• pars: A list with the values of the model parameters.

Usage

## S3 method for class 'IsothermalGrowth'
print(x, ...)

## S3 method for class 'IsothermalGrowth'
plot(
  x,
  y = NULL,
  ...,
  line_col = "black",
  line_size = 1,
  line_type = "solid",
  ylims = NULL,
  label_y = NULL,
  label_x = "time"
)

## S3 method for class 'IsothermalGrowth'
coef(object, ...)

Arguments

Methods (by generic)

• print(IsothermalGrowth): print of the model

• plot(IsothermalGrowth): plot of the predicted growth curve.

• coef(IsothermalGrowth): coefficients of the model

MCMCgrowth class

Description

The MCMCgrowth class contains the results of a growth prediction consider parameter variability based on a model fitted using an MCMC algorithm.

It is a subclass of list with items:

• sample: Parameter sample used for the calculations.

• simulations: Individual growth curves calculated based on the parameter sample.

• quantiles: Tibble with the limits of the credible intervals (5%, 10%, 50%, 90% and 95%) for each time point.

• model: Instance of FitDynamicGrowthMCMC used for predictions.

• env_conditions: A tibble with the environmental conditions of the simulation.

Usage

## S3 method for class 'MCMCgrowth'
print(x, ...)

## S3 method for class 'MCMCgrowth'
plot(
  x,
  y = NULL,
  ...,
  add_factor = NULL,
  alpha_80 = 0.5,
  fill_80 = "grey",
  alpha_90 = 0.5,
  fill_90 = "grey",
  label_y1 = "logN",
  label_y2 = add_factor,
  line_col = "black",
  line_type = 1,
  line_size = 1,
  line_type2 = 2,
  line_col2 = "black",
  line_size2 = 1,
  ylims = NULL
)

Arguments

Methods (by generic)

• print(MCMCgrowth): print of the model

• plot(MCMCgrowth): plot of predicted growth (prediction band).

Lag phase duration from Q0

Description

Convenience function to calculate the lag phase duration (lambda) of the Baranyi model from the maximum specific growth rate and the initial value of the variable Q.

Note that this function uses the unit system of biogrowth (i.e. log10). Care must be taken when using parameters obtained from other sources.

Usage

Q0_to_lambda(q0, mu, logbase_mu = 10)

Arguments

Secondary Rosso model for water activity

Description

Secondary model for water activity as defined by Aryani et al. (2001).

Usage

Rossoaw_model(x, xmin)

Arguments

Value

The corresponding gamma factor.

SecondaryComparison class

Description

The SecondaryComparison class contains several functions for model comparison and model selection of growth models. It should not be instanced directly. Instead, it should be constructed using compare_secondary_fits().

It includes two type of tools for model selection and comparison: statistical indexes and visual analyses. Please check the sections below for details.

Note that all these tools use the names defined in compare_secondary_fits(), so we recommend passing a named list to that function.

Usage

## S3 method for class 'SecondaryComparison'
coef(object, ...)

## S3 method for class 'SecondaryComparison'
summary(object, ...)

## S3 method for class 'SecondaryComparison'
print(x, ...)

## S3 method for class 'SecondaryComparison'
plot(x, y, ..., type = 1, add_trend = TRUE)

Arguments

Methods (by generic)

• coef(SecondaryComparison): table of parameter estimates

• summary(SecondaryComparison): summary table for the comparison

• print(SecondaryComparison): print of the model comparison

• plot(SecondaryComparison): illustrations comparing the fitted models

Statistical indexes

SecondaryComparison implements two S3 methods to obtain numerical values to facilitate model comparison and selection.

• the coef method returns a tibble with the values of the parameter estimates and their corresponding standard errors for each model.

• the summary returns a tibble with the AIC, number of degrees of freedom, mean error and root mean squared error for each model.

Visual analyses

The S3 plot method can generate three types of plots:

• when type = 1, the plot compares the observations against the model predictions for each model. The plot includes a linear model fitted to the residuals. In the case of a perfect fit, the line would have slope=1 and intercept=0 (shown as a black, dashed line).

• when type = 2, the plot compares the parameter estimates using error bars, where the limits of the error bars are the expected value +/- one standard error. In case one model does not has some model parameter (i.e. either because it is not defined or because it was fixed), the parameter is not included in the plot.

StochasticGrowth class

Description

The class StochasticGrowth has been deprecated by class GrowthUncertainty, which provides less misleading name.

Still, it is still returned if the deprecated predict_stochastic_growth() is called.

The StochasticGrowth class contains the results of a growth prediction under isothermal conditions considering parameter unceratinty. Its constructor is predict_stochastic_growth().

It is a subclass of list with the items:

• sample: parameter sample used for the calculations.

• simulations: growth curves predicted for each parameter.

• quantiles: limits of the credible intervals (5%, 10%, 50%, 90%, 95%) for each time point.

• model: Model used for the calculations.

• mus: Mean parameter values used for the simulations.

• sigma: Variance-covariance matrix used for the simulations.

Usage

## S3 method for class 'StochasticGrowth'
print(x, ...)

## S3 method for class 'StochasticGrowth'
plot(
  x,
  y = NULL,
  ...,
  line_col = "black",
  line_size = 0.5,
  line_type = "solid",
  ribbon80_fill = "grey",
  ribbon90_fill = "grey",
  alpha80 = 0.5,
  alpha90 = 0.4
)

Arguments

Details

FitIsoGrowth class

Methods (by generic)

• print(StochasticGrowth): print of the model

• plot(StochasticGrowth): Growth prediction (prediction band) considering parameter uncertainty.

TimeDistribution class

Description

The TimeDistribution class contains an estimate of the probability distribution of the time to reach a given microbial count. Its constructor is distribution_to_logcount().

It is a subclass of list with the items:

• distribution Sample of the distribution of times to reach log_count.

• summary Summary statistics of distribution (mean, sd, median, q10 and q90).

Usage

## S3 method for class 'TimeDistribution'
print(x, ...)

## S3 method for class 'TimeDistribution'
summary(object, ...)

## S3 method for class 'TimeDistribution'
plot(x, y = NULL, ..., bin_width = NULL)

Arguments

Methods (by generic)

• print(TimeDistribution): print of the model

• summary(TimeDistribution): summary of the model

• plot(TimeDistribution): plot of the distribution of the time to reach a microbial count.

Generates functions for linear interpolation of environmental conditions

Description

Generates functions for linear interpolation of environmental conditions

Usage

approx_env(env_conditions)

Arguments

Value

A list of functions that return the value of each environmental condition for some storage time

Number of tractors in the Arab World according to the World Bank

Description

A dataset showing the increase in tractors in the Arab World. It was retrieved from https://data.worldbank.org/indicator/AG.AGR.TRAC.NO?end=2009&start=1961&view=chart.

Usage

arabian_tractors

Format

A tibble with 40 rows (each corresponding to one year) and 7 columns:

year

Year for the recording

tractors

Number of tractors

Bilinear model with lag phase

Description

Bilinear model with lag phase

Usage

bilinear_lag(times, logN0, mu, lambda)

Arguments

Bilinear model with stationary phase

Description

Bilinear model with stationary phase

Usage

bilinear_stationary(times, logN0, mu, logNmax)

Arguments

Calculates every gamma factor

Description

A helper function for predict_dynamic_growth() that calculates the value of every gamma factor corresponding to some storage time.

Usage

calculate_gammas(this_t, env_func, sec_models)

Arguments

Value

A vector of gamma factors (one per environmental factor).

Gamma factors for fitting secondary models

Description

A helper for fitting the secondary gamma models. Calculates the gamma factors corresponding to the models defined and the experimental conditions. In order for it to work, the environmental factors must be named identically in the 3 arguments.

Usage

calculate_gammas_secondary(sec_model_names, my_data, secondary_models)

Arguments

Value

a numeric vector of length nrow(my_data) with the gamma factor for each experimental condition.

Visual check of an initial guess of the model parameters

Description

Generates a plot comparing a set of data points against the model prediction corresponding to an initial guess of the model parameters

Usage

check_growth_guess(
  fit_data,
  model_keys,
  guess,
  environment = "constant",
  env_conditions = NULL,
  approach = "single",
  logbase_mu = 10,
  formula = logN ~ time
)

Arguments

Value

A ggplot2::ggplot() comparing the model prediction against the data

Examples

## Examples under constant environmental conditions -------------------------

## We need some data

my_data <- data.frame(time = 0:9,
                      logN = c(2, 2.1, 1.8, 2.5, 3.1, 3.4, 4, 4.5, 4.8, 4.7)
                      )
                      
## We can directly plot the comparison for some values

check_growth_guess(my_data, list(primary = "modGompertz"),
                   c(logN0 = 1.5, mu = .8, lambda = 4, C = 3)
                   )
                   
## Ot it can be combined with the automatic initial guess

check_growth_guess(my_data, list(primary = "modGompertz"),
                   make_guess_primary(my_data, "modGompertz")
                   )
                   
## Examples under dynamic environmental conditions --------------------------

## We will use the datasets included in the package

data("example_dynamic_growth")
data("example_env_conditions")

## Model equations are assigned as in fit_growth

sec_models <- list(temperature = "CPM", aw = "CPM")

## Guesses of model parameters are also defined as in fit_growth

guess <- list(Nmax = 1e4, 
              N0 = 1e0, Q0 = 1e-3,
              mu_opt = 4, 
              temperature_n = 1,
              aw_xmax = 1, aw_xmin = .9, aw_n = 1,
              temperature_xmin = 25, temperature_xopt = 35,
              temperature_xmax = 40, aw_xopt = .95
              )
              
## We can now check our initial guess

check_growth_guess(example_dynamic_growth, sec_models, guess,
                   "dynamic",
                   example_env_conditions)

Basic check of parameters for primary models

Description

Checks that: the model name is correct, the right number of model parameters have been defined and that the parameters have the right names

Usage

check_primary_pars(model_name, pars)

Arguments

Value

If there is no error, the model function.

Basic checks of secondary parameters

Description

Checks that the model names are correct, that no parameter is defined twice, that every parameter is defined and that no unknown parameter has been defined. Raises an error if any of these conditions is not met.

Usage

check_secondary_pars(
  starting_point,
  known_pars,
  sec_model_names,
  primary_pars = "mu_opt"
)

Arguments

Model definition checks for predict_stochastic_growth

Description

Does several checks of the model parameters. Besides those by check_primary_pars, it checks that corr_matrix is square, that pars and corr_matrix have compatible dimensions, and that pars has the correct names.

Usage

check_stochastic_pars(model_name, pars, corr_matrix)

Arguments

Model comparison and selection for growth models

Description

This function is a constructor for GrowthComparison or GlobalGrowthComparison, a class that provides several functions for model comparison and model selection for growth models fitted using fit_growth(). Please see the help pages for GrowthComparison or GlobalGrowthComparison for further details.

Although it is not necessary, we recommend passing the models as a named list, as these names will later be kept in plots and tables.

Usage

compare_growth_fits(models)

Arguments

Examples

## Example 1 - Fitting under static environmental conditions ----------------

## We will use the data on growth of Salmonella included in the package

data("growth_salmonella")

## We will fit 3 different models to the data

fit1 <- fit_growth(growth_salmonella, 
                   list(primary = "Baranyi"),
                   start = c(lambda = 0, logNmax = 8, mu = .1, logN0 = 2),
                   known = c(),
                   environment = "constant",
                   )
                   
fit2 <- fit_growth(growth_salmonella,
                   list(primary = "Baranyi"),
                   start = c(logNmax = 8, mu = .1, logN0 = 2),
                   known = c(lambda = 0),
                   environment = "constant",
                   )
                   
fit3 <- fit_growth(growth_salmonella,
                   list(primary = "modGompertz"),
                   start = c(C = 8, mu = .1, logN0 = 2),
                   known = c(lambda = 0),
                   environment = "constant",
                   )
                   
## We can now put them in a (preferably named) list

my_models <- list(`Baranyi` = fit1, 
                  `Baranyi no lag` = fit2, 
                  `Gompertz no lag` = fit3)
                  
## And pass them to compare_growth_fits
                   
model_comparison <- compare_growth_fits(my_models)

##  The instance of GrowthComparison has useful S3 methods

print(model_comparison)
plot(model_comparison)
plot(model_comparison, type = 2)
plot(model_comparison, type = 3)

## The statistical indexes can be accessed through summary and coef

summary(model_comparison)
coef(model_comparison)

## Example 2 - Fitting under dynamic environmental conditions ---------------


## We will use one of the example datasets

data("example_dynamic_growth")
data("example_env_conditions")

## First model fitted

sec_models <- list(temperature = "CPM", aw = "CPM")

known_pars <- list(Nmax = 1e4, 
                   N0 = 1e0, Q0 = 1e-3, 
                   mu_opt = 4,
                   temperature_n = 1,
                   aw_xmax = 1, aw_xmin = .9, aw_n = 1 
                   )
                   
my_start <- list(temperature_xmin = 25, temperature_xopt = 35,
                 temperature_xmax = 40, aw_xopt = .95)
                 
dynamic_fit <- fit_growth(example_dynamic_growth,
                          sec_models,
                          my_start, known_pars,
                          environment = "dynamic",
                          env_conditions = example_env_conditions
                          )
                          
## Second model (different secondary model for temperature)

sec_models <- list(temperature = "Zwietering", aw = "CPM")

known_pars <- list(Nmax = 1e4, 
                   N0 = 1e0, Q0 = 1e-3,
                   mu_opt = 4,
                   temperature_n = 1,
                   aw_xmax = 1, aw_xmin = .9, aw_n = 1 
                   )
                   
my_start <- list(temperature_xmin = 25, temperature_xopt = 35,
                 aw_xopt = .95)
                 
dynamic_fit2 <- fit_growth(example_dynamic_growth,
                           sec_models,
                           my_start, known_pars,
                           environment = "dynamic",
                           env_conditions = example_env_conditions
                           )
                           
## Once both models have been fitted, we can call the function               

dynamic_comparison <- compare_growth_fits(list(m1 = dynamic_fit, m2 = dynamic_fit2))

## Which also returns an instance of GrowthComparison with the same S3 methods

print(dynamic_comparison)
plot(dynamic_comparison)
plot(dynamic_comparison, type = 2)
plot(dynamic_comparison, type = 3)

## The statistical indexes can be accessed through summary and coef

summary(dynamic_comparison)
coef(dynamic_comparison)


## Example 3 - Global fitting -----------------------------------------------


## We use the example data

data("multiple_counts")
data("multiple_conditions")

## We need to fit (at least) two models

sec_models <- list(temperature = "CPM", pH = "CPM")

known_pars <- list(Nmax = 1e8, N0 = 1e0, Q0 = 1e-3,
                   temperature_n = 2, temperature_xmin = 20, 
                   temperature_xmax = 35,
                   pH_n = 2, pH_xmin = 5.5, pH_xmax = 7.5, pH_xopt = 6.5)
                   
my_start <- list(mu_opt = .8, temperature_xopt = 30)

global_fit <- fit_growth(multiple_counts, 
                         sec_models, 
                         my_start, 
                         known_pars,
                         environment = "dynamic",
                         algorithm = "regression",
                         approach = "global",
                         env_conditions = multiple_conditions
                         ) 
                         
sec_models <- list(temperature = "CPM", pH = "CPM")

known_pars <- list(Nmax = 1e8, N0 = 1e0, Q0 = 1e-3,
                   temperature_n = 1, temperature_xmin = 20, 
                   temperature_xmax = 35,
                   pH_n = 2, pH_xmin = 5.5, pH_xmax = 7.5, pH_xopt = 6.5)
                   
my_start <- list(mu_opt = .8, temperature_xopt = 30)

global_fit2 <- fit_growth(multiple_counts, 
                          sec_models, 
                          my_start, 
                          known_pars,
                          environment = "dynamic",
                          algorithm = "regression",
                          approach = "global",
                          env_conditions = multiple_conditions
                          ) 
                          
## We can now pass both models to the function as a (named) list

global_comparison <- compare_growth_fits(list(`n=2` = global_fit, 
                                              `n=1` = global_fit2)
                                              )
                                              
## The residuals and model fits plots are divided by experiments

plot(global_comparison)
plot(global_comparison, type = 3)

## The remaining S3 methods are the same as before

print(global_comparison)
plot(global_comparison, type = 2)
summary(global_comparison)
coef(global_comparison)

Model comparison and selection for secondary growth models

Description

This function is a constructor for SecondaryComparison a class that provides several functions for model comparison and model selection for growth models fitted using fit_secondary_growth(). Please see the help pages for SecondaryComparison for further details.

Although it is not necessary, we recommend passing the models as a named list, as these names will later be kept in plots and tables.

Usage

compare_secondary_fits(models)

Arguments

Examples

## We first need to fit some models

data("example_cardinal")

sec_model_names <- c(temperature = "Zwietering", pH = "CPM")

known_pars <- list(mu_opt = 1.2, temperature_n = 1,
                   pH_n = 2, pH_xmax = 6.8, pH_xmin = 5.2)
                   
my_start <- list(temperature_xmin = 5, temperature_xopt = 35,
                 pH_xopt = 6.5)
                 
fit1 <- fit_secondary_growth(example_cardinal, my_start, known_pars, sec_model_names)

known_pars <- list(mu_opt = 1.2, temperature_n = 2,
                   pH_n = 2, pH_xmax = 6.8, pH_xmin = 5.2)
                   
 fit2 <- fit_secondary_growth(example_cardinal, my_start, known_pars, sec_model_names)
 
 ## We can now pass the models to the constructor

 comparison <- compare_secondary_fits(list(`n=1` = fit1, 
                                           `n=2` = fit2))
                                           
 ## The function includes several S3 methods for model selection and comparison
 
 print(comparison)
 
 plot(comparison)
 plot(comparison, type = 2)
 
 ## The numerical indexes can be accessed using coef and summary
 
 coef(comparison)
 summary(comparison)

Conditions during a dynamic growth experiment

Description

A dataset to demonstrate the use of fit_dynamic_growth. The observations environmental conditions are described in conditions_pH_temperature.

Usage

conditions_pH_temperature

Format

A tibble with 4 rows and 3 columns:

time

elapsed time

temperature

temperature

pH

pH

Residuals of the coupled Baranyi model

Description

Residuals of the coupled Baranyi model

Usage

cost_coupled_onestep(p, this_data, known)

Arguments

Value

the vector of model residuals

Cost for the coupled model fitted in two-steps

Description

Cost for the coupled model fitted in two-steps

Usage

cost_coupled_twosteps(p, this_data, weight = NULL, known)

Arguments

Value

vector of weighted residuals

Baranyi growth model

Description

Microbial growth model as defined in Baranyi and Roberts (1994). It has been implemented according to the requirements of deSolve::ode(). For consistency in the function for isothermal growth, calculations are done assuming the user input for mu is in log10 scale. In other words, the input is multiplied by ln(10).

Usage

dBaranyi(time, state, pars, env_func, sec_models)

Arguments

Value

A numeric vector of two components according to the requirements of deSolve::ode().

Distribution of times to reach a certain microbial count

Description

The function distribution_to_logcount() has been superseded by function time_to_size(), which provides more general interface.

Returns the probability distribution of the storage time required for the microbial count to reach log_count according to the predictions of a stochastic model. Calculations are done using linear interpolation of the individual model predictions.

Usage

distribution_to_logcount(model, log_count)

Arguments

Value

An instance of TimeDistribution().

Examples

## We need an instance of StochasticGrowth

my_model <- "modGompertz"
my_times <- seq(0, 30, length = 100)
n_sims <- 3000

library(tibble)

pars <- tribble(
    ~par, ~mean, ~sd, ~scale,
    "logN0", 0, .2, "original",
    "mu", 2, .3, "sqrt",
    "lambda", 4, .4, "sqrt",
    "C", 6, .5, "original"
)

stoc_growth <- predict_stochastic_growth(my_model, my_times, n_sims, pars)

Growth rates obtained for several growth experiments

Description

An example dataset illustrating the requirements of the fit_secondary_growth() function.

Usage

example_cardinal

Format

A data frame with 64 rows and 3 variables:

temperature

storage temperature (ºC)

pH

pH of the media

mu

specific growth rate (log10 CFU/h)

Example data for two-steps fitting of the Baranyi-Ratkowsky model

Description

This dataset serve as an example of the data input for fit_coupled_growth using the one-step mode.

Usage

example_coupled_onestep

Format

A tibble with three columns:

• temp: the treatment temperature

• time: the elapsed time of the sample

• logN: the (decimal) log microbial concentration

Example data for two-steps fitting of the Baranyi-Ratkowsky model

Description

This dataset serve as an example of the data input for fit_coupled_growth using the two-steps mode.

Usage

example_coupled_twosteps

Format

A tibble with three columns:

• temp: the treatment temperature

• mu: the value of mu estimated at each temperature

• lambda: the value of lambda estimated at each temperature

Microbial growth under dynamic conditions

Description

An example dataset illustrating the requirements of the fit_dynamic_growth() function.

Usage

example_dynamic_growth

Format

A data frame with 30 rows and 2 variables:

time

elapsed time (h)

logN

log population size (log10 CFU)

Environmental conditions during a dynamic experiment

Description

An example dataset illustrating the requirements of the fit_dynamic_growth() function.

Usage

example_env_conditions

Format

A data frame with 3 rows and 3 variables:

time

elapsed time (h)

temperature

storage temperature (ºC)

aw

water activity

A helper to build the primary models

Description

Most of the functions for fitting mix in the vectors parameters for the primary and secondary models, but the functions for making predictions need that they are separated. This one extracts the parameters of the primary model.

Usage

extract_primary_pars(this_p, known_pars)

Arguments

Value

A list with the parameters of the primary model

A helper to build the secondary models

Description

Most of the functions for fitting mix in the vectors parameters for the primary and secondary models, but the functions for making predictions need that they are separated. This one extracts the parameters of the secondary model.

Usage

extract_secondary_pars(this_p, known_pars, sec_model_names)

Arguments

Value

A nested list defining the secondary models.

Fit growth models using MCMC

Description

The function fit_MCMC_growth() has been superseded by the top-level function fit_growth(), which provides a unified approach for growth modelling.

But, it can still fit a growth model to a data obtained under dynamic conditions using the one-step approach (MCMC algorithm).

Usage

fit_MCMC_growth(
  fit_data,
  env_conditions,
  starting_point,
  known_pars,
  sec_model_names,
  niter,
  ...,
  check = TRUE,
  formula = logN ~ time,
  logbase_mu = logbase_logN,
  logbase_logN = 10
)

Arguments

Value

An instance of FitDynamicGrowthMCMC().

Examples

## We use the example data included in the package

data("example_dynamic_growth")
data("example_env_conditions")

## Definition of the secondary models
sec_model_names <- c(temperature = "CPM", aw= "CPM")

## Any model parameter can be fixed
known_pars <- list(Nmax = 1e4,  # Primary model
    N0 = 1e0, Q0 = 1e-3,  # Initial values of the primary model
    mu_opt = 4, # mu_opt of the gamma model
    temperature_n = 1,  # Secondary model for temperature
    aw_xmax = 1, aw_xmin = .9, aw_n = 1  # Secondary model for water activity
    )

## We need starting values for the remaining parameters

my_start <- list(temperature_xmin = 25, temperature_xopt = 35,
    temperature_xmax = 40,
    aw_xopt = .95)

## We can now call the fitting function

set.seed(12124) # Setting seed for repeatability

my_MCMC_fit <- fit_MCMC_growth(example_dynamic_growth, example_env_conditions,
    my_start, known_pars, sec_model_names, niter = 3000)

## Always check the MCMC chain!!

plot(my_MCMC_fit$fit_results)

## We can compare data against fitted curve

plot(my_MCMC_fit)

## Any environmental factor can be included using add_factor

plot(my_MCMC_fit, add_factor = "temperature",
    label_y1 = "Count (log CFU/ml)", label_y2 = "Temperature (C)")

Growth fitting considering link between mu and lambda for the Baranyi-Ratkowsky model

Description

This function implements the methodology suggested by Garre et al. (2025; doi: 10.1016/j.ijfoodmicro.2025.111078) for the Baranyi-Ratkowsky model. Rather than fitting independent models for mu and lambda, this approach considers a link between both secondary models, reducing the number of unknown parameters from 3 to 4.

The function implements too modes of fitting: two-steps and one-step. Please see the respective sections for further information.

Usage

fit_coupled_growth(
  fit_data,
  start,
  known = c(),
  mode = "two_steps",
  weight = "sd",
  ...,
  logbase_mu = exp(1),
  logbase_logN = 10
)

Arguments

Two-steps fitting

In this mode, it is assumed that primary models have been already fitted to each experiment. Therefore, the data is available as a table of values of mu and lambda estimated at each temperature. Hence, fit_data must be a tibble (or data.frame) with three columns: temp (storage temperature), mu (specific growth rate) and lambda (lag phase duration). By default, mu must be defined in the scale of natural logarithm, although this can be modified using the logbase_mu argument. The package includes the dataset example_coupled_twosteps as an illustration of the type of data.

One-step fitting

In this mode, secondary models are directly fitted to the observed (log) microbial counts. Hence, fit_data must be a tibble (or data.frame) with three columns: temp (storage temperature), time (the elapsed time) and logN (the log-microbial concentration). By default, logN must be defined in the scale of decimal logarithm, although this can be modified using the logbase_logN argument. The package includes the dataset example_coupled_onestep as an illustration of the type of data.

Examples

## Example 1: Two-steps fitting-------------------------------------------------

## We can use the example dataset 

data(example_coupled_twosteps)

## We need to define initial guesses for every parameter

guess <- c(logC0 = -1, b = .1, Tmin = 5)

## We can now call the fitting function

my_fit <- fit_coupled_growth(example_coupled_twosteps, 
                             start = guess,
                             mode = "two_steps")

## Common S3 methods are included

print(my_fit)
coef(my_fit)
summary(my_fit)
plot(my_fit)

## Any model parameter can be fixed using the known argument

known <- c(b = .01)

## Please note that the guess must be updated, as now parameter can appear both as a guess and known

guess <- c(logC0 = -1, Tmin =  0)


fixed_fit <- fit_coupled_growth(example_coupled_twosteps, 
                                start = guess,
                                known = known, 
                                mode = "two_steps")

print(fixed_fit)
coef(fixed_fit)
summary(fixed_fit)
plot(fixed_fit)

## Example 2: One-step fitting--------------------------------------------------

## We can use an example dataset with the right format

data("example_coupled_onestep")

## The function requires initial guesses for every model parameter

guess <- c(logN0 = 2, logNmax = 8, b = 0.04, logC0 = -4, Tmin = 5)

## We can now call the fitting function

my_fit <- fit_coupled_growth(example_coupled_onestep,
                             start = guess,
                             mode = "one_step")

## The package includes common S3 methods

print(my_fit)
coef(my_fit)
summary(my_fit)
plot(my_fit)

## Any model parameter can be fixed before fitting

known <- c(logNmax = 7)

## Guesses must be updated, so no parameter appears twice

guess <- c(logN0 = 2, b = 0.04, logC0 = -4, Tmin = 5)

## We can now call the fitting function

my_fit <- fit_coupled_growth(example_coupled_onestep,
                             start = guess,
                             known = known,
                             mode = "one_step")

## The package includes common S3 methods

print(my_fit)
coef(my_fit)
summary(my_fit)
plot(my_fit)

Fit dynamic growth models

Description

The function fit_dynamic_growth() has been superseded by the top-level function fit_growth(), which provides a unified approach for growth modelling.

Nonetheless, it can still fit a growth model to data obtained under dynamic conditions using the one-step approach (non-linear regression).

Usage

fit_dynamic_growth(
  fit_data,
  env_conditions,
  starting_point,
  known_pars,
  sec_model_names,
  ...,
  check = TRUE,
  logbase_mu = logbase_logN,
  logbase_logN = 10,
  formula = logN ~ time
)

Arguments

Value

An instance of FitDynamicGrowth().

Examples

## We use the datasets included in the package

data("example_dynamic_growth")
data("example_env_conditions")

## Define the secondary models

sec_model_names <- c(temperature = "CPM", aw= "CPM")

## Any model parameter can be fixed

known_pars <- list(Nmax = 1e4,  # Primary model
    N0 = 1e0, Q0 = 1e-3,  # Initial values of the primary model
    mu_opt = 4, # mu_opt of the gamma model
    temperature_n = 1,  # Secondary model for temperature
    aw_xmax = 1, aw_xmin = .9, aw_n = 1  # Secondary model for water activity
    )

## The remaining parameters need initial values

my_start <- list(temperature_xmin = 25, temperature_xopt = 35,
    temperature_xmax = 40, aw_xopt = .95)

## We can now call the fitting function

my_dyna_fit <- fit_dynamic_growth(example_dynamic_growth, example_env_conditions,
    my_start, known_pars, sec_model_names)

summary(my_dyna_fit)

## We can compare the data and the fitted curve

plot(my_dyna_fit)

## We can plot any environmental condition using add_factor

plot(my_dyna_fit, add_factor = "aw",
    label_y1 = "Log count (log CFU/ml)",
    label_y2 = "Water activity")

Fitting microbial growth

Description

This function provides a top-level interface for fitting growth models to data describing the variation of the population size through time, either under constant or dynamic environment conditions. See below for details on the calculations.

Usage

fit_growth(
  fit_data,
  model_keys,
  start,
  known,
  environment = "constant",
  algorithm = "regression",
  approach = "single",
  env_conditions = NULL,
  niter = NULL,
  ...,
  check = TRUE,
  logbase_mu = logbase_logN,
  logbase_logN = 10,
  formula = logN ~ time
)

Arguments

Value

If ⁠approach="single⁠, an instance of GrowthFit. If approach="multiple", an instance of GlobalGrowthFit

Please check the help pages of each class for additional information.

Fitting under constant conditions

When environment="constant", the functions fits a primary growth model to the population size observed during an experiment. In this case, the data has to be a tibble (or data.frame) with two columns:

• time: the elapsed time

• logN: the logarithm of the observed population size Nonetheless, the names of the columns can be modified with the formula argument.

The model equation is defined through the model_keys argument. It must include an entry named "primary" assigned to a model. Valid model keys can be retrieved calling primary_model_data().

The model is fitted by non-linear regression (using FME::modFit()). This algorithm needs initial guesses for every model parameter. This are defined as a named numeric vector. The names must be valid model keys, which can be retrieved using primary_model_data() (see example below). Apart from that, any model parameter can be fixed using the "known" argument. This is a named numeric vector, with the same convenctions as "start".

Fitting under dynamic conditions to a single experiment

When environment="constant" and approach="single", a dynamic growth model combining the Baranyi primary growth model with the gamma approach for the effect of the environmental conditions on the growth rate is fitted to an experiment gathered under dynamic conditions. In this case, the data is similar to fitting under constant conditions: a tibble (or data.frame) with two columns:

• time: the elapsed time

• logN: the logarithm of the observed population size Note that these default names can be changed using the formula argument.

The values of the experimental conditions during the experiment are defined using the "env_conditions" argument. It is a tibble (or data.frame) with one column named ("time") defining the elapsed time. Note that this default name can be modified using the formula argument of the function. The tibble needs to have as many additional columns as environmental conditions included in the model, providing the values of the environmental conditions.

The model equations are defined through the model_keys argument. It must be a named list where the names match the column names of "env_conditions" and the values are model keys. These can be retrieved using secondary_model_data().

The model can be fitted using regression (FME::modFit()) or an adaptive Monte Carlo algorithm (FME::modMCMC()). Both algorithms require initial guesses for every model parameter to fit. These are defined through the named numeric vector "start". Each parameter must be named as factor+"_"+parameter, where factor is the name of the environmental factor defined in "model_keys". The parameter is a valid key that can be retrieved from secondary_model_data(). For instance, parameter Xmin for the factor temperature would be defined as "temperature_xmin".

Note that the argument ... allows passing additional arguments to the fitting functions.

Fitting under dynamic conditions to multiple experiments (global fitting)

When environment="constant" and approach="global", fit_growth tries to find the vector of model parameters that best describe the observations of several growth experiments.

The input requirements are very similar to the case when approach="single". The models (equations, initial guesses, known parameters, algorithms...) are identical. The only difference is that "fit_data" must be a list, where each element describes the results of an experiment (using the same conventions as when approach="single"). In a similar fashion, "env_conditions" must be a list describing the values of the environmental factors during each experiment. Although it is not mandatory, it is recommended that the elements of both lists are named. Otherwise, the function assigns automatically-generated names, and matches them by order.#'

Examples

## Example 1 - Fitting a primary model --------------------------------------

## A dummy dataset describing the variation of the population size 

my_data <- data.frame(time = c(0, 25, 50, 75, 100), 
                      logN = c(2, 2.5, 7, 8, 8))
                      
## A list of model keys can be gathered from 

primary_model_data()
                      
## The primary model is defined as a list

models <- list(primary = "Baranyi")

## The keys of the model parameters can also be gathered from primary_model_data

primary_model_data("Baranyi")$pars

## Any model parameter can be fixed

known <- c(mu = .2)

## The remaining parameters need initial guesses 

start <- c(logNmax = 8, lambda = 25, logN0 = 2)

primary_fit <- fit_growth(my_data, models, start, known,
                          environment = "constant",
                          )
                          
## The instance of FitIsoGrowth includes several useful methods

print(primary_fit)
plot(primary_fit)
coef(primary_fit)
summary(primary_fit)

## time_to_size can be used to calculate the time for some concentration

time_to_size(primary_fit, 4)

## Example 2 - Fitting under dynamic conditions------------------------------

## We will use the example data included in the package

data("example_dynamic_growth")

## And the example environmental conditoins (temperature & aw)

data("example_env_conditions")

## Valid keys for secondary models can be retrived from

secondary_model_data()

## We need to assign a model equation (secondary model) to each environmental factor

sec_models <- list(temperature = "CPM", aw = "CPM")

## The keys of the model parameters can be gathered from the same function

secondary_model_data("CPM")$pars

## Any model parameter (of the primary or secondary models) can be fixed

known_pars <- list(Nmax = 1e4,  # Primary model
                   N0 = 1e0, Q0 = 1e-3,  # Initial values of the primary model
                   mu_opt = 4, # mu_opt of the gamma model
                   temperature_n = 1,  # Secondary model for temperature
                   aw_xmax = 1, aw_xmin = .9, aw_n = 1  # Secondary model for water activity
                   )
                   
## The rest, need initial guesses (you know, regression)

my_start <- list(temperature_xmin = 25, temperature_xopt = 35,
                 temperature_xmax = 40, aw_xopt = .95)
                 
## We can now fit the model


dynamic_fit <- fit_growth(example_dynamic_growth, 
                          sec_models, 
                          my_start, known_pars,
                          environment = "dynamic",
                          env_conditions = example_env_conditions
                          ) 
                          
## The instance of FitDynamicGrowth has several S3 methods

plot(dynamic_fit, add_factor = "temperature")
summary(dynamic_fit)

## We can use time_to_size to calculate the time required to reach a given size

time_to_size(dynamic_fit, 3)



## Example 3- Fitting under dynamic conditions using MCMC -------------------

## We can reuse most of the arguments from the previous example
## We just need to define the algorithm and the number of iterations


set.seed(12421)
MCMC_fit <- fit_growth(example_dynamic_growth, 
                       sec_models, 
                       my_start, known_pars,
                       environment = "dynamic",
                       env_conditions = example_env_conditions,
                       algorithm = "MCMC",
                       niter = 1000
                       ) 
                       
## The instance of FitDynamicGrowthMCMC has several S3 methods

plot(MCMC_fit, add_factor = "aw")
summary(MCMC_fit)

## We can use time_to_size to calculate the time required to reach a given size

time_to_size(MCMC_fit, 3)

## It can also make growth predictions including uncertainty

uncertain_growth <- predictMCMC(MCMC_fit, 
                                seq(0, 10, length = 1000),  
                                example_env_conditions, 
                                niter = 1000)

## The instance of MCMCgrowth includes several nice S3 methods

plot(uncertain_growth)
print(uncertain_growth)

## time_to_size can calculate the time to reach some count

time_to_size(uncertain_growth, 2)
time_to_size(uncertain_growth, 2, type = "distribution")



## Example 4 - Fitting a unique model to several dynamic experiments --------

## We will use the data included in the package

data("multiple_counts")
data("multiple_conditions")

## We need to assign a model equation for each environmental factor

sec_models <- list(temperature = "CPM", pH = "CPM")

## Any model parameter (of the primary or secondary models) can be fixed

known_pars <- list(Nmax = 1e8, N0 = 1e0, Q0 = 1e-3,
                   temperature_n = 2, temperature_xmin = 20, 
                   temperature_xmax = 35,
                   pH_n = 2, pH_xmin = 5.5, pH_xmax = 7.5, pH_xopt = 6.5)
                   
## The rest, need initial guesses

my_start <- list(mu_opt = .8, temperature_xopt = 30)

## We can now fit the model


global_fit <- fit_growth(multiple_counts, 
                         sec_models, 
                         my_start, 
                         known_pars,
                         environment = "dynamic",
                         algorithm = "regression",
                         approach = "global",
                         env_conditions = multiple_conditions
                         ) 
                         
## The instance of FitMultipleDynamicGrowth has nice S3 methods

plot(global_fit)
summary(global_fit)
print(global_fit)

## We can use time_to_size to calculate the time to reach a given size

time_to_size(global_fit, 4.5)



## Example 5 - MCMC fitting a unique model to several dynamic experiments ---

## Again, we can re-use all the arguments from the previous example
## We just need to define the right algorithm and the number of iterations
## On top of that, we will also pass upper and lower bounds to modMCMC


set.seed(12421)
global_MCMC <- fit_growth(multiple_counts, 
                         sec_models, 
                         my_start, 
                         known_pars,
                         environment = "dynamic",
                         algorithm = "MCMC",
                         approach = "global",
                         env_conditions = multiple_conditions,
                         niter = 1000,
                         lower = c(.2, 29),  # lower limits of the model parameters
                         upper = c(.8, 34)  # upper limits of the model parameters
                         ) 
                         
## The instance of FitMultipleDynamicGrowthMCMC has nice S3 methods

plot(global_MCMC)
summary(global_MCMC)
print(global_MCMC)

## We can use time_to_size to calculate the time to reach a given size

time_to_size(global_MCMC, 3)

## It can also be used to make model predictions with parameter uncertainty

uncertain_prediction <- predictMCMC(global_MCMC,
                                    seq(0, 50, length = 1000), 
                                    multiple_conditions[[1]], 
                                    niter = 100
                                    )

## The instance of MCMCgrowth includes several nice S3 methods

plot(uncertain_growth)
print(uncertain_growth)

## time_to_size can calculate the time to reach some count

time_to_size(uncertain_growth, 2)
time_to_size(uncertain_growth, 2, type = "distribution")

Fit primary growth models

Description

The function fit_isothermal_growth() has been superseded by the top-level function fit_growth(), which provides a unified approach for growth modelling.

Nonetheless, it can still fit a primary growth model to data obtained under static environmental conditions.

Usage

fit_isothermal_growth(
  fit_data,
  model_name,
  starting_point,
  known_pars,
  ...,
  check = TRUE,
  formula = logN ~ time,
  logbase_mu = logbase_logN,
  logbase_logN = 10
)

Arguments

Value

An instance of FitIsoGrowth().

Examples

## Some dummy data

library(tibble)

my_data <- tibble(time = c(0, 25, 50, 75, 100),
    logN = c(2, 2.5, 7, 8, 8))

## Choose the model

my_model <- "Baranyi"

## Initial values for the model parameters

start = c(logNmax = 8, lambda = 25, logN0 = 2)

## Any model parameter can be fixed

known <- c(mu = .2)

## Now, we can call the function

static_fit <- fit_isothermal_growth(my_data, my_model, start, known)

summary(static_fit)

## We can plot the fitted model against the observations

plot(static_fit)

Fitting growth models to multiple dynamic experiments

Description

The function fit_multiple_growth() has been superseded by the top-level function fit_growth(), which provides a unified approach for growth modelling.

But, if you so wish, this function still enables fitting a growth model using a dataset comprised of several experiments with potentially different dynamic experimental conditions. Note that the definition of secondary models must comply with the secondary_model_data function.

Usage

fit_multiple_growth(
  starting_point,
  experiment_data,
  known_pars,
  sec_model_names,
  ...,
  check = TRUE,
  formula = logN ~ time,
  logbase_mu = logbase_logN,
  logbase_logN = 10
)

Arguments

Value

An instance of FitMultipleDynamicGrowth().

Examples

## We will use the multiple_experiments data set

data("multiple_experiments")

## For each environmental factor, we need to defined a model

sec_names <- c(temperature = "CPM", pH = "CPM")

## Any model parameter can be fixed

known <- list(Nmax = 1e8, N0 = 1e0, Q0 = 1e-3,
    temperature_n = 2, temperature_xmin = 20, temperature_xmax = 35,
    pH_n = 2, pH_xmin = 5.5, pH_xmax = 7.5, pH_xopt = 6.5)

## The rest require starting values for model fitting

start <- list(mu_opt = .8, temperature_xopt = 30)

## We can now call the fitting function

global_fit <- fit_multiple_growth(start, multiple_experiments, known, sec_names)

## Parameter estimates can be retrieved with summary

summary(global_fit)

## We can compare fitted model against observations

plot(global_fit)

## Any single environmental factor can be added to the plot using add_factor

plot(global_fit, add_factor = "temperature")

Fitting growth models to multiple dynamic experiments using MCMC

Description

The function fit_multiple_growth_MCMC() has been superseded by the top-level function fit_growth(), which provides a unified approach for growth modelling.

However, this functions can still be used to fit a growth model using a dataset comprised of several experiments with potentially different dynamic experimental conditions.

Usage

fit_multiple_growth_MCMC(
  starting_point,
  experiment_data,
  known_pars,
  sec_model_names,
  niter,
  ...,
  check = TRUE,
  formula = logN ~ time,
  logbase_mu = logbase_logN,
  logbase_logN = 10
)

Arguments

Value

An instance of FitMultipleGrowthMCMC().

Examples

## We will use the multiple_experiments data set

data("multiple_experiments")

## For each environmental factor, we need to defined a model

sec_names <- c(temperature = "CPM", pH = "CPM")

## Any model parameter can be fixed

known <- list(Nmax = 1e8, N0 = 1e0, Q0 = 1e-3,
    temperature_n = 2, temperature_xmin = 20, temperature_xmax = 35,
    pH_n = 2, pH_xmin = 5.5, pH_xmax = 7.5, pH_xopt = 6.5)

## The rest require starting values for model fitting

start <- list(mu_opt = .8, temperature_xopt = 30)

## We can now call the fitting function

set.seed(12412)
global_MCMC <- fit_multiple_growth_MCMC(start, multiple_experiments, known, sec_names, niter = 1000,
   lower = c(.2, 29),  # lower limits of the model parameters
   upper = c(.8, 34))  # upper limits of the model parameters

## Parameter estimates can be retrieved with summary

summary(global_MCMC)

## We can compare fitted model against observations

plot(global_MCMC)

## Any single environmental factor can be added to the plot using add_factor

plot(global_MCMC, add_factor = "temperature")

Fit secondary growth models

Description

Fits a secondary growth model to a set of growth rates obtained experimentally. Modelling is done according to the gamma concept proposed by Zwietering (1992) and cardinal parameter models.

Usage

fit_secondary_growth(
  fit_data,
  starting_point,
  known_pars,
  sec_model_names,
  transformation = "sq",
  ...,
  check = TRUE,
  formula = mu ~ .
)

Arguments

Value

An instance of FitSecondaryGrowth().

Examples

## We use the data included in the package

data("example_cardinal")

## Define the models to fit

sec_model_names <- c(temperature = "Zwietering", pH = "CPM")

## Any model parameter can be fixed

known_pars <- list(mu_opt = 1.2, temperature_n = 1,
    pH_n = 2, pH_xmax = 6.8, pH_xmin = 5.2)

## Initial values must be given for every other parameter

my_start <- list(temperature_xmin = 5, temperature_xopt = 35,
    pH_xopt = 6.5)

## We can now call the fitting function

fit_cardinal <- fit_secondary_growth(example_cardinal, my_start, known_pars, sec_model_names)

## With summary, we can look at the parameter estimates

summary(fit_cardinal)

## The plot function compares predictions against observations

plot(fit_cardinal)

## Passing which = 2, generates a different kind of plot

plot(fit_cardinal, which = 2)
plot(fit_cardinal, which = 2, add_trend = TRUE)
plot(fit_cardinal, which = 2, add_segment = TRUE)

Full Ratkowsky model

Description

Gamma model adapted from the one by Ratkowsky et al. (1983).

Usage

full_Ratkowski(x, xmin, xmax, c)

Arguments

A helper for making the plots

Description

A helper for making the plots

Usage

get_all_predictions(model)

Arguments

Residuals of dynamic prediction

Description

Function for calculating residuals of a dynamic prediction according to the requirements of FME::modFit().

Usage

get_dyna_residuals(
  this_p,
  fit_data,
  env_conditions,
  known_pars,
  sec_model_names,
  cost = NULL,
  logbase_mu = logbase_logN,
  logbase_logN = 10
)

Arguments

Value

An instance of FME::modCost().

Residuals of isothermal prediction

Description

Residuals of isothermal prediction

Usage

get_iso_residuals(
  this_p,
  fit_data,
  model_name,
  known_pars,
  logbase_mu = logbase_logN,
  logbase_logN = 10
)

Arguments

Value

An instance of modCost.

Residuals of multiple dynamic predictions

Description

Function for calculating residuals of dynamic predictions under different conditions for the same model parameters according to the requirements of FME::modFit().

Usage

get_multi_dyna_residuals(
  this_p,
  experiment_data,
  known_pars,
  sec_model_names,
  logbase_mu = logbase_logN,
  logbase_logN = 10
)

Arguments

Value

an instance of modCost.

Residuals of secondary models

Description

Residual function for fit_secondary_growth().

Usage

get_secondary_residuals(
  this_p,
  my_data,
  known_pars,
  sec_model_names,
  transformation
)

Arguments

Value

A numeric vector of residuals.

Number of tractors in Greece according to the World Bank

Description

A dataset showing the increase in tractors in Greece. It was retrieved from https://data.worldbank.org/indicator/AG.AGR.TRAC.NO?end=2009&start=1961&view=chart.

Usage

greek_tractors

Format

A tibble with 46 rows (each corresponding to one year) and 7 columns:

year

Year for the recording

tractors

Number of tractors

Example of dynamic growth

Description

A dataset to demonstrate the use of fit_dynamic_growth. The values of the environmental conditions are described in conditions_pH_temperature.

Usage

growth_pH_temperature

Format

A tibble with 20 rows and 2 columns:

time

elapsed time

logN

decimal logarithm of the population size

Growth of Salmonella spp in broth

Description

An example dataset to illustrate fit_isothermal_growth(). It describes the growth of Salmonella spp. in broth. It was retrieved from ComBase (ID: B092_10).

Usage

growth_salmonella

Format

A tibble with 21 rows and 2 columns:

time

elapsed time in hours.

logN

observed population size (log CFU/g).

Secondary model for inhibitory compounds

Description

Secondary model for the effect of inhibitory compounds.

Usage

inhibitory_model(x, MIC, alpha)

Arguments

Value

The corresponding gamma factor.

Test of DynamicGrowth object

Description

Tests if an object is of class DynamicGrowth.

Usage

is.DynamicGrowth(x)

Arguments

Value

A boolean specifying whether x is of class DynamicGrowth

Test of FitDynamicGrowth object

Description

Tests if an object is of class FitDynamicGrowth.

Usage

is.FitDynamicGrowth(x)

Arguments

Value

A boolean specifying whether x is of class FitDynamicGrowth

Test of FitDynamicGrowthMCMC object

Description

Tests if an object is of class FitDynamicGrowthMCMC.

Usage

is.FitDynamicGrowthMCMC(x)

Arguments

Value

A boolean specifying whether x is of class FitDynamicGrowthMCMC

Test of FitIsoGrowth object

Description

Tests if an object is of class FitIsoGrowth.

Usage

is.FitIsoGrowth(x)

Arguments

Value

A boolean specifying whether x is of class FitIsoGrowth

Test of FitMultipleDynamicGrowth object

Description

Tests if an object is of class FitMultipleDynamicGrowth.

Usage

is.FitMultipleDynamicGrowth(x)

Arguments

Value

A boolean specifying whether x is of class FitMultipleDynamicGrowth

Test of FitMultipleDynamicGrowthMCMC object

Description

Tests if an object is of class FitMultipleDynamicGrowthMCMC.

Usage

is.FitMultipleDynamicGrowthMCMC(x)

Arguments

Value

A boolean specifying whether x is of class FitMultipleDynamicGrowthMCMC

Test of FitSecondaryGrowth object

Description

Tests if an object is of class FitSecondaryGrowth.

Usage

is.FitSecondaryGrowth(x)

Arguments

Value

A boolean specifying whether x is of class FitSecondaryGrowth

Test of GlobalGrowthFit object

Description

Tests if an object is of class GlobalGrowthFit

Usage

is.GlobalGrowthFit(x)

Arguments

Value

A boolean specifying whether x is of class GlobalGrowthFit

Test of GrowthFit object

Description

Tests if an object is of class GrowthFit

Usage

is.GrowthFit(x)

Arguments

Value

A boolean specifying whether x is of class GrowthFit

Test of GrowthPrediction object

Description

Tests if an object is of class GrowthPrediction

Usage

is.GrowthPrediction(x)

Arguments

Value

A boolean specifying whether x is of class GrowthPrediction

Test of GrowthUncertainty object

Description

Tests if an object is of class GrowthUncertainty

Usage

is.GrowthUncertainty(x)

Arguments

Value

A boolean specifying whether x is of class GrowthUncertainty

Test of IsothermalGrowth object

Description

Tests if an object is of class IsothermalGrowth.

Usage

is.IsothermalGrowth(x)

Arguments

Value

A boolean specifying whether x is of class IsothermalGrowth

Test of MCMCgrowth object

Description

Tests if an object is of class MCMCgrowth.

Usage

is.MCMCgrowth(x)

Arguments

Value

A boolean specifying whether x is of class MCMCgrowth

Test of StochasticGrowth object

Description

Tests if an object is of class StochasticGrowth.

Usage

is.StochasticGrowth(x)

Arguments

Value

A boolean specifying whether x is of class StochasticGrowth

Isothermal Baranyi model

Description

Baranyi growth model as defined by Baranyi and Roberts (1994). We use the solution calculated by Poschet et al. (2005, doi: https://doi.org/10.1016/j.ijfoodmicro.2004.10.008) after log-transformation according to MONTE CARLO ANALYSIS FOR MICROBIAL GROWTH CURVES, by Oksuz and Buzrul.

Usage

iso_Baranyi(times, logN0, mu, lambda, logNmax)

Arguments

Value

Numeric vector with the predicted microbial count.

Isothermal Baranyi model without lag phase

Description

Baranyi growth model as defined by Baranyi and Roberts (1994). We use the solution calculated by Poschet et al. (2005, doi: https://doi.org/10.1016/j.ijfoodmicro.2004.10.008) after log-transformation according to MONTE CARLO ANALYSIS FOR MICROBIAL GROWTH CURVES, by Oksuz and Buzrul.

Usage

iso_Baranyi_noLag(times, logN0, mu, logNmax)

Arguments

Value

Numeric vector with the predicted microbial count.

Isothermal Baranyi model without stationary phase

Description

Baranyi growth model as defined by Baranyi and Roberts (1994). We use the solution calculated by Poschet et al. (2005, doi: https://doi.org/10.1016/j.ijfoodmicro.2004.10.008) after log-transformation according to MONTE CARLO ANALYSIS FOR MICROBIAL GROWTH CURVES, by Oksuz and Buzrul.

Usage

iso_Baranyi_noStat(times, logN0, mu, lambda)

Arguments

Value

Numeric vector with the predicted microbial count.

Reparameterized Gompertz model

Description

Reparameterized Gompertz growth model defined by Zwietering et al. (1990).

Usage

iso_repGompertz(times, logN0, C, mu, lambda)

Arguments

Value

Numeric vector with the predicted microbial count.

Q0 from lag phase duration

Description

Convenience function to calculate the value of Q0 for the Baranyi model from the duration of the lag phase

Usage

lambda_to_Q0(lambda, mu, logbase_mu = 10)

Arguments

Logistic growth model

Description

Logistic growth model

Usage

logistic_model(times, logN0, mu, lambda, C)

Arguments

Value

Numeric vector with the predicted microbial count

Loglinear model

Description

Loglinear model

Usage

loglinear_model(times, logN0, mu)

Arguments

Initial guesses for the secondary model of one factor

Description

Initial guesses for the secondary model of one factor

Usage

make_guess_factor(fit_data, sec_model, factor)

Arguments

Initial guesses for fitting primary growth models

Description

The function uses some heuristics to provide initial guesses for the parameters of the growth model selected that can be used with fit_growth().

Usage

make_guess_primary(
  fit_data,
  primary_model,
  logbase_mu = 10,
  formula = logN ~ time
)

Arguments

Value

A named numeric vector of initial guesses for the model parameters

Examples

## An example of experimental data

my_data <- data.frame(time = 0:9, 
                      logN = c(2, 2.1, 1.8, 2.5, 3.1, 3.4, 4, 4.5, 4.8, 4.7))
                      
## We just need to pass the data and the model equation

make_guess_primary(my_data, "Logistic")

## We can use this together with fit_growth()

fit_growth(my_data,
           list(primary = "Logistic"),
           make_guess_primary(my_data, "Logistic"),
           c()
           )

## The parameters returned by the function are adapted to the model

make_guess_primary(my_data, "Baranyi")

## It can express mu in other logbases 

make_guess_primary(my_data, "Baranyi", logbase_mu = exp(1))  # natural
make_guess_primary(my_data, "Baranyi", logbase_mu = 2)  # base2

Initial guesses for the parameters of a secondary model

Description

Uses some heuristic rules to generate an initial guess of the model parameters of secondary growth models that can be used for model fitting with fit_secondary_growth().

Usage

make_guess_secondary(fit_data, sec_model_names)

Arguments

Examples

## We can use the example dataset included in the package

data("example_cardinal")

## We assign model equations to factors as usual

sec_model_names <- c(temperature = "Zwietering", pH = "fullRatkowsky")

## We can then calculate the initial guesses

make_guess_secondary(example_cardinal, sec_model_names)

## We can pass these parameters directly to fit_secondary_growth

fit_secondary_growth(example_cardinal, 
                     make_guess_secondary(example_cardinal, sec_model_names), 
                     c(), 
                     sec_model_names)

Environmental conditions during several dynamic experiments

Description

This dataset is paired with multiple_counts to illustrate the global fitting of fit_growth().

Usage

multiple_conditions

Format

A nested list with two elements, each one corresponding to one experiment. Each element is a data.frame with three columns:

• time: elapsed time

• temperature: observed temperature

• pH: observed pH

Population growth observed in several dynamic experiments

Description

This dataset is paired with multiple_conditions to illustrate the global fitting of fit_growth().

Usage

multiple_counts

Format

A nested list with two elements, each one corresponding to one experiment. Each element is a data.frame with two columns:

• time: elapsed time

• logN: log10 of the microbial concentration

A set of growth experiments under dynamic conditions

Description

An example dataset illustrating the requirements of fit_multiple_growth() and fit_multiple_growth_MCMC().

Usage

multiple_experiments

Format

A nested list with two elements. Each element corresponds to one experiment and is described by a list with two data frames:

data

a tibble describing the microbial counts. It has 2 columns: time (elapsed time) and logN (logarithm of the microbial count)

.

conditions

a tibble describing the environmental conditions. It has 3 columns: time (elapsed time), temperature (storage temperature) and pH (pH of the media).

Predictions of the coupled Baranyi model

Description

Predictions of the coupled Baranyi model

Usage

pred_coupled_baranyi(p, temp, times)

Arguments

Value

a numeric vector of predicted logN (in log CFU/TIME)

Prediction of lambda for the coupled model

Description

Prediction of lambda for the coupled model

Usage

pred_lambda(p, temp)

Arguments

Value

the values of lambda

Prediction of the square root of mu for the coupled model

Description

Prediction of the square root of mu for the coupled model

Usage

pred_sqmu(p, temp)

Arguments

Value

the values of the square root of mu (in ln CFU/TIME)

Generic for calculating predictions with uncertainty from fits

Description

Generic for calculating predictions with uncertainty from fits

Usage

predictMCMC(
  model,
  times,
  env_conditions,
  niter,
  newpars = NULL,
  formula = . ~ time
)

Arguments

Stochastic growth of MCMC fit

Description

The function predict_MCMC_growth() has been superseded by predictMCMC() S3 methods of the relevant classes.

Nonetheless, it can still make a prediction of microbial growth including parameter uncertainty based on a growth model fitted using fit_MCMC_growth() or fit_multiple_growth_MCMC(). This function predicts growth curves for niter samples (with replacement) of the samples of the MCMC algorithm. Then, credible intervals are calculated based on the quantiles of the model predictions at each time point.

Usage

predict_MCMC_growth(
  MCMCfit,
  times,
  env_conditions,
  niter,
  newpars = NULL,
  formula = . ~ time
)

Arguments

Value

An instance of MCMCgrowth().

Examples

## We need a FitDynamicGrowthMCMC object

data("example_dynamic_growth")
data("example_env_conditions")

sec_model_names <- c(temperature = "CPM", aw= "CPM")

known_pars <- list(Nmax = 1e4,  # Primary model
    N0 = 1e0, Q0 = 1e-3,  # Initial values of the primary model
    mu_opt = 4, # mu_opt of the gamma model
    temperature_n = 1,  # Secondary model for temperature
    aw_xmax = 1, aw_xmin = .9, aw_n = 1  # Secondary model for water activity
    )

my_start <- list(temperature_xmin = 25, temperature_xopt = 35,
    temperature_xmax = 40,
    aw_xopt = .95)

set.seed(12124) # Setting seed for repeatability

my_MCMC_fit <- fit_MCMC_growth(example_dynamic_growth, example_env_conditions,
    my_start, known_pars, sec_model_names, niter = 3000)

## Define the conditions for the simulation

my_times <- seq(0, 15, length = 50)
niter <- 2000

newpars <- list(N0 = 1e-1,  # A parameter that was fixed
                temperature_xmax = 120  # A parameter that was fitted
                )


## Make the simulations

my_MCMC_prediction <- predict_MCMC_growth(my_MCMC_fit,
    my_times,
    example_env_conditions, # It could be different from the one used for fitting
    niter,
    newpars)
    
## We can plot the prediction interval

plot(my_MCMC_prediction)

## We can also get the quantiles at each time point

print(my_MCMC_prediction$quantiles)

Growth under dynamic conditions

Description

The function predict_dynamic_growth() has been superseded by the top-level function predict_growth(), which provides a unified approach for growth modelling.

Regardless on that, it can still predict population growth under dynamic conditions based on the Baranyi model (Baranyi and Roberts, 1994) and secondary models based on the gamma concept (Zwietering et al. 1992).

Model predictions are done by linear interpolation of the environmental conditions defined in env_conditions.

Usage

predict_dynamic_growth(
  times,
  env_conditions,
  primary_pars,
  secondary_models,
  ...,
  check = TRUE,
  logbase_logN = 10,
  logbase_mu = logbase_logN,
  formula = . ~ time
)

Arguments

Value

An instance of DynamicGrowth().

Examples

## Definition of the environmental conditions

library(tibble)

my_conditions <- tibble(time = c(0, 5, 40),
    temperature = c(20, 30, 35),
    pH = c(7, 6.5, 5)
    )

## Definition of the model parameters

my_primary <- list(mu_opt = 2,
    Nmax = 1e8,N0 = 1e0,
    Q0 = 1e-3)

sec_temperature <- list(model = "Zwietering",
    xmin = 25, xopt = 35, n = 1)

sec_pH = list(model = "CPM",
    xmin = 5.5, xopt = 6.5,
    xmax = 7.5, n = 2)

my_secondary <- list(
    temperature = sec_temperature,
    pH = sec_pH
    )

my_times <- seq(0, 50, length = 1000)

## Do the simulation

dynamic_prediction <- predict_dynamic_growth(my_times,
    my_conditions, my_primary,
    my_secondary)

## Plot the results

plot(dynamic_prediction)

## We can plot some environmental factor with add_factor

plot(dynamic_prediction, add_factor = "temperature", ylims= c(0, 8),
    label_y1 = "Microbial count (log CFU/ml)",
    label_y2 = "Storage temperature (C)")

Prediction of microbial growth

Description

This function provides a top-level interface for predicting population growth. Predictions can be made either under constant or dynamic environmental conditions. See below for details on the calculations.

Usage

predict_growth(
  times,
  primary_model,
  environment = "constant",
  secondary_models = NULL,
  env_conditions = NULL,
  ...,
  check = TRUE,
  logbase_mu = logbase_logN,
  logbase_logN = 10,
  formula = . ~ time
)

Arguments

Details

To ease data input, the functions can convert between parameters defined in different scales. Namely, for predictions in constant environments (environment="constant"):

• "logN0" can be defined as "N0". The function automatically calculates the log-transformation.

• "logNmax" can be defined as "Nmax". The function automatically calculates the log-transformation.

• "mu" can be defined as "mu_opt". The function assumes the prediction is under optimal growth conditions.

• "lambda" can be defined by "Q0". The duration of the lag phase is calculated using Q0_to_lambda().

And, for predictions in dynamic environments (environment="dynamic"):

• "N0" can be defined as "N0". The function automatically calculates the antilog-transformation.

• "Nmax" can be defined as "logNmax". The function automatically calculates the antilog-transformation.

• "mu" can be defined as "mu_opt". The function assumes mu was calculated under optimal growth conditions.

• "Q0" can be defined by the value of "lambda" under dynamic conditions. Then, the value of Q0 is calculated using lambda_to_Q0().

Value

An instance of GrowthPrediction.

Predictions in constant environments

Predictions under constant environments are calculated using only primary models. Consequently, the arguments "secondary_models" and "env_conditions" are ignored. If these were passed, the function would return a warning. In this case, predictions are calculated using the algebraic form of the primary model (see vignette for details).

The growth model is defined through the "primary_model" argument using a named list. One of the list elements must be named "model" and must take take one of the valid keys returned by primary_model_data(). The remaining entries of the list define the values of the parameters of the selected model. A list of valid keys can be retrieved using primary_model_data() (see example below). Note that the functions can do some operations to facilitate the compatibility between constant and dynamic environments (see Details).

Predictions in dynamic environments

Predictions under dynamic environments are calculated by solving numerically the differential equation of the Baranyi growth model. The effect of changes in the environmental conditions in the growth rate are calculated according to the gamma approach. Therefore, one must define both primary and secondary models.

The dynamic environmental conditions are defined using a tibble (or data.frame) through the "env_conditions" argument. It must include one column named "time" stating the elapsed time and as many additional columns as environmental conditions included in the prediction. For values of time not included in the tibble, the values of the environmental conditions are calculated by linear interpolation.

Primary models are defined as a named list through the "primary_model" argument. It must include the following elements:

• N0: initial population size

• Nmax: maximum population size in the stationary growth phase

• mu_opt: growth rate under optimal growth conditions

• Q0: value defining the duration of the lag phase Additional details on these parameters can be found in the package vignettes.

Secondary models are defined as a nested list through the "secondary_models" argument. The list must have one entry per environmental condition, whose name must match those used in the "env_conditions" argument. Each of these entries must be a named list defining the secondary model for each environmental condition. The model equation is defined in an entry named "model" (valid keys can be retrieved from secondary_model_data()). Then, additional entries defined the values of each model parameters (valid keys can be retrieved from secondary_model_data())

For additional details on how to define the secondary models, please see the package vignettes (and examples below).

Examples

## Example 1 - Growth under constant conditions -----------------------------

## Valid model keys can be retrieved calling primary_model_data()

primary_model_data()

my_model <- "modGompertz"  # we will use the modified-Gompertz

## The keys of the model parameters can also be obtained from primary_model_data()

primary_model_data(my_model)$pars

## We define the primary model as a list

my_model <- list(model = "modGompertz", logN0 = 0, C = 6, mu = .2, lambda = 20)

## We can now make the predictions

my_time <- seq(0, 100, length = 1000)  # Vector of time points for the calculations

my_prediction <- predict_growth(my_time, my_model, environment = "constant")

## The instance of IsothermalGrowth includes several S3 methods 

print(my_prediction)
plot(my_prediction)
coef(my_prediction)

## Example 2 - Growth under dynamic conditions ------------------------------

## We will consider the effect of two factors: temperature and pH

my_conditions <- data.frame(time = c(0, 5, 40),
                            temperature = c(20, 30, 35),
                            pH = c(7, 6.5, 5)
                            )
                            
## The primary model is defined as a named list
                            
my_primary <- list(mu = 2, Nmax = 1e7, N0 = 1, Q0 = 1e-3)

## The secondary model is defined independently for each factor

sec_temperature <- list(model = "Zwietering",
    xmin = 25, xopt = 35, n = 1)

sec_pH = list(model = "CPM",
    xmin = 5.5, xopt = 6.5,
    xmax = 7.5, n = 2)
    
## Then, they are assigned to each factor using a named list

my_secondary <- list(
    temperature = sec_temperature,
    pH = sec_pH
    )
    
## We can call the function now

my_times <- seq(0, 50, length = 1000)  # Where the output is calculated

dynamic_prediction <- predict_growth(environment = "dynamic", 
                                     my_times, my_primary, my_secondary,
                                     my_conditions
                                     )
                                     
## The instance of DynamicGrowth includes several useful S3 methods

print(dynamic_prediction)
plot(dynamic_prediction)
plot(dynamic_prediction, add_factor = "pH")
coef(dynamic_prediction)

## The time_to_size function can predict the time to reach a population size

time_to_size(my_prediction, 3)

Isothermal growth with parameter uncertainty

Description

Simulation of microbial growth considering uncertianty in the model parameters. Calculations are based on Monte Carlo simulations, considering the parameters follow a multivariate normal distribution.

Usage

predict_growth_uncertainty(
  model_name,
  times,
  n_sims,
  pars,
  corr_matrix = diag(nrow(pars)),
  check = TRUE,
  logbase_mu = logbase_logN,
  logbase_logN = 10
)

Arguments

Details

The distributions of the model parameters are defined in the pars argument using a tibble with 4 columns:

• par: identifier of the model parameter (according to primary_model_data()),

• mean: mean value of the model parameter.,

• sd: standard deviation of the model parameter.,

• scale: scale at which the model parameter is defined. Valid values are 'original' (no transformation), 'sqrt' square root or 'log' log-scale. The parameter sample is generated considering the parameter follows a marginal normal distribution at this scale, and is later converted to the original scale for calculations.

Value

An instance of GrowthUncertainty().

Examples

## Definition of the simulation settings

my_model <- "Baranyi"
my_times <- seq(0, 30, length = 100)
n_sims <- 3000

library(tibble)

pars <- tribble(
    ~par, ~mean, ~sd, ~scale,
    "logN0", 0, .2, "original",
    "mu", 2, .3, "sqrt",
    "lambda", 4, .4, "sqrt",
    "logNmax", 6, .5, "original"
)

## Calling the function

stoc_growth <- predict_growth_uncertainty(my_model, my_times, n_sims, pars)

## We can plot the results

plot(stoc_growth)

## Adding parameter correlation

my_cor <- matrix(c(1,   0,   0, 0,
    0,   1, 0.7, 0,
    0, 0.7,   1, 0,
    0,   0,   0, 1),
    nrow = 4)

stoc_growth2 <- predict_growth_uncertainty(my_model, my_times, n_sims, pars, my_cor)

plot(stoc_growth2)

## The time_to_size function can calculate the median growth curve to reach a size

time_to_size(stoc_growth, 4)

## Or the distribution of times

dist <- time_to_size(stoc_growth, 4, type = "distribution")
plot(dist)

Isothermal microbial growth

Description

The function predict_isothermal_growth() has been superseded by the top-level function predict_growth(), which provides a unified approach for growth modelling.

Regardless of that, it can still be used to predict population growth under static environmental conditions (i.e. using primary models).

Usage

predict_isothermal_growth(
  model_name,
  times,
  model_pars,
  check = TRUE,
  logbase_mu = 10,
  logbase_logN = 10
)

Arguments

Value

An instance of IsothermalGrowth().

Examples

## Define the simulations parameters

my_model <- "modGompertz"
my_pars <- list(logN0 = 2, C = 6, mu = .2, lambda = 25)
my_time <- seq(0, 100, length = 1000)

## Do the simulation

static_prediction <- predict_isothermal_growth(my_model, my_time, my_pars)

## Plot the results

plot(static_prediction)

Deprecated isothermal growth with parameter uncertainty

Description

predict_stochastic_growth() was renamed predict_growth_uncertainty() because the original function name may be misleading, as this is not a stochastic differential equation

Usage

predict_stochastic_growth(
  model_name,
  times,
  n_sims,
  pars,
  corr_matrix = diag(nrow(pars)),
  check = TRUE
)

Arguments

Metainformation of primary growth models

Description

Provides different types of meta-data about the primary growth models included in biogrowth. This information is the basis of the automatic checks, and can also help in the definition of models for predict_growth() and fit_growth().

Usage

primary_model_data(model_name = NULL)

Arguments

Value

If model_name is NULL, returns a character string with the available models. If is a valid identifier, it returns a list with metainformation about the model. If model_name name is not a valid identifier, raises an error.

Temperature recorded in refrigerators

Description

This dataset includes the temperature recorded in refrigerators in households of the Catalonia region. The data was published as part of Jofre et al. (2019) Domestic refrigerator temperatures in Spain: Assessment of its impact on the safety and shelf-life of cooked meat products. Food Research International, 126, 108578. And was kindly provided by the original authors of the study.

Usage

refrigeratorSpain

Format

A tibble with three columns:

• time: elapsed time in hours

• A1: temperature observed in refrigerator "1"

• A2: temperature observed in refrigerator "2"

Residuals for lambda for the coupled model

Description

Residuals for lambda for the coupled model

Usage

residuals_lambda(p, my_d)

Arguments

Value

vector of residuals

Residuals for the square root of mu for the coupled model

Description

Residuals for the square root of mu for the coupled model

Usage

residuals_sqmu(p, my_d)

Arguments

Value

vector of residuals

Richards growth model

Description

Richards growth model

Usage

richards_model(times, logN0, mu, lambda, C, nu)

Arguments

Metainformation of secondary growth models

Description

Provides different types of meta-data about the secondary growth models included in biogrowth. This information is the basis of the automatic checks, and can also help in the definition of models for predict_growth() and fit_growth().

Usage

secondary_model_data(model_name = NULL)

Arguments

Value

If model_name is NULL, returns a character string with the available models. If is a valid identifier, it returns a list with metainformation about the model. If model_name name is not a valid identifier, raises an error.

Plot of the initial guess for growth under dynamic environmental conditions

Description

Compares the prediction corresponding to a guess of the parameters of the model against experimental data

Usage

show_guess_dynamic(
  fit_data,
  model_keys,
  guess,
  env_conditions,
  logbase_mu = 10,
  formula = logN ~ time
)

Arguments

Value

A ggplot2::ggplot() comparing the model prediction against the data

Plot of the initial guess for growth under constant environmental conditions

Description

Compares the prediction corresponding to a guess of the parameters of the primary model against experimental data

Usage

show_guess_primary(
  fit_data,
  model_name,
  guess,
  logbase_mu = 10,
  formula = logN ~ time
)

Arguments

Value

A ggplot2::ggplot() comparing the model prediction against the data

Time to reach a given microbial count

Description

The function time_to_logcount() has been superseded by function time_to_size(), which provides a more general interface.

But it still returns the storage time required for the microbial count to reach log_count according to the predictions of model. Calculations are done using linear interpolation of the model predictions.

Usage

time_to_logcount(model, log_count)

Arguments

Value

The predicted time to reach log_count.

Examples

## First of all, we will get an IsothermalGrowth object

my_model <- "modGompertz"
my_pars <- list(logN0 = 2, C = 6, mu = .2, lambda = 25)
my_time <- seq(0, 100, length = 1000)

static_prediction <- predict_isothermal_growth(my_model, my_time, my_pars)
plot(static_prediction)

## And now we calculate the time to reach a microbial count

time_to_logcount(static_prediction, 2.5)

## If log_count is outside the range of the predicted values, NA is returned

time_to_logcount(static_prediction, 20)

Time for the population to reach a given size

Description

Calculates the elapsed time required for the population to reach a given size (in log scale)

Usage

time_to_size(model, size, type = "discrete", logbase_logN = NULL)

Arguments

Details

The calculation method differs depending on the value of type. If type="discrete" (default), the function calculates by linear interpolation a discrete time to reach the target population size. If type="distribution", this calculation is repeated several times, generating a distribution of the time. Note that this is only possible for instances of GrowthUncertainty or MCMCgrowth.

Value

If type="discrete", a number. If type="distribution", an instance of TimeDistribution.

Examples

## Example 1 - Growth predictions -------------------------------------------

## The model is defined as usual with predict_growth

my_model <- list(model = "modGompertz", logN0 = 0, C = 6, mu = .2, lambda = 20)

my_time <- seq(0, 100, length = 1000)  # Vector of time points for the calculations

my_prediction <- predict_growth(my_time, my_model, environment = "constant")

plot(my_prediction)

## We just have to pass the model and the size (in log10)

time_to_size(my_prediction, 3)

## If the size is not reached, it returns NA

time_to_size(my_prediction, 8)

## By default, it considers the population size is defined in the same log-base
## as the prediction. But that can be changed using logbase_logN

time_to_size(my_prediction, 3)
time_to_size(my_prediction, 3, logbase_logN = 10)
time_to_size(my_prediction, log(100), logbase_logN = exp(1))

## Example 2 - Model fit ----------------------------------------------------

my_data <- data.frame(time = c(0, 25, 50, 75, 100), 
                      logN = c(2, 2.5, 7, 8, 8))
                      
models <- list(primary = "Baranyi")

known <- c(mu = .2)

start <- c(logNmax = 8, lambda = 25, logN0 = 2)

primary_fit <- fit_growth(my_data, models, start, known,
                          environment = "constant",
                          )
                          
plot(primary_fit)

time_to_size(primary_fit, 4)

## Example 3 - Global fitting -----------------------------------------------

## We need a model first

data("multiple_counts")
data("multiple_conditions")

sec_models <- list(temperature = "CPM", pH = "CPM")

known_pars <- list(Nmax = 1e8, N0 = 1e0, Q0 = 1e-3,
                   temperature_n = 2, temperature_xmin = 20, 
                   temperature_xmax = 35,
                   temperature_xopt = 30,
                   pH_n = 2, pH_xmin = 5.5, pH_xmax = 7.5, pH_xopt = 6.5)
                   
my_start <- list(mu_opt = .8)

global_fit <- fit_growth(multiple_counts, 
                         sec_models, 
                         my_start, 
                         known_pars,
                         environment = "dynamic",
                         algorithm = "regression",
                         approach = "global",
                         env_conditions = multiple_conditions
                         ) 
                         
plot(global_fit)

## The function calculates the time for each experiment

time_to_size(global_fit, 3)

## It returns NA for the particular experiment if the size is not reached

time_to_size(global_fit, 4.5)

Trilinear growth model

Description

Trilinear growth model defined by Buchanan et al. (1997).

Usage

trilinear_model(times, logN0, mu, lambda, logNmax)

Arguments

Value

Numeric vector with the predicted microbial count.

Zwietering gamma model

Description

Gamma model as defined by Zwietering et al. (1992). To avoid unreasonable predictions, it has been modified setting gamma=0 for values of x outside (xmin, xopt)

Usage

zwietering_gamma(x, xmin, xopt, n)

Arguments

Value

The corresponding gamma factor.