predict_growth: 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
)

Value

An instance of GrowthPrediction.

Arguments

times: numeric vector of time points for making the predictions
primary_model: named list defining the values of the parameters of the primary growth model
environment: type of environment. Either "constant" (default) or "dynamic" (see below for details on the calculations for each condition)
secondary_models: a nested list describing the secondary models. See below for details
env_conditions: Tibble describing the variation of the environmental conditions for dynamic experiments. It must have with the elapsed time (named time by default; can be changed with the "formula" argument), and as many additional columns as environmental factors. Ignored for "constant" environments.
...: Additional arguments for deSolve::ode().
check: Whether to check the validity of the models. TRUE by default.
logbase_mu: Base of the logarithm the growth rate is referred to. By default, the same as logbase_logN. See vignette about units for details.
logbase_logN: Base of the logarithm for the population size. By default, 10 (i.e. log10). See vignette about units for details.
formula: An object of class "formula" describing the x variable for predictions under dynamic conditions. . ~ time as a default.

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).

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().

Examples

Run this code


## 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)

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