fit_mitscherlich: Fit Mitscherlich model

In rumenGP: Rumen Gas Production Modeling, Comparison, and Visualization

Fit Mitscherlich model

Description

Fits the Mitscherlich gas-production model to each bottle in a rumen_gp dataset.

Usage

fit_mitscherlich(data, start = NULL)

Arguments

data	A rumen_gp object.
start	Optional list of starting values. May contain any of: A k d lambda

Details

Equation

V(t) = A \left[ 1 - \exp \left( -k(t-\lambda) - d \left( \sqrt{t+0.001} - \sqrt{\lambda+0.001} \right) \right) \right]

where:

• V(t) is cumulative gas production at time t

• A is asymptotic gas production

• k is the fractional rate constant

• d is a diffusion or shape parameter

• \lambda is lag time

Interpretation

The Mitscherlich model combines an exponential fermentation component with a diffusion-like term.

The parameter k describes the primary fermentation rate, while d provides additional flexibility for representing changes in fermentation dynamics over time.

Advantages

• Explicit lag parameter

• Flexible curve shape

• Can describe complex fermentation dynamics

• Often performs well when simple exponential models are inadequate

Limitations

• More complex than EXP0 or EXPL

• Increased parameter correlation

• Diffusion parameter may be less intuitive biologically

• May require careful starting values

Value

A mitscherlich_fit object containing:

• Parameter estimates

• Model diagnostics

• Predicted values

• Residuals

Examples

files <- example_data()

raw_data <- read_ankom(
  files$ankom
)

metadata <- read_metadata(
  files$metadata
)

gp <- process_ankom(
  raw_data,
  metadata,
  headspace_ml = 210,
  temperature_c = 39
)

# Fit using package default starting values
fit_default <- fit_mitscherlich(
  gp
)

summary(fit_default)

# Fit using custom starting values
fit_custom_start <- fit_mitscherlich(
  gp,
  start = list(
    A = 120,
    k = 0.05,
    d = 0.05,
    lambda = 0.50
  )
)

summary(fit_custom_start)

rumenGP documentation built on Oct. 2, 2026, 5:09 p.m.