Fit dual-pool logistic model

Fits a dual-pool logistic model representing rapidly and slowly degradable fractions.

Usage

fit_dual_logistic(data, start = NULL)

Arguments

data

A rumen_gp object.

start

Optional list of starting values. May contain any of:

• V1F

• V2F

• k1

• k2

• lambda

Value

A dual_logistic_fit object containing:

• Parameter estimates

• Model diagnostics

• Predicted values

• Residuals

• Rapid and slow pool estimates

Details

Equation

$$ V(t)= \frac{V1F} { 1+\exp\left[2-4k1(t-\lambda)\right] } + \frac{V2F} { 1+\exp\left[2-4k2(t-\lambda)\right] } $$

where:

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

• \(V1F\) is the final gas volume from the rapidly fermentable fraction

• \(V2F\) is the final gas volume from the slowly fermentable fraction

• \(k1\) is the fractional rate constant of the rapid fraction

• \(k2\) is the fractional rate constant of the slow fraction

• \(\lambda\) is lag time

Interpretation

The Dual Logistic model assumes that gas production originates from two independent fermentation pools:

• A rapidly degradable fraction (\(V1F\))

• A slowly degradable fraction (\(V2F\))

Each fraction follows a logistic fermentation pattern with its own rate constant.

Advantages

• Represents complex fermentation dynamics

• Separates rapid and slow fermentation pools

• Biologically meaningful parameterization

• Useful for heterogeneous substrates

Limitations

• Requires estimation of five parameters

• More computationally demanding

• Greater risk of parameter correlation

• May require careful starting values

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_dual_logistic(
  gp
)
#> Warning: Large negative pressure values detected. Minimum PSI = -1.274 . Please inspect the affected bottles.
#> rumenGP data validation passed.
#> Observations: 1752
#> Heads: 24
#> Treatments: 5

summary(fit_default)
#> 
#> Dual-pool Logistic model summary
#> --------------------------------
#> Total bottles: 24
#> Successful fits: 20
#> Failed fits: 4
#> Low R-squared (< 0.90): 0
#> Lambda at boundary: 1
#> 

# Fit using custom starting values
fit_custom_start <- fit_dual_logistic(
  gp,
  start = list(
    V1F = 30,
    V2F = 70,
    k1 = 0.20,
    k2 = 0.05,
    lambda = 0.50
  )
)
#> Warning: Large negative pressure values detected. Minimum PSI = -1.274 . Please inspect the affected bottles.
#> rumenGP data validation passed.
#> Observations: 1752
#> Heads: 24
#> Treatments: 5

summary(fit_custom_start)
#> 
#> Dual-pool Logistic model summary
#> --------------------------------
#> Total bottles: 24
#> Successful fits: 20
#> Failed fits: 4
#> Low R-squared (< 0.90): 0
#> Lambda at boundary: 1
#>