Trophic Magnification Factor
Fit natural-log lipid-normalized concentration against caller trophic levels and exponentiate the slope; ratios below one preserve trophic dilution and ecological causality is not inferred.
Description
Fit natural-log concentration against trophic level and exponentiate the slope to obtain a TMF.
A trophic magnification factor, or TMF, summarizes how chemical concentration changes along a food web. A log-linear regression relates a normalized concentration to trophic position; exponentiating its slope gives the multiplicative change per trophic-level increase.1
This tool expects concentrations already normalized to lipid and trophic levels already estimated. It uses natural logarithms and an unweighted linear fit. TMF above one indicates an increasing fitted concentration trend, while a value below one indicates a decreasing trend.
All concentrations must use the same unit and normalization basis, and trophic levels must share a reference convention. The reported R² describes the supplied regression; it does not test whether magnification is statistically supported.
When to use Trophic Magnification Factor
Use it to reproduce a simple food-web concentration regression from prepared observations, or check the natural-log slope-to-factor conversion.
How to use Trophic Magnification Factor and interpret its calculation
- Enter aligned trophicLevels and lipidNormalizedConcentrations lists with at least two observations. All values must be positive, and trophic levels must vary.
- Run the regression and read logConcentrationSlopePerTrophicLevel, trophicMagnificationFactor, and fitRSquared.
- Interpret the fitted factor alongside data quality, food-web membership, and uncertainty assessed separately.
ln(C) = a + b × trophic level; TMF = exp(b) C is the supplied lipid-normalized concentration; b is an unweighted ordinary least-squares slope.
The implementation logs concentrations but does not log trophic levels. It permits repeated trophic levels when the complete list has positive variation. If log concentrations are constant, its R² convention returns one even though the fitted slope is zero.
{
"input": {
"trophicLevels": [
1,
2,
3
],
"lipidNormalizedConcentrations": [
2,
4,
8
]
},
"output": {
"logConcentrationSlopePerTrophicLevel": 0.6931471805599453,
"trophicMagnificationFactor": 2,
"fitRSquared": 1
}
}A constant concentration list gives slope zero and TMF one. Identical trophic levels are rejected because the regression denominator is zero. Unsorted paired observations are accepted; zero concentrations cannot be logged and are rejected.
Limitations and assumptions
No lipid normalization, isotope-based trophic-level estimation, food-web selection, censoring treatment, weighting, or slope confidence interval is performed. A fitted TMF above one is not by itself a statistical or regulatory determination.
Confounding by habitat, exposure source, metabolism, tissue selection, and dependence among observations is outside this regression. Two observations can yield R² one without establishing a reliable ecological relationship.
Alternative or Complementary methods
A predator–prey ratio describes a specific paired comparison rather than a whole food-web trend. A kinetic BCF uses water uptake and elimination rates, so it measures another bioaccumulation relationship.
References
-
Guidance for measuring and evaluating biomagnification factors and trophic magnification factors of difficult substances: application to decabromodiphenylethane (Fremlin, Elliott, and Gobas, 2025) — Integrated Environmental Assessment and Management
Similar or alternative tools
- Biomagnification Factor
Compare paired predator and prey concentrations with lipid normalization.
- Bioconcentration Factor
Calculate rate-based water-to-organism concentration factors with and without growth dilution.