SSD HC5

Calculate a lognormal species-sensitivity hazardous concentration at a supplied species fraction (e.g. HC5); natural-log fit parameters are supplied and this is not a PNEC or confidence bound.

Description

Calculate a selected hazardous-concentration quantile from supplied natural-log SSD parameters.

A species sensitivity distribution, or SSD, describes variation in selected effect concentrations across species. A low distribution percentile summarizes the more sensitive end of those endpoints. HC5 denotes the fifth percentile; it does not mean that 5% of individuals die at that concentration.^[1]

This calculator assumes the numerical effect concentrations are lognormally distributed. You supply the mean and standard deviation of their natural logarithms, plus the desired species fraction. Despite the HC5 title, the fraction is configurable rather than fixed at 0.05.

The output uses the concentration unit underlying the fitted numerical values. Parameters based on log10 cannot be entered unchanged: convert both log mean and log standard deviation by multiplying by ln(10).

When to use SSD HC5

Use it to derive HC5 or another selected SSD percentile after fitting a compatible natural-log distribution to appropriately selected species endpoints.

How to use SSD HC5 and interpret its calculation

Enter logConcentrationMean and a positive logConcentrationSd on the natural-log scale.
Enter affectedSpeciesFraction strictly between 0 and 1; use 0.05 for HC5.
Run the calculator and interpret hazardousConcentration in the original fitted concentration unit, with the endpoint selection and distribution assumptions stated.

HCp = exp[μ + σ × Φ⁻¹(p)]

μ and σ describe natural-log concentrations, p is the selected distribution fraction, and Φ⁻¹ is a standard normal quantile.

The implementation obtains an approximate normal quantile and exponentiates the corresponding log concentration. It does not fit parameters, select species, or calculate uncertainty bounds.

json

{
  "input": {
    "logConcentrationMean": 0,
    "logConcentrationSd": 1,
    "affectedSpeciesFraction": 0.05
  },
  "output": {
    "hazardousConcentration": 0.19304081669873657
  }
}

At fraction 0.5, the output is exp(μ), the distribution median, regardless of the positive standard deviation. Fractions zero and one, and a zero standard deviation, are rejected. Extreme parameter combinations can overflow or underflow the numerical calculation.

Limitations and assumptions

Species representativeness, endpoint comparability, exposure duration, data censoring, and distribution choice must be assessed outside the tool. A small fitted percentile is not automatically a regulatory protective concentration.

No confidence interval or assessment factor is applied. The fraction describes the fitted distribution of species endpoints rather than an observed fraction of affected species at a site.

Alternative or Complementary methods

Fit the natural-log parameters from a curated concentration list before calculating a quantile. A reservoir concentration model supplies an exposure scenario; comparisons with the quantile require compatible units, durations, and effect endpoints.

References

Species Sensitivity Distribution (SSD) Toolbox — U.S. Environmental Protection Agency

Similar or alternative tools

SSD Curve Fitting
Estimate natural-log mean and sample standard deviation from supplied species concentrations.
PEC
Predict concentrations under constant loading, outflow, and degradation in a mixed reservoir.