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Fitting the decline: probits, σ, and Ki

Seed death in storage is remarkably well described by one curve family: viability, transformed to probits (inverse-normal units), falls as a straight line in time. That's the Ellis–Roberts viability equation, v = Ki − p/σ: Ki is the lot's starting level in probits, σ is how many days (or years) it takes to lose one probit. Fitting is maximum likelihood on the binomial counts — the same machinery as a probit GLM; intercept = Ki, slope = −1/σ.

σ, not P50, is the comparable number across lots and species: P50 is contaminated by where the lot started, σ measures only how fast it falls. The lab reports σ first everywhere for exactly this reason.

Two honesty notes. Small series can be perfectly separated (all pass, then all fail), where ordinary maximum likelihood has no finite answer — that's what bias-reduced fitting is for, not a bigger iteration limit. And a fitted curve is an interpolation machine; extrapolating it far past the last test is a prediction, and should be labeled as one.

Where this appears in the pipeline: Fitting the decline: probit regression that survives perfect data
Observed intervals, censoring, and honest notationSupport: when the uncertainty agrees with the point