PSRICalcSM: Plant Stress Response Index Calculator - Softmax Method

PSRICalcSM implements the softmax aggregation method for calculating Plant Stress Response Index (PSRI) from time-series germination data. Built on the methodological foundation of the Osmotic Stress Response Index (OSRI) framework developed by Walne et al. (2020), it is the companion package to PSRICalc (geometric mean method), providing a zero-robust alternative that eliminates the zero-collapse failure mode.

Why Softmax?

The geometric PSRI collapses to zero when any component equals zero:

PSRI_GM = (MSG × MRG × (1-MTG))^(1/3) × RVF
# If MRG = 0 → PSRI_GM = 0 (complete data loss)

The softmax PSRI handles zeros through adaptive reweighting:

PSRI_SM = Σ Wᵢ · Cᵢ
# If MRG = 0 → W_MRG ≈ 0, other weights renormalize
# Information from MSG and cMTG is preserved

In our prion-germination experiments: geometric PSRI lost 72% of barley replicates to zero-collapse; softmax PSRI retained 100%.

Installation

# From CRAN (when available)
install.packages("PSRICalcSM")

# Development version
# devtools::install_github("RFeissIV/PSRICalcSM")

Quick Start

library(PSRICalcSM)

# Basic PSRI_SM (3 components: MSG, MRG, cMTG)
compute_psri_sm(
  germination_counts = c(5, 15, 20),
  timepoints = c(3, 5, 7),
  total_seeds = 25
)

# With radicle vigor (4 components: MSG, MRG, cMTG, RVS)
compute_psri_sm(
  germination_counts = c(5, 15, 20),
  timepoints = c(3, 5, 7),
  total_seeds = 25,
  radicle_count = 18
)

# Detailed output with components and weights
result <- compute_psri_sm(
  germination_counts = c(5, 15, 20),
  timepoints = c(3, 5, 7),
  total_seeds = 25,
  radicle_count = 18,
  return_components = TRUE
)
result$psri_sm
result$components
result$weights

Temperature Calibration

The temperature parameter T controls how sharply the softmax concentrates weight on dominant components. The default T = 0.13 was calibrated via perplexity targeting (effective components ≈ 2.0 out of 3). For your own data:

# Gather representative component profiles from your experiment
profiles <- list(
  control = c(MSG = 0.80, MRG = 0.90, cMTG = 0.60),
  treated = c(MSG = 0.20, MRG = 0.15, cMTG = 0.50)
)

cal <- calibrate_temperature(profiles, target_perplexity = 2.0)
cal$optimal_T

# Use calibrated T
compute_psri_sm(
  germination_counts = c(5, 15, 20),
  timepoints = c(3, 5, 7),
  total_seeds = 25,
  temperature = cal$optimal_T
)

Method Selection Guide

Criterion	Geometric (`PSRICalc`)	Softmax (`PSRICalcSM`)
Zero components	Collapses to 0	Graceful degradation
Sample size	>25 seeds × 4 reps	Any size
Treatment effects	Significant expected	Any
Data retention	May lose replicates	100% retention
Radicle integration	Discrete (1.0/1.05/1.10)	Continuous (0–1)

Components

Component	Description	Range
MSG	Maximum Stress-adjusted Germination	[0, 1]
MRG	Maximum Rate of Germination	[0, ~3]
cMTG	Complementary Mean Time to Germination	[0, 1]
RVS	Radicle Vigor Score (optional)	[0, 1]

Citation

If you use this package, please cite:

Feiss, R.A. (2026). PSRICalcSM: Plant Stress Response Index Calculator
- Softmax Method. R package version 1.0.0.
https://CRAN.R-project.org/package=PSRICalcSM

Scientific Attribution

PSRICalcSM builds directly on the Osmotic Stress Response Index (OSRI) methodology established by:

Walne, C.H., Gaudin, A., Henry, W.B., and Reddy, K.R. (2020). In vitro seed germination response of corn hybrids to osmotic stress conditions. Agrosystems, Geosciences & Environment, 3(1), e20087. https://doi.org/10.1002/agg2.20087

References

Walne, C.H., Gaudin, A., Henry, W.B., & Reddy, K.R. (2020). In vitro seed germination response of corn hybrids to osmotic stress conditions. Agrosystems, Geosciences & Environment, 3(1), e20087. https://doi.org/10.1002/agg2.20087
Feiss, R.A. (2025). PSRICalc: Plant Stress Response Index Calculator. https://CRAN.R-project.org/package=PSRICalc

Human-AI Development Transparency

Development followed an iterative human-machine collaboration. All algorithmic design, statistical methodologies, and biological validation logic were conceptualized, tested, and iteratively refined by Richard A. Feiss through repeated cycles of running experimental data, evaluating analytical outputs, and selecting among candidate algorithms and approaches.

AI systems (Anthropic Claude and OpenAI GPT) served as coding assistants and analytical sounding boards under continuous human direction, helping with:

Code implementation and syntax validation
Exploratory analysis of candidate approaches
Documentation consistency and clarity
Package compliance checking

The selection of statistical methods, evaluation of biological plausibility, and all final methodology decisions were made by the human author. AI systems did not independently originate algorithms, statistical approaches, or scientific methodologies.

Author

Richard A. Feiss IV, Ph.D. Minnesota Center for Prion Research and Outreach (MNPRO) University of Minnesota