DoseResponseMixtures

Status: Early development. The package is being built incrementally as a side project; APIs will change without warning until a 1.0 release.

Overview

DoseResponseMixtures.jl is a Julia package for analyzing dose-response bioassays under the assumption that tolerance to a stressor (typically a pesticide) is a quantitative trait whose distribution in a population may be a mixture of components rather than a single unimodal distribution.

The classical bioassay infrastructure — probit analysis, the 2-parameter log-logistic model, and similar tools — assumes a single tolerance distribution. This assumption fails precisely when it matters most: during the spread of a resistance allele through a population, when the population is structurally a mixture of susceptible, heterozygous, and resistant individuals. The same failure occurs by design in refuge-based resistance management strategies (e.g., for Bt-resistant Helicoverpa zea), where the population is intended to be a mixture of genotypes.

This package provides:

• A mechanistic generative model of bioassay data, in which a population is parameterized by allele frequency, genotype-specific mean tolerances, dominance, and within-genotype variance, and bioassay outcomes follow from individual-level Bernoulli mortality.
• A suite of estimators ranging from the classical 2-parameter log-logistic to mixture models with explicit quantitative-genetic structure under Hardy-Weinberg equilibrium.
• Evaluation tooling for comparing estimators on bias, precision, and detection power across realistic experimental designs.

Scientific motivation

A more detailed discussion of the modeling choices is forthcoming in the documentation. In brief:

1. Pesticide tolerance has a polygenic basis and is reasonably modeled, on a log scale, as approximately normally distributed within a genotype class.
2. During the spread of a major-effect resistance allele, or in any population maintained as a genotype mixture by management practice, the phenotypic tolerance distribution is multimodal.
3. Estimators built on a unimodal assumption produce systematically biased point estimates and slope estimates under these conditions, and standard goodness-of-fit checks frequently fail to detect the problem at realistic sample sizes.
4. Phenomenological extensions of the classical model (e.g., the 5-parameter log-logistic) improve fit but do not recover the underlying genetic structure.
5. Explicit mixture models, particularly those constrained by Hardy-Weinberg expectations, recover biologically meaningful parameters (allele frequency, dominance, resistance magnitude) and provide a principled framework for resistance monitoring.

Installation

The package is not yet registered. To install the development version:

using Pkg
Pkg.add(url = "https://github.com/alejandromerchan/DoseResponseMixtures.jl")

Roadmap

• Generative model: single-population (unimodal) baseline matching the original R simulations
• Generative model: HWE-structured three-genotype population with dominance
• Estimator: classical 2-parameter log-logistic via GLM
• Estimator: 2-parameter log-logistic with background mortality
• Estimator: agnostic two-component mixture (Turing.jl)
• Estimator: HWE-constrained three-component mixture with dominance (Turing.jl)
• Grid-runner for factorial simulation experiments
• Evaluation utilities: bias, RMSE, coverage, detection power
• Plotting recipes for standard diagnostic figures
• Documentation and worked examples
• Manuscript reproduction script

License

MIT. See LICENSE.