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The R package mkin provides calculation routines for the analysis of chemical degradation data, including multicompartment kinetics as needed for modelling the formation and decline of transformation products, or if several degradation compartments are involved. It provides stable functionality for kinetic evaluations according to the FOCUS guidance (see below for details). In addition, it provides functionality to do hierarchical kinetics based on nonlinear mixed-effects models.


You can install the latest released version from CRAN from within R:


In the regulatory evaluation of chemical substances like plant protection products (pesticides), biocides and other chemicals, degradation data play an important role. For the evaluation of pesticide degradation experiments, detailed guidance and various helpful tools have been developed as detailed in ‘Credits and historical remarks’ below. This package aims to provide a one stop solution for degradation kinetics, addressing modellers that are willing to, or even prefer to work with R.

Basic usage

For a start, have a look at the code examples provided for plot.mkinfit and plot.mmkin, and at the package vignettes FOCUS L and FOCUS D.


The HTML documentation of the latest version released to CRAN is available at and github.

Documentation of the development version is found in the ‘dev’ subdirectory. In the articles section of this documentation, you can also find demonstrations of the application of nonlinear hierarchical models, also known as nonlinear mixed-effects models, to more complex data, including transformation products and covariates.



  • Highly flexible model specification using mkinmod, including equilibrium reactions and using the single first-order reversible binding (SFORB) model, which will automatically create two state variables for the observed variable.
  • Model solution (forward modelling) in the function mkinpredict is performed either using the analytical solution for the case of parent only degradation or some simple models involving a single transformation product, , an eigenvalue based solution if only simple first-order (SFO) or SFORB kinetics are used in the model, or using a numeric solver from the deSolve package (default is lsoda).
  • The usual one-sided t-test for significant difference from zero is shown based on estimators for the untransformed parameters.
  • Summary and plotting functions. The summary of an mkinfit object is in fact a full report that should give enough information to be able to approximately reproduce the fit with other tools.
  • The chi-squared error level as defined in the FOCUS kinetics guidance (see below) is calculated for each observed variable.
  • The ‘variance by variable’ error model which is often fitted using Iteratively Reweighted Least Squares (IRLS) can be specified as error_model = "obs".

Unique in mkin

  • Three different error models can be selected using the argument error_model to the mkinfit function. A two-component error model similar to the one proposed by Rocke and Lorenzato can be selected using the argument error_model = "tc".
  • Model comparisons using the Akaike Information Criterion (AIC) are supported which can also be used for non-constant variance. In such cases the FOCUS chi-squared error level is not meaningful.
  • By default, kinetic rate constants and kinetic formation fractions are transformed internally using transform_odeparms so their estimators can more reasonably be expected to follow a normal distribution.
  • When parameter estimates are backtransformed to match the model definition, confidence intervals calculated from standard errors are also backtransformed to the correct scale, and will not include meaningless values like negative rate constants or formation fractions adding up to more than 1, which cannot occur in a single experiment with a single defined radiolabel position.
  • When a metabolite decline phase is not described well by SFO kinetics, SFORB kinetics can be used for the metabolite. Mathematically, the SFORB model is equivalent to the DFOP model. However, the SFORB model has the advantage that there is a mechanistic interpretation of the model parameters.
  • Nonlinear mixed-effects models (hierarchical models) can be created from fits of the same degradation model to different datasets for the same compound by using the nlme.mmkin and saem.mmkin methods. Note that the convergence of the nlme fits depends on the quality of the data. Convergence is better for simple models and data for many groups (e.g. soils). The saem method uses the saemix package as a backend. Analytical solutions suitable for use with this package have been implemented for parent only models and the most important models including one metabolite (SFO-SFO and DFOP-SFO). Fitting other models with saem.mmkin, while it makes use of the compiled ODE models that mkin provides, has longer run times (from a couple of minutes to more than an hour).


  • Parallel fitting of several models to several datasets is supported, see for example plot.mmkin.
  • If a C compiler is installed, the kinetic models are compiled from automatically generated C code, see vignette compiled_models. The autogeneration of C code was inspired by the ccSolve package. Thanks to Karline Soetaert for her work on that.
  • Even if no compiler is installed, many degradation models still give very good performance, as current versions of mkin also have analytical solutions for some models with one metabolite, and if SFO or SFORB are used for the parent compound, Eigenvalue based solutions of the degradation model are available.


There is a graphical user interface that may be useful. Please refer to its documentation page for installation instructions and a manual. It only supports evaluations using (generalised) nonlinear regression, but not simultaneous fits using nonlinear mixed-effects models.


There is a list of changes for the latest CRAN release and one for each github branch, e.g. the main branch.

Credits and historical remarks

mkin would not be possible without the underlying software stack consisting of, among others, R and the package deSolve. In previous version, mkin was also using the functionality of the FME package. Please refer to the package page on CRAN for the full list of imported and suggested R packages. Also, Debian Linux, the vim editor and the Nvim-R plugin have been invaluable in its development.

mkin could not have been written without me being introduced to regulatory fate modelling of pesticides by Adrian Gurney during my time at Harlan Laboratories Ltd (formerly RCC Ltd). mkin greatly profits from and largely follows the work done by the FOCUS Degradation Kinetics Workgroup, as detailed in their guidance document from 2006, slightly updated in 2011 and in 2014.

Also, it was inspired by the first version of KinGUI developed by BayerCropScience, which is based on the MatLab runtime environment.

The companion package kinfit (now deprecated) was started in 2008 and first published on CRAN on 01 May 2010.

The first mkin code was published on 11 May 2010 and the first CRAN version on 18 May 2010.

In 2011, Bayer Crop Science started to distribute an R based successor to KinGUI named KinGUII whose R code is based on mkin, but which added, among other refinements, a closed source graphical user interface (GUI), iteratively reweighted least squares (IRLS) optimisation of the variance for each of the observed variables, and Markov Chain Monte Carlo (MCMC) simulation functionality, similar to what is available e.g. in the FME package.

Somewhat in parallel, Syngenta has sponsored the development of an mkin and KinGUII based GUI application called CAKE, which also adds IRLS and MCMC, is more limited in the model formulation, but puts more weight on usability. CAKE is available for download from the CAKE website, where you can also find a zip archive of the R scripts derived from mkin, published under the GPL license.

Finally, there is KineticEval, which contains some further development of the scripts used for KinGUII.

Thanks to René Lehmann, formerly working at the Umweltbundesamt, for the nice cooperation on parameter transformations, especially the isometric log-ratio transformation that is now used for formation fractions in case there are more than two transformation targets.

Many inspirations for improvements of mkin resulted from doing kinetic evaluations of degradation data for my clients while working at Harlan Laboratories and at Eurofins Regulatory AG, and now as an independent consultant.

Funding was received from the Umweltbundesamt in the course of the projects

  • Project Number 27452 (Testing and validation of modelling software as an alternative to ModelMaker 4.0, 2014-2015)
  • Project Number 56703 (Optimization of gmkin for routine use in the Umweltbundesamt, 2015)
  • Project Number 92570 (Update of Project Number 27452, 2017-2018)
  • Project Number 112407 (Testing the feasibility of using an error model according to Rocke and Lorenzato for more realistic parameter estimates in the kinetic evaluation of degradation data, 2018-2019)
  • Project Number 120667 (Development of objective criteria for the evaluation of the visual fit in the kinetic evaluation of degradation data, 2019-2020)
  • Project Number 146839 (Checking the feasibility of using mixed-effects models for the derivation of kinetic modelling parameters from degradation studies, 2020-2021)
  • Project Number 173340 (Application of nonlinear hierarchical models to the kinetic evaluation of chemical degradation data)

Thanks to everyone involved for collaboration and support!

Thanks are due also to Emmanuelle Comets, maintainer of the saemix package, for her interest and support for using the SAEM algorithm and its implementation in saemix for the evaluation of chemical degradation data.

Regarding the application of nonlinear mixed-effects models to degradation data, von Götz et al (1999) have already proposed to use this technique in the context of environmental risk assessments of pesticides. However, this work was apparently not followed up, which is why we had to independently arrive at the idea and missed to cite this previous work on the topic in our first publications.


Ranke J (2023) Application of nonlinear hierarchical models to the kinetic evaluation of chemical degradation data - Guidance for the use of an R markdown template file. Umweltbundesamt TEXTE 151/2023
Ranke J, Wöltjen J, Schmidt J, and Comets E (2021) Taking kinetic evaluations of degradation data to the next level with nonlinear mixed-effects models. Environments 8 (8) 71 doi:10.3390/environments8080071
Ranke J, Meinecke S (2019) Error Models for the Kinetic Evaluation of Chemical Degradation Data Environments 6 (12) 124 doi:10.3390/environments6120124
Ranke J, Wöltjen J, Meinecke S (2018) Comparison of software tools for kinetic evaluation of chemical degradation data Environmental Sciences Europe 30 17 doi:10.1186/s12302-018-0145-1
Von Götz N, Nörtersheuser P, Richter O (1999) Population based analysis of pesticide kinetics Chemosphere 38 7 doi:10.1016/S0045-6535(98)00388-9


Contributions are welcome!