Multi-layered linear stochastic differential equation inference

This page presents the supplementary material and software used for multi-layered analysis using vectorial linear stochastic differential equations. The reason for using stochastic differential equation is to facilitate studying irregularly spaced observations like those we find in our study dataset of micro-fossils. This work was performed in conjuction with doing the research for and writing the manuscript "Phenotypic Evolution studied by Layered Stochastic Differential Equations" by T. Reitan, T. Schweder and J. Henderiks.

Originally, this was used for modelling phenotypic evolution towards a optima that itself could be a stochastic process depending responding to layers below it (climate or primary optimum). However, it may well be that the method can be used for other applications as well, with a little tweaking.

Current versions of the analysis code:



Papers on theory and application:


R example code:

PS: All example datasets are provided in the package, so that the file reading is not necessary.

Example datasets (see in addition the example code):


Simulations can be used for testing the behaviour of the analysis.

Updates and older versions

Update history:

Older code:

The latest version of the analysis program and R package uses only the Lapack library. Older versions use the Hydrasub library for support. This library in turn uses GSL (Gnu Scientific Library). Plotting programs, such as 'vvgraph' and 'histogramme' are used for displaying the results. PS: If plotting in the program (rather than the R package) is to be used, then even the latest version requires the 'vvgraph' and 'histogramme' programs from the Hydrasub library. However, there are options for not doing plots and for sending plots to file instead.

The software (as well as the previously used underlying program library Hydrasub) is licenced as LGPL-based, meaning that anyone can modify and use it for other purposes than the original intent.

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Trond Reitan
Last modified: Fri Oct 14 11:34:00 CET 2019