Statistical Ecotoxicology using R – Module 2: Contemporary statistical methods for Ecotoxicologists July 4 – 5, 2019 (2 days)

$680.00 Excl. GST

8:30 am July 4 to 4:30 pm July 5 (2 days)

Charles Darwin University – Waterfront Campus

21 Kitchener Dr, Darwin City NT


Go beyond the basics. This course will give you hands-on experience with the most up-to-date methods for analysing ecotox. data using R. You will receive tuition on new methods introduced in the latest revision to the Australian and New Zealand Guidelines as well as being introduced to new ideas and concepts for C-R experimental design and analysis, SSD modelling and much more.

2 in stock



Course Content

Important note: Time constraints may preclude all topics being covered.

  1. Preliminaries
  • Quick review of some common discrete and continuous probability models useful in ecotoxicology
  • Quick review of basic R functions


  1. The General Linear Model
  • Recasting the simple regression model in matrix notation
  • Estimating and inference for model parameters
  • Recasting the one-way ANOVA model in matrix notation
    • Factor coding methods
    • Orthogonal designs
    • Using contrast vectors to make to test specific hypotheses


  1. Statistical pre-processing of ecotox. data
  • Examination of alternative methods for computing ACRs (acute-to-chronic ratios)
  • Computation of an ‘optimal’ ACR
  • Testing for bi-modality in toxicity data
    • Explanation of ‘new’ methods in revised Australian and New Zealand Guidelines
    • Writing R functions to compute skewness, kurtosis, and bimodality coefficients
  • Procedures for checking distributional assumptions
  • Transforming data


  1. Concentration-Response Modelling
  • Taxonomy of C-R models including threshold models and models incorporating hormesis
  • Writing R functions and using intrinsic non-linear solvers to find maximum likelihood estimates of C-R model parameters
  • Exploration of features and capabilities of the R package drc
  • Using the C-R model to obtain a toxicity estimate together with its uncertainty


  1. New Methods for SSD Modelling
  • Issues with fitting probability distributions to toxicity data
    • Problems of identifiability
    • Curse of small sample sizes
  • Review of Burrlioz software – strengths and weaknesses
  • New approaches to fitting SSDs
    • Model averaging
    • Mixture modelling
    • Bayesian methods
  • Exploration of new on-line tools from Europe and North America
  • Correcting the HCx for species selection bias


  1. Optimal experimental design
  • Advanced techniques for determining the optimal spacing in a C-R experiment. Using R to determine:
    • Allocation of fixed experimental effort between control and test concentrations
    • D-Optimal designs for C-R experiments


Breakout topics

A1              Review of vectors and matrices

  • Special matrices
  • Matrix algebra
  • Solving systems of linear equation
  • Regression models in matrix notation

A2              Likelihood Estimation

  • Definition of likelihood function
  • Maximising the likelihood function for simple pdfs
  • Using R non-linear solvers to find maximum likelihood estimates for more complex cases