Seed germination: fitting hydro-time models with R

Published at March 23, 2020 ·  17 min read

I am locked at home, due to the COVID-19 emergency in Italy. Luckily I am healthy, but there is not much to do, inside. I thought it might be nice to spend some time to talk about seed germination models and the connections with survival analysis. We all know that seeds need water to germinate. Indeed, the absorption of water activates the hydrolytic enzymes, which break down food resources stored in seeds and provide energy for germination....

A collection of self-starters for nonlinear regression in R

Published at February 26, 2020 ·  29 min read

Usually, the first step of every nonlinear regression analysis is to select the function \(f\), which best describes the phenomenon under study. The next step is to fit this function to the observed data, possibly by using some sort of nonlinear least squares algorithms. These algorithms are iterative, in the sense that they start from some initial values of model parameters and repeat a sequence of operations, which continuously improve the initial guesses, until the least squares solution is approximately reached....

Self-starting routines for nonlinear regression models

Published at February 14, 2020 ·  8 min read

In R, the drc package represents one of the main solutions for nonlinear regression and dose-response analyses (Ritz et al., 2015). It comes with a lot of nonlinear models, which are useful to describe several biological processes, from plant growth to bioassays, from herbicide degradation to seed germination. These models are provided with self-starting functions, which free the user from the hassle of providing initial guesses for model parameters. Indeed, getting these guesses may be a tricky task, both for students and for practitioners....

Some everyday data tasks: a few hints with R (revisited)

Published at January 28, 2020 ·  12 min read

One year ago, I published a post titled ‘Some everyday data tasks: a few hints with R’. In that post, I considered four data tasks, that we all need to accomplish daily, i.e. subsetting sorting casting melting In that post, I used the methods I was more familiar with. And, as a long-time R user, I have mainly incorporated in my workflow all the functions from the base R implementation....

Nonlinear combinations of model parameters in regression

Published at January 9, 2020 ·  11 min read

Nonlinear regression plays an important role in my research and teaching activities. While I often use the ‘drm()’ function in the ‘drc’ package for my research work, I tend to prefer the ‘nls()’ function for teaching purposes, mainly because, in my opinion, the transition from linear models to nonlinear models is smoother, for beginners. One problem with ‘nls()’ is that, in contrast to ‘drm()’, it is not specifically tailored to the needs of biologists or students in biology....

Fitting 'complex' mixed models with 'nlme': Example #4

Published at September 13, 2019 ·  10 min read

Testing for interactions in nonlinear regression Factorial experiments are very common in agriculture and they are usually laid down to test for the significance of interactions between experimental factors. For example, genotype assessments may be performed at two different nitrogen fertilisation levels (e.g. high and low) to understand whether the ranking of genotypes depends on nutrient availability. For those of you who are not very much into agriculture, I will only say that such an assessment is relevant, because we need to know whether we can recommend the same genotypes, e....

Fitting 'complex' mixed models with 'nlme': Example #3

Published at September 13, 2019 ·  11 min read

Accounting for the experimental design in regression analyses In this post, I am not going to talk about real complex models. However, I am going to talk about models that are often overlooked by agronomists and biologists, while they may be necessary in several circumstances, especially with field experiments. The point is that field experiments are very often laid down in blocks, using split-plot designs, strip-plot designs or other types of designs with grouping factors (blocks, main-plots, sub-plots)....

Fitting 'complex' mixed models with 'nlme': Example #2

Published at September 13, 2019 ·  9 min read

A repeated split-plot experiment with heteroscedastic errors Let’s imagine a field experiment, where different genotypes of khorasan wheat are to be compared under different nitrogen (N) fertilisation systems. Genotypes require bigger plots, with respect to fertilisation treatments and, therefore, the most convenient choice would be to lay-out the experiment as a split-plot, in a randomised complete block design. Genotypes would be randomly allocated to main plots, while fertilisation systems would be randomly allocated to sub-plots....

Fitting 'complex' mixed models with 'nlme'. Example #1

Published at August 20, 2019 ·  9 min read

The environmental variance model Fitting mixed models has become very common in biology and recent developments involve the manipulation of the variance-covariance matrix for random effects and residuals. To the best of my knowledge, within the frame of frequentist methods, the only freeware solution in R should be based on the ‘nlme’ package, as the ‘lmer’ package does not easily permit such manipulations. The ‘nlme’ package is fully described in Pinheiro and Bates (2000)....

Germination data and time-to-event methods: comparing germination curves

Published at July 20, 2019 ·  11 min read

Very often, seed scientists need to compare the germination behaviour of different seed populations, e.g., different plant species, or one single plant species submitted to different temperatures, light conditions, priming treatments and so on. How should such a comparison be performed? Let’s take a practical approach and start from an appropriate example: a few years ago, some collegues studied the germination behaviour for seeds of a plant species (Verbascum arcturus, BTW…), in different conditions....