1 Overview

The “growth models tutorials” will take place at Monday/Tuesday 6th and 7th February 2017. The idea is to open the door to the diverse field of mechanistic and statistical modelling of growth processes, especially for laboratory systems.

Prerequisites

A laptop with a recent version of R and Rstudio installed.
Basic knowledge of R and RStudio:

vectors, matrices, basic statistics
user-defined functions

The material below is from previuos workshops, to give you a first impression. Specific slides are still in preparation. The prerequitites are approximately at the level of sections 2.1 to 2.9 from http://www.simecol.de/courses/elements_en.pdf, in addition, you may have a look into:

You are welcome!

Thomas Petzoldt, TU Dresden, Institute of Hydrobiology

2 Schedule

2.1 Differential equations with R and the deSolve package

Monday 2017-02-06 15:00 – 17:00

Model specification
Solvers
Resource limited growth in a batch
A simple chemostat model
Optional: semi-continuous and turbidostat model (events and root finding)

Slides

ODE Growth models with package deSolve

Exercises

The selection of an exercise depends on your interest. The Chemostat model should be a good start.

Chemostat model
Nonstiff and stiff systems
Fit a two-compartment model
Compliled code
Plotting, forcing functions and other selected topics from the useR!Tutorial

2.2 Fitting growth models to data

Tuesday 2017-02-07 13:00 – 15:00

The heuristic “easy” method
Determination of \(\mu_{max}\) with smoothing splines
Parametric models: exponential, logistic, extended logistic, Baranyi
Outlook: fitting differential equation models

Slides

Growth curve fitting with package growthrates

Exercises

Introduction to growth rate estimation
Results (with figures)

Optional

Writing user defined functions
Results (with figures)

3 Background information

deSolve-Website: http://desolve.r-forge.r-project.org
TU Dresden, Institute of Hydrobiology http://tu-dresden.de/hydrobiologie
Modelling course Dresden 2015 http://www.simecol.de/modecol/dresden2015
My homepage

4 Examples

4.1 Example 1: Logistic growth model of learning (learning curve)

library("deSolve")

learning <- function(t, Knowledge, p) {
  with (as.list(p), {
    # knowledge increase
    dKnowledge <- rate*Knowledge*(1-Knowledge/maxKnowledge)
    list(dKnowledge)
  })
}
parms <- c (
   rate         = 0.1,    # rate at which new knowledge is acquired
   maxKnowledge = 1)      # maximal knowledge that can be acquired

# student 1
y1 <- c(Knowledge = 0.01)  # initial knowledge about the subject
times <- 1:100
out   <- ode(y = y1, times = times, parms = parms, func = learning)

# student 2: more initial knowledge
y2 <- c(Knowledge = 0.1)
out2  <- ode(y = y2, times = times, parms = parms, func = learning)

# student 3: good basic knowledge but too many other things
y3 <- c(Knowledge = 0.1)
parms2 <- parms; parms2["rate"] <- 0.05
out3  <- ode(y = y3, times = times, parms = parms2, func = learning)

plot(out, out2, out3)

4.2 Example 2: package growthrates

library("growthrates")

## Loading required package: lattice

data(bactgrowth)
splitted.data <- multisplit(bactgrowth, c("strain", "conc", "replicate"))

## Get table from single experiment
dat <- splitted.data[["D:0:1"]]

## (1) Spline fit
fit1 <- fit_spline(dat$time, dat$value, spar=0.5)

## derive start parameters from spline fit
p <- coef(fit1)

## (2) exponential model using the first 10 data points
first10 <-  dat[1:10, ]
fit2 <- fit_growthmodel(grow_exponential, p=p, time=first10$time, y=first10$value)

## (3) Logistic model for all data
p <- c(coef(fit1), K = max(dat$value))
fit3 <- fit_growthmodel(grow_logistic, p=p, time=dat$time, y=dat$value, transform="log")

plot(fit1)
lines(fit2, col="green")
lines(fit3, col="red")

https://tu-dresden.de/hydrobiology

Population Growth Models with R