1. Simulations and programming in R

2. Why to simulate and program in R at all? ADVANTAGES –All R facilities can be used in the simulations Random number generators Easy to create own R-functions –Simulation results are readily in R to be visualized and analyzed DISADVANTAGES –Loops may be slow Alternative solution –Compile C-code under R

3. Random numbers Random numbers are numbers drawn from a specific probability distribution Area of a bar approximates the probability of getting a number in that interval. These probabilities sum up to one.

4. Most common distributions CONTINUOUS Normal distribution: e.g. weight and length of an individual Exponential distribution: 'waiting time', e.g. lifetime of an individual Uniform distribution: flat distribution, i.e. values do not concentrate around some peak but are spread randomly within an interval DISCRETE Poisson distribution: number count, e.g. number of fish caught Binomial: 0 or 1, e.g. outcome of tossing coin, choice to metamorphose or not (Multinomial: same as binomial except more than two possible outcomes)

5. Random number generators Random number tools for normal distribution –rnorm() random number generator –dnorm() density function (probability function for discrete distributions) –pnorm() distribution function –qnorm() quantile function Similarly for binomial, Poisson, exponential, multinomial, uniform distributions… (and many others), e.g. –runif(), rexp(), rpois(), rbinom() -> DEMO 1

6. Creating an R-function “Name of the function” = function ( input parameters ){…} Procedures to be carried out All the input stuff needed for the procedures the function will perform DEMO 2

7. Basic programming loops in R Much of simulations is based on three loops: for ( ‘index’ in ‘index vector’ ) {…} –Repeats the procedure for all the indices while (‘a logical proposition’) {…} –Repeats the procedure until the logical proposition is FALSE if (‘a logical proposition’) {…} else {…} –If the condition holds, does the first procedure, otherwise the second. DEMO 3