Biodiversity Modelling Summer School 2021: Biodiversity Modelling Summer School

Resources and exercises

hemlock growth

hemlock <- readr::read_delim(
  "https://raw.githubusercontent.com/bios2/biodiversity_modelling_2021/master/data/hemlock.txt", 
  delim = " ",
  col_names = c("x","light", "growth"), skip = 1)

knitr::kable(head(hemlock, n = 3))

x	light	growth
1	32.34929	118.2052
2	58.84066	138.0278
3	75.05452	185.7844

Sutton trees

sutton <- readr::read_csv2("https://raw.githubusercontent.com/bios2/biodiversity_modelling_2021/master/data/sutton.csv")

knitr::kable(head(sutton, n = 3))

y	abba	acpe	acsa	beal	bepa	fagr
0	1	55	11	7	0	92
100	0	5	4	3	0	6
120	2	7	12	4	1	7

States

states <- readr::read_delim("https://raw.githubusercontent.com/bios2/biodiversity_modelling_2021/master/data/transitions.txt",
                            delim = " ",
                            col_names = c("x","ID", "temp", "state1",
                                          "state2", "interval"),
                            skip = 1)

knitr::kable(head(states, n = 2))

x	ID	temp	state1	state2	interval
1	685303	3.609000	B	B	9
2	685016	4.701333	M	M	7

Gibbs Sampler Example: guided step-by-step approach for programming a gibbs sampler
Cumulative exercise in “collecting” a statistical distribution for use in practice.
Simulated annealing code, presented in 2 styles.
Metropolis hastings code
Grid search demo
Excercise problems

Slides and lecture materials

Probabilities and distributions

16 August

know your data, define your problem.

Univariate probability distributions

Continuous distributions

distribution	positive or negative?	Quick description
Normal	positive or negative values	Can result from many small effects added together
Lornormal	positive values only	results from many things multiplied together
Gamma	positive values only	can be the time to wait for a given number of things to happen
Exponential	Positive only	Lengths of time between random events
Beta	Positive only	Between 0 and 1. Can be any proportion.

Discrete distributions

distribution	positive or negative?	Quick description
Poisson	Positive	Counting things that occur randomly over time
Negative Binomial	Positive	Counts of things as in the Poisson, but more variable. Also: the number of trials till a certain number of successes.
Binomial	Positive	Number of “successes” out of a number of trials, when probability of success is always the same

Maximum likelihood methods

18 August

write down equations for your model.

Optimization

Once we know how to calculate likelihood, we can apply this to a very general statistical practice: how do we find parameters that maximize the likelihood of the data? this is an optimization problem

Bayesian statistics

Sampling algorithms