# Biodiversity Modelling Summer School

Evaluating ecological models with data

Dominique Gravel, Ph.D. (Université de Sherbrooke) , Andrew MacDonald, Ph.D. (Université de Sherbrooke) , Willian Vieira, M. Sc. (Université de Sherbrooke)
2021-08-16

## 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)

``````
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")

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

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

## Slides and lecture materials

Probabilities and distributions

16 August

#### 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