01_introduction.Rmd

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title: "Introduction"
author: "Dominique Gravel"
date: "August 16th, 2021"
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# Model evaluation with ecological data

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## Introduction

<hr width="65%" align="left" size="0.3" color="orange" style="margin-bottom:40px;" alt="@Martin Sanchez"></hr>

.instructors[
  **ECL707/807** - Dominique Gravel
]

<img src="assets/img/logo.png" width="25%" style="margin-top:20px;"></img>

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# Let's start with a simple problem  

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  <img src="assets/img/coates.png" width="300px"></img>
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Coates and Burton (1999) studied the effect of light availability on the annual height increment as a function of an index of light availability, 5 years after they were planted. 

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# Let's start with a simple problem  

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  <img src="assets/img/coates.png" width="300px"></img>
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What could you tell from the data ? 

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# Let's start with a simple problem  

<div style='text-align:center;'>
  <img src="assets/img/coates.png" width="300px"></img>
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How would you fit a curve into this ? 

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# Let's start with a simple problem  

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  <img src="assets/img/coates.png" width="300px"></img>
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What equation to pick ?

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# Now try it !
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# Let's start with a simple problem  

<div style='text-align:center;'>
  <img src="assets/img/coates.png" width="300px"></img>
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What are the uncertainties in your model ?

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# Let's start with a simple problem  

<div style='text-align:center;'>
  <img src="assets/img/coates.png" width="300px"></img>
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What will happen if we sample more ?

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# Let's start with a simple problem  

<div style='text-align:center;'>
  <img src="assets/img/coates.png" width="300px"></img>
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Can we reduce this uncertainty ? 

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# Why to develop modelling skills ?

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# Develop innovative methods

Objective : detect events of suppression and release of understory saplings using time series

<div style='text-align:center;'>
  <img src="assets/img/canham.png" width="600px"></img>
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*Gravel et al. 2010. Large-scale synchrony of gap dynamics and the distribution of understory tree species in maple-beech forests. Oecologia 162 : 153-161.*

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# Complex probabilistic problems 

Objective : evaluate a logistic model with presence only-data

<div style='text-align:center;'>
  <img src="assets/img/bartomeus.png" width="850px"></img>
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*Bartomeus et al. 2016. A common framework for identifying linkage rules across different types of interactions. Functional Ecology 30: 1894-1903*

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# Complex probabilistic problems 

Objective : evaluate non-stationary auto-regressive multivariate models

<div style='text-align:center;'>
  <img src="assets/img/autoregression.png" width="800px"></img>
</div>

*Gravel et al. Evidence of critical slowing down of interaction networks before physiological meltdown. In prep.*

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# Transfer of information across scales

Objective : make sure that a species distribution model evaluated at continental scale is coherent with experiments done at the micro scale

<div style='text-align:center;'>
  <img src="assets/img/talluto.png" width="800px"></img>
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*Talluto et al. 2016. Cross-scale integration of knowledge for predicting species ranges : a metamodelling framework. Global Ecology and Biogeography 25 : 238-249.* 

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# Use all information available 

Objective : how to evaluate mortality rate of rare tropical trees with very few observations ?

<div style='text-align:center;'>
  <img src="assets/img/soberania.jpg" width="250px"></img>
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*Condit et al. 2006. The importance of dempraphic niches to tree diversity. Science 313: 98-101.*

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# Other motivations

- Philosophical motivation
- Representation of uncertainty
- Adaptive modelling
- Better understand statistics

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# What about you ?

<hr width="65%" size="0.3" color="orange" style="margin-top:-20px;"></hr>

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# Logistics

- On site and remote teaching
- Lectures are recorded
- Priority to exercises and problems
- Minimal interactive lectures
- Participation 

Any other suggestion ?

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# Content

1. Probabilities
2. Maximum likelihood estimation
3. Algorithms for optimization
4. Bayesian models
5. Algorithms for posterior distributions

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# Expectations

- Write down an equation for likelihood and code it in R
- Develop an algorithm to find the maximum likelihood estimates
- Have some notions of the philosophies of satistical inferrence
- Develop the full equation for the posterior distribution 
- Estimate posterior distribution by MCMC for a simple regression problem

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# Evaluation

- Pass or fail based on participation and progress
- Auto-evaluation form at the end of the course
- Possibility of doing a supervised project as a side