Introduction

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# Model evaluation with ecological data

## Introduction

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

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# Let's start with a simple problem

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

What could you tell from the data ?

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# Let's start with a simple problem

How would you fit a curve into this ?

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# Let's start with a simple problem

What equation to pick ?

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

What are the uncertainties in your model ?

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# Let's start with a simple problem

What will happen if we sample more ?

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# Let's start with a simple problem

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

*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

*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

*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

*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 ?

*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 ?

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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