# ANALYSIS OF ECOLOGICAL DATA

## Learning outcomes of the course unit

The main objective of the course is to provide students with the

theoretical and practical knowledge to apply the correct scientific

method in ecology. Students learn to test various types of

models preparing a experiment to effectively analyzing and presenting

the data collected.

The interpretation emphasis of is always on the data in order to develop a critical concept of the ecological science, free from any bias.

The student will learn the theory and practical skills to analyze data

("Knowledge and understanding"), learns to apply them to new cases,

first during class and then independently ("applied knowledge and

understanding"), learns to draw his own statistically correct

conclusions based on data and assumptions and tested models ("Making

judgments") and finally learns how to graphically present the results

in an effective manner ("Communication skills"). Student's progression

towards autonomy also promotes the development of so-called "Ability

to learn."

## Prerequisites

Students should have passed an introductory statistic course or a

elementary probability course during the previous degree.

## Course contents summary

# Introduction to R

* Advantages over other statistical packages

* Variables (vectors, matrices, arrays, data frame, list)

* Functions

* Control structures

* Graphics

# "Classic" Statistical tests with R

* The student's t

* Non-parametric tests

* Chi-square

* A permutation tests

# Analysis of variance in ecology

* Snova as interpretative model of ecological processes

* Preparation of the data matrix

* The function lm R

* Analysis and interpretation of statistical interaction

* Checking the assumptions

# Introduction to algebra matrix

* The sum and the product of matrices

* The determinant

* The inverse matrix

# The linear regression with matrices

* The model Y = Xb + e

* "Normal" equations

* Applications with R

# The ANOVA with matrices

* Applications with R

* Experimental Design

# Nonlinear fitting

* The nls function of R

* Choice of three different models

# Multivariate Statistical

* Principal components analysis

* Cluster Analysis and Principal Coordinates Analysis

# Introduction to Maximum Likelihood and Bayesian statistics

## Course contents

# Introduction to R

* Advantages over other statistical packages

* Variables (vectors, matrices, arrays, data frame, list)

* Functions

* Control structures

* Graphics

# "Classic" Statistical tests with R

* The student's t

* Non-parametric tests

* Chi-square

* A permutation tests

# Analysis of variance in ecology

* Snova as interpretative model of ecological processes

* Preparation of the data matrix

* The function lm R

* Analysis and interpretation of statistical interaction

* Checking the assumptions

# Introduction to algebra matrix

* The sum and the product of matrices

* The determinant

* The inverse matrix

# The linear regression with matrices

* The model Y = Xb + e

* "Normal" equations

* Applications with R

# The ANOVA with matrices

* Applications with R

* Experimental Design

# Nonlinear fitting

* The nls function of R

* Choice of three different models

# Multivariate Statistical

* Principal components analysis

* Cluster Analysis and Principal Coordinates Analysis

# Introduction to Maximum Likelihood and Bayesian statistics

## Recommended readings

Online Lecture notes written by the teacher are available.

## Teaching methods

The course has a strong practical content. All students will have

a computer and each lesson consists of a short

theoretical introduction followed by practical analysis of

ecological data guided by the teacher or a teaching assistant. Some

topics will be presented with a deductive approach to learn the

general law from computer simulations of different peculiar cases.

## Assessment methods and criteria

The final grade is the result of the average of the score obtained by each

student with two different modes

- During the course, at the end of each lesson, the teacher assigns

homework to be done independently. Students

apply the notions to new situations in the classroom. By

specific questions, the student's critical thinking,

correct statistical interpretation of data, data support to the hypothesis

and the testing of assumptions are assessed.

- At the end of the course a practical examination is carried out in

student total verified autonomy. A simulation of a session analysis of data

obtained from one or more ecological experiments is carried out and students

present the results graphically in a correct and effective way.