Organization of specialized course from 24th to 28th February 2020 about Qualitative Mathematical Modelling of Complex Socio-Ecological Systems at the Institute of Marine Science (ICM-CSIC), Barcelona, Spain.

Teacher: Dr. Jeffrey Dambacher (CSIRO, Hobart, Tasmania).

The course was an event of MarCons COST Action.

Summary:

Qualitative mathematical modelling was introduced as a means to understand and predict the dynamics of complex biological and socio-economic systems.

The technique poses the question: if all we know of a system is the general nature of the relationships between species and environmental or human variables, but not the precise intensity of these interactions, then what do we know?

It turns out that we know not everything, but quite a lot. Qualitative mathematical modelling describes complex systems through only the sign (0, +, -) of the effect or interactio

n between variables, and thus can easily include variables and processes that are important, yet difficult to measure.

Calculations of system stability and predictions of perturbation response proceed through analysis of the feedback properties of a system.

While model predictions are imprecise, there are nonetheless rigorously derived and readily testable.

This approach leads to many interesting, practical, multidisciplinary, and surprisingly overlooked applications to complex dynamical systems.

Coursework was divided between lecture and use of modelling software (provided); students will need access to computer laptops (or share with a partner) and at times will work in groups on applied problems.

Topics covered in the course included:

• Introduction, history and philosophy
• Derivation of community (Jacobian) matrix & defining relevant subsystem
• Modified (nonlinear) interactions & split variables
• Model building examples (Yellowstone Park wolves & urchin barrens)
• Press perturbation analysis
• Socio-economic & biophysical systems
• Qualitative measures of Lyapunov stability
• Predicting change in life expectancy
• Application to Bayes nets

From the 1st to the 4th of July 2019, we organized the first Stable Isotope Course Applied to Trophic Studies at the Institute of Marine Science (ICM-CSIC), Barcelona, Spain.

Instructors: Dr. Joan Giménez & Dr. Joan Navarro (ICM-CSIC) and Dr. Fran Ramírez (Universitat de Barcelona)

Organization of specialized course from the 27^th February to 2^nd March 2018, at the Institute of Marine Science (ICM-CSIC), Barcelona, Spain.

Teacher: Dr. Maria Gracia Pennino, Dr. David Conesa, Dr. Joaquín Martínez Minaya

Species Distribution Models (SDMs) are now widely used in many research fields for several purposes across terrestrial, freshwater, and marine realms. In all these contexts, the main issue is to link information on the presence/absence or abundance of a species to environmental variables to predict where (and how much of) a species is likely to be present in unsampled locations or time periods. In ecology, SDMs have been implemented in different theoretical and practical cases, including the identification of critical habitats, the study of the risk associated with invasive species, the potential effects of climate change, the design of protected areas and delineation of hot spots of biodiversity and species richness.
Many algorithms of spatial distribution models can be used to predict the distribution of species, however, these algorithms do not always provide accurate results as data can includes a large amount of variability and errors due to multiple factors (errors in the identification of the species, errors in taking the geographical coordinates , etc.). In this context, Bayesian spatial-temporal methods have several advantages over traditional ones, since they provide a more realistic and accurate estimate of uncertainty.

Objective: The general objective of this course is to provide a critical view of the existing techniques of species distribution models with a frequentist and Bayesian approach, discussing their strengths and limitations. At the end of the course, participants will learn about:

1. Formal knowledge about the main statistical approaches relating to SDMs;
2. Specific examples of SDMs with different model algorithms (GAMs, Random Forest, Boosted Regression Trees) using a frequentist approach;
3. An introduction to the Bayesian inference and modeling framework;
4. Specific examples of SDMs using a Bayesian approach