index

Objective of the course

“train young researchers in building and analyzing mathematical models that will help them better understand ecological data”

Organizers

Nicolas Casajus (CESAB)
Vincent Calcagno
Emanuel A. Fronhofer
Isabelle Gounand
Claire Jacquet
Sonia Kéfi
François Massol

Organizers/helpers/guests

Nicolas Casajus (CESAB)
Vincent Calcagno
Emanuel A. Fronhofer
Isabelle Gounand
Claire Jacquet
Sonia Kéfi
François Massol
Peter Kamal (Tues)
Quentin Petitjean (Wed)
Peter B Adler (Guest Mon)
Benjamin Rosenbaum (Guest Tues)
Kevin Painter (Guest Wed)
Matthieu Barbier (Guest Thu)

Your turn!

name, position (PhD/post-doc/engineer), institute (location)

Program of the week: courses

Day 1 (9h-17h00): Introduction to theoretical modeling
- S. Kéfi, I. Gounand, V. Calcagno
- Guest: P.B. Adler
Day 2 (9h30-17h): Temporal series and dynamics in ecology
- E. Fronhofer and P. Kamal
- Guest: B. Rosenbaum
Day 3 (9h-17h): Spatial data, macro-ecology and co-occurrences
- V. Calcagno and Q. Petitjean
- Guest: K. Painter
Day 4 (9h-17h): Interaction networks, trophic networks and complexity in ecology
- F. Massol, C. Jacquet
- Guest: M. Barbier
Day 5 (9h-17h): Group projects (mornings), presentations (afternoon)

Program of the week: afternoon seminars

Day 1: Introduction to modeling and theory
- 17h30-18h30: Peter Adler (U. State University, USA)
Day 2: Temporal series and dynamics in ecology
- 17h30-18h30: Benjamin Rosenbaum (iDiv, Germany)
Day 3: Spatial data, macro-ecology and co-occurrences
- 17h30-18h30: Kevin Painter (Politecnico Torino)
Day 4: Interaction networks, trophic networks and complexity in ecology
- 17h30-18h30: Sonia Kéfi (CNRS, Montpellier)
Day 5: Group projects (mornings), presentations (afternoon)

Program of the week: group projects

Day 1 (9h-18h30): Introduction to theoretical modeling
- S. Kéfi, I. Gounand, V. Calcagno; Evening talk: S. Otto
Day 2 (9h-18h30): Temporal series and dynamics in ecology
- E. Fronhofer and P. Kamal; Evening talk: B. Rosenbaum
Day 3 (9h-18h30): Spatial data, macro-ecology and co-occurrences
- V. Calcagno and Q. Petitjean; Evening talk: K. Painter
Day 4 (9h-18h30): Interaction networks, trophic networks and complexity in ecology
- F. Massol, C. Jacquet; Guest: M. Barbier; Evening talk: S. Kéfi
Day 5 (9h-17h): Group projects (mornings), presentations (afternoon)

Program of today

Why theoretical models?

Big data

https://blog.digitalcook.fr/big-data-et-intelligence-artificielle/
Every day, humanity generates 2.5 trillion (2.5 billion billion) bytes of text, image and sound data.

Big data

https://www.theguardian.com/society/2023/apr/30/artificial-intelligence-tool-identify-cancer-ai

Big data

Do we still need models and theory?

What do you mean ‘theory’?

“Scientific theories contain universal or general propositions regarding the system in question.”

Maris et al., 2017

What do you mean ‘theory’?

“The transformation of an idea in narrative form into a logical, testable theory often, though not always, involves the use of models.”

Otto and Rosales, 2020

What are models?

If I say the word “model” what comes to your mind (everything, even not related to science)? (write on board) What are the common elements?

PICTURES: Models (Claudia Schiffer): https://www.yahoo.com/lifestyle/17-black-models-look-fashion-151000791.html?guccounter=1&guce_referrer=aHR0cHM6Ly93d3cuZ29vZ2xlLmNvbS8&guce_referrer_sig=AQAAAFBD4rb8N9Nr2Krbglih49HjGV5q0FypwuPz2nUuiHvAC8sPvzO1np6G8jrU-Bm4eWG2G6nygxw3kiARhqUjswZVRkjiydfIDn0sCNfooxZKhoL8iD9LrSqSpI3pLa24kr5fs8MdNh_fhOr5jyjBkwOrfpcpMXiRF8-LVXP2qyOn Photo: Jamie McCarthy / Staff (Getty Images)

miniatures: https://www.bloomberg.com/news/articles/2015-02-02/play-god-with-this-customizable-miniature-city

cars: https://www.anmodelcars.com/en/blog/top-10-des-voitures-miniatures-les-plus-cheres-au-monde–b13.html

maps: https://www.ionos.fr/digitalguide/web-marketing/vendre-sur-internet/placer-des-reperes-sur-google-maps/

mathematical models: https://robotnor.no/expertise/fields-of-competence/mathematical-modeling-for-control/ https://www.imperial.ac.uk/news/162709/researchers-develop-more-reliable-method-working/

What are models?

Models are simplified, idealized representations of reality.

What are models?

They can be:

verbal
conceptual (diagram of boxes and arrows)
quantitative/mathematical (sets of equations)

What are models?

Note: Theory and maths are not inexorably linked.

Many excellent theories do not involve maths (e.g., Darwin’s theory of evolution), and many uses of maths in ecology are not theory (e.g., practical applications of statistics).

What are models?

“All models are wrong, but some models are useful”

George E.P. Box, 1976

https://en.wikipedia.org/wiki/All_models_are_wrong

What are models?

Ecological systems are complex…

How to capture the complexity of reality?
We can’t!

What are models?

Modeling implies a choice about what to include and what to leave out.

What are models?

A tension between realism, generality, and precision.

Levins, 1966

https://v4.chriskrycho.com/2016/realism-generality-and-precision-in-tension.html We want to work with manageable models which max generality, realism and precision towards the goals of understanding and predicting…. But this cannot be done. These goals typically compete with each other so real models are mathematical descriptions that result from trade offs among these goals which depend on our needs (cf Levins 1966). - One can sacrifice generality to realism and precision. E.g. fisheries; good measurement of shot-time behavior, numerical solution, precise testable predictions applicable to a particular situation). - One can sacrifice realism to generality and precision. E.g. physics-like models (general equations such as LV) -> the way in which nature deviates from theory will indicate where further complexity will be useful. - One can sacrifice precision to realism and generality. E.g. MacArthur 1965. People concerned with the qualitative behavior (not quantitative). Graphical models. UNCLEAR

What are models?

An model type classification:

Why do we need models/theory?

What for?

understand
- e.g. provide a mechanistic explanation for how plants grow as fast or slowly as they do
predict
- e.g. make predictions about the population size in the future

Science aims to explain and understand. https://undsci.berkeley.edu/understanding-science-101/what-is-science/science-aims-to-explain-and-understand/ Understanding: linking phenomena that seem disconnected; finding associations that are causal and express them as laws (often in the form of math equations) –> explaining and unifying facts by integrating them in the rest of knowledge -> sc understanding requires distinguishing causal from non-causal correlations “In addition, if it is to be useful, an acceptable modern theory must be able to turn data into predictions at a later time before those predictions become a reality. If, for example, data about a patient are to be used to guide medical care, then predictions about the impact of various treatments have to be both accurate and timely.” (Coveney et al. 2016 Phil A)

Models do not investigate nature. Instead, they investigate the validity of our own thinking. Models are ‘thinking aids’. They exist because we need them to help us explore things: none of us was born with a supercomputer (P. 8 Kokko). The most important function of models is to order our thoughts. With models, we formulate what we (think we) know about the world, and we may use them to perform thought experiments through ‘what if’ scenarios. Modèle = experimentation pour poser des questions. In sum, models allow to explore ideas that might not be doable experimentally or for financial reasons.

Another important use of models is to function as an idealization of the world. Models force us to make a choice concerning which aspects of ‘the real world’ we include into our description, and which ones we choose to ignore (for the moment). This is true for verbal as well as mathematical models. Mathematical formulations reveal implicit assumptions and thus force us to be explicit. The translation of ideas in a theoretician’ s mind into math on a page serves several purposes:

Note that the choice made on what to sacrifice might depend on the stage of a research program: At the conceptual stage of research models are used to further develop theory. Models allow to do thoughts experiments. ‘All else being equal’ what is the effect of a certain factor or process? Conceptual models are thinking aids rather than investigations of real phenomena. At the other extreme lies the practical stage, where models are used to closely examine real-life phenomena. At the practical stage models are used for purposes such as inference from empirical data, making quantitative predictions concerning future system dynamics, or effects of studied factors, and guiding management decisions. These models comprise ‘statistical’ models, ‘computer models’, etc. Their aim is to make accurate statements about the studied system given the circumstances in the real world.

Big data

reveal correlations
but correlations are not causality

Big data

https://www.tylervigen.com/spurious-correlations

Big data

do not distinguish causal from non-causal correlations
do not translate readily into understanding
can still be predictive!

Causal blindness: Big data does not allow to distinguish causal from non-causal correlation p. 111 –> there is a correlation but we don’t know why. They offer no structural explanation for the correlations. So we can find correlations, but we often don’t know why. So we can’t understand (understanding is finding associations that are causal). Data do not translate readily into understanding.

This does not mean big data (corr non causales) don’t have predictive power: they do! p. 73 Amazon, Netflix So we can learn from those data and their analysis, even without causal knowledge.

–> des connaissances peuvent émerger sans qu’on connaisse les lois, meme sans connaissance causale, fort pouvoir prédictif p.103 (parfois supérieur à causalité surtout quand inconnue, sans théorie)

Big data

BUT:

predictions can fail
predict without understanding…. act without understanding?

extrapolation incapacity - Pb of extrapolating beyond the range of existing data la machine ne prévoit que sur la base de ce qu’elle connait p. 107 It learns from what is sees. No matter their ‘depth’ and the sophistication of data-driven methods, such as artificial neural nets, in the end they merely fit curves to existing data. They may be capable of effective interpolation, but not of extrapolation beyond their training domain. –> it therefore really bad at predicting new situations/new context –> then bad extrapolation. –> incapable of true predictions ie of events in new circumstances or of events before they occur (ie not post hoc explanations) Financial crashes, elections in the US, 2007 subprime crisis in the US (very singular economic situation) –> Big data approaches can fail in circumstances beyond the range of the data used to train them because they are not designed to model the structural characteristics of the underlying system. We do not predict tomorrow’s weather by averaging historic records of that day’s weather. Mathematical models (essentially solving Navier–Stokes equations) do a much better job with real-time data from satellites and other sensors.

https://theconversation.com/six-ways-and-counting-that-big-data-systems-are-harming-society-88660 Some are raising concerns about how new uses of big data may negatively influence people’s abilities get housing or insurance – or to access education or get a job. And there are numerous reports of facial recognition systems that have problems identifying people who are not white. As argued here, this issue becomes increasingly important as facial recognition tools are adopted by government agencies, police and security systems. This kind of discrimination is not limited to skin colour. One study of Google ads found that men and women are being shown different job adverts, with men receiving ads for higher paying jobs more often. And data scientist Cathy O’Neil has raised concerns about how the personality tests and automated systems used by companies to sort through job applications may be using health information to disqualify certain applicants based on their history. There are also concerns that the use of crime prediction software can lead to the over-monitoring of poor communities, as O’Neil also found. The inclusion of nuisance crimes such as vagrancy in crime prediction models distorts the analysis and “creates a pernicious feedback loop” by drawing more police into the areas where there is likely to be vagrancy. This leads to more punishment and recorded crimes in these areas.

(because lacks of general rules, so extrapolations can fail; financial crisis, elections) mais prévoir sans comprendre –> agir sans comprendre ? Commerce ok mais justice, police…. p. 74 attention quand on ne cherche plus à comprendre mais à prédire et prévenir: danger p. 115, p. 119 Risks (cf justice, police, discriminations)

Big data don’t create theory, they need it to be exploited p. 111

Il n’est pas exclu que le big data avec les progrès des analyses puissent faire ça dans le futur p. 122 (de nouvelles analyses permettront peut-être d’abolir cette distinction corrélation-causalité p. 103)

Big data

do we still need models and theory?
yes!

Krivine p. 59: ” Une bonne théorie fait plus que résumer une masse de données empiriques, elle explique et anticipe des phénomènes inconnus”. Big data does not create understanding (first obj of science) and can fail at predicting (second obj). for next slide: - Not all data is reliable (pb to rely on various sources of data). Risk-assessment algorithms like COMPAS, used in U.S. courtrooms to predict recidivism, disproportionately labeled Black defendants as high-risk. The training data reflected existing racial biases in arrest and sentencing rates, leading to harsher outcomes for minorities - correlation is not a evidence of dependency (spurious correlations) - We need theory to help guide collection, curation and interpretation of data. - big data don’t create theory; they need theory to be exploited - (Note: this last statement could evolve in the future)

Big data

The scientific method

problem identification
hypothesis
prediction
testing
refinement

The scientific method is an empirical method for acquiring knowledge that has characterized the development of science since at least the 17th century.

Science (through the scientific method) can build on previous knowledge and develop a more sophisticated understanding of its topics of study over time.

‘Problem’ identification: It involves careful observation which leads to the formulation of a question.
Hypothesis: A hypothesis is a conjecture (hypothetical explanations), based on the observation/the knowledge obtained while formulating the question, that may explain any given behavior. A scientific hypothesis must be falsifiable, implying that it is possible to identify a possible outcome of an experiment or observation that conflicts with predictions deduced from the hypothesis; otherwise, the hypothesis cannot be meaningfully tested. Falsifiability is a deductive standard of evaluation of scientific theories and hypotheses, introduced by the philosopher of science Karl Popper in his book The Logic of Scientific Discovery (1934). A theory or hypothesis is falsifiable (or refutable) if it can be logically contradicted by an empirical test.
Prediction: The prediction step deduces the logical consequences of the hypothesis before the outcome is known.
Testing: Hypotheses are tested by conducting experiments or gathering observations. The purpose of the test is to determine whether observations agree with or conflict with the expectations deduced from a hypothesis.
Refinement (or elimination) of the hypotheses based on the experimental findings.

Although procedures vary from one field of inquiry to another, the underlying process is frequently the same. In sum, the process is as follows: making conjectures (hypotheses), deriving predictions from them as logical consequences, and then carrying out experiments based on those predictions to determine whether the original conjecture was correct.

The scientific method

The scientific method is an iterative, cyclical process through which information is continually revised.
A feedback loop involving data and models.
“Perception without conception is blind; conception without perception is empty” Kant, 1781

A scientific understanding of the biological world arises when ideas about how nature works are formalized, tested, refined, and then tested again.

Scientific inquiry should operate as a feedback loop in which theory that describes the natural world is developed, tested empirically through carefully articulated hypotheses, modified to better represent reality, and then tested again.

When this feedback loop works, theory provides a framework to guide inquiry, experimental design, and the interpretation of observed patterns, supplies mathematical tools to harness information from collected data, and connects individual experiments to general ideas about how nature operates.

In turn, empirical research can be used to support, refute, or revise theoretical predictions, indicate which theoretical assumptions are consistent with the natural world, and point theoreticians to overlooked processes that can be integrated into models.

BUT

A current disconnection between theoretical and empirical research.

45% of articles on empirical ecology make no mention of any theory (Scheiner 2013)
fewer than 10% of ecologists and evolutionary biologists agree with the statement that ‘theoretical findings drive empirical work’ in their fields (Haller 2014)

Why this disconnection?

A lack of theoretical training in ecology (Rossberg et al. 2019).
A lack of motivation from some theoreticians to engage with the language of empiricists (Grimm 1994) or with the elements of nature that empiricists focus on (Krebs 1988).
A lack of mutual appreciation between empiricists and theoreticians (Haller 2014).
Persistent communication barriers (Servedio 2020).

This barrier presents a major challenge to the full integration of theoretical and empirical work in ecology.
A better integration of theory into empirical work is needed!
This is especially important in the context of global change.
- Hence this course!

Objective of the course

Organizers

Organizers/helpers/guests

Your turn!

Program of the week: courses

Program of the week: afternoon seminars

Program of the week: group projects

Program of today

Why theoretical models?

Big data

Big data

Big data

Big data

What do you mean ‘theory’?

What do you mean ‘theory’?

What are models?

What are models?

What are models?

What are models?

What are models?

What are models?

What are models?

What are models?

What are models?

Why do we need models/theory?

Big data

Big data

Big data

Big data

Big data

Big data

The scientific method

The scientific method

BUT

Why this disconnection?

Thanks