Thèse présentée en vue de l'obtention du grade de docteur en sciences et technologie. Lire la suite
Functional traits are phenotypic traits that affect organism's performance and shape ecosystem-level processes. However, estimating functional diversity as a measure of biodiversity remains difficult in practice. One of the main challenges is to choose which phenotypic traits should be considered functional and measured, since effort and money are limited. As one way of dealing with this, Hodgson et al. (1999) introduced the idea of two types of traits, with soft traits that are easy and quick to quantify, and hard traits that are directly linked to ecosystem functioning but difficult to measure. If a link exists between the traits, then one could use soft traits as a proxy for hard traits for a quick but meaningful assessment of biodiversity. However, this is usually limited by two factors : (1) traits must be tighly connected to allow reliable prediction of one using the other ; (2) the relationship between traits must be monotonic and linear to be detected by the most commonly used statistical techniques (e.g. linear model, PCA). Following that logic, my aim during this thesis was to test the presence of such relationships by focusing on six functional traits of the protist species Tetrahymena thermophila. In the first experiment, I tested the presence of these relationships using linear and non-linear relationship detection methods in a stable environment. Then, in the second experiment, I tested how these relationships were varying along two environmental gradients using similar detection methods. Both times, the traits were proved to be rather independent, indicating that each represents a distinct aspect of functional diversity for this organism, and a high number of non-linear relationships and patterns between the traits were detected, highlighting the need to be careful about what statistical techniques one uses to estimate relationships between traits.
Introduction 1
1 The theory of locally D-presentable categories 9
1.1 D-filtered categories . . . . . . . . . . . . . . . . . . . . . 9
- D-flat functors and sound doctrines . . . . . . . . . . . . 12
1.2 D-accessible categories . . . . . . . . . . . . . . . . . . . . 15
- The D-ind completion . . . . . . . . . . . . . . . . . . . 15
- The full subcategory of D-presentable objects . . . . . . 18
1.3 Locally D-presentable categories . . . . . . . . . . . . . . 22
- Restricting Yoneda . . . . . . . . . . . . . . . . . . . . . 25
1.4 D-completeness and Cauchy completeness . . . . . . . . . 26
2 The duality theorem for a limit doctrine 29
2.1 The duality Theorem . . . . . . . . . . . . . . . . . . . . . 29
- The 2-functor " . . . . . . . . . . . . . . . . . . . . . . . 29
- The objects of D-cont[A, set] . . . . . . . . . . . . . . . 32
- The 2-functor " is a biequivalence . . . . . . . . . . . . . 35
2.2 Some applications . . . . . . . . . . . . . . . . . . . . . . 39
- Comparing sound doctrines . . . . . . . . . . . . . . . . 39
2.3 A characterisation in terms of strong generators . . . . . . 54
- The Dop-colimit completion . . . . . . . . . . . . . . . . 55
- Strong generators play an important role . . . . . . . . . 56
- Consequences . . . . . . . . . . . . . . . . . . . . . . . . 62
3 On geometric morphisms and localizations of presheaf categories 69
3.1 Rambling about the concept of localization . . . . . . . . 69
- Exact and/or extensive categories . . . . . . . . . . . . . 70
- The exact completion of Fam . . . . . . . . . . . . . . . 75
- Some conditions our functors might satisfy . . . . . . . . 83
3.2 The localizations of presheaf categories . . . . . . . . . . . 87- Comparing conditions . . . . . . . . . . . . . . . . . . . 94
- A sheaf-theoretical proof . . . . . . . . . . . . . . . . . . 98
4 On geometric morphisms and localizations of algebraic categories 121
4.1 Algebraic theories and algebraic categories . . . . . . . . . 121
4.2 A miscellany of preliminary results . . . . . . . . . . . . . 125
4.3 Some more conditions our functors might satisfy . . . . . 127
4.4 The coproduct completion and the exact completion in the case of an algebraic theory . .. 131
4.5 The localizations of (one sorted) algebraic categories . . . 152
4.6 The link with other characterisation theorems for localizations of algebraic categories . . 166
Acknowledgements 177
Bibliography 181