Les superpositions d'ondes modulées en amplitude et en fréquence (modes AM--FM) sont couramment utilisées pour modéliser de nombreux signaux du monde réel : cela inclut des signaux audio (musique, parole), médicaux (ECG), ou diverses séries temporelles (températures, consommation électrique). L'objectif de ce travail est l'analyse et la compréhension fine de tels signaux, dits "multicomposantes" car ils contiennent plusieurs modes. Les méthodes mises en oeuvre vont permettre de les représenter efficacement, d'identifier les différents modes puis de les démoduler (c'est-à-dire déterminer leur amplitude et fréquence instantanée), et enfin de les reconstruire. On se place pour cela dans le cadre bien établi de l'analyse temps-fréquence (avec la transformée de Fourier à court terme) ou temps-échelle (transformée en ondelettes continue). On s'intéressera également à une méthode plus algorithmique et moins fondée mathématiquement, basée sur la notion de symétrie des enveloppes des modes : la décomposition modale empirique. La première contribution de la thèse propose une alternative au processus dit ``de tamisage'' dans la décomposition modale empirique, dont la convergence et la stabilité ne sont pas garanties. \`A la place, une étape d'optimisation sous contraintes ainsi qu'une meilleure détection des extrema locaux du mode haute fréquence garantissent l'existence mathématique du mode, tout en donnant de bons résultats empiriques. La deuxième contribution concerne l'analyse des signaux multicomposantes par la transformée de Fourier à court terme et à la transformée en ondelettes continues, en exploitant leur structure particulière ``en ridge'' dans le plan temps-fréquence. Plus précisément, nous proposons une nouvelle méthode de reconstruction des modes par intégration locale, adaptée à la modulation fréquentielle, avec des garanties théoriques. Cette technique donne lieu à une nouvelle méthode de débruitage des signaux multicomposantes. La troisième contribution concerne l'amélioration de la qualité de la représentation au moyen de la ``réallocation'' et du ``synchrosqueezing''. Nous prolongeons le synchrosqueezing à la transformée de Fourier à court terme, et en proposons deux extensions inversibles et adaptées à des modulations fréquentielles importantes, que nous comparons aux méthodes originelles. Une généralisation du synchrosqueezing à la dimension 2 est enfin proposée, qui utilise le cadre de la transformée en ondelettes monogène. / Many signals from the physical world can be modeled accurately as a superposition of amplitude- and frequency-modulated waves. This includes audio signals (speech, music), medical data (ECG) as well as temporal series (temperature or electric consumption). This thesis deals with the analysis of such signals, called multicomponent because they contain several modes. The techniques involved allow for the detection of the different modes, their demodulation (ie, determination of their instantaneous amplitude and frequency) and reconstruction. The thesis uses the well-known framework of time-frequency and time-scale analysis through the use of the short-time Fourier and the continuous wavelet transforms. We will also consider a more recent algorithmic method based on the symmetry of the enveloppes : the empirical mode decomposition. The first contribution proposes a new way to avoid the iterative ``Sifting Process'' in the empirical mode decomposition, whose convergence and stability are not guaranteed. Instead, one uses a constrained optimization step together with an enhanced detection of the local extrema of the high-frequency mode. The second contribution analyses multicomponent signals through the short-time Fourier transform and the continuous wavelet transform, taking advantage of the ``ridge'' structure of such signals in the time-frequency or time-scale planes. More precisely, we propose a new reconstruction method based on local integration, adapted to the local frequency modulation. Some theoretical guarantees for this reconstruction are provided, as well as an application to multicomponent signal denoising. The third contribution deals with the quality of the time-frequency representation, using the reassignment method and the synchrosqueezing transform: we propose two extensions of the synchrosqueezing, that enable mode reconstruction while remaining efficient for strongly modulated waves. A generalization of the synchrosqueezing in dimension 2 is also proposed, based on the so-called monogenic wavelet transform.

Aposematic signals advertise chemical defense or other forms of unprofitability to predators and may be parasitized by dishonest signallers through Batesian mimicry. Warning signals do not provide perfect avoidance, however, meaning many aposematic phenotypes evolve to balance between signal saliency and mitigating detection. For Batesian mimics the cost of a predator encounter should be greater, which begs the question of whether imperfect mimicry leads Batesian mimics to exhibit more muted signals than their models. I sought to test this hypothesis and other related hypotheses using the Ameerega-Allobates poison frog mimicry complex native to the Ecuadorian Amazonian rainforest. In Chapter 2 I found that, while many elements of the mimic’s signal were less salient than in the model, the mimic had higher detectability than the model. I also found that saliency discrepancies across colour patches produced variation in detectability across different body postures and viewing angles in both species. In Chapter 3 I turned my focus to how the balance between cryptic and salient signal elements changes across ontogeny, and how shifts in that balance may affect detectability. I found that both species undergo ontogenetic colour change, with the mimic improving in resemblance to the model as it developed and the model refining its aposematic signal as it grew. These colour changes impacted the crypsis efficacy of the mimic in that different colour stages had differential detectability. In Chapter 4 I tested for behavioural associations with the ontogenetic increase in mimetic fidelity in Al. zaparo. I found that colouration alone did not explain variation in behaviour, and that body size and environmental conditions impacted boldness and activity. / Dissertation / Doctor of Philosophy (PhD) / Antipredator colouration can take many different forms and can function according to different underlying strategies. Crypsis, also known as camouflage, operates by evading detection – effective crypsis means that predators don’t see the prey in the first place, increasing the prey’s survival. Using crypsis as an antipredator strategy means that a species should only occupy space where its colours blend in, however, and when hiding from predators it’s difficult to attend to other ecological needs like foraging, conquering and/or defending territory, or pursuing reproduction. These opportunity costs are thought to be reduced under aposematism, or ‘warning colouration’, where an animal evolves bright colouration that advertises some sort of secondary defense like toxic stings or secretions. Aposematic protection stems from standing out in the environment and being distinguishable from other prey, providing reduced predator attention across contexts such as foraging, reproduction, thermoregulation, or simple movement throughout the environment. These benefits can then be parasitized by a dishonest ‘mimic’ species which has no chemical defense but copies the warning signal of a ‘model’. Warning signal protection isn’t perfect, however, and most aposematic species still experience some form of predation threat. This means that there may be a limit to how conspicuous a signal an aposematic species is favoured to evolve. Accordingly, evidence shows that aposematic species incorporate both cryptic and aposematic elements into their colouration. The aim of this thesis is to examine how this balance is achieved by a poison frog and a non-toxic mimic, how this balance may change across development, and whether there are behavioural implications of changes in colour strategy. I found that both species have evolved a salient colour patch that they can flexibly expose or hide to modulate their detectability. I also found that the balance between crypsis and aposematism in the mimic and model shifts over time through developmental colour change. Lastly, I found that body size and environmental conditions affect behaviour in developing individuals of the mimic species.