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Phylogenetic comparative methods often rely on simplifying complex biological traits into discrete categories, potentially obscuring evolutionary patterns and generally limiting inferences. This dissertation confronts this ``map versus territory" problem by developing and evaluating methodological approaches that integrate known and unknown trait complexity into macroevolutionary analyses. To establish the statistical power of discrete methods in detecting trait complexity, I first demonstrate the utility of structured hidden Markov models (SHMMs) for identifying underlying continuous architectures, like threshold traits, within simulated and empirical discrete datasets (Chapter ref{ch:1}). Taking bird migration as an example of a hard-to-measure complex trait, I then develop new continuous metrics of bird movement from large-scale community science (eBird) data, using entropy-based measures and phylogenetically aligned component analysis (PACA) to reveal a multi-dimensional structure of evolutionarily relevant combinations of traits, representing underlying movement behavior in North American birds (Chapter ref{ch:2}). Next, I fit SHMMs informed by this structure to global and North American bird phylogenies, testing hypotheses about how migration may have evolved, while accounting for classification ambiguity (Chapter ref{ch:3}). I show that models incorporating hidden states that imitate the structure from Chapter ref{ch:2} were often preferred over generalized hidden Markov models and standard Markov models, suggesting that migration both contains hidden complexity and evolves along specific pathways. Overall, this dissertation provides a methodological framework for integrating continuous data and theoretical knowledge into discrete trait analyses, demonstrating a more holistic treatment of how to treat complex discretized traits like avian migration in phylogenetic comparative methods. 

Vertebrate life histories evolve in response to selection imposed by abiotic and biotic environmental conditions while being limited by genetic, developmental, physiological, demographic and phylogenetic processes that constrain adaptation. Despite the well-recognized shifts in selective pressures accompanying transitions among environments, the conditions driving innovation and the consequences for life-history evolution remain outstanding questions. Here we compare the traits of vertebrates that occupy aquatic or terrestrial environments as juveniles to infer shifts in evolutionary constraints that explain differences in their life-history traits and thus their fundamental demographic rates. Our results emphasize the reduced potential for life-history diversification on land, especially that of reproductive strategies, which limits the scope of viable life-history strategies. Moreover, our study reveals differences between the evolution of viviparity in aquatic and terrestrial realms. Transitions from egg laying to live birth represent a major shift across life-history space for aquatic organisms, whereas terrestrial egg-laying organisms evolve live birth without drastic changes in life-history strategy. Whilst trade-offs in the allocation of resources place fundamental constraints on the way life histories can vary, ecological setting influences the position of species within the viable phenotypic space available for adaptive evolution.