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This paper introduces a novel multiscale dissimilarity measure, constructed by progressively refining transfer operators and accounting for finite-sampling uncertainty, to reconstruct phenotypic variation from behavioral data without pre-defined timescales. This dissimilarity defines a geometry of dynamical phenotypes, which are then mapped using diffusion maps, revealing that phenotypic coordinates align with directions of maximal dynamical sensitivity. The framework is validated on a stochastic model and applied to bacterial and larval zebrafish, identifying key behavioral drivers like run speed in bacteria and the impact of prey experience on zebrafish phenotypic space.
Prior prey experience dramatically reshapes larval zebrafish behavioral dynamics, concentrating them in a prey-capture-associated phenotypic space.
Behavioral variability reflects differences in internal and external parameters and provides a substrate for natural selection. However, uncovering its structure is challenging because behavior evolves nonlinearly across multiple timescales. Our goal is to reconstruct phenotypic variation from finite behavioral observations without prescribing the scales at which individuals should be compared. To achieve this, we introduce a multiscale dissimilarity that compares dynamics across all statistically resolvable resolutions by constructing reduced transfer operators at progressively finer scales and weighting their differences by finite-sampling uncertainty. This dissimilarity defines a geometry of dynamical phenotypes, which we reconstruct using diffusion maps. We show that the resulting phenotypic coordinates locally follow the parameter directions to which dynamics are most sensitive. We validate our approach in a stochastic model and apply it to bacterial and larval zebrafish behavior. In bacteria, we identify run speed as a major component of inter-individual variability, associated with the chemotaxis protein CheB. In zebrafish, we find that prior prey experience reshapes behavioral dynamics and phenotypic variability, with paramecia experience concentrating fish in a prey-capture-associated region of phenotypic space. Together, these results provide a framework for identifying internal and environmental variables that structure dynamical phenotypes across scales.