The aim of this thesis is to investigate the signatures of evolutionary optimization in biological systems, such as in proteins, human behaviours and transport tissues in vascular plants (xylems), by means of the Pareto optimality analysis and the calculus of variations. In the first part of this thesis, we address multi-objective optimization problems with tradeoffs through the Pareto optimality analysis ( [132],[69]), according which the best tradeoff solutions correspond to the optimal species, enclosed onto low-dimensional geometrical polytopes, defined as Pareto optimal fronts, in the space of physical traits, called morphospace. Chapter 3 is devoted to the Pareto optimality analysis in the Escherichia coli proteome by projecting proteins onto the space of solubility and hydrophobicity. In chapter 4 we analyze the HCP dataset of cognitive and behavioral scores in 1206 humans, in order to identify any signature of Pareto optimization in the space of Delay Discounting Task (DDT), which measures the tendency for people to prefer smaller, immediate monetary rewards over larger, delayed rewards. The second part of this thesis is devoted to solving an optimization problem regarding xylems, which are the internal conduits in angiosperms that deliver water and other nutrients from roots to petioles in plants. Based on the optimization criteria of minimizing the energy dissipated in a fluid flow, we propose in chapter 5 a biophysical model with the goal of explaining the underlying physical mechanism that affects the structure of xylem conduits in vascular plants, which results in tapered xylem profiles [104, 105, 117, 164]. We address this optimization problem by formulating the model in the context of the calculus of variations. The results of these investigations, besides providing quantitative support to previous theories of natural selection, demonstrate how processes of optimization can be identified in different biological systems by applying statistical methods such as the Pareto optimality and the variational one, showing the relevance of employing these statistical approaches to various biological systems.