Letter to the Editor Regarding Castagna et al 2021

Castigliano's theorem analyzes displacements and rotations in elastic structures. It relates the derivative of elastic strain energy to the applied forces or moments, allowing for the calculation of deformations. The theorem states that the partial derivative of the total strain energy of a system with respect to a specific load results in the displacement at the point where the load is applied. This principle applies to both forces and moments.

Biochemical reactions are occurring constantly in cells, converting starting substances to different products, usually with the help of enzymes that speed the reactions. Without enzymes, it would take far too long for most reactions to occur to be useful to the cell!

Most altruistic behavior—in which one animal helps another at a cost to themselves—occurs between relatives. Scientists think these altruistic behaviors evolved because they increase the inclusive fitness of the animal providing help.

Altruistic behaviors are “unselfish” behaviors—those that help another individual at the expense of the individual carrying out the behavior. Despite the negative consequences for the altruistic animal, these behaviors are thought to have evolved for several reasons.

Overview

Organisms that are well-adapted to their environment are more likely to survive and reproduce. However, natural selection does not lead to perfectly adapted organisms. Several factors constrain natural selection.