Relationship between Reactance and phase distribution of an antenna element

In Yagi -Uda antennas; the inductive nature of element is given to the reflector by choosing a length greater than resonant length; And for the director capacitive nature is given by choosing its length shorter than the resonant length; to acheive directivity of beam. What is the relationship between them?
And what mechanism makes the element to be inductive or capacitive according to its resonant length?