How does Santiago grow his ''relationship'' with the big fish and what does the big fish represent for Santiago?

Santiago feels that the Marlin is his true brother. The great Marlin gives him life and it gives him purpose,

"It is good that we do not have to try to kill the sun or the moon or the stars. It is enough to live on the sea and kill our true brothers."

Santiago has a greater connection with nature than he has with people (other than Manolin). Santiago muses about the sea birds, turtles.....The Marlin, however, holds a special place in his heart. In many ways the Marlin is symbolic of Santiago in his youth, strong and majestic. There are times when Santiago even wishes to sacrifice himself for the great fish. Santiago loves the Marlin because it validates him, even a broken old fisherman that he has become.