Explain the significance of starting the novel with the rat scene then how this scene foreshadows how Bigger is chased down at the end of the book

The novel opens with Bigger killing a fat black rat that has invaded their decrepit one-room apartment. Even as the rat is considered as an "invasion" to be killed, it is a symbol of the living conditions of urban black America and a foreshadowing metaphor for Bigger's psychological condition. The rat has hidden in the Thomas' apartment, growing fat on garbage before it is trapped and killed, largely for its physical repulsiveness. Symbolically, the rat is as "trapped" in the apartment as the family is; both are eating nutritionally deficient "garbage," none may escape and both are ultimately vulnerable to vicious murder. The relationship between the Thomas family and the rat is defined as "kill or be killed": Ma warns Bigger that if he lacks the "manhood" to kill the vicious rat, the rat will "cut their veins" while they sleep. This relationship, presented at the beginning of the novel, symbolizes Wright's perception of American race relations as evidenced in Bigger Thomas: Bigger must kill whites or be killed; whites must kill Bigger or be killed.

As a metaphor, the trapped and killed rat identifies Bigger's intense feelings of being trapped and hunted. Throughout the novel, Bigger alternates between the roles of predator (the rat that cuts veins) and the role of prey (the rat that is trapped and killed). Bigger's violence towards others resembles the rat's surmised violence; he threatens to cut his friend Gus, and just as the rat slashed a gash into his pants, Bigger slashes a gash in the felt of Doc's poolroom table. Bigger's ultimate act of violence, the defamation of Mary Dalton's dead body, is a struggle to cut the veins and bones of her neck, as she "sleeps," having been suffocated in her bed.