Bradbury's story revolves around what is known as the "Butterfly Effect," the phenomenon in which even the most minimal change in a complex system of some kind can have marked and lasting effects elsewhere. With regard to the theme of Man vs. Nature, the narrative of "A Sound of Thunder" hinges on the maintenance of what is termed the Balance of Nature, a theory not dissimilar to the Butterfly Effect:
The balance of nature is a theory that proposes that ecological systems are usually in a stable equilibrium (homeostasis), which is to say that a small change in some particular parameter (the size of a particular population, for example) will be corrected by some negative feedback.
Both theories are connected to the "chaos theory." When the terrified Eckels cannot shoot the Tyrannosaurus rex which has been selected to be shot because it died from the fall of a tree in prehistoric times, Travis and Lesperance [whose name means "hope"] must shoot it and retrieve the shells in order to not upset anything from the past. However, because Eckels has stepped off the anti-gravity path, inadvertently crushing a butterfly onto the sole of his shoe that he transports back to the present, the scene is still marred. Thus, the ending of the narrative evinces the chaos that has been effected by Eckels' false step into the future time of his present. Eckels has been cautioned against catastrophic effect by Mr. Travis, the Safari Leader, when he explains the purpose of the anti-gravity path that
Doesn't touch so much as one grass blade, flower, or tree. It's an anti-gravity metal. Its purpose is to keep you from touching this world of the past in any way. Stay on the Path. Don't go off it....For any reason! If you fall off, there's a penalty.
When Eckels returns from the Safari, having brought the butterfly on the bottom of his shoe, he has wrought the chaos predicted by the upsetting of the balance of nature/ the Butterfly Effect. The sign that he has read the other day now looks like this:
TYME SEFARI INC.
SEFARIS TU ANY YEER EN THE PAST.
YU NAIM THE ANIMALL.
WEE TAEK YU THAIR.
YU SHOOT ITT.
He cannot believe that the death of one butterfly has wrought such changes even in human beings. In retribution for the chaos he has caused, Eckels last sense is that of "a sound of thunder" in his ears as he is shot to death.