The Caveman's Seed

In Ray Bradbury's "A Sound of Thunder", Mr. Travis, the "Safari Guide in the Past" warns the "time hunters" against straying off the "Path", lest they set in motion, albeit by accident, a chain of events of disastrous repercussions. He illustrates his point saying that should they accidentally kill a mouse, they would be killing all that mouse's descendants along a line several million years long. Travis explains that the loss of one particular mouse could mean that future foxes or sabretooth tigers would not be able (perhaps) to feed off the (not anymore) future mice. Things get closer to home for, according to Travis, a Caveman goes hunting for sabretoothed tigers at some point in the far future (for them, deep past for us) and, finding none, starves to death. Again, the bigger loss (for Travis) is not the Caveman himself but his "seed", which is lost forever and which, for some reason, precludes such important events as Washington's crossing of the Delaware river from ever happening.
I agree that a world without mice would have been "different" from a fox's point of view. I cannot imagine a sabretoothed tiger hunting mice, though. As for the Caveman, and with all due respect for age and desperation, I honestly think that whomsoever rises one morning with the fanciful idea of hunting and eating sabretoothed tiger is bound for an early death. I cannot conceive how his "seed" could ever be considered a great loss.
Stretching Bradbury's idea a little further, I'd say that the Caveman's smarter brother (the one who said "hell no" that morning, when invited to come with) would probably have passed on his "seed" to future generations, with no particularly important change in the course of History, all the way to Washington. As for the poor mouse killed by accident when a disobedient time traveller steps on it, let's think of the other mouse (or proto-rodent) who decided to get out of the way and save itself. His seed must have been just as fine, perhaps more.