Re: How can an improved genetic response to the environment be passed on?

Natural selection occurs when a random genetic mutation results in a favorable trait that gives the organism an increased chance at survival and producing offspring. What you must remember is that by definition, the mutations that occur are completely random. So in that sense, you are right, it is arbitrary. However whether or not this mutation is favorable and will be "preserved" by natural selection is not at all arbrirary, but rather entirely dependent upon whether this mutation offers an increased chance at survival.

In the specific example you gave, let's assume that nose length is a genetic trait and that hypothetically all offspring will also have long noses. What this means is that all of this squirrel's children will have long noses. But remember that this does not mean that natural selection will preserve this trait. If long noses aren't a characteristic that increases survival, than this trait will be completely invisible to any forces of natural selection.