From the lexicon, here is the definition of reason: Reason is the faculty that identifies and integrates the material provided by man’s senses.
The definition, at the outset, seems a little vague. For example, other animals have a faculty that integrates materials provided by their senses. Does that mean, that faculty of theirs is also reason? What I am driving at, I guess, is where is the differentia? A proper definition should have both genus and differentia. Am I missing something?
The definition is accurate.
Genus: "faculty". Differentia: "which identifies and integrates the material provided by man's senses."
Man has other faculties, such as the faculty of vision, the faculty of hearing, and even the faculty of balance. Implicit in this definition is that reason is a faculty of man. It identifies a human faculty which identifies and integrates sense data. There is only one: reason.
A definition need not be an exhaustive description. A definition's responsibility is to guide your awareness to examples of a concept, given the context of knowledge you have.
Reason is the human ability to identify and integrate sense data. As for how reason operates, that's a huge topic, which is not properly addressed in the definition.
Do other animals possess reason? To answer this question, you cannot just look at Ayn Rand's definition, omit the word "man's" and see if the definition applies to animals. Instead, you look at reason, as humans practice it, and then observe animals and see if they practice it too.
That "man's" is in Ayn Rand's definition is not to nip in the bud the possibility that alien life forms might possess reason. It's there simply to guide one's awareness to a specific phenomenon, which man is the only species known to possess.
If you follow her definition, you'll find the phenomenon of reason. The next task is to describe it fully, so you might be able to find the phenomenon elsewhere if it shows up. And if you do find it elsewhere, then the definition would have to be amended.
Here is the text that Ideas for Life referred to (thanks!), from Leonard Peikoff's book Objectivism: The Philosophy of Ayn Rand, page 152: