Now we're getting into juicy language territory!
Group is a weird word that can correctly affect a singular or plural verb, depending on the interpretation of meaning and context in the sentence. I know, that sounds a little like weasel words. Bear with me for a minute...
Group can be used as a singular or plural noun. Here is an example of group used as a singular noun: A group of people is gathering around the scene of a horrible car accident. It's singular (is gathering) here because the people form a single cluster.
And here is an example of group used as a plural noun: The grade six scout group receive badges for participation. It's plural (receive) here because each member of the group (more than one person) gets a badge.
There are many words like group (class, flock, bag, etc.) that refer to a multitude of things.
In the original question, the "large percentage of animals" refers to a significant number of individual animals (many of them, i.e. plural), which are migrating. In this case, the many individuals is clearly plural.
English has quite a few of these wacky examples. They are wacky because they don't fit into easy rules. I kind of like them, even though they are wacky, because they make our language interesting (if extremely difficult to learn, even to native speakers/readers/writers).
