The Bible does not tell us the specific answer to this question, and neither does pure logic, therefore there is no official "Christian" answer. This means Christians are free to speculate about questions like this, keeping in mind that such speculations should not overshadow what is really important in our walk with Christ -- namely, what is clearly revealed in scripture.
Even though I personally have never seen this question asked or answered before, there are several possibilities that immediately spring to mind, any one of which seems perfectly reasonable within the Christian worldview.
1. God created animals divided into "kinds", not "species" (Genesis 1; 6:20). "Kinds" is the Bible's classification, whereas "species" is man's classification. We don't know exactly what "kind" means. It may mean that two polar bears were on the ark, and two black bears were on the ark, and two grizzly bears were on the ark, or it may simply mean that two bears were on the ark, and all grizzlies, blacks, and polars are descended from them. Thus, with respect to at least some of these creatures, a population WAS left behind as they traveled. The left-behind population simply consists of varied creatures within the original "kind". Christians who deny the possibility of kind-to-kind evolution do not take issue with variation within a particular "kind". I am taller than my father, for example. This is variation within the "kind" of humans. However, no one expects their next child to be anything other than human, because we all recognize that the only place things like that happen is within the pages of the National Enquirer.
2. God miraculously took them where He wanted them to be. After all, He brought them to the ark to begin with (Genesis 6:20), and the Bible tells us that he puts human civilizations in the exact places where He wants them, setting their boundaries as He wills (Acts 17:26). Thus there is no necessity for a purely naturalistic explanation.
3. The creatures left behind in the migrations are all extinct through natural mechanisms and their fossils simply have not yet been found (we can call this the "Appeal to the Evolutionist's Reasoning", since many evolutionists often say the same thing about transitional fossils and more specifically with regard to the infamous "missing link").
Any of these answers seem as plausible as any other answers as to how varied life forms arrived at their final destination. Ultimately, though, we simply do not know.