http://ncse.com/cej/4/1/impossible-voyage-noahs-ark#Accommodating All Those Animals
Limiting the cargo to "kinds."
Genetic problems.
Without going into the details of genetics, it can be stated that every inherited trait, however small, is coded for by one or more genes, and each gene locus may have a substantial number of variants (alleles), which accounts for the great variety observed in a given population. Any specific individual, however, has at most only two alleles per locus—one from each parent. [snip supporting quote by James C. King]
Hence, for a trait such as human pigmentation, "we can visualize not merely a few dozen interacting loci but an array of perhaps a dozen or so alleles at each locus" (p. 60).
From this we can see that the original canine baramin in Eden would have needed a fantastic set of giant chromosomes with alleles for every trait that would someday be manifest in coyotes, wolves, foxes, jackals, dingos, fennecs, and the myriad of minute variations in hair color (twenty-four genes at nine loci), height, face shape, and so forth that are seen in the domestic dog (cf. Hutt). So, too, for the feline kind, within which creationists Byron Nelson (p. 157) and Alfred Rehwinkel (p. 70) both place lions, tigers, leopards, and ocelots as well as housecats. Similar giant chromosomes would be required for the bovine kind, equine kind, and so on.
In the centuries before the deluge, these strange progenitors must have rapidly diversified into their potential species, as the fossil record shows. The equine kind developed not only zebras, horses, onagers, asses, and quaggas but Eohippus, Mesohippus, Merychippus, and other now-extinct species that paleontologists have misinterpreted as evidence for evolution. (Remember that creationists hold that the flood is responsible for the burial of most, if not all, fossil species. Therefore they had to already exist prior to the deluge.)
Then one day, many centuries later, the Lord told Noah to take two canines, two felines, two equines, two pinnipedians—one male and one female each—and put them aboard the ark. The trick is, which does our ancient zoologist choose? A male kit fox and a female Great Dane? A female lion and a male alley cat? An Eohippus and a Clydesdale? Which two individuals would possess the tremendous genetic complement that their ancestors in Eden had, to enable the many species to reappear after the flood? How could Noah tell? Creationist Dennis Wagner tells us that the original kinds degenerated through inbreeding so that their offspring would "never again reach the hereditary variability of the parent" (quoted in Awbrey...). Yet the unique couple aboard the ark needed the full genetic potential of the original kind, if not more, for a vast new array of climatic and geographic niches was opened up by the flood.
etc., etc., etc.