After their kind
Answers in Genesis makes a big issue about creatures reproducing "after their kind" as Scripture says. But that was part of a non-cursed world. What if reproducing "after their kind" was an arrangement maintained by God in a perfect world? If that is the case, we should expect to see a steady degradation of kinds as DNA is swapped between non-related organisms. In this view, reproducing after their kinds should have lasted for however long it took before the fall, but there was no death prior, so that would leave no fossil record. Post fall, pre-Deluge, there would be a degradation of kinds (or baramins), but the fossil evidence of that would be masked by the massive die off and sedimentary deposits of the flood. Post deluge, as populations splintered, any gene transfer would be overshadowed by the population bottlenecks of the post-flood expansion. So it would only be relatively recently that gene transfer would have a noticeable impact on populations.