Anurognathus was first described in 1923 and is said to be a Rhamphorhynchoid. While being a small species of Pterosaur with a wingspan of around two feet, it is believed to have been a good predator of insects and maybe other small animals and is believed to have been quite a fast flyer, at least for it's size. An adult Anurognathus is estimated to have had a 50 centimeter (20 inch) wingspan, and a 9 centimeter long body. With an estimated weight of roughly 50 grams.
Anurognathus' name is a reference to the fact that it has a small tail for a Rhamphorhychoid pterosaur, which are known for having long tails. It roughly translates to " Without Tail Jaw". To date, only a handful of fossil specimens have been obtained. The first being the holotype in 1923 by Ludwig Doderlein, and the second was described by S. Christopher Bennet 2007. The second specimen was much more well preserved and under UV light showed remains of thigh and arm muscles. And remains of the wing membrane are said to have been visible to the naked eye and were thought to have attached at the ankle, making the wings shorter and broader than many pterosaur species.
It is believed that Anurognathus was a swift and agile flyer, skimming the air for insects and has been compared to a Nightjar, a species of bird easily observable today. Though some believe it was a slow flying predator. Without observing a live animal this cannot be truly settled.
Under the Creation model found in Genesis all animals were originally made to be vegetarian. On that note it would be very interesting to see Anurognathus portrayed as a pollinator or frugivore (fruit eater) since the small, needle-like teeth would be well suited to eating fruits similar to modern fruit bats.
Having been described only in 1948, Batrachognathus is a fairly recent, albeit unique Pterosaur species. At an estimated 75cm (30 inch) wingspan and a 1.9 inch long skull, Batrachognathus is a petite species of Pterosaur. It is assumed that just Batrachognathus was insectivorous based on it's size and teeth, though this is heavily assumed. A strange aspect is that no Batrachognathus fossil yet unearthed has been found with a tail, so whether or not they had tails is debated.
Not much is known about Batrachognathus other than the small size of what fossils have been discovered. Most everything else is mere specualtion since there is so little evidence for anything else regarding it, and for all we know Batraognathus fossils found so far could be merely juveniles. If Batraognathus did not get much larger than the fossils found so far it would have likely occupied a niche simialr to small birds that we observe today. It would have been hard for such a small Pterosaur since even Dargonflies would have been larger than it, but this is assuming we know the full size of it.
Again, some reports of unkown flying creatures in modern times have strongly fit this species of small Pterosaur, making skeptics of living Pterosaurs say that it is impossible based on the size of of the animals in the fossil record. However it is unwise to assign sightings of such large creatures to one only known to attain a size many times smaller. It would be truly interesting to determine what niche Batraognathus existed in in the environment and to see one alive and well. Perhaps one day we will.