I am a genealogist and a client has asked me to determine the meanings of the markings on the butt of this rifle (a 1909 Oesterr Waffenfabr Ges. Steyr) I don't know who the original owner was, but assume Germany or Austria is the general region that the rifle was used.

I have attached the photos he sent me.

I believe that this shows his tallies of various animals he hunted. The abbreviations are:
H
Th.u.K
Db
G.u.K
Rb
G
S
U

with the TH.u.K and S being the most plentiful and the U the rarity.

I am hoping that someone with both hunting and German proficiency can offer some suggestions of what game each abbreviation might indicate. By using a German-English dictionary I have come up with some ideas, but I would love to hear from actual hunters!

Thank you.