Size shrinking

[LeoMan]

For some time i have a question it goes through my head and i've thought about it a lot,  but i can't really say if there is some scientific evidence behind it or it's just my opinion and point of view. Everybody knows that big cats have been around for a lot of time by now and they evolved over millions of years into the species we are familiar today, Lions, Tigers, Jaguars and Leopards. These 4 species lived on earth in their actual form (i mean without major biological changes) for hundred thousands years (if i not mistaken, feel free to correct this info). I have the feeling these animals went through a shrinking process in size by the time but i cannot prove it and i didn't have direct scientific evidence in the form of peer reviewed articles. Take for example the Siberian Tiger, we can safely assume in the past the species roamed a much much bigger territory than today's patch in Primorsky Krai. With the same logic the species counted many more specimens (i don't really know their numbers lets say 1000 years ago, anybody knows something about it) and surely had access to many more prey items. Also in the recent past (100 years) their numbers plummeted so quickly that is possible some kind of embreeding process took place on a large% of the population. All these factors combined could have been the cause for a major size shrinking in siberian tigers? And if it is the case what sizes these cats reached lets say 2000 years ago? Or all siberian tigers from every millenia were plus minus equal in maximum size? This question of course is extended to Lions Leopards Jaguars of the past the tiger is only one example. Does anybody know something about this topic? Reply