What does "the way of" mean in "To the deer it is a reminder of the way of all flesh ... "?

What does "the way of" mean in:

A deep chesty bawl echoes from rimrock to rimrock, rolls down the mountain, and fades into the far blackness of the night. … Every living thing (and perhaps many a dead one as well) pays heed to that call. To the deer it is a reminder of the way of all flesh, to the pine a forecast of midnight scuffles and of blood upon the snow, to the coyote a promise of gleanings to come, to the cowman a threat of red ink at the bank, to the hunter a challenge of fang against bullet. … Only the mountain has lived long enough to listen objectively to the howl of a wolf.

Context: Thinking Like a Mountain By Aldo Leopold

Solution 1:

Way means both a course of travel or movement, and a means of passing from one place or point to another, especially of entry or exit. It is widely used for both literal and figurative purposes. (OED)

The way of all flesh refers to experience common to all people as they pass through life.

2002 NFT Programme Booklet Sept. 11/1 Stroheim's cruelly ironic tale of a rakish Ruritanian aristocrat..who falls for an innocent young girl.., only for their love to go the way of all flesh.

To go the way of all flesh is a euphemism for dying

1836 Dickens Sketches by Boz 1st Ser. II. 27 He pardoned us off-hand, and allowed us something to live upon, till he went the way of all flesh.

The way(s) of the world uses 'way' in a similar fashion (meaning the customary course of events; the manner in which people typically think or behave; the way things are. Chiefly used to express resigned acceptance of a regrettable but predictable state of affairs).

Solution 2:

the way of all flesh is an idiom for death.

go the way of all flesh
1. To die.
2. To come to an end.
American Heritage® Dictionary of the English Language

The quoted sentence means: To the deer it is a reminder of its own mortality.

Solution 3:

"The way of all flesh" is an idiom meaning mortality. The origin is unclear, but Dictionary.com thinks it a misquotation from the Bible.