What Kind?

[dhall]

What is this tree it has little berries on it?

[Texas270wsm]

Chittamwood

[stinkbelly]

Does anything eat them besides rats?

[Texas270wsm]

Deer will browse the shrub with protein levels 20%+ for new leaf growth
Turkey, quail, dove eat the ripe fruits
As per “range plants of N. Central Texas “
Great book by Ricky J. Linex and highly recommended for identifying most native plants around us.

[tbgascorer]

Yep, we've always called them Bumelia. Moderately browsed species. They can grow into some big trees. Lots of thorns on them when handling.

[Briar Friar]

https://aggie-horticulture.tamu.edu/ornamentals/natives/BUMELIALANUGINOSA.HTM

Catepillars ravage mine in spring time...and they bounce back. Not fun getting stuck by them.