In real life trees don't need humans or clay pots to continue to reproduce, they do well replanting themselves.
Why have everyday have each full size tree check in a small radius and if there are less than, say ten or so trees near it, it has a chance to will plant a small sapling of its type on a random spot in that radius.
Therefore trees can replant themselves without human help but further trees won't be planted too close together. Maybe in grassland/heath-y biomes there can be fewer trees naturally planted close bye.
Maybe the new trees could even be affected by soil quality?