Looks like a fig tree to me.

Yes sure looks like a free fig tree.
Martin

Thanks for your replies - good to know! Here's another another that "flew" into my yard, and this one already has fruit, even though its at least 1 year or more younger than the non fruiting one.

Does this look like a fig tree too?

Irene

Yes that is also a fig plant.
Martin

Thanks again, Martin! The tall one seems a little skinny so I think I should water it more? But the short one seems to be doing well as it is, so I'm thinking I should do nothing and just let it be? Should I fertilize it? I have done absolutely nothing to nurture it so far, and it seems to be doing fine, so I'm thinking I should continue to leave it alone? Or should I start fertilizing, now it has fruit??

Any advise appreciated.

Irene

Irene ,going into winter its not good idea to fertilize as it will create growth that may not have chance to harden off and be damaged in winter.
But not familiar with your climate as well ,here in cold area we do not.

During spring and up to mid summer we fertilize our figs growing in containers and they respond well in growth.

Figs that you have not planted and sprout up probably were seeds deposited by a bird etc.
They eventually grow the fruit(as you shown) and at some point fall off due to needing pollination or possibly ripen not sure as I have not have had that happen here.

There are different types self pollinated and another group that
needs the fig wasp to pollinate or fruit will drop at some point.

As a side note.
Folks that recently moved into a home may not see plant in yard from previous owner planted until a season later as it may have died to soil level and re sprouted .
Martin

Thank you again, Martin, for your response. We've lived in this house for 18 years, so I know no one seeded this last year, other than some bird or the wind!

But I have a question about the burnt leaf. The skinny and taller tree, which gets less water, has burnt leaves on the side facing the sun. Can I prevent this in future growth by ensuring sufficient water to the plant?

Irene

It should help it along .
As plant gets more seasons old it should do better one would think after all some are seen in very arid places of the world.
Martin

Thanks Martin, you're right about it being found in arid places of the world. So glad the burnt leaves are now all gone in the winter and we'll get new leaves in the spring! Hadn't checked the forum in awhile and just saw your response.

Irene