spider timeshare

At around 7:10 in the morning, I saw a spider clamber over this lemon. Apparently I timeshare the kitchen with a spider. It takes the wee, quiet hours, and I take the noisier daylight ones. As you can see from the photo, the spider is now nowhere in sight. It may be chilling on the far side of the lemon--maybe that's the best spot in the whole kitchen? The whole point, from the spider's perspective, of participating in this timeshare? Or maybe, aware of overstaying, it's tucked itself away so...