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My lge. turtle (dinner plate size, a gift from another owner) keeps leaving our substantial sized outdoor fish pond, travels 50' or more, daily, under fence gate (now blocked). Do not think she is laying eggs since not exposed to partner. Is she/he hungry or searching for another water environment in the neighborhood? Do not know if this is a male or female. Is this common? Thanks for your thoughts and help.... :)

if it's female, having a male around isn't important. Females will lay unfertilized eggs...like a chicken would. Fence that pond in but do give her some land space. Not only can she escape, but she could make a good dinner for any animal that happens to notice her when she's out. Make sure nothing can get in or out when you build that fence.

Without being fenced in, she'll walk away for whatever reason. It would be good to extend the fence underground to keep predators from digging under it.