I don't know.
This is actually a pretty interesting question, and I'd appreciate input from experts in the subject. It seems to be the case that any PCIe 3.0 device will communicate with a PCIe 2.0 motherboard. Compatibility both ways is required in the PCIe specifications. So the answer that I learned for this question is "yes."
However, there is a shift from motherboards running BIOS to motherboards running UEFI, and I have heard that some graphics cards support only UEFI and will not work in BIOS-based boards. Is there truth to this and, if so, how can we tell which graphics cards require a UEFI motherboard?