Why antenna with lower permittivity substrate has wider bandwidth and higher gain?

I know the conclusion that antenna with lower permittivity substrate tends to have wider bandwidth, higher gain and excites less surface wave.
But I don't know how to explain. Can anybody help me? Thank you very much!

resonance frequency and the bandwidth of patch antennas is inversely related to the substrate permittivity. Hence, the lower the permittivity is, the higher the bandwidth will be.

I would refer to a fundamental law for electrical small antennas, that tells about a limit for the minimum Q-value related to the radius of a sphere where the antenna can be placed in. Using a higher permittivity substrate decreases the antenna size and thus increases Q respectively reduces the bandwidth.