Directivity vs frequency relationship of a directional antenna

Hi,

Can anyone tell me why does directivity of a directional antenna changes over frequency?

For example, I designed a patch antenna with -10 dB bandwidth from 3-5GHz. By simulation I obtained the 2d plot of directivity vs frequency. Directivity changes over frequency within 3-5 GHz. What may be the reason?

I would like to know the explanation. Thanks

the higher is the frequency the bigger is the antenna (in terms of wavelength), the bigger is the antenna the higher is the directivity.