Antenna Gain: High x Low Band

Design question: Given a tri-band Antenna, we see High Gain on 2500 band (17dBi gain) vs 800 band (15.5dBi).
Whats is the reason? Any logic behind this?

Not sure but as far as in remember:
Gain is directly related to square of frequency.
Plus this case be understood this way also that at higher frequency there will be more loss compare to lower band.
So to compensate higher losses, higher band antenna generally have more antenna gain.

Gain in any antenna system is achieved by directivity.
Hint: Please check horizontal and vertical beam width of both antennas you will get the idea.
Antenna gain does not have any relationship with high or low frequency.
Frequency just impact the size of antenna dipole then gain is achieved by narrowing the horizontal and vertical beam widths.
More narrower than beam higher gain in dBi.

Here is one post from techplayon about antenna gain calculation:

This is relation between the gain of the antenna and frequency:


I guess gx is the gain and gx does not depend on any frequency.
The equation shown here is for Prx which received power which depend on surface area and frequency as well as gain.
Please correct me if my understanding is wrong.