The use of special, non-lead alloys in the manufacturing of ammunition for air guns has led to greatly increased velocities. 

Gamo offers its .177 caliber Armor PBA® ammunition in 6.6-grain weight, with 20-percent better piercing power over lead and penetration improvements up to 100 percent in actual hunting situations and in ballistic mediums. 

The Raptor PBA®, at 5.4 grains in .177 caliber, shows similar improvements as well as increased muzzle velocity reaching 1,200 feet per second in the same guns that register 1,000 fps for lead. The Raptor ammo delivers groups averaging 1.06” at 30 yards. 

For my personal use, I have found lead ammo to be very adequate, and I shoot RWS Superpoint Extra in .177 caliber that weighs 8.2 grains. It is deadly on squirrels up to 30 yards if restricted to head shots and is more economical. 

The larger calibers are sometimes used for larger game, especially with the alloy ammunition that provides more penetration. Air guns of .22 and .25 caliber are capable of killing animals as large as feral hogs at close range.