The farther out your target is the more an initiative penalty your character gets. In another post I talked about tabletop RPG frames per second (FPS) and how long things take to propagate through the battlefield. Indicating that some effects, like arrow attacks, are not immediate. I came up with some modifiers for initiative based on range. Now I'll talk about another important element required for long range shooting: lead. Leading is the act of putting the arrow or bullet ahead of the target so the shot goes to where the target will be and not where it is now.
Now, you can't lead a target if you don't know the target speed, and you can't know the target speed if you don't measure it. To measure it you must wait, wait for the target to move enough to make an accurate guess. How does range affect initiative? Simply put, the further away the target is the harder it is to calculate the lead. The target will have to move more for your character to guess better and a bad guess will be more significant at that long range.
For example at Pathfinder lists the heavy repeating crossbow as having 120ft range, that's 40 yards. An 8 inch target at 40 yards measures 5 mils. At 80 yards the same target measures about 3 mils, 2 mils at about 120 yards and 1 mil at the weapon's max range of 200 yards. But 1 mil is so small you might not even see the target, much less notice it moving until it takes a step or two.
A simple rule is to add 1 point penalty for every range increment in range. If the weapon has a 80ft range anything up to 80ft has a 1 penalty to initiative if the shooter wants to lead the target, above 80ft and up to 160ft the penalty is 2, and so forth up to 5.
The shooter can fire without leading, but if the target moves in the round the shot enjoys a 1 point penalty for every range increment. For example, a bow with 80ft range fired at 140ft (less than 160ft which is 2x base range) suffers a 1 point penalty to initiative if the bowman leads the target or a 1 point penalty to hit if the bowman fires quickly and the target moves. These to hit penalties are added to the already calculated penalties for range.