Bow and Arrow:
The bow and arrow predates recorded history, therefore the origination is in question for most civilizations. The south American's utilized spears and developed the Atlatl which is actually utilized for more range and trajectory as well as clean fluid throws. Bow and arrows did show up as well to replace the spear as more could be carried at a time. For hunting the need was accuracy and distance with power. The main place that speed comes into play is in warfare specifically. A well shot arrow or spear will pretty much take down most creatures for hunting, especially when hunting in groups.
When one moves into fighting human opponents the odds of the other person getting you is as likely as you getting the other person. Thus strategy enters the situation and as the saying goes 'necessity is the mother of invention'. Since the bow and arrow predate recorded history the speed mention is vague at best and the most significance is in traditional art paintings and word of mouth that eventually became literature.
Warfare: The eastern archery has a much richer and more diverse history than the western culture here, the main reason for this is the tribal nature of the west until European settlers arrived. Most "warfare" related text regarding archery is from Europe and Asia. This is also the more prominent place as these are the places where territorial domination was practiced. Aztecs would be an exception, but relied on their fierce foot soldiers primarily over ranged combatants, but the Atlatl and bow and arrows were utilized. The arrival of Europeans brought guns which ultimately captured the warfare side as the power of the weapon was unprecedented. Speed was the only factor the bow and arrow had over the guns, even with improvements on muzzle loading speed, it was slower but the odds of a bullet not impacting a target with power versus an arrow not impacting with power the bullet wins with a lot less training to use.
Due to the tribal nature of western natives there was little need to become extremely dominate with speed shooting of bow and arrows as all warfare was over game/territory/disputes and none were into annihilation/genocide/domination of other parties. Select warriors through practice became proficient at high speeds similar to those proficient with muzzle loading became extremely fast and able to reload as fast as 7.5 seconds (depending on the year/type/proficiency - earlier is much slower). Archery speed became obsolete only when the revolvers and carbine rifles started appearing. Compared to the fire rate of those vs. bow and arrow the bow and arrow could no longer keep up and native Americans started swapping to guns.
Shooting rate on bow and arrow is muscular based instead of chemical reaction thus limiting the number of "realistic shots per minute" vs. "capable shots per minute". The historic number is around 6 per minute and 60-72 arrows per engagement for long bows. This is the medieval long bow records which is a heavier bow than most western bows. As native Americans didn't create written records until they were nearly done with the bow and arrow it's harder to gauge their speed, but due to the size of the long bow vs. the size of the smaller western bow and mathematical summation can be abstracted.
(70lbs*6 times)/60sec = target factor of 7
(45lbs*9 times)/60sec = 6.75 -> (45*10)/60 = 7.5
So someone should realistically with the same skill/strength level be able to fire 3 or 4 more arrows than a long bow in the same amount of time.
Dexterity Formula & Tricks for speed:
The variable that can't be measured, but is trained would be the ability to fit the arrow to the string in the amount of time. So assuming the dexterity of the archer is superb then the realistic average strength would fall in line with about 9-10 times per minute.
Tricks on how to dexterously load and shoot quickly are mostly scraped together from imagery and a few text on shooting. The rest is pieced together from actual trial and error experience from real practitioners. Here is one such person who has a number of videos from Lars Anderson on tricks for loading:
Hold arrows in your hand either draw or bow hand, but draw hand makes it quicker as that one fits the arrow to the string so you already have it in hand for repeat shots.
Shoot from the right side of the bow as the fitting into the bow is faster, this requires a different bow position than normal though so might be harder to master.
Fluid motions contribute so practice solid continuous movements over jerky movements. Once you have the movement down increase the speed while maintaining the movement to get faster and faster.
Muscular strength allows more pulls with less fatigue affect on the arm. This results in consistent and continuous movement.
Most of the archery developments came from word of mouth and observation with trial and error. This being said historical photos are important as they capture the bow, the person and position of the body for bow handling. This allows someone to imitate and reconstruct based on visual example without the textual references.
P.S. Please keep in mind that the tricks are not western archery, but pulled together from eastern text and practical application. Again this is the speed part and not the power part, so if you want them both together you need the tricks from the speed and then apply them to a higher weight bow and arrow and practice until you can get both down.
P.S.S. Keep in mind that western archery was primarily for hunting and was adapted for combat in a raiding capacity. Quick short bursts at a time and not prolonged lengthy combat like eastern sieges.