Does a diver's breath rate become slower when going deeper?
When a diver goes deeper, the air goes into the lung is compressed, compared to the state of air at sea-level ground. Accordingly, the oxygen partial pressure is higher than the ground. If a diver needs to absorb a certain mount (say, in number of O₂ molecules) of oxygen at a fixed time period, then the diver needs to breath slower to maintain the same oxygen influx, since each breath holds more oxygen at a deeper level.
On another thought, the assumption of absorbing the same rate of oxygen (# of O₂ per minute) may be incorrect. Since the gas exchange in the lung should depend on the partial pressure differential between the inhale gas and gas in the blood. Since both pressure increases, a diver should maintain roughly the same breath rate.
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Your breathing rate is not affected, although experienced divers always try and breath slow, deep and continuous, to conserve air and keep airways open.
The higher partial pressure of gasses does however have many other effect on the body, including gas narcosis, oxygen poisoning and increased risk of dysbarism.
(Just on a side note the pressure in your blood does not increase, but the amount of dissolved gasses does.)
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The urge to breathe is driven by the CO2 content which is still being produced at the same rate at depth as on the surface. We metabolise the oxygen and produce CO2 as a by-product. In fact at the surface we breathe out surplus oxygen, hence one can perform mouth-to-mouth resuscitation.
'Skip breathing', i.e. deliberately breathing slowly is really not a good idea as you will build up your CO2 content which can be extremely bad giving you a headache or worse. One of the absolute worse things that can happen underwater is a CO2 hit -- called hypercapnia -- which can be fatal. You'll be uncontrollably gasping for breath consuming an enormous quantities of gas and could even spit out your regulator. Divers I know who have experienced this never want to experience it again. Rebreather divers do a lot of training for this eventuality; it's much less common on open circuit.
Alas the high partial oxygen pressure at depth (up to 1.4 on the bottom and 1.6 when decompressing -- the air we're breathing now is 0.21) makes little or no difference to the amount of CO2 we produce and expel from our lungs when we breathe out.
One's breathing rate does tend to reduce when hanging at a decompression stop. The deeper and longer one goes, the longer these stops will be and they can easily exceed an hour. The breathing rate goes down simply because you're doing nothing; laying flat in the water for 30 mins watching your computer's timer appear to slow down. Good meditation practice - and no mobile phone signal.
The other thing that affects our breathing rate is stress. Novice divers tend to breathe more than experienced divers. But there's nothing like an instructor testing you and "breaking" your equipment to increase your SAC (Surface Air Consumption) rate. Or diving in a shark cage: happy happy, then when the shark appears... where's all that gas gone!
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