Typically in Shintaido we avoid explicit instruction concerning breathing and we say we breathe "naturally," but this is deceptively simple. It doesn't necessarily mean to just abandon being attentive to your breathing. However, there are other possibilities besides consciously controlling the breathing, which involve listening to the body taking priority over controlling it. If the body has it's own wisdom, then the communication between the body and the conscious mind (or will) is a two-way street. Signals go in both directions, and rather than trying to control our bodies to do certain movements (or to breathe in certain way), we might try to tune our bodies so that— like tuning an antenna— we can become more receptive to the rhythms of the universe that are naturally mirrored in each of our bodies.
The concept that fundamental natural processes are mirrored both in the larger universe (Japanese dai shizen 大自然, lit. "great nature" or Mother Nature) and within ourselves has a long tradition in Japanese and Chinese philosophy, especially Taoism and Neo-Confucianism. (Neo-Confucianism 理學 was a philosophical system in China that developed from the 9th to 13th centuries C.E. and synthesized Confucian, Taoist, and Buddhist thought).
From the scientific point of view, breathing is generally regulated by the autonomic nervous system (ANS), meaning that it carries on without conscious control (for example when sleeping or thinking about something else). However, unlike most other autonomic functions like heartbeat, digestion or dilation of the pupils, breathing can be consciously controlled quite easily (within limits) by anyone. So it lies in some ways on the cusp of conscious and autonomic functions.
This suggests that when we deliberately control the breathing using specific techniques (as in many types of Qigong and yoga), we are actually working with the the brain and the relationship between different parts of the nervous system. These kinds of techniques may be effective, but probably should not be approached lightly. Traditionally they pre-supposed complete dedication to an entire system of training, and were also considered potentially dangerous even for initiates. Generally this kind of control of breathing is not much practiced in Shintaido, which is intended to be safe and accessible to everyone.
However (as hinted at in Part 1), this doesn't mean that Shintaido entirely lacks a specific approach to breathing. Does Shintaido include some kind of "tuning" methods (as referred to above) that also concern breathing? A little bit of deeper investigation into the basic techniques of Shintaido that are taught to every beginner reveals many hidden treasures... stay tuned.