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Hypertrophy is an increase in DIAMETER size of skeletal muscle. With the muscle fiber this size is an increase in diameter of the muscle fiber referred to as the cross-sectional area of the muscle fiber. The changes causing this diamter size incrase are as follows;
In addressing this question, always refer to what increases, what doesn't change and what is debateable.
1) actin and myosin increase in diamter size
2) actin and myosin also increase in number
3) there is also an increase in the sarcoplasm in the muscle cell
4) Hyperplasia (the longitudinal splitting of one muscle fiber into two fibers) from training is a debatable issue in humans

In the first ~8-10 weeks of resistance training there are mimimal hypertrophy changes. However, a person is getting stronger.
This is reflective of neural drive.With neural drive, 1) more motor units are firing, 2) synergistic (other helper muscles) are helping with the force production, and 3) the motor units are firing with greater synchronicity (i.e., simultaneousness firing).