To date, the dynamic mechanisms by which the corticospinal tract (CST) and its alternative tract (i.e. the reticulospinal tract (RST)) interact and evolve after the CST has been damaged by stroke has not been fully explored. To gain insight into the mechanisms, we construct a computational model to reproduce several critical features of subscore distributions of the Fugl-Meyer assessment (FMA) for the upper extremity following stroke. Subscores of the FMA present clues about the working neural substrates affected by stroke, potentially distinguishing preferential uses of the CST and RST. A stochastic gradient descent method is employed to emulate biologically plausible phenomena, including activity- or use-dependent plasticity and the preferred use of more strongly connected neural circuits. The model replicates several segments of empirical evidence presented by imaging and neurophysiological studies. One of the main predictions is that substantial CST recovery is achievable unless the initial degree of residual corticospinal neurons following stroke falls below a certain level. Another prediction is that while the functional capabilities of the CST and RST increase in a harmonic way post-stroke, the degrees of functional capability those tracts reach are in a competitive relationship. We confirm that the neural system prioritizes optimizing a more strongly connected motor tract and uses the other tract in a supplementary manner to enhance overall motor capability. This model presents insights into efficient therapy designs.