  The ability of microswimmers to deploy optimal propulsion strategies is of
paramount importance for their locomotory performance and survival at low
Reynolds numbers. Although for perfectly spherical swimmers minimum dissipation
requires a neutral type swimming, any departure from the spherical shape may
lead the swimmer to adopt a new propulsion strategy, namely those of puller- or
pusher-type swimming. In this study, by using the minimum dissipation theorem
for microswimmers, we determine the flow field of an optimal nearly spherical
swimmer, and show that indeed depending on the shape profile, the optimal
swimmer can be a puller, pusher, or neutral. Using an asymptotic approach, we
find that amongst all the modes of the shape function, only the third mode
determines to leading order the swimming type of the optimal swimmer.
