MATHEMATICAL METHODS TO MAXIMIZE THE OVERALL MULTIPLICATION RATIO OF MICROPROPAGATION IN A DETERMINED PERIOD

Factors considered were the multiplication ratio(k>0) after a multiplication period (p>0), the loss ratio (0<c<1) in the period, and the total duration of time (t>0). Starting with the number of plantlets (N₀>0), the number of usable plantlets (M_n) would be produced after n multiplication period. The OMR after the period (t=n•p) was defined by R=M_n/N₀.

The increase in OMR with the changing values of p and k was investigated because they were dependent each other in any micropropagation process. It was revealed that parameters p and k had compensatory nature in obtaining constant OMR values. That is, the decrease of the propagation period to attain the same multiplication ratio may worth the increase of the multiplication ratio in the same propagation period.

For a micropropagation system which has a logistic growth curve, as one of the most typical example, the optimal values of multiplication period (p_o) that would give the maximal OMR value were investigated. The numerically obtained values of p_o for specified logistic relationships and the maximal OMR were shown graphically.

The necessary number of starting plantlets for the demand number of the final usable micropropagated plantlets can be determined as the smallest with this method.