Abstract: A change ratio model was made to analysis population density dynamic of Prorocentrun sigmoides Bohm in the Dapeng Bay, South China Sea. The data were based on the samples taken at intervals of 2nd from 30 March to 10 June 1990. On the basis of conductions of the previous papers, early days density and change ratio of Prorocentrun sigmoides Bohm, temperature and its change ratio, concentrations and change ratio of dissolved inorganic nitrogen(DIN, including NO₃-N and NO₂-N)and inorganic phosphate(DIP)were identified the relationship with change ratio of later stage Prorocentrun sigmoides Bohm. Using calculus of variations, the authors identified_the change ratio model of the population density dynamics of Prorocentrun sigmoides Bohm. Six change ratio models were established. The formula is: d Q_t/d_t=a₀+a₁*d Q_t-1/d_t+a₂Q_t-1 +a₃T_t+a₄*d T_t/d_t+a₅N_t+a₆*d N_t/d_t+a₇P_t+a₈*d P_t/d_t The fitting degree between the calculations and field data was quite accurate. The results provided a scientific basis for controlling redtide of Prorocentrun sigmoides Bohm.

Key words: forest restoration approach, ecosystem services, soil quality, principal component analysis, red soil region.