Abstract: Using some empirical formulae derived from regression analysis of experimental data. the author presents a mathematical expression which demonstrates the relationship among several essential factors including the amount of oxygen available for fish respiration (Rf, O2g·m-2), the existing phytoplankton biomass in pond water (B, g·m-3) and the effe ctive water depth (L,m):Rf=P0′Lc/lnRwlnP0′(Rw′/P0′)L·Lc-1-1-6.32×10-3B·L-0.306L-0.341 wherePo′=gross oxygen production (gO2·m-3·d-1) of surface water below iceRw′=oxygen consumption of pond water (gO2·m-3·d-1)Lc=compensation depth below ice(m)The relationships between phytoplankton biomass and other variables are as follows:Po′=4.08×10-2B+0.803Rw′=6.32×10-3B+0.379 Lc=2.104-2.12×10-2B From these formulae, optimum effective water depth and optimum phytoplankton biomass in over-wintering ponds with biological oxygen supply are determined to be 1.1—1.8m and 25—50g·m-3, respectively. Under such condition, Rf can reach 0.60—0.64g·m-2·d-1, which enables 0.9—1.9 kgm-2 of fish to pass the winter. Stocking density of tover-wintering fish can be 0.9—1.9 kg·m-2. Ponds with conspicuously greater depth is hought to be unfavourable to biological oxygen production.