Some basic problems in the Antarctic krill population

Abstract

Noting biomass, annual growth-rate, carrying capacity, annual consumption rate by Antarctic animals such as whales and seals and annual catching rate by mankind of Antarctic krill by Z, p, Z_∞, R and F_k respectively, a time-change rate of Z is simply expressed by dZ/dt=pZ(1-Z/Z_∞)-(R+F_k) The critical condition for not resulting in a catastrophic vanishment of Z is given by (R+F_k)≦pZ_∞/4 and Z≧(Z_∞-Q)/2,where Q≡Z_∞[1-4(R+F_k)/pZ_∞]^. The most plausible numerical values of p, Z_∞, and R at present will be p=1.0 (year)^, Z_∞=(10)^9 tons and R=1.1×(10)^8 tons/year. If so, F_k<1.1×(10)^8 tons/year will be the allowable upper limit for the krill catching at present. In such a case, however, an increase of whale biomass may not be expected. If F_k is considerably smaller than the critical value for (R+F_k), an increase of whale biomass can be expected.