Improved B_??_lehrádek's Equation for a Comprehensive Description of the Relationship between Environmental Factors and Metabolic Rates

抄録

An improvement to B_??_lehrádek's equation Y=a_??_(X_i-α_i)^bi(β_i-X_i)^ci is proposed, which can comprehensively describe metabolic rates or biological activities in relation tovarious environmental factors. Where Y is the rate of a certain metabolic function, X_i is the value of the ith environmental factor (i=1, ..., n), α_i, is the “biological lower critical value” of the ith environmental factor, β_i, is the “biological upper critical value” of the ith environmental factor and a, b_i and c_i are parameters. The former B_??_lehrádek's equation describes the relationship between the rate of a metabolic function and temperature except for the range close to the upper critical value, while the improved B_??_lehrádek's equation can describe the metabolic rate in relation to single or combinations of environmental factors over the entire range of the factor (s) that the organism is able to survive. As the improved B_??_lehrádek's equation is expressed as a product of exponential functions, it is consistent for mathematical operations by multiplication and division. It can also be expanded to a united formula with respect to growth which takes into account changes in the metabolic rates associated with growth. After applying the improved equation to data from previous papers, the empirical superiority and the weak points associated with the equation are discussed.