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

Abstract

An improvement to Bělehrádek's equation Y=a IIni=1 (Xi-αi)bi(βi-X i)ci is proposed, which can comprehensively describe metabolic rates or biological activities in relation to various environmental factors. Where Y is the rate of a certain metabolic function, Xi is the value of the ith environmental factor (i=1, . . . ,n), αi is the "biological lower critical value" of the ith environmental factor, βi is the "biological upper critical value" of the ith environmental factor and a, bi and ci are parameters. The former Bělehrádek'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 Bělehrádek'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 Bělehrádek'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.