212 GROWTH PRINCIPLES AND THEORY 2 



(«) Summary of models of growth 



As compared with the Weiss-Kavanau model, the Bertalanffy model has yielded 

 a considerable number of experimentally verified "dividends" which may be 

 briefly summarized: 



I. Calculation and satisfactory approximation of a large number of empirical 

 growth data representative of the major animal classes; — 2. Derivation of a 

 correlation between metabolic and growth types, verified in many examples; — 

 J. Prediction, from experimental determination of metabolic rate, of the existence 

 of the Third Growth Type which was subsequently verified by the growth curves 

 of the species concerned (Bertalanffy, 1941b; Bertalanffy and Miiller, 1943); — 

 4. Correct prediction of interfering factors from aberrations in the growth curve, 

 verified by more detailed analysis {e.g. plaice. Figs, 13, 14, p. I94f.); — 5- Correct 

 prediction of ratios of anabolic constants (p. 1 99) ; — 6. Correct prediction, in a 

 number of cases, of the numerical values of the catabolic constants (x), confirmed 

 by independent physiological determinations (p. i99f.); — 7. Derivation of equi- 

 finality of growth (p. 213); — 8. Prediction of the major characteristics of tem- 

 perature dependence of growth corresponding to ecological and experimental 

 evidence (p. 2 i6ff.) ; — 9. Prediction, from the calculation ofx values, of two growth 

 cycles in mammals which is confirmed [a] by inspection of empirical growth 

 rates; ib) by investigation of basal metabolism (Fig. 23), and {c) by numerous 

 other changes occurring at this critical period. In consequence, correct calculation 

 of growth in mammals (p. 2i8ff.) by simple mathematical expressions with a 

 consistency and precision not obtained with formulas containing a much larger 

 number of constants (p. 1 76) ; — 10. Correct prediction of the difference of growth 

 curves in spherical and rod-like microorganisms (p. i6if.); — 11. Empirical equa- 

 tions for embryonic growth appearing as special cases of the general growth 

 equation (p. 223f.) ; — 12. Interpretation of the growth of tissue cultures within 

 the framework of the theory (p. i66ff.); — 13. Derivation of equations for time 

 growth of organs which qualitatively correspond to observed growth curves and 

 are capable of numerical calculation (p. 236ff.). Correct prediction of the form of 

 organ-growth in time if the organism grows exponentially, and if the organs show 

 positive or negative allometry (Figs. 37, 38; p. 238); — 14. Deductive derivation of 

 the family of growth equations from a general scheme and few empirical charac- 

 teristics (p. 200ff.). 



Many of these items are verified not by one or a few isolated examples, but 

 an often considerable array of empirical instances. Beside individual examples, 

 the merit of the theory is in its successful application to seemingly unrelated 

 experiences and fields. 



In conclusion, it may be said that the theory doubtless is a first approximation, to 

 be refined and corrected with further analysis of the factors involved and with 

 consideration of more complicated cases. The large number of verified conse- 

 quences and deductions indicates, however, that the basic model and theory are 

 correctly chosen. 



