Stahl67 bmp

THE ROLE OF MODELS IN THEORETICAL BIOLOGY 167

possible the rational classification of virtually almost all reports dealing with biological models. The very large majority of citations in the reference list contain the words “model” or “simulation” in their titles and represent a fairly complete sampling of literaturę in the field.

This review shall not deal with animals considered as physical analogs or models of each other, although this subject is a special research interest of the author (Stahl, 1962, 1963a,b, 1964, 1965a,b). A volume now in preparation (Stahl, 1967) develops this viewpoint; it discusses a large yariety of dimensionless physiological variables which may be used for comparing the design and performance of mammals in the size rangę from the shrew to the whale. The same sort of criteria, however, that relate models and prototypes can also be used for comparing existing animals, considered as models or physical analogs of each other.

General References on Biological Modeling

Several published works review the whole problem of biological simulation. A volume edited by Beament (1960) has sections dealing with ąuantum mechanical, genetic, morphological, mechanical, statistical, electrical, and computational models, but presents little unifying theory for these diverse approaches, and almost no discussion of quantitative criteria of similarity governing models and prototypes.

A valuable collection of reports by Waterman and Morowitz (1965), devoted to mathematical-theoretical biology, includes introductory discussions by both Waterman and Morowitz which emphasize the great importance of physical biological modeling; this was also stressed elsewhere by Waterman (1962). For example, in the seventeenth century Borelli published a book De Motu Animalium which explained human musculoskeletal action in terms of generał lever systems, using diagrams as conceptual models (Lewis, 1966). Subseąuent analogies of this generał type included comparison of the lung with a bellows, heart with a pump, electric eel with a battery, and oxygen-burning organisms with fires, Chemical plants, or engines. Descartes suggested that animals should, in generał, be considered as machines, from both the physical and computational standpoints.

There has not been agreement on any definite classification scheme for biological models. In a series of papers dealing with biological modeling Berman (1963a,b; Berman and Schoenfeld, 1956) suggests that models based on multiple differential eąuations are the most generał for biological systems. It is now elear, however, that this approach fails to cover many physical analogs, such as flow models of the aorta, and the