173

THE ROLE OF MODELS IN THEORETICAL BIOLOGT

TABLE I (Continued)

Type of Model	Naturę of Modeling Criteria
Stochastic and probabilistic control	Characteristic ąuantities such as Information flow rates, autocorrelation functions, or signal-to-noise ratios
Comparative criteria for nat-ural models	Performance scores on intelligence, motor control, behayioral and other tests

IV. Abstract-Algorithmic models Automata and algebraic isomorphisms

Automata and robots	Identical “black box” behavior for defined
Relational model	enyironment; same state transition tables Inyariance of mapping functions or elemen-tary algebraic properties; inyariance of topological structure
Axiomatic and logical models	Deduction of same logical result when pre-sented with corresponding inputs
Algorithmic models	Representation of model and prototype by the same algorithmic language and com-putable inyariants within this language

V. Comparison of animals Objectiye comparative criteria

Physical design Dimensional constants and dimensionless

Biochemical kinetic behayior	numbers Numerical inyariants for sets of simultane-
Neurophysiological control Behayior	ous differential eąuations Performance scores in yarious tests Scores on special tests; same “black box” behayior in defined enyironments
Taxonomic similarity	Special numerical criteria of closeness in arbitrary “feature space,” based on em-pirical choice of features and weighting
Genetic similarity	Statistical similarity of DNA coding (ill-defined at present)
Disease and biomedical engi-neering models	Correspondence of specific characteristics, dimensional constants, performance scores, and other arbitrary measures

can simulate only restricted aspects of a prototype. (5) Geometrie similarity and smali size are not necessary conditions for a model, which may be governed by physical similarity or functional criteria which in no way pertain to outside shape and appearance, e.g., a Chemical pilot plant that looks completely different from its prototype or a Computer which aets like a brain but certainly does not much resemble one in intemal or extemal appearance.