Geoffrey R. Dolby, PhD One of the principal characteristics of a scientific theory is that it be falsifiable. It must contain predictions about the real world which can be put to experimental test. Another very important characteristic of a good theory is that it should take full cognisance of the literature of the discipline in which it is embedded, and that it should be able to explain, at least as well as its competitors, those experimental results which workers in the discipline accept without dispute. Readers of John Parks' book will be left in no doubt that his theory of the feed­ing and growth of animals meets both of the above criteria. The author's knowl­edge of the literature of animal science and the seriousness of his attempt to incorporate the results of much previous work into the framework of the present theory result in a rich and imaginative integration of diverse material concerned with the growth and feeding of animals through time, a theory which is made more precise through the judicious use of mathematics. The presentation is such that the key concepts are introduced gradually and readers not accustomed to a mathematical treatment will find that they can appreciate the ideas without undue trauma. The key concepts are clearly illustrated by means of a generous set of figures. The crux of the theory comprises three differential Eqs. (7. 1-7.

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1 Introduction.- 1.1 Phenomenology and Etiology.- 1.2 Growth Data and the Growth Equation.- 1.3 Present Mathematical Models of Growth in Perspective.- 1.4 Animals as White Boxes with Output Only.- 1.5 Animals as Black Boxes with Input and Output.- 1.6 Conclusions.- References.- 2 Ad Libitum Feeding and Growth Functions.- 2.1 Live Weight as a Function of Cumulative Food Consumed.- 2.2 The Ad Libitum Feeding Function.- 2.3 The Differential Equations of Ad Libitum Feeding and Growth 33.- References.- 3 A Stochastic Model of Animal Growth.- 3.1 Growth in the Food Consumed Domain as a Markov Process.- 3.2 The Markov Probability Transition Matrix.- 3.3 The Matrix Differential Equation of Animal Growth.- 3.4 Growth as the Solution of the Differential Equation.- 3.5 The Inherent Error ?(W) of Growth.- 3.6 Role of Food Intake.- 3.7 Solving the Differential Equation.- References.- 4 Treatment of Ad Libitum Feeding and Growth Data.- 4.1 Nonlinear Regression - Method and Results by Class of Data.- 4.2 Summary and Discussion of the Growth Parameters Across Species and Within Breeds Fed Ad Libitum.- 4.3 The Experimental Error s(W).- References.- 5 The Geometry of Ad Libitum Growth Curves.- 5.1 Ad Libitum Growth as a Trajectory in a Three Dimensional Euclidean Space.- 5.2 The Trace.- 5.3 The Growth Phase Plane.- 5.4 The Ad Libitum Feeding and Growth Discriminant (?).- 5.5 The Z Function.- 5.6 Comparing Ad Libitum Feeding and Growth Across Species Excepting Man.- References.- 6 Growth Response to Controlled Feeding.- 6.1 Controlled Feeding of Cattle.- 6.1.1 Responses to Constant Food Intake.- 6.1.2 Sinusoidal and Ramp Function Feeding.- 6.2 Controlled Feeding of Sheep.- 6.3 Controlled Feeding of Chickens.- 6.4 Complete and Partial Starvation.- 6.5 The Growth Phase Plane and the Taylor Diagonal.- 6.6 The Controlled Feeding and Growth Differential Equation.- 6.7 The Differential Equation of Controlled Feeding and Growth.- References.- 7 The Theory.- 7.1 The Theory as a Set of Differential Equations.- 7.2 The Plan and Execution of Experiment BG 54.- 7.3 The Results of Experiment and Their Analysis.- 7.4 Theory Versus the Results of the Experiment.- 7.4.1 Use of the Theory to Examine Mature Weight and Appetite Variation.- 7.4.2 Use of the Theory in the Problems of Production.- 7.4.3 The Poor Fit of the Theoretical Food Intake Function.- 7.5 Alternative Ad Libitum Feeding and Growth Functions.- 7.6 Rehabilitation from Controlled Feeding Stress.- 7.7 The Ad Libitum Growth Curve as an Optimum.- 7.8 Determination of Fraps' Productive Energy (PE) of a Foodstuff; a Critical Evaluation.- 7.9 Some Concluding Remarks.- References.- 8 A General Euclidean Vector Representation of Mixtures.- 8.1 Transformation of Mixture (xi) to Vector [yj].- 8.2 Geometric Representation of [yi] in a Euclidean Space.- 8.3 Some Useful Geometric Properties of the Mixture Space.- 8.4 Proteins as Mixtures of Amino Acids.- 8.5 Musculature of Animals as a Mixture of Specific Muscle Masses.- References.- 9 The Effects of Diet Composition on the Growth Parameters.- 9.1 Diet as a Mixture.- 9.2 Nutrient Composition of a Food as a Point in the Nutrition Space.- 9.3 Nutrition Space and Response Surfaces of Monogastrics.- 9.4 Metabolisable Energy as a Plane Response Surface.- 9.5 Dietary Energy and Growth Parameters.- 9.6 Dietary Protein and the Growth Parameters.- 9.7 Growth Promoting Ability of Proteins.- 9.8 Effect of Single Amino Acids on the Growth Parameters.- 9.9 Requirement.- References.- 10 The Growth Parameters and the Genetics of Growth and Feeding.- 10.1 Involvement of Growth Functions.- 10.1.1 An Experiment by Timon and Eisen on Mice.- 10.1.2 An Experiment by Ricard on Chickens.- 10.1.3 An Experiment by McCarthy and Bakker on Mice.- 10.1.4 An Experiment by Andrew Parratt.- 10.2 An Economic Problem and the Feeding and Growth Parameters.- 10.2.1 The First Problem and Its Solution.- 10.2.2 The Second Problem and Its Solution.- References.- 11 Energy, Feeding, and Growth.- 11.1 The Power Balance Equation.- 11.2 The Specific Whole Body Combustion Energy, ?.- 11.2.1 Cattle, Chickens, and Rats.- 11.2.2 Allometric Relation Between Fat and Body Weight.- 11.2.3 The Relation of ?(u) to the Thermochemical Efficiency of Growth and Fattening.- 11.2.4 The Effects of Dietary Protein.- 11.2.5 The Effects of Ambient Temperature.- 11.3 Power Balance and Work.- 11.3.1 A Theoretical Basis for the Effects of Work Routines on Mature Animals.- References.- Appendices.- A. Feeding and Growth Data.- B. Standard Deviation of Live Weight Data.- C. Partial and Complete Starvation Data.- D. Whole Body Combustion Data.- Glossary of Mathematical Symbols.- Glossary of Words and Phrases.