A THEORY OF THE SURVIVAL VALUE OF MOTILITY 



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where moving with a velocity v b just enables the organism to survive. 

 Energy is no longer available for growth, and the species is doomed 

 to extinction unless a more efficient method of collecting nutrient 

 can be developed. 



On the question of the efficiency of the motility mechanism it is 

 important to note that, no matter how inefficient the motility mechanism is, 

 it is always possible by moving to achieve a net gain in the collection of nu- 

 trient. This is a direct result of the parabolic relationship for energy 

 expenditure and the linear relationship for energy accumulation. The 

 zero initial slope of the parabolic relation guarantees that no matter 

 what the efficiency E of the mechanism, there will always be a range of veloci- 

 ties for which the energy intake will exceed the energy expended. Of course 

 as the concentration of nutrient falls in the environment, there will 



Fig. 1. Energy accumulation and expenditure diagrams for a motile 

 organism. In going from plot a to d the concentration of substrate in the en- 

 vironment decreases progressively and gives rise to the indicated changes in 

 the intersection of the $ s — v line with the P — v curve. For explanation 

 see text. 



