No. 548] SHORTER ARTICLES AND DISCUSSION 497 



to endless vicissitudes of internal and external relations that 

 influence the expression of characters. 



Thus the life-cycle spiral is not a single line, but is resolved 

 into a vast multiplicity of lines, tracing back to all the different 

 ancestors. The expression relations of the characters can be 

 analyzed, in a measure, by breeding experiments and by compar- 

 ing behavior under different conditions, but the nature of the 

 system is such that its most permanent and stable adjustments 

 are those that are farthest removed from the influences of the 

 environment. Hence the futility of mathematical treatments 

 that attempt to combine environmental vicissitudes with the 

 entirely inconsistent facts of biological evolution. Instead of 

 evolution representing a law of increasing probability of suc- 

 cessive states, the contrary would be more nearly true. The 

 more specialized the organization the less the probability of 

 passing to another state. Thousands of species are extinguished 

 to one that develops a higher type of organization. Instead of 

 evolution representing a summarized result of environmental 

 influences, it is rather to be considered as a history of ways of 

 avoiding such influences. There are no facts to show that evolu- 

 tionary progress is caused by environmental agencies or by in- 

 ternal mechanisms. The causes of evolution lie in the structure 

 of the species. 



The crowning complexity of the biological system is that the 

 life-cycle spirals do not remain separate and distinct from each 

 other, but are thoroughly interwoven to form a continuous net- 

 work of descent for each species or group of interbreeding indi- 

 viduals. It may be that a mathematical formula could be made 

 for a spiral wire mattress or a Turkish rug, but this would afford 

 only a faint analogy for the complications that attend the evolu- 

 tion of a species. To describe a species as a network of descent 

 may be only a figure of speech, lacking altogether in mathe- 

 matical exactness, but it is a way of pointing out a concrete 

 biological fact. When the facts are essentially complex any 

 statement that conceals or disregards the complexity is to that 

 extent specious and misleading. 



Many of the results of evolution can be described in simple 

 terms of quantity or sequence, but to consider such statements as 

 definitions, or to suppose that they confer any special license for 

 mathematical elaboration, is to disregard the true nature of the 

 facts and problems of biology. For purposes of phyM.-s 

 chemistry individual plants or animals may be considered as 

 machines, but for purposes of evolution the whole species repre- 

 sents the machine in which the patterns of new characters are 



