360 lotka: efficiency in organic evolution 



Type, bearing flowers and old spines, in the herbarium of the Mis- 

 souri Botanical Garden, no. 46838, collected in the vicinity of Rosario, 

 state of Sinaloa, Mexico, in 1849, by Dr. Josiah Gregg (no. 1135). 

 It is mounted on the same sheet with specimens of the spoon-thorn 

 acacia, A. cochUacantha H. & B. 



Cotype, a young branch with spines and leaves but without flowers 

 or fruit, in the United States National Herbarium, no. 716563, col- 

 lected near Acaponeta, Territory of Tepic, Mexico, July 30, 1897, 

 by Dr. J. N. Rose (no. 3792.) 



This species is closely allied to Acacia Standleyi and to A. hirtipes, 

 but differs from them both in its smooth, flattened, sword-shaped 

 spines, and in the form and color of its flowers. Though many of the 

 leaflets of the flowering branches are tipped with food bodies, as in 

 the true myrmecophilous acacias, the spines are much compressed 

 and, in the specimens observed, not inhabited by ants. 



ECONOMICS. — Efficiency as a factor in organic evolution. I.^ 

 Alfred J. Lotka. 



In an earlier issue of this Journal' the writer published a 

 paper on Evolution in discontinuous systems. In the first portion 

 of this paper the treatment of the subject was quantitative, and 

 made use of analytical methods. In the concluding section cer- 

 tain phases of the subject were touched upon, for which at that 

 time no method of quantitative analytical treatment could be 

 suggested. 



In the present paper it is proposed to resume the thread of 

 the former discussion, and to show how the qualitative analysis 

 of the problem then suggested has since fulfilled the author's 

 hopes in furnishing the basis for quantitative treatment. 



To recall briefly the point of view adopted in the paper cited, 

 we note that r, the rate of increase per head of a given type or 

 species of organisms, under given conditions, may be regarded 

 as a quantitative index of the fitness of such species, or of its 

 adaptation to the conditions given. 



The value of this index r of the fitness, depends, of course, 

 on the one hand, on the external conditions; on the other hand 



1 Paper read before the Washington Philosophical Societj^ on February 13, 

 1915. 



2 This Journal, 2: 2, 49, 66. 1912. 



