The Rate of Establishment of Giant Cactus. 237 



in 10 cm. intervals. From the smoothed curve the average 

 rates were taken for the 10 cm. intervals, and by summation a 

 set of figures was obtained showing the approximate age of the 

 Giant Cactus at successive heights, some of which are given here. 



10 cm 8.0 years 



20 " - 12.5 " 



40 " 19.1 " 



80 " : 27.3 " 



1 m. - - 30.3 " 



2 " _. 40.5 " 



3 " -- -. 47.5 " I 



4 " 54.0 " ! 



5 " 60.0 " 



In order to apply these figures to a determination of the rate 

 of establishment, an exact census was taken of some 240 Giant 

 Cacti, which formed the entire population of a portion of the 

 northern slope of Tumamoc Hill, including easterly and westerly 

 slopes. All the unbranched individuals less than 5 m. in height 

 were measured: the five individuals encountered which had 

 branched before reaching that height were disregarded in the 

 computation to follow, on account of the disturbance of their 

 growth rate due to the production of the branches. The indi- 

 viduals under 5 m. in height, which is to say those less than 60 

 years old, formed 36% of the total population, which would 

 indicate an average expectancy of life of 1 75 years for the Giant 

 Cactus in this location and habitat. On the steep rocky flank- 

 ing slopes of the hill there was a noticeable poverty in young 

 and middle-aged plants and an abundance of fallen skeletons, 

 while the number of younger j lants was greater on the gentle 

 slopes facing the east and west, which points to erosion as one 

 of the most important factors in limiting the length of life. 



The height measurements of the juvenile element of the 

 population — as we may term those under 5 m. in height — were 

 converted into ages, and these grouped into pentads. The 

 number of the surviving individuals of each pentad was then 

 plotted with reference to the years in w'hich their establishment 

 took place, with the resulting curve shown in Fig. 1. The va- 

 riations in the growth rate of difi"erent individuals make it pos- 

 sible for some of those that were measured to fall into the ad- 

 joining pentad to that in which they belong, or even, in extreme 



