7 

 experiment at Charley's Gulch had to be terminated after 1989 

 because plots were trampled by livestock. 



We used stage-based transition matrix models to compare the 

 performance of A,, fecunda populations between the plots from 

 which CL. maculosa was removed (treatment) and the controls. 

 Matrix projections assume fixed life-stage structures and 

 simulate changes in a population through time (Lefkovitch 1965, 

 Menges 1990) . One-year transition probabilities were estimated 

 as the number of plants in life-stage class i moving into class j 

 over the course of one year, divided by the number of plants in 

 stage i at the beginning of the year. This method assumes that 

 an individual's transition one year depends only on its life- 

 stage class at the beginning of the period, and is independent of 

 its transition the previous year. Transition probabilities for 

 the multi-year periods were made by summing the 1-year frequency 

 tables for the period (Caswell 1989, p. 81). The "mean" matrix 

 summarizes the behavior of the population over 2-3 years and 

 integrates the effects of fluctuating environment during this 

 period to give a more realistic estimate of the effect of the 

 treatment on population growth. This method of constructing a 

 mean matrix tends to minimize the effects of year-to-year 

 differences in demographic patterns, but the bias is usually 

 small (Huenneke and Marks 1987). The equilibrium growth rate 

 (lambda) is the dominant eigenvalue of the transition probability 

 matrix (Lefkovitch 1965, Caswell 1989). We estimated lambda and 



