the fruit contained evidence of insect predation. Weevil larvae 

 (Family Curculionidae) have been observed in the fruits of 

 Astragalus scaphoides (Lesica and Elliott 1987a) 



Data Analysis 



Stage-structured transition matrix projection models 

 summarize the way in which survival, growth and reproduction at 

 various life-history stages interact to determine population 

 growth (Caswell 1989, van Groenendael et al. 1988) . Matrix 

 projections assume fixed transition probabilities between stages 

 in a population through time (Lefkovitch 1965, Menges 1990). 

 They assume density-independent population growth and thus do not 

 give an accurate projection of long-term population future. 

 Nonetheless, they can be used to summarize short-term population 

 dynamics or compare the dynamics of two populations (Caswell 

 1989) . 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 depends only on its life-stage class at 

 the beginning of the period and is independent of its transition 

 the previous year. The equilibrium growth rate (X) is the 

 dominant eigenvalue of the transition matrix (Caswell 1989, 

 Lefkovitch 1965). X > 1.0 indicates population increase, while X 

 < 1.0 indicates decrease. X integrates the effects of survival, 

 growth and fecundity of the different life-history stages into a 

 single parameter. Details on the construction and use of matrix 

 population models can be found in Caswell (1989) and Menges 

 (1990) . 



Elasticity measures the relative change in the value of X in 

 response to changes in the value of a transition matrix element. 

 Elasticity matrices allow comparison of relative importance to 

 population growth and fitness among the various life history 

 transitions (de Kroon et al. 1986). Elasticities sum to unity 

 and regions of the matrix may be summed to compare the importance 

 of growth and survival to recruitment (Caswell 1989). 

 Elasticities for non-reproductive plants are sums from the small 

 (S) and large (L) classes. 



When the majority of seeds pass directly from production to 

 germination in less than one year, seeds should not appear as a 

 separate stage in matrix models (Caswell 1989, Silvertown et al. 

 1993) . Seeds of Astragalus scaphoides germinate readily without 

 stratification (Lesica and Elliott 1987b) , suggesting that most 

 seeds germinate the same year they are produced. Nonetheless, A. 

 scaphoides may form a seed bank. Not including a seed bank in 

 the matrix model may effect the value of X (Kalisz and McPeek 

 1992), especially when it is lower than 1.0. However, it will 

 have little effect on the analyses based on elasticities. I 

 calculated separate elasticities for reproductive transitions and 



