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 {k) 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 1986) . 



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 



