ci(dead)/dt = rate of transfer to dead com- 

 partment X standing crop dying - 

 rate of transfer out of dead 

 compartment x standing crop 

 dead (1,604 g./m.2) 



The rates of transfer needed to complete the 

 model were obtained from measurements of 

 growth rate and longevity of 92 individual 

 culms followed throughout their life history. 

 The model thus obtained had an input (growth) 

 of 735 g./m.2/year and annual rates of trans- 

 fer (out) for live, dying, and dead compartments 

 of 2.137, 1.458, and 0.458, respectively. The 

 equations defining the system were: 



d(live)/dt = 735 - 2.137 x live 

 d(dying)/dt = 2.137 x live - 1.458 x dying 

 d(dead)/dt = 1.458 x dying - 0.458 x dead 



The actual rate of input to the live compart- 

 ment fluctuated around its annual mean because 

 growth rate was significantly correlated with 

 air temperature (fig. 2). Temperature at 

 Beaufort, N.C., was approximated with a sine 

 curve, in which the start of a cycle, the data 

 equivalent to zero radians, was May 1 (fig. 3). 

 Equations for air temperature as a function 

 of season and growth rate as a function of air 

 temperature were combined into an equation 

 of growth rate as a function of season. The 

 rate of transfer from the live compartment to 

 the dying compartment was greatest in the fall, 

 and was significantly correlated with minus 

 cosine in the seasonal cycle starting May 1. 

 This transfer rate was therefore made a 

 function of cosine. The solution of the set of 

 differential equations representing the model 

 was completed with an analog computer. The 

 equations thus obtained were: 



d(live)/dt = 735 [1 + sin (Z n x year)] - 2.0 

 [1 - 0.436 x cos (2 TTxyear)] x Ijve 

 d(dying)/dt = 2.0 [1 - 0.436 x cos (2n-xyear)] 



x live - 1.458 x dying 

 d(dead)/dt = 1.458 x dying - 0.458 x dead 



10 15 20 26 30 

 AVERAGE AIR TEMPERATURE I °C.) 



Figure 2. — Growth in length of J uncus as a function of 

 average air temperature during the period of observa- 

 tion. 



There is reasonable agreement between the 

 observed and computed values for the live and 

 the dead compartments and poor agreement 

 between observed and computed values for the 

 dying compartment (fig. 3). The reasonfor this 

 poor agreement is unknown. This compart- 

 mental model of Juncus production, however, 

 does explain some of the observed seasonal 

 cycles in standing crop and suggests that ob- 

 servations on standing crop and on growth and 

 longevity form a coherent body of data. 



12 



