HYPOTHESIS DEVELOPMENT 

 AND ASSOCIATED HERBAGE 

 PRODUCTION POTENTIALS 



Estimates of specific forms and scales for the effects of 

 the independent variables were made from data trends, 

 within the general constraints of the hypothesized model. 

 In the modeling process, APR-effects were quantified first, 

 followed in order by cover, nitrification, and limestone. The 

 form of the relation was described mathematically accord- 

 ing to Jensen and Homeyer (1970, 1971) and Jensen (1973, 

 1976, 1979). This modeling process was used since it is 

 highly sensitive to curvilinear interaction, characteristic 

 of the expected relation. Some procedural detail is pre- 

 sented for those who may be interested in validating the 

 form and internal scales of the model with data from new 

 areas. Methods are also shown for simple reseating (refit- 

 ting) of the existing model in its entirety, to data from new 

 areas. 



The expected effect for APR on biomass production is, of 

 course, positive. Experience in the 5- to 25-inch (13- to 

 64-cm) precipitation zones of the Intermountain Area of the 

 West (Packer and others 1979, Stevens and others 1974) 

 suggests a flat to slightly concave-upward curve form. 

 APR to the 1 .35 power (APR ^■^^) appeared to be appropriate 

 for the Arizona data (Jensen and Homeyer 1971). Forced 

 through both zero and each herbage production value, 

 APR-effects were extended to APR=24 inches (61 cm) 

 (fig. 2) The APR-effect was scaled at that point to the scal- 

 ing height (YPAPR) for the Arizona data. YPAPR was then 

 explored for expected limestone-, sigmoidal cover-, ana 

 N-effects (fig. 3) (Some steps in the model development 



[fig. 2 and 3, and the Fortran IV program] are illustrated in 

 English units only. Model output [fig. 4 and table 1] is 

 shown in both English and SI units.) 



The expected negative limestone effect appeared to be at 

 least supported by the very few observations available on 

 limestone soils, and the expected cover- and N03-effects 

 were also fairly well expressed (fig. 3). The rather strong 

 trend indicated by the six data points of the upper line (NL, 

 N03 = 14.0), together with experience-based knowledge 

 that average-high productivity is not likely to exceed 4,500 

 lb/acre (5 040 kg/ha) (Stevens and others 1974), resulted in 

 specification of a sigmoid that asymptotes conservatively 

 at 4,200 lb/acre (4 704 kg/ha). It is possible that the 

 asymptote could be higher. The complete sigmoid is 

 reasonably well portrayed by the 10 data points for the 

 second line from the top (NL, N03 = 1.6). 



The sigmoids of the two bottom lines (L, N03 = 8.0 and 

 1 .0) are highly conjectural, but the greatly reduced scale of 

 these effects is one of the more important features of the 

 model. In general, the sigmoidal forms shown in figure 3 

 can be visualized as representing sections of figure 1 at 

 different N03 levels and with different scaling factors. 



The sigmoidal forms over cover were described using 

 (Jensen and Homeyer 1970, Jensen 1979). Associated 

 intercepts (FLORNL, FLORL), changing power (NNL, NL), 

 inflection points (INL, IL), and scaling heights (YPCNL, 

 YPCL) were all expressed as power functions of N03 

 (Jensen and Homeyer 1971; Jensen 1973, 1976). Note that 

 separate equations are developed for limestone and 

 noniimestone soils with each being displayed at two or 

 three N03 levels in figure 4. 



N03 



lb/acre 



kg/ha 





22 1 



X. 10 





W 



> 



o 

 a. 



z 

 o 



4000 r- 

 3000 

 2000 

 1000 

 L 



A : NONLIMESTONE SOILS 

 B : LIMESTONE SOILS 



4000 

 3000 

 2000 

 1000 



ORIGINAL 

 TREE COVER 

 (PERCENT) 



20 25 



20 30 40 50 60 (CM) 

 ANNUAL PRECIPITATION 



Figure 4. —Herbage production potential: the hypothesized 

 interactive relation involving annual precipitation, presence 

 or absence of limestone soils, tree crQwn cover, and nitrate 

 nitrogen in the soil. 



4 



