United States 

 Department of 

 Agriculture 



Forest Service 



Intermountain 

 Forest and Range 

 Experiment Station 



Research Paper 

 INT-279 



July 1981 



Mathematical 

 Hypothesis for 

 Herbage Production 

 Potential on Pinyon - 

 Juniper Areas 



INTRODUCTION 



Our concern here is the estimation of herbage pro- 

 duction potential on wooded sites being considered for 

 conversion to grassland. The relation between such 

 production potential and four major variables affecting it is 

 discussed. A mathematical model for the relation is 

 presented along with a Fortran IV program to produce 

 tabled model output. Some empirical inputs to the model 

 were derived from data collected in the pinyon-juniper 

 type of north-central Arizona. 



The general form of the relationship is expected to 

 apply to pinyon-juniper areas of the West and may have 

 conceptual relevance to other woody plant communities. 

 Testing or refitting of the mathematical model to data from 

 other woodland or shrub communities may result in 

 suitable prediction models for use by local land managers. 



HYPOTHESIS-COMPONENT 

 SOURCES 



Herbage production values for 19 clearcut pinyon- 

 juniper sites in north-central Arizona were subjected to 

 regression screening processes for the simple additive 

 effects of a variety of independent variables measured on 

 these same sites (Clary and Jameson 1981). These simple 

 hypotheses were regarded as having some theoretical 

 basis and as being generally meaningful. The most useful 

 of the effects appeared to be annual precipitation, tree 

 cover, soil nitrates, and presence or absence of limestone 

 soils. 



•We attempt in this paper to develop a model more 

 rigorously tuned to the interactive nature of the relation 

 wherein the effects of some or all of the independent 

 variables change, depending on the levels of others. This 

 model is proposed as a reasonable approximation of the 

 true relation. The basic model structure was developed 

 from information available in the literature, but specific 

 coefficients were estimated from the Arizona data set. 



DISCUSSION OF HYPOTHESIS 

 COMPONENTS 



Annual precipitation (APR) is the source of soil moisture 

 needed for plant growth on most terrestrial sites. Also, as 

 is known, regional differences in the capacity of land to 

 produce plant matter are strongly and positively related 

 to APR (Coe and others 1976; Sims and Singh 1978; Webb 

 and others 1978). These circumstances, along with the 

 widespread availability of APR information,^ have led to 

 its inclusion in the model as a prime and convenient 

 indicator of regional differences in productivity. 



Within a region of limited APR-range, gross 

 differences in soil parent material can be expected to have 

 a major effect on plant response to APR. In particular, 

 reduced plant production on limestone-derived soils 

 compared to that on many other soils is evidently a 

 worldwide phenomenon (Whittaker and Niering 1968), 

 although some variations to this can occur (Ffolliott 

 and Clary 1975). This reduced production seems to be 

 most likely to occur in areas where soils are poorly 

 developed and are derived from relatively pure limestone 

 parent material. It is least likely to occur where soils 

 are highly developed from soil parent material with 

 substantial amounts of impurities (Jenny 1941). Generally, 

 the trend across arid and humid climates is for natural 

 plant communities supported by limestone soils to exhibit 

 a more xeric character than adjacent communities on other 

 soils. This xeric nature is often characterized by 

 reduced plant densities, different species composition, 

 or changes in community physiognomy. Thus, we expect 

 herbage yields to be generally lower on the limestone 

 soils than on many nearby soils. 



Climatological data National Oceanic and Atmosptiere Administration. 

 National Climatic Center, Asheville. N C, 



1 



