THE MEASUREMENT AND SPATIAL VARIATION OF ‘ ' I MDDAL WHEAT CONCENTRATIONS IN THE AMERICAN NARA-7 ' ’ ' WINTER WHEAT BELT IN 1964 ' Thesis for the Degree of Ph. D MICHIGAN STATE UNIVERSITY RALPH D (moss 1968 "n \Hc'fijfl 1 This is to certifg that the thesis entitled The Measurement and Spatial Variation of Modal Wheat Concentrations in the American Hard Winter Wheat Belt in 1964 presented by Ralph D. Cross has been accepted towards fulfillment of the requirements for Ph. D. degree in We Major professor Dam Januar 31 1968 0-169 ABSTRACT THE MEASUREMENT AND SPATIAL VARIATION OF MODAL WHEAT CONCENTRATIONS IN THE AMERICAN HARD WINTER WHEAT BELT IN 1964 by Ralph D. Cross Past researchers have seen fit to describe a portion of the agricultural mid-west as the hard winter wheat belt. Empirical obser- vations show that while winter wheat is widespread within the region, in reality there are areas of concentration interspersed with areas of sparsity. This study is an attempt to delimit modal areas of wheat production in the American Hard Winter Wheat Belt and to explain the variables of production that are responsible for the spatial distribu— tion of the modal areas. The initial phase of the study involved the location and mapping of modal concentrations of wheat production within the region. This was accomplished by the implementation of a statistical location quotient model as defined by Shyam S. Bhatia. The second phase of the study consisted of variable selection and the statement of hypotheses of the probable relationships between the independent variable and the dependent variables. Thus eight variables were hypothesized to explain the distribution of modal wheat concen- trations, and a step-wise multiple regression format was used to measure their statistical significance. In the step—wise procedure the variable mix was scanned by the computer and the variables were then ranked in the order of their sta- tistical significance. The analysis of the step—wise program, together with mapped data indicated that three of the eight variables were contributing very little to the explanation. These were subsequently deleted to produce the final model. Y = X1 + X2 + X3 + X5 + X6 + e where: X1 is the number of acres of flat land per county. X2 is the number of acres of loam soils per county. X3 is the average amount of soil moisture per acre in each county. X5 is the distance to the nearest second order market. X6 is the average farm size per county. e is the random error term. The test of the model yielded a multiple correlation coefficient of 0.803, indicating that 80.3 percent of the spatial variation of modal wheat concentrations within the selected region could be explained by the variables included. It is suggested that many of the previous qualitative generaliza- tions concerning the spatial variation of modal wheat concentrations in the American Hard Winter Wheat Belt are substantiated and expanded upon by the results of this study. However, the importance of the substan- tiations should not be overemphasized. This study is limited in time as well as in area. In other countries or other regions where data may be collected in somewhat different fashion, or where cultural activities and/or the physical environment may differ greatly from the study area, there may be a necessity for operationalizing some new variables. How— ever, the variables selected in this study may well provide the start— ing point for other geographic studies of wheat concentrations. THE MEASUREMENT AND SPATIAL VARIATION OF MODAL WHEAT CONCENTRATIONS IN THE AMERICAN HARD WINTER WHEAT BELT IN 1964 BY .A .) Ralph DEACross A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Geography 1968 ACKNOWLEDGEMENTS Upon completion of a research project such as this one, it is difficult to single out everyone who has contributed to its compilation. I wish to express my appreciation to Orville W. Bidwell of Kansas State University for his assistance in data collection. Thanks are also due to Robert C. Brown who contributed substantial advice and criticisms, as did Jack E. Moore and my other colleagues at Oklahoma State University. A very special thanks is extended to Dr. Ian M. Matley who super- vised the preparation of this thesis and was very instrumental in building my self—confidence, as well as being a great inspiration to me. Acknowledgement also goes to the two Oklahoma State University research facilities which contributed to the completion of this work: the Research Foundation which made funds available for the research, and the Computer Center which provided computer time for the analysis of the data. Finally, I would like to acknowledge my family whose perseverance and sacrifices over the years have made this thesis possible. ii TABLE OF CONTENTS ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . LIST OF ILLUSTRATIONS . . . . . . . . . . . . . . . . . . Chapter I. INTRODUCTION. . . . . . . . . . . . . . . . . . . . Review of the Literature of Density Measurements Review of the Theoretical Literature . . . . . . Review of the Substantive Literature . . . . . . II. MODAL WHEAT CONCENTRATIONS IN THE AMERICAN HARD WINTER WHEAT BELT . . . . . . . . . . . . . III. THE PREDICTOR VARIABLES . . . . . . . . . . . . . . The Physical Variables . . . . . . . . . . . . . Economic and Social Variables . . . . . . . . . . IV. AN EMPIRICAL ANALYSIS . . . . . . . . . . . . . . . The Step—Wise Multiple Regression and Correlation Procedure . . . . . . . . . . Average Size of Farm . . . . . . . . . . . . . . Amount of Flat Land . . . . . . . . . . . . . Distance to Second Order Market . . . . . . . . . Loam Soils . . . . . . . . . . . . . . . . . . . Soil Moisture . . . . . . . . . . . . . . . . Rural Population Density . . . . . . . . . . Annual Growing Season Precipitation . . . . . . . Average Yield per Acre . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . V. CONCLUSIONS . . . . . . . . . . . . . . . . . . . . SELECTED BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . Page ii 10 15 29 40 4O 46 50 51 52 55 60 63 67 69 71 74 80 LIST OF TABLES Table Page 2.1 Sample Counties . . . . . . . . . . . . . . . . . . . . . . . 38 4.1 Step-Wise Procedure of the Model . . . . . . . . . . . . . . . 53 4.2 Simple Correlation Matrix . . . . . . . . . . . . . . . . . . 56 4.3 Relations Between Modal Wheat Concentrations and Independent Variables . . . . . . . . . . . . . . . . . 57 4.4 Model -— Elimination Sequence . . . . . . . . . . . . . . . . 72 iv 10. 11. 12. 13. LIST OF ILLUSTRATIONS Hard Winter Wheat Region . . . . . . . The American Hard Winter Wheat Belt . . Modal Concentrations in the American Hard Winter Wheat Belt . . . . . . . Modal Wheat Concentrations . . . . . . Sample Counties American Hard Winter Wheat Belt . . . . . . . . . . . . . Average Farm Size . . . . . . . . . . . Flat Land . . . . . . . . . . . . . . Average Distance to Second Order Market Loam Soils . . . . . . . . . . . . . . Soil Moisture . . . . . . . . . . . . Rural Population Density . . . . . . . Annual Growing Season Precipitation . . Average Yield per Acre . . . . . . . . Page 31 33 35 36 39 54 59 61 62 64 66 68 70 CHAPTER I INTRODUCTION Geographers, in their description of the spatial variation of agricultural phenomena, frequently have shown the tendency for various agricultural enterprises to be concentrated in certain areas. In many instances, these concentrations are so empirically apparent that they have been set apart and labeled as regions or belts. Considerable attention has been devoted to developing methods of delimiting boundaries for such agricultural regions. Often only one criterion, such as wheat, is used to provide a basis for boundary de- marcation. Despite the method used to delimit regional boundaries, the region is frequently treated as being homogeneous, at least in terms of the distribution of the one delimiting criterion. However, the homo- geneity of the distribution of the agricultural commodity is not neces- sarily real. Generally, there will be found zones of varying densities of the commodity throughout the region. It can also be noted that in many instances there are dense concentrations of one agricultural com— modity interspersed to a lesser degree with other less important agri- cultural commodities. Moreover, the presence of an agricultural commod- ity within such an area is usually explained in terms applicable to the entire region whereas in reality these conditions may or may not exist in the same degree throughout the region. Therefore, it can be seen that so—called homogeneous regions are not necessarily homogeneous in all aspects, but in reality consist of varying degrees of densities in the distribution of geographical pheno- mena within them. This thesis is focused on the measurement and explana— tion of these higher density patterns, here called modal concentrations, in one of these "homogeneous regions," the American Hard Winter Wheat Belt. Map analysis and comparison indicate that the general patterns of wheat observed on the_landscape are not significantly different from the patterns formed by other forms of agricultural land use. Thus, the following review of the literature on density measurements of agricul- tural land use provides a basis from which this research can be built. REVIEW OF THE LITERATURE OF DENSITY MEASUREMENTS The measurement and mapping of patterns of crop densities or crop concentrations have long been carried out by geographers. A very early and long-used method to measure and identify crop density patterns is the use of ratios and isopleths. The ratios are utilized to determine the area of concentrations, and the isopleths are used to identify these areas on maps. Many kinds of ratios have been employed by geographers. One of the most common is the ratio of population to area used to determine popu- lation density. Other examples are the ratio of area in crops to total land area, the amount of arable land in proportion to farm population, the area of crops to arable land, etc. Thus it can be seen that the possibility for the use of a great many ratios exists for the measure- ment of densities of various types. One of the first American geographers to employ the ratio—isopleth method was Wellington D. Jones.1 At the time Jones pointed out that the use of ratios as a geographical technique was not new. However, he indicated that the use of ratios had primarily appeared in the form of statistical tables and only seldom in the form of maps. He recognized the mapping of quantitative data in the form of dot maps to reveal re- gional similarities and differences in densities. He cited V. C. Finch and O. E. Baker2 as the first major contributors of dot maps portraying certain types of agricultural activities. However, ratios cannot be mapped by the dot method. The dot method is employed cartographically as a device to show density patterns of an individual phenomenon and not the relations between phenomena. Moreover, the relation between phenomena is frequently more meaningful than are the absolute values of individual phenomenon. Jones was convinced that in many phases of regional investigation the isopleth map was superior to the dot map. Jones' first study using ratios and isopleths consisted of a series of isopleth maps be constructed dealing with agriculture in India.3 He based his maps on ratios such as the area of all crops to total land area, and the area in one crop to areas in other crops or groups of crops. He later applied these techniques to other regions both alone and in conjunction with other geographers. Jones outlined his method as follows: 1Wellington D. Jones, "Ratios and Isopleth Maps in Regional Inves— tigation of Agricultural Land Occupance," Annals of the Association of American Geographers, Vol. XX (December, 1930), pp. 177—87. 2V. C. Finch and O. E. Baker, Geography of the World's Agriculture (Washington, D.C.: U.S.D.A., 1917) (Cited by Jones). 3Wellington D. Jones, "An Isopleth Map of Land Under Crops in India,” Geographical Review, Vol. XIX (July, 1939), pp. 495—96. The method followed by the writer in selecting ratio values for the identification of particular types of agri— culture is purely empirical. The figures on the maps are inspected in localities where field work or a study of ex— isting literature has shown a sharp change within a short distance from the dominance of one kind of agriculture to another. Isopleths for ratio values which show marked change within these localities are then drawn over the en- tire area covered by the maps. Thus, on the map of gallons of milk produced annually per acre in crops, the change in values from one tier of counties to another in northern Illinois is from sixty or above to forty or below. Iso- pleths of sixty, fifty, and forty, therefore, were drawn, with twenty-five added to show areas with very low milk production... Jones summarized: Ratio and isopleth maps, so far as they have been employed, appear to be useful tools in the regional in— vestigation of agriculture land occupance. New and bet— ter ways of using them, however, probably will be dis- covered. Certain it is that they constitute no infal- lible guide to the discovery and interpretation of much of significance in regional study. Insofar as their employment appears materially to aid such investigation, however, they may well receive more attention from geo- graphers than has been the case in the past. Foster Elliot and O. E. Baker were highly suggestive as to the utility of ratios and isopleth maps for the limitation of their broader regional classifications. Elliott, working for the U. S. Bureau of the Census, was concerned with classifying districts on the basis of farming type. His method was to use a percentage coefficient which was actually a ratio of farm income to type of farming source.6 Baker, in a series of articles, used ratios and isopleths in defining his agricultural 4Jones, "Ratios and Isopleth Maps," p. 181. 5Jones, "An Isopleth Map," pp. 495. 6Foster F. Elliot, Types of Farming in the United States (Washing- ton, D. C.: U.S. Government Printing Office, 1933), p. 5. regions of North America.7 He was primarily concerned with defining regional boundaries based on ratios of value of products to areal extent. Whereas Elliott and Baker relied heavily on value of crops, Hartshorne and Dicken followed Jones' lead and based their ratios largely on acreage in their comparative study of agricultural regions of Europe and North America. Hartshorne stated: ...the ratio based on acreage was regarded as more significant geographically than one based on value, not only because it is an actual area measurement, but also because it fluctuates much less widely from year to year. In a later study Hartshorne indicated that there are two sets of factors which are of basic importance in the agricultural geography of any area: the extent of productivity of arable land, and the agricul— tural population.9 In this study Hartshorne was attempting to show the relationship of cultivatable land to the distribution of farm population, the value of land in proportion to farm population, and, finally, the value of products in proportion to farm population. Hartshorne here was attempting to determine the degree to which the land was support- ing the population living on it in terms of the variables mentioned previously. 7O. E. Baker, "Agricultural Regions of North America," Economic Geography, Twelve Installments (October, 1926—1934). 8Richard Hartshorne, and Samuel Dicken, ”A Classification of the Agricultural Regions of Europe and North America on a Uniform Statisti— cal Basis," Annals of the Association of American Geographers, XXV (June, 1935), p. 102. 9Richard Hartshorne, "Agricultural Land in Proportion to Agricul— tural Population of the United States,” The Geogrgphical Review, XXIX (July, 1939), pp. 488—92. The land—population variable would appear to have an effect on or be the result of the kind of crops grown in a particular region, and also be influential in determining the concentration of certain agri- cultural commodities. These ratios are not so effective a means of explaining crop concentrations as are area to area ratios. They do, however, indicate that there is a relationship, in some instances, between farm population and crop concentrations. G. T. Renner, summing up a study conducted by the land section of the U. S. National Resources Board, which compiled data to use in the construction of a land-use problem regions map, mentioned the use of computed index factors to determine the value of land use.10 In this case a ratio of land use value to the area of minor civil divisions was used as a basis to determine land use problem regions. Griffith Taylor had a slightly different approach to the use of ratios and isopleths.11 Taylor used ratios between climate and topo- graphic structure in proportion to area in crops to explain the distri- bution of crops in southern Ontario. In preparing his maps he used isopleth values of each physical factor to show the relationship of it to the distribution of crops. Taylor also worked out a simple nomograph -- which he called a "quo—graph" -— for calculating densities. Taylor pointed out that such a technique had been used frequently by physicists but had not been used as extensively by geographers and economists. Following Taylor's lead, J. R. Whittaker conducted a study of the 10G. T. Renner, "Statistical Approach to Regions," Annals of the Association of American Geographers, XXV (September, 1935), p. 137-52. 11Griffith Taylor, "Climate and Crop Isopleths for Southern Ontario," Economic Geography, XIII (January, 1937), pp. 89—98. agricultural gradients of southern Ontario in which he constructed a map using isopleths of the percentage of farm land and crops per unit area to show the relationship between crOp distribution and physical fac— tors.12 He was successful in mapping areas of varying cropland densi— ties. In each of the above instances an attempt was made to identify crop densities. But in some studies only very loose densities were calculated for the purpose of drawing rather broad regional boundaries. In others, such as Whittaker's study, more precise densities were identified in order to show the relationship of certain aspects of crops to other phenomena. Helen L. Smith, writing about agricultural land use in Iowa, pre— sented much of her data in the form of isopleth maps.l3 Most of the ratios she used as bases for her maps were percentages of total crop- land in proportion to a variety of crop types or the number of animals or animal production per acre of cropland. These maps tended to show very well the general areas of concentrations of each crop for the State of Iowa. However, the intensity of the concentration in propor- tion to other parts of the corn belt, the dairy belt, etc., were not apparent. Thus, these concentrations, although suitable for the State of Iowa, are limited by political boundaries, and their validity as true concentrations, in View of the region as a whole, is questionable. Still another study worthy of mention here is John C. Weaver's analysis of changing patterns of cropland use in the Central United 12J. R. Whittaker, "Agricultural Gradients in Southern Ontario," Economic Geography, XIV (April, 1938), pp. 109—20. 13Helen L. Smith, "Agricultural Land Use in Iowa,‘' Economic Geo ra h , XXV (July, 1949), pp. 190-200. States. Weaver stated his purpose was ...to define and analyze the patterns of changes of these closely interrelated crop associations."14 He also selected ratios as a means of showing these interrelationships. Weaver's study resulted in a series of maps which show the various crop concentrations for 1940 and 1950. The changes in relative areal extent between the two periods were determined in regards to the farmer's , actual intent . Weaver had this to say about his choice of ratio: The ratio of seemingly most effective utility in ap— proaching an understanding of relative strength of specific crops in the evolving agricultural scene has been the per- centage of total harvest cropland occupied.15 Like Hartshorne, Weaver also regarded an area to area ratio as the most significant indicator of the spatial variation of cropland patterns. In support of this idea Weaver said: Acreage data have been assumed to be the most useable measure of the farmer's actual intent, and far more reliable as an index for the purposes of this study than the unstable and often short term variability of such measures as production (influenced so heavily by seasonal vagaries of yield) or value (involving rapidly changing market prices for which the establishment of satisfactory common denominators is extremely difficult and often misleading).1 Many of the studies by geographers mentioned in this brief review used an area to area ratio method as well as other types of ratios. 14John C. Weaver, "Changing Patterns of Crop Land Use in the Middle West," Economic Geography, XXX (January, 1954), pp. 1-47. 15Ibid, p. 2. 16Ibid. Hartshorne and Weaver suggested that the area to area ratio was far superior geographically to any other type in the measurement of agri— cultural concentration. Smith also strongly bmplied that the area to area ratio.was more practical than any other for much the same reasons. They felt that the areal ratio was more useful in the measurement of crop concentration than other ratios because it was an actual measure- ment of area and that it tended to be more stable from one year to the next. Smith utilized Jones' method of mapping ratios with the use of isopleths, as did Hartshorne and Weaver. However, like her predeces- sors, she failed to recognize the inadequacy of the application of the simple ratio of one variable in proportion to another as a means of outlining crop densities within a region. Moreover, she biased the density of her concentrations by limiting her analysis to an area within state boundaries. Thus her findings could neither be considered as valid for a comparison with the region as a whole nor for a compara- tive study with another state. Another kind of ratio which uses an area to area format and yet eliminates the difficulties for comparative analyses,as exemplified by Smith's study, is a ratio formulated by Shyam S. Bhatia.17 Bhatia suggested a more detailed kind of ratio which he evolved and used in an analysis of crop concentration and diversification in India. Bhatia calculated an index he called the "location quotient" which is used to determine the regional concentration of crops. 17Shyam S. Bhatia, "Patterns of Crop Concentration and Diversifi- cation in India," Economic Geography, XLI (January, 1965), pp. 39—56. 10 Area of Crop X in a Area of CrOp X in Index for deter— . component areal unit o the entire countr mining concentration = — of Cro X Area of all crops in the ’ Area of all crops in p component areal unit the entire country18 He described its use: If the index value is greater than unity, the com— ponent areal unit accounts for a share larger than it would have had if the distribution were uniform in the entire country, and, therefore, the component areal unit has a concentration of the agricultural distribution under study.19 The actual use of this sort of index in geographical studies did not originate with Bhatia's study; only the application of it was new. He pointed out in his paper that similar indexes have been used in studies of urban and industrial geography. He cited the work of three geographers who used similar ratios in studies of cities or industries. These are: L. L. Pownell, who did a study of the function of New Zealand towns;20 John W. Alexander, who demonstrated the use of a location quotient for manufacturing;21 and John W. Webb, who discussed the basic concept in the analysis of small urban centers in Minnesota.22 REVIEW OF THE THEORETICAL LITERATURE Because of the enormous number of contributions dealing with the 18Ibid., p. 40. 19Ibid. 20L. L. Pownell, "Function of New Zealand Towns," Annals of the Association of American Geographers, XLIII (December, 1953), pp. 332-50. John W. Alexander, "Location of Manufacturing: Methods of Mea— surement," Annals of the Association of American Geographers, XLVIII (March, 1958), pp. 20-26. 2John W. Webb, "Basic Concepts in the Analysis of Small Urban Centers of Minnesota," Annals of the Association of American Geo ra hers, XLIX (March, 1959), pp. 55—72. ll analysis of agricultural location, this review of the literature cannot be considered exhaustive. The purpose here is to merely provide a foundation upon which the current study can be built. Moreover, there is an apparent lack of studies in the literature pertaining to this specific sort of problem. Therefore, this review of the literature will serve only to provide a basis for the selection of variables suitable for explaining modal wheat concentrations. David Ricardo, the English economist, is generally considered to have initiated a basis for current locational theory with his evolve- ment of the theory of agricultural rent.23 Ricardo contended that the more fertile lands were brought into cultivation first, and that in- creases in population would necessitate the development of less fertile land, where the costs of production would be higher. Thus, the owner of the more fertile land would receive a net return (rent for his product) because of lower production costs. Although Ricardo recognized the factor of transportation costs, it was Johann Heinrich von ThNnen who developed it more fully. ThNnen's theory tries to account for the dis- tribution of agriculture around an urban center in an isolated state.24 Given certain premises, he postulated that agricultural activity will form around the urban center in the form of concentric rings and that the location of each activity will depend on the amount of rent it can demand at a particular location less the cost of production and the cost of transportation. 23David Ricardo, Princi 1es of Political Econom and Taxation, ed. by E. C. L. Gonner (London: C. Bell & Sons, Ltd., 1913). 24J. H. von Thanen, Von Thunen's Isolated State, English Edition; edited with an introduction by Peter Hall (New York: Pergamon Press, 1966). 12 Edgar S. Dunn has recently more fully developed and formalized the theory of economic rent as a prime factor in the location of agricul— ture.25 He attempts to develop the theory at three levels of aggrega- tion: (1) firm (the individual farm), (2) industry (particular crop or commodity), and (3) aggregative level (agricultural, manufacturing, and service segments of the economy). However, Dunn tends to emphasize the industry level of aggregation. Dunn also points out that location theory must encompass the totality of the economy with particular atten— tion focused on the distribution of inputs and outputs and prices and costs. Theodor Brinkman, an agricultural economist, also attempted to derive a few generalizations about agricultural location.26 He tried to compile all of the forms of spatial orientation into an algebraic formula which he refered to as the "index of savings." Supposedly, the product for which the index is greatest is situated in the most favor- able position near the market. Moreover, Brinkman also concluded that the farms situated nearest the market will be the most intensely culti- vated and the most diversified. August Lgsch incorporated some of the principles derived by both Brinkman and Thunen.27 Like ThNnen, and unlike Brinkman, he used 25Edgar S. Dunn, The Location of Agricultural Production (Gaines- ville: Unitersity of Florida Press, 1954). 26Theodor Brinkman, Economics of the Farm Business, English Edition; with introduction and notes by F. T. Benedict (Berkeley: University of California Press, 1935). 27August Lgsch, The Economics of Location, Translated by William H. Woglom and Wolfgang F. Stopler (New Haven: Yale University Press, 1954). l3 economic rent as the main determinant in the orientation of production. However, following Brinkman he attempted to establish a more exact algebraic formula for the forces of orientation. Lgsch then proceeded to develop three algebraic formulae which account for (l) the conditions for ring formation, (2) the reasons for ring formation, and (3) the boundary line between the two products which form the basis for his spatial arrangement system. The orientation principle can be extended somewhat by adapting the "central place theory" of Walter Christaller.28 Christaller advanced the central place theory in which he postulated that service centers would tend to be dispersed over the landscape in a uniform order with hexagonally shaped hinterlands. This postulation is based on two premises: (1) the topography is uniform to the extent that no one site has an advantage of slope or of physical influences on transportation routes, and (2) the economy is such that no one site has an advantage in the production of primary products. The central place theory was evolved to explain the distribution or spatial organization of urban places. It might also be used in ex— plaining the location of agricultural activity, since the urban places would serve as market foci for agricultural activity which would be distributed in an orderly fashion around these nodes. The study of areal organization of human activity in the form of field studies was pioneered in particular by R. J. Platt29 and 28Walter Christaller, Cgptral Places in Southern Germgpy, Trans— lated by C. W. Baskin (Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1966). 29R. S. Platt, "A Detail of Regional Geography: Ellison Bay Com- munity as an Industrial Organism," Annals of the Association of American Geographers, XVIII (March, 1928), pp. 81—126. 14 C. C. Colby.30 A. K. Philbrick developed this theme further into what he calls "areal functional organization."31 Philbrick contended that all human activity is dispersed in a more or less orderly fashion and that all human activity has nodes which are interconnected. ...individual interconnected areal units of occupance possess two kinds of areal relationships simultaneously. In one case it is the parallel relationship of similar— type units. In the other case it is a series of inter- connections between unlike establishments focusing upgn the core of a nodal area of functional organization. Later in his paper Philbrick added the nested hierarchy principle, thus implying a hierarchy of focal units. Following the premise that the focal units of agricultural activity beyond the farm itself are the market centers, there could then be found a hierarchy of market centers for agricultural commodities. Each of the foregoing theories have certain similarities, and several conclusions can be drawn from them. First, theoretically the principles of economic rent and/or the friction of transportation costs are the most significant economic factors in explaining the location of agricultural production. Second, agricultural activity will tend to be organized around market nodes in an orderly fashion. Third, juxtaposi- tion to market is most ideal because the closer to the market, the greater the economic rent and the smaller the transportation costs. Finally, with the exception of Ricardo, the physical factors of the 300. C. Colby, "Centrifugal and Centripetal Forces in Urban Geogra— phy," Annals of the Association of American Geographers, XXIII (March, 1933), pp. 1—20. 31A. K. Philbrick, "Principles of Areal Functional Organization in Regional Human Geography," Economic Geo ra h , XXXIII (October, 1957), pp. 299-336. 321bid., p. 307. 15 environment are either ignored by the theoreticians or considered as uniform throughOut, thereby contributing little or nothing to the understanding of the location of agricultural production.‘ Although Dunn does recognize the impact of physical factors on agricultural land use, he considers them as passive. He believes that man combines the conditions of production and resources for the best use. He said that man's motive for adjusting crop and livestock systems to the physical environment is the profits he derives. The question of net returns reveals that the active factors affecting the farm and extent of land use are the economic factors. These factors exert an influence upon types of farming through their effect upon returns in relation to the resources used. These economic forces operate through prices of products and prices of factor inputs. 3 REVIEW OF THE SUBSTANTIVE LITERATURE The foregoing section has dealt primarily with the general aSpects of the location of agricultural production. This section will deal more specifically with the location of wheat and/or cash-grain produc— tion. A large part of the literature concerning wheat farming has dealt with its quantitative distribution -— primarily the distribution of wheat yields -— and the relationships of production to variables, both physical and cultural. The research of such scientists as the crop ecologist, the agronomist, and the agricultural meteorologist has dealt primarily with the relation of various physical elements to wheat pro- duction, although social and economic factors have been considered as well. 33Dunn, Agricultural Production, p. l. In comparison, very little has been contributed to explain the areal distribution of cash grains within cash-grain regions. Only the variables accounting for the broader regional concentrations have been examined extensively. In this regard, the geographer, as well as others, has contributed substantially to the body of knowledge regarding the delimitation of broad regional concentrations. 0. E. Baker classifies the physical conditions which affect the production of wheat into four groups: 1. Temperature conditions, particularly growing season temperatures and dates of occurrence of spring and fall frosts. 2. Moisture conditions, i.e., rainfall, snowfall, hail, fog, humidity, rate of evaporation. 3. Topography, or land form, i.e., the configuration of the earth's surface, degree and direction of slope, roughness, or smoothness of the land. 4. Soils, including both physical structure and chemical and bacteriological characteristics.3 Baker describes the limits of world wheat production on the basis of his four groups of physical conditions. He uses dot maps to show wheat producing regions. He uses iSOpleths to show temperature and moisture conditions. He also explains the limitations imposed by the interrelations of the four groups of physical factors on land suitable for wheat production. Earl B. Shaw places some climatic limits on wheat production: The lower-temperature limit for wheat production is the 57° isotherm for the three summer months. It has 340. E. Baker, "The Potential Supply of Wheat," Economic Geography, 1 (1925), p. 21. 17 no high temperature limit when grown by practices of irrigation; but it will not grow well where heat is combined with high humidity, robably because of the severity of fungus diseases.3g His description of wheat location is stated in terms of production and involves mainly a ranking of production by country. Thus, Shaw de— fines the physical, social, and economic limits for wheat production in .various places throughout the world, but he makes no mention of factors which might result in the sporadic distribution of wheat within the various wheat belts. Likewise, J. Russell Smith,36 Loyal Durand,37 R. S. Thoman,38 J. S. Alexander,39 and several others have also suggested several deter- minants of a physical nature -- although not ignoring the social and economic factors -— to explain the regional concentration of wheat. K. H. Klages recognizes some of the physical conditions suggested by Baker, Shaw, and others as influential in crop distribution and limita- tion.40 Klages in particular suggests that soil factors may be very influential in explaining local concentrations of crops: 35Earl B. Shaw, World Economic Geography (New York: John Wiley and Sons, 1955), p. 308. 36 J. R. Smith, and others, Industrial and Commerical Geography (New York: Henry Holt and Co., 1955). 37Loyal Durand, Economic Geography (New York: Thomas Y. Crowell Co., 1961). 38 R. S. Thoman, The Geography of Economic Activity (New York: McGraw—Hill, 1962). 39J. W. Alexander, Economic Geography (Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1963). 40K. H. W. Klages, "Geographical Distribution of Variability in Yields of Field Crops in the States of the Mississippi," Ecology, XI (April, 1930). 18 The potential crop producing ability of a given area is dependent primarily on the existing climatic and soil conditions under which the crops in question must be grown. The specific effect of the climatic factors may be modified to a considerable degree by local soil con- ditions. The climatic factors are generally considered as having regional influences on plant behavior, while the edaphic factors may account for many local manifes- tations of plant-life.41 The edaphic factors are many, including soil fertility, biotic factors, and the physical structure of the soil. With the modern tech- nology of fertilization, the first two factors are minimized and the third factor is pointed out frequently in the literature as a location determinant. Van Royen stated that: Wheat prefers fertile silt or clay loam soils, especially those which contain a certain amount of lime. On the stony glacial soils of New England, where corn gives satisfactory yields, wheat has never done well, except during the first few years of cultivation. Although in this case climatic and soil factors are difficult to separate, the latter undoubtedly strongly affected yields. 0n the well—drained, fertile, marine clay silts of the Netherlands and northwestern Germany, wheat is successful- ly grown, but on adjoining sand and infertile glacial soils it cannot be economically produced. M. F. Morgan pointed out that: The principal soils of the subhumid to semiarid grass- lands of the Great Plains and Columbia Plateau that are used for wheat are the loans and silt loams of the smoother upland areas, although the Fargo Clay and the 4111mm, p. 293. 42William Van Royen and Nels A. Bengtson, Fundamentals of Economic Geography (Englewood Cliffs, N. J.: Prentice-Hall, Inc., 1965), p. 256. 19 Pullman and Richfield silty clay loams are exceptions both in texture and in their physiographic position.4§ L. P. Hoag is not in complete accord with Klages as he pointed out that.soil type or fertility is not necessarily a cause for the location of cash-grain crops: In each of three states, Minnesota, Iowa, and Illinois, it was specifically pointed out by agricultural experts who were interviewed that both highest corn yield per acre and the most fertile soils were not necessarily co—terminous with cash—grain areas. Fertile soils may be necessary for successful cash-grain farming, but not all fertile soils can be so used. 4 According to Klages, climatic factors (temperature and precipita- tion) are at least co—equal to the edaphic factors in their contribu- tions to crop production. These factors would tend to be more uniform than soil texture within a region such as the American Hard Winter Wheat Belt, but there would be a certain range within which the bulk of the wheat land would be situated. M. K. Bennett and H. C. Farnsworth gave a very good summary of the optimum rainfall range for wheat: More than half of the world wheat acreage lies in regions where annual rainfall averages 15—25 inches; and heaviest concentration is in the 15—20 inch zone. Only about 10 percent of the acreage lies in regions where annual pre— cipitation falls below 15 inches, and much of this is irrigated. Three—fourths of the acreage lies within the 15—35 inch zone, and only about 15 percent in zones of 45 higher rainfall and 10 percent in zones of lower rainfall. 43M. F. Morgan, et al., "The Soil Requirements of Economic Plants," Soils and Men, Yearbook of Agriculture (Washington, D.C.: U.S. Govern- ment Printing Office, 1938), p. 760. 44L. P. Hoag, ”Location Determinants for Cash-Grain Farming in the Corn Belt," The Professional Geographer (May, 1962), p. 5. 45M. K. Bennett and H. C. Farnsworth, "World Wheat Acreage, Yields, and Climates," Wheat Studies, XIII (March, 1937), p. 272. 20 Moreover, annual distribution of rainfall is also a significant factor in the production of wheat. Precipitation is desirable prior to and subsequent to planting in the fall and also desirable in the early spring. It is least desirable just prior to harvest. Temperature would vary greatly within a large region as well as from season to season. Like precipitation, optimum temperature condi- tions can be associated with wheat producing areas. Low temperature regimes are the most limiting, while high temperatures become critical only when combined with high humidity. The effect of temperature on the growth of wheat can be computed by several systems which have been devised for this purpose. One such system is the "doctrine of thermal constants" devised by F. A. F. Reaumur and elaborated upon by C. Abbe.46 M. Y. Nuttonson summed up Abbe's inter— pretation of the doctrine as follows: A given stage in the development of any plant is reached when that plant has received a certain amount of heat, regardless of the time required. For each plant and for each successive stage there was assumed to be a definite heat requirement, which generally received a mathematic expression in the form of so—called "heat units." The unit was a degree on one of the several thermometer scales. However taken, temperature observations were generally reduced to terms of average or mean daily temperatures. The readings for all the days involved in the period in question were combined, and the sum called the "thermal constant," since it was assumed to be constant for the plant where ever and when ever grown. Units based on this system are designated "day degrees."47 46Cleveland Abbe, "A First Report on the Relations Between Climates and Crops," U.S.D.A. Weather Bureau Bulletin No. 342, (1905). 47M. Y. Nuttonson, Phenology and Thermal Environment as a Means for a Physiological Classification of Wheat Varieties and Flora Physiological Classification of Wheat Varieties and for Predicting Maturity Dates of Wheat (Washington, D.C.: American Institute for Crop Ecology, 1953), p. 12. 21 A second system, the "remainder index system," according to Nuttonson, is the most widely used in studies attempting to correlate growth of wheat with temperature. The remainder index system is really only a modification of the thermal constant theory. Whereas Reaumur used the sum of all mean daily temperatures recorded, those who followed used only positive temperatures on the centigrade scale. Nuttonson pointed out that: Various methods of calculating day-degree summations of the growing period of wheat have been used. The most commonly used method is that of adding up all mean tempera— tures above 32° F. that might have occurred. Some workers considered, however, that a base line of 32° F. was less desirable for wheat than 38° to 42° F. —— the minimum temperature range at which wheat will germinate. The remaining systems bear mentioning even though they are not as widely used by crop ecologists as the remainder index system. The first of these is the "exponential system," the principle of which states that for each rise in temperature of 10 degrees, the rate of the chemical reaction involved increases by a multiple of two. The reaction pertains to the velocity of chemical reactions in response to tempera- ture changes. A second of these is the "physiological indices system," the object of which is to develop a means of ascertaining the quantity of heat required for the ripening of crops so isoclimes can be plotted on maps. A third method is the "evapotranspiration" or "growth unit" system. The main proponent of this system was C. W. Thornthwaite who developed an empirical expression for determining "potential 48M. Y. Nuttonson, Wheat Climate Relationships and the Use of Phenology in Ascertaining the Thermal and Photo—thermal Requirements of Wheat (Washington, D. C.: American Institute of Crop Ecology, 1955), p. 5. 22 evapotranspiration” from mean daily temperatures and the length of day.49 Thornthwaite defined a growth unit as the amount of development that will occur in a plant while a unit amount of water is being transpired. A fourth is the "photo—thermal system." In this system there is an attempt to combine the length of day with the heat summation to account for the intervals between phenological events. Other manifestations of these elements —- temperature and moisture -— when considered together or in conjunction with soil may be more meaningful as determinants. Moreover, some of the climatic conditions suggested by Baker, such as growing season temperature, date of first and last frosts, rainfall, snowfall, hail, and fog, would serve as regional delimiters, and yet not necessarily be very significant as location factors of wheat concentrations within these regions. Amount and distribution of rainfall are naturally important factors, as has been previously indicated in both a regional sense as well as in a local situation. But perhaps even more important is soil moisture which is the result of the interaction of precipitation, temperature, and the physical structure of the soil. In regard to soil moisture, Klages said, "In dry areas moisture is the main and frequently the only factor limiting crop production."50 It has been noted in several studies of wheat yields that wheat planted in soil with an adequate supply of stored soil moisture produced better than wheat planted under less favorable circumstances despite subsequent rainfall. 49C. W. Thornthwaite, "An Approach Toward a Rational Classification of Climate," Geographical Review, XXXVIII (January, 1948), pp. 55-94. 5OK. H. W. Klages, Ecological Crop Geography (New York: MacMillan Co., 1961), P. 207. 23 S. C. Salmon had this to say about soil moisture: If moisture in the surface soil is deficient, the seed may not germinate at all, or it may germinate the fol— lowing spring. If it does not germinate until spring and temperatures remain high after emergence, the plants will not head because the "winterness" requirements are not satisfied. In any event the crop will mature late and consequently is more likely than usual to be injured by rust, heat, and drought later in the year. The term "adequate moisture” as used here is defined as a quantity of soil moisture at or below field capacity, and yet substantially above the wilting coefficient. "Field capacity" is the amount of soil moisture remaining after the gravitational drainage of excess water. Available moisture varies with soil texture and ranges anywhere from five to forty percent of field capacity. Thus, the variation in soil moisture is primarily a function of soil texture. The final physical condition suggested by Baker is topography or slope. All of the wheat farming in the American Midwest is very highly mechanized, thus the slope factor is a very significant factor in wheat location. The United States Soil Conservation Service indicated that soils with a slope of zero to eight percent are suitable for mechanized farming. An eight percent slope is defined as an overall change in elevation of eight feet within a lOO-foot horizontal distance. However, wheat is grown on much steeper slopes, such as the white winter wheat area ("Palouse Country") of the Pacific Northwest. J. J. Hidore in his study of the relationship between cash-grain farming and landforms uses a slightly more restricted definition of level land in terms of farming. Hidore said: 518. C. Salmon, "Climate and Small Grains," Climate and Man, Year— book of Agriculture (Washington, D.C.: Government Printing Office, 1941), p. 325. 24 ...the definition of flat land had to be derived from existing literature, and investigation of which indi- cates a consensus that flat land may be acceptably de- fined as land with slopes of three degrees (5 percent) or less. Although the area Hidore used as a sample was centered on the Corn Belt, he arrived at some interesting conclusions. The results of his study tended to support his hypothesis that the pattern of cash—grain farming in the Midwest is spatially associated with the flatness of the land. Hidore found that his graphic and statistical analysis accounts for up to 56 percent of the variation in the distribution of cash—grain farming in the study area. L. P. Hoag also suggested that flat land is one of the major deter- minants of the location of cash-grain farming. His study was not a statistical analysis and Hoag summed up his feelings about the need for H such a study, ...a correlation as obvious as this one does not need statistical measurement, and that such a chore would be a needless waste of time and limited resources."53 Economic and social factors associated with broad regional concen— trations of wheat are many. Shaw mentioned a few of these: Wheat, like other crops, may be absent from regions where it grows best because another crop may pay better or be more desireable...Production may be limited by crop controls set by governments...Pro- duction may be encouraged by subsidies given by the government...Tariffs may restrict would be markets... Wars may bring about scarcity...New agricultural 52John J. Hidore, "The Relationships Between Cash-Grain Farming and Landforms," Economic Geography, XXX (January, 1963). P. 86. 53Hoag, Cash—Grain Farming, p. 7. 25 techniques may increase yields...The number of man-hours necessary for producing an acre of wheat may encourgge production in some places, dlscourage it in others. Generally such conditions would apply to the region as a whole'and not necessarily account for the concentration of wheat in any one part of the area. Most of the factors listed by Shaw are associated with pro- duction and yields. Thus, the whole region could be affected by a change in any one of them. About the only impact these factors would have on concentrations within a region would be to increase or decrease their size depending upon the demand. Hoag listed several variables he feels may or may not be significant in the location of cash-grain in the corn belt. With the exception of the physical factors mentioned previously these are: (l) proximity to market, (2) absence of much natural pasture and necessary livestock, (3) large size of farms, (4) types of buildings on farms, (5) grain handling equipment in nearby towns, (6) high rate of tenancy, (7) tra- dition, (8) nationality of farm operator, (9) personal likes and dis— likes, (10) preferential freight rates.55 Most of these factors can be discarded because of one or two reasons. First, some of these variables might be applicable to a corn belt system of farming but not to a wheat belt. For example, 2 and 4 might account for the location of corn but not necessarily wheat. Number 2 might apply in the corn belt because it is a stock fattening region and certain areas are set aside for pasture. However, in the wheat region, the only animals found are those which provide subsistence 54Shaw, Geography, p. 309. 55Hoag, Cash-Grain Farmin , p. 5. 26 for the farmer or serve as a secondary type of land use on land not in wheat production. Number 4 might also apply to the corn belt, but not necessarily to the wheat belt. J. W. Alexander pointed out the lack of a need for buildings on a wheat farm: Structures on grain farms are small and unpretentious compared to farmsteads in regions of dairy farming or of mixed—farming. With so few animals there is little need for large barns and silos to store feed, or for barns and sheds to shelter animals, or for large feed— lots. In addition to the family residence, the only building needed is a garage for the machinery. Second, several of the factors would have to be considered results of extensive grain farming rather than determinants of its location. Hoag, himself, discounted numbers 3, 4, 5, and 6 as being results rather than determinants. Alexander pointed out that large size farms are a necessary part of extensive farming: Unless they are irrigated, dry lands have low yields per acre; therefore, each farmer must work a great deal of land in order to earn a living. This requires machinery, that is extensive farming methods in which the ratio of number of acres to number of workers is high.57 W. R. Bailey said, "about a third of the operators are full ten- ants."58 He explained that the majority of the full tenants are young operators who are just getting started and have not saved enough for a down payment on a farm. Bailey pointed out that part owners (Operators 56Alexander, Economic Geography, p. 171. 57Ibid, p. 158. 58W. R. Bailey, "Land and Problems in the Wheat Regions," Land, Yearbook of Agriculture (Washington, D. C.: Government Printing Office, 1958), p. 158. was 1"" . 4. .49. J 27 who own land but also rent additional land) comprise about 40 percent of the operators. In any case, whether the operator is full owner, part owner, or full tenant, the nature of the labor demands on wheat farms make it possible for him to live in town or even hundreds of miles away, visiting his land only for planting and harvesting. Kollmorgen and Jenks pointed out the growing tendency toward "suitcase" and "sidewalk" farming and stated that the actual residence of the farmer has relatively little if anything to do with wheat concentration.59 Government allotments, not mentioned by Hoag, but suggested by Shaw and Bailey, would have to be considered as an influential factor. The allotment system was probably the largest curtailer of acreage in wheat production. Therefore, its primary effect on concentrations should be the removal of the poorer land from production and the concentration of wheat on the "best" physical land. It should be pointed out here that the government program may tend to reduce production of wheat on poorer land within farms but not necessarily between or among farms. The allotment system also tended to absorb the effect, if any, of some of the other variables mentioned by Hoag. The impact of tradition, nationality of farm operator, and personal likes and dislikes would be minimized by the restriction placed on wheat acreage by the allotment system. Bailey spoke of the average farmer in terms of the allotment system: Without acreage allotments, the average wheat farmer in west-central Kansas would seed 320 acres and produce four thousand bushels of wheat. He seeded 240 acres and pro— duced 2,600 bushels in 1955.6 59W. M. Kollmorgen and G. F. Jenks, "Suitcase Farming in Sully County, South Dakota," Annals of the Association of American Geographers, XLVIII (March, 1958), pp. 27—40. 60Bailey, Land and Problems, p. 155. 28 The main concept brought out in this review of the literature is that there are many forces at work which account for the location of agricultural production. Moreover, the most attention seems to have been directed toward explaining regional concentrations of agriculture with very little attempt to explain diversity within the region. How- ever, there is a strong indication that theflocation of the areal patterns of wheat within a wheat region, although dependent upon economic and social factors to a certain extent, seem to be influenced more by the variation of physical phenomena from place to place. As Dunn pointed out, man's attempt at adapting crop systems to the physical environment is based purely on a profit motive.61 And, the physical environment of the wheat region of the middle United States is economically most optimum for wheat. Moreover, the governmental controls on wheat tend to minimize the effect of several of the economic and social principles which might otherwise apply. Therefore, within this framework the dis- tribution of concentrations of wheat within the region should depend largely on the variation of physical phenomena within the region. The present research attempts to build from the basis of the work of these authors in explaining the distribution of wheat concentrations within this region. 61Dunn, Agricultural Production, p. l. CHAPTER II MODAL WHEAT CONCENTRATIONS IN THE AMERICAN HARD WINTER WHEAT BELT Past researchers have seen fit to describe a portion of the Agricultural Mid-West of the United States as the "Hard Winter Wheat Belt." William Van Royen said: The southern section of the plains wheat belt embraces parts of Nebraska, Kansas, eastern Colorado, Oklahoma, and Texas, the state of Kansas ranking first by far in production. This is the Hard Red Winter Wheat Region. J. Russell Smith described the limits of the Winter Wheat Belt in terms of climate: The Winter Wheat Belt in western Texas, Oklahoma, Kansas, and Nebraska and in eastern Colorado occupies the western portion of the corn and winter wheat climate region and extends well into the regions of temperate grassland climates. Warren R. Bailey defined the region strictly in terms of the states, or parts of states, in which it lies: The Hard Red Winter Wheat Region centers in Kansas, Nebraska, Oklahoma, and the panhandle of Texas. It includes parts of some adjacent states. 1William Van Royen and Nels A. Bengtson, Fundamentals of Economic Geography (Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1965), p. 260. 2J. R. Smith, and others, Industrial and Commerical Geography (New York: Henry Holt and Co., 1955), p. 77. 3W. R. Bailey, "Land and Problems in the Wheat Regions,” Land, Yearbook of Agriculture (Washington, D.C.: Government Printing Office, 1958), p. 151. 29 3O Loyal Durand gave a much more detailed description: The Hard Winter Wheat Belt centers in Kansas...from this center it spreads southward through western Oklahoma and the panhandle of Texas to a southern "hot" border at ap- proximately 34° north latitude. Northward from its Kansas core, the belt extends into Nebraska to the Platte River and to the Sand Hills region...north of the Sand Hills, winter wheat and spring wheat overlap in southwestern South Dakota. Westward from the heart of the belt, winter wheat is grown well into...the dry Steppes of eastern Colorado...eastward, there is a sharp border of the hard winter wheat belt...where...corn replaces wheat. From these verbal descriptions and from the graphic presentations of several authors (fig. 1), the conclusion can be drawn that the general area of the Hard Winter Wheat Belt is relatively well known and accepted. However, the boundaries, like the boundaries of many regions, are rather nebulous. There seems to be no uniform criteria for boundary selection on the maps, nor in the verbal descriptions. The limits are drawn most frequently on the basis of wheat production or number of acres in wheat. The exact point where the amount of wheat or land in wheat becomes too small to be included within the region is an arbitrary de- cision on the part of the researcher defining the boundary. Thus, there is a great amount of variation from one definition or map to the next. For the purpose of this study, none of these descriptions have been accepted, but, rather, a new measurement of the limitations of the American Hard Winter Wheat Belt has been utilized. The method of mea— surement has a two-fold purpose: (1) to define boundaries for the Hard Winter Wheat Belt, and (2) to set apart modal wheat concentrations within the region. 4Loyal Durand, Economic Geography, p. 233. 31 Iago (Edna (15>... ameoz m a F =an china I>xo mmo Siam» £19»... meOZ yuan: <>z mo4 >20 MIR-.1 oszm wmr... _ . I .4 4. II-..“ Didi. IMZIMI >1 «n n xpaquxonrn 32 The technique of measurement adopted is the "location quotient" proposed by Shyam Bhatia for use in studies of agricultural geography.5 Index for deter— Area of crop X in Area of Crop X in mining concentration . cgpponent areal unit e_the entire countpy of crop X Area of all crops in the Area of all crops in component areal unit the entire country6 This involves the use of three ratios based on 1964 data, the most recent data avilable from the agricultural census of the United States: (1) a ratio of acres of wheat to acres of cropland in component areal units, (2) a ratio of acres of wheat to acres of cropland in the nation, and (3) a ratio of (1) to (2) above. A ratio between the total acres of wheat to the total acres of cropland was computed for each county (the component areal unit) and for the United States as a whole. The third ratio was computed from the county-national ratios. This ratio and the ratios for the counties were initially calculated in the core of the Hard Winter Wheat Belt (western Kansas) and then the calculation process was radiated outward until the ratios between county and nation no longer exceeded unity. This then was considered to be the outer limits of the Hard Winter Wheat Belt. The area encompassed by this definition can readily be seen in figure 2. Empirical observations of wheat distribution patterns, together with the patterns yielded by the use of the location quotient, show that while production of winter wheat is widespread within the region, in reality there are areas of concentrations interspersed with areas of 5Shyam Bhatia, Patterns of Crop Concentration, p. 40. 6For a complete description of the location quotient, see pages 9 and 10 of this manuscript. 33 N m:u cwm_umh> mm._.2_>> om..... ...... IOOOQQ‘ ...... b.0000' JVVV&fi Qfifififi§9¢§ d?” ............4 ............. ............¢ ............. .. .........1 ............. ......o...... ............ .9..........« ........... ...........4 r........... ...........¢ r. O... O. a? .‘f ..%9%fi§ .. ...... I. 0 9.. .... 9’0 KANSAS I . . . . 0 09099090. 0 00000 09.6.... ...'...'.V V -........ ........ I ‘Qfifi?€¢§ OKLAHOMA O ’.’.:.. 9.:1fifig . . o . . a0202¢202...2.2.2.? BUSHELS PER ACRE 25—29 - 20-24 _ I5-I9 m I0—I4 m 5-9 [EITHER 100 l. I SCALE 1" MILES FIG. I3 7l slightly significant at the five percent level (table 4.2). The fact that the average wheat yield per acre may reflect the variation in pre- cipitation and/or soil moisture possibly could account for the small increase made in the R by putting the average yield per acre variable into the model. Nonetheless, it is retained in the equation deepite the possible collinearity with another variable, most likely on the basis of the relatively significant simple correlation. SUMMARY The preceding examinations of the tests of the hypotheses have demonstrated that the variables hypothesized had a varying degree of association with the criterion variable. Moreover, it is obvious that several of the variables used in this study measure very similar attri- butes. Therefore, it becomes necessary to delete some of these factors so as to obtain maximum explanation with minimum collinearity. With all variables retained in the equation, the coefficient of determination R? is .814 (table 4.4). This means with all variables considered, 81.4 percent of the variation in the dependent variable is explained. By examining the R? differences in table 4.4, it can be seen that the difference between the complete model and three deletions is only 1.1 percent; whereas the drop with four deletions is 1.7 per— centage points, and 4.1 percentage points with five deletions. With six deletions the decrease in explanation is 6.7 percentage points and with seven it is 30.2 percent. Conceivably, the deletion process could be stopped at six deletions and still retain a relatively significant explanation. However, it ap— pears that the maximal point to stop the deletion process without having ..‘I- i-': ."Iiflgkil "' 4 I'J :54: 72 TABLE 4.4 MODEL - ELIMINATION SEQUENCE All Variables One Deletion Two Deletions Three Deletions Four Deletions Five Deletions Six Deletions Seven Deletions .814 .812 .806 .803 .797 .773 .747 .512 .9023 .9009 .8980 .8962 .8929 .8795 .8643 .7158 73 excessive duplication is at three deletions. Thus, just a little over one percent of the explanation is lost by excluding these three variables. The variables deleted at this juncture are average yield per acre (X7), annual growing season precipitation (X4), and rural population density (X8). Therefore, the remaining variables are considered as being the most important of those examined for explaining the spatial variation of modal wheat concentrations in the area outlined for study in the American Hard Winter Wheat Belt. These variables are: average farm size per county (X6), number of acres of flat land per county (X1), distance to second order market (X5), number of acres of loam soils per county (X2), and the average soil moisture per acre in each county (X3). Thus, the final model is: Y=X1+X2rX3+X5+X6+e n 3 S 8 I .1 ... CHAPTER V CONCLUSIONS In this study several variables were initially hypothesized as having an important role in explaining the spatial variation of modal wheat concentrations in the American Hard Winter Wheat Belt. Further- more, it was hypothesized that the physical variables would be most indicative of where modal wheat concentrations would exist. This hypo— thesis was based on the assumption that the physical variables would tend greatly to influence man's land use decisions within the economic framework of the allotment system. The allotment system, being an acreage control system, was in effect at the time the data for this study was originated. As the work progressed, it became evident that all of the hypo- theses were not valid as stated. It also became apparent that the associations between a number of the predictor variables and the cri- terion variable was opposite to that anticipated. Moreover, there was a strong indication that several of the predictor variables were mea- Suring nearly the same attributes as other predictor variables. Finally, the coefficient of determinationR2 of 80.3 (table 4.4) shows that the variables chosen and retained in the final analysis are fairly signifi- cant in explaining the spatial variation of modal wheat concentrations in the study area. The most significant predictor variable proved to be the average 74 75 size of farm per component areal unit. According to Hoag, average farm size is a result, not a cause, of wheat concentration.l Nevertheless, as hypothesized, a group of N_size farms appearing together, even though a result of a particular type of farming, will indicate where a concen— tration of wheat exists. This variable proved to have an inVerse rela— tionship with the criterion variable. In other words, the smaller the average farm size in a component areal unit within the study area, the higher the concentration of wheat within that unit. The r2 of 51.2 shows that over 51 percent of the modal wheat concentrations in the study area can be explained by the average farm size of the county. The second most important variable for predicting a high concentra— tion of wheat in a county is the amount of flat land within that county. The results here tend to support Hidore's findings.2 However, the coef— ficient of determination, and, therefore, the significance of flat land as a predictor, was not as great as Hidore found in his study of cash— grains. The difference is probably due to the difference in the orien- tation of the two studies. First, Hidore's study was centered on the corn belt, including adjacent areas bordered by state boundaries, and, therefore, included only a small part of the region upon which this study was focused. Second, Hidore was attempting to explain the spatial variation of cash-grains, whereas this study is an attempt to explain the spatial variations of modal units of wheat concentration and not wheat concentration in itself. Flat land proved to have a direct association with modal wheat con— centrations. In other words, the larger the number of acres of flat land lHoag, Cash—Grain Farming, p. 5. 2Hidore, Cash—Grain Farming, p. 88. 5.--; 25210 as." 76 within a component areal unit in the study area, the higher the concen- tration of wheat within that unit. The coefficient of determination r2 of 23.5 shows that nearly 24 percent of the modal wheat concentrations in the study area can be accounted for by the amount of flat land within a county. The combined coefficient of determination of flat land and average farm size 3? of 74.7 (table 4.4) shows that these two variables account for nearly three—quarters of the variation of modal wheat con- centrations. The third most significant predictor variable is the distance to a second order market. This tends to reflect somewhat the distance decay function as theorized by the land economists such as Ricardo, Thanen, and others. The probable reason for this variable not being as impor- tant as theorized by the land economists is because this study is focused on only one small segment of the economy in a limited area and not on a total economy, on which much of their theory is based. As hypothesized, distance to a second order market is inversely associated with modal wheat concentrations. In other words, the nearer a county within the study area is to a second order market, the greater the possibility that that county will have a wheat concentration. The distance to second order market variable increased the R? to 77.3 (table 4.4), meaning that over 77 percent of the variation of modal wheat concentrations can be explained by the three previously mentioned variables. The fourth most significant predictor variable is the amount of loam soils within the component areal unit. The findings here would tend to substantiate the suggestions of Van Royen and Morgan that wheat is most frequently associated with soils of these textural classifica- 77 tions.3 As hypothesized, there is a direct relationship between the amount of loam soils and modal wheat concentrations. In other words, the greater the number of acres of loam soils within a component areal unit in the study area, the greater the possibility for that unit to have a concentration of wheat. This variable accounts for only a small percen— tage of the variation in the dependent variable, and, when considered with the previous variables, it increases the coefficient of determina- tion 32 to only 79.7 (table 4.4). The fifth most important predictor variable is soil moisture. The fact that this variable proved to be significant, even though only slightly so, substantiates the assumption that the amount of soil mois- ture is an indicator of the existence of modal wheat concentrations. There is a direct relationship between the amount of soil moisture and the dependent variable, thereby supporting the hypothesis that the greater the average amount of soil moisture per acre within a county in the study area, the greater the possibility that a modal wheat concen- tration will exist. With the addition of this variable, the total ex- planation of the variation of the criterion variable was raised to 80.3 percent (table 4.4). The remaining three predictor variables -- rural population density, county average growing season precipitation, and average yield per acre —— were discarded. Alone, each proved to be fairly significant pre- dictors, but, because they tended to measure a similar attribute as one of the foregoing variables and with less precision, they were eliminated. 3See pages 17, 18, and 19 of this manuscript. .. J 78 Rural population density showed a direct relationship to the criter— ion variable. This association was just the Opposite of the stated hypothesis that the lower the population density in a county within the study area, the more likely a concentration of wheat would exist. Thus, this hypothesis is rejected. Average yield per acre proved to have an inverse association with the dependent variable. This means that the higher the average yield per acre in a county within the study area, the less likely that that county would have a concentration of wheat. This was in opposition to the hypothesis advanced and thus the hypothesis as stated is rejected. The variable with which the average yield per acre variable is most collinear is not quite clear. However, there is slight statistical evidence that the spatial variation in average yield per acre is assoc- iated with the distribution of soil moisture and precipitation. Figure 13 tends to substantiate this since the highest yields are situated along the eastern margin of the study area. Average annual growing season precipitation measures the same thing as soil moisture, but, according to the step-wise procedure, not as well as soil moisture. The isohyet map (fig. 12), which is based on actual station records and not county averages as the variable was, tends to support the statements of Bennett and Farnsworth concerning the rela- tionships of annual precipitation and wheat concentration.4 Finally, the hypothesis that the physical variables are the most significant factors influencing man's land use decisions under the al- lotment system within the study area proved to be only partially correct. Three physical variables might be considered as relatively important 4See page 19 of this manuscript. a". .r-u‘ H.111!" ' 431R? no! *---1--.-:u:. 79 in man's land use decisions. These are flat land, loam soils, and soil moisture. Flat land would be by far the most significant physical influence while loam soils and soil moisture, and particularly the lat- ter, would, in comparison, contribute very little to land use decisions. The fact that farm size and distance to market rank first and third as predictors of modal wheat concentrations, and thus are probably very influential in how the land in the study area is used, leads to the con— clusion that the hypothesis as stated should be rejected. However, the important position of the flat land variable in this study suggests that future studies might be undertaken to test this hypothesis in other areas. Many of the previous qualitative generalizations concerning the spatial variation of modal wheat concentrations in the American Hard Winter Wheat Belt are substantiated and expanded upon by the results of this study. However, the importance of the substantiations should not be overemphasized. This study is limited in time as well as in area. In other countries or other regions where data may be collected in a somewhat different fashion, or where cultural activities and/or the physical environment may differ greatly from the study area, there may be a necessity for operationalizing some new variables. However, the variables selected in this study may well provide the starting point for other geographic studies of wheat concentrations. - '-.I. final. a'asm n1 SELECTED BIBLIOGRAPHY BOOKS Alexander, John W. Economic Geography. New Jersey: Prentice-Hall, Inc., 1964. Brinkman, Theodor. Economics of the Farm Business. English Edition. Berkeley: University of California Press, 1935. Christaller, Walter. Central Places in Southern Germany, Translated by Carlisle W. Baskin. New Jersey: Prentice Hall, Inc., 1966. Dunn, Edgar 5., Jr. The Location of Agricultural Production. Gains— ville: The University of Florida Press, 1954. Durand, Loyal C. Economic Geography. New York: Thomas Y. Crowell Co., 1961. Finch, V. C. and Baker, 0. E. Geography of the World's Agriculture. Washington, D. C.: U.S.D.A., 1917 (Cited by Jones). Klages, K. H. W. Ecological Crop Geography. New York: MacMillan Co., 1961. Losch, August. The Economics of Location. New Haven: Yale University Press, 1954. Nuttonson, M. Y. Phenology and Thermal Environment as a Means for a Physiological Classification of Wheat Varieties and Flora Physiological Classification of Wheat Varieties and for Predicting Maturity Dates of Wheat. Washington, D. C.: American Institute for Crop Ecology, 1953. . Wheat Climate Relationshi sland the Use of Phenolo in Ascer— taining the Thermal and Photo—Thermal Requirements of Wheat. Washington, D. C.: American Institute of Crop Ecology, 1955. Ricardo, David. Principles of Political Economy and Taxation. Edited by E. C. L. Gonner. London: G. Bell & Sons, Ltd., 1913. Shaw, Earl B. World Economic Geography. New York: John Wiley and Sons, 1955. 80 81 Smith, J. R., et a1° Industrial and Commerical Geography. New York: Henry Holt and Co., 1955. Thoman, R. S. The Geogrgphy of Economic Activity. New York: McGraw— Hill, 1962. Van Royen, William, and Bengtson, Nels A° Fundamentals of Economic Geography. Englewood Cliffs, N.J.: Prentice—Hall, Inc., 1965. Von Thunen, J. H. Von Thanen's Isolated State. English Edition; edited by Peter Hall. New York: Pergamon Press, 1966. ARTICLES AND PERIODICALS Alexander, John W. "Location of Manufacturing: Methods of Measurement," Annals of the Association of American Geographers, XXXXVIII (March, 1958), 20—26. Baker, 0. E. "Agricultural Regions of North America," Economic Geogra— phy, 12 installments (October, 1926—1934)e "The Potential Supply of Wheat," Economic Geography, I (March, 1925), 15-52. Bennett, M. K., and Farnsworth, H. D. "World Wheat Acreage, Yields and Climates," Wheat Studies, XIII (March, 1937), 265—308. Bhatia, Shyam. "Patterns of Crop Concentration and Diversification in India," Economic Geography, XXXXI (January, 1965), 39—56. Colby, C. C. "Centrifugal and Centripetal Forces in Urban Geography," Annals of the Association of American Geographers, XXIII (March, 1933), l—20. Hartshorne, Richard, and Dicken, Samuel. "A Classification of the Agricultural Regions of Europe and North America on a Uniform Statistical Basis," Annals of the Association of American Geographers, XXV (June, 1935), 99—120. ”Agricultural Land in Proportion to Agricultural Population in the United States,” The Geographical Review, XXIX (July, 1939), 488—492. Hidore, John J. "The Relationship Between Cash—Grain Farming and Land— Forms," Economic Geography, XXX (January, 1963), 84—89. Hoag, L. P. ”Location Determinants for Cash-Grain Farming in the Corn Belt," The Professional Geographer, XIV (May, 1962), 6—7. Jones, Wellington D. "An Isopleth Map of Land Under Crops in India," Geographical Review, XXX (July, 1929), 495—496. 82 "Ratios and Isopleth Maps in Regional Investigation of Agri— cultural Land Occupance," Annals of the Association of American Geographers, XX (December, 1930), 177—187. Klages, K. H. "Geographical Distribution of Variability in Yields of Field Crops in the States of the Mississippi," Ecology, XI (April, 1930), 293—306. Kollmorgen, W. M., and Jenks, G. F. "Suitcase Farming in Sully County, South Dakota," Annals of the Association of American Geographers, XXXXVIII (March, 1958), 27—40. Philbrick, A. K. "Principles of Areal Functional Organization in Re— gional Human Geography," Economic Geography, XXXIII (October, 1957), 299-336. Platt, R. S. "A Detail of Regional Geography: Ellison Bay Community as an Industrial Organism," Appals of the Association of American Geographers, XVIII (March, 1928), 81-126. Pownell, L. L. "Functions of New Zealand Towns," Annals of the Associa— tion of American Geographers, XXXXIII (December, 1953), 332-350. Renner, G. T. "The Statistical Approach to Regions," Annals of the Association of American Geographers, XXV (September, 1935), 137— 152. Smith, Helen L. "Agricultural Land Use in Iowa,” Economic Geography, xxv (July, 1949), 190-200. Taylor, Griffith. "Climate and Crop Isopleths for Southern Ontario," Economic Geography, XXIV (January, 1938), 89—97. Thornwaite, C. W. "An Approach Toward a Rational Classification of Climate," Geographical Review, XXXVIII (January, 1948), 55-94. Weaver, J. C° ”Changing Patterns of Cropland Use in the Middle West," Economic Geography, XXX (January, 1954), 1—47. Webb, J. W. "Basic Concepts in the Analysis of Small Urban Centers of Minnesota," Annals of the Association of American Geographers, XLIX (March, 1959), 55-72. Whitaker, J. R. "Agricultural Gradients in Southern Ontario,” Economic Geography, XIV (April, 1938), 109—120. REPORTS Abbe, Cleveland. "A First Report on the Relations Between Climates and Crops," U.S.D.A. Weather Bureau Bulletin No° 342 (Washington, D.C.: Government Printing Office, 1905). 83 Bailey, W. R. "Land and Problems in the Wheat Regions," Land, Yearbook of Agriculture, 1958 (Washington, D. C.: Government Printing Office, 1958). Elliot, Foster F. Types of Farming in the United States (Washington, D. C.: Government Printing Office, 1933). Martin, J. R., et al. Effect of Changes in Product Price Relationships on Farm Organization and Income —— Clay Soil Farms —— Southwestern Oklahoma. U.S.D.A. Bulletin B—621 (Stillwater, Oklahoma: Oklahoma State University Experiment Station, 1964). . Effect of Product Prices pp Farm Organization and Income —- Sandyland Farms ~— Southwestern Oklahoma. U.S.D.A. Bulletin B—625 (Stillwater, Oklahoma: Oklahoma State University Experiment Station, 1964). Minimum Land Reguirements and Adjustments for Specified Income Levels -— Southwestern Oklahoma. U.S.D.A. Bulletin B-608 (Stillwater, Okla- homa: Oklahoma State University Experiment Station, 1963). Morgan, M. F., et al. ”The Soil Requirements of Economic Plants," Soils and Men, Yearbook of Agriculture, 1938 (Washington, D.C.: Government Printing Office, 1938). Olmstead, L. B., and Smith, W. D. "Water Relations of Soils," Soils and Men, Yearbook of Agriculture, 1938 (Washington, D. C.: Govern- ment Printing Office, 1938). Salmon, S. C. "Climate and Small Grains," Climate and Man, Yearbook of Agriculture, 1941 (Washington, D. C.: Government Printing Office, 1941). UNPUBLISHED MATERIALS Brown, Robert C. "Spatial Variation of Idle Land in Tulsa, Oklahoma." Unpublished Ph.D. dissertation, Michigan State UniversifV,'l967. Cross, Ralph D. "A Study of Infiltration on a Sample Subwatershed of the Kalamazoo River Basin, and a Method of Infiltration Computa- tion for use with Studies of Large Watersheds." (Unpublished paper prepared at the Kellogg Gull Lake Biological Station), 1965. 47 0136 3 1293 030