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The purpose of this brief is to describe some of the general relationships which exist in nature and which influence the distribution and characteristics of agricultural production and whose understanding is of importance to decision analysis in such areas as planning and investment. A short introduction to decision analysis was provided in Brief No. 1 in this series.

In this brief the physical and quantitative relationships summarised in agricultural production functions, which describe the relationships between physical inputs and production achieved, are shown to be the fundamental foundation of the subsequent project evaluation components such as for environmental, economic, financial and social impact analyses. Indeed, without sound production functions the utility of any project as a basis for projecting likely output is doubtful and the confidence in projected economic and financial outcomes has to be low.

Crop productivity, the response of output to physical inputs, is determined by the phenotypic expression of the genotypes of plants under the influence of husbandry techniques applied. On the other hand production is also subject to the direct influence of predominant bioclimatic factors, the EWT complex, made up of:
  • edaphic regimes (E) - soil conditions including texture, structure and nutrient content
  • water regimes (W) - availability to roots and humidity of air
  • temperature regimes (T) - temperatures in the soil and ambient
Depending upon specific geographic location of production, the EWT complex will have a different but quantifable impact on a farm's production functions.

Within a specific global location the direct influence of the EWT complex on potential crop productivity varies with local topography, that is altitude and the general orientation of the land surface with respect to the sun.

The direct influence of the EWT complex on potential crop productivity varies with the global coordinates (longitude and latitude) of production sites.
The influence of the EWT complex on crop production is a constant factor whose intensity varies diurnally and throughout the year under the direct influence of insolation, a location's latitude, logitude, altitude and the predominant land surface slope orientation, if any, according to the compass.

The obvious question arises that if the EWT complex determines the types and productivity of crops in any location, then how does one discriminate between the economic components of the production function which are supplied by the farmer and those which come from the EWT complex?

One of the assumptions often made on the part of natural scientists is that the natural productivity of a region is defined by the EWT complex and this gives rise to "natural" crop production patterns which are related to the geographic distribution of variations in the components of the EWT complex. This is generally true but as the analysis set out in Part 2 of this brief will show, economic influences can over-ride "natural advantages" to a significant degree.

In 1925, R. A. Fisher published a paper Statistics Methods for Research Workers which reviewed the development of statistics up until that time. Fisher describes how the efforts in statistics of population were directed towards determining the average. No particular effort had been made to analyse the degree to which populations deviated from the average. Indeed, Fisher made significant contributions to the practical application of statistics by establishing methodologies which became a standard approach to the determination of the significance of experimental results. This was based upon a knowledge of the shape of a population curve and the variance about the mean, or average. If the response of say, a crop, to some input fell outside what would be a reasonable expectation of the normal variation, then results could be judged to be significant (at different degrees of confidence). A convenient way, perhaps too convenient, to provide a shorthand decription of a population became the declaration of the average and the observed coefficient of variance.

Fisher's work, and especially that relating to experimental design and the analysis of variance (ANOVA), became widely applied in the field of agricultural research and constituted an important contribution to the methods of experimental design.

In agricultural experimentation, performance trials and genetic selection work the convenience of such methods has, to some extent, encouraged work to become too focused on detecting the immediate interrelationships between the so-called explained variance attributable to the factors of interest to the researcher. Most other influences often became ignored or ended up in the residual data called "unexplained variance". Indeed, in many cases, what we refer to as the EWT complex, ends up in the unexplained variance category when it remains a fundamental deterinant of productivity. Naturally there are many cases where this is not true but rather than become involved in a detailed analysis of the justificaiton for such a statement it is more productive to simply confirm that in the workshop series the EWT complex will be a central factor in our approach to decision analysis which can include the design of experiments and surveys in the agricultural sector.

Fisher, although the designer of methods which have simplified experimental design and their analysis was completely aware of the limitations inherent in such an approach. Thus:

"No aphorism is more frequently repeated in connection with field trials, than that we must ask Nature few questions, or, ideally one question at a time. The writer is convinced that this view is wholly mistaken. Nature will best respond to a logical and carefully thought out questionnaire, indeed, if we ask her a single question, she will often refuse to answer until some other topic has been discussed"

R. A. Fisher (1926)3

It is somewhat perplexing that several thousand years after the Neolithic era when man is assumed to have begun to cultivate the land and over two thousand years following the release of Virgil's Georgics, there continues to be a tendency towards an atomization of agricultural data sets caused by different workers and researchers limiting their attention to specific aspects of the expression of a crop's response to some factor such as fertiliser.

But hopefully this trend will replaced with an approach which is not characterised by production for one interest group being unused waste to another. The resolution of the challenges facing us in the context of environmental preservation and the need to rationalise the analysis of the feedstock, fibre and foods complex will be difficult unless a more comprehensive or systems approach is adopted. As we know the logical generic approach is to speak in terms of biomass and then, depending upon the area of specific interest, divide the biomass into its component parts such as root, stem, tuber, fruit, seeds, leaf and others. One might say that this more botanical approach provides a more logical basis for analysis since the plant components contain, often, distinctly different chemical composition and physical constitution. Besides being more useful to the different consumers of output it also provides a more transparent interface to plant genetics. Indeed, it is often overlooked that what we make use of in agricultural output is the phenotypic expressions of the plant genotypes, that is the interaction of the plant genotype with the environment and husbandry practice.

After many human generations and centuries of agricultural seasons much information remains disjointed and unexplained. However, all who work in agriculture know that a good part of what remains unexplained lies in the yet to be better quantified influences of the EWT complex. What we have learned however is that crop production "depends on the weather!" And this, with the growing awareness of apparent climate change, is something we need to quantify and use to our benefit.

The growth and reproduction cycle in most organisms, and plants in particular, has well-established growth (production) relationships. All organic growth follows a S-shaped curve which represents the relationship between the supply of nutrition over time on the one hand and cell cell division and growth on the other. An example of such a growth curve is provided below.

Marginal growth is the rate of growth in biomass in response to the inputs which determine growth, such as nutrients.

Increasing marginal growth indicates accelerating growth marked by an increasing gradient (a-b).

Constant marginal growth indicates steady growth and gradient (b-c).

Decreasing marginal growth indicates a slowing down of growth, a declining gradient (c-d).

Most biological organism growth curves have different phases of growth which in the illustration are indicated as:
  • establishment
  • spurt
  • maturation
  • mature
The establisment phase is usually a critical growth phase when a plant is in the seed germination and early seedling stage when it is structurally delicate and particularly vulnerable to environmental conditions. On the other hand, this phase indicated by the section of the growth curve a-b is characterised by increasing marginal growth, that is the growth is accelerating from a very small biomass foundation. This is usually followed by the spurt which is a rapid constant growth, normally marked by close to constant marginal growth during which the majority of the structural growth occurs. This is indicated by the section of the growth curve b-c. This is followed by a maturation phase marked by a diminishing marginal growth rate, the growth curve segment c-d, until growth essentially stops when the plant is mature and at the harvest phase.

The dominant characteristic of the interaction between all essential inputs for plant production is that if the levels of input of all factors are held constant and the amount of a single factor, say fertilizer, is increased, the production response curve has a similar shape to the growth curve but the maximum achievable production is limited because the other factors have been held constant. Thus all of the other factors become limiting. This limitation is what creates a situation of diminishing returns to any particular input.

Experimenters tend to think of this production function relationship almost exclusively in terms of so-called variable inputs. That is those factors farmers apply during the growing season such as seed, fertilizer, herbicides and other pesticides as well as some types of physical work such as singling plants.

All rainfed production occurs on land where the EWT complex presents a combination of soil conditions, nutrients, water and termperature regimes. These natural resource inputs are, in themselves, if a farmer plants a field and adds no variable inputs, the main components of the production function. One can refer to this as a threshold production function or what is achievable by simply cultivating, planting and harvesting. This threshold production function is esentially the foundation upon which farmers build their own production functions by complementing the natural resource inputs with different types of variable input.

possible combinations of Sand, Silt & Clay.

There exist different classifications for what constitute the clay, silt and sand fractions in soils. The commonly used standards are set out in footnote 1 to this Brief.
Therefore in terms of decision analysis, the farmer is not starting off with a blank sheet but rather is manipulating a given production function with the objective of improving upon it in terms of profitable agricultural output.

The effects of the EWT complex components upon the production of plant biomass can be conveniently separated for the purposes of analysis but in practice they work in conjunction.

Soils surround the seed and plant roots and act as a "container" where nutrients are able to be absorbed by the plants in available water with oxygen being an important additional element for the operation of root physiology and metabolism. The water absorbed by the roots is used in crop transpiration which releases water into the atmosphere as well as in photosynthsis where water is combined with carbon dioxide to create plant biomass components in the form of carbohydrate and oxygen which is released to the atmosphere.

6CO2  +  6H2O  =C6H12O6  +6O2

For plants to grow adequately they require, according to their genotypes (genetic makeup), amongst other factors, an optimal range of:
  • water availability
  • temperature
  • nutrients
The availability of water to plants through the soil is determined by the composition of the soil as expressed in terms of particle size. Conventionally soils are classified by their composition of sand, silt and clay sized particles. The so called soil classification triangle is shown above.

Idealised notion of relationship of soil particle size to water availability.

By way of a generalization, soil particle size determines the availability of water to plant roots. Clay particles are so fine that they exert of strong capilliary action which is stronger than the suction which plant roots can exert, thus water can be present in the soil but is not available to the plants. Similarly, at the other end of the scale, large particled sandy soils are unable to hold water because of the lack of effective capilliary action and water either evaporates or descends through the soil out of reach of the roots.

Between these extremes there are many combinations of soil particloe sizes which hold water well and at a "tension" which is low enough as to make the water available to the plant roots. A conceptual version of the soil triangle indicating the degree of water availability in relation to particle size is show above.

The important points to notice is that the Edaphic axis has an important role in controlling the availability of water to plant roots. However, it is not the only determinant of water availability.

Soil also provides mineral nutrients to plants and this point will be covered below under "Optimal growth".

Annual, monthly and diurnal ambient temperatures vary with geogaphic latitude and longitude as well as with the particular topographical situation of a production site. Temperature is controlled by insolation and overall the resulting temperature regime is influenced by the altitude above sea level as well as the orientation of the slope or aspect of the land surface.

Naturally this has an inverse effect depending on whether a location is north or south of the equator. South-facing slopes being warmer in the Northern Hemisphere and North-facing slopes being warmer in the Southern Hemisphere.

Aviation pilot guide manuals on instrumentation and environmental conditions indicate that there is roughly a O.6oC fall in temperature for every 100 m gain in altitude in a situation of unimpeded air flow. However, this fall in temperature with altitude can vary with land vegetation cover. There is therefore a general fall in temperature as altitude is gained above sea level.

Showing a regional topography with an altitude of between 0 metres to 1,000 metres.

Showing the differential temperatures with respect to sea level, based on altitude.

This has been found to be true in terms of differences in recorded temperatures at meteorological stations at different altitudes. Thus the notional topography illustrated on the right showing a terrain of between 0 metres to 1,000 metres with 100 metre contour lines can be converted into a temperature correction model as illustrated in the diagram on the right.

The water which is available to crops comes largely from rainfall and indirectly via locally absorbed (trapped) run off as well as riverine water tables in zones close to rivers. Mention has been made of the fundamental importance of soil as a recepticle for holding available water for crop roots. Depending on the type of plant and its genotype, too little or excessive amounts of water can result in stunted growth or death of the plant.
There is, for any genotype an optimal range of water availability which permits unimpeded growth and a realization of genetic potential. On the other hand the temperature regime and available nutrients will also influence the phenotypic expression of the plants. Thus the Graph 1 on the right indicates the optimal levels of water availability and then, in the superimposed Graph 2, indicates the biomass response (growth) to a range of nutrient levels as well as to two different temperature regimes, with Temp B being higher than Temp A.

In all axes there are lower and upper limits of tolerance of plants with the intervening levels representing the domains within which useful crop growth can be achieved.

It is important to recognise the importance of the specificity of a plant genotype when discussing general relationships which exist in production functions. The response of a plant to its environment is a reflection of the plant's genotype. The genotype of a plant sets the genetic limits on the phenotypic expression of a plant in response to any environmental factors be these of the EWT complex or a farmer's management methods and additional inputs. The genotype will also establish what are optimal ranges for water availability, temperature and nutrient regimes as well as when it is best to plant and harvest a crop.

As in all input-output relationships using water, nutrients and temperature as inputs, and biomass as output, there are different ways of summarising and presenting the general relationship. The purpose of this brief is limited to providing an indication of the shape of the general relationship. More specific application and discussion will be developed during the forthcoming Workshops. The EWT complex provides input factors in a functional relationship involving at least three primary variables, nutrients (E) water (W) and temperature (T) with output, a single dependent variable, in the form of biomass (B). This is a difficult relationship to describe and present in graphic form because there are more than three dimensions.

The general form is that of a complex production function where the ranges of the main variables fall within the intervals which support crop reproduction and growth. The general simple form of the relationship is as follows:

B = (E*W*T)/(E*W + E*T + W*T)

B is biomass output;  E is the Edaphic axis2 (mainly nutrients);  W is the Water axis and, T is the Temperature axis.

Please Note:

More elaborate crop specific relationships require coefficients which relate the phenotypic biomass response of the genotype of the plant concerned to the relevant input factors. The Edaphic axis contribution to the relationship varies according to soil particulate make-up and structure as well as other factors. These matters are reviewed in more detail in Part 2 of this Brief where the specific determinants of the effective contributions of the EWT axes are described.

2 axis: this term is applied because each EWT component is not simply a single uni-morphic variable but is a result of other interactions. For example water can take the form of liquid as well as gaseous and humidity fractions and temperature varies according to location such as soil, ambient and as a result of microclimatic factors such as shading effects of other plants, slope and relative location.

A convenient summary for physical input-output relationships is the generation of a surface plot which represents the different E,W and T values which can generate the same output of biomass (B). The resulting surface is known as an iso-quantity or isoquant. An example of an isoquant surface is provided on the left for the EWT function relationship.

Even although this is an effective way of summarising a production function with three variables, it takes some getting used to and many people have some difficulty in visualising the relationship presented in the graph. The surface (isoquant) in this 3D diagram is concave to the viewer and convex to the origin, hidden by the isoquant.

An easier way to understand the isoquant approach and shape is to switch to 2-dimensions and view isoquant lines where one variable is fixed (say E) and the others varied to generate different isoquants. An example of this representation is provided below the isoquant surface graph.

The normal production function profile relates variations in one input to an output. Thus in order to produce comparable production functions using EWT data it is necessary to start off by setting any two of the main input variables at fixed values but within the range supportive of crop growth and then varying the third variable to calculate the biomass output response associated with each input level. This will result in the classic growth response curve shape which, with the general relationship equation described, shows the diminishing marginal returns in output of biomass to the input variable. This, as explained previously, is because at some point the other two factors become limiting or the genetic resources of the plant become the limiting factor in enabling any further response (especially when all inputs are at high levels).

Some simple online computer-generated production surfaces based on the EWT complex equation can be accessed here.

All briefs are subject to update. Current status of this brief. Updated 28th August, 2009, Version 1.06; previous update: 24th March 2007, Version 1.05.

Please Note:

References for briefs are being collected and collated and will be posted soon as part of an update

The Role of Micro-Bio-Climatic Zoning & Genotypic Mapping, McNeill H.W., SEEL, August, 2009.

Computer-based simulation of 3DPF, McNeill H.W. & Jino M., CNAE, NRC, Brazil, 1969.

The Analysis of Response in Crop & Livestock Production, Dillon J.L., Univ New England, Australia, Pergamon Press, London 1968. (Fisher citation)

A three-dimensional production function, McNeill H.W., Food Research Institute, TP in Trade & Development, Stanford, 1968.

Further reading: Recent contribtions in this area:

A simple height-based correction for temperature downscaling in complex terrain, Peter Sheridan, Samantha Smith, Andrew Brown and Simon Vosper Met Office, FitzRoy Road, Exeter EX1 3PB, UK, November 2009.

Footnote 1
Some commonly used soil particle size classification systems.

1 Hector McNeill is the Systems Coordinator at SEEL-Systems Engineering Economics Lab.
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