Farming is a complex agri-business where many activities are taken together like cultivation of cereals, fruits and vegetables, animal rearing and poultry. However, cultivation of various crops, including fruits and vegetables are generally the major components of a farming system.
Agronomic practices adopted for a crop depends on many factors that include climatic factors, ecological environment, resource availability, and the level of knowledge about agro-techniques required for the crop.
It is thus important to understand the impact of each factor on the growth and yield of the crop.
This can be done independently or in association with other factors. Crop models allow us to do this so that we can changes required to improve our overall management of the farm.
Crop model – definition
First let us understand what we mean by crop model. In very simple terms we can define a crop model as (i) a well thought-out plan of activities to grow the desired crop to get maximum possible yields of high quality produce with the given resources.
It can be a mental or a written exercise (a “schematic representation of the system”) that a farmer or a farm manager prepares for a crop or for an individual crop.
In other words, we can also say that a model is (ii) “an attempt to describe a certain process or system through the use of a simplified representation, preferably a quantitative mathematical expression, that focuses on a relatively a few key variables that control the process or system”.
Successful farming depends on our knowledge of the impact of ecological, climatic and economic factors on crop yields.
So, a model may be defined as (iii) “an attempt to describe a certain process or a system through the use of a simplified representation, preferably a quantitative mathematical expression that focuses on relatively few key variables that control the process or a system”.
Utility of crop models
Crop models help us to understand the crop production process or system in a more systematic way.
The process of modeling is often equated to solving of a puzzle. A puzzle has to be considered as a whole even if we need to fit a one small block. Crop models provide us quantitative information about the amount of inputs like the doses of fertilizers, number of irrigations, amount of insecticides/pesticides, etc. required.
These models also help us to consider various input requirements under different climatic conditions. This means models help us to get reasonably clearer picture of otherwise hazy scene.
It is also said that models provide us reasonably acceptable answers to questions where we can only have vague answers.
So we must be clear that models would not guarantee one hundred per cent accurate answers; even if we take a large number of variables into consideration. This is because crop cultivation is a biological activity and the final output depends on our knowledge of the state of climate that will prevail during the growing season, our knowledge about the appropriate technology required, availability of that technology, about input market conditions, about the biological risk factors associated with the crop, and such other factors.
It is clear from this discussion that in finalizing a crop model we have to assume some mean or standard values (based on the past record, experience, expert judgment, etc.) of the variables which we may not be taking explicitly in our model.
Since, there can be a large number of factors that may affect the crop, it becomes easier to understand their effect if these variables are grouped on some basis. Thus we may have a group of ecological variables, economic and social variables, technical and climatic factors that may need to be considered in our crop models.
Types of crop models
Based on different groups of variables that affect crops production, we can categories crop model or models as;
(i) ecological models, (ii) climatic models, and (iii) socio-economic models
The climate based models are formulated to predict the correlation of climatic variables (like temperature, rainfall or snowfall, humidity, day length, chilling hours, etc.) with a given biological phenomenon like survival rate of species, growth of vegetative parts, fruit-set, crop maturity or the crop yields, etc. These models are also used by the ecologists to identify the variables which affect the crop yields through their impact on modifying the local climate.
Understanding the interactions of farming systems with the surrounding environment is thus important for success in agribusiness and modelling helps us in doing the same.
The crop models with as many variables as possible are thus better in making predictions than the models with a few variables. However, modelling with a very large number of variables may not always be possible because of the problems of lack of relevant data, mathematical programming problems, etc. Most of the times, therefore, we have models with the variables in which we have the immediate interest.
Production Function – an algebraic representation of a model
Most common crop models are the economic models analyzing the effect of some inputs on crop yields.
In these models, influence of an independent variable is estimated on the crop yield or on the growth of the crop.
We know that a production process is a set of sequence of rules for using different inputs that needs to be followed for using different inputs.
The ultimate outcome of a production process is the final output of that process, i.e. the crop yield or the desired vegetative growth.
In a simple modeling scenario, a production process can be considered as a production function (a mathematical or the symbolic expression of a production process). A production function is the most common crop model. In general, a production function can be algebraically represented as;
Y = f (X),
Where; Y is the dependent variable (say output) which depends on the amount of input (X) used. Since we can change the level of input being used, X, is also called an independent variable. We assume that the level of technology being used remains the same during the production process.
For a multiple inputs case, a production function will take the following form; indicating that the final output depends on, or is a function of ‘n’ inputs or ‘n’ independent variables.
Y = f (X_{1}, X_{2}, X_{3}, . . . , X_{n-1}, X_{n})
However, it is common to analyze the effect of a single factor of production on an output; while the other variables are held constant at their mean use level or at predetermined levels. We can thus rewrite the above equation for a production function as follows;
Y = f (X1/ X2, X3, . . ., X_{n-1}, X_{n})
The equation shows that although the output, Y, is a function of ‘n’ independent variables, currently, however, the effect of a single variable, X1, is being analyzed and other variables have been kept constant (at their mean level of input use, or say at their current level of use). The functions can have linear, quadratic or other forms; and a suitable form is to be selected for detailed analysis.
We can graphically represent the response of a dose of an independent variable, or a package of inputs, on the dependent variable (output) by plotting the output obtained by the use of each dose of the input in a production trial. Such a representation of the production data is termed as the response curve or the total product curve (Fig. 16.1). The shape of the response curve for a product depends upon the nature of the product and the production process being used. The response of different inputs, under given production conditions may be different over the range of a response curve. Response to application of input(s) may be increasing, decreasing, or even constant. Technically, we refer to these responses as the increasing, decreasing or constant returns to variable inputs, respectively. To analyze the behaviour of the response curve, it is always helpful to look at the average and marginal components of this curve.
Figure 16. 1: Response curve or the total product curve
Average response, or average product (AP) as it is commonly known, is defined as the output produced per unit of input used. Marginal product (MP) or marginal response, on the other hand, is defined as the change in total output resulting from a unit increase in input. Algebraically;
AP = Y/X, and MP = Y/X. Where, denotes the change; so when we estimate the change in Y, as a result of a unit change in X, we have estimated the marginal product.
If we plot the average and marginal outputs, we can then add two more curves to the above figure showing the total response curve. It now becomes more intuitive to visualize as to what happens to the shape of the total product curve as the input use is increased. The two additional curves allow us the clearer picture of the average and marginal response to the input use.
Figure 16.2: Average and marginal product curves
We note that geometrically, MP is the slope of the total product curve. The behaviour of the marginal product curve reflects the output behaviour (i.e., the relationship between inputs and output) in response to the increase in a unit of input. When MP is increasing we say we have increasing marginal returns; that is when with the successive dose of input the addition to the total product is higher than the addition made by the previous dose of input. Similarly, when MP is decreasing, or constant, we have respectively the decreasing or constant marginal returns function. Summarizing, if;
Y_{1}/X_{1} Y_{2}/X_{2} - - - Y_{n}/X_{n} we have increasing marginal returns Y_{1}/X_{1} Y_{2}/X_{2} - - - Y_{n}/X_{n} we have decreasing marginal returns Y_{1}/X_{1} = Y_{2}/X_{2} = - - - = Y_{n}/X_{n} we have constant marginal returns
It is possible that for an activity we might notice increasing, constant and decreasing returns over the range of total product or response curve. This happens as a result of varying capacity utilization of the fixed resource due to increased use of variable inputs. As for example, in case crops the per unit response to input use is higher in the initial stages when the productive capacity of a fixed resource, say for example land, is not fully utilized. So when more input is used the output obtained per unit of additional input used is increasing. Later, the response may be constant over a restricted range and then it declines when the land resource gets over utilized. Most common examples of such responses are the fertilizer applications on a given piece of land or the number of irrigations in an irrigation trial. In both these cases, the yield response to initial input doses are higher and the response declines as we continue using additional doses of inputs. Finally, there may be losses due to toxicity or lodging etc., if the input use is continued beyond the absorptive capacity of land and the crop.
Thus, it becomes important to decide as to what level of production (and thus the level of input use) is desirable or profitable and where one should stop using the input. It is important to consider economic aspects (profitability) because the inputs are scarce and have to be paid for. If the inputs are not scarce or are not paid for, then in general, one might target the biologically maximum yield. This mostly is the case in research trials where we need to find out the maximum yield or total production of the crop.
Applications in horticulture:
Modeling has become relatively easy now with the use of computers. Computers help in reducing the complications of handling voluminous data. Therefore, apart from annual crops, modelling for perennial fruit trees is also commonly done. In the field of horticulture, the crop models are needed for modelling yield forecast, policy analysis and management options. It is very important to predict yields so as to prepare ourselves for marketing of the produce in a hassle-free manner. For example, it is important to know the timings of the arrivals of different produce in the market. If, through modelling, we can get an idea when the marketing season would be a lean season, and how we can change our harvesting to target this period, we can increase our profits. Similarly, we can target the production of flowers and pot-plants to suit the important fairs and festivals in a region. Well framed crop models can give us an idea of how we can improve some characteristics of the produce (e.g. in terms of length of stems, size of flowers etc.). The same is true for cultivation of vegetables.
In perennial crops/fruit trees we need to model “the architecture of fruit trees and the relations between pruning and flower and fruit development” for maintaining the vigour of the trees. Such modelling is generally called biological modelling. When we combine the biological and economic considerations, we say we are doing a bio-economic modelling. The economic content of the model relate to the costs and returns from the production process while the biological content refers to the physiological production processes from planting to maturity of the crop. The annual fruit production is determined by the biophysical model which may use factors like tree density, pruning/training regimes.
Fruit tree models:
The perennial nature of fruit tree implies that tree growth and the yields are also dependent on previous years’ growth and health of the tree. In deciduous fruit trees, for example, the number of flowers, and thus crop potential is determined by the condition of the plant in previous season. In fruit trees there is “a perennial woody skeleton which not only grows and develops during the annual cycle, but also accumulates and exports carbohydrates and other reserve materials. This complicates the estimation of the net increase in biomass of a fruit tree during the annual cycle”. Nevertheless, we model the response by taking various assumptions or by keeping some of the factors at a known level in the model. Goldschmidt & Lakso have suggested an option for an overall, quantitative description of fruit tree’s annual productivity through equations of carbon (C) supply and consumption. The equation is as under;
Pn + Sto = Sr + Rr +Dr + Fn.w.r + Pr + Sto where; Pn = photosynthetic production Sto = non-structural carbon reserves Sr = current year’s shoot mass (including leaves and stem) multiplied by a respiratory quotient Rr = current year’s root mass, multiplied by a respiratory quotient Dr = current year’s drop of flowers and fruit-lets, multiplied by a respiratory quotient Fn.w.r = fruit number, multiplied by fruit weight (w), multiplied by a respiratory quotient Pr = perennial organ mass, multiplied by a respiratory quotient
This expression indicates the major parameters that need to be determined experimentally or compiled from existing data in order to estimate annual productivity.