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Area under production of vegetables is increasing over the years despite the gradual fall in total cultivable area in India. Nonetheless, growth in area is not same for all the vegetables. To the assess growth in area and address its disparity, the present study was carried out for the state of Karnataka for the period 199899 to 2017–18. About forty percent increase in area of vegetables has been observed over the period of two decades. Among the vegetables potato, and leafy vegetables recorded negative growth rate. Inequality between districts has also been observed for growth in area under vegetables. Markov chain analysis was employed to obtain transitional probability matrix of area under different vegetables. Projection for area of individual vegetable/vegetable groups for period of eight years has been made by simulating the transition probabilities. Tomato, gourds, cole crops and other vegetables group show positive trend of area over the study period. However, onion and leafy vegetables would have more or less constant area over the projected period. The unbalanced growth within the vegetable group could impact to the economy either by affecting dietary diversity or increasing import dependency for vegetables.

Imbalance in growth of area under production of different vegetables is apparent in the past.

Projected figures for the same depicts, some vegetables occupying more area than others.

In India, horticulture production has outpaced food grain production since 2012–13, with food grain and horticulture production of 281.37 m tonnes and 314.87m tonnes, respectively in 2018–19. Over the last few years, contribution of vegetables remained significant to the whole horticulture production (about 59 to 61 %) (

Karnataka being one of the major vegetable growing State contributes about five per cent to the total countries production. As the state is epitome of the diversified agro-climatic zones of India, it has diversity in the range of vegetables grown and disparity between the districts in their production. Some vegetables are occupying more area than others. However, for the better nutritional status and agriculture growth, it is crucial to balance the production of different vegetables. Hence predicting the area change of different vegetables is needed to design the required policies. Hence the study was carried out to understand the pattern of change in area under different vegetables in Karnataka.

Study area comprised of all the districts of Karnataka. Major vegetables grown in the state which occupy more than 10% of the vegetable area were considered individually, viz., potato, tomato and onion. Further, major groups of vegetables such as gourds, cole crops and leafy vegetables were taken separately and rest of the vegetables were grouped to form Other vegetables category. Other vegetables group includes brinjal, beans, tapioca, sweet potato, peas, lady's finger, radish, beet root, carrot, capsicum and cluster beans. Thus in effect the analysis had seven vegetables/vegetable groups. This study is based on time series data of area under vegetable production, both district-wise and state total. Required secondary data was collected from Department of Horticulture, Bangalore for period between 1998–99 and 2017–18.

Compound growth rates of area were estimated to study the growth in area of vegetables/vegetable groups. Growth rates of vegetables area were obtained from exponential function as follows:

^{t}_{e}

CGR (%) = (Antilog b - 1) ^{*}100

where, CGR = Compound growth rate;

The ‘t’ test will be applied to test of significance of ‘b’.

Markov chain analysis was used to project the change in area under different vegetables in Karnataka. Markov chain approach is based on less stringent assumptions and provides more information than the regression approach (

When structural changes within the agricultural system are resulted from large number of individually small forces, the system can be treated as a stochastic process in which there are a finite number of possible states (

It should be noted that this techniques assumes the Markov property to forecast the area distribution. Since the predictions are not constrained by any

In addition, the transition probabilities have been estimated with assumption of constancy, i.e., all the forces which influenced agricultural structural change in the past will continue to do so in the future (

A stochastic matrix with the probability,

Where, _{ij}_{j}_{ij}

Here _{ij}

Consider a matrix M, also called as a fundamental matrix, defined as:

Let

Finally, this matrix may be reduced as below:

The

Since, the single value projections are less realistic and does not reveal the uncertainty of projections, complete distribution of projected value is more appropriate. Hence simulation was utilized to capture the complete distribution of projected values. Projection for area of individual vegetable/ vegetable groups for a period of eight years has been made by simulating the transition probabilities.

Area under the production of different vegetable in the previous period was taken as a start vector for simulating area in the successive years and ran One thousand simulations to incorporate the probabilistic distribution.

Transition probability matrix was build using Solver IDE and probabilities were simulated in Modelrisk 6.1.22 (Vose Software NV, Belgium) to project the area under vegetables. Mapping of district wise vegetable area for different periods was done using Tableau Public 2020.

Area under production of vegetables for periods between 1998–99 to 2017–18 is depicted in

Vegetable area has reported spike of about 40 per cent in the span of two decades, from 2.7 lakh ha to 3.7 lakh ha. However, the growth is not positive for all the vegetables, viz., potato, leafy vegetables, and other vegetables have recorded negative growth rate. Among vegetables onion had highest area under production followed by tomato and potato (

^{th} state moving to the j^{th} state. While, the diagonal element

Area under Production of major vegetables in Karnataka

Vegetables such as onion, tomato and potato have probability to retain major share (75 %, 52% and 50% respectively) of previous year area for their production compared to gourd and cole crops (26 % and 25 %). Onion followed by tomato had high probability to gain areas from other vegetables, which is also evident from the greater increase in area compared to the rest.

Applying the transition probabilities to the start vector of area under production of different vegetables, area for the same was projected for period of eight years starting from 2018–19.

Assuming, total area under production constant in future, simulated area for each of the vegetable/ vegetable groups is represented in series of graphs under the heading of

District-wise Area under Production of Vegetables in Karnataka for the Year 1998, 2008 and 2017 (values in hectares)

Area simulation of vegetables using Transition probability matrix for eight years

Some vegetables showed wide range for the projected values, viz., onion and leafy vegetables, indicating uncertainty associated in their projections, which could be due to inconsistency of time series data for those particular crops. Also range of projections for potato and tomato was too narrow, might be due to clear trend in data, thus making the projected values more reliable.

Akin to other high value crops, area under production of vegetables is also increasing over time. Nevertheless, there exists inequality in growth rates within the vegetable group. Hence the objective of this study is to understand the pattern of area allocation for vegetable and project area under different vegetables in future. Time series data of area for all vegetable crops, district-wise and state total was used for the analysis. Markov chain approach produces the forecast of the target variable,