1 Introduction

Elephant foot yam [Amorphophallus paeoniifolius (Dennst.) Nicolson] is a tropical tuber crop that is commonly used as a staple food for poor. This is a cash crop and can be cultivated in harsh environment. The plant and its tuber have a number of medicinal values. We consider yam plantation of ‘BidhanKusum’, a non-irritant high yielding variety in a harsh environment with alluvial soil full of gravels as in Giridih, Jharkhand. Sustainable agriculture is suitable for harsh agro-climatic condition of Jharkhand (23.35^oN, 85.33^oE).

Sensitivity of plants is under extensive study see e.g., Amador-Vegas et al. (2014), Shepherd (1999), Luo et al. (2010). Plants’ usual responses to changes in temperature, chemicals, touches etc., are by gradually altering its growth rate or its direction of growth. Plant behaviour under climatic stress is studied in Deryng et al. (2014). Extreme climatic stress has negative impact on crop yields. We consider some other form of stress that may suitable be utilised for higher growth of crops. In Dasgupta (2015a), it is shown that growth curve of an inadvertently hurt yam plant has significantly sharp upturn of yam growth in the remaining short lifetime. In a subsequent non-destructive yam plant experiment described in Dasgupta (2015b), growth slopes are seen follow normal distribution, and seed weight 650 g is seen to be the appropriate choice for agro-climatic condition of Giridih for higher yield. With slight modification in harvesting strategy, one may substantially increase yam yield in two- stage harvesting from individual plants compared to a single harvest. In immediate requirement of some unavailable spices like ginger or turmeric, a common practice in Indian household is to dig suitable plants off the ground in kitchen garden with care, collect some rhizome of relevant spices attached to the base of stems for use; and replants the structure for further growth of tubers. The proposed strategy is similar, and this is shown to be advantageous economically for farmers. Yam plants initiate retuberization when survival is endangered under stress of yam detachment. The total yield, early plus final harvest is more than usual yield due to fast growth of tuber after yam detachment, this is also evident from growth curve; and since early harvest fetches a good price in market, the two stage procedure is conducive to maximise the total revenue.

2 Materials and Methods

We study longitudinal growth of Elephant-foot-yam for sixty plants under stress in a field experiment conducted in the agricultural farm at Indian Statistical Institute, Giridih, with seed weights 500 g, 650 g and 800 g of yam.

The experimental layout consists of six columns, in each column there are ten equidistant pits at a distance of 1 m. First two columns are for seed weight 500 g, next two are for seed weight 650 g, and the last two columns are for plants with seed weight 800 g. Column to column distance is also 1m; the plants are numbered 1-10 in the first column, 11-20 in the second etc., see Dasgupta (2015b) for a non-destructive plant experiment on yam with similar layout.

Little organic manure like cow dung is given in the pits while planting the fungicide treated cut yam seed corms of specified weights at the start of the experiment on late March 2015 in Giridih farm of the Indian Statistical Institute. In the beginning of the experiment we consider an overall general stress viz., lack of weeding, little fertilizer and scanty irrigation till the time of first intervention on 7-8 September 2015. With 20 plants in each seed category, we plan to subject 10 plants to general stress of harsh environment. Further as a severe stress, for remaining 10 plants in each seed weight category, underground yam associated with root structure are detached in the middle of experiment on 7-8 September, and the remaining stem structure with a few roots still attached near the base of stems are replanted immediately in the same pit to continue experiment. For the 10 plants in each seed weight category under general stress, interim yam readings are recorded by taking plants off the ground with care, and underground yam volumes are measured by Archimedean principle of water displacement and the experiment is continued after replanting in same pit; see also Dasgupta (2015a), Dasgupta (2015b) for longitudinal studies on yam.

In all, out of 60 plants, there are 30 plants in destructive testing and detached yam weight is measured by a weighting machine. For 30 plants under non-destructive testing, weight is indirectly estimated by multiplying the volume of yam, obtained from Archimedean principle of displaced water volume, when only the yam part of a plant is immersed in a water container. Yam volume multiplied by density (≈4g /c.c) provides estimate of yam weight in non-destructive testing.

When yams are not detached from stems, stress is considered moderate for plants. Initial plant stress on start of experiment is followed by adequate care like manuring, weeding and irrigation starting from the time of first intervention made on 7-8 September 2015.

After a time gap from the first intervention, in order to measure subsequent yam growth, one more interim yam reading is taken by uprooting all surviving plants on 14 November 2015. With yams attached to stems, experiment continued with replanted structure till the end of plant lifetime.

Stress is severe on plants under yam detachment, plants aborted large stems after replanting, as sustaining these seems difficult for plants under stress with limited resources; secondary stems emerge soon afterwards, especially if the stem was single. Experiment continued with plants along with new stems. Size and shape of yam in final harvest also reflected the high levels of stress. Yam plants having moderate to small sized stems, continued to grow under stress; as seen from the shapes of yam on final harvest.

Two interim yam deposition readings were taken on living yam plants, apart from readings in the beginning and end of experiment.

Individual growth curves are drawn with linear interpolation in between, from four possible readings on underground yam per plant viz., one in the beginning, two interim readings during experiment, and one at the end of plant lifetime. Overall growth curves in each categories are drawn by computing the average response (mean / median) at specific time points where at least one yam observation is available in individual growth curves and then using nonparametric lowess / spline regression on averaged points, see Dasgupta (2015a), Dasgupta (2015b). The growth curves explain the inherent underground yam deposition process over plant life time.

Almost sure confidence bands are constructed to cover growth curve with probability one i.e., with certainty, see Dasgupta (2015c) for a general exposition on such bands. These nonparametric almost sure bands are of stronger assertion than conventional models based percentage probability confidence bands.

Our procedure of comparison of two strategies of yam harvest is mainly based on growth curve analysis. In addition, asymptotic normal test to compare two harvesting strategies of yam with seed weight 650 g is investigated. Nonparametric two-sample U-statistics test is also taken recourse to in the same endeavour. In earlier growth studies, seed weight 650 g of yam is seen to produce high yield in Giridih soil and environment. We investigate further the yam yield scenario for this seed weight.

3 Results

3.1 Parametric and nonparametric tests to compare different harvesting procedures

Asymptotic normal test for equality of mean for two procedures under the alternative that two-stage harvest is superior, indicates that two-stage procedure is superior compared to single harvest for seed weight 650 g at 5% level of significance, the observed value of z= 1.955951, p-value of significance in the upper tailed test is 0.0252.

Two-sample Wilcoxon U statistic test for the null hypothesis of equality of procedures under the alternative that two-stage harvest produces more yam, indicates that two-stage procedure is better compared to single harvest for seed weight 650 g at 5% level of significance, the observed value of standardized U is 1.814229; p-value of significance in the upper tailed test is 0.0348.

Two-stage harvest for seed weight 650 g is seen to be superior compared to single harvest with 83% more yield than a single harvest at the end of season, based on total yield of 10 yam plants in each group.

Under the assumption that the distribution of yield F(x) and G(x) arising from two procedures of single harvest and two stage harvest respectively, is a location shift of one another i.e., G(x)= F(x-θ); estimates of shift θ are available based on yields arranged in ascending order from 10 plants in each group.

10 yield coordinates in ascending order in each case represent the deciles of corresponding distributions. Differences of these 10 coordinate of two stage procedure minus the single stage are observed estimates of θ. These are:

0.100, 0.170, 0.202, 0.497, 0.704, 0.760, 0.625, 0.702, 0.291, 0.417

Median of the above values is 0.457. A robust estimate of shift θ is then 0.457. The procedure of two stage harvest is superior.

Next we proceed to state the features of growth curves in different situations.

3.2 Superior status of two-stage harvest via growth curve analysis of underground yam

Yam growth curves in non-destructive testing are shown in Figures 1-5. A sharp fall is seen in mean response curves due to plant stress. Figure 1 shows a downfall in median response in red color around the lifetime of 125 days.

Figure 1 Individual growth (1) of yam &medlan response curve

Figure 2 Individual growth (1) of yam & mean response curve for seed wt. 500 gm

Figure 3 Individual growth (1) of yam & mean response curve for seed wt. 650 gm

Figure 4 Individual growth (1) of yam & mean response curve for seed wt. 800 gm

Figure 5 Growth curve(1) of yam &mean response curve

Figure 2 with seed weight 500g is based on 8 plants. Plant no.6 and 9 are missing, as these ill nourished plants died soon from stress. Stress effect on mean curves is apparent due to lack of care in the beginning of the experiment. Growth recovery is observed subsequently, but overall dampening effect of stress is present, compared to earlier growth studies with adequate plant care. Figures 3-4 are drawn for 10 plants each.

There is no germination in pit no. 6 and 9, with seed weight 500 g. So there are 8 growth curves in black color joined by straight lines. Likewise other missing plants in pits are not represented in figure. Non-destructive experiment is marked by (1) in title. Two interim interventions of uprooting were made to record yam growth, in case the plant is alive at those time point. The overall median response curve in red i.e., median of y values is computed at a fixed value of time x, where at least one data point represented by a small circle in figure is available. The curve shows a decline near 125 days of plant lifetime due to stress. Growth data in general are highly fluctuating variables, a robust estimate like median is considered for representing overall response. The red curve is a bit erratic towards the end in presence of less number of points with high variation in magnitude.

Figure 5 shows the mean response curves under non destructive testing for 3 seed weights and the overall mean response curve based on 28 plants. The dashed curve in red starts slightly above 650 g, as two plants out of 10 with seed wt. 500 g is missing. Growth curve corresponding to 650 g under non-destructive testing seem superior for high elevation and less variability.

Yam growth curves in destructive testing are shown in Figures 6-10. A sharp fall is seen in mean response curves due to plant stress like shedding tall stems after detachment of underground yam. Figure 6 shows fall in median response in red color during the lifetime of 150-200 days.

Figures 7-8 are drawn for 10 plants each. Figure 9 with seed weight 800 g is based on 9 plants. Plant number 53 had missing stem, not visible at the time of first intervention; therefore no destructive testing of yam removal could be made on it. Stress effect on mean curves is apparent.

Figure 10 shows the mean response curves for each seed weight, and the overall mean response curve based on 29 plants under destructive testing. The dashed curve in red starts slightly below 650 g, as one plant (no.53) out of 10 with seed weight 800 g is missing. Growth curve for seed 650 g seems superior for less variability to withstand stress and high elevation.

Figure 6 Individual growth (2) of yam &medlan response curve

Figure 7 Individual growth (2) of yam & mean response curve for seed wt. 500 gm

Figure 8 Individual growth (2) of yam & mean response curve for seed wt. 650 gm

Figure 9 Individual growth (2) of yam & mean response curve for seed wt. 800 gm

Figure 10 Growth curve(2) of yam &mean response curve

Figure 11 shows almost sure confidence bands of the growth curves under moderate plant stress. The curves are distinct. Narrowness of the estimated bands indicates small fluctuations of the curves due to sampling. The blue curve corresponding to the seed weight 650 g has high elevation.

Figure 11 Growth curve(1) of yam with a.s. confidence band

Figure 12 shows almost sure confidence bands of the growth curves in two-stage harvest under severe plant stress of interim yam detachment in the middle of season for three seed weights. The curves are distinct in this case as well. Bands are of small fluctuations due to sampling. The blue curve corresponding to the seed weight 650 g has high elevation and less variability, indicating superior growth under stress.

Figure 12 Growth curve(2) of yam with a.s. confidence band

Figure 11-12 show almost sure confidence bands of the growth curves. Narrowness of the estimated bands indicates small fluctuations of the curves due to sampling.

3.3 Sensitivity of plants under stress affecting production in a positive manner

Curves in 2nd case under severe stress of yam detachment show an upper trend, indicating plants’ alertness to counter the extreme stress by gathering resources for subsequent higher growth.

Growth curves under destructive testing of yam (2^nd case) show upward trend compared to curves for nondestructive experiments, having implications in faster growth of yam; this is conducive for higher revenue for farmers from early yam harvest at the time first intervention in the middle of season and subsequent final crop produce. Facing an emergency, when survival is endangered under the stress of underground yam detachment, a vigorous retuberization starts by yam plants.

The growth curves are seen to be distinct in narrow almost sure confidence bands. From all growth curves for different seed weights and stress levels, the superior curve is easily identified. For two levels of stress, moderate and severe, yam growth curves corresponding to the seed weight 650g is superior. The strategy of detaching underground yam in the middle of experiment and replanting the remaining structure for experiment to be continued till full plant lifetime; has significantly increasing effect on total yield of yam. For rapid growth, sensitive yam plants accumulate available growth resources, when faced with severe stress of interim yam detachment. This optimises total yield, interim plus final yield, and hence farmers’ gain; as early marketing of crop fetch a good price.

4 Discussions

In the present investigation we see that a two stage harvest of yam produce significantly higher yield. Study methods practiced a new development and procedure on application of growth curve analysis. The results are new; analysis indicates that interim harvest of yam in the middle of season increases the total production. This provides additional income to farmers from early marketing of part of the crop. The study further describes the significantly high growth rate of underground deposition under duress of yam detachment in a new type of longitudinal study; thereby providing insight into an as yet unknown mechanism and poorly understood process.The findings provide a picture on affect of different stress levels on yam growth over time. Higher level of stress due to yam detachment pulls the growth curves up compared to those under moderate stress.

Almost sure confidence band that covers the growth curves with certainty, indicate that the seed weight 650 g of yam provide high yield under general stress as well as under severe stress. This particular seed weight is seen to be appropriate choice under normal cultivation scenarios for yield maximisation from earlier growth studies conducted in Giridih.

5 Conclusion

Crop yield in general may decrease under plant stress. Plant response under stress may suitably be utilised to increase crop yield. For agro-climatic conditions as in Giridih, 650 g of yam seed weight is recommended to farmers for high yield of Elephant-foot-yam with interim harvest of yam prescribed in the middle of season and final harvest at the end of season from replantation, leading to high revenue.

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