International Journal of Horticulture, 2017,Vol.7, No. 23, 205-218
206
Dasgupta (2017b) concentrated on second interim yam detachment strategy made at four and half months from
sprouting, and analysed the growth curve in terms of almost sure confidence band, proliferation rate, and
estimation of growth curve via mid band to contain fluctuations of curves around central line. Modeling the error
component by a Gaussian process was investigated. Estimation of process parameters from observed data by
different techniques including the method of maximum likelihood and from observed maximum fluctuation of the
growth curves were investigated. Test for the hypothesis that the error components are following a Brownian
motion is seen to be affirmative.
In the present study we analyse the data on three dimensional surface plotting, taking into account the variation of
the time dependent proliferation rate with seed weight in a continuous scale. The peak of the proliferation surface
starts with 500 g of seed weight at the front edge in a three dimensional figure. The said peak is towards the end
of time range for yam lifetime, and then the line of peaks of curved surface goes downward through the interior
of time range for other seed weights of higher values; the peaks of proliferation rates are attained inside the time
range of lifetime for other seed weights more than 500 g. This suggest, if plants with seed weight 500 g could be
nourished further after some time from sprouting, then yield from these would be much higher. Proliferation rates
when integrated provides logarithm of yield. Higher the rates, higher are the yield in those time regions.
If additional resources are made available at a later stage, farmers may like to use that for nourishing the plants
with seed weight 500 g in order to maximise yield in a harsh and extreme agro-climatic environment.
2 Materials and Methods
We studied longitudinal growth of Elephant-foot-yam for sixty plants under extreme agro-climatic 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 1 m; the plants are numbered 1-10 in the first
column, 11-20 in the second etc, see Dasgupta (2017a).
We analyse the characteristics derived from longitudinal growth curves in three dimensional analyses. The earlier
studies reported in Dasgupta (2017a), Dasgupta (2017b) indicated that yam detachment at the time of second
interim growth recording is superior. The longitudinal growth curves of yam growth from 31 plants over different
seed weights, all subjected to interim yam detachment at the time of second growth recording are shown in Figure
1. The figure appears as the first figure in Dasgupta (2017a). The Mean growth curves for different seed weights
are computed as mean of
y
coordinates in Figure 1, for fixed values of time
x
; when at least one growth data is
recorded in the field experiment at that time. The mean of
y
values are connected by straight lines as an
approximation of mean response and shown in Figure 2. Starting with this, we compute the proliferation rates i.e.,
the derivative of logarithm of yam yield with respect to time, in each group of plants with fixed seed weight viz.,
500 g, 650 g, 800 g. The computational procedure involves raw proliferation rates computed at fixed time
t
. A
smooth exponentially decaying weight function, that down-weights the raw rates, involving distant observations,
away at long time from
t
; is considered next. Averaging these weighted rates, or taking suitably trimmed mean of
these weighted rates are two possible options for consolidation in a single number. The latter option considered
previously produced too smooth rates. The former option of averaging and then smoothing the averaged rates
with the program smooth.spline in SPlus is considered as a modification; the procedure is described in Dasgupta
(2017c), and seen here to produce satisfactory result for proliferation rate over time, including extreme time
points. On the other hand, median or suitably trimmed mean of these weighted rates considered earlier, although
perform well otherwise, performs poor at extreme time points. We then concentrate on the time region where the
proliferation rate is high for a seed weight; this indicates rapid growth of underground yam in that time segment,
enabling comparison.
