EurAgEng
Paper no:
98-A-059
Title:
Seed Distribution Over The Area
Authors:
Hans-Werner Griepentrog
The Royal Veterinary and Agricultural University
Department of Agricultural Sciences, Agricultural Engineering
Agrovej 10, DK - 2630 Taastrup
Tel.: +45 3528 3575, Fax: +45 3528 3574, email: [email protected]
Summary:
Seed placement accuracy of sowing machines influences field emergence, development of
individual plants and hence yield. To evaluate seed placement the evenness of depth is of
importance as well as the horizontal distribution over the area. The quality of horizontal overall
distribution is influenced by row width and longitudinal distribution and of course plant or seed
density as a non technical parameter.
A method is presented to describe the arrangement of plants in row crops by allocating a
polygonal area of ground to each plant. This method is able to operate completely in a two
dimensional way. So it includes almost the main parameters effecting overall distribution and is
therefore a measure to characterize plant growth potential in relation to seed patterns.
The analysis of polygon size and circumference is able to evaluate the longitudinal distribution
of seeding machines in relation to the overall distribution and therefore to aspects of plant
development. Even longitudinal distributions led to an even distribution of single plant area and
therefore higher yields. Concerning row width the yield is not in every case increased by
decreasing this parameter.
The method of utilizing polygon calculations is a general possibility of describing seed and
plant overall distributions. Other crops like cereals or maize can also be the objective of further
investigations.
Seed Distribution Over the Area
Hans-Werner Griepentrog
The Royal Veterinary and Agricultural University, Agrovej 10, DK-2630 Taastrup
Introduction
Seed placement accuracy of sowing machines influences field emergence, development of
individual plants and hence yield. To evaluate seed placement the evenness of depth is of
importance as well as the horizontal distribution over the area. Optimizing plant spacing
should increase yield by minimizing competition between plants for available light, water
and nutrients. The quality of horizontal overall distribution is influenced by row width
and longitudinal distribution and of course plant or seed density as a non technical
parameter. These parameters together determine the area available for each single plant
and therefore the intra-specific competition concerning root and total crop development.
Most procedures to describe seed distributions operate in one dimension [1,2,3], but
conditions for plant development are described as two or better three dimensional
problems. The disadvantage of one dimensional parameters is that they do not directly
include row width and seed density.
A method is presented to describe the arrangement of plants in row crops by
allocating a polygonal area of ground to each plant. This method is able to operate
completely in a two dimensional way. So it includes almost the main parameters effecting
overall distribution and is therefore a measure to characterize plant growth potential in
relation to seed patterns. Data are calculated for distribution of polygon size and their
circumference as a descriptor of their shape. A new parameter called shape ratio is
introduced as a ratio between the circumference of a polygon and the ideal circle.
Literature Review
Seeding machines produce different characteristics of spacing accuracy mainly related to
their metering principle. Other components of the machine also have an influence on seed
accuracy for instance seed tubes and coulters [4]. Precision drilling is mainly used for
rather widely spaced crops, such as maize and beets. With closely spaced crops like
cereals and rape precision drilling is too expensive and therefore bulk drilling is common.
For precision drills the seed distances follow a multi culminate normal distribution,
which has the adjusted spacing as its maximum [2,5,6]. This distribution is merely an
approach to equidistant spacing because of several interferences involved.
For seeding machines with bulk drilling the frequency of distances corresponds to an
exponential function. This means, that the distribution does not result in any maximum in
the range of the adjusted spacing.
To describe longitudinal distributions it is common to use the coefficient of variation
(cv) and of course the average of seeds per unit length is still used [1,7,8]. For precision
drilling some special parameters as standard deviation or/and percentage of plants
positioned in a certain range around adjusted spacing are used [2].
The cv in the direction of travel with proper use of precision drilling is below 50 %
whereas with bulk drilling in the range of 100 to 150 %. For common grain drills a cv
with 100 % is a quite good accuracy achieved by well operating mechanical and
pneumatic machines. But often when using mechanical drills for rape the accuracy gets
less (cv 120 to 150 %) due to low seeding rates with less than 1 kg/ha and interference
by attrition of seed treatments [3].
The evaluation of technical parameters must consider plant growth conditions
otherwise the conclusions from them would be weak and not comprehensive. The overall
distribution of seeds is determined by intra-row accuracy and row width. The intra-row
accuracy (cv) can be used to compare different types of machines, but for plant growth
interpretations they are not suitable.
First approaches to two-dimensional parameters were made by transferring the in
plant ecology wellknown term of ‘mean distance to nearest neighbour’ to seed
distribution over the area [9,10,11]. Disadvantages of this procedure are the only view at
the nearest neighbour and not at all, less clearness and no possibility for calculating
further parameters. Any consideration of competitive effects must involve the definition
of a class of neighbours of a plant and the definition of the inter-plant effects between all
neighbours and the basic plant. So at first a method should be able to divide plants into
neighbours and non-neighbours.
A better way especially concerning neighbour recognition is the use of Thiessen or
Voronoi polygons for certain plant coordinates [12,13]. Polygons are formed by the
perpendicular bisectors of the lines between plants, see figure 1. The polygon around a
plant includes all points in the plane which are closer to that plant than to any other. The
polygon also defines the immediate neighbours of an individual. Modern software is able
to provide users with data for further statistical analysis and different purposes [14,15].
Figure 1: The construction of Thiessen or Voronoi polygons and Delaunay triangulation
Polygons have been proved to be predictors of plant size and shape [12,16]. So polygons
are a reasonable measure of two dimensional area regarding to seed and plant
distributions over the area. To characterize a polygon three parameters have to be de-
fined which describe its size, its shape and the position of the plant within the polygon,
called eccentricity.
With calculated polygon sizes statistical parameters like mean and standard deviation
can characterize evenness of size distributions. These frequency distributions can be
interpreted for analysing intra-specific competition. Investigations have verified the
relationship between polygon size and mortality [16].
Materials and Methods
For going more into details further information about properties of ground area allocated
to the plant are needed.
Polygons of the same size can differ concerning the shape. Of course the ability of
plants to utilize space depends on the plant species. For instance rape has a very high
adaptation capacity while maize is not able to compensate space insufficiency. So not
only the size of polygons is of interest but also the shape due to different adaptive
abilities.
The shape of a polygon can be described in several ways. Concerning plant arrangements the comparison to a circle is of interest, because a circular ground area is
supposed to be ideal for individual plant development.
The polygon method produces a system of only convex areas. Therefore an even
distribution over the area will create patterns which are merely an approach to ideal
circular areas. A circular ground area is the ideal shape to be aspired for single plants in
plant populations.
The circumference of the ideal circular ground area is calculated by the polygon area:
c = 2π A
π
A : polygon area
i
ideal
i
To qualify the pattern by determining the deviation from ideal circles a mean value called
shape ratio r is defined:
r=
c
c
1 n ci ideal
⋅∑
n i =1 ci real
ideal
real
: circumference ideal
: circumference real
To find a suitable parameter to describe the eccentricity of plant location to the
polygon may have an effect and will be investigated by the author. However, size and
shape values of polygons are believed to provide the most important parameters
concerning plant development.
To determine the influence of evenness of plant distribution on yield a simple model
has been created [17]. By knowing the single plant yield related to the occupied area in
the field and having the describing function it is possible to do a first approach for space-
yield relationship modelling. The data were taken from investigations about determining
intra-specific competition factors of rape, see figure 2 [18].
Figure 2: Function of single plant yield versus single plant area for rape
Results
Figure 3 shows produced
polygons for three different
working qualities, stated by the
coefficient of variation (cv):
150 % for the worst, 101 % for
a good or normal and 58 % for
the best longitudinal accuracy.
The calculations are based on
investigations with different
seed metering systems, especially concerning spacing data
of seeds [3].
Figure 3: Single plant area
(polygons) of drilled rape seeds
versus accuracy of longitudinal
distribution
These spacing data were taken to provide the polygon calculation routines with plant
coordinates. The evenness of polygon size distribution depends on the accuracy of
spacings in the row, see the table. The standard deviation of polygon sizes for using
precision drills (cv 58 %) is 56 cm² while using the volume metering machine (cv 101 to
150 %) in the range of 99 to 120 cm², see the table. Therefore precision drills produce a
higher evenness of single plant areas than bulk drills [17], see also figure 3.
Table: Polygon size distribution versus longitudinal distribution (seed density 60 1/m²)
longitudinal distribution cv [%]
mean area xm [cm²]
standard deviation s [cm²]
sample number n
58
170
56
983
101
169
99
974
150
163
120
979
An example for the shape ratio versus cv and row width is shown in figure 4. For bulk
drilling with a cv between 100 and 150 % it is possible to improve the overall
distribution by decreasing the row width. When plant pattern with rape are established by
precision drills (cv < 50 %) the best evenness is achieved by using 12 cm row width. The
reason for this is that for a seeding density of 60 plants/m² mean distance and row width
are about equal. To increase or decrease the row width of 12 cm means moving away
from the optimum pattern. So with precision drilling the narrowest row width will not
always work out the highest evenness of distribution over the area.
Figure 4: Shape ratio versus longitudinal distribution and row width
Utilizing the function of yield-area relationship for single rape plants, see figure 2, it is
possible to calculate the yield of a certain area, see figure 5. The yield potential for
establishing plants with equidistant patterns (cv = 0 %) is estimated to be about 11 %
higher than by seeding with bulk drills (cv = 100 %), see figure 5. The influence of row
width onto yield decreases with higher evenness of longitudinal distribution.
Figure 5: Yield versus evenness of longitudinal distribution and row width
Conclusions
The analysis of polygon size and circumference is able to evaluate the longitudinal
distribution of seeding machines in relation to the overall distribution and therefore to
aspects of plant development.
Even longitudinal distributions led to an even distribution of single plant area and
therefore higher yields. Concerning row width the yield is not in every case increased by
decreasing this parameter.
The method of utilizing polygon calculations is a general possibility of describing seed
and plant distributions. Other crops like cereals or maize can also be the objective of
further investigations.
References
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