Translated
by Judong Shen
Edited
by Mohan Ramaswamy
Source: Journal of Nanjing
Agricultural University [Nanjing Nongye Daxue Xuebao ISSN: 1000-2030] (1996) v.19(3)p.55-58
SPATIAL DISTRIBUTION AND SAMPLING TECHNIQUE OF APHIS GLYCINES MATSUMURA
Jianya Su, Kangshan Hao and Xiaoling Shi
(Institute of Agricultural Entomology, Nanjing Agric Univ., Nanjing 210095)
ABSTRACT The spatial
distribution of Aphis glycines Matsumura was studied. All sets of samples exhibited aggregated patterns of
spatial distribution, but did not fit Poisson, Neymann (n=0~4 and ∞), Poisson-binomial and compound Poisson distributions. Of 11 sets of
samples tested, 10 sets fitted the negative binomial distribution; only 1 set did
not fit. The fundamental components of the spatial distributions of Aphis
glycines are aggregated distribution of individual populations; the degrees
of aggregation increase with the population densities. The spatial distribution parameters (
, 
, 
,
,
) of the soybean aphids and species aggregation average
degree (
) were analyzed, the
reason of aggregation patterns of the aphids was discussed, and the relation
between the average sizes of the individual population and its average
densities was predicted. The theoretical sizes of sampling and sequential sampling plans of fixed levels
with precision were determined by utilizing estimated variance/mean
relationship obtained from Taylor’s power law regression. The theoretical
size of sampling is 
and the stop line of
fixed-precision-level sequential sampling is 
.
Key words Aphis glycines Matsumura; spatial distribution; sampling
Aphis glycines Matsumura is one of the serious pests on soybean in China. This paper is the first study about the analysis of the characterization of field distribution patterns and the spatial distribution parameters. The application of spatial distribution parameters on the sampling technique has also been explored.
1.
Data sources and methods
The population of A. glycines in the experimental fields of Nanjing Agriculture University was studied by sampling survey in 1995. The sampling unit was a compound leaf. Four hundred individual plants were investigated continuously. Three pieces of compound leaves were taken from the upper, middle and bottom parts of each individual plant. Totally, eleven fields were surveyed, thus the data of eleven groups of samples were obtained. Those data were applied for the analysis of the distribution pattern characteristics using frequency mapping, degree of aggregation indices and regression model methods respectively. Furthermore, the characteristics of the parameters were investigated.
2.
Results and Analysis
2.1 The determination of
the distribution patterns
The distribution patterns were analyzed using the frequency mapping, aggregation degree indices and regression model methods respectively.
2.1.1 Frequency mapping method
Eleven groups of sample
data were listed in the frequency distribution table, and the theoretical
frequencies of five kinds of distributions (Poisson distribution, negative
binominal distribution, Neymann
distribution (n=0~4 and n=∞),
Poisson-binomial and compound Poisson distribution) were calculated
using computers. Then the chi square value was calculated. The results showed
that of 11 sets of samples tested, 10
sets fitted the negative binomial distribution, only 1 set did not fit
(probably due to the discrete sample data), and all the samples did not fit
other distributions.
2.1.2 Degree of aggregation indices method
For each group of sample, the mean (
), variance (
), average degree of aggregation (
), k value of negative binomial distributions,
dispersion index (C), Kuno’s 
index, Moristita’s 
, cluster index (y), average size index of individual
population (
) were calculated respectively. The measurement standards are
given in Table 1. It has been shown from Table 2 that all aggregation indices
of A. glycines conform with the measurement standards [1~3],
which accounts for the result that all of the eleven groups of samples belong
to clustered distribution.
Table 1. Several aggregation parameters for measuring spatial pattern of insects
|
Distribution Pattern |
Dispersion index C |
Morisita’s |
Kuno’s |
Cluster index (y) |
Taylor’s b |
Twao’s |
|
Poisson |
1 |
1 |
0 |
1 |
1 |
1 |
|
Aggregation |
>1 |
>1 |
>0 |
>1 |
>1 |
>1 |
|
Regular |
<1 |
<1 |
<0 |
<1 |
<1 |
<1 |
|
Measurements |
|
|
|
|
|
|
Table 2. The aggregation parameters of A. glycines population
|
Date |
|
|
|
|
y |
|
|
Degrees of freedom |
Pattern |
|
1995-07-24 |
1.310
0 |
8.185
7 |
3.491
4 |
6.248
6 |
5.006
6 |
5.005
8 |
21.05 |
18 |
N.B.D. |
|
1995-07-26 |
0.987
5 |
5.205
0 |
3.661
8 |
5.270
9 |
5.325
0 |
5.325
0 |
32.19 |
15 |
C.D. |
|
1995-07-28 |
0.776
7 |
3.563
1 |
4.211
0 |
4.587
7 |
5.619
0 |
5.620
4 |
13.28 |
11 |
N.B.D. |
|
1995-07-30 |
0.510
0 |
2.145
0 |
4.882
4 |
4.205
9 |
7.286
1 |
7.291
2 |
3.95 |
11 |
N.B.D. |
|
1995-08-01 |
0.640
0 |
3.613
4 |
5.910
7 |
5.646
0 |
8.259
4 |
8.262
7 |
2.73 |
11 |
N.B.D. |
|
1995-08-03 |
0.429
2 |
1.851
5 |
6.121
6 |
4.314
2 |
8.821
8 |
8.731
1 |
10.24 |
8 |
N.B.D. |
|
1995-08-05 |
0.748
3 |
2.885
7 |
3.410
8 |
3.853
2 |
4.816
9 |
4.817
8 |
13.36 |
10 |
N.B.D. |
|
1995-08-07 |
0.459
2 |
1.908
3 |
5.284
0 |
4.155
9 |
7.872
6 |
7.879
9 |
8.01 |
11 |
N.B.D. |
|
1995-08-14 |
0.306
7 |
0.861
7 |
4.868
8 |
2.809
8 |
6.900
9 |
6.912
7 |
8.00 |
8 |
N.B.D. |
|
1995-08-16 |
0.317
5 |
1.312
8 |
5.591
9 |
4.134
8 |
10.873
4 |
10.891
0 |
10.96 |
8 |
N.B.D. |
|
1995-08-18 |
0.526
7 |
2.229
5 |
3.977
4 |
4.233
2 |
7.138
6 |
7.143
6 |
11.23 |
9 |
N.B.D. |
* N.B.D. = negative binomial distribution; C.D. = clustered distribution.
2.1.3 Regression model method
The eleven groups of sample data were used to check the distribution of A.
glycines based on the regression equation: 
, which consists of the relation between average degree of aggregation (
) and the mean (
). Iwao proposed this method. The results are as the
follows:
= 1.953 1 + 3.421 6
(r = 0.875 7, F=29.6)
The value of 
= 1.953 1>0 shows that the fundamental components of the
spatial distributions of A. glycines population are individual
populations. The value of 
= 3.421 6>1 shows that the fundamental components of the
distributions of A. glycines population are clustered distributions.
The Iwao model improved
by Rumei Xu is:
= 1.920 8 + 3.522 1
- 0.064 74
Its r value (r
= - 0.064 7) approaches 0 and there is little difference between its values of 
, 
and the values of 
, 
in the original Iwao model.
The results are as the follows tested by Taylor’s regression
equation: 
, which consists of the relation between variance (
) and the mean (
):
= 5.364 
(r = 0.976 6, F=185.5)
The values of a = 5.364 1>1 and b = 1.360 1>1 show that the distributions of A. glycines are all clustered distributions in all densities and the aggregation degrees increase with the population densities.
The F-value in analysis of variance showed that Taylor’s variance and
regression equation of means reflected the aggregation and distribution
patterns of A. glycines in fields more accurately than Iwao’s
average degree of aggregation and
regression of mean did. The relevant coefficients of Taylor’s regression
equation and F value were all greater than Iwao’s. The Taylor’s b value
was dependent on specific characters of insect species. As the life behaviors of
species vary form each other, the b values differ between species a lot.
While, for the species with the similar life behaviors and distribution
patterns, their b values are quite similar between each other. Thus, b
values are more suitable in the application of sampling experiments than Iwao’s
parameters.
2.2 The size analysis of
individual population of A. glycines
The spatial distribution
of A. glycines is the clustered distribution of individual population
structure in terms of the parameters 
and 
. Its aggregation size relates to the k value of
negative binomial distribution, which can be represented by the average size
index of individual population (L) [5]. The established relation
equation between L and average density (
) is: 
= 2.063 + 3.711 1
(r = 0.935 7). The size of individual population of A.
glycines is unstable since it increases with the population density.
2.3 Analysis of causes of aggregation
Average degree of
population aggregation (
) proposed by Blacksmith was used to examine the aggregation phenomenon
of A. glycines in fields. The formula to calculate the average degree of
population aggregation is:
in which k is the
parameter of negative binomial distribution, and r is the function of 
when the degrees of
freedom are 2k. The aggregation results from some environmental factors
when 
is less than 2.
However, when 
is greater than 2,
the aggregation results from the combined effects of both insects’ behaviors
and the environmental factors. The 
values in eleven
groups of samples are all less than 2, which shows that the aggregation
distribution of A. glycines results from the different characteristics
of the environment, and it is also related to the very low population density
of A. glycines.
2.4 Determination of the
theoretical sampling size
The theoretical sampling size and the stop lines of fixed-precision-level sequential sampling are determined using the parameters a and b in Taylor’s variance and mean equation. They are as follows respectively:
in which n is the size of sampling, 
is the cumulative
number of aphids, D is the precision index (n = 0.1, 0.2, 0.3). If the
values of a and b are substituted in the above equation, the
theoretical size of sampling and the stop lines of fixed-precision-level
sequential sampling under different aphid densities (
) and different precision requirements could be
obtained as follows:
It is shown in Figure 1 that the theoretical size of
sampling (n) will increase exponentially with the decrease of the aphid
densities (
). In the process of fixed-precision-level sequential
sampling, the investigation could be terminated when the accumulative aphid
number reaches the stop lines in Figure 2. In practice, the precision level
could be determined by the specific requirements. Usually, D is set to 0.2 in
large fields.
Fig. 1 Sample size curves for
leaf samples Fig. 2 Stop
lines for fixed-precision-level
of
A. glycines sequential sampling for A. glycines
(This paper was reviewed by Prof. Xianian Cheng. The authors acknowledge him)
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(Editor: Hongyan Zhao)