Sampling Aphis glycines (Homoptera: Aphididae) in Soybean Fields in Illinois

Abstract

The aphid Aphis glycines Matsumura, which was first observed in North America in 2000, is a pest of soybean, Glycine max L., in the United States and southern Canada. This study focused on the distribution and sampling of this aphid at two spatial scales: field and township. We sampled 14 soybean fields in each of two townships in Kendall and Champaign counties in Illinois on four sampling dates during the summers of 2001–2003. Generally, there was little synchrony of population dynamics (increases or decreases) across the fields in either township during the middle of the summers. There was significant field-to-field variability in mean number of aphids per plant. Thus, multiple fields must be sampled to accurately understand the infestation levels in a township. For Kendall Township in all years, drilled soybean fields always had the highest mean density at the second and third sampling dates, but fields with wide rows (0.61–0.76-m widths) had the highest mean density at the fourth date. However, row spacing had no significant influence on the mean density in most of the other analyses of variance. The probability of finding an infested field by mid-July when mean density in the township is less than two aphids per plant is 50% for Kendall County and 11% for Champaign County. Thus, at least two and 14 fields in Kendall and Champaign counties, respectively, must be sampled (50 plants per field) to have at least a 75% chance of finding a new invader in at least one infested field in a township during that period. Variance was related to mean number of aphids per plant, M, in a field by S2 = 6.39911 × M1.71779. This specific form of Taylor’s power law allowed us to calculate the appropriate sample sizes (plants/field) needed to obtain different levels of precision. Regression analysis showed no relationship between aphid density and distance from the field edge over the 50-m transects used in sampling. The relationship between the proportion of infested plants in a field, P, and mean aphid density, M, is represented by P = 1 − exp(−0.195764M). The proportion exceeds 0.99 for mean densities exceeding 24 aphids per plant in a field. Thus, our results suggest that aphids should be counted on 50 plants per field to obtain a reliable estimate of the population.

Full text

SAMPLING
Sampling Aphis glycines (Homoptera: Aphididae) in
Soybean Fields in Illinois
D. W. ONSTAD,
1
S. FANG,
1
D. J. VOEGTLIN,
2
AND M. G. JUST
1
Environ. Entomol. 34(1): 170Ð177 (2005)
ABSTRACT The aphid Aphis glycines Matsumura, which was Þrst observed in North America in 2000,
is a pest of soybean, Glycine max L., in the United States and southern Canada. This study focused on
the distribution and sampling of this aphid at two spatial scales: Þeld and township. We sampled 14
soybean Þelds in each of two townships in Kendall and Champaign counties in Illinois on four sampling
dates during the summers of 2001Ð2003. Generally, there was little synchrony of population dynamics
(increases or decreases) across the Þelds in either township during the middle of the summers. There
was signiÞcant Þeld-to-Þeld variability in mean number of aphids per plant. Thus, multiple Þelds must
be sampled to accurately understand the infestation levels in a township. For Kendall Township in
all years, drilled soybean Þelds always had the highest mean density at the second and third sampling
dates, but Þelds with wide rows (0.61Ð 0.76-m widths) had the highest mean density at the fourth date.
However, row spacing had no signiÞcant inßuence on the mean density in most of the other analyses
of variance. The probability of Þnding an infested Þeld by mid-July when mean density in the township
is less than two aphids per plant is 50% for Kendall County and 11% for Champaign County. Thus, at
least two and 14 Þelds in Kendall and Champaign counties, respectively, must be sampled (50 plants
per Þeld) to have at least a 75% chance of Þnding a new invader in at least one infested Þeld in a
township during that period. Variance was related to mean number of aphids per plant, M, in a Þeld
by S
2
⫽ 6.39911 ⫻ M
1.71779
. This speciÞc form of TaylorÕs power law allowed us to calculate the
appropriate sample sizes (plants/Þeld) needed to obtain different levels of precision. Regression
analysis showed no relationship between aphid density and distance from the Þeld edge over the 50-m
transects used in sampling. The relationship between the proportion of infested plants in a Þeld, P,
and mean aphid density, M, is represented by P ⫽ 1 ⫺ exp(⫺0.195764M). The proportion exceeds 0.99
for mean densities exceeding 24 aphids per plant in a Þeld. Thus, our results suggest that aphids should
be counted on 50 plants per Þeld to obtain a reliable estimate of the population.
KEY WORDS Glycine max, TaylorÕs power law, soybean aphid
THE APHID NATIVE TO CHINA, Japan, Korea, and southern
Asia, Aphis glycines Matsumura, has become a new
pest of soybean, Glycine max L., in North America and
has clearly shown that it is established and will remain
a pest. In 2000, the aphid was observed in several
states, including Wisconsin, Minnesota, Michigan, In-
diana, and Illinois (Hartman et al. 2001). In 2001, the
aphid returned, with infestation levels generally ex-
ceeding those observed in 2000.
A. glycines is a small greenish yellow aphid with
distinct black cornicles on its abdomen. On actively
growing soybean plants, colonies are found on the
stem apices and young leaves; on reproductive-stage
soybean, the aphids are found on the underside of the
leaves, stems, and pods throughout the plant. In Illi-
nois, it is rare to Þnd any other aphid species colo-
nizing soybean, so it is safe to assume, for the period
of our study, that colonies of tiny, yellow aphids on
soybean are A. glycines.
A. glycines undergoes a complex, holocyclic life cy-
cle, with as many as 18 generations annually, in which
two very different types of host are necessary for
survival in temperate regions. They overwinter as eggs
on buckthorn, Rhamnus cathartica L., with spring gen-
erations on buckthorn producing winged migrants
that ßy to soybean. In the fall, migrants produced on
soybean ßy back to buckthorn where the overwinter-
ing eggs are deposited.
Two studies in Asia have evaluated sampling of A.
glycines on plants or leaves. AreÞn and Ivliev (1985)
performed a 2-yr Þeld study in northern Asia that
allowed them to produce a sequential sampling plan
for the aphid. We were unable to determine whether
their sampling unit was 10 soybean plants or1mof
row. Peak densities in their Þelds ranged from 40 to 250
aphids per plant. Su et al. (1996) performed a 1-yr
study of A. glycines in China. With the trifoliate or
complex leaf as the sampling unit and with typical
1
Department of Natural Resources and Environmental Sciences,
University of Illinois, Urbana, IL 61801.
2
Center for Economic Entomology, Illinois Natural History Survey,
607 E. Peabody Dr., Champaign, IL 61820.
0046-225X/05/0170Ð0177$04.00/0 䉷 2005 Entomological Society of America

densities ⬍5 aphids per leaf, they concluded that the
aphid has a clumped distribution in soybean Þelds.
Cereal aphids may be the most commonly studied
aphids in Þeld crops. Elliott and Kieckhefer (1986)
found that four aphid species exhibited aggregated
spatial distributions across 0.3-m samples of winter
wheat. Feng and Nowierski (1992) found that another
set of four aphid species exhibited aggregated spatial
distributions across single-plant samples of spring
wheat. Both studies used TaylorÕs power law to de-
velop sampling plans with Þxed levels of precision.
In this article, we attempt to answer the following
questions. Does average density vary from Þeld to Þeld
within a county? How does row spacing inßuence
mean aphid density? How does variance change with
mean density? How does this help to determine the
number of plants to sample in a Þeld? How does the
mean density inßuence the proportion of plants in-
fested in a Þeld? Does density decrease or increase
from edge to center of Þeld (along transects)? How
many Þelds should be sampled to Þnd the Þrst invaders
into soybean Þelds in a township?
Materials and Methods
Fourteen commercial soybean Þelds were sampled
in each of two townships in Kendall and Champaign
counties in Illinois during the summers of 2001Ð2003.
Kendall Township is located at Yorkville, IL, at lati-
tude 41.6⬚ N and St. Joseph Township in Champaign
County is located several kilometers east of Cham-
paign-Urbana, IL, at 40.1⬚ N. These townships are
square regions encompassing 93 km
2
. In 2000, Kendall
County had several Þelds with high numbers of aphids
and the township is adjacent to the Fox River, which
has Rhamnus infestations along its corridor. Cham-
paign County was chosen because of its proximity to
the University of Illinois. Small numbers of aphids
were observed in only a few Þelds in Champaign
County in 2000.
Soybean Þelds were selected using three rules in
early June. To ensure adequate dispersion of the Þelds,
half of the Þelds were in the northern part of the
township and half were in the southern part. Each Þeld
was 1 km away from any other Þeld in that half. The
Þeld size was at least 2 ha. Thus, within each half
township, the selection of Þelds was relatively random.
Each two-person team randomly selected two start-
ing points for the 50-m transects within 1 m of the Þeld
edge near a road. Transects were at least 10 m apart.
Each person took whole-plant samples every2mfor
a total of 25 samples per transect and 50 samples for
each Þeld. We recorded the number of aphids on each
plant.
Townships were usually sampled every 3 wk from
late June or early July when aphids Þrst invaded the
counties to early September after populations had
usually declined. All townships were sampled four
times each year, except for St. Joseph Township in
2002 when it was not sampled because of low numbers.
Soybean Þelds in Kendall Township that were either
sprayed with an insecticide or severely damaged by
hail in 2003 were not sampled on all four dates.
We attempted to obtain information about soybean
cultivar, herbicide use, and insecticide use from all
farmers of the selected Þelds. (We also recorded row
spacing for each of the Þelds.) Only ⬇50% of the
growers over the 3 yr provided the requested infor-
mation. Table 1 shows the data concerning manage-
ment of the Þelds. No more than one soybean cultivar
was ever planted twice in any of our sets of 14 Þelds
in a single county per year. Thus, no statistical analysis
could be performed on cultivar inßuence. Two Þelds
received insecticide applications in Kendall Township
in 2003. Some Þelds were closer to woods or rivers than
others, but we did not use this information to select
Þelds nor did we analyze our data by using the infor-
mation.
We performed analyses of variance (PROC analysis
of variance [ANOVA], SAS Institute 1999) to test two
hypotheses. In each ANOVA, separate models were
generated for each combination of year, sampling
date, and county. By doing this, the Þelds of one
township at a speciÞc sampling date in one speciÞc
year were considered as a population for sampling.
We used Þeld as a class variable to test the Þrst null
hypothesis that the mean number of aphids per plant
in a Þeld is the same for all Þelds. For this analysis, we
used the original and transformed (natural logarithm
[x ⫹ 1]) data. We tested the data for skewness and
normality (ShapiroÐWilks test) by using PROC Uni-
variate (SAS Institute 1999). We used BartlettÕs test to
evaluate the homogeneity of the variances (Neter et
al. 1990). We compared the ANOVA with the graphs
Table 1. Summary of management information for soybean fields
Township/yr Planting date
a
Herbicide application
Mean no. Date
a
Kendall
2001 8 May (1Ð19 May) 1.08 19 June (7 JuneÐ12 July)
2002 17 May (11Ð27 May) 1.14 12 June (11 MayÐ9 July)
2003 16 May (5Ð23 May) 1.20 15 June (20 MayÐ2 July)
St. Joseph
2001 4 May (30 AprilÐ12 May) 1.00 10 June (24 MayÐ25 June)
2002 NA NA NA
2003 20 May (17Ð24 May) 1.33 13 June (19 MayÐ26 June)
a
Mean date and range. NA, not applicable.
February 2005 ONSTAD ET AL.: SAMPLING A. glycines 171

of 95% conÞdence interval (1.96 ⫻ SE) of the sample
mean of aphid density for each Þeld during each sam-
pling period.
We used soybean-row spacing as a class variable
(three levels: drilled, 0.30 Ð 0.46 m, and 0.61Ð 0.76 m) to
test the second null hypothesis that the mean number
of aphids per plant in a Þeld is the same for all three
types of row spacing. The original data were used in
this second ANOVA. We calculated the power of the
test for the second ANOVA for the effect of soybean-
row spacing in 2001 for Kendall Township. When
F-tests in ANOVA suggest rejecting the null hypoth-
esis, the power of tests is the chance to test that the
means of treatment levels are different (i.e., there is an
effect). Computation of the power was at 95% signif-
icance level and based on Neter et al. (1990).
Regression analysis (PROC REG, SAS Institute
1999) was used to Þt TaylorÕs power law, S
2
⫽ aM
b
(Southwood 1978, Ruesink 1980, Su et al. 1996) to the
data, where S is sample standard deviation and M is
sample mean number of aphids per Þeld. The natural
logarithm was used to transform the original variance
and mean number of aphids per plant in a Þeld. We
omitted all data when the Þeld mean or variance was
zero.
Regression analysis (PROC REG, SAS Institute
1999) also was used to investigate the relationship
between number of aphids per plant and the distance
from Þeld edge. The primary independent variable
was distance from the Þeld edge, including various
nonlinear (quadratic, cubic, reciprocal, and logarith-
mic) forms. Several dummy variables (year, county,
and observation time) also were considered in the
regressions. To eliminate the inßuence of the four
orders of magnitude in the range of numbers and the
inßuence of outliers on the regression analysis, we
normalized all densities by dividing the number of
aphids per plant for each plant (speciÞc distance) by
the total number of aphids in the given Þeld. Before
doing this, we added the densities at each distance for
the two transects in the Þeld.
We used PROC MODEL (SAS Institute 1999) to
estimate the parameter c in the following model: P ⫽
1 ⫺ exp(⫺cM), where P is the proportion of infested
plants in a Þeld (with at least one aphid per plant) and
M is the mean number of aphids per plant. In this case,
the mean aphid density and proportion of infested
plants are based on the entire 50-plant sample per
Þeld.
Results and Discussion
The sample means of aphid density and their 95%
conÞdence intervals are shown in Figs. 1Ð 6. Generally,
there was little synchrony of population dynamics
(increases or decreases) during the middle of the
summers. Densities in some Þelds continued to in-
crease, whereas others declined from the second to
third or fourth sampling date. We are preparing an-
other manuscript to address the population dynamics
and forecasting in greater detail (D.W.O., unpub-
lished data).
In the tests of normality and homogeneity, we fo-
cused on the Þrst two samples in 2002 in Kendall
Township. The Þrst sample could not be used for
Fig. 1. Mean number of aphids per plant with 95% con-
Þdence interval in each of 14 Þelds in St. Joseph Township,
Champaign County, IL, in 2001 for four sampling periods
(aÐd) separated by ⬇3 wk. The township means (SE) are 0.39
(0.33), 7.60 (2.81), 1.06 (0.12), and 1.95 (0.17) for the suc-
cessive sampling periods, respectively.
172 ENVIRONMENTAL ENTOMOLOGY Vol. 34, no. 1

BartlettÕs test because some Þelds have zeros. The
ShapiroÐWilk statistics for original and transformed
data from the Þrst sample are 0.057 and 0.146, respec-
tively. Their P values are both smaller than 0.0001. The
ShapiroÐWilk statistics for the second sample are 0.388
and 0.751 for original and transformed data, respec-
tively, but their P values are also both smaller than
0.0001. Hence, for both samples and both kinds of data,
normality can be rejected at 0.0001 (99.9999%) sig-
niÞcance level. For the second sample, the Bartlett test
rejects the hypothesis of homogeneity with P ⬍ 0.0001
for both original and transformed data, although cor-
responding
␹
2
values are, respectively, 835.9 and 111.3
for original and transformed data. For the Þrst sample,
the original and transformed data had skewness values
of 21 and 8, respectively; whereas for the second sam-
ple, they had values of 7 and 1. Thus, the transformed
data are more symmetric.
Table 2 contains the results of the ANOVA based on
transformed data for the inßuence of Þeld on mean
aphid density. The null hypothesis that all Þelds are
the same cannot be rejected in only two cases: the Þrst
two sampling periods in St. Joseph Township in 2003
have very low mean township densities. Analysis of
original data produced similar results, although with
higher P values and three more cases in which the null
hypothesis could not be rejected during the Þrst sam-
pling period. The conclusions from the statistical anal-
Fig. 2. Mean number of aphids per plant with 95% con-
Þdence interval in each of 14 Þelds in St. Joseph Township,
Champaign County, IL, in 2002 for the middle two sampling
periods (a and b) separated by ⬇3 wk. The township means
(SE) are 0 (0), 0.23 (0.14), and 0.33 (0.06) for the Þrst three
sampling periods, respectively.
Fig. 3. Mean number of aphids per plant with 95% con-
Þdence interval in each of 14 Þelds in St. Joseph Township,
Champaign County, IL, in 2003 for four sampling periods
(aÐd) separated by ⬇3 wk. The township means (SE) are 0
(0), 0.02 (0.01), 33.33 (1.31), and 1829 (71) for the successive
sampling periods, respectively.
February 2005 ONSTAD ET AL.: SAMPLING A. glycines 173

Fig. 4. Mean number of aphids per plant with 95% con-
Þdence interval in each of 14 Þelds in Kendall Township,
Kendall County, IL, in 2001 for four sampling periods (aÐd)
separated by ⬇3 wk. The township means (SE) are 1.57
(0.98), 16.45 (1.53), 19.82 (0.77), and 6.07 (0.30) for the
successive sampling periods, respectively.
Fig. 5. Mean number of aphids per plant with 95% con-
Þdence interval in each of 14 Þelds in Kendall Township,
Kendall County, IL, in 2002 for four sampling periods (aÐd)
separated by circa 3 wk. The township means (SE) are 0.19
(0.09), 5.09 (0.53), 34.37 (1.45), and 20.94 (1.01) for the
successive sampling periods, respectively.
174 ENVIRONMENTAL ENTOMOLOGY Vol. 34, no. 1

yses are consistent with a visual evaluation of the
conÞdence intervals in Figs. 1Ð6. Thus, multiple Þelds
must be sampled to accurately understand the infes-
tation levels in a township.
Table 3 contains the results for the ANOVA for the
inßuence of soybean-row spacing on mean aphid den-
sity. About half of the ANOVA results indicated that
there are no signiÞcant effects of row spacing in those
cases. This is particularly clear for St. Joseph Town-
ship. In St. Joseph Township, narrow rows were most
common, whereas the wide rows were rare (no Þelds
with wide rows in 2001; two Þelds in 2002). In Kendall
Township, ⬎50% of Þelds were planted by drilling,
whereas only one Þeld in all 3 yr was planted with
narrow rows. No pattern can be discerned from the
aphid densities and row spacings in the two cases of
signiÞcant effects for St. Joseph Township (Table 3).
For the last three sample dates for Kendall Township
in all years, drilled always had the highest mean den-
sity at the second and third dates, but the wide rows
(0.61Ð0.76-m widths) had the highest mean density at
the fourth date (Table 3). The ecological cause of this
pattern, if it is a true effect, is unclear.
We evaluated the power for some of the tests in
Table 3. For the Þrst sample of aphid density and row
spacing collected in 2001 at Kendall Township, the F
value and P value from the ANOVA do not allow us to
reject the null hypothesis at 95% signiÞcance level.
The power of this test is larger than 0.67, i.e., the
chance to conclude that the null hypothesis is true is
at least 0.67. In this sample, aphid density is very low,
but the power of its test is not low. For the next three
samples, the ANOVA rejects the null hypothesis at
95% signiÞcance level. The power of each of these
three tests is ⬎0.99. The chance to conclude that the
alternative hypothesis is true is very high.
Early in the season, the most important question
may be, How many Þelds should be sampled to Þnd the
Þrst invaders into soybean Þelds in a township? The
probability of Þnding an infested Þeld during the Þrst
or second sampling dates when mean density in the
township is less than two aphids per plant (Figs. 1Ð 6)
is 11% for Champaign County and 50% for Kendall
County. If we assume that the probability of observing
infested Þelds follows a binomial distribution, then the
probability of Þnding at least one infested Þeld equals
1 ⫺ (1 ⫺ q)
nf
, where q is the probability described
above and nf is the number of Þelds sampled by count-
ing aphids on 50 plants. With q ⫽ 0.11, sampling six and
14 Þelds will give 50 and 80% probabilities, respec-
tively, of Þnding at least one infested Þeld in a town-
ship. With q ⫽ 0.50, just two Þelds can be sampled to
have a 75% chance of Þnding at least one infested Þeld
in a township.
The two townships are ⬇170 km apart. Kendall
Township has at its northern edge a considerable
amount of wooded and pasture land as well as the city
of Yorkville and the Fox River corridor. In this part of
Illinois, the primary host, R. cathartica, is common
along roadsides, hedgerows, and woodlots, so ample
opportunity exists for successful overwintering by the
aphids and early season infestation of soybean Þelds.
Fig. 6. Mean number of aphids per plant with 95% con-
Þdence interval in each of 14 Þelds in Kendall Township,
Kendall County, IL, in 2003 for four sampling periods (aÐd)
separated by ⬇3 wk. The township means (SE) are 3.44
(0.39), 269 (11), 843 (41), and 20.92 (1.04) for the successive
sampling periods, respectively. The asterisk means the Þeld
was not sampled.
February 2005 ONSTAD ET AL.: SAMPLING A. glycines 175

Kendall Township also has signiÞcantly more relief (at
least for Illinois) than does St. Joseph Township in
Champaign County, which is mostly ßat. St. Joseph
Township has only limited wooded areas along a small
stream, and as far as we know, has no buckthorn.
Champaign-Urbana has buckthorn shrubs in the urban
landscape that are infested by A. glycines during the
fall (D.J.V. and D.W.O., unpublished data). We pre-
sume the colonization in this township is produced
primarily by winged aphids leaving other soybean
Þelds during the summer, not by spring migrants from
buckthorn. There is little difference in management
practices between these two counties (Table 1).
To determine whether the aphids were randomly
distributed or clumped, we Þt our data to TaylorÕs
power law,
S
2
⫽ 6.39911 ⫻ M
1.71779
[1]
where S and M are the standard deviation and mean
of the number of aphids per plant in each Þeld (n ⫽
232, r
2
⫽ 0.98). The coefÞcients 6.39911 and 1.71779
were signiÞcantly different from 0 and 1, respectively,
based on t-tests with the equation Þt with natural
logarithms (with both P ⬍ 0.0001). Hodgson et al.
(2004) report similar coefÞcients of 9.157 and 1.543 for
Minnesota Þelds. The value of the exponent is typical
of those for Þeld crop insects (Ruesink 1980) and
supports the previous observation of clumped spatial
distributions (Su et al. 1996).
For a desired level of precision, the required sample
size (n, number of soybean plants sampled per Þeld)
can be calculated by incorporating equation 1 into the
following equation (Su et al. 1996; Southwood 1978, p.
21).
n ⫽ 关S/共E ⫻ M兲兴
2
[2]
where S is standard deviation (aphids per plant), E is
the precision index (relative error), and M is the mean
number of aphids per plant. However, according to
Karandinos (1976) and Thompson (2002) (p. 38), the
reliability of the sampling should be increased by pro-
viding a 90% two-sided signiÞcance level,
n ⫽ Z
2
⫻ 关S/共 E ⫻ M兲兴
2
[3]
where Z(
␣
/2 ⫽ 0.05) ⫽ 1.64, instead of Z ⫽ 1in
equation 2. Figure 7 presents the sample sizes for both
values of Z and three precision levels (relative error ⫽
0.15, 0.20, and 0.25). Our results suggest that aphids
should be counted on 50 plants per Þeld to obtain a
reliable estimate of the population.
If there is no inßuence of distance from the Þeld
edge on the number or proportion of aphids sampled,
then we expect the slope of the regression line to be
zero or not signiÞcantly different from zero. When
distance from the Þeld edge was the only independent
variable in a model, regression analysis showed no
relationship between aphid density and distance. In
this case, the slope equals ⫺2.5 ⫻ 10
⫺05
with t ⫽⫺0.88,
indicating no signiÞcant difference from zero (n ⫽
5,824; r
2
⫽ 0.0001; P ⫽ 0.38). When we added other
nonlinear forms of the basic distance variable to the
model, the results were the same. When dummy vari-
ables were included, regression analysis had a little
higher but still very small r
2
, but the slope and its statistics
Table 2. Analysis of variance for the influence of field on the mean no. aphids per plant in a field by township, year, and sample date
based on transformed (ln 关X ⴙ 1兴) data
Sampling date First date Second date Third date Fourth date
Township Yr FP F P F P F P
St. Joseph 2001 6.01 ⬍0.0001 68.22 ⬍0.0001 14.75 ⬍0.0001 10.07 ⬍0.0001
2002
aa
5.01 ⬍0.0001 9.50 ⬍0.0001 No data No data
2003 1 0.4493 0.87 0.5797 26.74 ⬍0.0001 93.53 ⬍0.0001
Kendall 2001 5.01 0.0001 39.15 ⬍0.0001 19.70 ⬍0.0001 24.47 ⬍0.0001
2002 2.48 0.0026 24.92 ⬍0.0001 60.65 ⬍0.0001 33.08 ⬍0.0001
2003 8.29 ⬍0.0001 29.59 ⬍0.0001 262.34 ⬍0.0001 64.29 ⬍0.0001
Except for the tests of the last two dates in 2003 at Kendall, all Þrst and second degrees of freedom (df) are the same: 13 (Þrst) and 686
(second). The df are (12, 637) for third date and (9, 490) for fourth date in 2003 at Kendall.
a
Both mean and variance are zeros so there is no F statistic.
Table 3. Analysis of variance for the influence of row spacing on the mean no. aphids per plant in a soybean field by township, year,
and sample date
Sampling date First date Second date Third date Fourth date
Township Yr F df2
a
PFdf2 PFdf2 PFdf2 P
St. Joseph 2001 0.63 648 0.4285 2.09 648 0.1491 1.76 648 0.1856 6.14 648 0.0135
2002
bb b
0.68 648 0.5062 5.11 648 0.0062 No data
2003
bb b bb b
1.57 348 0.2103 0.73 348 0.3944
Kendall 2001 0.92 697 0.3998 12.58 697 ⬍0.0001 19.75 697 ⬍0.0001 21.56 697 ⬍0.0001
2002 0.95 648 0.3290 15.42 648 ⬍0.0001 85.63 648 ⬍0.0001 96.88 648 ⬍0.0001
2003 0.76 698 0.3841 8.63 698 0.0034 16.04 648 ⬍0.0001 19.71 498 ⬍0.0001
a
All Þrst degrees of freedom are 1 except for the values of 2 for Kendall 2001.
b
Both mean and variance are zeros so there is no F statistic. In St. Joseph Township in 2003, there are only data for row spacing for Þelds
8Ð14.
176 ENVIRONMENTAL ENTOMOLOGY Vol. 34, no. 1

remained the same. This means that farmers and inte-
grated pest management scouts should be able to sample
anywhere within 50 m of a soybean Þeld edge near a road
and obtain representative data. Future work may focus
on distances farther from the edge, but few people are
likely to sample farther from the road, especially after the
canopy closes in midsummer.
Can management plans be based on counting in-
fested plants in a Þeld rather than on counting aphids?
The relationship between the proportion of infested
plants in a Þeld, P, and the mean number of aphids per
plant, M, is
P ⫽ 1⫺exp 共⫺0.195764 M兲 [4]
With the coefÞcient signiÞcantly different from
zero (n ⫽ 320, t ⫽ 27.13, r
2
⫽ 0.93, P ⬍ 0.0001). For
mean densities exceeding 24 aphids per plant in a Þeld,
the proportion of infested plants exceeds 0.99. Because
24 aphids per plant is lower than all currently proposed
economic thresholds by an order of magnitude, inci-
dence of infestation (proportion of plants infested)
cannot be used for managing the pest. But see Hodg-
son et al. (2004) for a different analysis with tally
thresholds above 1.
Future work on economic thresholds will allow us
to specify the appropriate constant sample size or
produce a sequential sampling plan. If the mean Þeld
densities of concern are primarily between 250 and
500 aphids per plant, then Fig. 7 indicates that 50
whole plants should be sampled to obtain an estimate
of aphid density with relative error not larger than 0.25
at a 90% signiÞcant level. However, much time and
physical effort are needed to sample this many plants
when population densities are high and when the
soybean canopy is closed. For example, each person
required 1 min per plant when soybean plants were
small and infestations were light. But later in the sum-
mer, sampling a single plant required 4 Ð5 min per
plant or 90Ð120 min per Þeld for two people. Su et al.
(1996) found that 50 Ð100 trifoliate leaves were
enough to provide a reasonably precise estimate of the
mean number of aphids per leaf (at 68% signiÞcance
level). Perhaps multinomial classiÞcation using abun-
dance classes can be evaluated in the future.
Acknowledgments
We thank G. Bretthauer, H. R. Wells, R. Estes, R. Barrido, and
others for sampling the Þelds or facilitating interactions with
growers. We thank Professors Adam Martinsek and George
Gertner for statistical advice. We thank Bill Ruesink for review-
ing the manuscript and Dave Crowder and Charles Guse for the
Þgures. This work was supported by the Illinois Soybean Pro-
gram Operating Board and the State of Illinois through the
Illinois Council for Food and Agricultural Research.
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Fig. 7. Sample sizes (n, soybean plants per Þeld) based
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⫻ [S/(E ⫻ M)]
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February 2005 ONSTAD ET AL.: SAMPLING A. glycines 177