Three simple linear regression equations were developed to estimate the numbers of eggs in jack pine budworm, Choristoneura pinus pinus, egg masses in Michigan. One equation was developed for each of 2-row, 2-row +, and 3-row egg masses. A table of estimated numbers of eggs per egg mass is given for each of the three row types for egg mass lengths from 1 to 25 nun

Fowler, Gary W

Simmons, Gary A

English

Valparaiso University

The Great Lakes Entomologist Volume 20 Number 3 - Fall 1987 Number 3 - Fall 1987 Article 9 October 1987 Regression Equations and Table for Estimating Numbers of Eggs in Jack Pine Budworm (Lepidoptera: Tortricidae) Egg Masses in Michigan Gary W. Fowler University of Michigan Gary A. Simmons Michigan State University Follow this and additional works at: https://scholar.valpo.edu/tgle  Part of the Entomology Commons Recommended Citation Fowler, Gary W. and Simmons, Gary A. 1987. "Regression Equations and Table for Estimating Numbers of Eggs in Jack Pine Budworm (Lepidoptera: Tortricidae) Egg Masses in Michigan," The Great Lakes Entomologist, vol 20 (3) Available at: https://scholar.valpo.edu/tgle/vol20/iss3/9 This Peer-Review Article is brought to you for free and open access by the Department of Biology at ValpoScholar. It has been accepted for inclusion in The Great Lakes Entomologist by an authorized administrator of ValpoScholar. For more information, please contact a ValpoScholar staff member at scholar@valpo.edu. 1987 THE GREAT LAKES ENTOMOLOGIST 157 REGRESSION EQUATIONS AND TABLE FOR ESTIMATING NUMBERS OF EGGS IN JACK PINE BUDWORM (LEPIDOPTERA: TORTRICIDAE) EGG MASSES IN MICHIGAN} Gary w. Fowler2 and Gary A. Sinunons3 ABSTRACT Three simple linear regression equations were developed to estimate the numbers of eggs in jack pine budworm, Ch ristoneura pinus pinus, egg masses in Michigan. One equation was developed for each of 2-row, 2-row +, and 3-row egg masses. A table of estimated numbers of eggs per egg mass is given for each of the three row types for egg mass lengths from 1 to 25 nun. Numbers of eggs in jack pine bud worm, Choristoneura pinus pinus Freeman, egg masses yield useful information for population dynamics studies and general survey assessments (Morris 1955). The objective of this paper is to present prediction models for numbers of eggs in jack pine budworm egg masses in Michigan. These prediction models are the first ones developed for jack pine. METHODS AND MATERIALS The data used to evelop the prediction models were obtained from samples collected from five jack pine, Pinus banksiana Lambert, stands in Michigan's Lower Peninsula from 1981 to 1984, providing egg masses from a range of population densities from sparse to high. The pooled data set included 657 egg masses. Egg-mass length was measured to the nearest 0.1 nun with a microscope ocular micrometer. Only current-year, nonparasitized egg masses with clearly distinguishable chorions were included in the data set (Jennings and Addy 1968). Numbers of egg rows and numbers of eggs were counted and recorded. Egg masses either had 2 rows, 2 rows + (two rows with a partial third row), or 3 rows (Leonard et al. 1973). The significance of each regression equation was tested using the F-test (Neter et al. 1985). The analysis of covariance F-test was used to test equality among regression equations (Snedecor and Cochran 1968). Skewness and kurtosis coefficients and correlations between absolute error terms and egg mass lengths showed no serious departures from the assumptions of normality and homogeneity, respectively, for all hypothesis tests (Neter et al. 1985, Snedecor and Cochran 1968). Results of all hypothesis tests were considered significant i  the significance probability P < 0.05. 'Michigan Agricultural Experimental Station Iournal Article No. 12,225. 2School of Natural Resources, The University of Michigan, Ann Arbor, MI 48109-1115. 30epartment of Entomology, Michigan State University, East Lansing, MI 48824-1115. 1Fowler and Simmons: Regression Equations and Table for Estimating Numbers of Eggs inPublished by ValpoScholar, 1987158 THE GREAT LAKES ENTOMOLOGIST Vol. 20, No.3 RESULTS For the pooled data set, plots of numbers of eggs in an egg mass versus egg mass length for each row type indicated positive linear relationships. One simple linear regression was developed for each row type. All prediction models were highly significant (F, P < 0.001). The three row-type regressions were significantly different from each other (F, P < 0.001). Table 1 shows the estimated numbers of eggs per egg mass for various egg mass lengths for the three row types. The prediction models for each row type are also shown along with sample sizes (n), standard errors of the estimate (svx) and coefficients of determination (?). . Table 1. The estimated number of eggs per egg mass for various egg mass lengths for the three row types in Michigan, and the prediction models for each row type. Length Row Type (mm) 2-Rowa 3-Row' 1.0 1.23 6.81 1.5 3.38 9.09 2.0 1.93 5.52 11.38 2.5 4.03 7.66 13.66 3.0 6.13 9.80 15.94 3.5 8.23 11.95 18.23 4 0 10.33 14.09 20.51 4.5 12.43 16.23 22.79 5.0 14.53 18.38 25.08 5.5 16.63 20.52 27.36 6.0 18.73 22.66 29.64 6.5 20.83 24.80 31.93 7.0 22.93 26.95 34.21 7.5 25.03 29.09 36.49 8.0 27.13 31.23 38.78 8.5 29.23 33.37 41.06 9.0 31.33 35.52 43.34 9.5 33.43 37.66 45.63 10.0 35.54 39.80 47.91 10.5 37.64 41.95 50.19 11.0 39.74 44.09 52.48 11.5 41.84 46.23 54.76 12.0 43.94 48.37 57.04 12.5 46.04 50.52 59.33 13.0 48.14 52.66 61.61 13.5 50.24 54.80 63.89 14.0 52.34 56.94 66.18 14.5 54.44 55.09 68.46 15.0 56.54 61.23 70.74 15.5 58.64 63.37 73.03 16.0 60.74 65.51 75.31 16.5 62.84 67.66 77.59 17.0 64.94 69.80 79.88 17.5 67.04 71.94 82.16 18.0 69.15 74.09 84.44 18.5 71.25 76.23 86.73 2The Great Lakes Entomologist, Vol. 20, No. 3 [1987], Art. 9https://scholar.valpo.edu/tgle/vol20/iss3/91987 THE GREAT LAKES ENTOMOLOGIST 159 Table 1. (continued) Row Type Length (mm) 2-Rowa 2-Row+ b 3-RowC 19.0 73.35 19.5 75.45 20.0 77.55 20.5 79.65 21.0 81.75 21.5 83.85 22.0 85.95 22.5 88.05 23.0 90.15 23.5 92.25 24.0 94.35 24.5 96.45 25.0 98.55 78.37 80.51 82.66 84.80 86.94 89.08 91.23 93.37 95.51 97.66 99.80 101.94 104.08 89.01 91.29 93.58 95.86 98.14 100.43 102.71 104.99 107.28 109.56 111.84 114.13 116.41 aYi = -6.4771 + 4.2012 Xi, n = 230, Sy. x = 6.6842, r = 0.843 bYi = -3.0518 + 4.2854 Xi, n = 203, Sy.x = 7.4899, r = 0.790 cYi = 2.2450 + 4.5665 Xi, n = 224, Sy.x = 8.0727, r = 0.819 The average numbers of eggs per egg mass were 38.4, 49.7, and 59.4 for 2-row, 2-row +, and 3-row egg masses, respectively. The average length of egg masses was 10.7, 12.3, and 12.5 mm for 2-row, 2-row +, and 3-row egg masses, respectively. The range of length of egg masses was 2.0--22.5, 4.5-22.5, and 5.5-24.0 mm for 2-row, 2-row +, and 3-row egg masses, respectively. CONCLUDING REMARKS These prediction models should be adequate for most applications. However, it should be noted that the relationship between numbers of eggs in an egg mass and egg mass length will vary from stand to stand, over time, and with stage of infestation. ACKNOWLEDGMENTS Our thanks to Dr. John A. Witter, The University of Michigan, Ann Arbor, MI and Mr. Bruce A. Montgomery, Michigan State University, East Lansing, MI for their critical review. Thanks are also extended to Ray Drapek, James Laramie, and Steve Kvamberg for their assistance in the field and laboratory and to members f our field crews for their assistance: J. Cook, D. Huff, J Kowaleski, J. Kuiper, D. Lekas, L. Sloan, L. Stoeffler, C. Stout, and B. Tarabu1a. The work was supported by the School of Natural Resources, The University of Michigan; Department of Entomology, Michigan State University; and the McIntire-Stennis Cooperative Forestry Research Program. LITERATURE CITED Jennings, D. T., and N. D. Addy. 1968. A staining technique for jack pine budworm egg masses. J. Econ. Entomol. 61:1766. 3Fowler and Simmons: Regression Equations and Table for Estimating Numbers of Eggs inPublished by ValpoScholar, 1987160 THE GREAT LAKES ENTOMOLOGIST Vol. 20, No.3 Leonard, D, E., G. A. Simmons, and G, K. Van Derwerker. 1973, Spruce budwonn: techniques to improve counting of eggs. J, Econ. EntomoL 66:992. Morris, R. F. 1955. The development of sampling techniques for forest insect defoliators with particular reference to the spruce budwonn. Canadian J. Zoo!. 33:226-294, Neier, J., W. Wasserman, and M, H, Kutner. 1985, Applied linear statistical models, Richard D. Irwin, I c" Homewood, lL. Snedecor, G. W" and W. G. Cochran, 1968. Statistical methods, The Iowa State Vnlv, Press, Ames. 4The Great Lakes Entomologist, Vol. 20, No. 3 [1987], Art. 9https://scholar.valpo.edu/tgle/vol20/iss3/9

Regression Equations and Table for Estimating Numbers of Eggs in Jack Pine Budworm (Lepidoptera: Tortricidae) Egg Masses in Michigan

ValpoScholar

The Great Lakes Entomologist 
Volume 20 
Number 3 - Fall 1987 Number 3 - Fall 1987 Article 9 
October 1987 
Regression Equations and Table for Estimating Numbers of Eggs 
in Jack Pine Budworm (Lepidoptera: Tortricidae) Egg Masses in 
Michigan 
Gary W. Fowler 
University of Michigan 
Gary A. Simmons 
Michigan State University 
Follow this and additional works at: https://scholar.valpo.edu/tgle 
 Part of the Entomology Commons 
Recommended Citation 
Fowler, Gary W. and Simmons, Gary A. 1987. "Regression Equations and Table for Estimating Numbers of 
Eggs in Jack Pine Budworm (Lepidoptera: Tortricidae) Egg Masses in Michigan," The Great Lakes 
Entomologist, vol 20 (3) 
Available at: https://scholar.valpo.edu/tgle/vol20/iss3/9 
This Peer-Review Article is brought to you for free and open access by the Department of Biology at ValpoScholar. 
It has been accepted for inclusion in The Great Lakes Entomologist by an authorized administrator of ValpoScholar. 
For more information, please contact a ValpoScholar staff member at scholar@valpo.edu. 
1987 THE GREAT LAKES ENTOMOLOGIST 157 
REGRESSION EQUATIONS AND TABLE FOR ESTIMATING 

NUMBERS OF EGGS IN JACK PINE BUDWORM (LEPIDOPTERA: 

TORTRICIDAE) EGG MASSES IN MICHIGAN} 

Gary w. Fowler2 and Gary A. Sinunons3 
ABSTRACT 
Three simple linear regression equations were developed to estimate the numbers of 
eggs in jack pine budworm, Ch ristoneura pinus pinus, egg masses in Michigan. One 
equation was developed for each of 2-row, 2-row +, and 3-row egg masses. A table of 
estimated numbers of eggs per egg mass is given for each of the three row types for egg 
mass lengths from 1 to 25 nun. 
Numbers of eggs in jack pine bud worm, Choristoneura pinus pinus Freeman, egg 
masses yield useful information for population dynamics studies and general survey 
assessments (Morris 1955). The objective of this paper is to present prediction models for 
numbers of eggs in jack pine budworm egg masses in Michigan. These prediction models 
are the first ones developed for jack pine. 
METHODS AND MATERIALS 
The data used to evelop the prediction models were obtained from samples collected 
from five jack pine, Pinus banksiana Lambert, stands in Michigan's Lower Peninsula 
from 1981 to 1984, providing egg masses from a range of population densities from sparse 
to high. The pooled data set included 657 egg masses. 
Egg-mass length was measured to the nearest 0.1 nun with a microscope ocular 
micrometer. Only current-year, nonparasitized egg masses with clearly distinguishable 
chorions were included in the data set (Jennings and Addy 1968). Numbers of egg rows 
and numbers of eggs were counted and recorded. Egg masses either had 2 rows, 2 rows 
+ (two rows with a partial third row), or 3 rows (Leonard et al. 1973). 
The significance of each regression equation was tested using the F-test (Neter et al. 
1985). The analysis of covariance F-test was used to test equality among regression 
equations (Snedecor and Cochran 1968). Skewness and kurtosis coefficients and 
correlations between absolute error terms and egg mass lengths showed no serious 
departures from the assumptions of normality and homogeneity, respectively, for all 
hypothesis tests (Neter et al. 1985, Snedecor and Cochran 1968). Results of all hypothesis 
tests were considered significant i  the significance probability P < 0.05. 
'Michigan Agricultural Experimental Station Iournal Article No. 12,225. 

2S
chool 
of Natural Resources, The University of Michigan, Ann Arbor, MI 48109-1115. 

30epartment of Entomology, Michigan State University, East Lansing, MI 48824-1115. 

1
Fowler and Simmons: Regression Equations and Table for Estimating Numbers of Eggs in
Published by ValpoScholar, 1987
158 THE GREAT LAKES ENTOMOLOGIST Vol. 20, No.3 
RESULTS 
For the pooled data set, plots of numbers of eggs in an egg mass versus egg mass length 
for each row type indicated positive linear relationships. One simple linear regression was 
developed for each row type. All prediction models were highly significant (F, 
P < 0.001). The three row-type regressions were significantly different from each other 
(F, P < 0.001). 
Table 1 shows the estimated numbers of eggs per egg mass for various egg mass lengths 
for the three row types. The prediction models for each row type are also shown along 
with sample sizes (n), standard errors of the estimate (svx) and coefficients of 
determination (?). . 
Table 1. The estimated number of eggs per egg mass for various egg mass lengths for the three row 
types in Michigan, and the prediction models for each row type. 
Length 
Row Type 
(mm) 2-Rowa 3-Row' 
1.0 1.23 6.81 
1.5 3.38 9.09 
2.0 
1.93 5.52 11.38 
2.5 4.03 7.66 13.66 
3.0 6.13 9.80 15.94 
3.5 8.23 11.95 18.23 4 0 
10.33 14.09 20.51 
4.5 12.43 16.23 22.79 
5.0 14.53 18.38 25.08 
5.5 16.63 20.52 27.36 6.0 
18.73 22.66 29.64 
6.5 20.83 24.80 31.93 7.0 
22.93 26.95 34.21 
7.5 25.03 29.09 36.49 
8.0 27.13 31.23 38.78 
8.5 29.23 33.37 41.06 9.0 
31.33 35.52 43.34 
9.5 33.43 37.66 45.63 10.0 35.54 39.80 47.91 
10.5 37.64 41.95 50.19 
11.0 39.74 44.09 52.48 
11.5 41.84 46.23 54.76 
12.0 43.94 48.37 57.04 
12.5 46.04 50.52 59.33 
13.0 48.14 52.66 61.61 
13.5 50.24 54.80 63.89 
14.0 52.34 56.94 66.18 
14.5 54.44 55.09 68.46 
15.0 56.54 61.23 70.74 
15.5 58.64 63.37 73.03 
16.0 60.74 65.51 75.31 
16.5 62.84 67.66 77.59 
17.0 64.94 69.80 79.88 
17.5 67.04 71.94 82.16 
18.0 69.15 74.09 84.44 
18.5 71.25 76.23 86.73 
2
The Great Lakes Entomologist, Vol. 20, No. 3 [1987], Art. 9
https://scholar.valpo.edu/tgle/vol20/iss3/9
1987 THE GREAT LAKES ENTOMOLOGIST 159 
Table 1. (continued) 
Row Type 
Length 
(mm) 2-Rowa 2-Row+ b 3-RowC 
19.0 73.35 
19.5 75.45 
20.0 77.55 
20.5 79.65 
21.0 81.75 
21.5 83.85 
22.0 85.95 
22.5 88.05 
23.0 90.15 
23.5 92.25 
24.0 94.35 
24.5 96.45 
25.0 98.55 
78.37 
80.51 
82.66 
84.80 
86.94 
89.08 
91.23 
93.37 
95.51 
97.66 
99.80 
101.94 
104.08 
89.01 
91.29 
93.58 
95.86 
98.14 
100.43 
102.71 
104.99 
107.28 
109.56 
111.84 
114.13 
116.41 
aYi = -6.4771 + 4.2012 Xi, n = 230, Sy. x = 6.6842, r = 0.843 
bYi = -3.0518 + 4.2854 Xi, n = 203, Sy.x = 7.4899, r = 0.790 
cYi = 2.2450 + 4.5665 Xi, n = 224, Sy.x = 8.0727, r = 0.819 
The average numbers of eggs per egg mass were 38.4, 49.7, and 59.4 for 2-row, 2-row 
+, and 3-row egg masses, respectively. The average length of egg masses was 10.7, 
12.3, and 12.5 mm for 2-row, 2-row +, and 3-row egg masses, respectively. The range 
of 
length 
of egg masses was 2.0--22.5, 4.5-22.5, and 5.5-24.0 mm for 2-row, 2-row +, 
and 3-row egg masses, respectively. 
CONCLUDING REMARKS 
These prediction models should be adequate for most applications. However, it should 
be noted that the relationship between numbers of eggs in an egg mass and egg mass 
length will vary from stand to stand, over time, and with stage of infestation. 
ACKNOWLEDGMENTS 
Our thanks to Dr. John A. Witter, The University of Michigan, Ann Arbor, MI and Mr. 
Bruce A. Montgomery, Michigan State University, East Lansing, MI for their critical 
review. Thanks are also extended to Ray Drapek, James Laramie, and Steve Kvamberg 
for their assistance in the field and laboratory and to members f our field crews for their 
assistance: J. Cook, D. Huff, J Kowaleski, J. Kuiper, D. Lekas, L. Sloan, L. Stoeffler, 
C. Stout, and B. Tarabu1a. The work was supported by the School of Natural Resources, 
The University of Michigan; Department of Entomology, Michigan State University; and 
the McIntire-Stennis Cooperative Forestry Research Program. 
LITERATURE CITED 
Jennings, D. T., and N. D. Addy. 1968. A staining technique for jack pine budworm egg masses. 
J. Econ. Entomol. 61:1766. 
3
Fowler and Simmons: Regression Equations and Table for Estimating Numbers of Eggs in
Published by ValpoScholar, 1987
160 THE GREAT LAKES ENTOMOLOGIST Vol. 20, No.3 
Leonard, D, E., G. A. Simmons, and G, K. Van Derwerker. 1973, Spruce budwonn: techniques to 
improve counting of eggs. J, Econ. EntomoL 66:992. 
Morris, R. F. 1955. The development of sampling techniques for forest insect defoliators with 
particular reference to the spruce budwonn. Canadian J. Zoo!. 33:226-294, 
Neier, J., W. Wasserman, and M, H, Kutner. 1985, Applied linear statistical models, Richard D. 
Irwin, I c" Homewood, lL. 
Snedecor, G. W" and W. G. Cochran, 1968. Statistical methods, The Iowa State Vnlv, Press, 
Ames. 
4
The Great Lakes Entomologist, Vol. 20, No. 3 [1987], Art. 9
https://scholar.valpo.edu/tgle/vol20/iss3/9


https://scholar.valpo.edu/cgi/viewcontent.cgi?article=1615&context=tgle

Regression Equations and Table for Estimating Numbers of Eggs in Jack Pine Budworm (Lepidoptera: Tortricidae) Egg Masses in Michigan

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