STUDIES ON THE CLOVER ROOT BORER,
HYMSTINUS OBSCURUS (KARSHAM)
DISSERTATION
Presented in Partial FuliiIlment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University
By
KENNETH PAUL FRUESS, B.S., M.S.
The Ohio State University 1957
Approved by:
Adviser Department of Zoology and Entomology ACKSQttffiCMST^TS
?he research for this dissertation was done a t the Ohio
Agricultural Experiment Station, W o o s t e r , Ohio, w h e r e I was employed as a Research Assistant from June, 1 9 5 ^ j to March, 1957. I am grateful for the facilities offered t > y this instituition and for the aid of .many members of the stafr d u r i n g my s t a y there.
I wish especially to thank Dr, C » -ft. Weaver, wino encouraged this research and offered many h e l p f u H suggestions and criticisms.
I also wish to thank Dr, Ralph H . Davidson, w h o acted as n y adviser at The Ohio State University a n d directed m y work there.
Valuable information was supplied t y the f ol lowing persons a m is gratefully acknowledged: Mr. A, Dickason, Oregon State
College; Dr, Ray T, Everly, Purdue University,* Dr. G-eorge G.
Gyrisco and Mr, Carlton S, Koehler, C o r n e l l University; and Dr,
A. K. Woodside, Virginia Agricultural Experiment Sts/tion.
ii TABLE OF CON TENTS
Page
INTRODUCTION ...... 1
PART I. THE CLOVER ROOT BORER ...... 2
Taxonomic Position ...... 2
Distribution...... 3
Spread in Ohio ...... 6
Economic Importance ...... 7
BIOLOGY AND ECOLOGY...... 13
Introduction ...... 13
The A d u l t ...... 13
Fall Behavior...... IS
Early Spring Behavior ...... * 16
Flight ...... 17
Traps for Determining Flight ...... 1?
Sexual Development ...... 19
Relation of Temperature toFlight ...... 20
A Temperature Summation Method of Predicting F l i g h t ...... 21
Mating ...... 2$
Sex Ra t i o ...... 26
Secondary Sexual Characteristics 27
Flight Range ...... 28
exposition ...... 28
Reproductive Potential...... 29
iii Page
Longevity ...... 30
Natural-Snemi.es ...... 31 Effect of Moisture on Adults ... 32
Effect of Host Condition on Ovipositaon ... 34
The Egg ...... 36
Description ...... 36
Incubation Period ...... 36
Natural Enemies ...... 37
The L a r v a ...... 37
Description...... 37
Rate of Development...... 33
Effect of Plant Condition on Development .... 39
Number of Instars ...... 1*0
Rearing Methods...... 4l
Natural Enemies...... bh
The Pupa ...... itU
Description...... 144-
Rate of Development...... 45
Natural Enemies...... 46
SEASONAL HISTORY...... 46
NUMBER OF GENERATIONS...... $0
HOST PLANTS...... 51
VARIETAL RESISTANCE OF CLOVER TO ROOT BORER ...... 54
iv Page
DAMAGE ...... 57
Effect of Moisture on Damage ...... 58
ESTIMATION OF YIELD REDUCTION ...... 6U
CONTROL ...... 71
Introduction ...... 71
Control Experiments ...... 73
Residual Action of Soil Insecticides ...... 76
PART H. EVALUATION OF CLOVER ROOT BORER POPULATIONS 78
INTRODUCTION...... 78
DISTRIBUTION OF ROOT BORER COUNTS...... 79
Distribution of Individual Root Counts...... 79
Introduction ...... 79
Negative Binomial Distribution...... 80
Neyssan’s Contagious Distributions ...... 83
Fitting Neyman1 s Distribution ...... 83
Fitting Neyman1 s Distribution for n ■ 0 ..... 85
Fitting Neyman's Distribution for n^ co .... 87
Double Poisson...... 87
SuEssary of Frequency Distributions ... 89
Distribution of Sample Mean.s ...... 90
Five Root Samples ..... 91
Ten Root Samples .... 91
Conclusion...... 91
v Page
TRANSFORMATIONS...... 92
Introduction...... *...... 92
Transforming Individual RootCounts ...... 9U
Estimation of q ...... 102
Transformation of Multiple RootCounts ...... 102
Conclusion 10 8
VALUE OF TRANSFORMATIONS...... 108
Effect on Additivity ...... Ill
Homogeneity of Variance ...... 116
Application of Inverse Hyperbolic Sine Transforma tion ...... 117
Other Tests ...... 120
t - t e s t ...... 121
EFFICIENCY OF TRANSFORMATION...... 123
EFFICIENCY OF SAMPLING DESIGNS ...... 128
1955 Sampling Experiment...... 128
1956 Sampling Study ...... 131
SEQUENTIAL SAMPLING FOR CLOVER ROOT BORER SURVEYS 135
Introduction ..... 135
Homogeneity of k ...... lUo
Calculation of Acceptance and RejectionLines .... i M
Application of Sequential P l a n ...... 151
ESTIMATING BORERS PER ROOT FROM PER CENT INFESTED ROOTS 152
SUMMARY AND CONCLUSIONS...... 15U
Part I ...... 1
vi Page
Part II ...... l£6
APPENDIX A. MATHEMATICAL DISTRIBUTION OP CLOVER ROOT BORER COUNTS...... 158
LITERATURE CITH)...... 172
vii LIST OF TABLES
Number Page
1 Direction of flight of root borers ...... ,. 18
2 Effectiveness of vertical vs. horizontal traps ... 20
3 Comparison of methods for predicting spring flight 23
h Sex ratio ...... 26
5 Estimation of offspring per f e male ...... 31
6 Effect of rainfall on borer populations .... 3b
7 Populations and development in early vs. late cut fields ...... 35
8 Number and development in dead vs. living roots .. 1*0
9 Composition of artificial medium ...... k3
10 Seasonal development of borer, 195U-1956...... JU7
11 Extreme dates for various stages in life history . 50
12 Host plants for root borer ...... 53
13 Borer populations in five varieties of red clover . 55
lb Summary of 1956 variety trial at Wooster ..... 56
15 Clover yields under different levels of rainfall and root borers ...... 60
16 ---- . .Analysis of variance for Table 15 ...... 6l
17 Clover yields under different levels of rainfall and root borers, 1956 ...... 62
18 Analysis of variance for Table 17 ...... 63
19 Summary of yield reductions by root borer under different levels of rainfall...... 63
viii Number Page
20 Test for curvilinear! ty of regression of weight on crown diameter...... 60
21 Cojsputation of correlation coefficients among four measurements on red clover p lants.... 6?
22 Calculation of Gauss multipliers for data in Table 21 ...... 65
23 Test of significance of four variable regression . 69
2k Summary of yield reductions by root borer in three fields ...... 71
20 Root borer control by surface applications of al- drin at time of band seeding ...... 7li
26 Control of root borer by granules ...... 76
27 Borers in plots treated in 1902 ...... 77
28 Method of fitting negative binomial...... 82
29 Calculation of recurrent coefficients for Neyman's distribution ...... 85
30 Summary of frequency distributions fitted to Vir ginia counts. Treated plots, experiment 1. 190k ...... 86
31 Distribution of borers in 0 root samples ...... 92
32 Distribution of borers in 10 root samples 93
33 Values of inverse hyperbolic sine transformation . 99
3U Test for non-additivity, 1905 moisture experiment, untransformed ...... 112
30 Test for non-additivity, 1900 moisture experiment, transformed ...... 113
36 Test for non-additivity, 1906 moisture experiment, untransformed ...... 113
37. Test for non-additivity, 1906 moisture experiment, transformed ...... U u
ix Humber Page
38 Test for non-additivity, Frye 909 experiment 1, untransformed ...... Ill*
39 Test for non-additivity, Frye 909 experiment 1, transformed ...... XI5
UO Test for non-additivity, Frye 909 experiment 2, untransformed...... 115
ill Test for non-additivity, Frye 909 experiment 2, transformed ...... 115
1x2 Test for homogeneity cf variance, 19$$ moisture experiment, untransformed ...... 116
U3 Comparison of homogeneity of variance for trans formed and untransformed data ...... 117
hh Test for non-additivity, 19$$ moisture experiment, individual roots transformed ...... 118
hS Test for non-additivity, 1956 moisture experiment, individual roots transformed...... 119
U6 Test for non-additivity, Frye 909 experiment 1, individual roots transformed ...... 119
U? Test for non-additivity, Frye 909 experiment 2, individual roots transformed ...... 120
US Analysis of aldrin band application test, un transformed ...... 121
ii9 Analysis of aldrin band application test, trans formed ...... 121
50 Analysis of Grafton test, transformed ...... 122
51 Comparison of t values for untransformed vs. transformed counts ...... 122
>2 Jhimber of one root samples to discover specific differences, untransformed ...... 12i|
53 Number of one root samples to discover specific differences, transformed ...... 125
x Number Page
5U Number of 10 root samples to discover specific differences, untransformed ...... 126
55 Number of 10 root samples to discover specific differences, transformed ...... 126
56 Analysis of 1955 sampling s t u d y ...... 129
57 Relative efficiencies of sampling designs based on 1955 study ...... 130
58 Relative efficiencies of sampling designs based on modification of 1955 data...... 131
5? Analysis of 1956 sampling s t u d y ...... 132
60 Analysis of modified 1956 sampling study ...... 133
61 Relative efficiencies of sampling designs based on 1956 study...... 13U
62 Relative efficiencies of sampling designs based an modification of 1956 data ...... 13U
63 Summary of 195U root borer populations ...... 137
6U Calculation of constants for separating infesta tion classes ...... 139
65 Test for homogeneity of k ...... 1U2
66 Calculation of operating characteristic curve and average sanqfLe number curve ...... 1)48
67 Sequential sampling table for separating infesta tion classes ..... i5o
68 Distribution of borers in fields having a mean of 0 to 1 borers per root, Ohio survey...... 158
69 Distribution of borers in fields having a mean of 1 to 1^ borers per root, Ohio survey .... 159
70 Distribution of borers in fields having a mean of 1^ to 2 borers per root, Ohio survey ..... 159 71 Distribution of borers in fields having a mean of 2 to 2-| borers per root, Ohio survey ...... 160
xi Number Page
72 Distribution of borers in fields having a mean of to 3 borers per root, Ohio survey ...... 160
73 Distribution of borers in fields having a mean of 3 to borers per root, Ohio.survey...... l6l
7ii Distribution of borers in Indiana airplane test .. l6l
75 Distribution of borers in fields having a mean of U to 5 borers per root, Ohio survey...... 162
76 Distribution of borers in 1955 tests in Indiana .. 162
77 Distribution of borers in fields having a mean of 5 to 6 borers per root, Ohio survey ...... 163
78 Distribution of borers in 195k tests in Indiana . • 163
79 Distribution of borers in fields having a mean of 6 to 8 borers per root, Ohio survey...... 161+
80 Distribution of borers in treated plots, Virginia, experiment 2, 195U ...... 16U
81 Distribution of borers in fields having a mean of more than 8 borers per root, Ohio survey .... 165
82 Distribution of borers in 1955 sampling study .... 166
83 Distribution of borers in treated plots, Virginia, experiment 1, 1955 ...... 166
8>Lr- Distribution of borers in treated plots, Ohio, 19&-1955 ...... 167
85 Distribution of borers in treated plots, Virginia, experiment 2, 1955 ...... 16?
86 Distribution of borers in treated plots, Oregon .. 168
87 Distribution of borers in check plots, Virginia, experiments 1-U, 1955 ...... 169
88 Distribution of borers in check plots, Virginia, experiments 1 and 2, 195k ...... 169
xii Number Page
09 Distribution of borers in treated plots, Virginia, experiment 3,1955 ...... 170 90 Distribution of borers in treated plots, Virginia, experiment ij,1955 ...... 170
91 Distribution of borers in New York, 1956...... 171
xiii LIST CF FIGURES
Number Page
1 Distribution of root borer in United States. . 5
2 Distribution of root borer in Oh i o ...... 8
3 Distribution of red clover in Ohio ...... 8
1 Width of head capsule of larvae, pupae, and adults 1|2
5 Seasonal history of root borer in O h i o ...... i|8
6 Extreme dates for different stages of root borer in Ohio ...... h9
7 Estimates of root borer damage for three fields .. 70
8 Relationship of mean and variance of untrans formed individual root counts ...... 95
9 Relationship of mean and variance of individual root counts transformed b y / ( x + ir) ...... 96
10 Relationship of mean and variance of individual root counts transformed by log (x + 1) .... 97
11 Relationship of mean and variance of individual root counts transformed by inverse hyperbolic s i n e ...... 101
12 Estimation of q for different m e a n s ...... 103
13 Relationship of mean and variance of 5 root sam ples, untransformed...... 10l*
Hi Relationship of mean and variance of 10 root sam ples, untransformed ...... loU
35 Relationship of mean and variance of 5 root sam ples transformed by log (x + 1) ...... 106
16 Relationship of mean and variance of 5 root sam ples transformed by inverse hyperbolic sine, q - 1 . 0 ...... 106
xiv Number Page
17 Relationship of mean and variance of $ root sam ples transformed by inverse hyperbolic sine, q * O.b ...... 106
18 Relationship of mean and variance of 10 root sam ples transformed by log (x+ 1) ...... 107
19 Relationship of mean and variance of 10 root sam ples transformed by square r o o t ...... 107
20 Relationship of mean and variance of 10 root sam ples transformed by inverse hyperbolic sine . 107
21 Relationship of mean and variance of 10 root sam ples when individual roots transformed by inverse hyperbolic sine ...... 109
22 Relationship between transformed and untransformed means for 10 root samples ...... 109
23 Relationship between transformed and untransformed means for individual root samples ...... 110
2k Number of one root samples to discover specific differences, transformed vs. untransformed .. 127
25 Number of 10 root samples to discover specific differences, transformed vs. untransformed .. 127
26 Acceptance and rejection lines for sequential sampling plan •••••...... ll|6
27 Operating characteristic curves for sequential sampling plan ...... ll*7
28 Average sample number curves for sequential sampling plan ...... 1U9
29 Relationship between borers per root and propor tion infested roots for 20 root samples .....l$2mH
30 Relationship between borers per root and propor tion infested roots for 50 root saraoles .....l£2*d
xv STUDIES ON THE CLOVER ROOT BORER,
HYLASTINUS OBSCURUS (MARSHAM)
INTRODUCTION
The clover root borer, Hylastinus obscurus (Marsham), Is a serious pest of red clover in the United States and Canada, Al though control measures are available, the economic feasibility of such practices are questionable and none of them have been widely adopted.
Further studies on the biological and ecological factors governing root borer populations appear necessary if control mea sures are to be effectively coordinated with the biological ac tivity of the root borer* As most ecological and control tests are designed so that statistical interpretation of the results is possible, a study of the considerations involved in evaluating clover root borer populations is desirable.
The purpose of this dissertation is to summarize our present knowledge of the clover root borer; to present original investi gations on its biology, ecology, and control; and to study the evaluation of populations.
1 PART I. THE CLOVER ROOT BORER
Taxonomic Position
The clover root borer, Hylastinus obscurus (Marsham), is a
bark beetle of the family ScolyfcLdae# The genus Hylastinus con
tains six species, all Palearctic, except the clover root borer
which has also been introduced into the He arctic region. Most,
if not all, spe cies of the genus breed in plants of the family
leguminosae. The clover root borer, however, is the only species
breeding in a herbaceous plant although it has also been taken
from woody members of the family#
The genus Rylastinus is readily distinguished from related
genera by the white meso and metathoracic episterna# This white
color is due to tiny, silver-colored, imbricate scales. The an
tennae consist of a seven segmented funicle and four segmented club
with the first two segments of the club much larger than the
terminal two#
Hylastinus obscurus was first described by Marsham (1602) as
Ips obscurus# Mueller (1807) redescribed the species as Bostrichus
trifolii. Schmitt (l8Ui) placed Mueller's species in the genua
Hylesinus. Bedel (1888) reduced Mueller's species to synonymy with Marsham's species and erected a new genus, Hylas tinus, for
the clover root borer* Swaine (1909), Hagedom (1910), and
Rockwood (1926) review the more important synonymy#
2 3
While the name H, obscurus (Marsham) is generally accepted by
American authors, many European workers use H, trifolii (Mueller)
on the contention that Marsham*s description is inadequate. Seid-
litz (1891) says,"Dass Marsham’s j^s obscurus auf unsere Art bezogen
werden milsste, dafitr bietet Marsham1 s Beschreibung keinen gentigenden
Anhalt,11 Marsham's type material, if existing, should be examined
to clarify the status of this name*
Distribution
The clover root borer is generally distributed over western
Europe from Denmark to Italy and from Great Britain to Russia.
Iintner (1891) states that this insect prctoably reached the
United States about 1875 although the first actual record is that
of Riley (1879) who reported the root borer from Yates County, New
York in 18?8*
Spread of this insect was rapid in North America. It was in
jurious at Edmonton, Ontario in 1887 according to White (1888).
Weed (1888) and Riley (I889) identified specimens from Ohio in 1888,
Davis (I89I1) states that it had reached Monroe County, Michigan by
1889* Webster (1899) states that the borer was injurious in
Paulding and Mercer Counties, Ohio in 1893 and Webster (1893) re ported injury in Dearborn and Franklin Counties, Indiana, Sling er- land (1895) reported injury due to root borers in LaGrange County,
Indiana, and Folsom (1909) reports the borer from Monticello, Ill inois by 1907* By I896 it had reached the west coast as Cardiey h
(I696) recorded it from Oregon,
The present distribution in the United States is shown on the
nap in figure 1. The areas in solid black indicate those counties
from which the root borer has been reported in the literature and
the stippled areas those localities in which the root borer un
doubtedly occurs. The solid black line shows the limits of areas
of important red clover production and therefore the likely extremes
of root borer distribution,
Webster’s (1892) record from Iowa has not been substantiated
by specimens although root borers surely must be present. Golem an
et al. (195l4)> however, failed to find it in five fields sampled,
lugger (1899) predicted the borer would soon reach Minnesota
but Bodge (1938) in his study of the bark beetles of Minnesota
failed to find the clover root borer although admitting its probable
occurrence* Rockwood (1926) includes Minnesota in his distribution map but does not say where he obtained this r ecord.
Case (1881) reported that the root borer had not reached
Wisconsin and was not reported from this state until Hanson (1953)
listed it as a serious pest in the east central part of that state.
Garman (1906) could not find the root borer in Kentucky al
though it must occur* Westgate and Hillman (1905), while not specifically stating that it occurs in Kentucky, say that it waa
nnot abundant smith of Virginia and Kentucky*1 •
Herrick (1925) gives a distribution map which includes Wis consin, Kansas, Texas, Kentucky, Tennessee, and all the New England Fig. 1-Distribution of the clover root borer in the United States. 6
states* The Texas record may be in error as almost no red clover is
grown in central Texas, However there is the possibility that the
root borer may have other hosts in the southern United States*
Balachowsky (19U9) states that it occurs in all the states and also
reports it from Mexico*
State records have been published from Connecticut by Britton
(1920), from New Jersey by Smith (1900), and from New Hampshire and
Massachusetts by Rockwood (1926), Rockwood (1926) records it from
Washington, Oregon, Idaho, and Utah; Mills (19U1) from Montana; and
USDA (1939) and Lockwood (1952) from California,
Spread in Ohio
The first authentic record of the clover root borer in Ohio
is that of Riley (1889) • He identified specimens submitted by
W. B, Hall of Wakeman in Lorain County as this species. Weed (1888)
diagnosed injury in Stark County as that of the root borer. In
both cases severe damage was noted in 1888,
By 1893 this insect was generally distributed in northern Ohio with severe injury reported in Paulding County according to Webster
(189U)* At this time it was present throughout the northern two
tiers of counties and in western Ohio from Cincinnati to Mercer
County and east to Dayton. Webster (1899) reports that 1896 was
the earliest date that the barer was known at Wooster and (1898 )
reported it as injurious in Delaware County*
Webster (1899) prepared an interesting map in which he plotted
the probable movement of the borer through Ohio* If his prediction was correct, central Ohio was the last part of the state to be in
vaded which agrees with published records of injury. He surmised
that the early infestation near Cincinnati could be attributed to
spread of infested clover plants in floods on the Ohio river.
Figure 2 shows the Ohio counties in which the clover root borer was collected curing a survey in 195k as well as other records taken from the literature, A map showing the relative abundance of the root borer throughout Ohio was given by USDA (19!?U) and these lines of equal abundance are also shown on figure 2, Figure 3 shows the per cent of farm land in Ohio seeded to red clover (19$0 census).
It will be noted that the greatest concentration of red clover is in northeastern Ohio and roughly corresponds to the area of greatest root borer abundance.
Economic Importance
While the clover root borer has been known in Europe for more than 1$0 years, it has rarely been an important pest. The more important references pertaining to root borer injury in Europe are listed chronologically below.
1803 Mueller Reported serious injury near Mainz, Germany, Because most clover seedings made in 1802 were lost due to extremely hot dry weather a large acreage of second year clover was retained for another season. Mueller con cluded that borer was responsible for almost total loss of clover during third year* 8
M/i
UW
SPECIMEN UTERATURE
Fig. >,-Distribution of the clover root borer in Ohio.
Fig. 3.-Per cent of agricultural land in Ohio seeded to red clover# 9
16UU Schmitt Concluded that red clover died from natural causes in third year and that root borer at tacked only dying plants. He presents an excellent life history.
1850 Nordlinger Found heavy infestation of borers in red (Ref. in clover but did not notice any damage. vendal (1898)
1865 Tascbenberg Reported on biology and economic importance.
1869 Chapman Studied life history on furze and scotch broom. He questioned that the borer could breed in clover.
1871 Kflnstler Reports injury to clover in Germany.
1872 Kalteabach lists root borer in his book on injurious insects.
1876 Perris Refuted ability of borer to breed in clover.
1876 Bedel Studied life history and damage in France.
1899 Cecconi Discusses biology of borer in Cytisus al- pinus.
1913 Vassiliev Lists root borer as pest of alfalfa in Russia.
1913 Wahl & Muller Red clover injured in Baden.
192k Marchal Red clover injured in the Gironde*
1935 DelGuerci© Red clover damaged in Tuscany.
1936 BaXachowsky Discuss life history and describe damage. & Mesnil
1951 Hnrber Second year clover injured in Switzerland.
1953 Knotb Lists borer as important pest in Germany.
The literature on clover root borer damage in North America is much more extensive. A selected chronological record is given below. 187 9 Riley life history, morphology, and economic im portance are discussed.
1879 Lintner Severe damage (100 % infestation) at Bristol Springs, N. Y.
1880 Riley Abundant at Ithaca, H. Y.
1880 Henry Every plant in Genesee Co., N. Y, injured.
1888 White Abundant at Edmonton, Ontario.
1889 Riley Injurious at Wakeman, Ohio.
18?2 Webster Damage reported in Iowa.
1893 Webster Injurious in Dearborn and Franklin Counties, Indiana.
1893 Smith Attacking garden peas in Ohio.
1893 Buckhout Damage in Lancaster Co., Pa.
189k Davis Generally distributed and injurious in southern Michigan.
1895 Slingerland Less damage to mammoth than red clover in Indiana but reverse true in Michigan.
189k Howard Clover crop in Michigan complete failure.
1896 Webster Clover injured in Mercer Co., Ohio.
1897 Fletcher Injury in Ontario, Canada.
1898 Webster Injury in Delaware Co., Ohio.
1899 Webster Report on life history, distribution, and damage in Ohio.
1900 Lockhead Damage reported at london, Picton, and Ottawa, Canada.
1905 Westgate & Destructive in West Virginia, Ohio, and Hillman Indiana. Seed crop lost in latter state.
1908 Westgate & Injurious at Vancouver, Washington. Hillman 11
1909a Folsom Alsike and red clover Injured in central Illinois.
1909b Folsom Seed yield nil in Illinois.
1911 Gibson Damage near Ottawa, Canada.
1911 Gossard Seed yields reduced in Ohio.
1911 Swaine Injurious in Canada in Montreal region.
1911 Troop Numerous complaints in Indiana.
1932 Surface Mammoth more severely injured than red clover in Pennsylvania; alsike less subject to attack.
1913 Swaine Root borer injurious in parts of Quebec and Ontario.
1913 Gibson Borer reported working freely in alfalfa in Canada.
19 lU Duporte Borer especially destructive in dry year of 1913 in Canada.
1915 Herrick Injurious at Prattsburg, New York.
192U Pieters Root borer most important insect pest of red clover.
1926 Rockwood Most complete report ever published on life history, distribution, and damage of clover root borer.
1927 Canada Red and alsike clover gradually exterminated in British Columbia.
1931 usda Injury reported in Oregon.
1936 Sorenson Reported in Bear River Valley, Utah*
1936 USDA Austrian winter field peas 30 per cent injured in Oregon. 02
1938 USDA Fields in Lancaster Co., Pa. heavily in fested. Clover injured at Jerome, Idaho.
1939 USDA Destructive in western Hew York in 1938.
1939 Knowltm Root borer found in alfalfa in Utah.
1939 USDA Serious injury throughout south central Idaho. Reported in vetch in California.
1 9 UO USDA Borer very destructive in Idaho. Most fields being plowed up.
1918 Newsom Thesis on biology and economic importance of root borer in New York.
19U8 Pa. A.E.S. Stands of clover lost in Pennsylvania in 19U7 due to root borer*
1951 Carnahan & Combination of root borer and Fusarium Hanson wilt kills most plants in Pennsylvania.
19^2 Stivers Thesis on biology of root borer in Pa.
1953 USDA Crimson clover damaged in California.
1953 USDA Damage reported in northern Indiana.
1953 Elliott Fusarium root rot generally associated with borer injury in West Virginia.
1953 USDA Severe injury in Washington.
1953 Hanson Severe injury reported in Wisconsin in I9I46 to 19U8.
1 9 5 U USDA Severe injury in northern Indiana, Illinois, Ohio, Pennsylvania, and Virginia. Report of state survey in Ohio showing abundance.
1 9 5 5 USDA Root borers abundant and injurious in Virginia, Pennsylvania, Ohio and Idaho.
19^5 Dickason & Clover, peas, and vetch attacked in Willa Every mette Valley, Oregon.
1956 USDA Reports of damage from Oregon, Virginia, West Virginia, Michigan, m d Ohio. BIOLOGY AND 3C0IAGY
Introduction
Adults of the clover root borer overwinter in clover roots
in old fields where they matured the previous summer. As tem
peratures become higher in the spring, these borers resume feeding.
On warm days, usually in May, the adults mate and fly to new
fields. Here they burrow into the roots and construct their egg
galleries, Oviposition continues from May to July* As; the eggs
hatch the young larvae burrow downward in the roots, forming a
pupal cell at the end of their tunnels upon maturity. New adults
usually appear from late July to October. There is but one
generation a year.
The Adult
The adult root borer is a typical scolytud. Rockwood (1926)
provides a good illustration and describes it as follows:
The body of the adult is oblong oval; pronotura slightly wider than long, a little narrower than elytra, sides rounded, unarmed, strongly arcuate, narrowed roundly anteriorly, without anterior constriction dor sally; head visible from above; elytra deeply striate but unarmed except for shagreening posteriorly and laterally, roundly convex posteriorly. The face, prothorax, elytra, legs, antennae, and venter are distinctly clothed with short golden-brown hairs, hairs longer on venter than on dorsum; side pieces of mesothorax and metathorax, that is, the metathoracic epistemum of Hopkins1 and mesothoraeic
Hopkins, A. D. 1909* Contributions toward a monograph of the scolytid beetles. I. The Genus Bendroctonus• USDA Bur. Ent, Tech. Ser. 17(1) :l-l6U. xl*
episternum and epimeron, clothed with oval, gray or silvery, fringed scales, ftie convex head is finely and shal lowly punctured with a faint transverse median impression at the base of the short beak. The antennae, whose scrobes are distinctly separated from the front of the elliptical eyes, have a 7-segmented funicle, about as long as the distally inflated scape, and a short oval-connate, slightly compressed club, of which only the first suture is strongly chitinized and distinct, the first and second segments about equal and each longer than the third and fourth together. The prothorax is closely and deeply punctured, punc tures irregular in size and shape, with a tendency to rugosity, vestiture of hairs short, fine, obscure. Median line absent, or present and more or less interrupted and obscure, usually vestigial, scarcely elevated if at all when present, marked by dividing line between prothoracic hairs even when not otherwise evident. Elytra clothed with three types of vestiture, punctures of striae large, deeply indented, and tending to rectangular, each with a very fine, appressed, obscure, pale hairj interspaces sure finely aid obscurely punctured, punctures well separated, each accompanied by a single, coarse, brown, backward-directed scalelike hair. The interspaces are roughened between and around punctures, becoming sha green ed or granulate posteriorly and laterally, and sparsely clothed with shorter golden-brown appressed scalelike bristles. Interspaces and striae almost straight. Ventrally, the anterior coxae are widely separated and clothed wi th long golden hairs, the second visible ventral abdominal segment, or stemite of Hop kins, about as long as the fifth, or sternite 7 of Hop kins, and nearly double the third, or sternite 5 of Hop kins. Venter and legs shallowly and evenly punctured and clothed with hair. The tibiae are toothed and dilated, the anterior pair with exterior angle of anterior margin nearly rectangular, with four short, blunt, recurved teeth close together on anterior margin and a stronger lateral tooth usually posterior to others on outer marginj the median pair have three strong teeth along aaterior half of outer marginj the posterior pair have two well-separated strong teeth along outer marginj the third joint of the tarsus is deeply bilob ed.
Hockwood (1926) found that adults varied in size from 1,82 ran. by 0.S2 am, to 2.$ mm. by 1.18 mm. with an average of 2,2 by
0,92 mm. 15
Very little work has been done on the anatomy of this species despite the fine volumes on bark beetles in general. Riley (1879) illustrates the antennae, tibia, and epistoma; DelGuercio (1915) the tibia and tarsus; Swaine (1917) describes the proventriculus;
Swaine (1917), Bruck (1936), Chamberlin (1939), aid Balachowsky
(19U9) figure the antenna; and Dillery (1955) figures the hind wing*
Upon emergence from the pupa, the new adult is soft and cream colored, gradually becoming brown# Older adults become a deep red brown, often almost black# Old adults can be distinguished from the new generation by the color differences, the adults not usually attaining their blackened color until spring#
It requires at least a week for the beetle to become suffi ciently hardened to feed#
Fall Behavior
Although borers may remain in their pupal cells until the fol lowing spring, most chew their way out of these cells, either back through the old larval tunnel or directly to the outside of the root. These then congregate near the top of the root. Webster
(1899), hcwever, did not believe that borers ever left these cells until the following spring.
Those borers in dead plants, if sufficiently matured, chew their way out and leave such roots as they become dry. However as 16 long as these dead roots remain upunky" most adults remain in them.
Such roots probably constitute the most favorable location for overwintering •
Those borers leaving dry roots migrate on foot to living plants where they congregate in the crowns. Weaver et al. (1950) state that migration to new fields may occur in the fall if weather conditions are favorable, Rockwood (1926) caught borers in flight after Sept. 18, 1918 but did not state whether these were the old or new generation. However, he concluded that any fall migration to new fields was on foot. Although migrations within a field from dead to living plas ts is coimion, any movement of more than a few yards remains questionable. Only if a new field were ad jacent to an old one would there be any great chance of it be coming infested during the fall. No borers could be found in a new field in September 195U although considerable movement was known to have occurred within the old field.
Early Spring Behavior
Little development occurs during the winter although borers may become active and feed on mild days. However, as temperatures moderate, borers resume feeding in the spring. On warm days in
March and April borers which have overwintered in dead plaits may leave these and crawl on foot to living plaits where they cheer short feeding burrows in the crowns. Rockwood (1926) indicates 17
that borers may even migrate on foot to new fields at this time,
Rockwood (1926) and Negley (1953) nave concluded that a soil tem
perature of h$° F, is essential for adult activity. On favorable
days, borers feed and during this time build up stores of reserve
food material.
Flight
Root borers usually migrate by flying to new fields in the
spring. In Ohio such flight occurs on warm, sunny, days in late
April or May.
Borers climb to the highest available point prior to be
ginning flight. At this time they may be swept in large numbers,
72 being taken in 100 sweeps at Wooster, Ohio on May 3, 1955.
Rockwood (1926) describes flight as being rather slow and
steady with most of the borers flying six to ten feet above the
ground. More than 60 per cent of the beetles taken on a $0 fcot high screen by Rockwood were within 20 feet of the ground.
However, it seems significant that considerable numbers were taken between iiO and 50 feet even at the edge of the field.
Rockwood (1926) states that borers fly against the wind in
Oregon but Negley (1953)> working in Pennsylvania, came to the conclusion that most migration is with the wind. Examining
Rockwood1 s data, we find that in the experiment referred to he had but one screen at the edge of a second year field and, taking 18
more beetles on the side towards the old field, apparently arrived
at this unjustified conclusion.
In 1956 an experiment was designed to test the direction of
movement. Three box-like traps, each 12" X 12" X 12", were set
18" above the ground in a line through the center of an old red
clover field and coated with tree banding material.^ One trap of
similar design was also set in the center of a new field. Using
this method, it was found that 81 per cent of all beetles trapped
in flight in 1956 were flying with the wind. Figures are presented
in Table 1.
Table 1, Direction of flight of clover root borers# Wooster, Ohio. 1956.
Date Wind Side of Trap Total Number Direction NS £ W Borers Flying With Wind May 1 - 1 2 SW* 0 1 0 1 2 2 May 13 SW 2 37 3 22 61 59 May 13 (NF) SW 1 1 1 0 3i 1 May 20 SW 0 8 3 5 16 13 May 22 SW 1 10 3 2 15 12 May 22 (NF) SW 1 1 0 7 9 8 May 23 - June 2 S* 1 5 1 3 10 5 June 3 - 13 S* 3 1 1 0 5 1 Totals 9 61 12 Uo 325 101 * Prevailing wind direction for period (NF) ■ New field; others in old field
We can only conclude that either Rockwood was in error or that the clover root borer behaves differently in Oregon.
l"Stop" tree banding material, Acme White Lead and Color Works, Detroit, Michigan. 19
Traps for Determining Flight
Various types of traps for taking root borers in flight have
been used. Some type of sticky material has been universally ap
plied for retaining the beetles, Rockwood (1926), Stivers (1952)
and Negley (1953) used various sorts of screens; Newsom (19^8) used barrels; and Marshall et al. (19U9), Gyrisco and Marshall
(1950) and App (1953) used boards.
Various "types of boards were employed, at Wooster, Ohio during
1955 and 1956, In 1955 boards 12" X 18" nailed horizontally to stakes about 18" above the ground were used. Although these traps have apparently proved successful in New York, they were deemed unsatisfactory in these tests because of the few beetles taken in 1955. In 1956 open boxes as previously described were con structed and set on four stakes about 18" above the ground. Such traps not only afforded a means of determining in what direction borers were flying at g round level but were also useful In com paring the number of beetles taken on a horizontal as opposed to a vertical surface. Table 2 indicates that almost four times as many borers were taken on vertical surfaces than on horizontal.
Sexual Development
Mo studies concerning spermatogenesis in the male have been made but Rockwood (1926) found males had well developed testes in September. Sexual maturity of the female is much slower as 20
Table 2. Effectiveness of vertical vs. horizontal surfaces for trapping clover root borers in flight. Wooster, (Mo. 1956. Number of Borers Caught Date Vertical Horizontal Surface Surface
May U - 13 69 6 May 20 - 22 hi 2 June 2-13 15 0 Totals 129 8 Number per Sq. Ft, 31 8
indicated by Rockwood's work. Early stages of egg development in the ovary may rarely occur in the fall but in most cases not until after mating just prior to spring flight. Egg maturity in the ovary appears to require about two weeks with never more than two eggs developing at tfche same tame (one in each ovary).
Relation of Temperature to Flight
Temperature plays a major role in the spring behavior of the adult. Adults become active and resume feeding in the spring when soil temperatures reach about U5° F. according to Rockwood (1926) and Negley (1953). Flight ordinarily occurs at temperatures of
68° F. or above on sunny afternoons.
Because the value of sprays for root borer control seems to depend on Application near the time of peak flight, there is need for a method of predicting peak flight. In eastern United States there is usually only one major flight over a period of but two or 21
three days.
Negley (1953) questioned that any temperature summation
method would work for predicting flight as he found the number of
borers in flight to be correlated with soil and air temperature.
However it does not seem that this relationship should preclude the
use of summation methods in determining when flight will begin
even though it may be of primary importance after the first
flight. As borers almost never fly on the first warm day that
is otherwise suitable, it seems almost certain that some pre
flight period of development is necessary. Rockwood (1926) has
shown that borers feed before flight with food reserves being
stored during this feeding period. Therefore various tempera
ture summation methods were tried for predicting flight.
A Temperature Summation Method for Predicting Flight
First and/or peak flight records are available for a number of
dates at various stations throughout the United States. Using various bases, effective temperatures have been summed for these
stations with the aid of U. S. Weather Bureau records published in CUmatolcgical Data.
Using a 50° base and summing all temperatures above this mean beginning March 1, proved quite satisfactory in eastern United
States. Rockwood (1926) and most workers since then have generally concluded that root borers do not fly at air temperatures below
68° F. Assuming that root borers will fly on the first day on 22 which the temperature reaches 68° F. after l£o day degrees, peak flight was predicted with an error of 0 to 1$ days with an average error of 3*3 days for the 18 eastern stations for which reliable records were available.
However this method was totally unsuitable on the west coast, borers flying much earlier than predicted in most years. Temper atures in Oregon and Washington are generally milder during the winter than in eastern United States but there are fewer days of high temperature in the spring. But if we reduce our base to
U5° F., the temperature Rockwood (1926) and Negley (1953) state is necessary for borer activity, and limit our summation for any one day to 10 day degrees, we can quite accurately predict flight for Oregon if we assume 170 dsy degrees to be the effective tem perature. Furthermore this method works as well as the 50° base method in the eastern states.
Table 3 summarizes the accuracy of these two methods. The error given is maximum error because some weather conditions re main unknown. We must assume that any day on which the tempera ture reaches 68° F. is suitable for flight. However other fac tors may prevent borers from flying on this date. As borers ordi narily fly only in the afternoon according to Ropkwood (1926) and observations made in Ohio, this maul mum occurring at any other time of the day would be ineffective. Sunshine must be near max imum as Rockwood (1926) found that only temporary obscuring of the 23
Table 3. Comparison of two methods of predicting spring flight of clover root borer. Loca- First Peak ^ Predicted ^ tion Flight Flight Date ~kS° 5o°" k$° 5o° Eastern United States
1 li/2 7 /l5 It/29 li/2 5 2 2 2 5 /2 2 /ltO 5/22 5/21 0 1 3 U/2E/U2 5 /1 A 2 5A lt/30 3 1 3 U/23/U6 5/15A 6 5/15 5/20 0 5 3 5/19/1*7 5/23A 7 5/21 5/21 2 2 3 5/2 A 8 5/27A 8 5/12 5/18 15 9 3 5/7 A 9 5 /7 A 9 5/6 5 /5 1 2 3 5/15/50 5/23/50 5/21 5/23 2 0 3 5/1 / 5 l 5/22/51 5/19 5/21 3 1 3 2/ 5>/9-lit/52 5/10/52 5/20 5/2li 10 lit 3 2/ 5/151/53 5/13 5/13 1 1 h Si} iS l 5 /2 / 51 5/8 5/H t '6 12 5 it /26/99 It/29 U/26 3 0 5 U/30/55 5 /2 /55 ii/2it 5 /1 9 2 5 5/13/56 5/13/56 5/lU 5/13 1 0 6 5 /6 -lo /5 b 5/5 5/6 11 0 6 5/8 o 5 6 U/29 & 3 2 Mean Error for Eastern U. S. 3 .5 3 .3
Station numbers are as follows: 1 ■ Hagerstown, Mi. - weather records for Chewsville 2 * Ithaca, S. T. 3 " Minetto, H. Y. - weather records for Ithaca It * State College, pa. $ ■ Wooster, Ohio 6 ■ Colombos, Ohio 1/ Used for estimating error when available j otherwise first flight assumed to be peak 2/ May 10 probable peak 3/ May lit probable peak Ty May 6 probable peak J/ Kay 8 probable peak 2k
Table 3. (Continued)
Loca First Peak Predicted tion Flight Flight Date Error kS° 50° li5° 50° Western United States 7 5/18/12 5/11 5/16 7 2 8 5/5 /17 5/10/17 5/10 5/20 0 20 9 U/16/15 U/15 ii/10 1 6 9 5/8 /L7 5/8 5/29 0 21 9 U/19/18 li/20 5/1 1 12 9 U/22/19 li/2li 5/13 2 21 9 Ii/26/20 5/13 6/k 17 39 9 ii/8 /21 li/17 5/21 9 ii3 9 3/28/30 li/7 5/1 ID 3U 9 li/25/31 h/2h 5/2 1 7 Mean Error for Western U, S, it.8 19.5 Mean Error for all samples U.o 9.1
Station numbers are as follows: 7 " Murray, Utah - Weather records for Ogden 8 ■ Wapato, Wash, - weather records for N, Yakima 9 ■ Forest Grove, Oregon - weather records for Portland used jn 1915, 1918
sun by a cloud caused borers to return to the ground. Sunshine records are generally unavailable. Needless to say rainfall during the afternoon will prevent flight.
The 170 day degree method also held true in the laboratory.
Beetles brought into the laboratory on December 20, 1956 were ob served in large numbers on the side of the jar on January 7, 1957,
If we allow 10° for each day, 180 day degrees were required. However
if borers are subjected to intense heat, they will leave the roots 25 much sooner, Negley (1953) induced borers to leave roots in only a few hours in a Berlese funnel with a light bulb as the source of heat. However this premature exit is on foot rather than wing.
Mating
New adults, when brought into the laboratory in the fall, will often attempt copulation. However it is not known whether females may be fertilized at this time. No reliable cases of egg production by females of the new generation have been observed until the following spring. Mating usually occurs just prior to flight. Stivers (1952) and Rockwood (1926) described observed cases of mating. The males chose females which were partially concealed in tunnels* Both cases that Stivers describes occurred after flight but Rockwood has shown that mating usually occurs before flight. Schmitt (I8it4) observed beetles in copula on clover plants and Rockwood (1926) in a tunnel in old roots. Mating, however, occurs most cosmonly on the ground or clover crowns.
Females appear to fly out of the old fields earlier than males* Rockwood found that fmales comprised 85 to 95 per cent of the flight in the early days, Nearly 90 per cent of all females had been fertilized prior to flight. He thinks borers may mate more than once during the season as males are often found accom panying females in their egg galleries. 26
Sex Ratio
All borers taken on traps during 1?55 and 19$6 were dissected and their sex determined by examination of the genitalia. Samples of 50 borers taken from roots just before flight and in December were also sexed. These data are presented in Table 1*. While sam ples taken from roots did not differ from a 1:1 sex ratio, females predominated in flight, especially in the early days. Koehler (1957) found the ratio of males to females to vary from 1 .3U :1 for callow adults to 1:10 for beetles in second crop year roots.
Table U. Sex ratio of beetles taken in flight during 19$5 and 19#*
Date Males Females Total I2
1 9 # April 27 - May 6 1 1* 5 May 7 5 2 7 May 8-27 2 1 3
19# Totals 8 7 15 0.00
19# May 2 - 23 20 52 72 May 20 - 22 10 31 ia June 2-13 10 11 21 1 9 # Totals 1*8 101 2i*9 18.ll***
Field Samples April 28, 1 9 # 23 27 50 0.18 December 20, 19# 28 22 5o o.5o
** Adjusted J? significant at 0.01
Although trapping had to be discontinued before flight was complete, it appears doubtful that the number of males taken late 27
in the season would make "the ratio of total borers caught in
flight 1 :1 . to other species of bark beetle s many males never fly
and it seems likely that this may also be the c ase with the clover
root borer#
Secondary Sexual Characteristics
Rockwood (1926) reports no good secondary sexual charac
teristics for spearating males and females of the root borer.
The head of the male tends to be narrower but this is not always
the case.
Newsom (I9I4.8) sexed living adults in the following manner:
Beetles were held lightly with forceps head down, dorsal surface outward, posterior tilted slightly inward. The female extruded her abdomen and the sixth and s eventh tergites became visible.
The male extruded only the seventh which is larger and more heavily sclerotized. This method was found unsatisfactory in these tests. Koehler (1957) modified Newsom's method. Beetles were placed on their dorsum on a smooth metal surface and a light brought near to incite activity. The number of exposed segments could be counted as the beetle struggled to right itself*
The only method used in Ohio was dissection of genitalia which of course involved killing the beetles.
Riley (1879) gives illustrations of the epistoma which shew differences between males and females. Ho such differences were 28
found in specimens examined in Ohio.
Flight Range
No accurate work has ever been done to determine the flight
range of the clover root borer during spring migration. Negley
(1953) released beetles marked with a paint fluorescing under
ultraviolet light and then trapped these beetles at varying points
from the release station on boards covered with tree banding material. However all of the beetles successfully caught were coated with this material which also fluoresced.
Rockwood (1926) found beetles flying into fields more than two miles from the nearest known source of infestation in the spring.
Oviposit! on
Rockwood (1926) and Stivers (1952) describe oviposition.
After mating has occurred the female burrows into the clover root, either in a new field after flight, or into roots in the old field. The egg gallery is usually started on the side of the root near the crown but may be as much as two inches below the soil level. Rockwood (1926) and Stivers (1952) describe borers starting their galleries and agree that the borer eats most of the material taken from the burrow* Egg galleries may be either grooves on the
Surface or be completely enclosed, with enclosed burrows being 29 much more common in Ohio. After burrowing to a depth of six to ten mm. a niche is constructed in the side of the gallery; the female backs out of the burrow, backs in, and deposits a single egg in this niche. This is then sealed over with frass cemented together with a sticky material. This process is then apparently- repeated for each egg. Distance between egg pockets varies con siderably but is usually three to four nm. in the first gallery constructed by the female. In galleries made late in the season eggs may be much closer together. The first gallery may contain three to eight eggs while a dozen or more may seme times be found in later galleries.
If the gallery is completely enclosed, eggs are laid alter nately on two sides of the tunnel but if "the egg gallery is a surface groove, all eggs are laid on the side nearest the center of the root,
Rookwood (1926) and Balachcwsky (19U9) state that a female may form two or three galleries during the season. This agrees with data taken in Ohio. Completion of the first gallery requires about a month while later galleries are completed in about three weeks each.
Reproductive Potential
Most authors agree that t he reproductive potential of the root borer is low. Balachowsky (I9U9) quotes Webster (1910) as 30
stating that the total offspring of a pair of borers is about six.
However, although Webster says that about six eggs are laid in a
tunnel, I fail to find where he concludes this is necessarily the
limit of offspring*
Rockwood (1926), in cage tests, never obtained more than 21
borers from a pair and a mean of only lh. Newsom (19^8) reared
borers in the laboratory on pieces of clover roots. In this way
he obtained an average of 36 offspring per pair of beetles col
lected early in the season.
While no tests were conducted in Ohio, an estimate of the off
spring may be obtained in the following way. Assuming that one-
half of the adults found in roots in new fields in the spring are
females, the offspring per female “ 2x/a where x - borers per root
(exclusive of old adults) in the fall after oviposition has ceased
and a ® adults per root in the spring just after flight is com
plete. Data for 1955 and 1956 is presented in Table 5. This data
agrees rather closely with Rockwood's estimates. Therefore it
appears that, although reproductive potential is relatively high
as shown by Newsom, such a rate is rarely if ever achieved in the
field.
Longevity
Populations of old borers taper off rapidly after the first part of June and very few are alive in September, Newsom (191*8) 31
Table 5. Estimation of offspring per female root borer.
Adults per Borers per Offspring Year Root in Root in Per Female Spring Fall
1955 0.933 5.833 12.50
1956 0.500 1.500 6.00
however had 10 pairs of borers which were alive at the end of the first year and survived a second winter. These females 3a id an average of 22 eggs during their second summer and one pair was still alive that fall when his experiments were concluded. Although
Newsom used only adults during the second year in which both sexes of the original pair survived, he made no mention of whether re peated matings occurred* Also he does not state if individuals of other pairs were alive. It is not known whether beetles ever survive more than one year under field conditions.
Natural Enemies
Very few natural enemies of the root borer have been observed.
The entcmophagous fungus3 Beauvaria bassiaaa^ Is the only common disease that has been observed. This disease is present every year; however during the spring of 1955 it was especially prevalent, mor tality ranging from three per cent on May 11 to 57 per cent on
May 31. Riley (1679) records Telephorus billneata (Coleoptera: Can- tharidae) as an eneny of the root borer but failed to say what stage was attacked. One larva of a cantharid of undetermined species was observed feeding on an adult borer in its tunnel at
Hoytville, Ohio on August 17, 1956.
Large numbers of adult staphylinids have sometimes been found in clover root borer tunnels but no instances of predation have been observed.
Rockwood (1926) collected birds during spring flight of the borer and examined their stomach contents. The followingspecies were found to feed on adult root borers:
Common Name Scientific Marne Streaked horned lark Qtocoris alpestris strigata Hensh. Brewer blackbird Scolecophagus cyanocephalus Wagl. Oregon vesper sparrow Pooecetes gramineus affinis Miller Townsend sparrow Fasserella iliaca unalaschcsnsis Gael. Golden-crowned sparrow Zonotrichia coronata Pall. Cliff swallow Petrochelidon lunifroms Say- Northern violet-green swallow Tachycineta thalassina lepida Meams Pacific house wren Troglodytes aedon parkmanii Aud.
Effect of Moisture on Adults
Adult root borers are extremely sensitive to dryness. One control measure is based on this knowledge. If infestedfields are plowed in the summer so that roots are exposed to the air, only those borers old enough to chew their way out will survive.
In laboratory tests beetles placed in petri dishes on filter 33
paper seldom survived longer than 2h hours while if the paper were moistened they could be maintained several days without food.
Survival in dry atmospheres is longer at lower temperatures.
Although a certain amount of moisture is essential for sur vival, the critical level is rarely reached under normal field conditions* Many workers believe development to be more rapid and populations higher during dry seasons.
During 1955 and 1956 an experiment was conducted to determine the effect of moisture on the root borer and on damage. The design of this experiment is discussed on page 58. After the third cut ting of hay was made, the roots were dug in each pot and dissected to determine the number and stage of borers present* As there seemed to be no difference in the stage of development, only totals of all stages are presented in Table 6 which summarizes thdse data.
An analysis of variance showed the differences between water levels to be significant.
5he regression coefficient for borers on water, b ■ -0*859
(s^ “ 0 .221), was significant at 0 .01 .
Although higher populations were found in lower moisture levels, it is not certain whether this can be attributed to at tractiveness to adults, increased oviposition, or greater larval survival. 34
Table 6. Effect of different levels of monthly rainfall on clover root borer populations. Wooster, Ohio.
Year Number Eorers in 10 Pots ¥ l'» 2" 4" 6”
1955 So 22 33 15
1956 46 57 38 19 Totals 46 107 60 52 15 Borers/Pot 4,6 5.4 3.0 2.6 1.5
Analysis of Variance Source of Degrees Mean F Variation Freedom Square
Total 79 Water 4 55.0 3.31* Error 75 16.6
Effect of Host Condition on Oviposition
Many authors, including Schmitt (18140 and Riley (1879) believe that adult borers prefer weakened plants for oviposition, A small amount of data was obtained which tends to support this theory. In
1955 part of the field from which weekly samples were being taken was clipped early in May shortly after migration was complete.
Repeated clipping early in the season weakened these plants and most were dead by the middle of June, Samples from the clipped and unclipped portions, although showing significant differences on only one sampling date, were higher on all but the last date in the clipped portion. At this tome many of the early cut plants were 35 dead arid rotted and therefore likely missed in sampling. Figures are presented in Table 7, The t-test was used to test differences between sample means while the Chi-square analysis was used to test for differences in rate of development as indicated by the proportion of borers in each of four stages of development. As this experiment could not be replicated further tests would be desirable.
Table 7* Clover root borer populations and development in early vs, late cut portions of field, Wooster, Ohio, 1955, Date and Time Stage of Development Total 2 of Cutting Egg Larva Pupa Adult Borers
July 5 Early 8 12U 6 138 2.33 20.0** Late 19 52 0 71 July 12 Early 6 11*9 23 1y 179 1.96 10.3** Late 9 100 k 0 U 3 July 19 Early 8 103 2k 13 21*8 1.21 15.5** Late 9 9k 9 0 112
July 26 Early 5 108 21 18 152 1.16 lU.9** Late 10 91 8 3 112 August 2 p/ Early—/ 1 k9 23 12 85 1.58 19.3** Late 9 89 17 3 116
i/ Lumped with pupae in % analysis 2/ Mary plants dead and rotted and likely missed in sample * Significant at 0,05 ** Significant at 0.01 36
THE EGG
Description
Eggs are laid individually in niches in the sides of galleries
in red clover roots. Excellent photographs of eggs in galleries are
given by Swaine (1911) and Stivers (1952). Rockwood describes the
egg as follows:
The egg is short-oval in shape, with one side some what less rounded than the other, pearly white in color, smooth and glistening* Eggs in which development has begun are transparent at one end because of r etraction of the egg contents j whereas the fresh eggs are altogether opaque* The egg measures 0*67 by 8.1*3 mm. wide at the widest part.
Incubation Period
Various authors have given widely varying periods of time necessary for hatching. Schmitt (181*1*) states that eggs hatch in
8 days in Germany. Parker, working in Maryland, found the incuba tion period to be 10 or 11 days according to Rockwood (1926).
Rockwood presents data to show the effect of temperature on hatching.
He found it to vary from about 32 days in early May at a mean temperature of 5U° F. to about 16 days in June at a mean tempera ture of 62° F. Stivers (1952) found the incubation period in
Pennsylvania to be only 7 days.
Field observations in Ohio indicate that in early spring the incubation period may be as long as 30 days while in the laboratory it is about 7 days. Natural Enemies
No egg parasites or predators have ever been reported. From
May 2h to June 7, 1955 large numbers of a white mite were found
in egg tunnels. Dr. E. W. Baker (USDA) identified these as Swie-
bea sp. and asked for additional specimens. In the meantime a
culture, supposedly of this species, had been started on moist
filter paper, and additional specimens were submitted fro® this
culture, These, however, were identified as Rhizog Typhus solani Oed.
80(1 Caloglyphus sp., neither known to be predaceous. As no actual
instances of predation were obsdrved, it is likely that these were feeding only on plant tissue or borer frass.
THE LARVA
Description
Rockwood (1926) and Peterson (195>1) give excellent illustra
tions of the larva and Rockwood describes it as follows:
The mature larva is of the usual scolytid type, short subcylindrical, wrinkled, and legless. The thoracic re gion is distinctly larger than the abdominal region, which tapers gradually posteriorly. The body setae are short, fine and sparse, very obscure. The color is creaay white, with straw-yellow to light-brown head capsule and red- brown, triangular, dark-tipped mandibles, which have two broadly blunt teeth at the apices. The immature and still feeding larvae appear dirty white or gray, because of the contents of the intestinal tract. The setae of the head are light colored, fine, somewhat longer than the body setae. The head capsule has the epicranial suture strongly impressed j front with a convexity anterior to the middle, with oblique ridges extending above to the sutures of the 38
front on either side and below to the angles of the epi- storaa, forming concavities between the ridges. Front with posterior apex subacute. Lab rum with raised median tri angular area, truncate, or faintly emarginate. Clypeus with raised W-like rugosity with corresponding lateral and anterior mesial concavities; anterior margin truncate or obscurely broadly emarginate. Mature head capsules in pupation chambers vary greatly in dimensions, the minimum being 0.55 mm. long without mandibles, front 0.31 mm* by 0.29 mm., epistoma 0.23 mm., pleurostoraa 0.12 mm.; the maximum 0.70 ram. long without mandibles, front 0.36 mm. by 0,3U mm., epistoma 0.28 mm., pleuro- stoma 0.15 mm.
The first instar larvae, upon hatching, burrow at right angles to the egg gallery. At the first molt, the second instar makes a right angle turn, usually burrowing more or less parallel to the root and downward, but this is not always true. Larvae hatching from exposed eggs on flat surfaces appear unable to begin this first tunnel.
The galleries are usually somewhat sinuous but may be almost straight in the latter stages and often run down the center of the root, Except for the first few millimeters, the entire gallery is usually packed with the brown excrement.
Rate of Development
Rockwood (1926) states that the larval period varies with the temperature. He also states that Webster found this period to be about 1*0 days at Wooster, Ohio. Newsom (191*8) found the larval period to vary from 1*0 to 77 days with a mean of 60 in 19h2 at
Ithaca, New York while in 191*6 it varied from 30 to 70 with a mean 39
of 44. Based on samples taken in the field in Ohio, the mlnimm
larval period was 42 days in 1955 and 40 days in 1956 although in
a third year field sampled in 1955 the larval stage may have been passed in less than 30 days.
Effect of Plant Condition on Development
Rockwood (1926) and Riley (1879) state that borers not only prefer weakened plants but develop faster in such hosts* Half a red clover field was weakened by early cutting as previously de scribed on page 34. Samples taken from the two parts of this field indicated that borer development was advanced almost two weeks in the weakened plants. Table 7 summarized these data.
In 1954 many plants died early in the season. Eroja July 26 to August 9, separate samples were taken of dead and living plants.
The total number of borers was significantly higher in dead plants as shown in Table 8. However it is not known whether the death of these plants was caused by an early, high infestation, or whether weakening of plants stimulated oviposition and development. Borers in dead plants were elmost two weeks further advanced. An analysis of these data is also given in Table 8.
Somewhat more conclusive results were obtained in 1955. In
Ohio almost no red clover is retained for a second harvest year.
However the old field sampled in 1954 was retained until the summer of 1955. Eggs were being laid in this field prior to spring flight iiO
Table 3. Comparison of number and development of borers in dead vs. living roots. Wooster, Ohio. 195U.
Date and Root Stage of Development Total t X2 Condition Borers Larva Pupa Adult July 26 living D a 17 6 16U 1.63 20.5** Dead 162 55 28 21*5 August 2 living 81 20 18 119 2.L0* 27,7** Dead 76 5U 70 200
AuguBt 9 Living 56 12 7 75 2.72*-* 57.1** Dead 1*8 28 101 177
* Significant at 0.05 ** Significant at 0.01 or about one week before any eggs were found in an adjacent new field. Hatching was delayed in the old field and occurred at about the same time as in new fields. Development after hatching, however, was rapid with pupae occurring two weeks earlier than in new fields.
Again this Berves as evidence that development is more rapid on weakened plants. Few plants in this old field were living after
June 1.
Number of Ins tars
The number of instars has never been accurately determined and is probably variable* Rockwood (1926) concluded that there are usually four or five but perhaps only three in some cases* Bala- la
chowsky and Kesnil (1936) state that there are four instars.
Koehler (1957) found the number to vary from four to six based on
cast skins in roots.
Newly molted larvae often show little increase in size and
each instar is quite variable. Figure h shows the results of
measurements made on 1*6$ larvae* Although certain peaks are evi
dent, no conclusive evidence is given. Except for the first instar,
relatively few specimens of the other early instars were measured.
Thirty-eight first instar larvae were measured shortly after
hatching from eggs in the laboratory and before feeding. The
range in width of the head capsule was 0.258 to 0.351* mm. with a
mean of 0.329 mm. The width of the head capsules of 50 pupae and
100 adults was also obtained and these figures are presented
graphically in Figure 1* also. It is to be noted that each curve is
definitely bimodal and that this condition is likely true for at
least the last instar larvae. While adult males tend to have nar
rower heads than females and can be separated by dissection of their
genitalia, methods for sexing the pupal and larval stages are un
known.
Rearing Methods
Rockwood (1926) and Newsom (191*8) were able to rear root borers on pieces of clover roots in salve boxes. U2
4 0
35
30 4 6 5 LARVAE a Ld > 25 CL Id V) CD ° 20 a: id CD 5 15 D Z
ADULTS'
0 .25 3 7 .55 .61 .67 73
WIDTH OF HEAD CAPSULE IN MM.
Fig. L.-Width of head capsules of larvae, pupae, and adults of the clover root borer. 43
Daring this study an attempt was made to rear root borers on
a sterile artificial medium. The greatest problem seams to be in
obtaining a medium of proper texture. Media must be rather solid
and yet contain adequate moisture. Most agar base media are too
jelly-like, the young larvae failing to begin their burrows. Only
two borers were reared in such a medium and it was far from ’’arti
ficial'* in composition as shown in Table 9.
Table 9. Canposition of artificial medium used in rearing clover root bo rer. Nutrient Quantity
Agar 4.0 g. Lyophilized clover roots 20.0 g. Butoben (Antibiotic^ 0.2 g. Water 125.0 ml.
Eggs were sterilized by placing in two per cent NaGfH plus two per cent formaldehyde for 10 minutes, after which they were rinsed
in alcohol. This treatment caused no mortality. They were then inserted into holes punched in the medium with a sterilized teasing needle. These holes were then plugged with the medium.
One dish of medium in which four eggs were placed on May 31,
1955 contained one full grown larva and one new adult when next, examined on July 11. Larval life was therefore completed in about
35 days in this case. Another vial of the same medium contained one small living larva between the medium and glass. This larva U l i was first observed on June 15 and showed no noticeable growth during the ensuing period. Because of severe contamination in this vial it was discarded and an unsuccessful attempt made to transfer the larva to fresh media.
Natural Enemies
iev natural enemies of root borer larvae are known. Beauvaria bassiana is said to attack larvae and pupae as well as adults but was never observed on the immature stages in Ohio*
A few dead larvae were found which were deep black in color.
These were submitted to the USDA, for identification of the pathogen but to date no identification has been received. The cantharid larva, Cantharis bilineatus may feed upon larvae. Rockwood (1926) says that H. L* Parker reared Chauliognathus pennsylvanicus DeG. from larvae which ate root borer larvae.
THE PUPA
Description
Rockwood (1926) illustrates the pupa and gives the following description:
The pupa is truncate fusiform in shape, with the apex of the abdomen squarely truncated on a line between the caudal spines on the ninth abdominal segment. The wing pads extend to near the hind margin of the sixth, and the elytral pads to near the hind margin of the fifth abdom inal segment* The color of the fresh pupa is pearly white US
to white and shining. Setae on all parts of pupa are short, fine, and inconspicuous, Setal spines are also short and inconspicuous, except the two anterior dorsal spines on the prothorax, which are considerably more prominent than other thoracic spines and setae, and the two recurved caudal spines on the ninth abdominal seg ment. The two frontal setal spines opposite the upper inside margin of the eye mark the vertical limits of cari- nae which form the outside margins of crescent-shaped con cave areas. There is also a median inverted V-shaped concavity, just above the pseudolabrum on fresh pupae, The sculpture of the head varies with the age of the pupa. Anterior and middle femora with two setae of unequal size on small papillae, Elytral pads rugose, The pupa becomes pigmented as it matures; the eyes and mandibles become red-brown; wing pads dusky; the area around the mouth parts shows faint chitinization; later the face, legs, prothorax, and elytral pads assume a faint brownish tinge. The size varies considerably, typically 2.5 mm. to 2,7 mm, long by 1,1 mm. wide. The pupa is found in a chamber at die end of the larval mine inside of the clover root.
Negley (1953) gives photographs showing the pupa at different
ages.
Rate of Development
Rockwood (1926) found that the pupal period was shorter
in the summer than in the fall. This difference was probably due
to temperature. In Oregon the pupal period varied from ID days in
mid-August to 12 or 13 days in late September. Webster and Mally,
according to Rockwood, recorded a pupal period of 7 to 11 days in
. Ohio; Rockwood says that Parker noted a pupal period of 7 or 8 days
in August 1916 at Hagerstown, Maryland; and Stivers (1952) reported
it as 6 to 7 days in the laboratory in Pennsylvania. Newsom (19U8) U6
found that the pupal period varied from five to lU days with an
average of 11 days in 19U2 and from 7 to 20 days with a mean of
13 in 19U6 in New York. The difference can probably be attributed
to the fact that pupation occurred about two weeks later in 19^6
and weather was cooler.
Natural Enemies
^ery few natural enemies of the pupa are known and these are
the same as listed for larvae,
SEASONAL HISTORY
Weekly samples of red clover roots were taken during the sum
mers of 195k to 1956, inclusive, and dissected to determine the
number aid stages of borers present. Thhsedata are summarized in
Table 10 and presented graphically in Figure 5.
Rate of development was almost identical in 195k and 1955,
In 1956 ill stages of development were about three weeks later,
. Samples in 19SU were from Mammoth clover while the other two sea
son's data were from common red clover.
Extreme dates for the various stages in Ohio are summarized
in Table 11 and Figure 6.
More than 95 per cent of all overwintering borers in Ohio are
adults, ^exy few larvae overwinter. These transform to pupae U7
Table 10. Suimary of seasonal development of clover root borer. Wooster, Ohio. 195U-1956. Figures are per cent of borers in sample in indicated stage of growth. ——r't-.. . .. Date^/ 195ii 1955 L956 A E L p NA A E L P NA A E LP NA
May 3 100 0 0 0 0 May 11 86 U 4 0 0 0 May 17 38 62 0 0 0 May 2h 32 66 2 0 0 80 20 0 0 0 May 30 11 70 19 0 0
June 5 2it 32 hk 0 0 June 12 20 31 h9 0 0 75 25 0 0 0 June 19 m 17 69 0 0 15 85 0 0 0 June 27 5 8 87 0 0 7 13 80 0 0 5o 5o 0 0 0
July 5 h k 92 0 0 5 32 80 3 0 25 5o 25 0 0 July 11 31 6 83 T 0 3 5 83 9 T 19 50 31 0 0 July 18 8 3 80 9 0 h 6 73 12 5 22 11 67 0 0 July 25 32 1 75 9 3 2 5 7k 11 8 lk 32:5U 0 0 Aug, 1 5 0 65 16 lit 3 5 66 19 7 2 37 61 0 0 Aug. 9 6 0 70 15 Q✓ 2 2 66 18 32 Aug, 16 2 0 28 1*0 30 2 1 68 17 12 Aug* 23 1 0 9 35 55 1 0 29 3k 36 Aug. 30 2 0 20 5 73 0 0 26 15 59
Sept. 5 1 0 13 3 83 0 0 22 7 71 0 0 66 27 7 Sept. 13 0 0 U 3 93 Sept. 21 0 0 1 2 97 0 0 16 29 55
2/ Approximate A ■ Adult, E ■ Egg, L » Larva, P - Pupa, NA “ Hew Mult, T * Trace
during May or early June as shown in Figure 8. Negley (1953) re ported a few borers overwintering as pupae in Pennsylvania but other authors have never observed borers overwintering in this stage. too OLD FIELD 1954 1955 80 OU) 60 A0ULT- ADULT
40
20
z O i— 100 < _! NEW FIELD D 1955 oCL 80 LARVA CL
ADULT
20 - F- Z Ul A O 0 u 100' a. 80- 1956
60 — t / EGG
ADULT,
5/3 6/7 7/5 8/2 9/6 DATE Fig. Seasons! history of the clover root borer at Wooster, Ohio in !9$h to 1956, inclusive. h9
LARVAE
PUPAE
NEW ADULTS 1954
5/3 5J24. 6/14 7/5 7/26 6/16 3 S 9-27 DATE Fig, 6.-£rtrene and peak dates for different stages in the life cycle of the clover root borer in Ohio. ?0
Table 11. Earliest, latest and peak dates for various stages in life history of clover root borer in Ohio.
Stage Location Year Dates Earliest Latest Maximum
Egg Wooster 19?U July 26 Carroll Co. 19SU Aug. 18 Wooster 195? May 3 Aug. 16 May 2U-30 Wooster 1956 May 23 Aug. 22 June 19 Grafton 19?6 Sept. ?
Larva Wooster 19?U July 6 Wooster 1955 May 2k July 5-19 Wooster 1956 July 1 Aug. Ill
Pupa Lorain Co. 195U July 13 Wooster 19SU July 19 Aug. 16 Wooster 195? June 20 Aug. 23 Wooster 19?6 July 30 Sept. ll«2li
Adult Wooster 195U July 26 Wooster 19?? July 12 Wooster 1956 Sept. U
NUMBER OF GENERATIONS
Hopkins and Rumsey (1896) state that there are probably two or three generations a year in the United States. However all authors who have studied the species are unanimous in their opinion that there is but one generation.
In Europe there has been some difference of opinion on the number of generations. All except BelGuercio (191?) who concluded there were three generations, agree that there is but one generation 51
on red clover. However other authors who studied the life history
in furze and Scotch broom report two or three generations* Chapman
(186?) and DelGuercio (1915) have made such reports. However there
is some question as to whether this is the same species. DelGuercio
(1915) believed that the form breeding in Cytisus alpinus repre
sented a different biological race* However recent European tax
onomists have found no morphological differences in these forms.
Therefore we must either conclude that the root borer has
an entirely different life history and behavior in different hosts
or that two or more species are being confused under the name
Bylastimis obscurus.
HOST PLANTS
Red clover, Trifolium pratense L., is by far the most im
portant host of the clover root borer. Nevertheless this fact remained in doubt for almost 80 years after the original descrip
tion of the insect.
Mueller (1807) studied the root borer in 1803 when a serious infestation occurred near Mainz. Schmitt (18U1*) and Bach (18U9) also recognized red clover as the true host of the species.
Chapman (1869) published an account of this species and states that red clover is rarely attacked and questions the ability of H. obscurus to reproduce on this host. He concluded that furze, Ulex enropaecs, and Scotch broom, Cytisus scoparius, were the normal 52 hosts.
As late as lfi?6 Perris stated that H, trifolii Mueller was surely a misnomer as he had never found this species on clover.
Bedel (1876) refuted this statement and listed three hosts, of which I. pratense was preferred.
DelGuercio (1915) found H. obscurus breeding in both red clover and Cytisus laburnum but decided that two biological races were involved,
A list of recorded hosts and authorities for these records is given in Table 12. In many cases only adults have been col lected and reproduction is questionable* These cases are indi cated by a question mark under the heading "Reproduction".
Sob® of the European records could possibly refer to Byiastinus fankhauseri Reitter but Rockwood (1926) retains these, following the published lists of noted European taxonomists such as Bedel
(1876) and Eichoff (1881). Kleine (1935) who is an authority on the Scolytidae includes most of these hosts in his list*
In Ohio, field collections have been made from red, mammoth, and alsike clover with reproduction occurring in all three al though populations were light in the few fields of alsike examined.
Adults are commonly swept from alfalfa in the spring but none have been observed tunneling in the roots in the fields However, adults tunneled freely in pieces of alfalfa roots in the lab oratory when other plant material was unavailable. Therefore, it Table 12. List of host plants for the clover root borer. Common Name Scientific Name Repro References duction Red Clover Trifolium pratanse L. Yes Mueller (1807), Schmitt (I8kk), Bach (18k9)» Bedel (1876), Rockwood (1926), Kleine (193*0 Alsike clover Trifolium hybridum L. Yes Folsom (1909), Rockwood (1926), Kleine (193k) Crimson Clover Trifolium incarnatum L, Yes USDA (1939), Armitage (1953) Mammoth Glover Trii? olium medium L. Yes Rockwood (1926), Kleine (193k) White Dutch Clover Trifolium r'epens L. ? Swaine (1918) Spariium junceum L. * 9» Reitter (1916) Scotch Broom Cytisus scoparius (L.) Yes Chapman (1869), Nordlinger (1869), Bedel (1876), Kleine (193k) Cytisus nigricans L, Yes Kleine (193k) Cytisus laburnum L. Yes DelGuercio (1915), Kleine (193k) Cytisus alpinus Mill. Yes Cecconi (1899) Ononis natrfic li# 9• Bedel (1876), Kleine (193k) Furze Ulex europaeus L. Yes Chapman (I869), Kleine (193k) Alfalfa Medicago’ sativa L* Yes Kaltenbach (187k), Gibson (1913), Vasailiev (1913), Folsom (1909). Rockwood (1926), Knowlton (1939) Sweet Clover Melilotus officinalis (L.) No Chamberlin (1939) Meliiotus alba i^esr. No Chamberlin (1939) Sanfoin Qnobryehis sativa Lam. No Swaine (1918) Common Vetch Vicia sp. ? Rockwood (1926), Dickason & Every (1955) Austrian Winter jK'sum arvense (L,) ? USDA (1936) Field Peas Garden Peas Pi sum sativum L. ? Webster (1899), Rockwood (1926), Dick ason & Every (1955) Beans Phaseolus vulgare L. No Chamberlin (1939) Lupine Lupinus sp. No Rockwood (1926) seems possible that borers might breed in alfalfa in the absence
of other hosts*
VARIETAL RESISTANCE OF CLOVER TO ROOT BORER
There is little evidence that any commercial variety of red
clover is resistant to clover root borer. Stivers (1952) sampled
red clover variety plots in Pennsylvania and found Craig and
Mammoth Commercial to have fewer borers per root than other va rieties. Negley (1953) also found few borers in Craig but
commented that roots of this variety were small. Newsom (191*8) has shown that large roots in general contain more borers.
Lincoln (19Ul) thought that resistance was the most practical approach to borer control. Gyrisco and Marshall (19U9) state that of 30 varieties tested, no highly resistant varieties were found.
App (1953) found Cumberland to have considerably higher popula tions than Kenland or Van Fossen in Ohio.
During 1955 and 1956 red clover variety plots were sampled at three locations in Ohio. The results of these samplings are shown in Table 13* A statistical analysis of the five varieties present in all tests failed to show any significant differences as indicated in Table 13. In 1956, the crown diameter was measured on each plant as an indication of root size. An analysis of covariance of the Wooster data is given in Table lh. Again the
F value indicated there were no significant differences between 55 varieties.
Table 13. Mean number of borers per root in five varieties of red clover. Variety Year and Location Mean Stev. Doll. Penn. Midi. Kenl.
1955 Hoytville 1.1*0 0.95 1.15 1.60 1.30 1.28 Mahoning Co, 3.60 1.75 2.55 2.30 2.75 2.59 Mean 2.50 1.35 1.85 1.95 2,02 1.9U 1956 Hoytville 0.90 0.55 0.85 1.00 0.65 0.79 Mahoning Co, 1.60 0.30 0.90 1.1*5 0.75 1.00 Wooster 1.60 1.55 2.20 1.15 3.05 1.91 Mean 1.37 0,80 1.32 1.20 1.1*8 1.23
Grand Mean 1.82 1.02 1.53 i.5 o 1.70 1.51
Analysis of Variance Source of Degrees Mean Variation Freedom Square F Total 1*9 Variety 1* 93.25 1,90 Reps 9 1*55.30 9.25** Error 36 1*9.20
Negley (1953) found that survival of Cumberland, Kenland and
Pennscott was greatest in August while stands of Mammoth and Craig were poor at this tajae. The variety trial at Wooster was rated on September h, 1956 with the results given in Table li*. Of the twelve varieties given in Table ll*, best stands of Stevens were noted while Mammoth was poorest. These seemed to be little re lationship between stand and borer populations. 56
Table llu Summary of root borer populations in red clover varie ties. Wooster, Ohio. 1956. Borers Mean Borers per Standi/ Variety Per Root Crown 10 mm. Rating Diameter (mm.) LaSalle 2.15 12 Mo 1.73 1.50
Bollard 1.55 11.75 1.32 1.75
Kenland 3.05 12.50 2.1*1* 2.75
Stevens 1.60 11.20 1.1*3 3.75
Midland 1.15 10.90 1.06 1.50
Wise. Syn. 1.1*0 11.75 1.19 3.00
Van Atta 0.85 10.80 0.79 3.00
Mammoth l.5o 12.80 1.17 0,25
Purdue 2.15 11.55 1,86 1.50
Van Fossen 2.55 11.60 2.20 2.00
Libel 1.25 10.70 1.17 1.00
Pennscott 2.20 11.60 1.90 3.00
1/ Rating of 1* best; 0 Worst
Analysis of Covariance <3 l Source of Degrees Sum of Squares Errors O Variation rreeaam Sxy Sy2 SS DF MS Total 1*7 2075.7 181*1.6 3U96.0 Variety 11 1*50.7 272.6 502.8 Block 1 52.1 15.6 ii.7 Date 1 30.1 29.3 28.5 Error 3k 151*2.8 152U.1 2960.0 11*51*.1* 33 1*1*.07 Variety + Error US 1993.5 1796.7 3U62.8 181*3. 5 1*1* Difference 389.1 11 35.37 F - 35.37/1*1*.07 » 0.80 DAMAGE
Root borer damage is not usually noted until after the first
cutting. At this time heavily infested plants may fail to grow
back. Rockwood (1926) describes wilting of small plants in May
caused by feeding of adults. Such injury has not been observed
in Ohio. By the time of the second cutting general wilting and
often death of entire plants is noted. Sometimes dead stems will remain bat as the tunneled root decays, these usually fall over and rot also. Often at the time of the second cutting few living plants are present.
Although many authors, including G os sard (1911), Folsom (19096),
Westgate and Hillman (1915) and others, have stated that seed yields are greatly reduced, others such as App (1953) have failed to obtain increases in seed yields by controlling the borer. The amount of seed reduction apparently depends on how late in the season plants are killed.
In most areas of the United States little clover survives into a second harvest year. While the clover root borer is the princi pal cause of death in some areas, in others, especially in the more southern parts of the red clover belt, diseases are largely responsible. Several authors, including Pennsylvania (19U8),
Manis and Portman (1950), Carnahan and Hanson (1951), and Elliott
(1953) have hypothesized that the root borer is largely responsible 58 for dissemination of disease organisms. Others such as Hegley
(1953) and App (1953) have found no relationship between root borer and disease damage* Koehler (1957) has isolated disease organisms from .root borers but has no data on the role of the borer in dissemination of these organisms.
Surface (1912) and other authors state that seedling clover is not injured. Rockwood (1926) however gives several instances of injury to red clover in the seedling year.
Effect of Moisture on Damage
Many authors have stated that injury is more severe in dry seasons* In the absence of root borers, red clover produces much greater second cuttings in wet years. As some data is available which indicates that reproduction is greater and development more rapid in weakened plants, this would seem to be a reasonable statement as made by Mueller (1807), Folsom (1909), DuPorte (19lU) and Rockwood (1926).
To test the effects of water on red clover yields and root borer damage, the following experiment was designed. Eighty glazed pots were buried to their rims at Wooster, Ohio; filled with a sandy soil; and shelters constructed over them to keep out rain but permit free wind movement and light penetration. These structures were about 2k inches wide and 18 inches high. % e top 59 was covered with celloglass.
In 1955 two first harvest year Kenland red clover plants were set in each pot in April, Plants were watered twice weekly with amounts equivalent to 1, 2, k, and 6 inches per month, For each moisture level, half of the pots were treated with dieldrin at two pounds per acre while adult root borers were released in the other half. This gave a total of eight treatments with 10 repli cates each.
Three cuttings of hay were made in 1955, these being on
June 2, July 18, and August 25. ' Both green and dry weight were taken of each pot at each cutting. Dry weight data are summarized in Table 1$ and the analysis of variance given in Table 16. Green weight yields gave essentially the same results and are not re ported here.
A similar experiment was conducted in 1956, Four plants per pot were reset September 12, 1955 and allowed to become well established before roofing on April 18, 1956, In 1956 plants were watered at f-, 1, 2, and h inches per month. Unfortunately driving rains obscured most moisture effects during the first two cuttings made on June 12 and July 2l*. A third cutting was made on September
12. These data are summarized in Tables 17 and 18.
The presence of root borers caused reduction in yield in all three cuttings. In neither year was the interaction between Table 15. Dry matter yields in grams of red clover subjected to clover root borer attack under different levels of monthly rainfall. Wooster, Ohio. 1955. • Rainfall in Inches per Month Gutting Total Cutting 2 k 6 Total With No With No With No With No With No Borers Borers Borers Borers Borers Borers Borers Borers Borers Borers
First 90 115 129 166 201 260 262 290 682 831 1513
| —» | O Second vn. 2 k9 207 375 302 U31 2 99 U52 958 1507 2U65
Third 31 7k h$ 9k 53 106 1*9 103 178 377 555
Totals 271 U38 381 635 556 797 610 8U5 1816 2715 U533
Rainfall Totals 709 1DDS 1353 1U55 61
Table 16. Analysis of variance of clover yields as given in Table 1$.
Factor Sum of Degrees Mean F Squares Freedom Square Total i*6028 239 Replicates 23h5 9 261.6 Water 5759 3 1919.7 i*7.U0** Borers 3353 1 3353.0 82.79** Cutting 22801 2 nUoo.5 281.U9** B X W 76 3 25.3 0.62 B X C 1187 2 593.5 lU .65** W X C 203U 6 339.0 8.37** B X W X C 99 6 16.5 O.Ul Error 837U 207 Uo.5
■a* Significant at 0*01
borers and moisture significant. However, in 1956 the second order
interaction was significant and indicated that yield reductions
were increased in the two low moisture levels at the time of the
third cutting as compared to the previous cuttings#
Although large yield reductions were noted in the borer in
fested pots, damage was but little greater in dry conditions despite the fact that more borers were present in the low moisture levels as shown in Table 6. Table 19 summarizes the yield re ductions. These percentage losses seem quite high and must be due
to the combined action of a number of insect pests. Table 17. Dry matter yields in grams of red clover subjected to clover root borer attack under different levels of monthly rainfall, Wooster, Ohio. 1956. Rainfall in Inches Per Month Total Cutting Cutting ^ i______£______It______Total With No With No with No With No With No Borers Borers Borers Borers Borers Borers Borers Borers Borers Borers
First 371* 1*01 337 397 269 1*09 279 358 1259 1565 2821*
Second 256 266 191 281* 171 287 210 282 828 1119 191*7
Third 1*5 52 36 88 14* 67 71* 111 199 318 517
Totals 675 719 561* 769 1*81* 763 563 751 2286 3002 5288
Rainfall Totals 139k 1333 121+7 1311* Table 18, dialysis of variance of clover yields as given in Table 17.
Factor Sum of Degrees Mean F Squares Freedom Square
Total 57600 239 Replicates 2017 9 221.1 Borers 2136 1 2136,0 27.28** Water 181 3 61.3 0.78 Cutting 33901 2 16950.5 236.18** B I W 183 3 161.0 2.06 B X C 270 2 135.0 1.72 W X c 708 6 118.0 i.5i B X W X C 1683 6 280.5 3.58** Error 16218 207 78.3
*•* Significant at 0,01
Table 19. Summary of yield reductions attributed to clover root borer under different levels of monthly rainfall. Wooster, Ohio. 1955 and 1956.
Rainfall in Inches and Per Cent Tear Cutting Reduction in Yield Mean i 1 2 1 6
1955 First 21.8 22.3 22.7 9.7 18.0 Second 39.8 11.8 30.9 33.8 36.1 Third 58.1 52.1 50.0 52.1 52.8 Mean 38.1 lo.o 30.2 27.8 33.0
1956 First 9.3 15.1 31.2 22.1 19.6 Second 3.8 32.7 10.1 25.5 26.0 Third 13.5 59.1 31.3 33.3 37.1 Mean 6.1 26.7 36.6 25.0 23.9 6k
ESTIMATION OF YIEID REDUCTION
Estimates of insect damage are usually difficult to make with any great degree of accuracy. Often damage is estimated by the increase in yield due to the control of that particular insect.
However, numerous other insects also damage red clover and it is difficult to control the clover root borer without controlling at least some of these other insects. Perhaps the best method of estimating damage, therefore, is to determine the effect of root borers on individual plants in untreated plots, assuming that the presence of the root barer is independent of the presence of other factors reducing red clover yields.
During a sampling study, 320 plants were dug in each of three red clover fields. The top of each plant was weighed, the diameter of the root measured at the crown, and the root dissected to de termine the number of borers present. larger rooted plants not only tended to weigh more but also had more borers on the average.
Thus it was not surprising to find that the average weight of uninfested plants was slightly less than that for plants which contained root borers. Let's look briefly at these relationships between borers, crown diameter and weight in one of these fields.
The following examples apply to field 1.
If we consider only those plants that were free of borers we find that the correlation coefficient between weight and crown 65 diameter is 0.8032. ^irvilinear regression improves this rela tionship (R * 0.8093), but a third degree curve shows no further reduction in sums of squares due to deviations from regression
(R " 0.8093). This analysis is given in Table 20.
Table 20. Test of departure from linear regression. Regression of weight on crown diameter. Field 1, Wooster, Ohio. 1956.
Source of Degrees Sum of Mean F Variation Freedom Squares Square Deviations from linear regression 160 110.5372 Deviations from curved regression 159 107.U8U8 0.6760 Curvilinearity of regression 1 3.0521* 3.0521* 1*.52*
* Significant at 0.05
Correlation of crown diameter and borers yielded r ■ 0.271*0 which is significant at 0.01. A second degree curve gives R -
0.3072. A test similar to that given above shows a significant curvilinearity in the regression of borers on crown diameter#
The correlation between weight and borers was not significant.
However, to estimate the actual effect of borers on weight, we must also consider the effects of crown diameter on weight and borers. Since these latter relationships were both shown to be curvilinear it appears best to include yet another variable, the square of crown diameter. Now we have a multiple regression 66
problem with four variables.
A summary of the calculations is given in Table 21 andcom
putation of the Gauss multipliers, following the method given by
Snedecor (191*6), is given in Table 22.
The Gauss multipliers are used to calculate the regression
coefficients:
byl. 23 “ cn sxiy * c128x2y * c13sx3y ' 1,31,05
V .1 3 ' C12,xly + “a z 'V * c32sX3y ' °-2010
by3.12 ’ c13sxiy * c23sX2y * C3 3 V ’ -1*671*7 2 The sum of squares attributable to regression, s* ■ tyi#23sx-jy
* V.13ax2y * by3.12V ’ l^SOl.0 6 . 2 The sum of squares of deviations from regression, Sd^
- ay2 - S/ • «**>•*> sy.l232 ■ “ y . ^ - 1- • 257-82i sy.X23 - 16.057 where d.f. - N - 3 - 317.
The multiple correlation coefficient, R » /(S-^/S .^) * 0.761*1*. y y The standard deviations of the regression coefficients;
®byl.23 " sy.l23/cH " 1-5118
Sby2.13 ’ Sy.l23/c22 “ 0*°5"
\ 3 . 1 2 " 3y.l23^°33 “ Thus it appears that the clover root borer has indeed re
duced yields, the reduction in yield per plant caused by each borer being 1.67U7 * 0.8028 grams. 67
Table 21. Computation of correlation coefficients among four measurements on red clover plants.
Crown Crown Diameter Diameter Borers Weight N - 320 Squared xx x3 Y *2 Sum 3U50.0 U0223.0 U78.0 10720.0 Mean 10.7812 125.6969 1.U938 33.5000 1. SX2, etc. 1;0223.0 50792U.0 5782.0 133U55.0 2. Correction 37195.3 U3365U.2 5153.U 115575.0 3. S 2. etc. 3027.7 7U269.8 628.6 17880.0 U. /S* , etc. 55.02 75751.0 2293.8 2U356.8 5. r12i *13 > ryl 0.9801; 0.27l;0 0 .731a
*2 !• SX2, etc. 695llUil;.0 738U1.0 1803607.0 2. Correction 5055905.1; 60083.1 13U7U70.5 3. S^2. etc. 1895538.6 13757.9 1;56136.5 h. etc. 1376.79 57398.1; 609U91.2 5. r23> ry2 0.2397 0.7U8U X3 1. SX2, etc. 2U52.0 16700.0 2. Correction 71l;.0 16013.0 3. Sjc2 . etc. 1738.0 66770 U. n c j etc. Ul.69 18U55.7 5. ry3 0.0372 Y 1. SI2 555092.0 2. Correction 359120.0 3* 195972.0 U. 10*2.69 5. 21;. 786
If we eliminate the variable (square of crown diameter) from our multiple regression we find that our estimate of the re gression of weight on borers, independent of crown diameter, is not greatly affected. Here we obtain by^ * 1*8816 * 0.8021;. Table 22, Calculation of multipliers for red clover data of Table 21 Coefficients of Solution Number Line Directions 1 2 C1 c2 c3 3 1) Copy from lines 3027.7 71*269.8 628,6 1.0 0.0 0.0 2) no. 3, Table 21 71*269,8 1895538.6 13757.9 0.0 1.0 0.0 3) 628.6 13757.9 1738.0 0.0 0,0 1.0
( li) Divide (l)/628.6 1*. 816577 118.151129 1.00000 .00159081* 0.0 0.0 ( 5) Divide (2)/l3757»9 5.398338 137.778193 1.00000 0.0 .00007269 0.0 ( 6) Divide (3)/l738.0 0.361680 7.915938 1.00000 0.0 0.0 .00057537
( 7) 00 - (5) -0.581761 -19.627061* 0.00000 .00159081* -.00007269 0.0 ( 8) (5) - (6) 5.036658 129.862255 0.00000 0.0 .00007269 -.00057537 ( 9) Divide (7)/l9.627 -0.02961*1 -1.000000 .00008105 -.00000370 0.0 (10) Divide (8)/l29.86 0.038785 1.000000 0.0 .00000056 -.000001*1*3 (11) (9) ♦ (10) 0.00911*1* .00008105 -.00000311* -.000001*1*3
(12) Divide (ll)/0.0091 C1 .00886371* -.00031*339 -.0001*81*1*7 (13) Substitute in (9) c2 -.00031*378 .00001388 .000011*36 (U*) Substitute ci & Cn c3 -.0001*81*05 .000011*02 .00063681* in (5) and (U) 69
Is this fourth variable then really necessary'.'1 Let’s look at
our multiple correlation coefficients. For three variables we
find R2 * 0.5680 and for four variables R2 * 0.58U3* Testing the
reduction in deviations from regression due to the fourth variable, we find that reduction to be highly significant as shown in
Table 23. Thus it appears appropriate to include this fourth variable.
Table 23* Test of significance of four variable regression. Field 1, Wooster, Ohio. 1956.
Source of Degrees Sum of Mean F Variation Freedom Squares Square
Deviations from three vari able regression 317 81*659.9 Deviations from four vari able regression 316 811*70.0 257.82 Deviations explained by- fourth variable 1 3189.0 3189.00 12.37**
•a* Significant at 0.01
Similar analyses were carried out for the other two fields with the results shown in Table 21*. From this data we can estimate how much damage other numbers of borers would cause in various sized plants. Figure 7 gives these estimates for the three fields. and ID borers in different sized plants for three fields. three for plants sized different in borers ID and Fig. 7.-Estimates cf yield reductions caused toy caused reductions yield cf 7.-Estimates Fig.
PER CENT REDUCTION IN YIELD SOI 20 10 - T IMTR N MM. IN DIAMETER N W O R C tO 8 T * T T T IL I FIELD IL 3 FIELD T 14 IL 2 FIELD T 16 T 20 ,2 > 5*3>2,1,
Table 2lu Summary of yield reductions caused by clover root borer in three red clover fields. Borers Mean Mean Estimated Per Field Per Crown Weight Mean Weight Cent Root Diameter Of Plants In Absence of Loss Root Borer
1 1.1*9 10.78 33.50 36.01 7.0
2 0.81* 3i*.3 3 110.37 112.93 2.3
3 1.26 9.56 28.20 28.97 2.7
CONTROL
Introduction
Various physical and chemical control measures have been uti
lised against the clover root borer. A brief chronological history
is given below.
1871 Xunstler Suggests sweeping with net in spring and digging up infested plants.
1882 Idntner Recommends plowing under infestfed fields and then applying gas-lime at 100 bushels per acre to kill any surviving borers.
188U lintner Suggests all farmers quit growing clover for three or four years.
189k Davis Nitrate of Soda, Muriate of Potash, and Kainit at one ton per acre failed to kill borers but injured clover.
189U McCarthy States that 50 to 75 bushels gas-lime per acre kills all borers but also plants.
1899 Webster Recommends plowing infested fields in summer to kill newly emerged adults# 72
1918 Crosby & Recommend high fertility, tiling, and short Leonard rotation.
19U2 Lincoln Paradichlorobenzene at 1000 lbs. per acre, applied before flight, acted as repellant. Napthalene at 2000 lbs. per acre prevented infestation. Oichlorethyletner showed promise as fumigant after roots infested.
I9h8 Newsom BHC and chlordaae at 2|- lbs* per acre as dusts gave good control.
19k9 Marshall et al, One application of BHC at 1-| lbs. per acre applied as dust at peak flight effective,
1950 App BHC and chlordane' applied as dusts in fall as effective as spring applications. Aldrin also goodj me thoxychlor, DDT aid. toxaphene ineffective.
1950 App & Everly Same results reported by App (1950).
1951 Horber Chlordane and BHC effective in Switzerland.
1952 Stivers Low dosages of aldrin. BHC and dieldrin (about \ lb. per acre) ineffective as sprays,
1952 Blackburn & Aldrin and lindane a t 1 lb. and BHC, dieldrin Stivers and toxaphene at 2 lbs. ineffective as sprays.
1952 Everly et al. Recommend 1^ lbs. BHC, 2 lbs. aldrin, or lbs, chlordane as dust or spray in either fall or spring.
1952 Lockwood & Infestation in California materially re Gammon duced by destruction of infested clover.
1953 App Aldrin, heptachlcr or BHC as dust in either fall or spring superior to sprays.
1953 Negley BHC, chlordane and dieldrin effective as sprays if properly timed.
195b- Gyrisco et al. Aldrin, dieldrin, isodrin, heptachlor, lin dane, and chlordaae effective. Masts more reliable than sprays. 73
195k Weaver Suggests 1^ lbs. aldrin or 1^ lbs. BHC applied at seeding time in bands in root zone*
1955 Weaver & Aldrin or BHC at 0.75 16, per acre applied Haynes at tLme of band seeding effective.
1956 App Heptachlor, aldrin and BHC as dusts in fall or spring effective* inconsistent results obtained with iprays.
1956 Woodside & BHC at 1 lb. as dust, spray, or granules Turner effective, Dieldrin, aldrin, endrin, iso- drin, and heptachlor also good.
Notable increases in second cutting hay yields resulting
from clover root borer control have been reported by Weaver and
Haynes (1955), App (1956), and Woodside and Turner (1956). Al
though Folsom (1909), Bossard (1911), and Westgate and Hillman
(1915) state that the root borer may seriously decrease seed
yields, App (1953) found no increases attributable to root borer
control.
Control Experiments
Weaver and Haynes (1955) report on a method of seeding in which insecticides are applied at seeding time in oats to control
the root borer a year later. This method, however, is not
sxdtable for seeding clover in wheat. Therefore an experiment was designed to test the effectiveness of surface applications of
aldrin in bands at the time of seeding in •wheat. Aldrin was ap plied at 3A anct li lbs, per acre on March 29, 1955 to 30 by 35 foot plots. An Oliver gear-driven seed box mounted on a wheel barrow frame and pushed by hand was used to apply the material which was formulated as 30/60 mesh granules. Each treatment was replicated four times in a randomized block design. Samples taken
August 15> 1956 indicated that surface applications applied a year earlier were effective for root borer control. The results of this test are presented in Table 25.
Table 25. Control of clover root borer by surface applications of aldrin at time of band seeding in wheat. Wooster, Ohio, 1956.
Rate of Borers Per Cent Application Per Root Control
0.75 lb. 0.35 7U.1
1.50 lb. 0.06 95.1*
Check 1.1*8
Although several workers have obtained good results by ap plying dusts in the spring, only Woodside and ^urner (1956) report on the use of granules. As many farmers do not have suitable equipment for applying dusts, and because sprays are generally in effective, an experiment was designed to test the effectiveness of several insecticides when applied as granules. Nearly every farmer has a drill which can readily be adapted for applying insecticides in this fora. 75
Lindane, heptachlor, aldrin, and endrin were formulated as
2, 5, and 10 per cent granules on 30/60 mesh attaclay. These for
mulations were made by spraying the insecticide onto the granules
while mixing in a concrete mixer.
These four insecticides were applied to 21 by 21 foot plots
replicated four times. An Oliver grain box previously described
was used for application. The 2, 5, and 10 per cent materials
were applied at 50, 20, and 10 pounds per acre, respectively, on
April 25, 1956 at Grafton, Ohio.
On September 5, 1956, 10 roots were dug in each plot. The
results of this experiment are presented in Table 26. We can
conclude that 10 pounds per acre of 10 per cent insecticide is as
effective as 50 of two per cent in the case of all materials
tested. Heptachlor and aldrin, however, were slightly more ef
fective than lindane and endrin for clover root borer control.
Counts of spittlebugs and lesser clover leaf weevils indi
cated that good spittlebug control was obtained by all insecti
cides and reductions of lesser clover leaf weevil were noted. Al
though one pound per acre is a higher dosage than is consaonly used for the meadow spittlebug, farmers could perhaps afford to
adopt this dosage if one treatment can be shown to control most forage insects. 76
Table 26. Control of clover root borer by one pound per acre of four different insecticides applied as granules in dif ferent amounts of carrier. Grafton, Ohio. 1956.
Borers Per Root and Pounds Per Insecticide Acre Carrier Mean 10 20 50
Endrin 0.18 0.12 0.25 0.18 Aldrin 0.02 0.02 0.00 0.02 Heptachlor 0.00 0.00 0.00 0.00 Lindane 0.22 0.10 0.1*5 0.26 Mean 0.11 0.06 0.18 Check ■ 1.1*9 Borers/Root
Analysis of Variance Source of Degrees Mean F Variation Freedom Square
Total 1*7 Insecticide 3 19.21* 5.99** Rate 2 5.1U 1.60 1 X 8 6 Ili.37 l*.i*8** Error 36 3.21
Residual Action of Soil Insecticides
Plots to which BHC and aldrin were applied at the time of band seeding of clover in 1952 and which controlled the root borer
the following year, were in red clover again in 1956. On August
3, 1956, 10 roots per plot were dug from these old treatments.
Results are given in Table 27.
We must conclude that none of these treatments were effective after four years.
4 77
Table 27. Borers per root in plots treated with aldrin and lindane in 19$2* Wooster, Ohio. 1956.
Rate of Borers per Root Application Aldrin Lindane
l A lb. 2.93 3.77
3/ii lb. 2.73 3.80
Check 3.20 U.13 PART II
EVALUATION OF CLOVER ROOT BORER POPULATIONS
INTRODUCTION
The evaluation of populations is an important part of most experiments on the ecology or control of an insect. If our data arete be subjected to statistical analysis, we must know not only the mechanics of our tests, but also design our experiment in such a way that these tests are applicable*
Probably the two most important statistical tests in ento mological research are the t and F tests. These are both founded on certain assumptions which must be fulfilled if they are to be correctly applied, and valid interpretations are to be derived from our data*
In the second part of this dissertation we will be primarily concerned with these assumptions and how they may be fulfilled,
This section will therefore consist of studies on root borer popu lations, embodying discussions on the mathematical distribution of counts, sampling procedures, and transformation and analysis of such data*
78 DISTRIBUTION OF ROOT BORER COUNTS
Distribution of Individual Root Counts
Introduction
One of the most important assumptions of both the t and F
tests is that our data is normally distributed or, if it is not*
that appropriate transformations be made. In most sampling data
the root is the sample unit and our analyses are based on the
number of borers per root.
While purely empirical distributions may be fitted to any
set of data, such methods contribute little to our understanding
of the factors affecting distributions and can be of value only
for those particular instances for which they are fitted. How
ever if we can find a mathematical rule which embraces those fac
tors determining the distribution of a species, then we have a
solid working basis aid ready reference for any later samplings
and analyses. It is our intent to investigate here those fre
quency distributions which appear applicable to root borer counts.
Three years sampling data were available for Ohio, including
extensive data from a state survey made in 19£U. Several sampling
studies gave additional information on the distribution of $ and
10 root samples as well as the distribution of borers in indi vidual roots* These data were supplemented with root counts sup-
79 80 plied by Dr. Ray T. Everly from Indiana, Mr. Carlton S. Koehler from New York, Mr. E. A. Dickason from Oregon, and Dr. A. M,
Woodside from Virginia whose assistance is gratefully acknow ledged.
Of the many frequency distributions which have been fitted to various insect counts, the poisson and negative binomial are the most familiar. In the absence of other information a normal dis tribution is often assumed. A brief glance at a typical distri bution as given in Table 28 indicates that neither the normal or poisson is applicable to these data. Calculation of the moments will confirm this observation.
It is noted that in the experiment shown in Table 28 there are many roots having no borers and a second mode apparently oc curring at about three borers per root. Such bimodality is not unusual in clover root borer counts# Most distributions also have a rather long tail, often more extreme than in the example given here#
Although not appearing especially apt in this example, the negative binomial was first fitted to this data and later compared with other distributions..
The Negative Binomial Distribution
The negative binomial is given by (q - p)"^ which on expansion gives q** (p/ Although k is always positive, it need not be integral. If k Is not an integer, certain problems arise in calculating the factorials which are best resolved by expressing the distribution as follows: (p/q)x xj f k Pearson (1930) gives tables of the Gamma function, Fisher (191+1) and Bliss (1953) discuss the efficiency of different methods of estimating k. In fitting all frequency distributions, k was estimated from the mean and variance of the original counts. However in a later section on sequential sampling another method was used and will be discussed there. Using data from Virginia given in Table 28, the method of fitting the negative binomial was as follows: Mean * kp * 1,1+933 Variance ■ kpq ■ 7,5367 q * kpq/kp “ 0.01+701 p « q - 1 - 1+.01+701 k - kp/p - 0.36899 Converting to logarithms, log q-k- - -0.2591+1 legl~( 1 ♦ k) ■ -0.05090 log He » 0.38208 log (p/q) • -0.09590 Then log P0 - -0.2591+1 - 0.71+059 - 1 leg Pi - -0.2591+1 + (-0.00090) - (0.38208) + (0.09090) - -0.78829 - 0.21171 - 1 E®eh succeeding term is conveniently computed from the pro ceeding by adding log (n - 1), subtracting log n, and adding 82 Table 28, Observed distribution of clover root borer and distri bution calculated by negative binomial. Virginia, Experiment l, 1951* (treated plots). Borers Observed Calculated frequency Contri Per Fre bution Root quency !°g Px antilog Calculated to X2 Px Frequency 0 199 0.7U059 - 1 0.5503 165.1 6.96 1 12 0.21171 - 1 0.1628 i48.6 27.75 21 17 0.95118 - 2 0.0895 26.8 3.58 3 23 0.75273 - 2 0.0566 17.0 2.12 k 10 0.58227 - 2 0.0382 11.5 0.20 5 11 0.1*2778 - 2 0.0268 8.0 1.12 6 6 0.28362 - 2 0.0192 5.8 0.01 7 7 0.11*669 - 2 0.011*0 U,2) 3.03! 8 $ 0.01511 - 2 0 .010U 3.11 9 3 \ 10 3 11 0 12 0 0.0322 9.7 O.of 13 1 lb 2 13 1 1 300 1.0000 300.0 1*U.7B 2 Probability of X for 6 d.f, ■ log (p/q)• ^able 20 shows the observed distribution and summarizes the method of fitting and results. The high value of Chi-square indicates that the negative binomial gave an exceedingly poor fit in this case. However for some sets of data the observed values closely followed the expected. This case was chosen because it was useful in comparing other distributions which will be discussed shortly. 83 Neyman's Contagious distributions Neyman (1939) proposed a new class of distributions ap plicable to certain insect counts, ^eall and ^escia (19^3) showed that his distributions were only the first members of an infinite set of distributions and give methods for fitting these. These distributions are b ased on the assumption that egg groups are originally randomly distributed and that migration then occurs in a limited area* While not exactly agreeing in theory with root borer behavior, this distribution has been found to fit other data for which no apparent basis was obvious. Later workers have also interpreted the biological significance of these distributions in other ways* The general case of this distribution may be given by f(0) - nJt-mo-»)(e-°8 - S™ (-"g)3) s-0 81 One great disadvantage of this class of curves is that there is no efficient method of estimating the parameter n. However as n increases the proportion of zeros decreases and n may be rather efficiently estimated by fitting only the first one or two frequencies. It has been shown that a change in n has little effect on the tail frequencies. Fitting heyman * s distribution The fitting of this class of distributions for different 81* values of n will be illustrated using the same Virginia data previously fitted by the negative binomial. The parameters and nv, be estimated from the sample mean and variance, *or accurate fitting a larger number of decimal places than indicated here should be kept, Beall and Rescia (1953) recommend 9 places. One further note: for fitting these distributions our estimate of the variance, U2 ■ (x - x)- 2/N instead of dividing by N - 1 which is the usual procedure. Fitting the Virginia data for n * 1. the calculations pro ceed as follows: m2 ■ (n + 2)(u2 - u ^ / 2 ^ - 6.07051 mjL ■ (n + lHu-j^/nig - 0*1:9199 where u^ ■ 1,1*933 and-Ug “ 7*5367, f(0) - -0,161*73(0.00231 - 1) - 0.161*35 Fq - (mg * n)f(O) - a - (7.705D (0.161*35) - 1 - 0.16201* *1 " ((mo +n)2 + n)f(0) - nCtmp + n) + 1) - 50.99211(0.161*35) - 8.07051 “ 0,31001* Calculation of the recurrent coefficients is most conveniently done as shown in Table 29. Using the values obtained for m^F^. in the last column of Table 29, we can calculate the probabilities for each x. PQ » e"®lemlf^0^ - 0.66290 P1 " (lnlF0)P0 “ °*05285 P2 “ ((ralF0)Pl + (id1F1)P0)/2 " °*o528$ 85 P3 - ((ntLF0)P2 + (ni1F1)P1 + ( m ^ P ^ « 0.05267 etc. Table 29. Illustration of calculation of recurrent coefficients for fitting Neyman1s distribution for n * 1. (1) (2) (3) a ) (3) + Cl*) X *2 * n * x *0 + n + x _ ~jn2)n. p x ^ l l x - 2 *lFx 0 0.07972 1 0.15251* 2 9.07051 0.69181 -0.1*8391* 0.20787 3 10.07051 0.69779 -0.1*6300 0.23U79 k 11.07051 0.61*981 -0 .it 2062 0.22919 5 12.07051 0.55329 -0.35632 0.19697 6 13.07051 0.1*2908 -0.27826 0.15082 7 lit .07051 0.30316 -0.19928 0.10388 8 15.07051 0.19569 -0.13079 0.061*90 The expected value for each frequency is then simply calcu lated by multiplying N by the respective values of P^. The fitted distribution is given in Table 30. For the special c ases where n * 0 or n - do the calculations, though lengthy, are rather simple. Fitting Neymants Distribution for n *» 0 Fitting a curve to t he same d ata as in the preceeding section for n ■ 0 we need make only the following computations! F0 - » 0.07072; F± • - 0.28620; F? - 1*^/2 = 0.57913; F3 - *2*2 /3 - 0.78125; etc. Table 30. Summary of frequency distributions fitted to clover root borer data, Virginia, Experiment 1, 1932* (treated plots). Borers Observed Calculated Frequency jpQ£» Fro** — »■■■■■ I - — '■II^MIKI— ■■■ MU ■ i .l.ll ■ ■ ill - I I. I I —HU — ■.■■I ■■■ i . i. m . ii I - Root quency Negative Neyman______Double Poisson Binomial n . 0 n - 1 n^oo Method 1 Method 2 0 199 165*1 208.8 198.9 183.1 211.6 199.0 1 12 1*8.8 5.5 15.8 29.9 2.8? 32.0 2 17 26.8 ll.l 15.8 22.5 9.3) 23.1* 3 23 17.0 15.2 15.0 16.8 15.1 2U.3 U ID n.5 15.7 13.1* 12.5 1.8) 15.5 5 11 8.0 13.U 11.2 9.3 13.U> 7.0 6 6 5.8 9.9 8.8 6.9 9.0 3.0) 7 7 iu2 6.7 6.5 5.1 6.0 1.0 / 6 5 3.1 U.5 1*.6 3.8 2.2 0.2 ( 9* 10 9.7 9.2 10.0 10.1 28.8 lii.6) 300 300.0 300.0 300.0 300.0 300.0 300.0 X2 14u78 19. 1*6 7.09 17.75 38.70 10.56 PX2 <0.01 <0.01 0.22 <0.01 <0.01 0.06 8 7 The values and rrp, are calculated as in the proceeding sec tion but have new values because of the change in n, Were we find » 0.36899 and * i*.01*70. PQ . . - 4 .“l6'"2 . 0.6959 Calculation of the subsequent probabilities than proceeds as before. The results of this fitting are shown in Table 30* Fitting Nqyman’s Distribution for n ■> 00 The special case for n ^ o» is rather simple and the calcu lations for the same set of data as before is as follows: Calculate c - (112 - u-^/u^ ■ lw0U70 - 2 U;l/ c - 0.73798 r a ^ - (Uu1 )/(2 + c)2 - 0.16335 - ( 2 c / ( 2 + c))(m1F0) - 0 . 2 1 8 6 5 ®2*2 " (3/2)(c/(2 * O K r a ^ ) • 0 . 2 1 9 5 0 ; etc. P - eC"2* ! ^ 2 * c) 0 The subsequent probabilities are again calculated as for the general case with the results given in Table 30* Double Poisson One other distribution was investigated which showed some promise* This was the double poisson as proposed by Thomas (19U9). This distribution was originally designed to fit plant distribu 88 tions in which colonies arise from randomly dispersed plants. In the case of the clover root borer we would assume the original population of adult borers in the spring to be randomly distributed in the roots in the form of a poisson distribution and that the number of eggs laid in each gallery to be similarly distributed. The resultant distribution of borers may then be expressed in the following manner: P - .<£. trl)X' V r> x r«l rl (k - r)i For the 1951* data from Virginia (treated plots, experiment 1), the distribution was fitted as follows: The moments may be found from the theoretical relationship - m(l + h) - 1,1*933 ■ m(l + 3 A + X 2) - 7.5367 Expressing Tv, in terms of m we find Tv - (1,1*933 - m)/m and substituting this value in the first equation we obtain 2 m + 6,Ol*3Ura - 2,2299 ■ 0, Solving for m by the quadratic we obtain m ■ 0*3U89. Then \ *■ 3,2800. A second, and simpler method, is to estimate a and A from the frequencies of 0 and 1 borers per root where e""111 ■ n^/N * 0,66333 and me" « ti^/h q - 0,06031. Then a « 0,1*101*8 and \ •* 1,91801. Expaading the double poisson theorem we find 89 e + mi2e"" e e-21" e 21 P^ ■ me P^ « me etc. These probabilities are readily accumulated by converting to logarithms. The resulting distributions are given in Table 30. While fitting these data quite poorly these curves a re ©f interest for their possibility of showing pronounced multimodality and may fit other sets of data somewhat better. One biological factor of interest is that m should be an estimate of tne mean number of egg galleries per root and 1 + A, of the number of eggs per gallery. Summary of Frequency fiistributions Both the negative binomial and at least one of Neyraan’s curves were fitted to a number of sets of root borer data* The observed distributions and goodness of fit of the theoretical ones are summarized in the tables in Appendix I. The negative binomial, although approximating the observed values, failed to give a satisfactory fit in 9 instances. On the 90 other hand one or more of Neyman’s distributions gave a good fit in 22 of 26 cases* The few exceptions were not surprising since only a slight deviation from the theoretical distribution may be come significant if large samples are observed, as was the case here. Also, there was a strong likelihood that discordant dis tributions were combined in some instances. This possibility must always be considered when fitting one curve to data taken from several fields as was done with the Ohio survey data. Because either n ■ 0 or n oo fit most sets of data quite well, other values of n were not generally tried, While a ju dicious choice of n may have improved the fit somewhat in several cases, it was not considered worthwhile fitting these because of the computational problems. The important fact is that Neyman's contagious distributions, as extended by Beall and Rescia (1953), appear to be generally applicable to clover root borer data. Distribution of Sample Means It has been clearly shown that individual root counts of the clover root borer are not normally distributed and therefore that the usual statistical analyses are not valid. However, it is known that far many distributions which are not themselves normal that the distribution of sums, or means, of large samples taken from such populations are often normally distributed. Therefore 91 it was decided to investigate the distribution of borers in 5 and 10 root samples. Five Root Samples During a 1954 sampling study 256 sets of 5 roots each were dug. The distribution of the sums of these semples is shown in Table 31 as well as the distribution calculated by Neyman's dis tribution for n oo . Considering the irregularity, of the observed counts, we must admit that Neyman's distribution gave an excellent fit of these data. ,v Ten Boot Samples The same set of data just used to illustrate the distribution of borers in 5 root samples is also readily arranged as 128 samples of 10 roots each. These data were also excellently fitted by Ney- man’s distribution for n co as shown in Table 32. Conclusion We can only conclude that the sums, or means of 5 and 10 root sauries are not normally distributed but that they closely agree with Neyman's contagious distribution. Sufficient samples of larger size were unavailable to accurately study frequency distributions. However samples even as large as 20 roots still 92 appear to follow the same sort of distribution. Table 31* Observed distribution of borers in 5 root samples and dis tribution as calculated by Neyman’s distribution for n oo. Wooster, Ohio. 195U. Borers Borers In 5 Observed Calculated In 5 Observed Calcula ted Roots Roots 0 5 U.l 13 2k 12.2 1 6 6.U Ik 10 11.0 2 10 8.9 25 8 9.9 3 13 11.2 16 5 8.8 U 12 12.8 17 5 7.7 5 17 lh, 5 18 7 6.7 6 15 15.5 19 5 5.8 7 15 15.9 20 5 5.0 8 9 16.0 21 8 U.3) 9 15 15.7 22 3 3.6 / 10 9 15.1 23 3 3.o( 11 22 2h. 3 2h+ 16 lh.3 12 8 13.3 256 - 256.0 X2 - 28.61; Px2 “ 0.08 TRANSFORMATIONS Introduction Bartlett (1914.7) and Beall (19h2) discuss the transformation of entomological data so that statistical analyses are appropriate. The test most frequently used in entomological research is the F test* The use of this test assumes that certain assumptions are fulfilled. cochran (19h7) and Bisenhart (19U7) discuss these assumptions and the consequences if they are not fulfilled. 9 3 Table 32. Observed distribution of borers in 10 root samples and distribution calculated by Neyman1s distribution for n co • Wooster, Ohio. 195h» Borers Borers In 10 Observed Calculated In 10 Observed Calculated Roots Roots 0 0 0.1) 17 5 5.0 1 0 0.2 18 3 5.0) 2 1 o.U 19 2 5.0’ 3 0 0.7 20 3 U.9) h 2 1.0 21 2 U.8I 5 1 l.U 22 7 U.7 6 2 1.7 23 k U.5) 7 h 2.2^ 2h 5 U.3) 8 5 2.6) 25 5 lt.l / 9 3 3.0 26 7 3.9) 10 1 3.U 27 h 3.6) 11 k 3.7) 28 h 3.U) 12 2 U.O 29 6 3.2) 13 7 U.3 30 2 2.9i Ih 5 U.6 31+ 2h 25.8 15 2 h.7) US 6 128.0 X2 - 12.78j Px2 - 0.37 We have previously discussed the normality of distribution and shown that root borer data are not normally distributed. The sums of samples as large as 10 roots or more still depart from normality. A second assumption is that the mean and variance are inde pendent over the entire range of the mean. If this assumption can be fulfilled, -the assumption of normal distribution becomes less important. We shall therefore proceed to investigate the transformation of root counts to stabilise the variance. 9U Transforming Individuai Root Counts The mean and variances of samples from 103 fields taken daring a state survey in 195k were equated and a linear regression line fitted, ^ach sample consisted of about 30 roots although a few were as small as 15 or as large as U5. No adjustment was made for difference in size of sample in fitting the regression line. A second degree curve was also fitted to this data and gave a significantly better fit. Figure 8 is a scatter diagram showing these two fitted regression lines. Were this relationship linear, a square root transformation would, be suggested. However the variance became disproportion ately large as the mean increased. Nevertheless, this data was transformed by /(x + ^). The relationship between transformed mean and variance is shown in Figure 9. This transformation was unsatisfactory, as expected, with variance increasing with the mean. While no work has been done with transformations for counts agreeing with Neyman's distributions, log (x + 1) has been used when the variance is roughly proportional to the mean. Accordingly, the counts from these 103 fields were transformed in this way and the mean and variance again plotted as shown in Figure 10. ^ markedly curvilinear relationship resulted, with variance being VARIANCE wo 140 too 120 80 0 4 80 20 showing linear and curvilinear regression and lines.showing linear curvilinear regression Fig. 8.-Relationship of mean and variance of untransfomed 8.-Relationshipandof untransfomed of Fig.mean variance 2 EN UBR OES E ROOT PER BORERS NUMBER MEAN 3 5 10 6 74 8 14 9 individual root counts counts root individual I12 II 13 VARIANCE 2.2 2.0 1.2 4 - Fig,d.-Relationship of mean and varianceof individual root countstransformed by • • • • *• • • • • • • 1.6 MEAN 2.0 2.2 2.4 6 . 2 2.8 3.0 . 3.4 3.2 VARIANCE by logby (ac 1).+ Fig,IQ,-Relationship of mean and varianceof individual root countstransformed •I .2 ,4 .6 .8 MEAN 1.0 1.2 1.4 1.6 1.8 2-0 lowest for extremely low or high populations and highest for medium populations* Beall (l$*2) proposed an inverse hyperbolic sine transfor mation for negative binomial data and Beall and Rescia (19^3) suggest that this may be useful for counts agreeing with Neyman’s distributions. This transformation is given by x' ■ q^sinh^Cqx)^ and shades from a square root transformation at q * 0 to logrithmic at q 4 00. An estimate of the constant, q, may be obtained from the mean and variance of the original counts by the relationship Ug - u-^ ♦ qu-^ where x and s are used as estimates of u^ and Ug Beall (19^2) gives a good discussion on the estimation of q from field data. He also gives a table of this transformation which is partially reproduced in Table 33* It has also been extended here for q * 1,$ and q ■ 3«0 which appear to be useful values for root borer data. A common value of q was chosen (q ■ 1*0) and these 103 sam ples transformed. % e mean and variance were again plotted as shown in Figure II, The straight line regression was not sig nificant. However a second degree curve was highly significant and indicated that variance was highest for samples of inter mediate populations. However q decreases as the mean increases and was therefore inexactly applied over the entire range of the mean. Nevertheless this transformation did a good job of both 99 Table 33. Values of the inverse hyperbolic sine transformation as -given by Beall (19hZ) and extended for q ■ 1.5 and 3.0. q X 0.10 0.20 0.30 OJiO 0.50 0.60 0.80 1.00 1.50 3.00 0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1 0.98 0.97 0.96 0.9a 0.93 0.92 0.90 0.88 o.sa 0.76 2 1.37 1.33 1.30 1.27 1.25 1.22 1.18 1.15 1.08 0.9a 3 1.66 1.59 1. 5a 1.50 i.a 6 i.a2 1.37 1.32 1.22 1.05 a 1.89 1.80 1.73 1.67 1.62 1.58 1.50 i.aa 1.33 1.13 5 2.08 1.97 1.88 1.81 1.75 1.70 1.61 1. 5a i . a i 1.19 6 2.25 2.12 2.01 1.93 1.86 1.80 1.71 1.63 i.a? 1.2a 7 2. ill 2.25 2.13 2.oa 1.96 1.89 1.78 1.70 1. 5a 1.29 8 2. 5a 2.36 2.23 2.13 2.oa 1.97 1.85 1.76 1.60 1.32 9 2.67 2.a7 2.32 2.21 2.12 2.oa 1.92 1.82 1.6a 1.36 10 2.79 2.56 2.ao 2.28 2.18 2.10 1.97 1.87 1.68 1.39 11 2.89 2.65 2.a8 2.35 2.25 2.16 2.02 1.91 1.72 i . a i 12 3.00 2.73 2.55 2.a i 2.30 2.21 2.07 1.96 1.76 i.aa 13 3.09 2.81 2.62 2.a7 2.36 2.26 2.11 1.99 1.79 i.a6 1U 3.18 2.88 2.68 2.52 2j*0 2.31 2.15 2.03 1.82 1JU8 15 3.26 2.9a 2.73 2.57 2 .as 2.35 2.19 2.06 1.85 1.50 16 3.3a 3.01 2.7 9 2.62 2ji9 2.39 2.22 2.09 1.87 1.52 17 3.a2 3.07 2. 8a 2.67 2.53 2.a2 2*25 2.12 1.89 1.5a 18 3.a9 3.12 2.88 2.71 2.57 2.a6 2.28 2.15 1.92 1.55 19 3.56 3.18 2.93 2.75 2.61 2.a9 2.31 2.18 1.9a 1.57 20 3.62 3.23 2.97 2.79 2.6a 2.52 2.3a 2.20 1.96 1.59 21 3.69 3.28 3.01 2.82 2.68 2.56 2.37 2.23 1.98 1.60 22 3.75 3.32 3.05 2.86 2.71 2.58 2.39 2.25 2.00 1.61 23 3.81 3.37 3.09 2.89 2.7a 2.61 2*a2 2.27 2.02 1.62 2U 3.86 3 .a i 3.13 2.92 2.77 2. 6a 2.aa 2.29 2.03 1.6a 25 3.92 3.as 3.16 2.95 2.79 2.66 2.a6 2.31 2.05 i.6a 26 3.97 3.a9 3.20 2.98 2.82 2.69 2.a8 2.33 27 a.02 3.53 3.23 3.01 2.85 2.71 2.51 2.35 28 a. 07 3.57 3.26 3.0a 2.87 2.73 2.53 2.37 29 a.22 3.61 3.29 3.07 2.89 2.76 2.5a 2.39 30 a.16 3. 6a 3.32 3.09 2.92 2.78 2.56 2 J1O 100 Table 33• Continued. X q 0.10 0.20 0.30 0 .1*0 o .5g 0.60 6.80 1.00 31 1*.21 3.67 3.35 3.12 2.9U 2.80 2.58 2.1*2 32 1*.25 3.71 3.38 3.H* 2.96 2.82 2 .6o 2.1*3 33 i*.30 3.71* 3 .1*0 3.16 2.98 2.81* 2.62 2.1*5 3h i*.3l* 3.77 3.1*3 3.19 3.00 2.86 2.63 2.1*6 35 i*.38 3.80 3.U5 3.21 3.02 2.88 2.65 2 .1*8 36 I* .1*2 3.83 3 .1*8 3.23 3.01* 2.89 2.66 2.1*9 37 1*.1*6 3.86 3.50 3.2 5 3.06 2.91 2.68 2.51 38 1**1*9 3.89 3.53 3.27 3.08 2.93 2.69 2.52 3 9 1*.53 3.91 3.55 3.29 3.10 2.91* 2.71 2.53 1*0 1*.57 3.91* 3.57 3.31 3.12 2.96 2.72 2.51* la 1**60 3.97 3.59 3.33 3.13 2.98 2.73 2.56 1*2 1*.63 3.99 3.61 3.35 3.15 2.99 2.75 2.57 1*3 14.67 i*.02 3.63 3.37 3.17 3.01 2.76 2.58 1*1* 1*.70 l*.oU 3.65 3.39 3.18 3.02 2.77 2.59 1*5 1**73 1*.07 3.67 3.1*0 3.20 3.03 2.79 2.60 1*6 1**76 1*.09 3.69 3.1*2 3.21 3.05 2.80 2.61 1*7 1**80 i*.n 3.71 3.1*1* 3.23 3.06 2.81 2.62 1*8 1**83 1*.13 3.73 3.U5 3.21* 3.08 2.82 2.63 1*9 1**85 1*.16 3.75 3.1*7 3.26 3.09 2.83 2.61* 50 1**88 i*.l8 3.77 3.1*8 3.27 3.10 2.81* 2.65 55 5.02 1*.28 3.85 3.56 3.31* 3.16 2.90 2.70 60 5*15 1**37 3.93 3.62 3.1*0 3.22 2.9l* 2.71* 65 5*27 l*.i*6 1*.00 3.69 3.1*5 3.27 2.99 2.78 70 5.38 i*.5i* 1**07 3.7I* 3.50 3.32 3.03 2.82 75 5.1*8 I* .61 i*.13 3.80 3.55 3.36 3.07 2.86 80 5.57 i*.68 I*.19 3.85 3.60 3.1*0 3.10 2.89 85 5.66 U.75 l*.2l* 3.90 3.61* 3.1*1* 3.U* 2.92 90 5.75 1**81 1*.29 3.9l* 3.68 3.1*8 3.17 2.95 95 5 .83 i*.87 U*3U 3.98 3.72 3.51 3.20 2.97 100 5.91 1**93 l*.39 U.02 3.75 3.51* 3.23 3.00 reducing and stabilizing variance. In most cases data would not be available over such a wide range of the mean and this transforma tion should prove quite satisfactory. • • 08 04 00 .1 .2 .3 * 4 5 .6 .7 8 .9 1.0 MEAN Fig, 11,-Relationship of mean and variance of individual root counts transformed by inverse hyperbolic sine# Sat ligation of q. It may not ba necessary to calculate q. for each set of data but one may estimate it from the mean alone, Various values of q for transforming individual root counts were calculated from the curved regression line in Figure 8 and these data are plotted in Figure 12. The lines in Figure 12 for 5 and 10 root samples were calculated from the regression lines of Figures 13 and 14, respectively. Transformation of Multiple Boot Counts The regression of variance on means of 5 root counts was computed in the same manner as for individual root counts. These data were all obtained from sampling studies conducted in 1955 and 1956. Again there was a definite increase in variance of un transformed counts as the mean increased as shown in Figure 13. Curvilinearlty of regression was not apparent in this case. A simple logarithmic as well as inverse hyperbolic sine transforma tion was applied to the sums and the relationship of mean and variance again plotted as shown in Figure 15 for the logarithmic and Figure 16 for the inverse hyperbolic sine. While the logarithmic transformation showed no significant relationship between mean and variance, the inverse hyperbolic sine was again better from the standpoint of reducing variance. 103 I R O O T 5 ROOTS 2 3 4 5 6 7 BORERS PER ROOT Fig. 12 .-Estimates of q for 1, 3, and 10 root samples for different means for use in inverse hyperbolic sine transformation. loU Ui u ec- < cc 5 o BORERS PER 5 ROOTS ui 30- ! Ti 10 20 25 30 BORERS PER 10 ROOTS Fig. 13 * Relationship of mean. and variance of un trans formed five root samples (top)* Fig* lit.-Relationship of mean and variance of untrans formed ten root samples (bottom)* 105 Judicious choice of q in, this transformation is important as il lustrated by Figures 16 and 17. For q = 1, as shown in Figure 16, there was a definite linear relationship between the mean and vari ance while for the correct value of q * O.ii as computed from the sample means and variances, the mean and variance were but slightly- related as shown in Figure 17. Similar transformations were made for 10 root samples. Figure lit shows the relationship between mean and variance of the original samples, Figure 18 the same when transformed by log (x + l), 1 Figure 19 for x2, and Figure 20 for the inverse hyperbolic sine transformation for q « 0.3. It is noted that for samples of this size these three trans formations all tended to reduce and stabilize variance although scattering of points was much greater about the regression line for the log transformation. Work presented later indicates that these transformations lead to over-conservatism in interpreting data. However, if the inverse hyperbolic sine transformation is applied to the indi vidual root in all cases and the sum of these transformed values used, markedly different conclusions are often reached than when untransformed counts are analyzed. The same data used in preparing Figure lU was transformed as individual roots and the means and variances of the sums of 10 root samples calculated. This relationship is shown in 106 .24 .12- .60 .50 1.0 1.2 1.6 .8- 1.2 ZA 2.8 BORERS in 5 ROOTS Relationship of mean and variance of five root samples transformed, by log (x 4 1) (Fig. 15); by inverse hyperbolic sine, q * 1.0 (Fig. 16); and by inverse hyperbolic sine, q “ OJ* (Fig. 17). .2 4 -, 107 .22 18 .20 .16 .1 9- .14 .12-1 .00 r> t - ■■r* “I— T— T* ■■I11"1 .6 .7 1.0 1.1 1.2 1.3 1.4 1.5 3.0- 2. 0- 1.5- '2,0 2.5 3 .0 3 .5 5 .0 5,5 20 1.0 - . 6- .4- 2.0 2.a BORERS in I? ROOTS Relationship of mean and variance of 10 root samples trans formed by log (x + 1) (Fig. l8)j b y square root (Fig. 19); and by inverse hyperbolic sine (Fig. 20). 1 0 8 Figure 21. Here the mean and variance are unrelated* Figure 22 shows the relationship between transformed and untransformed means, ^he relationship is practically identical to that shown in Figure 23 for individual roots which is as we would expect* Conclusion The inverse hyperbolic sine transformation appears suitable for all root borer counts up to the sums of 10 roots. Log (x + 1) or appear equally suitable for the sums of 5 or 1 0 root samples but are inferior to the inverse hyperbolic sine transformation for individual root counts. It is suggested that for multiple root samples the number of borers in each individual root be transformed and then summed rather than transforming the sums themselves. VALUE OF TRANSFORMATIONS It has been adequately demonstrated that transformation of clover root borer counts, even of the sums of samples up to 10 roots in size, is appropriate. However the true measure of the value of a transformation is probably obtained by its effect on the interpretation of data* For this reason the inverse hyper bolic sine transformation was applied to several sets of actual 1 0 9 1.2 1.0 w .0 v 2 < AC < .6 > • • * • .4 .2 ■0 i .. . .2 .3 .4 .5 *6 .7 MEAN Fig* 21,-Relationship of mean and v a r i a n c e of ten root samp3.es when individual roots are transformed by inverse hyperbolic sine* I.O-i .8 *- O S g 2 .6 tc £ Ua I Pu. io to Z 4 a: < *^ u i tc ec |_ o to .2 0.5 1.0 1.5 2.0 2.5 3.0 BORERS PER ROOT- UNTRANSFORMED Fig, 22,-Relationship between transformed and untransformed means for ten root samples. borers per r o o t - transformed 2 2 1.4 . . 2-1 0 . 0-1 - root samples, Fig.23.-Relationship between transformedand untransformed meansfor individual • • 2 OES E RO - UNTRANSFORMED - ROOT PER BORERS 3 4 S 6 7 8 9 10 It 12 314 13 Ill data and the results of various statistical analyses compared with those for untransformed data. Effect on Additivity Cfcie of the assumptions of the analysis of variance is that the treatment effects are additive. Tukey (19U9) considers the fulfillment of this assumption as important a s normality or in dependence of mean and variance and gives a test for non-addi tivity. Several sets of root borer data were available which were suitable for testing by Tukey's method. These data and the analyses are presented in Tables 3k, 3$, 38, and 1*0, The method of calculating the sums of squares far the one degree of freedom for non-additivity is shown in Table 3km De viations of the replicate and treatment means from the grand mean are obtained. The sum of cross-products is obtained by multiplying the treatment totals for each replicate by the corresponding deviation of treatment mean from the grand mean and summing these for each replicate. Then we multiply each cross-product sum by the deviation in the same row and sum these. The sum of squares for non-additivity is now equal to (S(dev. I x-products))V((S rep. dev.^)(S row dev.^)) or, using figures in Table 62, SS for non-additivity * (133,88)^/((31.35) (6 .69 )) - 85,1*6. 122 The outstanding factor about the 1955 moisture experiment given in Table 3^ was the non-additivity. The inverse hyper bolic sine for q ■ 1,0 was applied to the as data and the trans formed data reanalyzed. Although the treatment effects were not shown to be different by either analysis, the transformation successfully eliminated the non-additivity effects as shown in Table 35. Table 3k• Tost for non-additivity, 1955 moisture experiment, Untransformed data. Rep. Treatment Sums Means Devia Sum of x- 1 2 3 it tions products 1 13 2 2 1 18 it.5o +I.it5 +23.00 2 3 1 1 0 5 1.25 - 1.80 + 5.U5 3 7 it 1 0 12 3.00 -0.05 +11.30 It 3 0 0 6 9 2.25 - 0.80 - 3.it5 5 0 0 2 2 it 1.00 -2.05 - 2.60 6 1 3 5 0 9 2.25 -0.80 + 1.25 7 2 0 5 3 10 2.50 -0*55 + o.5o 8 13 9 it 1 27 6.75 +3.70 +18,95 9 7 3 11 0 21 5.25 +2.20 +Hi.ii5 10 1 2 2 2 7 1.75 -1.30 - 1.95 Sum 50 2lt 33 15 122 0.00 +133.88 Mean 5.oo 2.1t0 3.30 i.5 o 3.05 31.35 Dev, +1.95 —0.65 +0.25 -1.55 0.00 6 ^ 9 85.ii6 Analysis of Variance Factor Degrees Mean F Freedom Square Total 39 Eeps. 9 13.93 1.91 Treat, 3 22.30 3.05 Sea-Add. 1 85.U6 11.69** Error 26 7.31 113 Table 35. Test for non-additivity. 1955 moisture experiment. Figures in Table 3U transformed by inverse hyperbolic sine transformation for k ■ 1,0. Factor Degrees Mean F Freedom Square Total 39 Reps. 9 0.326 0.87 Treat. 3 0.698 1.87 Non-Add. 1 0.831 2.22 Error 26 0.37U The 1956 moisture experiment showed no signs of non-additivity when the original, counts were analyzed. Also treatments were not found to be different as shown in Table 36. The inverse hyperbolic sine transformation for q * 1,0 was applied to this experiment with similar results as shown in Table 37. Table 36. Test for non-additivity. 1956 moisture experiment. Untransformed data. Factor Degrees Mean F Freedom Square Total 39 Reps. 9 18,27 3.26 Treat. 3 25.67 1.0? Non-Add. 1 27.25 1.13 Error 26 2iu01 Ill* Table 37. Test for non-additivity. 1956 moisture experiment. Inverse hyperbolic sine transformation applied to totals for q - 1.0. Factor Degrees Mean F Freedom Square Total 39 Heps. 9 0.1*98 l.ll* Treat. 3 1.281 2.93 Non-Add. 1 0.981 2.21* Error 26 0.1*37 Similar tests were applied to the two sets of control data with the results given in Tables 38 and 1*0., Transformation had no effect on the conclusions drawn from experiment 1 as shcam in Table 39* However in experiment 2> treatment effects becamei non- significant as shown in Table 1*1. In neither case were the origi nal treatment effects non-additive nee* did the transformation have any effects on additivity. Table 38* Test for non-additivity. Frye 909, experiment 1, 1955. Untransformed data. Factor Degrees Mean F Freedom Square Total 17 Herts. 2 12.0 0.35 Treat. 5 252.9 7.35** M an-Add * 1 27.9 0.81 Error 9 3U M 115 Table 39. Test for non-additivity. Frye 909, experiment 1, 1955* Inverse hyperbolic sine transformation applied to totals for q - 0,3. Factor Degrees Mean F Freedom Square Total 17 Reps. 2 0.12 0.23 Treat, 5 3JU0 6.5U** Non-Add, 1 1.65 3.17 Error 9 0.52 Table ItO. Test for non-additivity. Frye 909, experiment 2, 1955. Untransformed data. Factor Degrees Mean F Freedom Square Total m Reps. 2 11.25 0.itl Treat, h 236.25 8.58** Mon-Add, 1 7.20 0.26 Error 7 27.57 Table itl. Test for non-additivity. &rye 909, experiment 2, 1955. Inverse hyperbolic sine transformation applied to totals for q « O.ii. Total Degrees Mean F Freedom Square Total lit Reps. 2 0.18 0.19 Treat. it 1.72 1.81 Non-Add. 1 0.11 0.12 Error 7 0.95 116 Homogeneity of Variance Another assumption of the analysis of variance is that the experimental errors are homogeneous. Bartlett (1937) and Snedecor (19U6) give a test for homogeneity of variance. This test was applied to the four sets of data previously- used for tests of non-additivity. The method of calcuia ting the homogeneity Chi-square is shown in Table U2. The results of this test for the original data are compared with those for the transformed counts in Table U3. Table U2. Test for homogeneity of variance. Moisture experiment, 1955. On transformed data. Treatment 1 2 3 k St So 2k 33 15 SX2 i*60 12k 201 55 (SX)2/n 250.0 57.6 108.9 22.5 ax2 210.0 66 ,U 92.1 32.5 s2 23.33 7.38 10.23 3.61 log s2 1.3679 0.8681 1.0099 0.5575 Ss2 - hk.SS S log s2 * 3.803U —2 s2 « 11,138 log S “ I.0U68 n log s2 - I4..I872 S log s2 - 3.803U 0.3838 X2 - 2.3026(k - l)(n log s2 - S log »2 ) m 2.306(9X0.3828) - 7.9536 Correction - 1 *_(a + l)/((3n)(k - 1) “ l*0h63 Corrected X2 - X2/ Correction «■ 7,60 117 Table U3» Cocp&rison of homogeneity Chi-square for transformed and untransformed data. Transformed Experiment Untransformed Sums Individual Roots Moisture 1955 X2 7.60 o.5U ?x2 0.06 0.89 Moisture 1956 X2 6.56 1.55 0.66 V 0.09 Frye 909 (1) X2 7.06 5.15 2.06 0.22 V 0.37 0.83 Frye 909 (2) X2 3.33 U.77 1.U5 0.50 0.32 0.83 FI2 In no case was the Chi-square value for homogeneity of variance for un transformed counts significant although it was under "the 10 per cant level for the two moisture experiments* It is believed that larger samples would have shown it to be significant* The inverse hyperbolic sine transformation removed any doubts of non-homogeneity in all cases. Application of Inverse Hyperbolic Sine Transformation The inverse hyperbolic sine transformation appears to lead to overly conservative estimates of treatment effects when applied to 118 the sums of groups of root counts. This may be explained by the fact that the transformed values change less and less rapidly as the number of borers increases. Therefore, especially if counts are high, as was the case in the Frye 909 experiment 2 (Table UO), little difference between treatments is apparent after transforma tion. This fact suggests a solution to the problem. If instead of transforming the totals, we transform the individual root counts and them base our analyses on these sums for each replicate, we have what appears a much more realistic test. Using this technique, the data were again analyzed for the same four experiments. These analyses led to markedly different conclusions in several cases. In the 195# moisture experiment, treatment effects now be came significant. This transformation, however, did little towards eliminating non-additivity as shown in Table 3lU. Table Ul*. Test for non-additivity. Moisture experiment, 1955. Inverse hyperbolic sine transformation for q “ 1.0 ap plied to individual roots and analysis based on totals. Factor Degrees Mean F Freedom Square Total 39 Reps. 9 1.111 2.17 Treat, 3 1.635 3.19* Non-Add. 1 5.577 10.86*# Error 26 0.513 119 This transformation made no important changes in our inter pretation of the 1956 moisture data, all effects remaining non significant as shown in Table Table U5. Test for non-additivity. Moisture experiment, 1956. Inverse hyperbolic sine transformation for q - 3.0 applied to individual roots and analysis based on totals for four roots. Factor Degrees Mean F Freedom Square Total' 3 9 Reps. 9 1.575 1.51 Treat, 3 1.265 1.21 Non-Add. 1 0.113 0.11 Error 26 1 M For the two Frye 909 experiments the F values for treatment effects were considerably increased as shown in Tables U6 and 1*7. Other effects due to transformation were not noted. Table U6. Test for non-additivity. Frye 909> experiment 1, 1955. Inverse hyperbolic s ine transformation for q » 3.0 ap plied to individual roots and analysis based on totals of 10 root samples. ” ” " B .. .. " Factor egrees Mean F Freedom Square Total 17 Reps, 2 0.62 0.3U Treat. 5 2U.70 13.57** Non-Add. 1 0.12 0.07 0 Error / 1.82 120 Table 1*7. Test for non-additivity. Frye 909, experiment 2, 1955• Inverse hyperbolic sine transformation for q * 3*0 ap plied to individual roots and analysis based on totals of 10 root samples. Factor Degrees Mean F Freedom Square Total 31 Reps, 2 1.01 0.63 Treat. k 22.57 31.11#* Non-Add. 1 0.19 0.12 Error 7 1.60 The inverse hyperbolic sine transformation, when applied to individual roots, was extremely effective in stabilizing variance as indicated by homogeneity Chi-square values calculated for the two Frye experiments. These figures are included in Table k3* Other tests Data from two other tests Were available which were not suitable for the present tests of non-additivity or homogeneity of variance without some modifications. However, these data were transformed and an analysis carried out on the new variable in each case. The analysis of the aldrin band application data is given in Table h8 for untransformed and in Table U9 for transformed data. The F value was increased by transformation though being signifi cant at 0.01 even in the original analysis. 121 Table 1*8. Analysis of variance of aldrin band application test, 1956. Untransformed data. Factor Degrees Kean F Freedom Square Total 11 Treat. 2 21U.55 26.16#* Error 9 8.20 Table 1*9. Analysis of variance of aldrin band application test, 1956. Inverse hyperbolic sine transformation for q ■ 3,0 applied to individual roots and analysis based on totals of 10 root samples. Total Degrees Mean F Freedom Square Total 11 Treat. 2 25.86 U8.79** Error 9 0.53 The analysis for the transformed Grafton data in Table 50 may be compared with the original analysis given in Table 26* The transformation had no effect on our interpretation of the main treatment effects. However, the insecticide-ccncentration inter action which appeared highly significant in the original analysis new became non-significant. t-test Bata hare been presented in Table 7 which compares borer popu lations in early and late cut fields and in Table 8 for borers in 122 Table 50. Analysis of variance for Orafton control test, 1956* Inverse hyperbolic sine transformation for q - 3.0 applied to individual roots and analysis based on totals of 10 root samples. Factor Degrees Kean F Freedom Square Total 1*7 Insect. 3 2.5033 5.06** Cone. 2 0.1106 0.22 I z c 6 0.1665 0.31* Error 36 0.1*91*7 early and late cut fields and in Table 8 for borers in dead vs. living plants. These same comparisons were made using the inverse hyperbolic sine transformation for q ■ 0.5. The transformed and untransformed results are compared in Table $1. The tendency was for this transformation to increase the significance of differences. Table 5l. Comparison of t values for untransformed vs. counts transformed by inverse hyperbolic sine for q - 0.5. t Experiment Not Transformed Transformed live vs. Dead Roots (1951*) July 26 1.63 2,20* August 2 2j*0* 2.1*5* August 9 2.72%* 3J+8** Early vs. Late Cut (1955) July 5 2.33* 2.9l*** July 12 1.96 1.29 July 19 1.21 1.83 July 26 1.16 1.21* August 2 1.58 0.1*6 123 EFFICIENCY OF TRANSFORMATION We have seen that transformation of clover root borer data often leads to different conclusions than would be drawn from un transformed counts. We have not, however, demonstrated any clear su periority of transformed data in discovering differences. There fore we will now find the number of samples to discover a specific difference from a population mean at different levels of the mean. In estimating a difference we are confronted with two types of error: (I)**, the probability of deciding we have a difference when in reality none exists and (2) &, the probability of failing to discover a difference that exists. Although it is desirable to have both and 0 at a minimum, we are also concerned with the limitations imposed by size of sample in attaining specific levels of or 0 • Ordinarily if we make any sacrifice it is in & as we need not be too concerned with failing to discover small differences while we do not wish to make wrong decisions. Therefore has been set at 0.05 and /3 at 0.10 in most of our calculations. The power of the test is given by 1 Using tables of standard normal deviates, we obtain h - -1.96 m and h « 1,61* - y/n m where n ■ number of s s samples, s ■ standard deviation, and m * difference to be dis covered. If we wish to discover a specific difference with a five 12ii per cent chance of making a wrong decision we can determine the size of sample necessary from the relationship h ■ /n m/s. For our original untransformed data we have previously found that variance increases as the mean increases as shown in Figure 8. therefore the size of sample to discover a specific difference would be expected to vary over the range of the mean. If for various mean population levels we substitute the appropriate standard deviation, we can complete the calculations with results shown in Table 52. Table 52# Number of one root samples to discover a specific dif ference at different population means. Untransformed data# Mean 0.5 1.0 2.0 3.0 5.0 8.0 Std. Dev. 1.7 2.2 3.0 3.8 5.2 7.3 Difference to be Discovered Number Samples 0.5 b/r hk»k 7h.h 138.3 222 .2 U6.0 818.7 1.0 B/R 11.1 18.6 3h.6 55.6 loU.o 20*u6 2.0 B/R U.6 8.6 13.9 26.0 51.2 It is apparent that it requires a much larger sample to dis cover a specific difference at a high population than at a low one due entirely to the rapid increase in variance with the mean. We can now do a similar analysis for our transformed counts. The only new problem arising here is that a unit change in borers per root is not a uniform change in the transformed variable, but 125 changes as the mean changes. However we can calculate this change from Figure 23 which shows how the transformed mean changes with the original mean. Again the variance is not en tirely independent of the mean and has been estimated for dif ferent means from Figure 11. Making these adjustments, our calculation of sample sizes to discover a specific difference in terms of borers per root is given in Table 53* The difference to be discovered must also be expressed in terms of the transformed variable. This also changes with the mean. For example, a difference of 1.0 borers per root expressed in terms of the new variable changes from 0.35 at a mean of 0,5 borers per root to 0.08 at a mean of 8.0 borers per root. Table 53. Number of one root samples to discover a specific dif ference at different population means* Data transformed by inverse hyperbolic sine. Mean o*5 1.0 2.0 3.0 5.0 8.0 Transf. Mean 0.25 o*k5 0.71 0.91 1.23 1.59 Transf. Std. Dev. 0.52 0.62 0.70 0.73 0.71 0.62 Difference to be Discovered Number Samples 0.5 B/R 19.7 51.9 188.0 255.6 1*00.0 912.5 1.0 B/R 5.1 12.2 1*2.6 63.9 100.0 228.1 2.0 B/R 3.0 8.9 15.9 23.3 50.5 Similar calculations have been made for untransformed and transformed data for 10 root samples. These results are shown in 126 Tables 5U and 55. Table 5U. Number of 10 root samples to discover a specific dif ference at different population means. Untransformed data. Mean 0 .5 1.0 2 .0 3 .0 5 .0 8 .0 Std. Dev. 5Ji7 7.75 10.95 13.U2 17.32 21.91 Difference to be Discovered Number Samples 0.5 B/R U.6 9.2 18.U 27.7 U6.1 73.8 1.0 B/R 1.2 2 .3 U.6 6.9 11.5 18.U 2.0 B/R 0.3 0.6 1 .1 1.7 2.9 U.6 Table 55* Number of 10 root samples to discover a specific dif ference at different population means. Inverse hyper bolic sine transformation applied to individual roots and analysis based on sums of 10 roots. Mean 0.5 1.0 2.0 3.0 5.0 8.0 Transf. Mean 0.25 0.U5 0.71 0.91 1.23 1.59 Transf. Std. Derv. 0.52 0.62 0.70 0.73 0.72 a62 Difference to be Discovered Number Samples 0.5 B/R 3.1 6.7 19.3 23.9 38.3 120.6 1.0 B/fc 0.8 1.6 U.U 6.0 9.8 30.1 2.0 B/R OJi 0.9 1.5 2.3 6.7 We must conclude that transformations make little difference insofar as efficiency is. concerned. Figure 2U compares the number of one root samples to discover differences of Jr, 1, and 2 borers per root for both transformed and untransformed counts. Tfte two curves closely parallel one another in all cases although there is 4 0O-, 12? ~ UNTRANSFORMED - T RANS c ORME0 3 5 0 - OC LJ 150- CO 2 I 100- B/R 5 0 - 2 B/R 0 5 MEAN F ig , 2lu-Number of one root samples to discover specific dif- 50-, UNTRANSFORMED TRANSFORMED 4 0 UJ ^ 3 0 - 0 .5 B/R 20 - MEAN Fig# 25* Number of ten root samples to discover specific dif ferences# 128 a slight tendency for the transformation to be more efficient at low population means and to lose power at high means. Figure 2$ makes a similar comparison for 10 root samples. Again there is little difference between the curves for trans formed and untransformed counts. EFFICIENCY OF SAMPLING DESIGNS It is desirable that any sample which we take give an ef ficient estimation of the population. In our sampling of root borer populations, whether in a chemical control experiment or in a survey, we would like to choose that experimental design which gives us the most reliable estimate of the population value but at the same time minimizes sampling cost. Accordingly two ex periments were designed to give us information about the distri bution of root counts within a field. 1955 Sampling Experiment A field at Wooster, Ohio was divided into four areas, one area being taken in each of the four corners of toe field. Each area was further subdivided into four blocks and each block into four plots* Four sets of five roots each were dug in each plot. Plots measured 20 by 50 feet. 129 Using the method given by Snedecor (191*6), the analysis of variance given in Table 56 was obtained. Table 56. Analysis of 1955 sampling study. Factor Degrees Mean Component Freedom Square Total 1279 Areas 3 51.3733 0.091*8 Blocks 12 21.0258 0 .11*63 Plots 1*8 9.3233 0.0510 Sets 192 8.3026 0.3938 Roots 1021* 6.3336 6.3336 The variance of the mean, V, is equal to the sum of the com ponents divided by their respective number of divisions. In this experiment V « 6.3336/1280 + 0.3938/256 + 0.05l0/61* + 0.11*63/16 + 0.09U8A - O.OGl*95 + 0.0015U ♦ 0.00080 ♦ 0.00911* ♦ 0.02370 - 0.01*013. The outstanding feature of this experiment was the notable difference in population in the four areas of the field and within blocks in these areas* Within each block, however, most of the variability could be attributed to the differences in individual roots. From our model we can estimate the efficiency of other de signs for estimating the population in this field. Substituting other values into the denominator, we obtained the examples given in Table 57. 130 Table 57. Relative efficiency of various sampling designs for estimating population in a red clover field based on 1955 sampling study. Alternative Total Number Relative Areas Blocks Plots Sets Roots Roots V Efficiency Per Per Per Per Sampled Area Block Plot Set k k k k 5 1280 0 .0U013 1.000 8 k 2 b 5 1280 0.02371 1.693 16 2 2 k 5 1280 0.01778 2.295 8 k 1 h 5 61*0 0.03099 1.295 26 2 1 k 5 61*0 0.02506 1.601 16 2 1 1 5 160 0.06397 0.627 16 2 1 5 1 160 0.051*12 0.7U2 32 1 1 1 5 160 0.06101 0.658 32 1 1 5 l l6 0 0.05116 0.781* Thus it appears that the most practical way to increase our efficiency is to increase the number of areas sampled while de creasing the number of roots taken within each area. However this analysis is not entirely realistic as four areas were all that were available for sampling in this case. Likewise we were limited to i6 blocks and 61* plots. The only possibility, therefore, was to take different numbers of sets or roots. If we include the area and block variation in the plot variation we obtain the following estimate of V* V - 6.3336/1280 + 0.3938/256 + 0.2625/61* - O.OOi*95 ♦ 0.OO1& + 0.001*10 - 0.01059. Again trying other alternatives, we obtain the results given in Table 58. 131 Table 58. Relative efficiency of various sampling designs for estimating root borer populations as based on 1955 sampling study. Area and block variation of Table 56 included in plot variation. Alternative Total Number V Relative Plots Sets Roots Roots Efficiency Per Plot Per Set Sampled 61* h 5 1280 o.oio59 1.000 61* 2 10 1280 0.01213 0.873 61* 5 1* 1280 0.01028 1.030 61* 10 2 1280 0.0096? 1*095 61* 20 1 1280 0.00936 1.131 32 20 2 1280 0.01292 0.820 6It 1 10 61*0 0.01520 0.697 61* 10 1 61*0 0.011*62 0.721* 32 10 2 61*0 0.01933 0.5U8 Using this analysis, it is seen that the only way of obtaining a better estimate would be to actually increase the number of sets and roots sampled. Taking only 1280 roots it is possible to in crease our efficiency by only 13 per cent and this increase is possible only by taking each root at random rather than in sets. E a s it appears that we lose but little information by taking roots in sets of five rather than individually. 1956 Sampling Study A similar study was conducted in 1956 during August. The 1955 study was made in September after some migration was known to have occurred and which may have reduced the root variation. The 1956 132 studies were made before most root borers had matured; therefore no migration was possible. In the 1956 study, three fields were sampled. In each field two areas were sampled, bach area was divided into two blocks of four plots each. Plots were again 20 by 50 feet. rour sets of five roots each were sampled per plot* The analysis was similar to that for 1955 and is presented in Table 59. Table 59. Analysis of 1956 sampling study. Factor Degrees Mean Component Contribu Freedom Square tion to V Field 2 35.i*ooo 0.0895 0.02983 Area 3 6.7667 0.0022 0.00037 Block 6 6.1*167 0.0015 0.00012 Plot 36 5.7500 0.0000* 0.00000 Set i M 6.2951 0.5526 0.00288 Root 768 3.5322 3.5322 0.00368 Total 959 * Aitual estimate ■ -0.0273 It is apparent from Table 59 that in the 1956 experiment areas, blocks and plots contributed little to the variation. % e largest variation was due to field differences while within fields most variation was attributable to sets and roots. &ven if we include the area and block variation in the plot variation we obtain a negative component for plot variation. 133 It appears that if small plots are used so that the entire experiment can be included in a small area, no replication would be necessary J However if larger plots are used so that an experi ment covers considerable area some variation would be expected to occur. If we were to make our plots 50 by 80 feet, corresponding to the size of blocks in this experiment, we obtain the analysis given in -able 6o. Area variation has been included in the plot variation in this analysis. Table 6 0 . Analysis of 1956 sampling study. Modification of data in Table 59, including area variation in block variation. Factor Degrees Mean Component Contribu Freedom Square tion to V Field 2 35.1*000 0.0895 0.02983 Plot (-Block) 9 6.5333 0.0030 0.00025 Sub-plot (-Hot) 36 5.7500 0.0000 0.00000 Set 1 M 6.2951 0.5526 0.00288 Root 768 3.5322 3.5322 0.00368 Tbe estimates of efficiencies of different designs are shown in ^able 61 for the original data and in Table 62 for the revised analysis using 50 by 80 foot plots and including area variation in this plot variation. From; either analysis we must conclude that the only means of increasing efficiency in a given field is to increase the number of roots sampled. Only little information is lost by taking these 13k Table 6l. Relative efficiencies of various designs for estimating root barer populations as based on 1956 sampling study. Fields Plots Sets Roots Total Relative Per Per Per Roots V Efficiency Field# Plot Set 3 16 u 5 960 0.03639 1.000 3 16 2 10 960 0.0392? 0.927 3 16 10 2 960 0.03k66 i,o5o 6 16 u 5 1920 0.01820 1.999 6 16 2 5 960 0.021it8 1.69k 12 16 1 5 960 0.011i02 2.596 6 16 i 5 U80 0.0280k 1.298 3 1 32 10 960 0.03927 0.927 * No contribution j however reduction in plots decreases total roots sampled and therefore relative efficiency. Table 62* Relative efficiencies of various designs for estimating root borer populations based on modified 1956 sampling study using 50 by 80 foot plots. Fields Plots Sets Roots Total Relative Per Per Per Roots V Efficiency Field Plot Set 3 k 16 5 960 0.0366k 1.000 3 8 8 5 960 0.03651 1.00k 3 2 16 10 - 960 0.03977 0.921 3 h ko 2 960 0.03k91 1.050 6 2 16 5 960 0.02173 1.686 6 2 8 5 U80 0.02829 1.295 12 2 20 1 k80 0.0l6lk 2.270 12 2 h 5 U80 0.02Q70 1.770 3 U 80 l 960 0.03k3k 1.067 3 h Ug 1 k8o 0.03859 0.9k9 3 h 8 5 k8o 0.0k320 0.8k8 135 roots in sets of five rather than choosing each individual root at random if fairly large samples are taken. However as our sample size becomes smaller, a definite increase in the accuracy of our estimate may be expected by random selection of individual roots. For survey work it appears desirable to sample as many fields as possible, decreasing the size of sample taken in each field if necessary. This same statement may apply to ecological investi gations or control tests. However any reduction in the number of replicates v/ithin a field can be made up for by increasing the number of roots taken per replicate. SEQUENTIAL SAMPLING FOR CLOVER ROOT BORER SURVEYS Introduction A survey was conducted in Ohio JLn 1954 to determine the dis tribution and abundance of the clover root borer. Samples were gathered from 104 fields in 51 counties, each sample consisting of 30 roots (with a few exceptions). These roots were dissected and the number of borers in each recorded. This sampling plan re quired considerable time and labor, especially in making the dis sections. A summary of these data is given in Table 63. A study of these samples, along with data from field experi ments in Oregon, Indiana, and Ohio which were provided by other workers, led to the developaent of a sequential sampling plan. 136 Sequential sampling plans have no fixed sample size and are especially useful In survey work in that they permit the classi fication of infestation levels within predetermined degrees of accuracy with a minimum number of samples. The plan chosen for the clover root borer is based on a negative binomial distribution. This work was completed prior to the discovery that Heyman’s distribution gave a better fit. Al though the distribution of borers in roots does not fit the negative binomial as well as Neymants distribution, the plan based on the negative binomial seems to be the best of those for which sequential methods have been developed. Morris (1951*) de veloped a sequential plan which has been used in Canada for spruce budworm egg surveys. This plan is the basis for the plan proposed for sampling clover root borer populations and his notations are used in this section. For use in Ohio three infestation classes were chosen - light, moderate, and severe - as follows: Infestation Borers per Root light 1 or less Moderate 2 to 3 Severe 6 or more These classes may be varied as desired using the methods given in the discussion to follow. Once we have decided on our 137 Table 63. Summary of clover root barer populations in Ohio in 195k* Per Cent Borers Per Cent Borers County Infested Per County Infested Per Root Root Allen 50.0 1.13 Geauga 77.1 2.69 73.3 2.20 Greene 68.6 1*.5U Ashland 60.0 3.90 100.0 7.63 Hamilton ll*.3 0.1*3 18.0 0 .1*8 Ashtabula. 90.0 6.86 56.7 2.70 Hancock 52.0 1.92 90.0 i*.i*3 5o.o 1.33 Athens 12.0 0.68 Hardin 76.7 3.33 63.3 2.13 Auglaize 86.7 5.95 5o.o 1.07 Holmes 86.7 5.50 88.0 1**96 Carroll 52.0 2 .21* 83.3 1*.00 56.7 2.90 Huron 96.7 6.53 Clinton 1*1.5 1.61 72.0 1*.6I* Coshocton 80,0 3.87 Jefferson 53.3 1*63 77.8 6.19 liO.O 0.80 78.6 1**7 5 Knox 80.0 1**72 Crawford 96.0 8.32 36.0 1 .1*1* 92.0 8.00 72.0 2.2i* 100.0 7.37 Cuyahoga 57.5 U.09 licking 72.0 3*1*U Delaware 61*.o 1.92 80.0 3.20 1*8.0 2.56 Lorain 80.0 5.66 Erie 90.0 8.1*7 100.0 13.68 Fairfield 73.0 2.69 Madison 72.0 2.1*8 2l*.0 0.72 76.0 2.16 72. .0 i*jil* 70.0 1.37 Franklin 73.0 2.69 Mahoning 75.6 1**17 2U.0 0.72 72.0 l*.i*l* Medina 93.3 7.1*0 138 Table 63. Continued, Per Cent Borers Per Cent Borers County Infested Per County Infested Per Root Root Medina 73.3 3.1i3 Stark 76.? 5.63 96.7 8.50 75.0 5.61 80.0 3.b7 U l r c e r 80.0 5.55 66.7 2.30 Trumbull 81.1 6.73 86.7 5.bo Monroe 20.0 0.52 Tuscarawas 76.0 li.OO Morgan 26.7 0.67 70.0 b.93 60.9 2.8? Morrow 57.0 b.36 80.0 b.bO Noble Uo.o 0.90 Union 80.0 2.20 ilO.O 0.27 60.0 1.88 Ottawa 63.3 3.13 Van Wert 70.0 2.b6 6b, 0 5.36 86.7 2.80 73.3 2.78 Paulding 76.0 3.2b 50.0 1.20 Warren 9.0 0.61 26.2 1.6b Pickaway 28.0 0.76 66.7 2.60 Washington 23.3 0.83 Portage 87.1 b.8b Wayne 37.5 1.29 90.6 5.91 83.3 6.50 70.3 2.09 Putnam 83.3 3.b0 50.0 1.00 Wood 76.7 b.20 Richland 70.0 2.73 Wyandot 83.3 5.91 80.0 b.10 80.0 3.26 Sandusky 63.3 2.87 State Mean 67.ii 3.69 66.7 6.07 Seneca 100.0 8.88 72.0 3.76 139 infestation classes, we set up two alternative hypothesis (HQ and H^) as followst ■* To distinguish between light and moderate infestations: Hq - that the number of borers per root is 1 or less. % - that the number of borers per root is 2 or more. To distinguish between moderate and severe infestations: Hq - that the number of borers per root is 3 or less. - that the number of borers per root is 6 or more. It will be noted that gaps were intentiohally left between these infestation classes. It can be shown mathematically that a population intermediate between two classes must eventually termi nate in a decision and that the larger the gap between classes the sooner such a decision will be made. In other words, it re quires a larger sample to discover small differences than to dis cover relatively large differences between populations. The values of the constants under each hypothesis can now be calculated as shown in Table 64. Table 64. Calculation of constants for separating infestation classes. Infestation Constant k - 0 ,ltf light Moderate Moderate Severe «0 H1 % H1 mean ■ kp 1,000 2.000 3.000 6.000 p - kp/k 2 , ola 4.062 6.122 12.245 q "ltp 3 .o la 5.082 7.122 13.245 variance - kpq 3 .o 4i 10.163 21.36? 56.020 lUo Homogeneity of k This sampling plan assumes that k is constant for all popu lation levels, Bliss (19^3 ) discusses the efficiency of various methods of estimating k. He gives a method for computing a common value of k for a number of samples and a Chi-square test for test ing the homogeneity of k. This method is as follows: Scores (z^) are computed from trial values of k^1, selected so that they bracket the required estimate, k, for which z^ » Sum 0^0*^' * x) - N ln(l +■ x/k^*) where In designates a natural logarithm. The first step is to compute theaccumulated frequency in all units containing more than x borers which is written opposite each x* The reciprocals, 1/Qc^* * x), are multiplied in turn by and the products accumulated to obtain the summation in the first term. The second term may be determined as the common logarithm of (1 + 3 0 ^ ) multiplied by 2.3026N. The first score z^ is computed from previous estimates of k. The second trial value, kg', depends on the sign of If z^ is 1 1 1 positive, kg is greater than k^ j if negative, kg is less than k^ * • A third and subsequent values of k^ are then cfotained by interpolation and the process repeated. The homogeneity of the k ’s in the component distributions t depends on the and z^ in each individual series for k^ and k^*. The ratio z ^ ( k ^ - ky)/(zj •* z 0 is computed from each lU li for moderate vs. severe and for light vs. moderate populations on two different values of k. Calculations similar to those previously given indicate that k * 1.08 would be our best estimate for population means above two borers per root while k ■ 0.2U would be more appropriate for those under two borers per root. Calculation of Acceptance and Rejection lines Each pair of hypotheses (Hq and E^) is attended by two "types of error: (l) *< - the probability of accepting when is the true situation, and (2) the probability of accepting when is the true situation. Botfa oL and were set at 0.10. While this probability of error may seem large, it substantially reduced the size of sanples needed. In survey work a few aberrant points are of little importance in mapping populations and are more than made up for by any increase in the number of sampling points made possible by the reduction in time and labor involved in taking a sample. The acceptance and rejection lines for the light vs. moderate infestation classes can now be calculated from the following formulae? d » sn + hQ and 3 ■ sn ♦ h^ where d is the cumulative number of borersj n is the number of roots sampled; the slope of the lines, s, 1US . k .108 (qi/qp) . 1>U007 log (Pxqo/po^iV and the intercepts hQ ------12.2308 log (p1q0/p 0q1) - log_A_ - 12.2307 log (Piqc/Po^l) where B - # / ( l - <* ) and A " (1 -/3)/«< . The acceptance and rejection lines for moderate vs. severe infestations are calculated in the same way. The lines may now be plotted as shown in Figure 26 or put up in a sequential table as given in Table 6?* . We may now calculate the operating characteristic curves which show the probability, P, of accepting HQ for any level of the population mean. When the mean, kp, is 1, the probability of accepting is 0.1 and the probability of accepting Hq is 0.9* The reverse is true when kp is 2. At these two levels of kp, the probabilities correspond to those previously set for and /3 , As kp decreases below 1, P for Hq becomes very low. At kp « 1.U the chances of accepting and Hq are about equal. Likewise at kp * l+.O the chances of accepting a population as being moderate or severe are equal. These two operating characteristic curves are shown in Figure 27. TOTAL BORERS fig.26.-Acceptance and rejection lines for sequential sampling plan. UBR F OT SAMPLED ROOTS OF NUMBER 5 10 15 20 25 MODERATE LIGHT 30 lit? MODERATE VS. SEVERE LIG HT VS MODERATE 2 4 6 8 BORERS PER ROOT Fig. 27.-Operating characteristic curves for sequential sam pling plan. ll*8 The operating characteristic curve is calculated from V - , and p - 1 “ (q0/ Ah ~ Bh An example of the calculations is given in Table 66 for the operating characteristic curve for light vs. moderate infestation classes. Also shown are the average sample numbers, A(n), for the different levels of kp. Table 6 6 . Calculation of operating characteristic curve and average sample number curve for light vs. moderate infestation classes. h p kp p A(n) 00 0.000 0.000 1.00 8.7 1 2.0i*l 1.000 0.90 2l*.l* 1 2 2 .1*09 1.180 0.75 27.7 1A 2.625 1.286 0.63 27.7 3.120 1.529 0.37 21*.8 4 3.1*09 1.670 0.25 22.7 •**1 1*.082 2.000 0.10 16.3 U.912 2.1*07 o.ol* 11.2 00 00 0.00 0.0 The number of roots that must be sampled at any population level can be predicted from the average sample number curves liiich are shown in Figure 28. The peaks in such curves occur at popula tions intermediate between light and moderate and between moderate and severe populations. For different values of kp, A(n) is fig , 28.-Average sample number curves for sequential sampling plan, plan, sampling sequential sample number for curves 28.-Average , fig AVERAGE SAMPLE NUMBER 5 2 0 3 20 OES E ROOT PER BORERS £ MODERATE LIGHT VS. OEAE VS MODERATE r SEVERE ------a iSo Table 6 7 • Sequential sampling table for separating light, moderate, and severe infestation classes. Number Total Nucier Borers Roots Sampled light vs* Moderate Moderate vs. Severe (Continue Sampling) (Continue Sampling) 1 0 - 12 0 - 33 2 0 lit 00 - 37 3 *■ 0 i s 0 - i l l U 0 16 0 - US S 0 - 18 0 - So 6 0 M 19 0 - SU 7 0 •W21 0 - S8 8 0 22 h - 62 9 1 23 8 - 66 10 2 CM2 S 12 - 70 11 k - 26 16 - 7S 12 s •M 28 20 - 79 13 6 29 § 25 - 83 1U s 8 CM30 £ 29 - 87 IS ki 9 •M 32 33 - 91 16 g 11 33 37 - 96 17 12 3S e U l - 100 18 M 13 36 H US - 10U 19 H 15 37 So - 108 20 | 16 39 I SU - 112 21 18 CMho 0 S8 **116 22 9 19 U2 8 62 - 121 23 20 - U3 66 — 125 2k 22 a. UU 71 *-■ 129 2S 23 —U6 75 - 133 26 25 *■* U7 79 - 137 27 26 k9 83 « 1U1 28 27 - So 87 - 1U6 29 29 - S i 91 - 1S0 30 30 S3 96 - lSU 31 32 rmSU 100 - 1S8 32 33 - SS 10U - 1 6 2 33 3b - 57 108 - 167 3U 36 CMS8 112 - 171 35 37 CMC60 116 - 17S l£l calculated from A(n ) . hl * 0*0 - hi)P kp h s Application of Sequential Plan In applying the plan, either the sequential table (Table 67) or the graph (Figure 26) may be used. It may not always prove practical to continue sampling until a decision is r eached but may be desirable to resolve intermediate populations by setting a limit of, say, 30 roots to be sampled in any one field. This sequential method was compared with the method used in the 1 9 5 k clover root borer survey by reanalyzing these root counts by the sequential method. In 6 9 oases, or 66 per cent of the time, a decision could have been reached by sampling less than 30 roots. For these 6 9 cases, the average sample size was l6 .l4.fj roots. Had a limit of 30 roots been set on sample size taken in any one field, a saving of 30 per cent in the number of roots sampled would have been possible. ESTIMATING BORERS PER ROOT FROM PER CENT INFESTED ROOTS Most analyses of root borer populations are based on the number of borers per root or on the per cent infested roots. Only the former method gives a true measure of the population. However 152 this involves careful dissection of each root if all borers are to be located while it is much simpler to determine only whether or not a root is infested* If borers per root and per cent in fested roots are closely related, as we might expect, then an estimate obtained in one way can be converted to the other. This relationship was investigated for 20 and 50 root samples. During sampling studies conducted in Ohio in 1955 and. 1956 a number of 20 root samples were dissected. The observed rela tionship between borers per root and per cent infestation is shown in Figure 29. A second degree curve was fitted to these data as a means of estimating borers per root from proportion infested roots. As at 0 per cent infestation we must have 0 borers per root, it appeared desirable that the regression line intersect the y axis at 0. This was accomplished by fitting the curve to the quantities x/p and p where x « borers per root and p “ proportion infested roots. The second degree curve is given by x/p - a + bp + cp . The constants a, b, and c are calculated by the usual methods which are given by Snedecor (1950). Now to have our curve intersect the y axis at 0 instead of a, we need only multiply both sides by p, obtaining x * ap + bp + cp3 which at x “ 0 must give p “ 0. Using our data we find x “ 3.1I15P - 2.2255P2 + 3-2755P3. 352 -JL 7 -5 1.0 PROPORTION INFESTED ROOTS Fig* 29.*JEtelationship between, borers per root and proportion infested roots for 2 0 root samples. n o> PROPORTION INFESTED ROOTS Fig* 30.-Relationship between borers per root and proportion infested roots for $ 0 root samples. 153 The standard deviation of this estimate was calculated from the standard deviation of each set of samples at each level of infestation* This relationship appeared linear and gives an esti mate of s - 0.1*25. Similarly for 38 sets of 56 root counts from Virginia we find x ■ 1.2l*9p + 3*311 + O.U59p^* For these data there were so few samples that an estimate of the standard deviation could not be obtained as was done for the 20 root samples. However reference to Figure 30 shows variance about this regression line to be low. We can estimate borers per root from a knowledge of per cent infested roots with an error of 10.95 borers per root for 20 root samples* Fifty root samples appear to give a more reliable estimate of borers per root using this method# SUMMARY AND CONCLUSIONS This disseration consists of two parts. Part I is an ex- tensive literature review with original investigations on the biology, ecology, and control of the clover root borer, Rylastinus obscums (Marsham) in Ohio. Part II is a mathematical treatment of root borer populations, dealing with the transformation and analysis of root borer data. Part I Seasonal histories are presented for the years 195U-1956, inclusive. Root borer populations in 195U and 1955 were high and development normal. In 1956 populations throughout northern Ohio were low and development was delayed more than three weeks over the previous years. Spring flight of borers may be accurately predicted by a temperature summation method* Beginning March 1 and summing all daily mean temperatures over 1*5° F., but not adding more than 10° any day, borers can be predicted to fly on the first day the temperature reaches 68° F. after 170 day degrees have been summed. Flight of borers is primarily with the wind. Females pre- dpminated in flight in 1956 but no difference in sex ratio was observed in 1955* 15U : T&$ Fall migration of adult borers of the new generation from dead to living plants was observed. Evidence is presented which indicates that borers develop faster and populations are higher in weakened plants. Although populations were higher under dry conditions, little increase in damage was noted. A multiple regression analysis led to the development of a method for estimating damage. The regression equation is given by Y » a + bX, + cX- 4- dX where Y * green weight of foliage, *1 - crown diameter, % z - i f , and - borers. Use of sig- nificantly increased the multiple correlation coefficient. Large roots tend to have more borers. An increase in borers increases damage. Damage by a given number of borers is greater in small plants. No red clover varieties were observed which were resistant to the root borer* Bollard had consistently lower populations but differences were not significant* Surface applications of aldrin at 1^ lbs. per acre at the time of band seeding gave good control the following year. A 3/U lb. rate was slightly less effective. Aldrin, endrin, heptachlor and lindane at 1 lb. per acre applied as granules in the spring were effective, with aldrin and heptachlor being slightly superior. Ten pounds per acre of 10 per cent granules was as good as f>0 pounds of two per cent material. 156 Soil applications of aldrin and lindane applied four years previously were ineffective, *» Part II A mathematical study of the distribution of root borers in red clover plants indicated that these counts closely agreed with Neyman*s contagious distributions. An excellent fit with these distributions feu* n =* 0 and/or n ^ oo was obtained in most cases, These distributions were generally superior to the negative binomial and also fitted the sums of 5 and 10 root samples. An inverse hyperbolic sine transformation, given by x* * i:-. „ i '' 1 q2sinh (cpc)53, is proposed for root borer data. This trans formation successfully stabilized the variance but was not entirely effective in eliminating non-additivity. At low popu lation means this transformation led to more decisions than untransforraed data but lost power at high means. In cases in which analyses are based on the sums of borers in several roots, it is suggested that the individual roots be transformed before summing# This led to a more powerful test than transforming the suras# Conclusions drawn from transformed data frequently differed from those drawn from analysis of original counts# These dif ferences, however, were not usually great. l£7 Sampling studies indicated that the best method for increasing the efficiency of estimates of populations was to increase the number of roots sampled. Increased replication appeared of little value. Roots could be taken in sets of 5 with only slight loss in efficiency. For survey work efficiency is improved by increasing the number of fields sampled with a reduction in the number of roots taken per field if necessary. A sequential sampling technique for surveys was developed. This plan was based on the negative binomial and was 30 per cent more efficient than the plan of taking 30 roots per field as used in a state survey in 19%h* B o r e r s per root can be accurately estimated from the pro portion of infested roots if E>0 root samples are used. Effi ciency of this method is somewhat lower for 20 root samples. APPENDIX A MATHEMATICAL DISTRIBUTION OF CLOVER ROOT BORER COUNTS Table 68. Distribution of borers in fields having a mean of 0 to 1 borer per root. Ohio survey, 195U. Borers Observed Calculated Frequency Frequency Per N©yman Root Negative 1 / Binomial n co 0 237 232.0 21*2.8 1 2U 38.9 25.3 2 2k 18.1 16.9 3 17 10.2 11.2 k 7 6.21 7.U 5 2 U.o) 6 2 ) 7 3 8.6} ■1U.U t 8+ 2 ) ) 318 318.0 318.0 i 2 12.71 8.23 pi2 0.01 0.08 In this and subsequent tables, brackets indicate that these frequencies have been lumped for computing Chi-square. l£8 159 Table 69. Distribution of borers in fields having a mean of 1 to 1 ^ borers pe r root* Ohio survey, 1951* • Borers Observed Calculated Frequency Per Frequency Root Negative Neyman Binomial n 00 0 118 106.1 111.5 1 1*1 53.5 1*5.9 2 21 29.5 29.1 3 21 16.7 17.8 1* 13 9.6 10.6 5 6 5.3 6.2 6 1* 7 1* 8 .3 } 7.9} 8 1 ) ) 229 229.0 229.0 X2 9.16 1*J*3 0.16 0.1*8 V. Table 70* Distribution of borers in fields having a mean of !§• to 2 borers per root. Ohio survey, 19$l*. Borers Observed Calculated Frequency Per Frequency Root Negative Neyman Binomial n 00 0 100 92.8 10l*.i* 1 18 32*9 20.9 2 26 18.9 15.9 3 13 12.2 12.0 1* 10 8.1* 9.0 5 6 5.9 6.7 6 3 l*.3l 5.0) 7 2 3.1> 3.71 8 3 9.5 j 10.1*j 9 + 7 188 188.0 188.0 X* 1 1 .11* 8.85 .*&■ 0.08 0.18 ISO Table 71. Distribution of borers in fields having a mean of 2 to 2-|- borers per root. Ohio survey, 1954. Borers Observed Calculated Frequenter Per Frequency Root Negative Neyman Binomial n '•* oo 0 81 68.4 76.4 1 43 53.5 45.3 2 29 38.6 35.8 3 29 27.1 26.9 4 19 18.7 19.5 5 19 12,. 8 13.8 6 9 8.7 9.5 7 3 5.9 6.5 8 5 4.0 I 9+ 9 8.3 32.3) 246 246.0 246.0 X 2 11.64 5.96 ^ x 2 0.17 0.54 Table 72. Distribution of borers in fields having a mean of 2i to 3 borers per root. Ohio survey, 1954. Borers Observed Calculated Frequency Per Frequency Root Negative Neyman Binomial n co 0 106 95.7 114.8 1 4i 58.9 42.2 2 43 41.0 34.5 3 32 29.6 27.8 4 2$ 21.8 22.1 5 19 16.3 17.3 6 11 12.2 13.4 7 7 9.2 10.4 8 9 7.0 7.9 9 6 5.3 6.0 10+ 15 17.0 17.6 ' '-'V ■ 314 314.0 314.0 X2 9.32 6.04 px2 0.41 0.74 161 Table 73. Distribution of borers in fields having a mean of 3 to li borers per root* Ohio survey, 195U. Borers Observed Calculated Frequency Per Frequency R o o t Negative Neyman Binomial n co 0 97 75.9 92.2 1 53 72.9 58.8 2 52 61.8 52.8 3 k 6 U5.0 U5.5 h h h 7 35.6 37.9 5 38 27.7 30.8 6 2k 21.ii 2ii.6 7 16 l6.1i 19.2 8 11 12 .5 lli.9 9 Hi 9.5 11.3 10 5 7.2 11 8 5Ji ► 12 Ii l+.l lil.O 13+ Hi 33.6 U29 ii29.0 U29.0 X2 36.3U 9.35 40.01 A 2 0.1*0 Table 7 k . Dis tribution of borers in Indiana airplane test, 1955. Borers Observed Calculated Frequency Per Frequency Negative Neyman Root Binomial n ^ oo 0 U9 50.6 58.1+ 1 16 15.8 8.7 2 Hi 9.1 6.3 3 6 6.1 5.5 Ii 3 lt.3* U.3 5 2 ) 6 1 7.3 8.21 7 2 8+ 7 6.8 8.6 100 100.0 100.0 X2 3.81 19.03 <0.01 ^X^ 0.69 162 Table 75. Distribution of borers in fields having a mean of 1+ to 5 borers per root. Ohio survey, 195U* Borers Observed Calculated Frequency Per Frequency Negative Neyman Root Binomial n oo 0 13U 130.2 121.6 1 1+5 75.9 59.9 2 1+7 55.1 53.8 3 h7 1+2.6 1+7.2 k 1+6 33.9 1+0.5 5 36 27.5 3U.3 6 36 22.5 28.6 7 2U 18.6 23.5 8 21 15.5 19.2 9 u+ 12.9 15.5 10 8 10.8 12.5 11 . 6 9.1 12 8 7.7 I 13 7 6.5 1+5.1+Y 11+ 6 5.5 v 15+ 21 31.7 V 5o6 5o6.o 5o6.0 X2 38.1+8 10.56 <0.01 0.39 Table 76* Distribution of borers in Indiana tests, 1955. Borers Observed Calculated Frequency Per Frequenter Root Negative Neyman Binomial n cd 0 359 3W+.2 360.0 1 1+9 67.0 1+5.7 2 27 31.2 29.7 3 21 17.1+ 19.2 1+ 10 10.5 12.1+ 5 ■ 9 . 6.6 7.9 6 7 1+.3 5.1 7+ 8 8.8 10.0 1+90 1+90.0 1+90.0 X2 9.38 2.38 0.22 0.91 163 Table 77- Distribution of borers in fields having a mean of 5 to ______6 borers per root- Ohio survey, 195U* Borers Observed Calculated Frequency Per Frequency Negative Neyman Root Binomial n ^ co 0 9 1 Uk.6 67.6 1 23 37.3 26.6 2 30 31.9 16 . 1 3 27 27.1 21.6 b 2U 23.1 19.3 5 23 19.6 17-2 6 20 16.7 15.3 7 16 Ik.2 13.5 8 13 12.0 11.8 9 12 10-2 10.3 10 9 8.7 8.9 11 9 7.U 12 U 6.2 1 3 h 9 . 3 71.8V XU. 7 k . 9 15+ 26 31-2 ) 300 300.0 300.0 X 2 16.23 29.23 ^ X 2 0.29 < 0 . 0 1 Table 78- Distribution of borers in Indiana tests, 195U. Borers Observed Calculated Frequency- Per Frequency Negative Neyman itoov Binomial n co 0 h 3 U 9 . 9 UxJk 1 9 7.2 10.1 2 k 3.1 h . 7 3+ k k . 2 3.8 6 0 60.0 6 0 . 0 X 2 0.86 0.29 0.96 ■ ■ ’ *x? 0.83 Table 79. Distribution of borers in fields having a mean of 6 to 8 borers per root. Ohio survey, 195U. Borers Observed Calculated Frequency Per Frequency Root Negative Neyman Binomial n c d 0 36 20.5 33.2 1 17 26.8 23.3 2 26 28.U 2U.1 3 22 27.7 23.9 k 26 25.9 23.0 5 22 23.5 21.6 6 22 21.0 19.9 7 16 18.5 18.1 8 17 16.1 16.2 9 15 lU.O 1k.k 10 13 12.0 12.6 11 10 10.3 11.0 12 12 8.7 9.5 13+ Uh U5.6 1*8.2 299 299.0 299.0 X2 17.63 U.13 Px2 0.12 0.98 Table 80. Distribution of borers in insecticidally treated plots. Virginia, experiment 2, 195U. Borers Observed Calculated Frequency Per Frequency Negative Neyman Binomial n * oo 0 227 219.7 222.0 1 35 50.2 Ii-5-7 2 23 17.8 19.2 12 7.1 7.9 3 \ k 1 :■ 5 1 ■■■■■■: 5.2V 5.2’ 6 ;■ .'I-- ) 300 300.0 300.0 X2 10.67 6.1*3 0.01 0.09 V: 165 Table 81, Distribution of borers in fields having a mean of more than 8 borers per root, Ohio survey, 195U. Borers Observed Calculated Frequency Per Frequency Neyman Root Negative Binomial n ao 0 5 U.U 8.7 1 3 7,0 6,8 2 10 8*5 7.6 3 8 9.2 8.0 U 8 9.U 8.2 5 12 9.3 8.2 6 5 8.9 8.0 7 10 8.U 7.8 8 10 7,8 7.U 9 8 7.1 6.9 10 8 6.5 6.U 11 6 5.8 5.9 12 6 5.2 5.U 13 7 ■U.7 lit 6 U.l) IS 3 -3.71 16 1 3.2) 17 1 2 . 8 V 38.7 18 5 2.5/ 19 2 2.1( A 20 2 1.9) A 21+ 8 11.5 ; 13U 13U.0 13U.0 z2 7.99 9.7U 0.6k *3? 0.89 Table 82. Distribution of borers in 1955 sampling study. Wooster, Ohio. Borers Observed Calculated Frequency Per Frequency Root Negative Neyman Binomial n oo 0 U23 395.9 aa3.5 1 227 275.7 22^.8 2 206 190.3 17a. 8 33 133 131.0 130.5 a 83 90.1 9a.7 s 70 61.8 67.2 6 h9 U2.U a6.9 7 33 29.1 32.2 8 20 20.0 21.8 9 9 13.7 ia .7 10 6 9.U 9.7 11 6 6 .a ) 12 6 a.ai 18.2i 13 3 3.0) 1h + 6 6 .8 1 1280 1280.0 1280.0 X2 18.29 12JU6 0.1 0 o.ao Table 83. Distribution of borers in insecticidally treated plots. Virginia, experiment 1 , 1953. Borers Observed Calculated Frequency Per Frequency Negative Neyman Root Binomial n 00 0 207 195.1 203.9 1 38 U9.2 37.0 2 Ik 23.3 23.0 3 19 12.7 i a .2 h 5 7 .a 8.7 5 6 a . 5 5.3 6+ 11 7 .8 7.9 300 300.0 300.0 X2 12.69 8.10 ^ 2 0.03 0 . 1a 167 Table 81*. Distribution of borers in insec ticidally treated plots. ______Wooster, Ohio, 1951*-55. ___ Borers Observed Calculated Frequency Per Frequency Root Negative Neyman Binomial n e co 0 10?6 1036.7 H25.3 1 182 256.9 158.0 2 126 133.7 115.1 3 81* 81.8 83.6 1* 60 53.8 58.0 5 1*6 36.8 1*1.7 6 31 26.0 29.9 7 21* 18.5 21.1* 8 15 13.1* 15.3 9 9 9.8 10.9 10 3 7.31 1 11 5 5.1*1 12 1* l*.l) 13 1 3.11 37.7 H* k 2 .1*1 15 2 - 1.71 1 16+ 5 5.6 1 1697 1697.0 1697-0 X2 3l*.l*8 11.63 <0.01 0.31 Table 85. Distribution of borers in insecticidally treated plots • Virginia, experiment 2, 1955. Borers Observed Calculated Frequency Per Frequency Root Negative Neyman ■ • v U V Binomial n e co 0 319 312.3 318.5 1 35 1*8.2 38.2 2 2l* 19.3 20.1* 3 ' 11 9.2 10.8 1* 5 lu8 5.7 5 ■: 1* 2.7) 3.0 6+ 2 3.5} 3.3 1*00 1*00.0 1*00.0 X2 5.26 1.81* 0.1*0 0.87 PX2 Table 86. Distribution of borers in insecticidally treated plots, Oregon, Borers Observed Calculated Frequency Per Frequency Negative Neyman Root Binomial n oo 0 1325 1168.0 13U6.7 1 115 231.2 90.5 2 79 126.5 7U.5 3 67 8U.1 6U17 k U5 60.7 5U.7 5 51 U5.9 U6.2 6 31 35.9 39.0 7 U8 28.5 33.0 8 26 23.1 27.8 9 22 18.9 23.5 10 16 15.6 19.8 11 35 12.9 16.7 12 15 11.0 liul 13 10 9.3 11.8 1U 12 7.7 10.0 15 5 - 6.6 8.U 16 8 5.6 17 3 k.8\ 18 1 ii.Ol 19 6 3.5 U6.6 20 7 3.1' 21 8 2.7) 22 3 2.3) 23+ 10 16.1 I 1928 1928,0 1928.0 X2 135.95 21.25 Px 2 <0.01 0.16 Table 87. Distribution of. borers in check plots* Virginia, ex periments 1 - U* 1955. Borers Observed Calculated Frequency Per Frequency Root Negative Neyman Neyman Binomial n ■ 0 n •+ ao 0 J+3 2b. 7 28.6 26 #U 1 17 39.5 36.2 38 .k 2 33 b0.6 38.3 39 .b 3 U6 3b.l 33.5 33.7 U 21 25.U 25.9 25.6 5 17 17.b 18.3 17.6 6 15 11.3 12.1 11.7 7 8 7.0 17.ll 7.3 8+ 10 10.0 j 9.7 210 210.0 210.0 210.0 I? 3b.07 2U.59 29.78 P2? <0.01 <0.01 <0.01 Table 88. Distribution of borers in check plots* Virginia, ex periments 1 and 2, 195U. Borers Observed Calculated Frequency Per Frequency Root Negative Neyman Binomial n oo 0 8 7.2 8.6 1 10 12.3 11.8 2 7 lb.2 13 ob 3 23 13.8 13.2 k lb 12 .2 11.9 5 10 10.2 10.1 6 12 8.0 8.2 7 U 6.2 6.b 8 2 b.6) } 9 1 3.bf _ , 1 10 U 2.UV 16 .Ur 11+ __5 5.5 ) 100 100.0 100.0 X 2 ib.5i lb.86 o.oU 0.0b PX?'' 170 Table 89 o Distribution of borers in insec ticidally treated plots. Virginia, experiment 3, 1955. Borers Observed Calculated Frequency <■» Per Frequency Root Negative Neyman Neyman Binomial n “ 0 n ^ co 0 226 195.0 221.5 205.7 1 27 68.8 30.8 5U.1 2 27 35.2 33.7 3U.it 3 30 19.9 25.9 21.6 it 20 11.8 16.5 13 .it 5 9 7.2 9.6 8.2 6+ 11 12.1 12.0 12.6 350 350.0 350.0 350.0 x2 U3.59 3.U0 23.97 ^x2 <0.01 0.63 <0.01 Table 90. Distribution of borers in insec ticidally treated plots. Virginia, experiment it, 1955. Borers Observed Calculated Frequency Per Frequency Negative Root Neyman Neyman Binomial n - 0 n co 0 219 199.5 221.it 208.5 1 19 U7.1 I6.it 3U.7 2 21 22.1 20.0 21.7 3 20 12.0 16.9 13*5 it 7 7.1 11.2 8.it 5 it 7.1 6.3 5.2 6+ 10 5.1 7.8 8.0 300 300.0 300.0 300.0 X2 2U.32 it;io 11.79 171 Table 91* Distribution of borers in red clover roots. Fulton, New York, 1956. Neyman's distribution for n •+ oo. Borers June Counts July Counts* August Counts Per Root Obs. Expect, Obs. Expect. Obs. Expect. 0 52 1+9*3 15 15.0 5 5.6 1 5 6.2 U 6.9 k 3.6) 2 2 5.U 6 6.8 5 3.91 3 5 lu8 12 6.6 3 k.l) U 6 U.3 11 6.3 5 U.21 5 6 3.8) 5 5.9 3 U.21 6 2 3.31 U 5.6 h U.ll 7 3 2.9) 7 5.1 U 1+.0I 8 1 2.61 6 U.7 5 3.9i 9 2 2.2) 1 1+.3) 3 3 *II 10 3 2.0! 5 3.91 3 3.5! 11 2 3 7 3.3) 12 1 2 3 3.1» 13 1 13.2 ' 2 28.9 2 2.8) lit 2 3 3 2.61 15+ 7 1U i • 20 &2..U 100 100.0 100 100.0 79 79.0 X 2 3.87 12.33 3.23 0.69 0.31+ 0.78 * 57.111)25 used as estimate of variance for calculations in stead of sample variance. 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U9:6U0-6U3* AUTOBIOGRAPHY I, Kenneth Paul Pruess, was b o m near Troy, Indiana, June 21, 1932 * t Mfcr secondary school education was obtained in the public schools of Spencer County, Indiana, I received the degree Bachelor of Science in Agriculture at Purdue University in 1 9 5 b . During the summers of 1 9 5 2 and 1 9 5 3 I worked in the Entomology Department at the Indiana Agricultural Experiment Station. I received the Master of Science degree from The Ohio State University in 1955. I held a research assistantship at the Ohio Agricultural Experiment Station from June, 1 9 5 U , to March, 1 9 5 7 , and completed my research for the degree Doctor of Philosophy while employed there. 182