Title: Attraction of insects to odorant sources in a warehouse
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00099251/00001
 Material Information
Title: Attraction of insects to odorant sources in a warehouse
Physical Description: vi, 71 leaves : ill. ; 28 cm.
Language: English
Creator: Mankin, Richard Wendell, 1948-
Publication Date: 1979
Copyright Date: 1979
Subject: Insects -- Behavior   ( lcsh )
Pheromones   ( lcsh )
Indian-meal moth -- Behavior   ( lcsh )
Entomology and Nematology thesis Ph. D
Dissertations, Academic -- Entomology and Nematology -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
Thesis: Thesis--University of Florida.
Bibliography: Bibliography: leaves 63-70.
General Note: Typescript.
General Note: Vita.
Statement of Responsibility: by Richard Wendell Mankin.
 Record Information
Bibliographic ID: UF00099251
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000014105
oclc - 06158456
notis - AAB7299


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During this study I was employed by the U.S. Depart-

ment of Agriculture, Insect Attractants, Behavior, and

Basic Biology Laboratory in Gainesville, Fla. I thank the

director, Dr. Darrell Chambers and my supervisors, Dr.

P. S. Callahan and Dr. J. C. Webb for their cooperation

and support services.

I also thank Drs. K. W. Vick, J. C. Coffelt, R. Pepin-

ski, and A. Nevis for their advice and encouragement, and

Drs. M. S. Mayer, J. L. Nation, J. Anderson, and R. Cohen

for serving on my committee. Cheryl Steward and Maribeth

Michaud provided assistance with the bioassays.

Special thanks go to Dr. P. S. Callahan, Committee

Chairman and Dr. M. S. Mayer for their technical, editorial,

and advocatory efforts.

Lastly, I salute the insects who bravely but unknow-

ingly donated their lives for the sake of the project.



ACKNOWLEDGEMENTS......... ................. ............ ii

ABSTRACT............................................. iv

INTRODUCTION......................................... 1


INDIAN MEAL MOTH, Plodia interpunctella
SEX PHEROMONE.............................. 3

Methods and Materials.................... 4
Results ................................. 12
Discussion .............................. 18


Case I: Molecular Diffusion............ 23
Case II: Dispersal in Airflow of Zero
Average Velocity............... ....... 35
Case III: Dispersal in Airflow of
Constant Average Velocity.............. 36
Results ................................. 40
Discussion .............................. 53

CONCLUSIONS.......................................... 58

APPENDIX............................................. 60

REFERENCES ........................................... 63

BIOGRAPHICAL SKETCH .................................. 71


Abstract of Dissertation Presented to the Graduate
Council of the University of Florida in Partial
Fulfillment of the Requirements for the
Degree of Doctor of Philosophy



Richard Wendell Mankin

August 1979

Chairman: P. S. Callahan
Major Department: Entomology and Nematology

Methods are presented for determining the behavior of

an insect stimulated by an attractant source in still air,

turbulent air of zero average velocity, and turbulent or

laminar air currents of constant, nonzero average velocity.

Plodia interpunctella (Hubner) (IMM) is the chief test in-

sect for application of the methods. To use the IMM, it

was first necessary to measure the effect of different con-

centrations cf the sex pheromone (Z,E)-9,12-tetradecadien-

1-ol acetate on the upwind anemotactic behavior of the male.

A bioassay was performed to obtain stimulus-response regres-

sion lines at 23C and 34C. The regression lines-were ana-

lyzed by a new procedure that accounts for control respon-

ses in the absence of pheromone and also peak responses well

below 100% at pheromone concentrations considerably above

the lowest detectable levels. On the basis of this analysis,

the upwind anemotactic threshold is 1.34 x 106 molecules/cm3

at 23 C and 1.65 x 104 molecules/cm at 34 C. Departures

from the 2 lines occurred at the highest pheromone concen-
8 3
trations tested, near 10 molecules/cm This suggests

that the upwind anemotactic behavior changes qualitatively

above an altered-behavior threshold about 2 orders of magni-

tude above the upwind anemotactic threshold. The decreased

response at 23C compared to 34 C suggests that flight in

response to pheromonal stimulation is inhibited at cool


Calculations of the above methods using the IMM thres-

holds and similar thresholds of other insects indicate the

following: (1) In a warehouse a searching insect is likely

to be attracted to a calling insect if it comes within an

attraction space, a sphere surrounding the calling insect,

ranging from 0.4 to 2.4 m in radius. (2) The attraction

spaces of typical sex pheromone traps, emitting pheromone

at rates greater than 0.01 ng/sec, extend beyond the boun-

daries of a 10 x 10 x 10-m warehouse. (3) The searching

behavior of an attracted insect.is likely to be altered

from an extensive to an intensive pattern if it comes within

a calling insect's altered-behavior space, a sphere 6-60 cm

in radius. (4) The altered-behavior space of a trap emit-

ting 0.76 ng/sec extends beyond the boundaries of a 10 x 10 x

10-m warehouse. (5) Pheromone does not fall unless it is

emittedalong with a large amount of a high-vapor pressure

solvent. The calculations are used in support of the following:

(1) The effect of an adsorptive surface on the odorant

concentration after an extended period of emission is

negligible except at positions near the surface. (2) Traps

with odorant sources of small dimensions have greater trap-

ping efficiency than otherwise identical traps with sources

of large dimensions. (3) The function of the altered-be-

havior threshold may be to increase the probability of a

stimulated insect finding a calling insect. Additional

applications and hypotheses are also presented for conditions

outisde a warehouse.


The probability of an insect finding an attractant

source is determined by the pattern and intensity of its

searching behavior, which are strongly affected by the

attractant concentration and the dynamics of the airflow

(Roelofs, 1975; Shorey and McKelvey, 1977). Several dif-

ferent mathematical expressions of these relationships

have been presented in insect attractance models by Wright

(1958), Bossert and Wilson (1963), Bossert (1968), Hart-

stack et al. (1976), Hircoka and Suwanai (1976), Aylor (1976),

Aylor et al. (1976), Nakamura (1976), Nakamura and Kawasaki

(1977), and Roelofs (1978). None of these models considers

jointly 3 problems frequently encountered in a warehouse en-

vironment: deposition of attractant onto exposed surfaces,

restricted dispersal of attractant near obstructions, and

the complicated rapidly changing pattern of the airflow.

The need for methods to treat such problems is demonstrated

by the growing number of sex pheromone trapping experiments

involving postharvest pests (Sower et al., 1975; Barak and

Burkholder, 1976; Read and Haines, 1976; Von Reichmuth et al.,

1976, 1978; Shapas, 1977; and Vick et al., 1979).

Although the model derived below is applied primarily

to attraction in a warehouse, it also applies to field and

forest environments, incorporating many elements of pre-

vious models. Like the Bossert and Wilson (1963) model it

can be used to calculate an odorant source's attraction

space, a zone where the average odorant concentration is

above a perceptual or behavioral threshold, under either

still air or steady airflow conditions. Like the Aylor

(1976) model it treats the effects of turbulence in detail.

Like the Roelofs (1978) model it includes the effects of an

altered-behavior threshold, occurring about 3 orders of mag-

nitude above the perceptual threshold. Moreover, it con-

siders adsorption processes, boundary positions, gravitation,

and the instantaneous structure of the odorant plume.

The model is tested using the Indian meal moth (IMM),

Plodia interpunctella (Hubner) (Lepidoptera:Pyralidae). A

bioassay to determine parameters included in the model is

presented in Chapter I. The model is derived and applied to

several problems in Chapter II.

Plodia interpunctella (HUBNER) (LEPIDOPTERA:

An insect's threshold of response to sex pheromone is

an important parameter of many uses in olfactory physiology

(Kaissling, 1971) and applied entomology (see Chapter II).

The IMM is a widespread postharvest pest whose pheromonal

physiology has been studied extensively, but whose behavior-

al response to pheromone has not been quantified in exact

units. IMM populations have been monitored using sex phero-

mone traps (Vick et al., 1979); thus, there is some prac-

tical interest in the incorporation of an exactly quanti-

fied response threshold for IMM into a trapping model. Of

all the measurable thresholds, the one most appropriate for

use in a trapping model is the threshold for upwind anemo-

taxis, because an insect stimulated to fly has a greater

likelihood of being captured by a trap than an insect sti-

mulated merely to respond orthokinetically (by antennal

vibration or wing flutter). To compare the pheromonal re-

sponse of the IMM with that of other insects and to determine

a representative threshold for use in postharvest pest trap-

ping models, the upwind anemotactic response of the male IMM

was measured at 23 C and 340C.

Methods and Materials


Male pupae were transferred at 3-day intervals from a

laboratory colony (Silhacek and Miller, 1972) to an envi-

ronmental chamber at 270C and 60% RH on a 16:8 L:D cycle

(20-W GE #F201-T2-CW light source in photophase, <0.05 lux

in scotophase). During the photophase, groups of 50-75

newly-emerged adults were placed into plastic boxes (20 x

10 x 10 cm) with screen lids, where they remained without

food or water until testing began 3-5 days later.


The IMM pheromone, (Z,E)-9,12-tetradecadien-l-ol ace-

tate (ZETA), purchased from Storey Chemical Co., Willoughby,

OH, was purified twice before use by elution with benzene

through a column of 25% AgNO3 on silicic acid. Gas and

thin layer chromatographic analyses indicated that the

purified ZETA was at least 99% pure. Between tests the

ZETA was stored at -25 C.

The ZETA was dispensed from a glass tube made by redu-

cing the unground ends of a 14 cm long by 2 cm ID assembly

of 24/40 ground-glass joints to 0.5 cm ID (Mayer, 1973).

About 5 min before a test the inside of the assembly was

coated evenly with a 0.5 ml aliquot of ZETA in diethyl ether.

The levels of ZETA in the dispenser ranged from 0 (control)

to 105 ng. After the ether evaporated, the assembled tube

was stoppered until the test began.


The bicassay was done in 3 (0.3 x 0.3 x 3.5 m) olfac-

tometer tunnels described previously by Mayer (1973). Each

tunnel had 4 closable sections designated S1-S4 in upwind

to downwind order in Fig. 1. Sl, S2, and S4 were 56 cm long,

and S3 was 140 cm long. The outlet of a pheromone dispenser

was placed near the center of S2 at point PD. Moths were

released near the center of S4 at point IR, 3 m downwind

from PD. The tunnels were supplied with filtered air (55-
4 3
60% RH, 3.6 x 10 cm /sec flow rate, 35-50 cm/sec velocity)

in one of 2 temperature ranges: 22-24 or 33-350C. Light

was provided by 8, rheostat-dimmed, 60 W tungsten bulbs

placed separately inside diffuser boxes spaced uniformly

around the perimeter of the room at the ceiling. The aver-

age light intensity inside the tunnels was monitored at 1

lux = 1.5 mw/m2.

The airflow pattern in the tunnels was depicted by

smoke plumes. The plumes were produced by either passing

humidified air through a dispenser tube at PD containing a

cotton swab soaked in a 1:1 mixture of TiC14 in CC14, or by

substituting a smoke generator (TEM Eng., Ltd., Crawley,

England) for the tube. Both methods generated plumes that

quickly dispersed into less and less distinct filaments.

Within 2 m downwind from PD, there was no more than a 4:1

variation in the observed smoke density across the tunnel's

cross-section. Because pheromone molecules disperse at



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least as fast as smoke particles (Miller and Roelofs, 1978),

these observations indicate that the average pheromone

concentration at IR is reasonably approximated by the ratio

of the dispenser's emission rate to the tunnel's airflow.

Bioassay Procedure

After preliminary experimentation the following proce-

dure was standardized: (1) During the first 2-5 h of the

scotophase, 40-50 male IMM were loaded into a screen cage

(17.5 x 20.3 x 25.4 cm) and placed at point IR in a tunnel.

(2) A period of 0.5-3 h ensued to allow acclimation. (3)

A dosed, stoppered dispenser tube was placed at PD. The

stoppers were removed and filtered air (22 C, 60 ml/min)

was passed through the tube. (4) Within 10 sec the holding

cage was opened allowing the IMM freedom to move within the

tunnel. After an additional 60 sec the sections were closed

and the number of IMM in each section was counted. The

upwind anemotactic response was estimated by the fractional

response, Fr, the number in S2 and S3 divided by the total

number in S1-S4. (5) The dispenser tubes and the holding

cages were washed and baked for 12 h at 2000C after each

use, and the tunnels were cleaned with ethanol twice a week

to minimize the possibility of pheromonal contamination.

The bioassay had an incomplete block design. A treat-

ment was one of 20 combinations of 2 temperatures (230, 340

C) and 10 tube doses (blank control, 0.3, 1, 10, 102, 103

3 x 103, 104, 3 x 104, and 10 ng). Tests were also done

o 4
at 17 C using 10 ng doses, but were discontinued because

of the negligible response. A block was a set of 6 treat-

ments tested on a given day at a given temperature. One

of the 6 was always a blank, placed randomly within the

block. At least 3 other treatments were randomized within

the remainder of the block to eliminate day-to-day varia-

tion in the IMM response from comparison of the treatments.

Response Analysis

The standard procedure for calculating a behavioral

threshold is to adjust the fractional response for the con-

trol (Abbot, 1925) and then to analyze the regression of

the probit adjusted response on dose (Finney, 1971). How-

ever, the stringency of the upwind anemotactic response

criterion kept the maximal response in this bioassay well

below 100%, contrary to the normal distribution of response

frequency assumed in probit analysis. If the response fre-

quency were normally distributed there would be a concen-

tration above which the response would approach 100%, just

as there would be a concentration below which the response

would approach 0%. The standard Abbot's correction accounts

only for deviations from the normal distribution at the 0%

limit. By contrast, the following 3-step procedure accounts

for deviations at both the 0% and the 100% limits, and is

more generally applicable to quantal bioassays.

First, the response was transformed to probit coor-

dinates using the normalizing equation (Box et al., 1978):

Nr = Prob (100(Fr-Frc) (I.1)

Where: Nr is the normalized response, in units of


Fr is the uncorrected fractional response;

Frc is the average fractional response in the


Frm is the maximum average fractional response

at the given temperature;

Prob is the integral operator (Finney, 1971).

In the usual Abbot's correction, Frm = 1. Next, the nor-

malized responses from Eq.I.l were fitted by the standard

probit analysis to the equation:

Nr = I + S Log (DD) (1.2)

Where: I is the temperature-dependent intercept, in

units of probits;

S is the temperature-dependent slope, probits

DD is the dispenser dose, g.
DD is the dispenser dose, vg.

Finally the Nr-DD regression line, Eq. 1.2, was converted

to Abbot's-corrected coordinates using the inverse transfor-


Pr = (Frm Frc) prcb-1 (Nr) (I.3)
1 Frc

Where: Pr is the Abbot's corrected % response (Abbot,

Prob- is the inverse probit operator.

To convert behavioral thresholds measured in units of

Vg dose to thresholds in the more practical units of mole-

cules/cm3, the relationship between a dispenser tube's dose

and the concentration in the tunnel must be quantified.

This relationship was determined by a calibration of the

tube's emission rate.

Calibration of Dispenser

At room temperature pheromone volatizes from a dispen-

ser tube at a rate proportional to the initial dose and in-

versely proportional to the duration of emission. To in-

vestigate this relationship, emissions from dispenser tubes

loaded with the pheromone (Z)-7-dodecen-l-ol acetate (Z7AC)

were collected in 1 mm ID x 30 cm long glass, or 1 mm ID x

70 cm long, stainless steel capillaries using a thermal

gradient GLC capillary collector (Brownlee and Silverstein,

1968), and quantified by standard gas chromatographic pro-

cedures. The results indicated that over doses of 1-175 ig

and emission durations of 15-180 sec, the emission rate

was a constant proportion of dose, independent of time

(Mayer and Mankin, in preparation). The constant of pro-

portionality between the dose and the output of ZETA, Ke,

was measured by a separate calibration bioassay at 23C,

similar to that described 2 sections previously, except for

step 3 which was changed to: (3') a polyethylene cap

emitting ZETA at a rate of 0.13 + 0.07 SE ng/sec, as mea-

sured by the method of Vick et al. (1978), was suspended at

PD. The tube dose evoking the same average blank-corrected

response as the cap was divided into the measured emission

rate of the cap to estimate Ke.


The fraction of tested IMM attracted to a dispenser

was sigmoidally proportional to the logarithm of the dose,

as shown in Fig. 2, and uniformly higher at 34 C than at

24 C. Each data point in Fig. 2 represents the mean of 8-10

treatment replications, with the vertical line indicating

the 95% confidence interval. The slope and intercept para-

meters of each regression line are listed in Table 1. Both

the slopes and the intercepts of the 2 lines are statisti-

cally different (t = 4.9 p <0.01, and t = 57.3 p <0.001,

respectively). The good fit of the regression lines to the

data, indicated by the low x2 values (p >0.5 at 23C and p

>0.75 at 340C), supports the use of the modified probit ana-

lysis for interpreting pheromonal stimulus-response relation-


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The pheromone concentration In an olfactometer at the

point of insect release, IR, was calculated d by assuming

that the dispenser output dispers'-s uniformly in the 3.6 x

104 cm3/sec airflow (Methods: oiractometer section).

The dispenser output is the produ0't of the dispenser dose,

DD, and the constant of proportionality between dose and

output, Ke, which can be estimate'i using point CP in Fig. 1,

the intersection of the 23 C dose response regression line

with the mean Abbot's corrected % response for 8 cap dis-

penser test replications. The Ke is the ratio of the cap's
emission rate to the tube dose at CP: 0.13 ng sec /2500

ng = 5.2 x 105 sec1. Thus, the concentration at IR is

C = 5.2 x 10-5 sec-/3.6 104 cm3 sec -1 DD
-9 -3
=1.44 x 10 cm DD (.4)

The threshold of upwind anemtaxis for a male IMM was

calculated using Table 1 and Eq. (.4. Following the stan-

dard procedure of probit analysis, the threshold was de-

fined as the concentration at whiCh the normalized fraction

of response was 0.5 (5 in probit Olits). Using the 2 values

of DD for Nr = 5 in Eq. 1.4 gives thresholds of 1.34 x 106

and 1.65 x 104 molecules cm-3 (2.'2 x 1015 and 2.74 x 10-17

molar) at 230C and 34 C, respecti\el, which are compared

with other reported thresholds in tablee 2.

Table 1. Analysis of the dose-response regression lines in
Fig. 1. Symbols I, S, Nr, and DD are defined in
Eqs. 1.1-2.

Temperature (oC)


I (probits)

I Standard error

S (probits/pg)

S Standard error

DD for Nr = 5 (ug)

Upper limit DD (95%)

Lower limit DD (95%)

Degrees of freedom










1.66 P>0.5










1.77 P>0.75



Table 2. Pheromonal behavioral thresholds of some insects.
Other thresholds are reported in Kaissling (1971).
The behavioral response criterion was upwind
anemotaxis for the IMM and orthokinesis for the
other insects.

Insect: Pheromone 3 References
(10 mol)

Bombyx mori:
17 C (E,Z)-10,12-hexadecadien-l-ol


Trichoplusia ni:

24 C Z7AC

Kaissling &

Priesner 1970

Sower et al.


Plodia interpunctella:

34 C

23 C





Chapter I

Trogoderma glabrum:
27 C (-)-14-methyl-(Z)-8-hexadecenal


Lymantria dispar:

25 C (Z)-7,8-epoxy-2-methyl octadecane

Shapas 1977

Aylor et al.



The results of the tioassay demonstrated that the upwind

anemotaxis threshold of the male IMM for its sex pheromone

is similar to the t-resholds of other insects for their re-

spective sex pheromncies. Inspection of Table 2 reveals that

the IMM 340C upwind anelnotactic threshold is similar to the

Bombyx mori (Linn;s- .;,?r Trichoplusia ni (Hubner) ortho-

kinetic thresholds, whilethe 23C threshold is closer to

the Trogoderma glabrum (Herbst) and Lymantria dispar (F.)

orthokinetic thresi.-)ds. 'IBy contrast, human olfactory
8 11 3
thresholds generally range from 10 to 10 molecules/cm

while the theoretical limit of olfactory perception is

about 200 molecules/Qni ':IKaissling, 1971). Because the 4

lowest thresholds in Table 2 approach this limit, it can be

assumed that these behavioral thresholds approximate the

corresponding perceptual thresholds. In addition, all of

the reported s2::phieromone behavioral thresholds are within

4 orders of' .>', 'e tie'-tis lower limit. Thus, if a trap-

ping model is applied to any insect whose threshold for

attraction .to.ex pheronone is unknown, the threshold can be

estimetedi'to l'.ie in '..e-nge of 10 to 10 molecules/cm3

Dose Dependence of the Attraction Response

In most respects, the attraction responses in Fig. 2

follow the standard sigmoidal relationship obtained with

many other insects (Schneider et al., 1967; Kaissling and

Priesner, 1970; Sower et al., 1971; Mayer, 1973; Shapas, 1977).

In particular, the change from 0 to 100% normalized response

occurs within about 4 concentration decades. However, de-

partures from the sigmoidal relationship appear to occur at

the highest tested doses. At 34C the response to 10 pg is

lower than the response to 1 pg, and at 23 the response to

100 pg is lower than the response to 30 pg. Neither of these

decreases are statistically significant, but they are sys-

tematic. In addition, similar decreases in response with

increasing dose have been reported in olfactometer studies

of other insects (Mayer, 1973; Fuyama, 1976; Hawkins, 1978),

and decreases in trap catch with increasing dose have been

reported in field trapping studies (Wolf et al., 1967;

Shorey et al., 1967; Gaston et al., 1971; Vick et al.,

1979). This suggests that the observed decreases are not

statistical irregularities.

One hypothesis for the response decrement is that the

pheromone could be contaminated with a slight amount of the

homolog (Z,Z)-9,12-tetradecadien-l-oi acetate, which is

known to act as an inhibitor of attraction behavior (Vick

and Sower, 1973). Such contamination is unlikely, however,

because the purified pheromone was found to be at least 99%

pure by gas and thin layer chromatography. More likely, the

observed decrease is the effect of an altered-behavior thres-

hold (Roelofs, 1978). The relationship between the upwind

anemotactic threshold and the concentration at which the

response begins to depart from the sigmoid supports this

hypothesis. According to Roelofs (1978), the altered-be-

havior threshold of an insect is typically about 3 orders of

magnitude above the orthokinetic threshold, which is somewhat

lower than the upwind anemotactic threshold. The observed

departure occurs near 10-5 ng/cm3, 2-3 orders of magnitude

above the upwind anemotactic threshold as predicted.

Temperature Dependence of the Attraction Response

The effect of temperature on the IMM upwind anemotac-

tic behavioral threshold is similar to that reported pre-

viously for the orthokinetic threshold of B. mori (see

Table 2). The B. mori threshold shifted 0.13 log units/oC

while the IMM threshold shifted 0.19 log units/C. A re-

lated effect on the percentage mating of T. ni was reported

by Shorey (1966). The most likely hypothesis for the ob-

served increase in threshold with decreasing temperature is

that the lower temperatures tend to inhibit flight in re-

sponse to pheromone. Indeed, in several preliminary assays

done at 17 C the IMM exhibited no response to 10 Pg doses

that were highly stimulatory at 230C. This effect may be

related to low temperature effects on flying activity re-

ported in a variety of other insects (Taylor, 1963; Bursell,

1964; Sanders et al., 1978; and references therein).

The findings regarding temperature effects suggest

that sex pheromone traps may capture more IMM at warm tem-

peratures than cool temperatures. Similar effects of tem-

perature on the pheromone trapping of other insects have

been reported by Showers et al. (1974), Marks (1977), and

Coster et al. (1978). The effects of temperature on trap-

ping are more complicated than the effects on attraction

behavior, however, because the temperature also affects the

rate of pheromonal emission from the trap and temperature

stratification can affect the pheromonal dispersal pattern

(see Chapter II). In addition, the temperature variation

may have a greater influence on the behavior of some

insects than the average temperature (Showers et al., 1974).

In summary, the upwind anemotactic threshold of the

male IMM to its sex pheromone is similar to the sex phero-

mone thresholds reported for other insects. The threshold

depends on temperature, mostly because the upwind anemotac-

tic response to pheromone is inhibited at low temperatures.

About 2 orders of magnitude above the behavioral threshold

there may be an altered-behavior threshold that causes a

modification of the attraction response.


The derivation of the model proceeds in stages of in-

creasing complexity. First, the general problem of attrac-

tion to an odorant source is simplified and expressed mathe-

matically in terms of quantifiable parameters. Then the

scope and complexity of the problem are increased by examin-

ing the qualitative effects of several unquantified factors.

Considerable simplification of the attraction problem is

achieved by adopting the following assumptions: (1) An

attractant chemical has a threshold concentration below

which its probability of stimulating an insect is nil. (2)

An attractant has a corresponding altered-behavior threshold

concentration above which the probability of the insect find-

ing a distant source decreases. (3) The attraction and

altered-behavior thresholds depend upon the insect's species

and age, the temperature, and the chemical nature of the

attractant, all of which are fixed in a given application of

the model. (4) The emission rate of the attractant source

is constant. None of these assumptions are strictly valid

under the usual modeling applications in which insect age,

ambient temperature, and source emission rate vary, but they

are nevertheless useful heuristically.

Because attraction and altered-behavior thresholds can

be measured by bioassay, the simplified problem obtained

using assumptions 1-4 is essentially solved once the at-

tractant distribution is determined. But even this is a

formidable task. The plume emitted from an attractant source

disperses in a complicated pattern that depends on the

characteristics of the airflow (Skelland, 1974). Three dif-

ferent cases will be considered in the derivation: dis-

persal in still air by molecular diffusion, dispersal in

turbulent air currents of zero average speed and direction,

and dispersal in turbulent or laminar air currents of con-

stant average speed and direction.

Case I: Molecular Diffusion

In still air, an attractant plume disperses by molecu-

lar diffusion, which is described by the mass-balance equa-

tion (Veigele and Head, 1978):

q = (- -DV2) C, (II.1)

Where: q is the rate of emission per unit volume, with

units of g sec-1 cm-3;

D is the diffusion coefficient, cm2 sec-1
C is the attractant concentration, g cm-3

represents differentiation with respect to time;
72 represents the Laplacian differential operator

(Protter and Morrey, 1966; p. 567).

Theoretically Eq. II.1 has many solutions, depending on the

initial concentration distribution and the first partial

derivative, 3C/3r, at all boundary surfaces. For heuristic

purposes it is convenient to assume that the source is sur-

rounded by a single boundary surface and the initial (t = 0)

concentration is zero everywhere inside the boundary. The

value of 3C/ar at this boundary is (Chamberlain, 1953;

Judeikis and Stewart, 1976; Draxler and Elliot, 1977):

DC d
r D C, (11.2)

Where: Vd is an empirical parameter, the deposition

velocity, cm sec-.

The solution to Eqs. 11.1-2 for dispersal inside a spheri-

cal boundary is (Carslaw and Jaeger, 1967, p. 367, and Ap-


2 22
(ah-l) 2+ a
Q n
2rnarD 2 2
n=l a 6 + ah(ah-l)
[sin(r6 )/6 ][l-exp(-D62t)], (11.3)
n n n

Where: Q is the emission rate of the source, g sec

a is the radial distance of the boundary sphere,

from the source cm;

r is the radial distance of the measurement po-

sition from the source, cm;

t is the duration of emission, sec;
h is the ratio Vd/D, cm ;

6 is the nth positive root of the equation
a cot (ae) + ah = 1. (11.4)

Equations 11.3-4 are not restricted particularly to

attraction problems with spherical boundaries because most

attractants have values of D and Vd that fall within fairly

narrow ranges, limiting the extent of boundary effects. The

molecular diffusion coefficient of a sex pheromone is about

0.05 cm2/sec (Wilson et al., 1969; Hirooka and Suwanai, 1976),

and most other attractants have molecular diffusion coeffi-

cients near 0.03-0.07 cm /sec (Monchiek and Mason, 1961;

Lugg, 1968). However, unless conditions are strictly con-

trolled, air currents usually occur that effectively in-

crease D to 0.1-0.5 cm /sec (Bossert and Wilson, 1963). The

magnitude of the deposition velocity depends primarily upon

the forces causing adsorption of the attractant vapor to

the substrate. Interfaces composed of different vapors and

different substrates have similar deposition velocities inas-

much as the vapor-substrate interactive forces are similar

(Judeikis and Stewart, 1976). Measurements of deposition

velocity typically vary over the range 0.1 to 10 cm/sec for

Iodine-plastic, SO2-concrete, and pheromone-vegetation in-

terfaces (Chamberlain, 1953, 1966; Judeikis and Stewart,

1976; Nakamura and Kawasaki, 1977). The following analysis

of Eqs. 11.3-4 shows that, when D and Vd fall within the

ranges given above, the effect of a boundary on the attrac-

tant distribution is usually small.

The spatial variation of the relative concentration,

Cr = C/Q, is depicted in Figs. 3-6 at several different

values of a, D, Vd, and t. The curves were calculated

from the first 700 terms of the series in Eq. 11.3, which

converged after about 200 terms except at small r and t.

The curve for a = corresponds to the boundless case, pre-

viously discussed by Bossert and Wilson (1963), whose solu-

tion reduces to:

C Q erfc (r/(4Dt)1/2) (I.5)
r 2TDr

Where: erfc is the complimentary error function (Carslaw

and Jaeger, 1967).

Inspection of Figs. 3-4 shows that the smaller the

boundary radius the smaller the variation of C with time,

and as t increases the difference between C in a bounded
and a boundless environment decreases. The 2 curves for

a = differ considerably from each other, but the curve

for a = 150 at t = 60 sec is quite similar to the curve for

a = 100 at t = 8.6 x 105 sec. After about 103 sec, there

is very little difference between the curves a = m, a = 1000,

and a = 100, short distances away from the respective boun-

daries. The curves for 103 sec are not plotted because they

Spatial variation of the relative concentration,
Cr = C/Q, at t = 60 sec. The regression lines
are calculated from Eqs. 11.3-4 with D = 1 cm2/
sec, and Vd = 1 cm/sec. The radius of the boun-
dary sphere, a, has units of cm.

Figure 3.

a=cc I a=1000
a = 150



o -3


Figure 4. Spatial variation of the relative concentration,
C = C/Q at t = 8.6 x 105 sec. The regression
lines are calculated from Eqs. 11.3-4 with D = 1
cm2/sec, and Vd = 1 cm/sec. The radius of the
boundary sphere, a, has units of cm.

= o00

a 10


1 2 3

Figure 5. Variation of the relative concentration, C =
C/Q, with respect to the diffusion coefficient D.
The regression lines are calculated from Eqs.
II.3-4 with t = 8.6 x 105 sec, Vd = 1 cm/sec,
and a = 1000 cm. D has units of cm2/sec.

~' -2-
D= I. O

D =10
-4 -
.J -5-



C 8-
I 2 3
LOG (r)

Figure 6. Variation of the relative concentration, C =
C/Q, with respect to the deposition velocity,
Vd. The regression lines arecalculated from
Eqs. 11.3-4 with t = 8.6 x 10 sec, D = 1 cm2/
sec, and a = 1000 cm. Vd has units of cm/sec.

I 2 3
LOG (r)

are quite similar to the curves in Fig. 4. Indeed, the

effect of the boundary can be disregarded so long as r/a<

0.9, unless D is considerably smaller than 1 cm2/sec.
Thisis sownin Fgs.-2
This is shown in Figs. 5-6, where D ranges from 10-2 to

102 cm2/sec, and Vd from 10-5 to 102 cm/sec, at t = 8.6 x

105 sec and a = 1000 cm. Even at the hypothetical lower

limit of the molecular diffusion coefficient, 0.1 cm2/sec,

the influence of the boundary is negligible until r/a>0.75.

Under these conditions, the exact geometry of a boundary

is unimportant, and the solution to Eqs. 11.1-2 under

any boundary geometry is similar to Eqs. 11.3-4. This

justifies the general use of Eqs. 11.3-4 in a model for

attraction in still air, provided that the results are

interpreted with caution and when the emission duration

is less than about an hour and/or r/a>0.9.

Case II: Dispersal in Airflow of Zero Average Velocity

The next step of the derivation is to consider the

effect of random air currents on the diffusion process.

In most applications of a model the air has some movement.

Often, random fluctuations of speed and direction occur,

caused by superimposed whirls or eddies of various sizes.

Eddies with a diameter greater than about 100 cm or less

than about 5 cm have little effect on an attractant plume

but eddies of intermediate diameter cause the plume to

disperse rapidly (Aylor, 1976).

This kind of dispersal, called turbulent or eddy dif-

fusion, is analogous to molecular diffusion. If the air-

flow has a near-zero average velocity, eddy diffusion is

described via Eq. II.1, replacing the molecular diffusion

coefficient with the sum of the molecular and eddy diffu-

sion coefficients. The eddy diffusion coefficient of a

vapor or an aerosol is 0.1-10 cm2/sec in a calm environment

(Sutton, 1953; Pasquill, 1961; Bossert and Wilson, 1963;

Allen, 1975). Just as in molecular diffusion, Eqs. 11.3-4

can be used as a general solution to the turbulent diffu-

sion problem, provided that the results are interpreted

with caution when t<3600 sec and/or r/a> 0.9.

Case III: Dispersal in Airflow of
Constant Average Velocity

The derivation of an attraction model is now completed

by considering the effect of relatively stable convection

on molecular and turbulent diffusion processes. An exact

mathematical description of convective-diffusive dispersal

does not exist, but many time-averaged statistical descrip-

tions have been published (e.g., Sutton, 1953; Pasquill,

1961; Lamb et al., 1975). The Sutton equation is:

2 2
C = 2Q exp[-x1.75 Y2 Z2 (I.6)
1.75 K K
K KvX y y

where: C is the attractant concentration, with units

of g sec-;

Q is the attractant's emission rate, g sec-1l

v is the mean air velocity, cm sec-;

X is the distance from the source along the

airflow axis, cm;

Y is the distance from the source along cross-

wind horizontal axis, cm;

Z is the distance from the source along the

vertical axis, cm;

K ,K are empirical constants whose values have been

tabulated for different turbulence levels,

cm0.125 (Gifford, 1960).

Equation II.6 has been incorporated into several of the mo-

dels cited in the introduction.

However, there are several cautions to using Eq. 11.6.

When barriers or thermal stratification interfere with free

air movement, or the airflow becomes highly unstable, tab-

ulated values of K and K are not very reliable (Sutton,
Y z
1953). Under such conditions, the dispersal pattern can be

observed directly by using smoke plumes, and the tabulated

values of K and K can be replaced with values determined
y z
by the extent of the plumes (Pasquill, 1961). Even allowing

for these effects, Eq. 11.6 provides no information about

the instantaneous concentration distribution, which is a

more important determinant of the insect's searching behavior

than the average distribution (Aylor, 1976). Qualitative

effects of differences in the instantaneous distribution can

nevertheless be incorporated into the model as follows.

An attractant plume typically consists of 3 distinct

regions that differ in shape (Aylor, 1976; J. Kittredge,

personal communication). Region I extends 0.5-10 m down-

wind of the source. The plume in this region is a single

filament whose width is smaller than the widths of the

smallest eddies; thus, it disperses solely by the slew pro-

cess of molecular diffusion. It splits into several fila-

ments in Region II, which extends from the edge of Region I

to about 50-70 m downwind, depending on the turbulence and

the air velocity (Hinze, 1975). In addition, it begins to

expand rapidly because its width is now comparable to the

widths of the smaller eddies, allowing dispersal by tur-

bulent diffusion. This expansion continues until the limits

of the plume become indistinct in the final region, which

extends downwind indefinitely from the edge of region II.

The plume has greater definition in region I than in region

II, and the least definition in region III.

The regional differences in plume shape can be used to

improve the model's estimates of the attraction space. Ac-

cording to current theories of flight orientation behavior

(Farkas and Shorey, 1974; Kennedy, 1974; and references

therein), an insect finds it easier to steer toward a source

when the plume structure is well-defined. A model incorpor-

ating this hypothesis predicts that an insect is more likely

to reach the source if it enters region I than if it enters

the other 2 regions. A corollary is that the smaller the

dimensions of the source, the greater the extent of region

I, and the greater the probability of an insect finding

the source.

The choice whether to use Eq. 11.6 or Eqs. 11.3-4 in

a particular application of the model depends upon the tur-

bulence level, the obstructing boundaries, and the shape of

the plume. If the shape of the plume is unknown, it can be

determined by smoke plume observations (see Chapter I).

Generally Case I dispersal, characterized by the absence of

turbulence, occurs only in a highly controlled environment.

If a plume in turbulent air is nearly spherical, Case II ap-

plies, and if it is ellipsoidal, Case III applies. The move-

ment of a plume in sheltered areas, cul-de-sacs, or a

closed, empty warehouse with an isothermal temperature dis-

tribution usually fits a Case II dispersal pattern, while

Case III dispersal is more likely to occur in open venti-

lated corridors or highly stratified air.

Before proceeding with applications of the model it is

appropriate to consider briefly the validity of Assumptions

1-4 and the precision of the dispersal equations. The sim-

plified problem obtained by adopting these assumptions ne-

glects such behavioral factors as visual attraction (Shorey

and Gaston, 1965; Hienton, 1974), anemotaxis (Kennedy, 1974),

habituation (Thompson and Spencer, 1966; Traynier, 1968;

Sower et al., 1973; Marks, 1978) and changes in the in-

tensity of a response at different attractant concentrations

(Cain and Engen, 1969; Mayer, 1973; Bartell and Lawrence,

1977). None of these factors are quantified very precisely;

consequently, their inclusion in the model would not neces-

sarily improve its precision at this time. The model also

neglects such physical factors as pheromonal liability (Lund-

berg, 1961; Sower et al., 1975) differences in the ratios

of attractant components (Roelofs, 1978), and changes in

the emission rate of the source at different temperatures

and airflows. These factors, as well as the statistical

nature of atmospheric mass-transfer processes, limit the

precision of the dispersal equations used in the model.

Because of these limitations, the model must be used in

conjunction with, rather than instead of experimental

studies. Notwithstanding, the model provides considerable

insight into the attraction process, as shown by the follow-

ing applications.


The applications presented here are concerned primari-

ly with Case II dispersal because Case I is of little prac-

tical interest and Case III has been treated in detail by

the models cited earlier. Under Case I dispersal, the model

treats the hypothesis (Traynier, 1968; Perez and Hensley,

1973) that pheromone-laden air tends to sink. Under Case II,

attraction spaces and altered-behavior spaces are calculated

for calling insects and sex pheromone traps. The model

also deals with attraction to competing sources. Under

Case III, the model entertains the possibility that insects

can be attracted from outside a warehouse.

Case I Dispersal: Effect of Gravity on Pheromone in Still

Equations 1.1, 3, and 4 do not consider gravitation;

thus, by default they predict that the dispersal of phero-

mone in still air is unaffected by the high molecular

weight of pheromone molecules relative to the weight of air

molecules. It will now be shown that this prediction re-

mains unchanged after gravitation is incorporated into the


The effect of gravity is determined by Archimedes'

principle (Sears, 1958, p. 365), in that an air-pheromone

mixture is subject to a gravitational force proportional to

the difference between the density of the mixture and the

density of the air surrounding it. The standard density of
-3 3
air is p = 1.3 x 10 g/cm (Sears, 1958). The density of

the air-pheromone mixture is, by definition:

p = m + m (II.7)
ap a p

Where: m is the mass of air inside V, g;
m is the mass of pheromone inside V, g;
V is the volume, cm3.

The pheromone vapor density, m /V, reaches a maximum

at partial pressures approaching the vapor pressure, the

pressure exerted by the pheromone vapor when the air is

saturated. The vapor pressure and the corresponding sa-

turated vapor density of a 12-16 carbon sex pheromone are

about 1 x 10-4 cm-Hg and 10 ng/cm3, respectively (Hirooka

and Suwanai, 1976). The magnitude of m /V in Eq. II.7 can

be calculated by combining Dalton's Law of Partial Pres-

sures, the Ideal Gas Law, and the relationship between

mass and molecular weight which are respectively,

P = P + P (II.8)
at P a

PV = NRT, (11.9)


m = NM, (II.10)

Where: P is the pressure in units of cm Hg or dyne

N is the number of moles;

R is the gas constant, 8.31 x 107 ergs mole-1


T is the temperature, deg Kelvin;

m is the mass, g;

M is the molecular weight, g/mole.

The subscripts a, p, and at, refer to unadulterated

air, pheromone, and atmosphere, respectively. The result

of combining Eqs. II.8-10 is

m /V = p m M /VM (II.11)
a a pa p

Accordingly, Eq. 11.7 can be rewritten:

P = p + m (l-M /M )/V. (11.12)
ap a p a p

M the molecular weight of air, is about 29 g/mole and M ,
a p
the molecular weight of the pheromone, is about 225 g/mole.

Given a maximum value of 10 ng/cm for m /V, the maximum
density of the air-pheromone mixture is:

-3 -9 3
P = 1.3 x 10 + 8.7 x 10 g/cm (11.13)

This shows that there is essentially no difference between

the density of the air-pheromone mixture and the unadulter-

ated air; so by Archimedes' principle, gravity has little

effect on the mixture.

By contrast, a solvent such as diethyl ether may sink

in still air because it has a high vapor pressure, about

442 mm-Hg. Using Eq. 11.9 and the conversion factor 1 cm-Hg

= 1.33 x 104 dynes/cm,

-3 3
m = M P = 1.75 x 10 g/cm (11.14)
e e

where: M is the molecular weight of diethyl ether,
74 g/mole;

m is the mass of ether inside V, g.

Accordingly, the density of the air-diethyl ether mixture

is p = 2.36 x 10-3 g/cm3
The net force on 1 ml of ether-saturated air is, by

Archimedes' principle:

F = (p -p ) 980 cm4/sec2 = 1.04 dynes.
ae a

After 1 sec a ml of ether-saturated air falls at the


V x 1 ml (1 sec) = 440.7 cm/sec.

This is about half the rate of fall of a solid object. How-

ever, immediately after the mixture is emitted it begins to

disperse into the air. Within a short period of time the

density inside V equilibrates with that of the surrounding

air and the rate of fall decreases to zero.

Case II Dispersal: Attraction and Altered Behavior
Spaces of IMM

If the attraction and altered--behavior thresholds of

an insect are known, Figs. 3 and 4 provide estimates of the

attraction and altered-behavior spaces of an attractant

source in a Case II environment. The insect considered

here is the widespread postharvest pest, P. interpunctella

(IMM). A male IMM has an upwind anemotactic threshold of

6.8 x 10-9 ng/cm3 (10-17 molar) at 34C, 5.6 x 10 ng/cm3

at 23 C, and it has a hypothetical altered-behavior thres-

hold of about 10-5 ng/cm3 (see Chapter I). A calling vir-

gin female IMM emits pheromone at 8 x 10-4 ng/sec (Sower and

Fish, 1975), and typical sex pheromone traps for capturing

IMM emit 0.01-0.76 ng/sec (Vick et al., 1979). The rela-

tive thresholds for each emission rate and temperature are

given in Table 3. Insertion of the IMM female's relative

attraction threshold into Fig. 3 demonstrates that the at-

traction space of a female after one min of calling is

rather insensitive to temperature but somewhat dependent

on boundary position. The entire volume inside a boundary

of 150 cm radius is an attraction space. The attraction

space inside a boundary of 1000 cm radius is a sphere of

about 250 cm radius. In a boundless environment, the at-

traction sphere has a radius of about 40 cm. Actually,

there is little practical difference among these radii. The

spaces calculated by the model for the IMM are compared with

Table 3. Relative attraction thresholds, C = C/Q, and
relative altered-behavior thresholds, Crd, for a
female IMM and 2 sex pheromone traps emitting at
different rates. Units of Cr and Crd are sec/

Female Pheromone Pheromone
Parameter IMM trap trap

Q (ng/sec) 8 x 10-4 0.01 0.76

Cr at 23 C 7 x 10-4 5.6 x 10- 7.4 x 10-7

34 C 8.5 x 10-6 6.8 x 10-7 8.9 x 109

C 1.25 x 102 10-3 1.3 x 105

the spaces for different insects in Table 4. The difference

between the first 2 estimates, derived from Eq. II.1, and

the last 2 estimates, derived from Eq. 1.6, indicates

primarily the effect of convection on the pheromone disper-

sal pattern.

Hitherto, the concept of an altered-behavior space has

been applied to traps but not to calling insects, perhaps

because it had been assumed that the concentration around a

calling insect does not rise above the altered-behavior

threshold. According to the model however, calling females

of both IMM and Trichoplusia ni (Hubner) species are sur-

rounded by altered behavior spaces of small but definite
extent. Using Table 3 and Fig. 3, the altered-behavior

threshold of a female IMM occurs at about 6 cm. A female

Trichoplusia ni (Hubner) emits pheromone at the rate of 0.1

ng/sec, and a male has an activation threshold of about

3 x 10- ng/cm3 (Sower et al., 1971). If it is assumed that

the altered behavior threshold is 10-4 ng/cm3, 3 orders of

magnitude above the activation threshold (Roelofs, 1978),

the relative threshold is Crd = 10-3 sec/cm3, and from Fig.

3, the altered-behavior space is a sphere of about 15-60

cm radius.

The attraction and altered-behavior spaces of IMM sex

pheromone traps can be determined using Table 3 and Fig. 4.

If either trap in Table 3 is the source, essentially the

entire volume inside a boundary of 10 or 1000 cm radius is


Table 4. Calculated values for the maximal communication
distance or attractive range of an insect, using
either Eqs. 11.3-4 or Eq. 11.6.


Plodia interpunctella (Hubner)

Pogonomyrmex badius (Latreille)

Trogoderma glabrum (Herbst)

Hyphantria cunea (Drury)

Spodoptera litura (F.)

Trichoplusia ni (Hubner)

Range(m) Reference

0.4-2.5 Chapter II

1.04 Bossert & Wilson


0.8-10 Shapas (1977)

3-10 Hirooka &

Suwanai (1976)

80 Nakamura &

Kawasaki (1976)

1-100 Sower et al.


above the attraction threshold. At 0.76 ng/sec the entire

volume is also above the altered-behavior threshold. By

contrast, the 0.01 ng/sec trap has an altered-behavior

sphere of 71 cm radius inside a 1000 cm boundary and 45 cm

radius inside a 100 cm boundary. This suggests that a trap

emitting 1 ng/sec might capture fewer IMM than an otherwise

identical trap emitting 10-3 ng/sec.

Because the male IMM anemotactic threshold to sex

pheromone is about 2 orders of magnitude higher at 230C

than at 34 C, it is surprising that there is little effect

of temperature on the predicted attraction space of a cal-

ling female or a pheromone trap. This result is due to a

rapid decrease in C with respect to position once C falls
r r
below about 10-4 sec/cm3. The temperature could have a
large effect if the threshold C were higher than 104 sec/
cm Such high threshold values of C may occur for non-
pheromonal attractants.

The model cannot be used to calculate attraction to

competing sources unless the attraction spaces are nonover-

lapping or the principal searching mechanism is chemotaxis.

If the insect searches by additional mechanisms, e.g.

klinokinesis, chemokinesis or vision (Wright, 1958; Farkas

and Shorey, 1974; Wall and Perry, 1978; Baker and Carde,

1979) the problem of attraction to competing sources becomes

very complicated, particularly if trap-female competition is

considered. For example, a female IMM generally calls from

- 11 ' I


walls, ceilings, or other exposed surfaces. Typically, a

male IMM stimulated by sex pheromone orients visually to

such surfaces, investigating objects resembling female IMM

(Sower et al., 1975). This behavior increases the proba-

bility of locating a female but decreases the probability

of capture by a trap unless the trap is highly attractive

visually. Thus, as the density of female IMM increases,

a trap could lose efficiency much more rapidly than the

model would predict from comparisons of the attraction


However, if the attraction spaces are nonoverlapping

or the principal searching mechanism is chemotaxis, attrac-

tion to competing sources can be calculated by superposi-

tion of individual solutions of the model equations. The

procedure for nonoverlapping sources has been treated in

detail elsewhere (Knipling and McGuire, 1966; Nakamura and

Oyama, 1978), so only attraction under chemotaxis will be

considered here. Suppose 2 sources, El and E2, are located

500 cm apart in a warehouse whose length-width-height dimen-

sions are about 20 m each. If the emission rates of El and

E2 are equal and the attraction spaces overlap, an insect

inside the overlapping region will fly to the closest source.

If the emission rates are unequal, the probability of at-

traction to either source can be predicted using Fig. 4,

which indicates that a 10-fold decrease in pheromone concen-

tration is roughly equivalent to a 10-fold increase in the

distance from the source. Accordingly, when the emission

rate of El is 10-fold greater than that of E2, an insect

inside the overlapping space flies to El unless it is

within about 45 cm of E2.

Case III Dispersal: Attraction of Insects from
Outside a Warehouse

Equations 11.3-4 can be combined with Eq. 11.6 to

determine whether emission from a trap inside a warehouse

produces an above-threshold concentration of pheromone out-

side. Suppose that a trap emitting IMM sex pheromone at the

rate of 0.1 ng/sec is placed near the middle of a warehouse

whose length-width-height dimensions are about 20 m each.

After several days a 2 x 2 m door is opened. The ambient

temperature is 27 C, and the outside airflow is a constant

50 cm/sec. The Ky and K in Eq. 11.6 are assumed to have

the values tabulated by Sutton (1953) for dispersal under
stable conditions, 0.4 and 0.2 cm respectively. The

maximum rate of flow of pheromone through the door is

(Judeikis and Stewart, 1976):

Q = (RT/21M p)/2 C(4 x 104 cm2). (11.17)

The values of R and M are given in the Results: Case I

section. The concentration, C, is found by inspection of

Fig. 4, which indicates that the pheromone concentration
1-6 3 -5 3
near the door is about 10 ng/cm (C = 10 sec/cm ).

Inserting these values into Eq. 11.17 gives Q = 168 ng/sec.

This rate decreases immediately after the door is opened,

and continues to decrease to 0.1 ng/sec. For estimation

purposes it is convenient to choose Q = 10 ng/sec and Y =

Z = 0 in Eq. 11.6, which then reduces to

-9 -1.25 -1.75
C = 1.59 x 10 g cm x (11.18)

The behavioral threshold of a male IMM is ca. 10-17 g/cm3

(see Chapter I). Accordingly, the maximum downwind dis-

tance from which a male IMM can be attracted is

X = (1017 g cm-3/1.59 x 109 g cm- 125 -51

= 4.82 x 104 cm. (II.19)

If the pheromone is emitted from a 1 cm2 hole instead

of a 2 m x 2 m door, the emission rate is Q 4.2 x 1012

g/sec. At this rate Eq. 11.6 reduces to

-17 -3 -13 -1.25, -0.571
X = (10 g cm /6.68 x 10 g cm

= 569 cm. (II.20)

Thus, the attraction of insects from outside the warehouse

cannot be neglected unless the external openings are less

than about 1 cm area.


Some of the predictions resulting from the incorpora-

tion of boundary effects, plume shape effects, altered-

behavior thresholds, and gravitation into the attraction

model warrant further discussion. These factors are con-

sidered in order below, in the context of previously pub-

lished work.

Inclusion of boundary effects in the model results in

2 predictions. First, according to Figs. 3-4, the position

of the boundary is important at short emission durations ap-

plicable to a calling insect, but not at long emission dur-

ations applicable to a trap. Second, near a typical

boundary surface the attractant concentration is much lower

than it would be without the boundary, although the concen-

tration may remain at high levels if the deposition velo-

city is extremely low, e.g., 10-5 cm/sec in Fig. 6. Such a

boundary would be considered a reflector rather than an

adsorber. These predictions suggest that a flying insect

is more likely to be stimulated by sex pheromone or other

attractants than an insect sitting or walking on an adsorp-

tive surface. Observations by Visser (1976) on the host-

plant searching behavior of Leptinotarsa decemlineata Say

support such a hypothesis. A corollary hypothesis is that

a calling insect extending its pheromone gland away from

the surface on which it is sitting has a larger attraction

space than insect calling directly from the surface. The

former calling behavior occurs frequently in female IMM,

Bombyx mori (L.), and several other insects (e.g., Hammack

et al., 1976).

Consideration of plume shape effects in the Methods:

Case III section, led to the hypothesis that well-defined

plumes from attractant sources of small dimensions are more

efficient in attracting insects than indistinct plumes from

attractant sources of large dimensions. There are at least

2 experimental studies bearing in part on this hypothesis.

Lewis and Macaulay (1976) found that traps emitting well-

defined smoke plumes tended to capture more insects than

those emitting indistinct smoke plumes. In a related study

Macaulay and Lewis (1977) tested the effect of source

dimensions on trap catches with inconclusive results. How-

ever, there are objections to the methodology of the 2nd

study, in that the large-sized sources had 10-fold to 100-

fold greater emission rates than the small-sized sources.

Because the resulting attraction spaces of the large-sized

sources were much larger than the spaces of the small-sized

sources, the attraction efficiencies cannot be compared di-

rectly and further study is needed to confirm or deny the

hypothesized plume shape effect.

The altered-behavior spaces predicted by the model are

of theoretical use, not only for explaining decreases in

trap catches with increases in emission rate, but also for

suggesting the function of the altered-behavior threshold.

This is illustrated by the calculations in the Results:

Case II section, for the altered-behavior spaces of IMM sex

pheromone traps and calling females. Because the entire

volume inside a 100 or 1000 cm active space of a trap

emitting 0.1 ng/sec was an altered-behavior space, it was

proposed that a trap emitting 10-3 ng/sec might have a grea-

ter efficiency in a warehouse than a trap emitting 1 ng/

sec. Such an effect has not been observed with IMM, but

Vick et al. (1979) reported a similar effect in trapping

studies of Sitotroga cerealella (Olivier). In a 6.1 x 6.1

x 2 m room, traps emitting S. cerealella sex pheromone at

0.02 ng/sec captured more males than traps emitting 0.2


The finding that calling females of both IMM and T. ni

emit pheromone at rates sufficient to create small altered-

behavior spaces suggests a function for the altered-behavior

threshold. Under Case II dispersal the threshold occurs

about 6 cm away from an IMM female and 60 cm from a T. ni

female. The corresponding distances can also be calculated

for Case III dispersal using Eq. 11.6. In a relatively

calm airflow of 50 cm/sec, the altered-behavior threshold

occurs about 4 cm downwind from an IMM female and 18 cm

downwind from a T. ni female, using K K = 0.08 cm0"25
y z
Crd = 1.25 x 10-2 sec/cm3 for IMM and Crd = 10-3 sec/cm3

for T. ni. The existence of this threshold may increase

the probability of a stimulatedinsect finding a calling

insect because it alters the searching behavior from an

extensive search pattern to a more intensive search pattern

(Roelofs, 1978). The limited range for the altered-behavior

spaces of the 2 insects supports this hypothesis.

It remains to discuss hypotheses explaining why search-

ing insects tend to approach calling insects or traps from

below in still or nearly still air (Traynier, 1968; Killiner

and Ost, 1971; Murliss and Bettany, 1977). The usual hypo-

thesis is that pheromone falls in still air, but this is

shown to be invalid in the Results: Case I section. One

alternative hypothesis is that the presence of a reflective

boundary below the source could result in a greater concen-

tration of pheromone just above the boundary surface than at

positions some distance above the plume axis. Inspection of

Figs. 3, 4, and 6 indicates that this could happen if both

Vd and t are small. Another hypothesis is that the turbu-

lence level tends to be proportional to height above ground;

thus, the plume may be more well-defined and easier to fol-

low near the ground than at greater heights. However,

neither hypothesis explains why an insect would approach the

trap from below in low airspeeds but not in high airspeeds.

It is also possible that the behavior is relatively indepen-

dent of the actual pheromone distribution. Further study is

necessary to resolve these questions.

Considerations of predictions based on the model leads

to the following hypotheses for optimizing sex pheromone

trap design and placement: (1) Sources of small dimensions

produce more well-defined plumes for longer distances than

sources of large dimensions. Thus, trap catches could be

improved by reducing the dimensions of the source. (2) If

the insect has an altered-behavior threshold, a trap emit-

ting a high rate and producing an above-threshold concentra-

tions could capture fewer insects than a trap with a low

emission rate. Thus, an experimental design using a large

number of traps with small active spaces may be a more

effective monitor of the pest population than a design using

a small number of traps with large active spaces. A side

benefit of the former design is that it mitigates the ef-

fects of temperature inversion and barriers on pheromonal

distribution. (3) If there are openings greater than about

1 cm2 in a warehouse, pheromone sources inside can attract

pests from outside the warehouse. Warehouse pest monitor-

ing experiments should be designed to account for this effect.


A model of insect attraction to odorant sources was

derived, unique in its treatment of adsorptive boundaries

obstructing odorant flow. The generality and versatility

of the model was demonstrated by considering the attraction

of several different insects to sex pheromone sources in

warehouse, field, and still-air environments. Because the

important relationships of the model are presented graphi-

cally as well as mathematically, and because pheromonal be-

havioral thresholds generally range between 102 and 106

molecules/cm the procedure for estimating attraction of

other insects to sex pheromone sources is manifest. Calcu-

lations of the model resulted in testable, experimentally

supported hypotheses regarding optimal trap designs, and the

effects of different parameters on the odorant concentra-

tion distribution. Further improvement in the precision

of the model requires a better understanding of searching

behavior, rather than a more precise quantitation of odor-

ant dispersal. These considerations lead to the following

conclusions: (1) The model can be applied to a wider range

of attraction problems than previous models, which increases

its usefulness for pest management studies and theoretical

analyses of the attraction process. (2) It offers new in-

sights into improving techniques for monitoring insect



pest populations. (3) Future experimental and theoretical

studies of insect attraction should be directed more toward

increasing the quantitative and qualitative understanding

of searching behavior and less toward refining calculations

of the odorant concentration distribution.


Because the mathematics of thermal and mass diffusion

are equivalent, Eq. 11.3 can be derived from the heat-

transfer equation for a unit instantaneous heat source

(Carslaw and Jaeger, 1959, p. 367):

2 2 2
m (ah'-1) + a 0
T = 1
2Trarr a2 2 + ah'(ah'-l) (A.1)
n=l n

sin(rn ) sin(r'e ) exp (-K2 t),
n n n

Where: T is the temperature, deg C;

a is the boundary radius, cm;

r is the radius at which the temperature is

calculated, cm;

r' is the radius of the source, cm;
h' is the ratio H/K, cm ;

H is the coefficient of surface heat transfer,
-2 -2 -1 1
cal cm sec sec deg C;

K is the thermal conductivity, cal sec-1 cm-1
deg C;

K is the thermometric conductivity, cm sec- ;

6 is the nth positive root of the equation
a cot(aO) + (ah'-l) = 0. (A.2)


The boundary conditions specify that 0
unit instantaneous source at r = r'. Heat transfer at a

is governed by the equation

S= HT, (A.3)

where: O is the flux, the number of calories trans-

ferred across a 1 cm2 surface in 1 sec

(Carslaw and Jaeger, 1967, p. 19).

The heat diffusion equation can be transformed to a mass

diffusion equation by replacing T with C, K with D, and H

with V (Carslaw and Jaeger, 1967, p. 28):

2 22
S(ah-l) + a 0
C = 1 E
2 arr' 2 2 (A.4)
n=l a 2 + ah(ah-l)

[sin(ro )sin(r'e )exp(-De t)],
n n n

where: h is the ratio, V /D, cm

To convert from a diffusion equation for a unit instan-

taneous source to the equation for a source emitting at the

constant rate, Q, Eq. A.4 must be integrated over the mea-

surement period. It is also convenient to use the approxi-


sin(r'0 )
n =1, (A.5)
r' en

which is valid for r'<< a. Accordingly,

(ah-l)2 + a2 82
C = E (e ) sin (r )
S2nar 2 2 (0n) sin (rOn)
n=l a 2 + ah(ah-l)
t 2
I exp [-D2 (t-t')] dt',
o n

which gives Eq. 11.3 in the text:

2 22
(ah-l) + a e
C = Q ___ n (A.7)
2 2
2iarD n=l a 9 + ah(ah-l)

[sin(re )/o ][l-exp(-D 2t)].
n n n


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The author was born on Valentine's day 1948. From

1966 to 1970 he attended New Mexico State University on

a National Merit Scholarship, obtaining a B.S. in physics

and a B.S. in mathematics. Concurrently, he worked part

time at the Physical Science Laboratory in Las Cruces,

New Mexico, testing quality control in telemetry antennas

for rockets. From 1970 to 1973 he participated in the

graduate physics program at the University of Florida,

majoring in biophysics. Then he became a laboratory

technician at the U. S. Department of Agriculture, Insect

Attractants, Behavior, and Basic Biology Research Laboratory

in Gainesville, Florida.

A master's thesis in 1976 and this dissertation both

stem from work performed under this tenure.

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.

Philip '. Callahan, Chairman
Professor of Entomology

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.

Marion S. Mayer
Associate Professor of Entomology

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.

/James L. Nation /
SProfessor of Entomology

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.

Robert / Cohen
Associate Professor of

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.

John F. Anderson
Associate Professor of Zoology

This dissertation was submitted to the Graduate Faculty of
the College of Agriculture and to the Graduate Council,
and was accepted as partial fulfillment of the requirements
for the degree of Doctor of Philosophy.

August 1979

Dean College of Agr ilture

Dean, Graduate School

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