ity LT
99
at a target temperature of 46°C, and 2 the decrease in LT
99
due to lethality in the range 42 – 46°C which results in insect mortality as mea-
sured at 46°C. The mortality of fruit fly eggs associated with any temperature ramp from 30 to
46°C can be described by this model.
2. Material and methods
All experiments were carried out at the Poc- quereux Research Station, New Caledonia.
2
.
1
. Insects Adult B. tryoni were field collected and subse-
quently maintained in the laboratory on yeast, fruit fly bacteria Enterobacter cloacae Jordon,
water and sugar, under natural light at 26 9 1°C. Fruit fly colony rearing methods were very similar
to those described by Clare 1997. Eggs were collected from adult females which oviposited
through holes punched in the side of plastic cylin- ders 30 mm internal diameter by 46 mm long by
1 mm wide. The inside surface of the cylinders were smeared with diet consisting of banana fruit
pulp, and were then exposed to the adults for 2 h. Eggs were washed from the cylinders with water,
placed on dampened filter paper in a closed petri dish and incubated for 24 h in a photoperiod of
12:12 L:D at 26 9 1°C for treatment as mature eggs 26 – 28 h old.
2
.
2
. Heat treatment Eggs were heat-treated in plexiglass tubes 34
mm internal diam. by 50 mm length. Fine mate- rial gauze 5.5 strands per mm, 35 open area
inserts were placed into the end of each tube to keep the eggs in the tube while facilitating rapid
water movement through the tube. Treatments were applied in a water bath system Purbeck
Limited, New Lynn, Auckland, NZ consisting of four 25 l water baths. Heater units Grant, Cam-
bridge, UK Model ZD, temperature accuracy 9 0.01°C
on each
bath were
independently controlled by a laptop computer running Work-
bench PC for Windows data acquisition and con- trol software Strawberry Tree, Sunnyvale, CA
94086. The target temperatures were verified for each test using an electronic reference thermome-
ter Model RT200, Measurements Standards Lab- oratory of New Zealand, Industrial Research
Limited, Wellington, NZ certified for accuracy under the Measurements Standards Act 1992 by
the Measurements Standards Laboratory.
Immediately before treatment, approximately 200 eggs were washed into each treatment tube
with between eight and 14 tubes prepared for each test. Treatment tubes were simultaneously im-
mersed at the start of each test. Immediately following the selected immersion time 1 min to
13 h depending on treatment, individual tubes were removed from the hot water bath, drained
and immersed in 25.0 9 1.0°C water for 2 min hydro-cooling cycle. Control insects for each
treatment were hydro-cooled for a period that exceeded the longest hot water immersion of that
treatment by 2 min.
Following immersion in 25.0 9 1.0°C water, the treated and control eggs were washed from each
tube onto gauze material and placed on moist filter paper inside petri dishes 9 cm diameter.
Each petri dish was sealed with a strip of Parafilm
®
to prevent egg desiccation.
2
.
3
. Static temperature lethal heat treatments To assess mortality response to constant static
temperature treatments in the lethal range \ 42°C, B. tryoni eggs were immersed in static
temperature water baths at 42, 43, 44, 45, 46, 47 and 48°C for various times 1.5 – 380 min, depend-
ing on temperature. The mortality observed for each temperature, T, at intervals t
i
gave a direct value for mortality as a function of static temper-
ature treatment time. After heat treatment the eggs were hydro-cooled as described above. Three
to six replicates were completed at each immer- sion temperature.
2
.
4
. Static temperature conditioning heat treatments
In order to determine the effects of exposure to temperatures in the non-lethal range 30 – 42°C
on the mortality response, B. tryoni eggs were first immersed in a water bath at 32, 34, 36, 38, 40 or
42°C for times ranging from 15 min to 12 h depending on the temperature bath employed.
The tubes containing eggs were removed from the pretreatment bath, drained of hot water and
within 2 min simultaneously immersed in a second water bath operating at 46°C. Samples were re-
moved after various exposures 0 – 70 min until the lethal time for 99 mortality LT
99
could be established. The samples were then hydro-cooled.
Comparison of LT
99
for conditioned and non- conditioned eggs provided a quantitative measure
of the conditioning as a function of temperature and time of the treatment. The temperatures and
exposure durations of the pretreatment were cho- sen so that conditioning and not mortality would
result. This was verified in each test with a second control, which experienced the pretreatment com-
ponent only. Three to seven replicates were com- pleted at each pretreatment time and temperature
combination. Fig. 1 illustrates the procedure sche- matically for a case where the first group of
samples was immersed directly in the 46°C target bath, the second group of samples was pretreated
at 38°C for 30 min and then immersed in the target 46°C bath, and a final group of samples
was pretreated at 38°C for 60 min before being immersed in the target 46°C bath. Samples were
removed at intervals from the 46°C bath, the number of non-hatched eggs determined for each
sample and the LT
99
times evaluated.
2
.
5
. Ramped heating Although the static temperature treatment re-
sults provide an assessment of mortality due to exposure to particular temperatures in the range
30 – 48°C, it is the effect of the continuously changing temperature during ramped heating that
comes closer to addressing the insect mortality response as it occurs in whole fruit. To mimic
this, B. tryoni eggs were immersed in a water bath which changed temperature linearly with time
from 30 to 46°C in 1, 3, 6, or 9 h heating rates of 16, 5.3, 2.7 and 1.8°C h
− 1
respectively. The eggs so treated were then maintained at 46°C until the
LT
99
value could be established. A comparison of the LT
99
for eggs undergoing ramped heating and the LT
99
s for eggs immersed in 46°C without prior treatment then provided a direct measure of the
conditioning due to temperatures and times en- countered for a particular ramp. The effect of
ramped heating from 25 to 48°C in 1 h 23°C h
− 1
was also determined. Longer ramp times to a target of 48°C were of limited value because of
the high levels of kill at 48°C and temperatures near this target. Three replicate tests were con-
ducted at each ramp. Fig. 2 contains a schematic of the procedure for the smooth linear ramp used
in experiments as well as a step-wise ramp which will be used later to illustrate the connection
between static and ramped treatments.
2
.
6
. Mortality assessment Egg hatch normally begins about 40 h after
laying. Treated and control eggs were held at 26 9 1.0°C for 3 days to ensure all hatching was
complete and then examined for mortality using a binocular microscope 10 – 40 × magnification.
Egg mortality was based on the presence or ab- sence of an exit rupture in the chorion.
Fig. 1. Conditioning of B. tryoni eggs in 38°C water prior to immersion in 46°C resulted in the generation of ‘extra time’
needed at 46°C to achieve LT
99
estimated lethal times neces- sary to achieve 99 mortality. An extra 19 and 26 min were
generated for the 30 and 60 min conditioning treatments, respectively i.e. time required in addition to the 19 min for
non-conditioned eggs.
Fig. 2. Ramped heating treatments, where B. tryoni eggs were immersed in water which was then heated from 30°C to the
lethal target 46 or 48°C, and maintained at target until the LT
99
could be determined, were conducted over 1 depicted, 3, 6 and 9 h intervals. Smooth linear ramps were achieved in
the water bath trials while the step-wise ramp was used in the mathematical model to estimate the magnitude of conditioning
and lethality over the ramping period.
of the data. This method handles the variability in the response associated with occasional large
outliers Maindonald, 1992. Confidence intervals were calculated so that
non-overlap was equivalent to a statistically sig- nificant difference in a Student’s t-test at the 1
level. Although the log – log analysis of Eq. 1 can
be used successfully to determine LT
99
times we have utilized a kinetic expression for mortality
to model the response of B. tryoni eggs over the entire treatment history. Rather than use per-
centage mortality we shall use its complement, percentage survivors,
ST, t = 100 1 − mortality
1 − control mortality which incorporates Abbott’s method Abbott,
1925 to correct for control mortality. The treat- ment time, t, is the independent variable and the
equation used for S at each temperature is
ST, t = 100e
− k
L
t
2
2 This form is obtained by simplifying a form,
S = 100e
− c + kt1a
, suggested by earlier workers King et al., 1979 and used by several authors
to model lethal response of fruit flies Jang, 1986; Laidlaw and Hayes, 1990. The constant
‘c’ is normally small and was omitted, ‘1a’ ranges from 1.5 to 2.5 and was set near the
mid-point of the range so that only the ‘rate’ constant, k
L
, was retained as a temperature de- pendent parameter. To simplify notation we
drop the explicit reference to the independent variables and write ST, t = S.
2
.
8
. Model cur6e fitting The curve fits shown were initially obtained
using the defined-fit option of the Kaleidagraph suite of programs Kaleidagraph, 1997 and were
confirmed using the non-linear platform of the JMPIN suite of programs JMPIN, 1997. The
latter program also provided the confidence lim- its for the parameters obtained in the curve
fitting functions.
2
.
7
. Statistical methods for assessing LT
99
Analyses of observed mortality due to treat- ment at individual temperatures from 42 to 48°C
used the model:
log − log1 − p = a + bt, 1
where p was the expected observed mortality, and t was the treatment time in minutes Preisler
and Robertson, 1989. This gave approximate linearity in time. The estimated LT
99
, which re- lates to mortality after there has been allowance
for control mortality, was calculated to give an expected mortality of c + 1 − c0.99, where c
was the control mortality as determined in the 25°C immersion treatments. Eq. 1 was fitted
using a robust version of the generalized linear model analysis available in S-Plus Chambers
and Hastie, 1991 that assumed that any vari- ance was proportional to that of a binomial dis-
tribution. The robust version reduces the weight given to points lying away from the main body
3. Results
