Science, Irving K. Barber Faculty of (Okanagan)
DSpace
UBCO
Chambers, Ian
Master of Science - MSc
University of British Columbia
Codling moth is an invasive species in Canada that damages pomme fruit crops across the globe and has proven difficult to manage through the use of chemical sprays and the sterile insect technique (SIT). In my research I examine how codling moth populations may be evolving under the SIT to avoid management pressures. Photoperiod dictates the onset of diapause in codling moths and the SIT may be causing a change in the timing of diapause across wild populations by selecting for specific critical photoperiods. Previous modelling of the SIT has failed to address how diapause might be affecting the efficacy of the SIT. Furthermore, no one has examined if the critical photoperiod distribution of a population, and therefore the mean timing of diapause, in wild codling moth populations might change under the selection pressure exerted by the SIT. I hypothesize that the SIT as is being applied in the Okanagan Valley, selects for longer critical photoperiods in wild codling moths, causing them to enter diapause earlier in the year and avoid the higher SIT pressures present in the warmer months of the summer. I developed two mathematical models incorporating the SIT and diapause as a function of critical photoperiod to investigate how the distribution of critical photoperiod within a population may evolve under the SIT. This approach aims to help understand why the SIT has not led to eradication of codling moths as originally predicted, and contribute to future management efforts. I find that the SIT may be selecting for longer critical photoperiods, causing a higher proportion of the population to enter diapause after the first generation.
Evolution of Critical Photoperiod inCodling Moths Subject to the SterileInsect TechniquebyIan ChambersB.Sc., The University of British Columbia, 2016A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinThe College of Graduate Studies(Interdisciplinary Studies)(Sustainability)THE UNIVERSITY OF BRITISH COLUMBIA(Okanagan)May 2023© Ian Chambers 2023The following individuals certify that they have read, and recommendto the College of Graduate Studies for acceptance, a thesis/dissertation en-titled:Evolution of Critical Photoperiod in Codling Moths Subject to the SterileInsect Techniquesubmitted by Ian Chambers in partial fulfillment of the requirements forthe degree of Master of Science in Interdisciplinary Studies SustainabilityDr. Rebecca Tyson, Irving K. Barber School of Arts and SciencesSupervisorDr. Gary Judd, Agriculture and Agri-Food CanadaSupervisory Committee MemberDr. Robert Lalonde, Irving K. Barber School of Arts and SciencesSupervisory Committee MemberDr. Michael Noonan, Irving K. Barber School of Arts and SciencesUniversity ExamineriiAbstractCodling moth is an invasive species in Canada that damages pomme fruitcrops across the globe and has proven difficult to manage through the useof chemical sprays and the sterile insect technique (SIT). In my research Iexamine how codling moth populations may be evolving under the SIT toavoid management pressures. Photoperiod dictates the onset of diapause incodling moths and the SIT may be causing a change in the timing of dia-pause across wild populations by selecting for specific critical photoperiods.Previous modelling of the SIT has failed to address how diapause might beaffecting the efficacy of the SIT. Furthermore, no one has examined if thecritical photoperiod distribution of a population, and therefore the meantiming of diapause, in wild codling moth populations might change underthe selection pressure exerted by the SIT. I hypothesize that the SIT as isbeing applied in the Okanagan Valley, selects for longer critical photope-riods in wild codling moths, causing them to enter diapause earlier in theyear and avoid the higher SIT pressures present in the warmer months ofthe summer. I developed two mathematical models incorporating the SITand diapause as a function of critical photoperiod to investigate how thedistribution of critical photoperiod within a population may evolve underthe SIT. This approach aims to help understand why the SIT has not ledto eradication of codling moths as originally predicted, and contribute tofuture management efforts. I find that the SIT may be selecting for longercritical photoperiods, causing a higher proportion of the population to enterdiapause after the first generation.iiLay SummaryCodling moth is an invasive species that damages pomme fruit crops acrossthe globe and has proven difficult to eradicate. In this thesis, I use math-ematical models to investigate how the timing of entry into diapause asregulated by critical photoperiod, may be evolving under the sterile insecttechnique to avoid management pressures.iiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Life Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Diapause and Photoperiod . . . . . . . . . . . . . . . . . . . 21.4 Degree Days . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.5 Sterile Insect Technique . . . . . . . . . . . . . . . . . . . . . 41.6 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.7 Modelling evolution of critical photoperiod . . . . . . . . . . 82 Field Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3 Data Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 Population Dynamics Model . . . . . . . . . . . . . . . . . . . 173.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.2.1 Mathematical Model . . . . . . . . . . . . . . . . . . 203.2.2 Simulation Experiments . . . . . . . . . . . . . . . . . 263.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.3.1 Modelling Studies . . . . . . . . . . . . . . . . . . . . 27ivTable of Contents3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334 Daily Time-step Model . . . . . . . . . . . . . . . . . . . . . . 374.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.2 Daily Time-step Model . . . . . . . . . . . . . . . . . . . . . 384.2.1 First Generation . . . . . . . . . . . . . . . . . . . . . 394.2.2 Second Generation . . . . . . . . . . . . . . . . . . . 424.3 Simulation Experiments . . . . . . . . . . . . . . . . . . . . . 454.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.4.1 Model Adjustment . . . . . . . . . . . . . . . . . . . . 454.4.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . 465 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49vList of Tables2.1 Collected field data for weekly samplings of codling moth pu-pae and larvae. Data includes the number of pupae and lar-vae collected each week, the number that emerged as adultcodling moth, the number that entered diapause and the num-ber that died, as well as average weekly photoperiods for eachcollection date. . . . . . . . . . . . . . . . . . . . . . . . . . . 123.1 Table of the population dynamics model variables. . . . . . . 223.2 Table of the population dynamics model parameters. . . . . . 26viList of Figures2.1 Cumulative density function of the weekly proportion of codlingmoth entering diapause versus the average weekly criticalphotoperiod fit that was fit to field data. . . . . . . . . . . . . 142.2 Probability density function of the weekly proportion of codlingmoth entering diapause versus the average weekly criticalphotoperiod that was derived from the probability densityfunction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.1 Compartmental diagram showing the life stages and corre-sponding state variable of the population dynamics model . . 213.2 Critical photoperiod distribution over 5 years with and without sterile insects. . . . . . . . . . . . . . . . . . . . . . . . . 283.3 Distribution of critical photoperiod from simulations withsterile insects compared to the distribution calculated fromfield work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.4 The effects of the competitiveness of sterile insects in firstand second generations on the percentage of 5th instar larvaeentering diapause after the first and second generation . . . . 303.5 The effects of the overflooding ratio and first generation ster-ile competitiveness on the percent of population entering di-apause after the first and second generation. . . . . . . . . . . 313.6 The effects of the overflooding ratio and first generation sterilecompetitiveness on the population size after five years. . . . . 313.7 Sensitivity analysis on model parameters using partial rankcorrelation coefficients . . . . . . . . . . . . . . . . . . . . . . 334.1 Compartmental diagram of daily time-step model . . . . . . . 39viiChapter 1Introduction1.1 IntroductionCodling moth (Cydia pomonella L.) (Lepidoptera: Tortricidae), a key pest ofpomme fruits like apple and pear, that causes significant economic damageworldwide (Graf et al., 2018). Codling moth originated in central Eura-sia, but has since spread to most every apple growing region of the world,including locations on all six continents except Antarctica (Welter, 2009).Codling moth was noted as a pest in Europe as early as 1635, and its pres-ence was first recorded in North America in 1750 (Welter, 2009). Codlingmoth was first discovered in the Okanagan Valley in 1905 (Thistlewood andJudd, 2019).1.2 Life CycleCodling moth can have one or more generations each year, depending onfood availability and climatic factors such as air temperature, humidity,moisture, and photoperiod, and food availability (Blomefield and Giliomee,2011; Welter, 2009) . This means its reproductive potential can vary byits geographical location, for example, in Denmark a single generation oc-curs each year whereas in Pakistan four generations occur each year (Milo-rad, 1963). Okanagan pomme-fruit growers usually see two generations ofcodling moth each year, with a partial third generation sometimes showingup in southern regions in warmer than normal years (Thistlewood and Judd,2019).In the spring, adult codling moth begin to emerge from pupae oncethe overwintering larvae and subsequent spring puparia have accumulatedenough heat units (degree days). In spring, newly-emerged female codlingmoth tend to stay near trees on which the larvae overwintered on. Within24 hours of emergence female codling moth begin to secrete a sex pheromoneknown as codlemone that attracts male codling moths for mating pur-poses(Roelofs et al., 1971).11.3. Diapause and PhotoperiodMated females typically lay eggs on leaves near fruit located on the topouter edges of trees which are close to those trees where adult eclosion tookplace (Witzgall et al., 1999). Eggs are usually laid singly. Female fecundityis temperature dependent, with females becoming sterile in environmentsthat are either too warm or too cool (Blomefield and Giliomee, 2011). Onaverage, each female lays 40-60 eggs, however, clutch sizes of 10-100 eggshave been reported (Blomefield and Giliomee, 2011). An average of seventyfive percent of the eggs usually survive to hatch (Brown et al., 1978).The timing of egg hatching depends on climatic conditions, with hatchinginto 1st instar larvae, occurring on average, within nine to ten days of beingdeposited (Caesar, 1911). Upon hatching, a small (0.5-2 mm) pale yellow1st instar larva emerges from the egg and searches for fruit. Larvae feed onthe fruit skin and within a few hours enter the fruit, eventually eating theirway to the core of the fruit while proceeding through 5 larval stages (L1- L5) of development. On average each larvae spends 25 to 26 days insidethe fruit before emerging as a 5th instar larva (L5). The L5 are between18-20mm in length with a light brown colouring with darker brown spots(Milorad, 1963).Fifth-instar larvae use silk threads to lower themselves to the groundwhere they begin to look for a site to cocoon(Milorad, 1963). The 5th instarlarvae can detect light and use this ability to find the silhouettes of trees.The L5 larvae then climb the trunks of host trees looking for suitable sitesto spin their silken cocoons, usually in the crevices on the bark. Fifth-instarlarvae may also cocoon on the ground, but survival of ground-cocooninglarvae is low, and as such, these sites are less preferred (Brown et al., 1978).Cocooning 5th instar larvae can either pupate immediately, and becomeadults that form the next generation, or they enter diapause. Diapausing 5thinstar larvae stay in this suspended state of development until the followingspring when they pupate and emerge as adults.1.3 Diapause and PhotoperiodDiapause is a state of suspended development, similar to hibernation, thatallows survival under unfavourable conditions. In temperate climate regionsinsects must cope with future uncertainty due to seasonal environmentalfluctuations (Boivin et al., 2004). Diapause is a response to regular andrecurring periods of adverse environmental conditions as seasons change,allowing survival under conditions inappropriate for growth and reproduc-tion (Boivin et al., 2004). Diapause creates significant life-history trade-offs21.3. Diapause and Photoperiodbetween survival and reproduction if the favourable season extends beyondthe predicted period (Boivin et al., 2004). Therefore, the optimal timing ofdiapause in the life cycle is important.In temperate climate regions, seasonal changes in daylight length (pho-toperiod) are highly correlated with seasonal changes in environmental fac-tors affecting development such as temperature and food availability (Boivinet al., 2004). For example, summer temperatures usually rise after the sol-stice, but as air temperatures increase, daily photoperiod decreases. De-creasing photoperiod during the summer has been shown to be the majordriver for the timing of diapause (Boivin et al., 2004; Steinberg et al., 1992).Photoperiod at any point in time is also a function of latitude, and thephotoperiod triggering diapause has been shown to increase with latitude,though there is natural variability within populations due to genetic varia-tion (Boivin et al., 2004).In codling moth, the onset of diapause is controlled by the photoperiodto which the 5th instar larvae are exposed. Each individual larva has acritical photoperiod, and when the amount of light in a day drops belowthat critical photoperiod, the larva is triggered to initiate diapause (Boivinet al., 2004). Within populations the critical photoperiod varies among in-dividuals (R. H. Smith, 1989). Critical photoperiod, and thus the timingof diapause onset, is a heritable trait which can be selected for throughevolutionary pressures (R. H. Smith, 1989; Boivin et al., 2004). Kroonet al. (2004) found that as predation increased in spider mites (Tetrany-chus urticae) the percentage of individuals entering diapause also increased.Tougeron et al. (2017) found that increased competition to find hosts in ce-real aphids (Aphidius avenae (Haliday)) increased the number of individualsentering diapause. Boivin et al. (2004) showed that insecticide use selectedfor insecticide resistant genes, which corresponded to a shift towards highercritical photoperiods for diapause induction in codling moth populations.By entering diapause individuals can avoid periods of increased mortalityfrom predation, parasitoidism and insecticides, increasing their chances ofsurvival. Other methods of insect control, such as the sterile insect tech-nique (SIT), may also exert evolutionary pressure selecting for populationchanges in critical photoperiod.Although photoperiod is the main regulator of diapause in codling moth,other factors such as temperature, humidity, food availability, and densitycan act as modifiers (Steinberg et al., 1992; Boivin et al., 2004). For ex-ample, as temperature is important for codling moth development, cooltemperatures could slow development of larvae enough that it exposes more5th instar larvae to shorter day lengths (Steinberg et al., 1992). Similarly,31.4. Degree Daysif there is low food availability or poor quality, as a result of high densityof codling moth larvae in fruit, diapause could be triggered at longer daylengths than might otherwise happen, in order to avoid these unfavourableconditions and enhance survival (Steinberg et al., 1992).1.4 Degree DaysCodling moth, like all ectotherms, cannot actively control its body tem-perature. Development and growth rates of ectotherms are directly relatedto the environmental temperatures they experience. As temperatures in-crease, development speeds up, and as temperatures decrease, developmentslows down. Most development occurs between upper and lower tempera-ture thresholds that are unique to each species. Over this temperature rangedevelopment is a near linear function of temperature but outside this range,at the extremes, there is a nonlinear relationship between development andtemperature. Codling moth has a lower developmental temperature thresh-old of about 10 degrees centigrade (◦C) and an upper developmental tem-perature threshold of about 31◦C (Jones, 2020).Degree days are a measure of the heat units accumulated by an organismover a single 24-hour period. A single degree day is accumulated when theaverage daily temperature remains one degree above the lower developmenttemperature threshold for one entire 24-hour day. The degree-day methodhas proven useful for predicting codling moth development for managementefforts (Jones, 2020; Judd, 2020).1.5 Sterile Insect TechniqueThe sterile insect technique (SIT) was conceived by Knipling in 1955with the idea that releasing sterile insects into a wild population in suf-ficiently large numbers would interrupt natural reproduction and lead topopulation decline (Knipling1979). In order for this technique to properlyfunction, Knipling noted that knowledge of the target population’s repro-ductive biology, behaviour, and population dynamics are necessary (Dunnand Follett, 2017). Assumptions of a successful SIT programme include thata large number of individuals can be reared and sterilized, that sterile insectsmix thoroughly with the wild population and can successfully compete formates, and that the target population is closed (Dunn and Follett, 2017).Proverbs began researching the application of the SIT to control codlingmoths in the Okanagan region after becoming concerned with the impacts41.5. Sterile Insect Techniqueof insecticide use in apple production(Thistlewood and Judd, 2019). From1965 to 1980, Proverbs et al. (1982) showed that codling moth popula-tions could be reduced to undetectable levels with an area wide applicationof the SIT (Thistlewood and Judd, 2019). Roughly ten years later, theOkanagan-Kootenay Sterile Insect Release (OKSIR) programme began op-erating (Dyck and Gardiner, 1992) as the first programme to use the SITagainst codling moth populations (Thistlewood and Judd, 2019). Initiallythe goal of the OKSIR programme was to eradicate codling moth from theregion, which was later modified to an area-wide management programmefocused on reducing fruit damage from codling moth to low levels, and re-ducing insecticide use. The OKSIR Programme is now the world’s longestrunning area-wide management programme for codling moth (Thistlewoodand Judd, 2019). When the programme first began it operated on 7331hectares of pomme fruit orchards and has now grown to include approxi-mately 21,000 square kilometers including over 24,000 noncommercial sitessuch as parks, gardens, and road-sides (Thistlewood and Judd, 2019). El-ements of the OKSIR programme were developed from theory, applied re-search, and from adaptation of existing sterile insect programmes for otherspecies(Thistlewood and Judd, 2019). Little to no modelling of this specificmanagement system has been done.Mass rearing of codling moths is described in detail by Dyck (2010). Abrief summary will be presented here based on Dyck (2010) and Thistle-wood and Judd (2019). The OKSIR programme uses rotating cylindricalovipositing chambers lined with paper that is waxed on both sides. The cageis slowly rotated to ensure uniform distribution of the eggs on the wax paper.The wax paper is then removed from the cage, cut and placed on trays con-taining a sawdust-based diet in a temperature-controlled room. Hatchingand larval development are allowed to occur, and then the trays are movedto emergence rooms. Once the adults emerge, they fly upwards toward anultraviolet lamp where they are gently sucked through a collecting systemand deposited into bins in a cold room. The adults are then packed intopetri dishes, treated with radiation, and then returned to cold storage untiltheir release (Judd, Arthur, et al., 2011).Tuning the radiation dose so that the codling moths are rendered sterilebut remain competitive with wild moths is complicated and controversial. Adistinct feature of lepidopteran radiation biology is inherited sterility, whereindividuals can be partially sterile and produce offspring that are partially tofully sterile. Estimates of radiation doses that induce sterility in irradiatedcodling moths have varied from as little as 100 Gy to 400 Gy. Radiation hasother physiological effects that decrease competitiveness of the sterile moths51.5. Sterile Insect Techniquein their ability to successfully find a mate. The radiation causes sterileinsects to be more sensitive to temperature and moisture, which in turneffects their mobility and thus their competitiveness. Sterile moths are lesscompetitive than their wild counterparts, particularly in the spring whenconditions are cooler and wetter, allowing for increased mating betweenwild moths and decreasing the efficacy of the SIT (Judd and Gardiner,2006; Judd, Arthur, et al., 2011). When conditions are warmer and drier inthe summer, sterile codling moths are more competitive. Experiments haveshown that wild male moths are better synchronized than sterile moths inresponding to the calling of females looking for mates (Judd and Gardiner,2006). The radiation dose employed therefore is a compromise betweenthe level of sterility achieved, and the competitiveness of mating with wildmoths. The OKSIR programme has used a range of different radiation dosesfrom as little as 150 Gy to as much as 330 Gy. As of 2019 OKSIR employeda radiation dose of 200 Gy.The SIT works by overwhelming the wild population when a target ster-ile to wild ratio (overflooding ratio) is achieved across the entire site thatthe target population inhabits, to ensure sufficient mixing of the sterile andwild insects (Proverbs et al., 1982). Proverbs et al. (1982) identified anoverflooding ratio of forty sterile insects to one wild insect to be sufficientfor inducing a decline in the wild population (Thistlewood and Judd, 2019).For eradication, ratios between sixty to one up to 120 to one were suggested(Thistlewood and Judd, 2019). Currently the OKSIR programme targetsan overflooding ratio of 40:1 (Thistlewood and Judd, 2019). The currentgoals of the OKSIR Programme do not include eradication, rather the pro-gramme focuses on reducing the impacts of codling moth damage to lowlevels, reducing the use of insecticides, and achieving a low cost steady stateof operations (Thistlewood and Judd, 2019). Therefore, an overfloodingratio of 40:1 is used as it has been proven to reduce the wild populationlevel. Sterile insects are released weekly using a mechanical hopper andfan attached to an all-terrain vehicle that gently blows moths into the or-chard while driving up and down the rows (Thistlewood and Judd, 2019).The operational overflooding ratios achieved by the OKSIR programme areestimated on a weekly basis by counting wild and sterile male moths inpheromone traps. Sterile moths are identified by an internal red dye thatthey sequester during larval feeding in the mass-rearing facility.61.6. Models1.6 ModelsMathematical models are powerful tools that help explain the behaviourof systems, the effects different components have on the outcome, and allowus to make predictions into the future. Mathematical models allow us toinvestigate codling moth population dynamics more quickly and cheaplythan can be done in the field, and as a result, many models have beendeveloped for codling moths to aid in management efforts.Structured population models use transition equations to represent indi-vidual life stages. These models have been used to predict population trendsof codling moths over long time periods(Brown et al., 1978), and have beenused to predict the efficacy of insecticide application (Jones, 2020) and theSIT(Kean, Suckling, et al., 2011). Kean, Suckling, et al. (2011) developeda structured population model to investigate how inherited sterility wouldcontribute to the SIT. A drawback of these models is that they do not ac-count for changes in the environment within a season, such as temperature,which plays an important role in codling moth development. In addition, todate, no models have considered what the effects of having sub-populationsof individuals entering diapause at different times of the season might haveon the rate of extinction under SIT. Entering diapause early has been shownto be an effective method of escaping predators (Schroeder and Dalin, 2016;Kroon et al., 2004), parasitoids (Tougeron et al., 2017; Li et al., 2015) andinsecticides (Bird et al., 2020; Boivin et al., 2004). By entering diapauseearly, individuals escape periods of increased pressure, thereby increasingtheir chance of survival. The SIT exerts increased pressure on wild codlingmoths in the second generation, therefore entering diapause after the firstgeneration may be beneficial to allow individuals to avoid this increasedpressure.Several models based on ordinary differential equations (ODE) were usedin the development of SIT theory. Barclay (1980) used an ODE modelto determine the number of sterile insects that should be released. ODEmodels indicated that using sterile males or a combination of sterile malesand females could lead to eradication, however using only sterile femaleswould not (Barclay, 1980). ODE models were also used to investigate thestability of pest populations under SIT that were also affected by parasitoids(Barclay, 1987), predation (Barclay and Driessche, 1990), or by competitionfrom other species (Barclay, 1981).Time-varying distributed delay models have been used extensively in en-tomology as they allow individuals to progress through development at dif-ferent rates, and can incorporate changing environmental conditions. These71.7. Modelling evolution of critical photoperiodmodels have been used for codling moths to determine when specific lifestages will occur, and thus the appropriate timing of management interven-tions (Graf et al., 2018). For example, these models can indicate when eggshave been laid but not yet hatched to guide when ovicides should be appliedagainst codling moth (Jones, 2020).An individual-based model has been used to investigate how sterile in-sects interact with the wild population. They have been used to understandhow wild codling moth aggregations and wild female dispersal inhibit theability of sterile insects to disrupt wild pair mating (Tyson, Newton, Thistle-wood, et al., 2008). This model was used to investigate the impact of anobserved asynchrony between the mating times of sterile and wild codlingmoths (Tyson, Newton, Thistlewood, et al., 2008).Diffusion models have been developed to investigate how sterile insectsdisperse in an orchard setting and to guide the OKSIR program in its mothdelivery strategy (Tyson, Thistlewood, et al., 2007). This approach indi-cated that the most efficient area to release sterile insects is in the downwindedge of pomme fruit orchards (Tyson, Thistlewood, et al., 2007). Addition-ally, a strip of non-pomme fruit trees planted on the upwind edge of theorchard may act as a sink for wild male moths (Tyson, Thistlewood, et al.,2007).1.7 Modelling evolution of critical photoperiodDiapause is an important part of codling moth biology. Diapause is alife-history mechanism that is a response to ennvironmental cues, mainlyphotoperiod, that allows insects to avoid unfavourable circumstances to en-sure survival (Boivin et al., 2004). SIT creates competition for wild codlingmoths, specifically in the summer, when sterile insects are more competitive,decreasing the fitness of wild codling moths. I hypothesize that increasedcompetition from sterile insects in the summer exerts an evolutionary pres-sure on codling moth populations. This evolutionary pressure might selectfor critical photoperiods that trigger early diapause before increased com-petition from sterile insects occur.Previously, no one has considered the impacts of early diapause on thelong-term efficacy of the SIT. In the development of the OKSIR Programme,scientists predicted that eradication of the wild codling moth would occurin 3 to 6 years, i.e., in 6-12 generations (Dyck and Gardiner, 1992) whichevidently has not occurred (Thistlewood and Judd, 2019). In this thesis, Iassume that the critical photoperiod controlling diapause is a heritable trait,81.7. Modelling evolution of critical photoperiodand use population dynamics models that incorporate diapause as a func-tion of photoperiod to investigate if the SIT provides enough evolutionarypressure to select for longer critical photoperiods in populations of codlingmoth. Further, if the SIT is providing evolutionary pressures, could codlingmoths still be eradicated by the SIT.9Chapter 2Field Work2.1 BackgroundIn order to model how the SIT might influence the evolution of criticalphotoperiod that controls diapause in populations of codling moth, it isnecessary to measure the distribution of critical photoperiod within a naturalpopulation of codling moth 5th instar larvae. Field work was conductedin order to determine the distribution of critical photoperiod within a wildpopulation of codling moths. Because the OKSIR programme is governmentmandated, and operates in all pomme fruit orchards within the OkanaganValley, it is impossible to find a local population that has not been subjectedto the SIT. Thus, my field work will provide insight into the distribution ofcritical photoperiod in a wild population that has been subject to the SITsince 1994 (Thistlewood and Judd, 2019). The observed critical photoperioddistribution serves as a starting point for my studies.2.2 MethodsField work was conducted in 2021 and 2022 to investigate the currentdistribution of critical photoperiod in a population of codling moths in theOkanagan. The study site is an organically-managed apple orchard locatedon the Trout Creek property of the Agriculture and Agri-Food Canada, Sum-merland Research and Development Centre, in Summerland, B.C., Canada.This orchard consists of 22 rows of gala apples on semi-dwarfing M9 root-stock with approximately 70 trees in each row.Early in the season, before adult codling moths began emerging in theorchard, corrugated cardboard bands were wrapped around the trunk ofevery tree in the orchard at a height of 25cm above ground. These bandsare deployed to capture 5th instar codling moth larvae that emerge fromfruit infested in the current season (Judd, Gardiner, and Thomson, 1997).Once adult codling moths began emerging, as determined from pheromonetraps hung in the orchard, every banded tree was surveyed for fruit damage102.2. Methodsfrom codling moths. Trees with damage were marked with flagging tapeand a three-by-three quadrat of trees was established with the tree sustain-ing damage centered in the middle of the quadrat. Once each week thecardboard bands from all trees in each quadrat were removed and replaced.Removed bands were inspected for codling moth larvae; any captured larvaemust have been caught during the previous week. A sample of 297 trees wassurveyed each week from June 29th to September 27th, 2021. Field data areshow in Table 2.1.In total, 666 larvae and 24 pupae were collected. Larvae were placedin sealed, clear plastic containers labelled with the collection date. Theselarvae were held at 24◦C in the laboratory where they were placed next to awindow, exposing them to natural daily photoperiods. Temperature can actas a modifier for the onset of diapause, therefore by maintaining collectedlarvae at a constant 24◦C we remove the ability for temperature to modifydiapause. All collected larvae were examined weekly for the remainder ofthe season to determine the number that eventually pupated and emergedas adults. No adult emergence was detected from larvae collected afterAugust 10th, indicating that all individuals collected after that date hadeither entered diapause or died.On November 1st, 2021 all remaining larvae that appeared to be in di-apause or dead were transferred to an environmental chamber where theywere held at 2◦C in complete darkness until April 1st, 2022. This cold periodis needed to break diapause and allow further development. On April 1stall larvae were transferred to another environmental chamber where theywere held at 24◦C under a 16:8 Light:Dark photoperiodic regime. Any post-diapause larvae that did not pupate after 30 days at 24◦C were deemed tohave died. Those larvae that emerged from diapause were assigned a criticalphotoperiod corresponding to the average photoperiod of the week preced-ing the band collection date. Those that did not emerge were deemed tohave died and were not included in the total number of diapausing larvae.The photoperiod assigned to each larva was obtained from data as fol-lows. Daily photoperiods were calculated from online data (Okanagan-Similkameen, 2021) as the time interval between the onset of civil twilightin the morning to the end of civil twilight in the evening. Civil twilight isdefined as the time when the sun is just below the horizon, so the sky isbright but the sun is not visible. Daily photoperiods were then averagedover the days between larvae collection dates, and this average assigned asthe photoperiod for the larvae collected. All of the critical photoperiodsthus assigned give an estimate of the distribution of critical photoperiodsacross the population in each generation.112.2. MethodsSamplingDateMean Pho-toperiod(hours)Num-ber Col-lectedNumberEmergedNumberEnteredDia-pauseNumberDiedJune 29th 17:43:22 6 1 1 4July 6th 17:37:05 7 2 3 2July 13th 17:26:13 4 3 1 0July 20th 17:10:34 19 3 10 6July 27th 16:51:32 5 3 2 0Aug. 4th 16:28:16 8 1 5 2Aug. 10th 16:04:41 18 1 15 2Aug 17th 15:41:34 85 0 85 0Aug. 24th 15:15:55 70 0 70 0Aug. 31st 14:49:48 101 0 101 0Sept. 7th 14:23:28 123 0 123 0Sept. 13th 13:58:59 106 0 106 0Sept. 20th 13:34:37 79 0 79 0Sept. 27th 13:08:35 59 0 59 0Table 2.1: Weekly numbers of codling moth 5th instar larvae and pupaecollected at a test orchard at the Agriculture and Agri-food Research Cen-tre in Summerland B.C. in 2021. Mean photoperiod is the average dailyphotoperiod for seven days preceding the sampling date in column 1.Small numbers of larvae were collected from June 29th to August 10th,giving me a small sample size for early season diapause. This is not idealfor distribution fitting, as larger sample sizes tend to better represent thepopulation. In order to increase the confidence in the distribution fittingto longer photoperiods as experienced early in the season, a second year offield data collection was attempted in the summer of 2022. Unfortunately,the Okanagan experienced a cool spring in 2022, which delayed the codlingmoth life cycle, resulting in a lower number of larvae being collected than in2021, for the period between June 29th and August 10th. As a result, fieldwork in 2022 was abandoned.122.3. Data Fitting2.3 Data FittingThe proportion of collected individuals that entered diapause was calculatedfor each collection date. A beta distribution was fit to these proportions withthe calculated average daily photoperiod on the horizontal axis. Distributionfitting was done in Rstudio 1.3.1093, using a general additive model. Theequation of the fitted distribution ise−821.8172+157.8293x−9.9032x2+0.2037x31 + e−821.8172+157.8293x−9.9032x2+0.2037x3(2.1)Goodness of fit was tested using the R-squared value (R2 = 0.873) andAkaike information criterion (AIC=-367.532).132.3. Data FittingFigure 2.1: Curve showing Beta distribution fitted to weekly proportions of5th instar larvae entering diapause in relation to mean daily photoperiodsduring that collection week. Grey dots are the proportion of larvae enteringdiapause as calculated from the data in Table 2.1 The dark grey region is the95% confidence interval. Goodness of fit was assessed using the R-squaredvalue (R2 = 0.873) and Akaike information criterion (AIC = -367.532, p-value = 0.044).This fitted distribution was then derived in order to calculate the prob-ability density function (PDF) to be used in my models. The PDF is shownin Figure 2.1. This figure shows the critical photoperiod distribution of thewild codling moth population. The area under the curve, to the right ofa specific critical photoperiod represents the proportion of the population142.4. Discussionthat is triggered to enter diapause at that critical photoperiod. For exam-ple at a photoperiod of 14.12 hours, the entire population is triggered toenter diapause. At a photoperiod of 16.85 hours, 50% of the population istriggered to enter diapause. In the Okanagan, the SIT is mandated for allpomme fruit orchards, therefore the critical photoperiod distribution deter-mined from the field data is representative of a population that has beensubject to the SIT for many years.Figure 2.2: Critical photoperiod distribution derived from beta distribution(Figure 2.1) fitted to diapause data in Table 2.1.2.4 DiscussionThe fitted PDF from Figure 2.2 shows that on the longest day of the yearthere are some individuals entering diapause. On the far right of the graph,at a photoperiod of 18 hours, we see approximately 12% of individuals en-tering diapause. My field data showed that on the collection date with thelongest critical photoperiod of 17.43 hours, 16% of collected individuals en-152.4. Discussiontered diapause. This suggests that under photoperiod conditions found inthe Okanagan there may be a portion of the wild codling moth populationthat is behaving as an obligate univoltine subpopulation. This observationis consistent with the literature (Stoeckli et al., 2012; Brown et al., 1978).The overall distribution appears normally distributed, centered around aphotoperiod of 16.85 hours.In North American populations of codling moth critical photoperiodsthat control timing of diapause have been found to increase as latitude in-creases Riedl and Croft (1978). The point where 50% of the individualsenter diapause is known as the CPhP50. (Riedl and Croft, 1978) fit a lin-ear regression line of CPhP50 against latitude for different codling mothpopulations in North America. They found that a 10 degree shift Northcorresponded with an increase of about 1.25h in the CPhP50. Summerlandhas a latitude of 49.36◦N, which is outside of the range of the regression linecalculated by Riedl and Croft (1978). However, if I use their regression lineand the Summerland latitude where I conducted my field studies, I wouldexpect to see a CPhP50 of 16.28 hours. The CPhP50 that I see with myfitted distribution in figure 2.1 is 16.85 hours, which is within 2 standarddeviations of the regression line (Riedl and Croft, 1978). The CPhP50 that Isee with the fitted cumulative desity function from figure 2.2 is 17.01 hours,which is again within 2 standard deviations.The difference between the CPhP50 from my fitted distribution and thepredicted value from the regression by Riedl and Croft (1978) could beexplained by the effects of the SIT. The CPhP50 calculated from my fielddata is longer than what is predicted by the regression from Riedl and Croft(1978). I hypothesize that the SIT selects for longer critical photoperiods,causing more individuals to enter diapause after the first generation. Thisearly diapause would provide a temporal escape from increased competitionwith sterile insects in the second generation. As my field data were collectedfrom a population that has been exposed to the SIT for many years, it ispossible that the SIT has selected for longer critical photoperiods, makingits CPhP50 longer than predicted (Riedl and Croft, 1978).To ensure the population is well represented by our data, increased sam-ple sizes, specifically between the dates of June 29th and August 10th wouldbe ideal. Small sample sizes decrease the power of distribution fitting, in-creasing the range of our confidence interval. It is possible that my data isnot completely representative of the population.16Chapter 3Population Dynamics Model3.1 BackgroundCodling moth (Cydia pomonella L.), is an invasive pest in Canada thatoriginated in central Asia and spread around the globe, now infesting allpomme-fruit growing regions with the exception of Japan (Welter, 2009). Ifleft uncontrolled, codling moth can cause significant fruit loss and economicdamage worth millions of dollars annually (Graf et al., 2018). Traditionalmanagement efforts include extensive use of insecticides. Alternatively, how-ever, the Sterile Insect Technique (SIT) has been employed to reduce relianceon chemical sprays (Thistlewood and Judd, 2019) and, ideally, to eradicatethe pest population. The SIT has been successful in eradicating the Mediter-ranean fruit fly (Ceratitis capitata Weidemann) from parts of Latin America(Enkerlin et al., 2017; Gonzalez and Troncoso, 2007) and in controlling thepopulation of the prickly pear moth (Cactoblastis cactorum Berg) in theMexican state of Quintana Roo (Perez-Staples et al., 2020). The new worldscrewworm (Cochliomyia hominivorax Coquerel) was also eradicated fromNorth America through the use of the SIT (Andrew Paul Gutierrez andPonti, 2014).The Okanagan-Kootenay Sterile Insect Release Programme (OKSIR)was the world’s first operational SIT programme for codling moth. Initiatedin 1994, the stated aim of the OKSIR Programme was regional eradicationof codling moth (Dyck and Gardiner, 1992). Since its inception, the OK-SIR Programme has significantly reduced the codling moth population, buteradication has not occurred (Judd, Thistlewood, et al., 2006; Thistlewoodand Judd, 2019). There are several plausible explanations for this result, butgenerally all pertain to a lack of competitiveness of the sterile moths due tobehavioural differences between wild and sterile moths (Judd, Thistlewood,et al., 2006; Judd, Arthur, et al., 2011; Tyson, Newton, wood, et al., 2008).The SIT consists of the following steps: (1) large-scale mass-rearing ofthe target insect pest, (2) sterilization of the mass-reared insects, usuallywith radiation, and then (3) release of the sterile insects into the field insufficient numbers where (4) mating with the wild population occurs. Mat-173.1. Backgrounding’s between sterile and wild moths produce no offspring. The basic prin-ciple underlying the SIT is that wild population growth is reduced whenwild-wild mating’s are reduced and sterile-wild mating’s increase, becausesterile insects outnumber wild insects by some critical ratio, often called theoverflooding ratio (Judd, Thistlewood, et al., 2006). Proverbs et al. (1982)determined that an overflooding ratio of forty sterile insects to one wildinsect (40:1) would lead to eradication of codling moths within six genera-tions. Currently the OKSIR Programme targets a 40:1 overflooding ratio inits operations but often this is not achieved (Thistlewood and Judd, 2019).Original codling moth SIT studies and calculations, including those usedby Proverbs et al. (1982) and Dyck and Gardiner (1992), assumed sterileinsects to be equally competitive with their wild counterparts. Further re-search, however, has shown that sterilization, mass-rearing procedures andparticularly cold storage of moths before release, produces physiological sideeffects that significantly reduce sterile insect competitiveness (Judd, Thistle-wood, et al., 2006; Judd, Arthur, et al., 2011). In particular, sterile codlingmoths are much less competitive in spring when the weather can be cooland/or wet (Judd, Thistlewood, et al., 2006). In the spring, when codlingmoths are emerging from winter diapause and seeking mates, cool and wetconditions occur regularly. As a result, the sterile male moths are muchless effective at mating than the wild male moths (Thistlewood and Judd,2019), leading to continued wild-wild mating in the spring, and localizedpersistence of the wild codling moth populations.As of 2022, wild codling moth populations in the Okanagan region havecoexisted with the OKSIR Programme for 29 years, representing at least58 generations. During this period, wild insects may have had sufficienttime to evolve adaptations that could further reduce the effectiveness ofthe SIT. In particular, the wild insects might have evolved a propensity toenter diapause early in the summer, i.e., after just one spring generation,rather than continuing development into adults that give rise to a second oreven third generation in late summer and early fall. Early diapause meanspart of a wild codling moth population could escape the effects of the SITduring the summer generation(s) when sterile male insects are far moreactive and effective at mating with wild females than they are in spring(Thistlewood and Judd, 2019). To understand how early diapause mightaffect seasonal population growth and eradication, and in turn evolve, Iconsider the physiological basis for diapause and the environmental variablesthat drive it.Codling moths overwinter as diapausing 5th larvae (Judd, Thistlewood,et al., 2006). Diapause is a state of suspended development that allows in-183.1. Backgroundsects to survive under unfavourable conditions such as those characterizingwinter in temperate clines like the Okanagan winter (Judd, Thistlewood,et al., 2006). The onset of diapause in many insects including codling mothhas been shown to be influenced by the number of hours of daylight, i.e., thedaily photoperiod to which the 4th and 5th instar larvae are exposed. Eachindividual larva has a critical photoperiod that determines the light condi-tions under which it enters diapause. When the amount of daylight dropsbelow the critical photoperiod of an individual larva, diapause is initiated(Boivin et al., 2004). Propensity to diapause under a specific photoperiodicregime is considered to be a selectable trait (Boivin et al., 2004). Severalstudies have shown that management tactics, like use of insecticides canselect for particular diapause traits (Bird et al., 2020; Boivin et al., 2004).Although photoperiod is the main regulator of diapause in codling moth,other factors such as temperature, humidity, food availability, and densitycan act as modifiers (Steinberg et al., 1992; Boivin et al., 2004)Codling moths can enter diapause during the 5th larval developmentalstage of any generation (Judd, Thistlewood, et al., 2006). In the Okanagan,there are generally two generations each season, but in the south Okanagan,especially in years with early, warm springs, a third generation is possible(Thistlewood and Judd, 2019). Following the summer solstice, which usuallyoccurs around the 21st of June, summertime day lengths begin to decreaseuntil the winter solstice. Therefore, larvae that enter diapause after the firstgeneration must have longer critical photoperiods than individuals enteringdiapause after the second generation.Individuals from the first generation that do not enter diapause, but in-stead pupate and emerge as adults, have an extra opportunity to reproduceand pass on their genetic line. Individual insects with shorter critical pho-toperiods (i.e., a propensity to enter diapause after the second generation)would thus tend to have increased individual reproductive fitness. In theOkanagan, and most temperate climates however, the second generation isgenerally exposed to warmer temperatures, less rainfall, and more stableweather patterns with less wind than during the first generation. Theseenvironmental conditions are ideal for the sterile insects, allowing them tosuccessfully mate more often than during the first generation. For wild indi-viduals, therefore, having a shorter critical photoperiod means having boththe advantage of increased fitness from a second opportunity to reproduce,and the opposing disadvantage of increased competition from sterile malesunder the SIT.In this thesis I want to test how a starting distribution of the criticalphotoperiods in a population of wild codling moth might change over time193.2. Methodsunder the selection forces provided by the SIT. Additionally, I want to eval-uate how the differences in competitiveness of sterile insects between thegenerations of wild codling moth might influence the evolution of criticalphotoperiod. Finally, I wanted to understand how the overflooding ratioof sterile insects may influence the evolution of critical photoperiod, and ifincreasing the overflooding ratio could lead to eradication. I hypothesizethat the differing competitiveness of sterile insects across generations mightselect for individuals with longer critical photoperiods in wild codling moths.In other words, individuals that diapause early escape the SIT in summer.In order to investigate my hypothesis, I use a modelling approach, com-bined with field work quantifying a distribution of critical photoperiod. Formy field study, I collected data from an existing codling moth populationthat has coexisted with the OKSIR Programme for 29 years. For my model,I modify a discrete stage-structured model developed by Brown et al. (1978),that had been carefully validated against historic codling moth populationdata. I adapt this model to include the effect of the SIT on mating, and theeffect of photoperiod on diapause. The heritability of critical photoperiod ismodelled using a redistribution kernel, where I assume the offspring is morelikely to have a critical photoperiod that is similar to their parent. I thenallow photoperiod to evolve across generations, under different degrees ofSIT mating disruption.3.2 Methods3.2.1 Mathematical ModelThe original population dynamics model developed by Brown et al.(1978) is based on the concept of state dynamics (compartmental mod-elling) where entities flow from one life stage to the next. This model wasdeveloped to predict population sizes of specific life stages in order to aidmanagement efforts. Brown et al. (1978) modeled diapause as a one geneand two allele trait, with alleles controlling voltinism. The model compart-ments are illustrated in Figure 3.1, and include the two annual generationsexperienced in the Okanagan. Following Brown et al. (1978), I model thetransitions through the five larval stages in each generation as a single tran-sition from the 1st to the 5th larval stage. Each developmental stage in themodel is represented by a unique state variable that is given in Table 3.1.In my version of the model, the state variables are all functions of criticalphotoperiod x. Critical photoperiod ranges from 12 to 18 hours, and is con-tinuous.The number of individuals with critical photoperiod x is calculated203.2. MethodsFigure 3.1: Compartmental diagram of the model. First-generation adultsemerge in the spring, mate and lay eggs, which hatch into 1st instar larvae.The larvae develop through several instars, until reaching the 5th instar.Some 5th instar larvae enter diapause, while the remainder emerge as adultsto repeat the life stages of the first generation. The diapausing 5th instarlarvae from the first and second summer generations remain in diapausethroughout the winter, and then contribute together to the first-generationadults of the following spring.at each developmental stage, giving a distribution of critical photoperiodacross the entire population, and at each stage of development. The heri-tability of diapause is poorly understood in most insect species, includingcodling moths, and can differ between species (Tougeron, 2019). Diapause isinfluenced by several factors, the main one being photoperiod which appearsto have a genetic basis (R. H. Smith, 1989; Boivin et al., 2004). However,other factors such as food availability, temperature, humidity and densitycan act as modifiers to this genetic basis (Steinberg et al., 1992; Boivin et al.,2004). Therefore, in my model I represent critical photoperiod heritabilityas multifactorial inheritance, where the offspring are more likely to have acritical photoperiod the same as or similar to their parent. The heritabilityof diapause in my model is discussed in detail in section 3.2.1. Generationnumber is indicated by the subscript i, and year by the subscript t. Themodel equations, with the exception of the dependence on photoperiod, aretaken from Brown et al. (1978). They are introduced and described in detailbelow.213.2. MethodsVariable DefinitionGi,t(x) Number of adults that emerge in the ith generation of yeart with critical photoperiod xEi,t(x) Number of eggs in the ith generation of year t with criticalphotoperiod x (redistributed offspring photoperiod)L1,i,t(x) Number of 1st instar larvae in the ith generation of year twith critical photoperiod xL5,i,t(x) Number of 5th instar larvae in the ith generation of year twith critical photoperiod xD1,t(x) Number of larvae entering diapause after the first generationin year tD2,t(x) Number of larvae entering diapause after the second gener-ation in year tTable 3.1: Table of the population dynamics model variables.ReproductionThe number of eggs produced is given by the equationθ(x) = f(x)s(x), (3.1)where θ(x) is the number of eggs produced in generation i of year t, f(x) isthe individual fecundity (eggs produced per female), and s(x) accounts formating interference by sterile insects. I describe f(x) and s(x) below.The fecundity term is given byf(x) = 53.8e−0.593√(∫L1,t−1(x)dx/A). (3.2)On average, a female lays 53.8 eggs, but this number is limited by theamount of nutrient each female is able to acquire in her larval stage. As aproxy for nutrient availability, the total number of larvae from the previousgeneration,∫L1,t−1(x)dx, is divided by the number of apples, A, present inthe orchard. Brown et al. (1978) found that the appropriate limiting termis the exponential in equation eq:fecundity.The sterile mating interference term, s(x), is given by the equations(x) =(12Gi,t(x)ciSi,t +12Gi,t(x))12Gi,t(x), (3.3)223.2. Methodswhere Gi,t is the number of wild codling moth adults in generation i of yeart. Likewise, the sterile moth population has a 1:1 sex ratio. I assume thatthe wild population is half male and half female. Si,t is the number of malesterile insects released in generation i of year t, and ci < 1 is a competitive-ness factor to account for the physiological side effects of the sterilizationprocess. The number of sterile insects is calculated by multiplying the to-tal number of wild moths, Gi,t, by 40, to achieve the OKSIR Programmestarget overflooding ratio of 40:1. The effective number of wild males thatare available for mating is given by the ratio of wild males 1/2G(x) to aweighted sum of total males, where the sterile portion is reduced by thecompetitiveness factor ci. This ratio is multiplied by the number of wildfemales to determine the number of wild pair mating’s.Combining equations eq:reproductionsimp, eq:fecundity, and eq:sterile,I arrive at the equationθ(x) = 53.8e−0.593√(∫L1,t−1(x)dx/A)(12Gi,t(x)ciSi,t +12Gi,t(x))12Gi,t(x). (3.4)The quantity θ(x) is not the final expression for the egg population,as I still need to allow for some evolution of critical photoperiod in theproduction of offspring. This step is described in the next section.PhotoperiodIn the calculations above, each egg has the same critical photoperiod asthe parents (mating only occurs between parents with the same photope-riod, see eq:sterile). I expect, however, that photoperiod can shift from onegeneration to the next, and so I perform a redistribution of the critical pho-toperiods of the egg population, θ(x), via a redistribution kernel k(z). Inother words, I take the photoperiod distribution of θ(x), of the parents, andthen multiply it by a function (the kernel) to obtain the photoperiod distri-bution of the offspring. The kernel gives the probability that an offspringof photoperiod x had parents with photoperiod y. So, the kernel integratesto 1, and is generally symmetric and unimodal with the peak at 0 (x = y).The width of the kernel corresponds to the likelihood that the offspring traitvalue is different from that of the parent. For simplicity, I use a Gaussiankernel. This type of kernel is widely used to model the evolution of traits,such as a boldness trait (Chan and Kim, 2014; Morota et al., 2013; Ober etal., 2011). The area under the distribution is equal to the total population,233.2. Methodsand the height of the curve at a given photoperiod (x-value) is the numberof individuals with that critical photoperiod. The redistribution kernel doesnot describe the genetic process behind the inheritance of critical photope-riod, which is unknown, but summarizes a possible outcome of this process.The distribution of critical photoperiod in the egg population is thus givenbyΘ(x) = 0.75∫ 1812k(x− y)θ(y)dy, (3.5)where the integral is over all possible photoperiods in the adults, y, givingrise to eggs with photoperiod x. The integral is taken between 12 and18 as that is the range of photoperiod experienced here in the Okanagan.The integral is multiplied by 0.75 to account for the fact that only aboutthree quarters of the eggs laid survive to the first larval stage. I assumethat critical photoperiod does not affect the mortality rate. Note that theredistribution step eq:eggs-2 may result in some eggs with photoperiodsoutside the allowable interval, 12 ≤ x ≤ 18. To address this problem, I takethe individuals that fall outside the allowable interval and redistribute themevenly across the photoperiod domain. The relative size of the populationin these tails is always very small in my simulations. I defineQ =∫ 12−∞Θ(x)dx+∫ +∞18Θ(x)dx, (3.6)and then can write the final equation for the egg population asEi,t(x) = {Θ (x) +Q/6, if12 ≤ x ≤ 18, 0, else. (3.7)Larval DevelopmentBrown et al. (1978) found that approximately 91 percent of first-instarlarvae survive, though survival is dependent on the amount of apple surfacearea that is present. The amount of surface area available per larva isdetermined by taking the integral of equation eq:photoperiod to obtain thetotal number of eggs, and dividing this quantity by the apple surface area,As. The appropriate survival reduction term was obtained by fitting to data(Brown et al., 1978), and is given by exp(−2.9√(∫Ei,t(x)dx/As)). This termmodifies the 91 percent survival rate so that survival decreases as the ratiobetween the number of eggs and apple surface area increases. The survivalrate is then multiplied by the number of eggs to calculate the total numberof 1st instar larvae. The 1st instar larval population is thus given by the243.2. MethodsequationL1,i,t(x) =0.91e(−2.9√(∫Ei,t(x)dx/As))Ei,t(x). (3.8)As for 1st instar larvae, the equation for 5th instar larvae is essentiallythe same as that used by Brown et al. (1978), except that state variables area function of critical photoperiod. Brown et al. (1978) found that about 86percent of 5th instar larvae survive, but this survival is reduced by crowding,i.e., decreases with increasing density of larvae within the apples. To esti-mate this density, we take the integral of equation eq:firstinstar to calculatethe total number of 5th larvae that survive, and then divide that populationby the number of apples. The appropriate reduction term, obtained by fit-ting to data (Brown et al., 1978), is exp(−0.417√(∫L1,t(x)dx− 1)/A. The5th instar larval population is thus given byL5,i,t(x) =0.862e(−0.417√(∫L1,t(x)dx−1)/AL1,i,t(x). (3.9)DiapauseUpon completing the 5th larval instar stage, codling moth larvae can eitherenter diapause, or pupate and emerge as adults to mate and initiate a newgeneration. The decision to enter diapause is triggered by daily photoperiodand sometimes modified by nutrition (Boivin et al., 2004). The sensitivity ofeach individual larva to a particular photoperiod, referred to as its criticalphotoperiod for diapause (henceforth,“critical photoperiod”), is set by itsgenetics and unique natural history. In the Okanagan, there are at least twogenerations of codling moth each year, so there are at least two opportunitiesfor codling moth larvae to enter diapause. The last 5th instar larva from thefirst generation to complete its 5th instar stage usually does so near theend of July which, in Summerland, B.C., Canada (49.6032°N, 119.6834°W),corresponds to a photoperiod of about 16.5 hours, when civil twilight isincluded. I use this value as the critical photoperiod boundary, B, betweengenerations in my model. Any individual first generation larva with a criticalphotoperiod above 16.5 hours will be programmed to enter diapause onceit exits the fruit and searches for a cocooning site. The number of first-generation larvae that enter diapause is thus given byD1,t(x) = L5,1,t(x)forB < x < 18. (3.10)253.2. MethodsThe remaining larvae emerge as adults to start a second generation.The last individuals of the second generation to complete the 5th instarlarval stage do so near the beginning of September which, in Summerland,corresponds to a photoperiod of 12 hours. All second-generation individualswith a critical photoperiod above 12 hours will be programmed to enterdiapause. The number of second-generation larvae that enter diapause isthus given byD2,t(x) = L5,2,t(x), for12 < x < 18. (3.11)The maximum number of individuals that are available to emerge in thespring of a given year, is the sum of the individuals that entered diapause inboth generations of the previous year. The total number of individuals thatenter diapause in any given year is multiplied by a winter survival rate whichis dependent on the location where the larvae spin their overwintering co-coons before the onset of diapause occurs. Larvae that cocoon on trees havehigher survival rates than those that cocoon on the ground (Thistlewoodand Judd, 2019). Thus I haveG1,t+1(x) = ctstD1,t(x) + cgsgD1,t(x) + ctstD2,t(x) + cgsgD2,t(x). (3.12)where ct and cg = 1 − ct are the proportion of cocoons in trees and on theground, respectively, and st and sg are the survival rates for cocoons in treesand on the ground, respectively.Parameter Description ValueA number of apples 10000As total surface area of apples 3000c1 sterile insect competitiveness in generation 1 0.2c2 sterile insect competitiveness in generation 2 0.8cg proportion cocooning on ground 0.05ct proportion cocooning on tree 0.95sg cocooning on ground survival 0.3st cocooning on tree survival 0.8B critical photoperiod boundary 16.5Table 3.2: Table of the population dynamics model parameters.3.2.2 Simulation ExperimentsThe resource level in all of my simulations represents that typical of anorchard of size 1 acre, thus A = 10, 000 fruit. I set the initial wild codling263.3. Resultsmoth population to 200 individuals, of which 100 were males and 100 werefemales.I first simulated the population growth dynamics in the absence of ster-ile insects. I then simulated the effect of the SIT with the OKSIR targetoverflooding ratio of 40 sterile insects to 1 wild insect. I also ran a se-ries of simulations maintaining a 40:1 overflooding ratio, and varying thecompetitiveness of sterile insects in both the first and second generations.Finally, I ran a series of simulation experiments in which I varied bothcompetitiveness and overflooding ratio in each generation. All simulationswere run using Matlab R2020b. The redistribution kernel integral in Equa-tion eq:photoperiod was numerically solved using the method described inLutscher (2019).3.3 Results3.3.1 Modelling StudiesEffect of the sterile insect technique on the distribution ofcritical photoperiodMy simulations show that, in the absence of sterile insects, wild codlingmoth populations increase until they are limited by the availability of ap-ples, and then the populatio size remains constant. In the absence of sterileinsects, the wild codling moth populations evolve toward a critical photope-riod distribution that favours shorter critical photoperiods (Figure 3.2, left).This result corresponds to an entry into diapause that is skewed toward latesummer. In other words, in the wild state, more individuals enter diapauseafter the second generation in the summer, rather than after the first gen-eration in the spring.273.3. ResultsFigure 3.2: Distribution of critical photoperiod (non-normalized) over 5years with no sterile insects (left) and with sterile insects (right) maintainedat a 40:1 overflooding ratio. The blue lines in each graph panel represent thesame initial distribution, however they appear different due to the differingscale of each y-axis. The parameter values used are given in Table 3.2. Theinitial population is 200 insects, where I assume there are 100 males and 100females. The initial critical photoperiod distribution is a normal distributioncentered at a critical photoperiod of 16.5 with a standard deviation of 0.1Conversely, in the presence of sterile insects deployed at a 40:1 over-flooding ratio and with competitiveness parameters set at the default valuesshown in Table 3.2, I find that the codling moth population decreases andevolves to have a critical photoperiod distribution tending towards longercritical photoperiods (Figure 3.2, right). This shift indicates that more indi-viduals enter diapause after the first generation than after the second gener-ation. Note that the SIT also has the effect of reducing the wild population(compare the vertical axes in the two subplots in Figure 3.2). After 5 years,the wild population has, in both cases, reached the steady-state distributionfor the parameter values used, indicating eradication is not achieved.Figure 3.3 shows the critical photoperiod from simulations with sterileinsects after five years compared to the distribution of critical photoperiodcalculated from field data in chapter 2. The field work distribution wasnormalized and multiplied by the area under the distribution from year fivein simulations in order to best compare the distributions. Both distributionsare relatively normally distributed centered around about 17 hours, witha long tail to the left. In the Okanagan the SIT is mandated, thereforethe distribution calculated from field data is representative of a populationthat has been subject to the SIT for many years, which is why it is beingcompared to simulations with sterile insects. The similarity of the curves283.3. Resultssuggests that the parameterization used in the model is relatively realistic.Figure 3.3: The distribution of critical photoperiod in year 5 of simulationswith sterile insects, compared to the distribution that was fitted to field datafrom chapter 2.Effect of sterile male competitiveness on the evolution of criticalphotoperiodThe effect of spring and summer competitiveness factors adds nuance to thebinary result above. In simulations maintaining the current OKSIR target40:1 overflooding ratio (Figure 2.3 (left plot)), I find that the distributionof critical photoperiod in wild codling moths remains skewed toward spring(green to yellow regions), unless sterile insect competitiveness in the summeris sufficiently low, i.e., c2 <≈ 0.2. Note that the generation of entry intodiapause varies very little with changes in spring competitiveness given afixed value of summer competitiveness, while, if spring competitiveness isheld fixed, changes in summer competitiveness have a strong effect. Forc2 < 0.2, wild codling moths evolve to have critical photoperiods favouringdiapause after the second generation in the summer, regardless of the valueof c1. For c2 >= 0.35, again regardless of the value of c1, wild codlingmoths evolve to have critical photoperiods that favour diapause after thefirst generation in the spring.First generation adults mate mid June to early July dependent on tem-perature. In warmer years they will mate earlier, and in cooler years they willmate later. The competitiveness of sterile insects at this time is dependent293.3. Resultson several factors, one of which is temperature, however spring tempera-tures tend to be cooler than in the summer, therefore, competitiveness isassumed to be lower in the first generation. Sterile insect competitivenessis difficult to quantify, therefore multiple simulations were ran with vary-ing competitiveness values to determine how competitiveness influences theevolution of critical photoperiod and the wild population size. When firstgeneration sterile insect competitiveness is sufficiently low, i.e., c1 <= 0.15,regardless of the value of the second generation sterile competitiveness, c2,the final population is always larger than the initial population. Likewise,when c2 <= 0.05, regardless of the value of c1, the final population is alwayslarger than the initial population. When c1 >≈= 0.8 and c2 >≈= 0.7 thepopulation size has been reduced to below one, suggesting eradication. Thelighter blue/turquoise regions represent final populations that are smallerthan the initial population, but where eradication has not occurred.Figure 3.4: Heat map showing the effects of competitiveness on the percent-age of 1st generation larvae entering diapause (left) and the log transformedfinal population (right), when the overflooding ratio is maintained at 40:1.The colour indicates the percentage of the population entering diapause afterthe first generation (left) as shown in the right y-axis legend: Green-yellowindicates that the population is skewed to enter diapause after the first gen-eration and blue-violet indicates diapause after the second generation. Thecolour indicates the log transformed final population size (right) as shownin the right y-axis legend: Green-yellow indicates a large population (thou-sands), blue-violet represents a small population (less than 100).Further investigation using different overflooding ratios confirms thatthe spring competitiveness factor has little effect on the evolution of critical303.3. ResultsFigure 3.5: The interacting effects of overflooding ratio and spring sterileinsect competitiveness on the percentage of 1st generation larvae enteringdiapause. The colour indicates the percentage of the population enteringdiapause after the first generation. Summer sterile insect competitivenesswas maintained at (left) c2 = 0.5 and spring sterile competitiveness wasmaintained at (right) c1 = 0.25.Figure 3.6: The interacting effects of overflooding ratio and first genera-tion (left) and second generation (right) sterile insect competitiveness onpopulation size. Summer sterile insect competitiveness was maintained at(left) c2 = 0.5 and spring sterile competitiveness was maintained at (right)c1 = 0.25.313.3. Resultsphotoperiod, as long as sterile insects are present and have at least somecompetitiveness in the summer (Figure 3.5 (left plot)). I also repeated thesimulations of Figure 3.5 for other values of c2, and found similar resultsas long as c2 > 0.1. Summer competitiveness together with overfloodingratio drive the evolution of critical photoperiod (Figure 3.5 (right plot)).If either one is too low, critical photoperiod in the wild population remainsskewed towards a summer entry into diapause. As soon as one of the twoparameters increases beyond this minimum, a sufficient increase in the otherwill drive critical photoperiod evolution in the wild population toward anearly entry into diapause.The final population size decreases as sterile competitiveness in eithergeneration increases, and as the overflooding ratio increases (Figure 3.6).Interestingly, the effect of summer competitiveness and overflooding ratioon the final population size is similar to their effect on the percentage ofindividuals entering diapause after the first generation. When there is alow percentage of individuals entering diapause after the first generation(blue in Figure 3.5 (right plot)), we see a larger final population (yellowin Figure 3.6 (right plot)). Likewise, when there is a large percentage ofindividuals entering diapause after the first generation (yellow in Figure 3.5(right plot)), we see a smaller final population (blue in Figure 3.6 (rightplot)).Sensitivity analysisA sensitivity analysis was conducted on model parameters with unknownvalues from the literature. Results from a partial rank correlation coeffi-cient (PRCC) sensitivity analysis are shown in Figure 3.7. I found that theparameters with the largest effect on the percentage of the population enter-ing diapause in the spring are (1) the critical photoperiod boundary betweenspring (early) and summer (late) diapause, (2) the summer competitivenessof sterile insects, and (3) the overflooding ratio of sterile insects in the sum-mer. These results are consistent with Figures 3.3.1- 3.5. A decrease in thevalue of the critical photoperiod boundary would increase the proportionof the summer during which the conditions are considered to be ”spring”when sterile males are less competitive. Thus, an increase/decrease in thelength of cool and/or wet spring-like conditions would favour evolution to-ward second/first-generation entry into diapause.To further investigate how the paramaterization of the model influencedthe results, multiple simulations were run while altering the parameter val-ues. While these simulations provided different results, the trends remained323.4. Discussionthe same. That is that the critical photoperiod distribution still evolves tolonger photoperiods in the presence of sterile insects.Figure 3.7: Partial rank correlation coefficients of model parameters.3.4 DiscussionIn this chapter, I investigated the hypothesis that the SIT could lead toa shift in the critical photoperiod distribution in the wild codling mothpopulation. I assumed that the critical photoperiod for the induction oflarval diapause in codling moth is an evolvable trait, with offspring having acritical photoperiod that is close to, but different from, that of their parents.In order to test my hypothesis, I adapted an existing model for codlingmoth population growth, and extended it to include evolution of criticalphotoperiod.My simulations show that, if critical photoperiod is an evolvable trait,the SIT can indeed have a strong effect on the critical photoperiod for wildmoths. Changes in the critical photoperiod will change the relative pro-portion of larvae entering diapause in the first vs second generation eachyear. In the absence of sterile insects, I find that wild codling moths tendto enter diapause after the second generation, taking advantage of the ex-tra opportunity to reproduce and pass on their genetic line. With sterileinsects present, however, sterile mating interference during the second gen-333.4. Discussioneration significantly reduces the likelihood of successful reproduction. In mysimulations, this competition with steriles results in a shift of the criticalphotoperiods in the wild population, such that more individuals tend to en-ter diapause after just the first generation. This observation is consistentwith my field study results (Chapter 3).In my model, this SIT-driven shift in the critical photoperiod distributionis due to the differing competitiveness of sterile insects between generations.The rearing, sterilization and handling processes to which sterile codlingmoth are exposed has a significant effect on their behaviour, a key one be-ing reduced dispersal activity and flight ability during cool spring weather(Judd, Thistlewood, et al., 2006). This temperature sensitivity means thatthe sterile moths are generally much less mobile than the wild moths inthe cooler conditions typical of springtime. Lower mobility decreases thesterile insects’ ability to fly and respond to mating calls. Consequently,the wild codling moths of the first generation, which emerge in the spring,outcompete their sterile counterparts for mates, resulting in more wild pairmating’s and more wild offspring. In the summer, around the time of secondgeneration emergence and when temperatures are generally warmer, sterileinsects are only slightly less mobile than their wild counterparts. The sum-mer sterile insects are therefore more effectively able to respond to matingcalls, decreasing the number of wild pair mating’s and therefore decreasingthe number of wild offspring produced.Since summer competitiveness is such an important factor in the out-come, the warming and weather extremes due to climate change could sig-nificantly affect predictions. In the Okanagan it is predicted that averagetemperatures will increase throughout the entire year, and that we will re-ceive more precipitation in every season except the summer (Kelowna, 2020).Warmer and drier summers may favour sterile insects and increase the over-all effectiveness of the SIT. On the other hand, warmer temperatures mayincrease the speed of codling moth development, leading to a third genera-tion of wild codling moths. To represent climate change in my model, thecompetitiveness of sterile insects in the spring, c1, and summer, c2, could beincreased. Increasing the competitiveness of sterile insects, specifically in thespring, would make the SIT more effective at reducing the wild population(Fig. 3.5).My simulation results are consistent with observations in the field: Af-ter 25 years of effort, the OKSIR programme in the Okanagan has beenunable to eradicate the codling moth population, and has instead simplyreduced it to a much lower level (Proverbs et al., 1982; Judd, Thistlewood,et al., 2006). Why the eradication effort failed has been the subject of much343.4. Discussionresearch (Tyson, Newton, wood, et al., 2008; Tyson, Thistlewood, et al.,2007; Judd and Gardiner, 2005; Carpenter et al., 2013). Here I investigatethe possibility that evolution of critical photoperiod, combined with weaksterile insect effectiveness in the spring, may be a contributing factors. Theoriginal models used in the design of the OKSIR programme did not includediapause nor its potential to change over time as an evolvable function ofSIT control, and also assumed sterile insects were equally as competitiveas wild codling moths. My simulations indicate that an evolvable criticalphotoperiod would allow the wild codling moth population to escape thenegative pressure of the SIT by restricting reproduction to the spring gen-eration and entering diapause immediately after. When competitiveness ofthe first generation sterile insects is lower than second generation steriles,critical photoperiod evolves so that over 50% of the population enters dia-pause after the first generation. When first generation competitiveness was 0and second generation competitiveness was 1, the percent entering diapauseafter the first generation was 99%. The increased percentage of individualsentering diapause after the first generation prevents eradication, and mayexplain why the SIT has reduced population levels but failed to eradicatecodling moth.One of the key factors in a sterile insect release programme is the over-flooding ratio Perez-Staples et al. (2020) and Thistlewood and Judd (2019).My simulations show that a 40:1 sterile:wild overflooding ratio, currentlyused as a target by the OKSIR Programme, is effective at substantially de-creasing the size of the wild codling moth population, but is insufficient toeradicate it. After five years (in simulations) the wild population of codlingmoths has reached equilibrium and the population size no longer decreases.My simulations show eradication could be achieved with a very high over-flooding ratio, but producing so many sterile moths and maintaining theseratios would likely be excessively expensive. Furthermore, in my model Iassumed that the overflooding ratio is maintained throughout the seasonand uniformly throughout the domain; a situation that is very difficult toachieve in practice. As long as the moths have a refuge from the SIT, repre-sented by spring entry into diapause, eradication by the SIT alone appearsunlikely.The SIT is most effective when used to control insects that are short-lived, semelparous (females mating only once per lifetime), and that do nothave elaborate courtship rituals (Perez-Staples et al., 2020). Codling mothssatisfy the first and last requirements, but females can mate multiple times(Thistlewood and Judd, 2019). It has been observed that occasionally a wildfemale will be unsatisfied with a sterile males spermatophore and continue353.4. Discussionto call for a mate (Knight, 2007).My model uses a Gaussian redistribution kernel to represent the evo-lution of critical photoperiod from one generation to the next. That is, Iassume that offspring can have any critical photoperiod, but are most likelyto have a critical photoperiod that is the same as, or similar to, that of theirparents. My model is consistent with multifactorial inheritance, however,the genetic basis of critical photoperiod is unknown.My model is a useful first step in understanding how the SIT and evo-lution of critical photoperiod might interact and change the effectiveness ofthe SIT. Moving forward, there are several limitations of the model thatcould be addressed in future work. I discuss a few of these here.First, temperature is the main environmental variable that affects sur-vival, reproduction, movement and development of many insect species, in-cluding codling moths (Rebaudo and Rabhi, 2018; Graf et al., 2018). Tem-perature has also been shown to influence sterile codling moth movement,and thereby their competitiveness with wild codling moths Thistlewood andJudd (2019). My model could be modified to include temperature to explainthe daily development rate of codling moths, and the sterile moth competi-tiveness.Second, my model runs on a generational time step, which assumes in-dividuals progress through each stage of development simultaneously. Thisassumption is a simplification, as there is natural variation in the develop-ment rate of individuals Graf et al. (2018). Running simulations on a smallertime step would allow for variation in individual development rates.Finally, the sterile to wild overflooding ratio remains constant in mysimulations. In reality, it is very difficult to maintain a constant overfloodingratio through time and space. Sterile insects are released weekly, creatinga temporal pulse of sterile insects Thistlewood and Judd (2019). Sterileinsects are also not released uniformly across orchards. Incorporating weeklyreleases and subsequent daily fluctuations in the overflooding ratio due tomortality and weather would provide more accurate overflooding ratios.36Chapter 4Daily Time-step Model4.1 BackgroundThe initial model developed in Chapter 2 has several limitations. First, themodel assumes that there is a constant number of sterile insects. Sterileinsects are released weekly, and then slowly die off, disperse or emigrate.Maintaining a constant number of sterile insects overestimates the numberof sterile insects in the model. As a result, the model predicts a highernumber of wild pair matings and therefore a greater reduction in the wildpopulation than would be seen in reality.Another key limitation of the model from Chapter 2 is that all indi-viduals proceed through each developmental stage simultaneously, and theeffects of variations in temperature are not taken into account. Individu-als proceed through developmental stages at different rates, with emergencefrom each stage occurring over a period of days or weeks. Development incodling moths is directly related to temperature, with development occur-ring faster as temperatures increases. Several studies have been conducted toinvestigate the relationship between development of codling moth and tem-perature (Ferro, R. R. Sluss, et al., 1975; Glenn, 1922; Rock and Shaffer,1983). It has been shown that the codling moth has a lower developmentalthreshold of approximately 10 degrees centigrade (10◦C) and an upper de-velopmental threshold of 31◦C (Judd, 2020). When temperatures are below10◦C or above 31◦C codling moths can not develop (Judd, 2020). Whentemperatures are between the upper and lower developmental thresholds,development is approximately linear and can be predicted using degree days(Ferro, R. R. Sluss, et al., 1975; Glenn, 1922; Rock and Shaffer, 1983). Onedegree day is achieved when temperatures one degree over the lower devel-opmental threshold (10◦C) persist for 24 hours. The use of degree days hasbeen widely used in phenology models to predict the occurrence of specificlife stages (Joshi et al., 2016; Blomefield and Giliomee, 2014; Knight, 2007;Riedl and Croft, 1978; Rebaudo and Rabhi, 2018; Graf et al., 2018).In cooler years development will slow down, leading to later emergenceand exposing more 5th instar larvae to shorter photoperiods. In warmer374.2. Daily Time-step Modelyears development will speed up, leading to earlier emergence and exposingmore larvae to longer photoperiods. The timing of development thus affectsthe photoperiod to which each individual is exposed at the 5th instar lar-val stage, which controls the initiation of diapause. In cooler years, withmore individuals being exposed to shorter critical photoperiods at the 5thinstar larval stage, a larger proportion of the population will enter diapauseafter the first generation. In warmer years, with more individuals being ex-posed to longer critical photoperiods at the 5th instar larval stage, a smallerproportion of the population will enter diapause after the first generation.My work in Chapter 2 showed that the SIT selects for longer criticalphotoperiods, causing more individuals to enter diapause after the first gen-eration. This result may be altered by changes in seasonal temperaturesanticipated under climate change. Here I present a preliminary model to in-corporate the codling moth development rate as a function of temperature(degree days). This model provides a framework for future work study-ing evolution of diapause under climate change scenarios and the resultingconsequences for SIT management.4.2 Daily Time-step ModelI model the growth rate through all of the larval stages using the classicdegree-day approach, i.e., the accumulation of degree days for each day.Graf et al. (2018) conducted controlled codling moth experiments to deter-mine the degree day values at which emergence from each developmentalstage begins and is completed. For this model, I use the degree day de-velopment values identified by Graf et al. (2018) and the number of degreedays accumulated each day of the simulation, starting from January 1st, todetermine the rate of development r within each life stage. We know thatr is a function of the degree day ratio, Dr. The degree day ratio is thenumber of degree days accumulated up to day t, divided by the differencein the number of degree days between when emergence from each life stagebegins and ends. That isDr =Dt −DsDe −Ds , (4.1)where Dt is the degree days accumulated up to day t, Ds is the degree-day accumulation value at which emergence from the developmental stagebegins, and De is the degree-day accumulation value at which emergencefrom the developmental stage is completed. The rate of development can384.2. Daily Time-step Modelthen be writtenrt(x) = f(Dr)pt(x). (4.2)This development rate function is used for every life stage in the model equa-tions below. Since detailed information regarding the nature of the functionf(Dr) is lacking, we assume for simplicity that this function is linear, and,in fact, equal to Dr. Below, I denote the number of individuals emergingfrom life stage i on day t as ri,t. The number of individuals remaining in lifestage i on day t is denoted by pi,t. As in Chapter 2, state variables are allfunctions of critical photoperiod x. A compartmental diagram of the dailytime-step model is presented in figure 4.2.Figure 4.1: Compartmental diagram of the life stages in the daily time-stepmodel. First generation adults emerge in the spring, mate and lay eggs,which hatch into 1st instar larvae. The larvae develop through several in-stars, until reaching the 5th instar. Some 5th instar larvae enter diapause,while the remainder emerge as adults to repeat the life stages of the firstgeneration. The diapausing 5th instar larvae from the first and second gen-erations remain in diapause throughout the winter, and then contributetogether to the first generation adults of the following spring. Progressthrough each of these stages is not simultaneous, so each day the number ofindividuals that is in each compartment is updated to account for emergencefrom one life stage into the next.4.2.1 First GenerationAdult EmergenceFirst generation adults begin emerging from diapause at 103 degree days,and by 522 degree days all individuals have emerged Graf et al., 2018. Wethus arrive at the degree-day ratio,(Dt − 103419), (4.3)394.2. Daily Time-step Modelwhere Dt is the degree days accumulated up to day t. This term is thenmultiplied by p1, t(x) which is the number of individuals that are in diapauseon day t, to give us the number of adults r1,t emerging from diapause onday t, i.e.,r1,t(x) =(Dt − 103419)p1,t(x). (4.4)The number of individuals remaining in diapause is then updated to accountfor the individuals that emerged using the equationp1,t(x) = p1,t−1(x)− r1,t−1(x). (4.5)ReproductionFor simplicity, we assume that the adults emerging on day t will completemating and egg-laying that same day. The number of male and femalecodling moths on day t is 12r1,t(x) which is half of the number of individualsthat emerged from diapause on day t.The number of sterile insects present on day t, St, is also calculateddaily. The OKSIR programme releases 400 sterile codling moths per acreon a weekly basis, so I include a pulse of 400 sterile insects every 7 days.The sterile insects then die off at an exponential rate. We thus arrive at theequation,St = { 4 00 + St−1fort = n7, n ∈ RSt−1e−telse (4.6)These sterile insects affect the number of wild-wild matings through thereproduction equation eq:reproduction.The reproduction equation gives the number of eggs produced by parentswith photoperiod x on day t, and is given byθ1,t(x) =(53.8e−0.593√(∑r2,i−1/A))( 12r1,t(x)cSt +12r1,t(x))12r1,t(x). (4.7)which is essentially the same as equation eq:eggs from Chapter 2.Photoperiod RedistributionIn equation eq:reproduction, the critical photoperiod of the adults r1,t(x) iscarried over to the offspring θ1,t(x). In reality there is likely some variationbetween the critical photoperiod of the offspring and that of the parents. Toaccount for this difference, I used a redistribution kernel (Lutscher, 2019).404.2. Daily Time-step ModelThe method is the same as that described in Chapter2, Section 3.2.1. Wetherefore arrive at the critical photoperiod redistribution equation,Θ1,t(x) = 0.75∫ 1812k(x− y)θ1,t(y)dy. (4.8)Θ1,t is the number of eggs with photoperiod x that are laid on day t in thefirst generation.Egg HatchingEggs begin hatching at 169.7 degree days and all eggs have hatched by 612.7degree days (Graf et al., 2018), giving the degree day ratio(Dt − 169.7443). (4.9)To determine the number of eggs hatching on day t, we multiply the degreeday ratio term by the number of eggs that have been laid up until day t. Onlythree quarters of the eggs that are laid survive, so I multiply the quantity ofeggs by 0.75, yielding the equation for the number of eggs hatching on dayt,r2,t(x) = 0.75(Dt − 612.7443)p2,t(x). (4.10)The number of eggs that have been laid up until day t is equal to the numberof eggs that had been laid up until the previous day, minus the number ofeggs that hatched the previous day, plus the number of eggs that were laidthe previous day. I thus arrive at the equation,p2,t(x) = p2,t−1(x)− r2,t−1(x) + Θ1,t−1(x). (4.11)Larval DevelopmentThe first 5th instar larva of the first generation emerges at 381.3 degreedays, and by 1152.7 degree days all 5th instar larva have emerged (Graf etal., 2018), giving the degree day ratio(Dt − 381.3771.4). (4.12)To determine the number of 5th instar larvae that emerge on day t, thedegree day ratio term is multiplied by the number of larvae. The number of414.2. Daily Time-step Modellarvae emerging is also multiplied by the survival term, s3 that is given inChapter 2. Altogether giving the equationr3,t(x) =(Dt − 381.3771.4)p3,t(x)s3. (4.13)The number of larvae on day t is equal to the number of larvae from theprevious day, plus the number of 1st instar larvae that hatched the previousday (r2,t−1), minus the number of 5th instar larvae that emerged the previousday, giving the equationp3,t(x) = p3,t−1(x)− r3,t−1(x) + r2,t−1(x). (4.14)DiapauseOnce a 5th instar larva emerges, it can either enter diapause in which stateit remains until the following year, or it can pupate, becoming an adult,forming the next generation. The decision to enter diapause or pupate iscontrolled by critical photoperiod. Each individual larva has a predeter-mined critical photoperiod, which operates as follows: When the amountof light in a day drops below the critical photoperiod the larva is triggeredto enter diapause. If lt is the photoperiod on day t, the number of larvaeentering diapause on day t is thus given byd1,t(x) = r3,t(x)forlt < x. (4.15)Individuals with a critical photoperiod below the actual photoperiod (sothe amount of light in the day is still above the critical photoperiod) go onto pupate and form the second generation of adults, g2,t(x), given by theequationg2,t(x) = r3,t(x)forx < lt. (4.16)4.2.2 Second GenerationThe equations for each developmental stage in the second generation areidentical to those presented above for the first generation. The only differ-ence is the degree day values used in each life stage, which I will presenthere, along with the model equations.Adult EmergenceSecond generation adults begin emerging at 529.9 degree days, and by 1323.7degree days all second generation adults have emerged (Graf et al., 2018).424.2. Daily Time-step ModelThe number of second generation adults emerging on day t is given by theequationr4,t(x) =(Dt − 529.9793.8)p4,t(x). (4.17)The number of individuals in diapause is then updated to account for theindividuals that emerged using the equationp4,t(x) = p4,t−1(x)− r4,t−1(x) + g2,t(x). (4.18)ReproductionThe number of eggs produced on day t by adults with critical photoperiodx is given by the equationθ2,t(x) =(53.8e−0.593√(∑r2,i/A))( 12r4,t(x)cSt +12r4,t(x))12r4,t(x), (4.19)which is the same as the reproduction equation 4.7 in section 4.2.1.Photoperiod RedistributionTo redistribute the critical photoperiod of the parents to the offspring, I usethe equationΘ2,t(x) = 0.75∫ 1812k(x− y)θ2,t(y)dy, (4.20)which is the same as that presented in section 4.2.1. The quantity Θ2,t(x) isthe number of eggs of photoperiod x laid on day t in the second generation.Egg HatchingSecond generation egg hatching begins at 596.6 degree days and by 1414.4degree days, all eggs have hatched. The number of eggs hatching on day tis given byr5,t(x) = 0.75(Dt − 596.6817.7)p5,t(x), (4.21)where the number of eggs still waiting to hatch is given by the equationp5,t(x) = p5,t−1(x)− r5,t−1(x) + Eo,t−1(x). (4.22)434.2. Daily Time-step ModelLarval DevelopmentIn the second generation, the first 5th instar larva emerges at 808.2 degreedays, and by 1954.4 degree days, the last 5th instar larva emerges. Thenumber of 5th instar larva emerging on day t is given by the equationr6,t(x) =(Dt − 808.21146.2)p6,t(x)s6, (4.23)where the number of larva still developing is given byp6,t(x) = p6,t−1(x)− r6,t−1(x) + r5,t−1(x). (4.24)Diapause5th instar larvae then make the decision to either enter diapause or pupateand form the next generation. To determine the number of individuals thatwill enter diapause on day t we compare the critical photoperiod of theemerged 5th instar larvae to the photoperiod on day t. Individuals with acritical photoperiod higher than the calculated photoperiod for that day, lt,will enter diapause, given by the equationd2,t(x) = r6,t(x)forlt < x. (4.25)Individuals with a critical photoperiod lower than the actual photoperiodwill pupate and form the next generation. In the Okanagan we normally seeonly 2 full generations in a year, therefore any second generation individualsthat do not enter diapause are considered to have died before mating andforming a third generation.The number of individuals in diapause waiting to emerge the followingspring is the sum of all the individuals that entered diapause in each of thesummer generations. The number of individuals in diapause is multipliedby a survival term that is dependent on the location where larvae spin theiroverwintering cocoons. Individuals can cocoon on the ground or on trees,the number of individuals cocooning in each location is denoted by cg andct, respectively. Individuals cocooning on the ground have lower survivalrates than individuals cocooning on trees, denoted sg and st, respectively.We thus obtain the number of individuals that will emerge from diapausethe following spring,p1,t+1(x) = ctstD1,t(x) + cgsgD1,t(x) + ctstD2,t(x) + cgsgD2,t(x). (4.26)444.3. Simulation Experiments4.3 Simulation ExperimentsPreliminary simulations of the model revealed complex solution behaviour,with decreasing oscillations in both the critical photoperiod distribution andpopulation size. The observed oscillations persisted through 200 generations,and so the population steady state could not be determined. I also foundthat the initial trends in shifts in the critical photoperiod distribution andpopulation size appeared to be misaligned with the results from Chapter 2.Critical photoperiod always shifted to longer critical photoperiods, even inthe absence of sterile insects. More work is therefore needed to understandmodel behaviour and, at this point, we cannot rule out the possibility thatthe model may need to be adjusted. Therefore, I will not be presentinghere the results of simulation experiments; instead, I will discuss a potentialmodification of the model to address the possible misalignment and, oncethe model is finalised, how my modelling approach could be used in futurework.4.4 Discussion4.4.1 Model AdjustmentThe apparent disagreement, between the preliminary simulation results forthe daily time-step model and the two-season model presented in Chapter 2,indicates that there may still be some problems with the daily time-stepmodel. Preliminary simulations showed that, in the absence of sterile in-sects, the critical photoperiod distribution was evolving to longer criticalphotoperiods, with a greater proportion of individuals entering diapause af-ter the first generation than after the second generation. It is possible thatthis behaviour is due to individuals proceeding through the developmentalstages in my model too slowly. Slow development would cause more individ-uals in the first generation to emerge at a time of lower photoperiods, thusstimulating more individuals to enter diapause after the first generation.Additionally, in the second generation, slow development would prevent in-dividuals from reaching the 5th instar larval stage in time to enter diapausebefore exposure to lethal winter conditions. A higher death rate beforediapause in the second generation would remove individuals with shorterphotoperiods from the population, also causing evolution of the populationtoward longer photoperiods.The problem of slow development may be due to my assumption thatthe development rate of codling moths is a linear function of the degree454.4. Discussionday ratio term. Evidence suggests that development may not be a linearfunction of degree days, but follow a nonlinear distribution (Jones, 2020).With a nonlinear function, more individuals can emerge from a given lifestage at an earlier time. That is, the emergence rate does not linearly in-crease as the degree days accumulated increase, but follows a curve wherethe maximum emergence rate occurs somewhere near the midpoint betweenthe degree day values where emergence begins and ends. An increased de-velopmental rate would also allow second generation individuals to completetheir life cycle and enter diapause before exposure to lethal winter condi-tions. The increased rate of development should produce results similar tothose presented in Chapter 2, where, in the absence of sterile insects, moreindividuals enter diapause after the second generation than after the first,and the critical photoperiod distribution evolves to shorter photoperiods.4.4.2 Future WorkThis model provides an initial framework for investigating the evolution ofdiapause under the dual effects of the SIT and future climatic conditions.Climate change is projected to increase the length of the growing season andaverage annual temperatures, as well as the frequency of extreme weatherevents in the Okanagan (Kelowna, 2020). A study of the effect of climatechange on the codling moth system should include consideration of extremeevents as well as shifts in mean temperatures, as there is mounting researchthat both are ecologically important (Turner et al., 2020; McCarty, 2001;O’Neill et al., 2017). These changes could affect the efficacy of the SIT in twodifferent ways. Sterile insect competitiveness and the rate of codling mothdevelopment both increase with temperature, to a threshold. With longergrowing seasons, the increased rate of codling moth development may leadto a third generation in the Okanagan. In California, where temperaturesare warmer and the growing season longer, codling moth can have up to fourgenerations each year (Agriculture and Natural Resources, 2022).The effect of additional generations on the SIT would depend on thecompetitiveness of sterile insects in those generations. It is predicted thatthe summer and fall will be warmer and drier (Kelowna, 2020), howeverpredictions are not specific enough to estimate exact climatic conditions inthe late summer or early fall when the third generation would occur (R.Smith and Fraser, 2002; Rodenhuis et al., 2007). If a third generation oc-curs at a time when conditions are similar to the current second generationand the competitiveness of sterile insects is high, fecundity would decreaseand critical photoperiod would likely continue to evolve to longer critical464.4. Discussionphotoperiods with more individuals entering diapause after the first gener-ation. If, however, the third generation occurs during cooler temperaturesduring the transition to fall, competitiveness could possibly be lower, theresult would be a second temporal refuge from the SIT in the third genera-tion. Selection might then favour both long and short critical photoperiods.In order to reach the third generation, however, individuals would have tosurvive increased competition in the second generation. The framework Iintroduce here could be used to investigate whether or not the cost of per-sisting through the second generation outweighs the benefit of making it tothe third generation.Under current climatic conditions, recent temperature data could beused to determine the degree days accumulated for each day of the year.Simulations similar to those in Chapter 2 could then be run to investigatehow annual variations in temperature affect the development rate of thecodling moth population and evolution of the critical photoperiod distribu-tion. Simulations could be run keeping the temperature data for each yearat the values for the warmest year on record, and then repeated using thecoldest year on record. A comparison of the results could indicate how thedevelopment rate and critical photoperiod distribution are affected by tem-perature. Simulations could also be run with consecutive years changingfrom the warmest on record to the coolest, and coolest to warmest, to seehow drastic annual variations in temperature affect the development rateand critical photoperiod distribution. A simulation using temperature datafrom 1992 to the present could be used to investigate how the codling mothdevelopment rate and critical photoperiod distribution may have evolvedsince the OKSIR programme began operating.To understand how future climatic conditions may affect the develop-ment rate of the codling moth population and the evolution of critical pho-toperiod, an optional third generation could be added to the model. Climatemodel predictions could be used for the degree days accumulated during eachday of the simulation. Juszczak et al. (2012) investigated the potential ef-fects of climate change on the development and emergence rates of codlingmoth in Poland using two IPCC climate change models and a daily weathergenerator. Similar methods could be used for these simulations. Multiplesimulation experiments could be ran using temperature forecasts from thesemodels ranging from the most conservative to extreme predictions. It wouldbe ideal to incorporate the competitiveness of sterile insects as a functionof temperature, but the specific nature of this relationship is currently un-known. Moisture is another environmental factor that effects sterile insectcompetitiveness that could be considered in the model (Judd, Thistlewood,474.4. Discussionet al., 2006). Future empirical work establishing sterile insect competitive-ness across a range of conditions, incorporating both extreme and meanclimate predictions, will be important for the design of management effortsmoving forward (Chiu et al., 2019; Nyamukondiwa et al., 2013). This workis key for not just the codling moth system but across applications of theSIT (A. P. Gutierrez et al., 2019; Dyck, Hendrichs, et al., 2005).48Chapter 5ConclusionsThis thesis represents the first study of evolution in critical photoperiodinducing diapause as a possible factor in the efficacy of the SIT. The timeat which to enter diapause, i.e., after the first or second generation in asummer, involves a critical trade-off between fitness and survival, where theincreased fitness of producing the next generation is counteracted by the costof increased mortality (Roff, 1980). It has previously been shown that enter-ing diapause early is an effective method of escaping predators (Schroederand Dalin, 2016; Kroon et al., 2004), parasitoids (Tougeron et al., 2017; Liet al., 2015) and insecticides (Bird et al., 2020; Boivin et al., 2004). Asthese negative pressures increase, individual likelihood of survival can be in-creased through early entry into diapause. In my thesis, I hypothesized thatincreased competition from sterile insects in the summer may sufficiently re-duce the fitness of second generation wild codling moths to induce selectionfor early diapause in the first generation.In order to test my hypothesis, I developed a new population dynamicsmodel that includes diapause as a function of critical photoperiod. Whileearlier codling moth population dynamics models did not include this fea-ture, the research literature has widely discussed photoperiod as the mainfactor controlling diapause (Ferro, Robert R. Sluss, et al., 1974; Boivin etal., 2004; Stoeckli et al., 2012; Thistlewood and Judd, 2019). In my thesisI incorporated diapause as a function of critical photoperiod, which evolvedfrom one generation to the next by means of a redistribution kernel. Thisapproach is consistent with multifactorial inheritance (Hu et al., 2022).My work shows that if the critical photoperiod that controls diapause isa heritable trait, the SIT may exert an evolutionary pressure selecting forlonger critical photoperiods in wild codling moths. The selection for longercritical photoperiods corresponds to an increasing tendency for wild codlingmoths to enter diapause after the first generation. My simulations also showthat having an increased tendency for early diapause decreases the chances ofwild codling moth eradication via the SIT. These results are corroboratedby my field data, gathered in a wild codling moth population that hadbeen subject to the SIT for 25 years. In this population I found a critical49Chapter 5. Conclusionsphotoperiod distribution skewed toward longer photoperiods, which mightbe a key factor in the failure of the SIT to eradicate the wild population.In order to achieve eradication within five years, my work suggests thatincreasing the competitiveness of sterile insects in the first generation and/orsubstantially increasing the overflooding ratio is required. Increasing thecompetitiveness of sterile insects in the first generation, c1, to 0.85 whilemaintaining the current overflooding ratio of 40:1 leads to eradication. Ifthe estimated sterile insect competitiveness remains at 0.2 in the spring(c1 = 0.2) and 0.8 in the summer (c2 = 0.8), eradication can not be achieveduntil the overflooding ratio is increased to 114:1. This model does not includespatial aspects of codling moths in the orchard which would influence theefficacy of the sterile insect technique. Sterile insects are not uniformlydistributed throughout the orchard.The SIT is successful at decreasing the wild population, however, eradi-cation appears unlikely. Little can be done to increase the competitivenessof sterile insects, as their competitiveness is dependent on the ambient tem-perature in the orchard (Thistlewood and Judd, 2019). Increasing the over-flooding ratio substantially may lead to eradication, but the increased costsof producing and maintaining these ratios makes such increases unlikely. Iferadication is the goal, a combination of management efforts is thus required,such as SIT coupled with the application of insecticides, or pheromone-basedmating disruption products (Thistlewood and Judd, 2019). Specifically, amanagement technique targeted at the first generation of codling mothswhen the SIT is less effective would be recommended. Targeting the firstgeneration would no longer make early diapause a temporal refuge frommanagement efforts, and help decrease the population size of the first gen-eration.In my work here I only considered complete sterility in the sterile in-sects, consistent with the current SIT program in the Okanagan. Inheritedsterility, however, is another possibility (Knipling, 1970). Inherited sterilityinvolves partially sterilizing lab raised insects in such a way that they cansuccessfully mate but produce sterile offspring (Knipling, 1970; Kean, Wee,et al., 2008). Inherited sterility may be beneficial for the goal of eradication,as a single partially sterile insect could produce many fully sterile offspring,substantially increasing the overflooding ratio of the next generation. In or-der to achieve a target overflooding ratio using inherited sterility, more workwould need to be done to understand the reproduction of partially sterileinsects. The sterilization process may have an effect on the reproductivesystem, causing fewer offspring to be produced on average as compared towild codling moths. There could also be an effect on the survival and de-50Chapter 5. Conclusionsvelopment rates of the fully sterile offspring, as well as on the factors thatinfluence diapause. The risk of inherited sterility is that partially sterilizedinsects could produce offspring that are not sterile (Kean, Wee, et al., 2008).Future work modelling the effects of inherited sterility on the SIT would bebeneficial.More work could be done to determine what a distribution of criticalphotoperiod in a codling moth population looks like. The data set that wasused in this thesis was relatively small and collected over one year or twogenerations. The data was also collected from a single orchard. Collectingmore data over longer time spans, and in more locations may be beneficialin understanding what a distribution of critical photoperiod looks like inCodling moth populations. Additionally, collecting data on a wild codlingmoth population that has not been subject to the SIT would be ideal.Future work could also aim to identify the genetic component of criticalphotoperiod. I only allowed individuals with the same critical photoperiodto mate and assumed that offspring would be more likely to have a crit-ical photoperiod the same as, or similar to their parents. Understandingthe genetics of critical photoperiod would be beneficial for defining and pa-rameterizing the redistribution kernel. Also a better understanding of thegenetic component would allow individuals with different critical photope-riods to mate, which would be more realistic.Climate change poses a significant threat that could alter ecosystemdynamics (Malhi et al., 2020). Understanding how these dynamics maychange is important for conservation and management efforts (Malhi et al.,2020). As sterile insect competitiveness and codling moth development aredirectly related to temperature, climate change has the potential to altercodling moth population dynamics, which could, in turn, affect the efficacyof the SIT. Annual mean temperature increases are expected to speed upthe development rate of the codling moth population and could lead to athird generation. Extreme weather events, such as the heat dome of 2021(Orginization, 2021), could also have significant impacts on the developmentand survival rates of codling moths. As these impacts could be either pos-itive or negative, they are potentially confounding to the effects of meantemperature increase. The heat dome, for example, produced temperaturessignificantly above the codling moth upper developmental threshold of 31◦C,thus slowing the development rate and possibly decreasing survival (Judd,2020). Investigating the effects of climate change on codling moth popu-lation dynamics and the SIT would help determine what adjustments areneeded to maintain the effectiveness of management efforts moving forward.Diapause has been shown to be an effective method of avoiding times of51Chapter 5. Conclusionsdecreased survival from insecticides (Bird et al., 2020; Boivin et al., 2004),parasitoids (Tougeron et al., 2017; Li et al., 2015), and predators(Schroederand Dalin, 2016; Kroon et al., 2004). Similar methods to those I havepresented in this thesis could be used to understand how diapause evolvesfrom the pressures of insecticides, parasitoids and predators. Competition,either interspecific or intraspecific, may be another factor that could alterthe timing of diapause in a population.The OKSIR programme began operating in 1992, and to date has re-ceived taxpayer funding exceeding one hundred million dollars (Thistlewoodand Judd, 2019). The programme’s initial goal was eradication of codlingmoth from the Okanagan. This goal was subsequently changed in 2000 toarea-wide management (Thistlewood and Judd, 2019). The programme hasbeen successful in decreasing the wild codling moth population to levelsthat do not have significant economic impact on growers while also reducingpesticide use (Thistlewood and Judd, 2019). The continued success of theOKSIR programme is thus environmentally beneficial and also important forthe security of the pomme-fruit growing industry in the Okanagan. Under-standing how the critical photoperiod distribution may evolve under futureclimatic conditions is important for the OKSIR programme to be preparedfor future management efforts.52BibliographyAgriculture and University of California Natural Resources (2022). StatewideIntegrated Pest Management Program. url: https://ipm.ucanr.edu/QT/codlingmothcard.html (visited on 01/30/2023).Barclay, Hugh J. 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Thesis/Dissertation
eng
Interdisciplinary Studies
Vancouver : University of British Columbia Library
Attribution-NoDerivatives 4.0 International
Graduate
Tyson, Rebecca
Evolution of critical photoperiod in codling moths subject to the sterile insect technique
Text