Browse Subject Areas

Click through the PLOS taxonomy to find articles in your field.

For more information about PLOS Subject Areas, click here.

  • Loading metrics

Linear relationship between peak and season-long abundances in insects

  • Ksenia S. Onufrieva ,

    Contributed equally to this work with: Ksenia S. Onufrieva, Alexey V. Onufriev

    Roles Conceptualization, Data curation, Investigation, Validation, Writing – original draft, Writing – review & editing

    Affiliation Department of Entomology, Virginia Tech, Blacksburg, VA, United States of America

  • Alexey V. Onufriev

    Contributed equally to this work with: Ksenia S. Onufrieva, Alexey V. Onufriev

    Roles Conceptualization, Formal analysis, Methodology, Validation, Writing – original draft, Writing – review & editing

    Affiliations Department of Computer Science, Virginia Tech, Blacksburg, VA, United States of America, Department of Physics, Virginia Tech, Blacksburg, VA, United States of America, Center for High End Computer Systems, Virginia Tech, Blacksburg, VA, United States of America

Linear relationship between peak and season-long abundances in insects

  • Ksenia S. Onufrieva, 
  • Alexey V. Onufriev


An accurate quantitative relationship between key characteristics of an insect population, such as season-long and peak abundances, can be very useful in pest management programs. To the best of our knowledge, no such relationship has yet been established. Here we establish a predictive linear relationship between insect catch Mpw during the week of peak abundance, the length of seasonal flight period, F (number of weeks) and season-long cumulative catch (abundance) A = 0.41MpwF. The derivation of the equation is based on several general assumptions and does not involve fitting to experimental data, which implies generality of the result. A quantitative criterion for the validity of the model is presented. The equation was tested using extensive data collected on captures of male gypsy moths Lymantria dispar (L.) (Lepidoptera: Erebidae) in pheromone-baited traps during 15 years. The model was also tested using trap catch data for two species of mosquitoes, Culex pipiens (L.) (Diptera: Culicidae) and Aedes albopictus (Skuse) (Diptera: Culicidae), in Gravid and BG-sentinel mosquito traps, respectively. The simple, parameter-free equation approximates experimental data points with relative error of 13% and R2 = 0.997, across all of the species tested. For gypsy moth, we also related season-long and weekly trap catches to the daily trap catches during peak flight. We describe several usage scenarios, in which the derived relationships are employed to help link results of small-scale field studies to the operational pest management programs.


Surveys are crucial for monitoring insect activity, crop pest levels, local movement, long-range migration, feeding and reproduction, and are widely used in pest management programs. Various tools are used for insect surveys, including several types of traps, which are deployed extensively to detect and monitor insect population levels, presence of invading populations and phenological development, for purposes of both applied pest management and research [111]. The scale of the enterprise is evident from the following two examples. At least 20 million pheromone lures are produced for monitoring and mass trapping annually worldwide [10]. In the United States, over 100,000 pheromone-baited traps are deployed annually just to monitor gypsy moth [12].

Insect surveys also play an important role in research on population dynamics, seasonal phenology, mating success and mating disruption in various species, including but not limited to gypsy moth, codling moth, light brown apple moth and oriental fruit moth [1328]. Many of the studies are conducted using releases of laboratory reared insects rather than wild populations, which helps to ensure similar population densities among experimental plots and can provide a longer season of flight for data collection [13, 1618, 21, 25, 26].

Due to logistics and experimental design, researchers often work with daily or weekly insect catches [1720, 2527, 29], while large-scale management programs normally have access to season-long catches only [30], which makes it challenging to relate research results to the management programs. To the best of our knowledge, no method currently exists to relate daily or weekly catches to season-long catches. However, relating daily and weekly catches to season-long catches as well as the converse problem of predicting maximum daily catches from the known season-long ones would facilitate interpretation of research results and their application in the management programs. For many species of interest, these population characteristics cannot be assumed constant, which makes it hard to design optimal management protocols. Knowledge of strong correlations between population characteristics can help significantly. Since collecting daily or weekly data in a large-scale management program is very costly and impractical even for a single insect species, a model that relates daily and weekly population characteristics to the easy to obtain season-long catches should be of practical benefit.

More broadly, with about a million insect species currently known [31], it is all but impossible to obtain purely empirical, i.e. based solely on collected data, predictive relationship of the type we seek for even a small fraction of the known species. It may take years or even decades to establish one empirically for a single species, should the need arise. The availability of a theoretical predictive model that is likely to give a quick and reasonable estimate of what to expect should therefore be of value.

Materials and methods

Experimental design and available data

Gypsy moth.

We used data from standard USDA milk carton pheromone-baited traps [32] deployed in 2000 and 2001 in George Washington National Forest, VA [UTM 637052 E, 4223294 N to 614250 E, 4192715 N, NAD 27, zone 17], in 2001, 2002, 2004 and 2006 in Appomattox-Buckingham and Cumberland State Forests, VA [UTM 746246 E, 4166292 N to 700180 E, 4136389 N, NAD 27, zone 17], in 2013 and 2014 in Goshen Wildlife Management Area, VA [UTM 637052 E, 4223294 N to 614250 E, 4192715 N, NAD 27, zone 17], and in 2016 in Blacksburg, VA [UTM 553841 E, 4121358 N, zone 17]. Permissions to conduct experiments were obtained from VA Department of Forestry and VA Department of Game and Inland Fisheries. At each location, 5 to 20 USDA pheromone-baited traps were deployed, checked and emptied weekly to monitor the flight period of wild gypsy moth populations as part of ongoing research experiments. Captures from all traps in a given location were averaged and considered a single observation. Since 2013, we began to monitor the traps on a daily basis: in 2013, traps were monitored from June 14 to August 4; in 2014, traps were monitored from June 30 to August 8. In both 2013 and 2014, 2 sentinel traps were deployed and checked daily for 5 days each week. In 2016, a trap was placed in Blacksburg, VA and monitored every day from June 20 to August 10.

A standard assumption often made by others [8, 33, 34] is that the distribution of trap captures as a function of time is Gaussian. We have verified this assumption explicitly for two randomly selected years (2006 and 2014) of gypsy moth trap catches, (Fig 1).

Fig 1.

Weekly male gypsy moth catches in pheromone baited traps, 2006 (A) and 2014 (B) and least-square fit of experimental data points to a normal distribution. In both cases, the correlation R2 > 0.99. Vertical arrows indicate the time points where the insect population reaches the trap sensitivity threshold.


Testing of the proposed model requires high temporal resolution data on insect abundance not readily available for the vast majority of insect species. Fortunately, mosquitoes is an exception. Since in the US, mosquitoes vector important diseases of humans, such as West Nile Virus and Eastern Equine Encephalitis, mosquito risk is often evaluated throughout the season as part of Integrated Mosquito Management Program. Many Mosquito Management Programs conduct weekly trap counts, which are labor intensive and, therefore, are not justifiable for many other pest management programs. We obtained mosquito trapping data from the Mosquito and Forest Pest Management program, Prince William County, VA in 2015. We randomly chose Culex pipiens catches in CDC Gravid Traps [35] and Aedes albopictus catches in BG-Sentinel traps [36]. The trap data were collected weekly from May 3 to October 23, 2015.

The main model and its derivation

The model describes the relationship between insect catches Mpw during the week of peak activity, the flight period F, and season-long cumulative catches A, which is a direct measure of the insect abundance. It is known that pheromone traps achieve detection probability of nearly 100% even for relatively sparse populations [37]. It is therefore reasonable to assume high sensitivity of the traps. Specifically, we assume that traps are sensitive enough to start catching insects when their population reaches 1% of the maximum population, consistent with our own experiments (Fig 2). We also demonstrate below that the specific value of “trap sensitivity” is not very important for as long as it is high enough–the mathematical structure of the resulting equation is such that it is insensitive to the value of the “sensitivity threshold”. For a symmetric distribution, the flight period F is defined as follows: the traps begin to catch insects at t = tp−F/2, when the insect density rises above the 1% trap sensitivity threshold, and stop at t = tp + F/2, once the insect density drops below this threshold (Fig 1). We model the distribution of insects caught as a function of time as a Gaussian function , centered around the peak flight time point tp (Fig 1). Then, the cumulative catch (A)

Fig 2. Season-long trap catches depend linearly on the product of trap catch during the peak flight week and the length of the flight period.

The relationship, derived on general arguments rather than fitting to experimental data, holds true for several different insect species and catch methods. Error bars (for gypsy moth): vertical bars represent standard error; horizontal error bards correspond to the temporal resolution of the experimental data points, which is about 3% for most points.

The full width F of a Gaussian function at 1/100 (1%) of the maximum is related to σ via

Therefore, (Eq 1) which is the main result of this work. Its robustness to the assumptions made in the derivation is discussed below, and is demonstrated experimentally.

We stress that the derivation of Eq 1 does not involve any fitting to experimental data. The relationship is expected to hold as long as the following conditions are satisfied: (1) The seasonal change in the insect population as a function of time (weekly averages) can be reasonably approximated by a Gaussian function; (2) The trap method is sensitive enough to detect insects during most of the flight period; (3) Traps do not saturate. The importance of (1) and (2) for our model is self-evident. To understand the importance of the last assumption, consider a situation where it breaks down completely: at very high population density during several weeks, high enough so the traps are completely saturated. Obviously, if this were the case, the weekly catch estimates would be flat around the peak, no longer representative of the true insect abundance [38, 39], and the model that assumes a Gaussian distribution would fail.

Robustness of the model

Assumptions (2) and (3) essentially state that the catch method is, in some sense, “well designed”. As long as this is the case, Eq 1 is not very sensitive to details such as the exact value of the trap sensitivity threshold. Indeed, consider a trap that faithfully represents the true population density in the following sense: catch = α*(true population density), where the constant α stays the same within a given year and experiment, but may vary for different species and years. Now suppose a different trap is used, which changes the value of α by a factor of 2 for a different species/year. Both A and Mpw in Eq 1 will change by a factor of 2, without affecting the linear nature of the relationship. There will be a slight effect on the proportionality constant K in A = K*Mpw*F due to the use of more/less sensitive trap (e.g. one that can sense 1/200 instead of 1/100 of the maximum population, which will affect the trap sensitivity threshold, Fig 2), but note that the functional dependence of K on the trap sensitivity threshold is extremely weak, . In the above example of the threshold changing from 1/100 to 1/200, the difference in the proportionality constant in Eq 1 is vs. , or 3.03 vs. 3.25, which is small.

Assumption (1) has been explicitly verified on our experimental data points for gypsy moth. As we shall see below, even with a relaxed assumption that the seasonal distribution of insect abundance is not strictly Gaussian, but nevertheless has a distinct start, end, and sharp peak, the model is likely to work reasonably well. While assumption (1) (or its relaxed version) is likely to hold for many other species, it implies that the insects are short-lived relative to their entire developmental periods. Otherwise, even if the developmental period itself is normally distributed (which is approximately true even for humans [40]), the abundance can reach a long plateau during the season, inconsistent with the Gaussian shape. For such insects we expect appreciable deviations from the model predictions. For example, tropical species may not have a distinct start and end of flight points, and so the model may not be applicable.

However, as we shall see below, the simple and parameter-free model described by Eq 1 has so far worked surprisingly well for completely different insect species and trapping methods in the temperate climate zones. We stress that we have not used any of the gypsy moth specific parameters in the derivation of Eq 1.

Relationship between season-long abundance and daily trap catch for gypsy moth

Our main result, Eq 1, describes weekly trap catches. Here we seek to establish a predictive relationship for the daily catches. Unlike the weekly catches, in which day-to-day fluctuations of insect catches are automatically averaged out to produce a smooth distribution that deviates little from the expected Gaussian distribution (Fig 1), individual daily values are too variable for a single characteristic such as daily average to be useful in practice. Here we seek to estimate a conservative range for the upper and lower bounds on the daily trap catches. It is probably hopeless to try to derive the range from first principles; instead, we deduce it from our experimental data for gypsy moth (described below), which we re-interpret as follows. Since the beginning of peak flight week assignment is arbitrary and depends on the day a trap was checked, we simulated different week assignments using a sliding window of 7 days to determine the week of peak flight, making sure that the maximum observed value of daily catch is always included in the “peak flight” week. In effect, the procedure simulates 7 different experimental outcomes from a single data set. The analysis yields a range of proportionality coefficients between trap catch during the peak flight week and the peak daily value.

Daily gypsy moth male trap catches were not available to us prior to 2013. Once daily trap catches became available in 2013, followed by 2014 and 2016, we also sought to relate maximum daily trap catch at peak flight to the season-long trap catch. For this relationship, we used daily trap catches collected in 2014 as a training set, and daily trap catches collected in 2013 and 2016 served as test sets.

In an idealized scenario, without random day-to-day variation, trap catches during the peak week of flight period can be calculated as: where Mpd is the daily peak, that is the absolute maximum of the distribution. In the idealized case this simple relationship holds because for the species discussed here, σ is considerably larger than 7 days, and so the integrand varies little over the integration range in the above expression. However, in reality, daily values fluctuate significantly around the predicted Gaussian peak, resulting in two effects. First, the proportionality coefficient K in Mpw = KMpd becomes less than 7, with daily peak values that deviate stronger from the Gaussian-based expectation resulting in lower K. Second, K will vary from year to year. In 2014, K ranged from 2.35 to 4.66. Below we estimate maximum and minimum bounds on K, based on the variation in daily trap catches inferred from our analysis of the experimental data on gypsy moth from 2014. Our estimate is that 2.35Mpd < Mpw < 7Mpd, or conversely, (Eq 2)

Below we use data points from 2013 and 2016 to validate the estimate.

Using our main result (Eq 1) A = 0.41MpwF, we arrive at another useful relationship: (Eq 3)

Eqs 2 and 3 establish a connection between daily peak values Mpd, and other measurable parameters of insect abundance for gypsy moth. While the values of the numerical factors in Eq 2 may be species specific, the over-all approach to deriving the inequality is general.


Season-long trap catch for gypsy moth

Experimentally observed season-long trap catches are highly variable, showing strong dependence of the season-long cumulative catch (abundance) A on both the length of the flight period F and the trap catch during the week of peak flight, Mpw (Fig 2). Trap catches during peak flight cannot be predicted from the flight period alone.

Experimental verification of the model

Our data strongly confirms the proposed functional dependence, Eq 1, between the season-long trap catch, the flight duration and the trap catch during peak flight (Fig 2).

The predicted season-long trap catches from trap catches during the week of peak flight correlate strongly with the actual, measured season-long trap catches for all three species tested (R2 = 0.9977, SD = 0.13, Fig 2).

We stress the significant range spanned by the data points in our test sets (see Methods). The season-long male gypsy moth trap catches span almost two orders of magnitude, ranging from 7.3 to 462 males/trap/week; flight duration ranged from 3.7 to 7 weeks; and maximum trap catch during peak week ranged from 4.4 to 172 males/trap. Season-long trap catches of C. pipiens and A. albopictus span an order of magnitude, ranging from 6.22 to 60.72 and from 0.12 to 31.12, respectively. Flight duration of both species was 24 weeks.

Robustness of the model to insect and trap type

Our main result (Eq 1) is robust to insect and trap type (Fig 2).

It is remarkable that the accuracy of Eq 1 is the same for all of the species tested, even though the biology, catch methods, and the geographical areas are different. Moreover, for the mosquito species the catch distributions (Fig 3) are not as close to idealized Gaussian as they are for the gypsy moth (Fig 1). This observation suggests strong robustness of the proposed model, and its potential to work for other species as well. We explain this robustness as follows, based on the mosquito example. Let’s approximate the actual catch distribution by a triangular shape with the top vertex at the experimental peak point (Fig 4) rather than by a pure Gaussian. Then, the total catch (abundance) is the area under the triangle A = 0.5MpwF. The coefficient 0.5 in this equation is not that different from 0.41 in our main Eq 1. As one can see from Fig 4, the experimental data points lie mostly below the triangle, which explains why the original formula A = 0.41MpwF works even better than the one based on the triangle.

Fig 3. Weekly A. albopictus catches in BG-sentinel mosquito traps (2006) and least-square fits of a normal and a triangular distributions to experimental data points.

Fig 4.

Daily gypsy moth male catches in pheromone-baited traps in Virginia, 2013 (A) and 2016 (B). Lines indicate estimated minimum and maximum possible daily values estimated from the maximum observed weekly peak value.

A quantitative criterion for model applicability

To conclude this discussion, consider a hypothetical insect for which Eq 1 does not work because the main assumption on the catch distribution is violated. Namely, consider a catch distribution where instead of a single clear peak there is a long plateau of near constant abundance Mpw, whose duration P is comparable to the total flight time F. The distribution will look like a trapezoid in this case, giving for the total abundance A = 0.5MpwF + 0.5MpwP, where the second term can be regarded as the error term relative to the main expression A = 0.5MpwF. The relative error is then simply P/F, which gives us a simple practical criterion for the application of Eq 1: the time interval over which the population is close to its peak value must be much less than the total flight period.

Daily trap catch for gypsy moth

Experimental daily trap catches ranged from 0 to 13.5 males/trap/day in 2013, from 0 to 10 males/trap/day in 2014, and from 0 to 15 in 2016. (Fig 4). Clearly, the maximum daily catch during the week of peak flight is within the estimated lower and upper bounds given by Eq 2.

Eq 3 is tested using the same two data sets. In both years, observed abundance was within the predicted range given by Eq 3 (Table 1).

Table 1. Predicted vs. observed abundance (A) of gypsy moth males in Virginia.


In this paper, we have established a predictive linear relationship between insect catch Mpw during the week of peak abundance, the length of seasonal flight period, F (number of weeks) and season-long cumulative catch A = 0.41MpwF. This relationship was derived without any fitting to experiment, based on very general assumptions, which likely explains its remarkable accuracy and the fact that it works across the three tested species with very different biology, behavior, and trapping methods: Lymantria dispar (Lepidoptera: Lymantriidae), Culex pipiens (Diptera: Culicidae) and Aedes albopictus (Diptera: Culicidae). Although the model has so far been validated using only three species of insects, we expect the relationship, Eq 1, between maximum weekly catches and season-long catches to hold true for many other species, as long as their emergence has a clear start and end points, a clear maximum, and as long the collection method is sensitive and faithfully reflects variation in abundance. A quantitative criterion for the model applicability is also provided: the time interval over which the population is close to its peak value must be much less than the total flight period. The expectation that the model will work for many species is based on the generality of the arguments used in the derivation, absence of fitting to a specific species or trap type, and the already established agreement with experiment across three species.

For a theoretical model to work for a very broad variety of animal species, it must be based on very general principles that transgress specific biology of individual species. A good existing example is allometric laws in biology, which relate various biological characteristics to animal body mass. Originally, some of these laws were established purely empirically for a handful of species, then rigorously derived [41] based on general principles of energy conservation and distribution networks, which extended their applicability to essentially any species.

The data collected on gypsy moth phenology over the past 16 years allowed us to conduct a comprehensive analysis and relate season-long and weekly trap catches and flight duration to the daily trap catches. The data collectively indicate a significant variability in flight duration as estimated using pheromone-baited traps, which in turn causes significant variability in peak trap catches in populations with the same density as measured by male moth catches in pheromone-baited traps. To account for this observed variability, the model provides a range for a daily peak value, to allow researches and managers to estimate best and worst case scenarios, predict efficacy of control tactic, and make decisions to ensure optimal results. In addition to the immediate application in gypsy moth management programs, this model may be utilized to predict mating success of gypsy moth females and likelihood of persistence of isolated low-density populations [6, 42, 43]. Daily trap catch data collected over the entire activity season are not easy to obtain, however, should this data become available for species other than gypsy moth, it would be interesting to evaluate this model for these species as well.

Two interrelated scenarios of the potential model use in practical applications are exemplified below:

Example usage Scenario I

Eq 1, A = 0.41MpwF, can be used to estimate the hard-to-measure peak abundance Mpw from the other two population parameters, A and F, which themselves do not require intense monitoring. Thus, data collected as part of monitoring in the pest management program can be analyzed using this formula and appropriate method of control can be chosen based on the maximum daily value. This is important in large-scale control/monitoring programs, in which a method of control depends on the population density. For example, currently, in the Slow The Spread of the gypsy moth program (STS), the low dosage (6 g AI/acre) of mating disruptant is recommended for use in low-density gypsy moth populations, in which trap catches do not exceed 30 males/trap/season [7]. Ability to directly relate weekly trap catches from experimental plots to the season-long trap catches used by STS decision algorithm [44, 45] may allow us to improve the method of mating disruption used against gypsy moth by accurately estimating population densities during peak flight and using more appropriate control measures.

Example usage Scenario II

Eq 3, 0.96MpdF < A < 2.87MpdF, can be used to estimate the unknown season-long trap catch for a population based on the maximum daily peak abundance. This is useful for model (artificially created) populations used in research studies, in which maximum daily values are available by experimental design, while the season-long trap catches are not available. In many mark–release–recapture studies, researchers are not trying to simulate flight, they simply repeatedly release similar numbers of insects to assess treatment efficacy. Therefore, the total of all captured insects in an experimental plot cannot be interpreted as the true season-long catch, which, therefore, would be unknown. Instead, each trap catch can be treated as the maximum daily catch during peak flight and the season-long trap catch can be estimated using the proposed formula. This approach allows to estimate the population density for which the treatment efficacy is assessed, to better interpret research results and to appropriately apply them in the management programs [46].


We thank Slow the Spread of the gypsy moth Program Technical committee for helpful discussions and support for the research that lead to this analysis; Andrea Hickman, Samuel Newcomer, and Michael Merz for field assistance; Timothy McGonegal for providing mosquito trapping data. We also thank Andrew Liebhold (USDA Forest Service) for his valuable comments on an earlier version of the manuscript. Funding to cover publication fees was provided by Virginia Tech Open Access Subvention Fund.


  1. 1. Abell K, Poland TM, Cosse A, Bauer LS. Trapping techniques for emerald ash borer and its introduced parasitoids. In: Van Driesche RG, Reardon RC, editors. Biology and control of emerald ash borer FHTET-2014-09. Morgantown, WV U.S. Department of Agriculture, Forest Service, Forest Health Technology Enterprise Team; 2015. p. 113–27.
  2. 2. El-Sayed AM, Suckling DM, Wearing CH, Byers JA. Potential of mass trapping for long-term pest management and eradication of invasive species. J Econ Entomol. 2006;99(5):1550–64. pmid:17066782
  3. 3. Elkinton JS, Cardé RT. The use of pheromone traps to monitor the distribution and population trends of the gypsy moth. In: Mitchell ED, editor. Management of insect pests with semiochemicals. New York: Plenum; 1981. p. 41–55.
  4. 4. Liebhold AM, Tobin PC. Population ecology of insect invasions and their management. Annual Review of Entomology. 2008;53(1):387–408.
  5. 5. Poland TM, McCullough DG. Emerald ash borer: invasion of the urban forest and the threat to North America’s ash resource. J Forest. 2006;104(3):118–24.
  6. 6. Sharov AA, Liebhold AM, Ravlin FW. Prediction of gypsy moth (Lepidoptera: Lymantriidae) mating success from pheromone trap counts. Environ Entomol. 1995;24:1239–44.
  7. 7. Thorpe K, Reardon R, Tcheslavskaia K, Leonard D, Mastro V. A review of the use of mating disruption to manage gypsy moth, Lymantria dispar (L.): FHTET-2006–13. U.S. Department of Agriculture, Forest Service, Forest Health Technology Enterprise Team; 2006.
  8. 8. Tobin PC, Klein KT, Leonard DS. Gypsy moth (Lepidoptera: Lymantriidae) flight behavior and phenology based on field-deployed automated pheromone-baited traps. Environ Entomol. 2009;38(6):1555–62. pmid:20021749
  9. 9. Wall C, Perry J. Range of action of moth sex‐attractant sources. Entomologia experimentalis et applicata. 1987;44(1):5–14.
  10. 10. Witzgall P, Kirsch P, Cork A. Sex Pheromones and Their Impact on Pest Management. Journal of Chemical Ecology. 2010;36(1):80–100. pmid:20108027
  11. 11. Witzgall P, Stelinski L, Gut L, Thomson D. Codling moth management and chemical ecology. Annual Review of Entomology. 2008;53:503–22. pmid:17877451
  12. 12. Roberts EA, Ziegler AH. Gypsy Moth Population Monitoring and Data Collection. In: Tobin P, Blackbum LM, editors. Slow the Spread: A National Program to Manage the Gypsy Moth. Newtown Square, PA: USDA Forest Service Northern Research Station; 2007.
  13. 13. Casado D, Cave F, Welter S. Puffer Ū-CM dispensers for mating disruption of codling moth: Area of influence and impacts on trap finding success by males. IOBC-WPRS Bulletin. 2014;99:25–31.
  14. 14. Epstein DL, Stelinski LL, Reed TP, Miller JR, Gut LJ. Higher Densities of Distributed Pheromone Sources Provide Disruption of Codling Moth (Lepidoptera: Tortricidae) Superior to That of Lower Densities of Clumped Sources. J Econ Entomol. 2006;99(4):1327–33. pmid:16937689
  15. 15. Knight AL, Basoalto E, Witzgall P. Improving the Performance of the Granulosis Virus of Codling Moth (Lepidoptera: Tortricidae) by Adding the Yeast Saccharomyces cerevisiae with Sugar. Environ Entomol. 2015;44(2):252–9. pmid:26313179
  16. 16. Onufrieva K, Thorpe K, Hickman A, Leonard D, Roberts E, Tobin P. Persistence of the gypsy moth pheromone, disparlure, in the environment in various climates. Insects. 2013;4(1):104–16. pmid:26466798
  17. 17. Onufrieva KS, Brewster CC, Thorpe KW, Sharov AA, Leonard DS, Reardon RC, et al. Effects of the 3M (TM) MEC Sprayable Pheromone (R) formulation on gypsy moth mating success. J Appl Entomol. 2008;132(6):461–8.
  18. 18. Onufrieva KS, Thorpe KW, Hickman AD, Tobin PC, Leonard DS, Roberts EA. Effects of SPLAT (R) GM sprayable pheromone formulation on gypsy moth mating success. Entomologia Experimentalis et Applicata. 2010;136(2):109–15.
  19. 19. Pfeiffer DG. Mating Disruption for Control of Damage by Codling Moth in Virginia Apple Orchards. Entomologia experimentalis et applicata. 1993;67(1):57–64.
  20. 20. Sharov AA, Thorpe KW, Tcheslavskaia K. Effect of synthetic pheromone on gypsy moth (Lepidoptera: Lymantriidae) trap catch and mating success beyond treated areas. Environ Entomol. 2002;31(6):1119–27.
  21. 21. Stelinski LL, Gut LJ, Miller JR. An Attempt to Increase Efficacy of Moth Mating Disruption by Co-Releasing Pheromones With Kairomones and to Understand Possible Underlying Mechanisms of This Technique. Environ Entomol. 2013;42(1):158–66. pmid:23339797
  22. 22. Stelinski LL, Gut LJ, Pierzchala AV, Miller JR. Field observations quantifying attraction of four tortricid moths to high-dosage pheromone dispensers in untreated and pheromone-treated orchards. Entomologia Experimentalis et Applicata. 2004;117:187–96.
  23. 23. Stelinski LL, Lapointe SL, Meyer WL. Season-long mating disruption of citrus leafminer, Phyllocnistis citrella Stainton, with an emulsified wax formulation of pheromone. J Appl Entomol. 2010;134(6):512–20.
  24. 24. Stelinski LL, Miller JR, Ledebuhr R, Siegert P, Gut LJ. Season-long mating disruption of Grapholita molesta (Lepidoptera: Tortricidae) by one machine application of pheromone in wax drops (SPLAT-OFM). J Pest Sci. 2007;80(2):109–17.
  25. 25. Tcheslavskaia KS, Thorpe KW, Brewster CC, Sharov AA, Leonard DS, Reardon RC, et al. Optimization of pheromone dosage for gypsy moth mating disruption. Entomologia Experimentalis et Applicata. 2005;115(3):355–61.
  26. 26. Tcheslavskaia K, Brewster C, Thorpe K, Sharov A, Leonard D, Roberts A. Effects of intentional gaps in spray coverage on the efficacy of gypsy moth mating disruption. J Appl Entomol. 2005;129(9–10):475–80.
  27. 27. Thorpe KW, Mastro VC, Leonard DS, Leonhardt BA, McLane W, Reardon RC, et al. Comparative efficacy of two controlled-release gypsy moth mating disruption formulations. Entomologia Experimentalis et Applicata. 1999;90(3):267–77.
  28. 28. Thorpe KW, Tcheslavskaia KS, Tobin PC, Blackbum LM, Leonard DS, Roberts EA. Persistent effects of aerial applications of disparlure on gypsy moth: trap catch and mating success. Entomologia Experimentalis et Applicata. 2007;125(3):223–9.
  29. 29. Thorpe KW, Ridgway RL, Leonhardt BA. Relationship between Gypsy-Moth (Lepidoptera, Lymantriidae) Pheromone Trap Catch and Population-Density—Comparison of Traps Baited with 1 and 500 Mu-G (+)-Disparlure Lures. J Econ Entomol. 1993;86(1):86–92.
  30. 30. Tobin PC, Blackburn LM. Slow the spread: a national program to manage the gypsy moth. General Technical Report NRS-6. Newtown Square, PA: USDA Forest Service 2007.
  31. 31. Stork NE. How Many Species of Insects and Other Terrestrial Arthropods Are There on Earth? Annu Rev Entomol. 2018;63:31–45. pmid:28938083
  32. 32. Webb RE. Mass trapping of the gypsy moth. In: Kydonieus AF, Beroza M, editors. Insect suppression with controlled release pheromone systems. II. Boca Raton, Fla.: CRC Press; 1982. p. 27–56.
  33. 33. Hokyo N, Kiritani K. A method for estimating natural survival rate and mean fecundity of an adult insect population by dissecting the female reproductive organs. Res Popul Ecol. 1967;9(2):130–42.
  34. 34. Robinet C, Liebhold A, Gray D. Variation in developmental time affects mating success and Allee effects. Oikos. 2007;116(7):1227–37.
  35. 35. Reiter P, Jakob WL, Francy DB, Mullenix JB. Evaluation of the CDC gravid trap for the surveillance of St. Louis encephalitis vectors in Memphis, Tennessee. J Am Mosq Control Assoc. 1986;2(2):209–11. pmid:3507491
  36. 36. Maciel-de-Freitas R, Eiras ÁE, Lourenço-de-Oliveira R. Field evaluation of effectiveness of the BG-Sentinel, a new trap for capturing adult Aedes aegypti (Diptera: Culicidae). Mem I Oswaldo Cruz. 2006;101(3):321–5.
  37. 37. Larsson MC. Pheromones and Other Semiochemicals for Monitoring Rare and Endangered Species. Journal of Chemical Ecology. 2016;42(9):853–68. pmid:27624066
  38. 38. Elkinton J. Changes in efficiency of the pheromone-baited milk-carton trap as it fills with male gypsy moths (Lepidoptera: Lymantriidae). J Econ Entomol. 1987;80(4):754–7.
  39. 39. Liebhold AM, Elkinton JS, Zhou G, Hohn ME, Rossi RE, Boettner GK, et al. Regional Correlation of Gypsy-Moth (Lepidoptera, Lymantriidae) Defoliation with Counts of Egg Masses, Pupae, and Male Moths. Environ Entomol. 1995;24(2):193–203.
  40. 40. Kieler H, Axelsson O, Nilsson S, Waldenströ U. The length of human pregnancy as calculated by ultrasonographic measurement of the fetal biparietal diameter. Ultrasound in obstetrics & gynecology. 1995;6(5):353–7.
  41. 41. Contarini M, Onufrieva KS, Thorpe KW, Raffa KF, Tobin PC. Mate-finding failure as an important cause of Allee effects along the leading edge of an invading insect population. Entomologia Experimentalis et Applicata. 2009;133(3):307–14.
  42. 42. Tobin PC, Onufrieva KS, Thorpe KW. The relationship between male moth density and female mating success in invading populations of Lymantria dispar. Entomologia Experimentalis et Applicata. 2013;146(1):103–11.
  43. 43. West GB, Brown JH, Enquist BJ. A General Model for the Origin of Allometric Scaling Laws in Biology. Science. 1997;276(5309):122–6. pmid:9082983
  44. 44. Tobin P, Sharov A. The Decision Algorithm: Selection of and Recommendation for Potential Problem Areas. In: Tobin P, Blackbum LM, editors. Slow the Spread: A National Program to Manage the Gypsy Moth. General Technical Report NRS-6. Newtown Square, PA: USDA Forest Service; 2007. p. 47–61.
  45. 45. Tobin PC, Sharov AA, Liebhold AA, Leonard DS. Management of the gypsy moth through a Decision Algorithm under the STS Project. American entomologist (Lanham, Md). 2004;50(4):200–209.
  46. 46. Onufrieva K, Hickman A, Leonard D, Tobin P. Threshold Gypsy Moth Populations Appropriate for Control by Mating Disruption. Annual Gypsy Moth Review; 2016; Columbus, OH.