## INTRODUCTION

Classic models of malaria epidemiology identified the importance of *Anopheles* mosquito survival to human malaria case reproductive rates.^{1}^{–}^{3} A recent study^{4} has reiterated that substantial reductions in malaria case reproduction can be brought about by modest reductions to vector survival. This principal is currently driving efforts to reduce dengue transmission through infection of *Aedes aegypti* (L.) by life-shortening *Wolbachia* bacteria.^{5}^{,}^{6} To estimate the daily survival rates (DSRs) of mosquito populations and the efficacy of new control strategies, suitable methods are required to determine the ages of individual mosquitoes with greater levels of accuracy than those afforded by dissection based methods of mosquito age grading.^{7}^{–}^{11}

Insect cuticular hydrocarbons (CHs) provide a barrier against dehydration and include a variety of communication-related compounds.^{12}^{,}^{13} These include sex pheromones,^{14}^{,}^{15} signals for task allocation among social insects,^{16} and possibly species or caste recognition cues.^{12} Signature patterns in the abundance of CHs have been used to separate closely related insect taxa, including sibling species within the *Anopheles gambiae* complex^{17}^{–}^{20} and between strains of *Anopheles stephensi* Liston^{21} and *Aedes albopictus* (Skuse).^{22} Age-related changes in hydrocarbon abundances are likely to constitute a confounding factor in these analyses.^{23}

Age-related changes in the abundance of CHs in mosquitoes were first identified in *Culex quinquefasciatus* Say.^{24} The CHs were quantified using gas chromatography/flame ionization detection and mathematical equations were developed to predict the age of individual mosquitoes. Changes to the relative abundance of CHs were subsequently incorporated into age-predicting equations for *Ae. aegypti*.^{25}^{,}^{26} Recently, the ratio of the abundance of two CHs has been used to predict whether *An. stephensi* females were older than a critical age for malaria transmission.^{27} These applications of CH analysis have been among the most accurate applications of mosquito age grading. However, the use of hydrocarbons for the prediction of mosquito age has not been universally validated or validated for Australasian mosquito vectors; including Australian strains of *Ae. aegypti*, the Australasian malaria vector, *Anopheles farauti* Laveran, or the Ross River virus vector *Ochlerotatus vigilax* (Skuse).

Although age grading techniques focus on individual mosquitoes, survival rates are estimated from age information at the population level. A number of methods have been proposed to estimate survival rates from the age structure of a mosquito population. These have often been referred to as vertical methods of survival rate estimation. However, few of these methods address the precision and accuracy of the resulting survival rate estimates. Exceptions include adaptations of the Davidson parous rate method,^{28} including the provision of standard errors for the survival rate estimates derived from the binomial formula^{29} and simulation studies to determine the influences of population immigration^{30}^{,}^{31} and sampling biases.^{31} In particular, bias towards sampling a particular age group resulted in major reductions in the accuracy of survival rate estimates. The CH-based age grading methods now facilitate alternative measures of population age structure suitable for the determination of mosquito survival rates. However, possible sources of error affecting survival rate estimates, such as inaccuracy in CH age estimates, have not been investigated.

The process of estimating mosquito survival rates could be greatly expedited by sequential sampling techniques, which are methods used to determine the minimum sample size required for a parameter estimate as sampling progresses. Sequential sampling techniques were originally developed for quality control analysis and were subsequently developed to classify insect infestation levels in forestry and agriculture.^{32} Sequential sampling is widely used for estimating insect abundance,^{33}^{,}^{34} often with the goal of facilitating decisions whether to initiate control measures, based on critical insect abundance levels.^{35} Applications of sequential sampling plans to mosquito populations have generally been limited to larval and adult abundance surveys.^{36}^{–}^{39} However, similar principles were applied to the estimation of mosquito survival rates using the time-series parous rate method.^{29} In this case, the appropriate duration of sampling was determined; sampling was concluded when daily survival rate estimates stabilized at constant values. Sequential sampling techniques remain under-used for the estimation of mosquito survival rates and would be valuable for reducing the time and resources required for estimates of survival rates based on CH age data.

To determine whether age-related changes to CH abundance could be used to estimate the age of *Ae. aegypti*, *Oc. vigilax*, and *An. farauti*, cohorts of each species were reared under laboratory conditions and CHs were extracted from individual mosquitoes and assayed using a gas chromatography/mass spectroscopy (GC/MS) method. Multiple linear regression and logistic regression was used to develop predictive models to estimate the age of individual mosquitoes. A simulation model was then used to evaluate whether the predictive models of mosquito age could be used to estimate mosquito survival rates and a sequential sampling plan was developed for field applications of the age predicting models.

## MATERIALS AND METHODS

### Mosquitoes.

*Anopheles farauti* (formerly *An. farauti* No. 1) were obtained as pupae from a colony maintained at the Australian Army Malaria Institute. The colony was established from collections in Rabaul, Papua New Guinea, in 1972. Larvae were reared in a mixture of dam water and aged tap water and fed finely-ground Nutrafin fish food flakes (Hagen Pet Foods Inc., Waverly, NY) *ad libitum*. Pupae were transferred to distilled water in a plastic container within a cage. The pupal container was transferred to a new cage at eight-hour intervals to maintain separate age cohorts of adults. Adults were maintained in the Queensland Institute of Medical Research (QIMR) insectary (temperature = 27°C, relative humidity = 70%, and a 12:12 hour light dark cycle with one-hour crepuscular periods). An anesthetized guinea pig was provided as a blood source twice a week after mosquitoes had reached an age of 3–4 days (QIMR Animal Ethics Protocol P361). A plastic container (18 × 12 × 6 cm) with 500 mL of distilled water was placed in the cage to enable oviposition. Female adults were sampled at 48 ± 4-hour intervals from 1 to 21 days old and stored in glass test tubes at −60°C.

*Aedes aegypti* larvae were hatched from eggs obtained from a colony (Cairns, 2000) maintained at QIMR. General colony maintenance was performed as described for the *An. farauti* colony, with the exception that larvae were reared in aged tap water and fed liver powder (Sigma-Aldrich, St. Louis, MO) *ad libitum*. To provide uniformly sized mosquitoes for CH analysis, groups of 50 first instars were reared in plastic containers (18 × 12 × 6 cm) containing 500 mL of distilled water and fed liver powder according to a feeding regimen described previously.^{25} Age cohorts of adults were maintained and sampled as described for *An. farauti*. Oviposition containers were lined inside with filter paper.

*Ochlerotatus vigilax* larvae were hatched from eggs obtained from a colony (Brisbane, 2000) maintained at QIMR. Groups of 50 first instars were placed into plastic containers (18 × 12 × 6 cm) containing 500 mL of 50% seawater/50% distilled water. Larvae were fed ground fish food pellets according to a medium diet regimen (0.05 mg per larva at eclosion and on day 1, 0.10 mg on day 2, 0.48 mg on days 3 and 4, 0.95 mg on days 5–7, and 0.48 mg on day 8). Age cohorts were maintained and sampled as described for *An. farauti*, with the exception that females received their first blood meal at an age of 5–6 days to allow for the autogenous development of the first batch of eggs. Towels moistened with distilled water were placed on top of the cages to enable oviposition.

### Extraction of CHs from individual mosquitoes.

The CHs were extracted from mosquito legs based on the method of Desena and others.^{26} The legs from each mosquito were removed and transferred to a separate glass reaction vial using stainless steel tweezers and a dissecting microscope (reaction vials and tweezers were washed in hexane prior to use). One hundred microliters of redistilled hexane was added using a hexane-washed glass microvolume syringe (Scientific Glass Engineering, Melbourne, Victoria, Australia). Five minutes were allowed for CH extraction. The hexane extract was transferred to a limited-volume glass insert in an auto-sampler vial (Alltech Associates, Deerfield, IL) using a pasteur pipette (all unwashed, single-use materials).

The hexane extract was evaporated to dryness under a light stream of nitrogen. Ten microliters of redistilled hexane containing 1 ng/μL of octadecane C_{18}H_{38} (as an internal standard referred to as C18) was added using a microvolume syringe. Approximately 1 mL of hexane was added to the autosampler vial, outside the limited volume insert, to increase the partial pressure of hexane and reduce further evaporation of the CH sample. The autosampler vial was sealed with a teflon-lined autosampler cap. The caps were previously shown by GC/MS analysis to be inert to hexane (Holling N, unpublished data).

### Analysis of hydrocarbons by GC/MS.

Gas chromatography/mass spectroscopy was performed using a Varian 3400 gas chromatograph (Varian Inc., Palo Alto, CA) coupled to a Finnigan SSQ710 mass selective detector (Thermo Finnigan, San Jose, CA). The gas chromatograph was operated in split-less mode and was fitted with a J&W Scientific DB-1 column (Agilent, Palo Alto, CA) with an approximate length of 20 meters, internal diameter of 0.2 mm, and film thickness of 0.33 μm, and using helium as the carrier gas. Multiple samples were processed using a Finnigan A 200S autosampler. Since the autosampler did not have a cooling capability, a maximum number of 30 samples could be run before the samples eventually evaporated to dryness. Injection volume was 1 μL with an injection vaporization temperature of 295°C. Column temperature was maintained at 120°C for 1 minute, then increased to 295°C at a rate of 30°C per minute and held at 295°C for 17 minutes.

Mass spectroscopy was performed using single ion monitoring (SIM) to improve the specificity and sensitivity of detection of selected *n*-alkanes between C18 and C29. The SIM was limited to ion 57 (common to all hydrocarbons) and the following molecular ions: 254, 352, 366, 380, 394, and 408. Molecular ions (MIs) are specific to particular hydrocarbons (Table 1). The correspondence of GC/MS peaks to molecular ions was confirmed by the comparison of retention times with the times of MIs from known *n-*alkane standards. Sample blanks (volumes of hexane passed through the sample preparation procedure without contact with mosquito specimens) were included in the analysis at regular intervals.

### Analysis.

#### Construction of regression models for age predictions of mosquitoes.

Variables were constructed from relative hydrocarbon abundances, which were calculated as the abundance of single hydrocarbons divided by combinations other hydrocarbons from the same specimen. The values used for the calculation of relative abundances were the peak areas of the MIs specific for the hydrocarbons. The relative abundance variables were tested as predictor variables in least squares linear regression analysis for the prediction of age. The contribution of additional relative abundance variables to the prediction of age was tested for significance using Multiple-variable least squares linear regression. Optimized single or multiple-variable linear regression models were tested for each mosquito species separately.

Adjusted predicted ages were calculated for individual mosquitoes using the regression models. Adjusted predicted values are equivalent to the predicted value if the regression was re-run omitting that observation from the analysis. Multiple linear regression models were tested for bias in the prediction of age by testing the similarity of the coefficients of the regression line and the predicted equals actual line. To test each model, a dummy variable was constructed with values 1 for the mosquito age estimates and 0 for the theoretical predicted equals actual age estimates. A second variable was constructed that equaled the product of the actual age and the dummy variable. Linear regression was performed with the predicted age as the dependent variable and actual age and the product variable as predictors. Significance of the coefficient of the product variable indicated that the regression coefficients of the two lines were significantly different.

Nominal logistic regression analysis was used to classify individual mosquitoes into age groups to increase the accuracy of predictions. Constructed variables were included as predictor variables as for linear regression analysis. The analysis was repeated using the CH profiles for the same mosquitoes analyzed using linear regression. The number of age groups and the boundaries between the groups were varied to maximize the accuracy of age predictions.

#### Simulation modeling of survival rate estimates.

A simulation modeling procedure was used to estimate the DSR of a mosquito population based on estimations of the age structure of a random population sample. All simulations were performed using Microsoft Excel (Microsoft Corporation, Redmond, WA). Six theoretical populations of 10,000 mosquitoes were constructed with each population representing a different DSR (0.50, 0.60, 0.70, 0.80, 0.90, and 0.95). Mosquitoes were represented by an age in days (at two-day age intervals) with the frequency distribution of each age in the population determined by the DSR. The model randomly selected samples of n mosquitoes (20, 50, 100, 200, and 500) from each population. Each mosquito was then assigned a predicted age based on the results of the CH and mosquito age model. The model also included misclassifications of mosquitoes using the frequencies and bias of misclassifications from the experimental analysis. The model then estimated the proportions of a sample of mosquitoes ≥ 5 days of age or ≥ 9 days of age. A schematic representation of the simulation model is shown in Figure 1. Simulations of the model were repeated 250 times for each combination of DSR and sample size to provide a range of estimates for the proportions of a sample ≥ 5 days of age or ≥ 9 days of age and 95% confidence limits were calculated.

The simulation modeling was performed using the experimental age predictions of mosquitoes at two-day age intervals. For this reason, the assumption was made that mosquitoes younger than one day were not sampled and the frequency of even-numbered ages in the populations were the same as the frequency of the preceding odd-numbered ages. Other assumptions of the model were that survival rates were independent of age and that births and immigration to the mosquito population equaled the number of deaths and emigration.

Expected DSRs were determined from the integral of the exponential density function (adjusted for the absence of < 1-day-old mosquitoes):

where *x* = age (days) and *PROP* is the proportion of individuals surviving to be ≥ *x* days of age. The variable *x* was set at five days for *An. farauti* and nine days for *Ae. aegypti* because these were the lower boundaries of the most accurately predicted age groups for these species. These estimates were equivalent to the DSR if there was no error because of misclassifications of age or random sampling error.

## RESULTS

### Analysis of hydrocarbons by GC/MS.

The CH profiles were obtained from female *An. farauti* (n = 108), *Ae. aegypti* (n = 124), and *Oc. vigilax* (n = 85) mosquitoes at two-day age intervals. The hydrocarbon profile from a three-day-old *An. farauti* female was dominated by a relatively high quantity of C29 and, to a lesser extent heptacosane C_{27}H_{56} (C27, Figure 2a). The profile of a three-day-old *Ae. aegypti* female was dominated by the abundance of C27. A three-day-old female *Oc. vigilax* hydrocarbon profile was also dominated by C27, with an elevated abundance of C25 (Figure 2c). Hydrocarbons varying in abundance the most with age were C27 and C29 for *An. farauti* (Figure 3a) and C25 and C27 for *Ae. aegypti* (Figure 3b) and *Oc. vigilax* (Figure 3c).

### Investigation of age-dependent trends and age prediction.

The change in the hydrocarbon profile of *An. farauti* with age was dominated by a linear increase in the abundance of C29 (as determined from the ratio of the 408 ion to the internal standard ion 254) (*R ^{2}* = 0.647,

*F*= 194.67, degrees of freedom [df] = 1, 106,

*P*< 0.001) (Figure 4a). Despite the linear change of C29 with age, the change in abundance of C29 relative to other hydrocarbons with age was characterized by strong curvilinear trends. This was most evident from the abundance of C29 relative to C27, which was described by the variable

*far1*:

where values for the hydrocarbons in the formula are the GC/MS peak areas of the specific hydrocarbon MIs (denoted by the subscripts). The change in *far1* with age followed a linear increase from one to five days of age, then stabilized and remained relatively constant in mosquitoes more than seven days of age (Figure 4b). The pattern could not be transformed to linearity and was not suitable for least squares linear regression analysis for the prediction of age. However, the variable enabled the classification of mosquitoes into two age groups (1 to < 5 days of age and ≥ 5 days of age) using nominal logistic regression analysis. The logistic regression model resulted in perfect classifications of the age of *An. farauti* into the two age groups (Figure 5).

For *Ae. aegypti*, two variables constructed from CH abundances showed age-dependent changes. The first variable (*aeg1*) was constructed from the abundance of C25 relative to C29, and the second (*aeg2*) was constructed from the abundance of C28 relative to C25

The variable *aeg1* showed a strong relationship to age (*R ^{2}* = 0.70,

*F*= 280.51, df = 1, 122,

*P*< 0.001) characterized by an approximately two-fold decrease (Figure 6a). The variable

*aeg2*showed a weak but significant increase with age (

*R*= 0.24,

^{2}*F*= 37.59, df = 1, 122,

*P*< 0.001) (Figure 6b). The addition of

*aeg2*in a multiple-variable linear regression model for the prediction of age increased the regression coefficient by 6.9% over a single-variable model with

*aeg1*alone (

*F*= 25.094, df = 1, 121,

*P*< 0.001). The two-variable linear regression model for the prediction of age was

where numbers in square brackets are the standard errors of the coefficients. Additional combinations of hydrocarbons added to the model did not significantly increase the regression coefficient.

Adjusted predicted ages for individual *Ae. aegypti* females showed a strong relationship to the actual ages (*R ^{2}* = 0.74,

*F*= 343.09, df = 2, 122,

*P*< 0.001) (Figure 7a). The slope of the regression line was significantly lower than the slope of the predicted = actual line (

*t*= −6.242,

*P*< 0.001), which indicated that the model significantly underestimated age. In addition, there was a spread of approximately five days in the predicted ages for each actual age and the distribution of residuals from the analysis was non-normal. The residuals could not be normalized by transformation of the independent variables, thus indicating that the error in the predicted age was not uniform across all age groups. The predicted ages of 3- and 11-day-old mosquitoes were the most biased.

Nominal logistic regression was used to predict mosquito age into age groups to reduce the bias of age predictions. The highest percentage of correct classifications (83.1%) was achieved when age was categorized into three groups (1 to < 5, 5 to < 9, and ≥ 9 days old). When the proportions of correct classifications and misclassifications was determined for each actual age (Figure 7b), it became evident that there remained a slight tendency towards underestimation of the age of individual mosquitoes.

In contrast to age-related changes in CH abundance in *An. farauti* and *Ae. aegypti*, there was an absence of strong associations between CH abundance and age in *Oc. vigilax.* Variables showing age-dependent changes for the other species, as well as additional algebraic combinations of hydrocarbon abundances, were tested. The relative abundance of the five analyzed hydrocarbons was included in multiple-variable linear regression model to predict age; however, only the relative abundance of C28 significantly contributed to the prediction of age (*R ^{2}* = 0.33,

*F*= 40.74, df = 1, 83,

*P*< 0.001). The variable

*vig1*describes the abundance of C28 relative to the sum of the other

*n*-alkanes measured:

The single variable linear regression model for the prediction of age for *Oc. vigilax* was

Adjusted predicted ages showed a weak relationship to actual ages (*R ^{2}* = 0.30,

*F*= 35.30, df = 1, 83,

*P*< 0.01). There was also a large significant departure of the regression line from the predicted equals actual line (

*t*= −12.799,

*P*< 0.001).

### Simulation modeling of survival rate estimates.

Simulations for *An. farauti* based on the estimated proportion of a sample ≥ 5-days of age are shown in Figure 8. Increasing the sample size increased the precision of the estimates of the DSR (as indicated by smaller 95% confidence intervals at larger sample sizes compared with smaller sample sizes). The simulations also showed that DSR estimates were without bias (as indicated by the symmetry of the 95% confidence limits about the expected DSR line).

Simulations of *Ae. aegypti* DSR estimates based on the estimated proportion ≥ 5 days of age are shown in Figure 9. Increasing the sample size increased the precision of the estimates; however, the DSR was consistently underestimated (as indicated by the expected DSR being above the 95% confidence limits at all but the highest sample proportions when the sample size is high). Simulations for *Ae. aegypti* DSR estimates based on the proportion ≥ 9 days of age are shown in Figure 10. Unlike the estimates based on the ≥ 5-day-old proportion, there was no bias in the estimates of the DSR based on the ≥ 9-day-old proportion.

The results from the simulation modeling were also used to investigate the relationship between the number of mosquitoes analyzed and the accuracy of individual DSR estimates. Separate analyses were undertaken for *An. farauti* (≥ 5 days of age) (Figure 11), *Ae. aegypti* (≥ 5 days of age), and *Ae. aegypti* (≥ 9 days of age) (Figure 12). For example, if 100 *An. farauti* were analyzed using GC/MS and the resulting hydrocarbon patterns indicated that 40% of mosquitoes were ≥ 5 days of age, then the integral of the exponential density function (equation 1) can be used to estimate the DSR (0.77). Figure 11 can then be used to estimate the accuracy of this estimate, and in this case (n = 100 mosquitoes, 40% ≥ 5 days of age), the survival rate can be estimated to within ± 0.075 of the actual survival rate with 95% confidence. Alternatively, the figures can be used in a sequential sampling plan to determine the minimum sample size required to estimate the DSR to a desired accuracy.

Generally, higher sample sizes resulted in more accurate estimates of DSR, except for when the proportion of *Ae. aegypti* ≥ 5 days of age is less than 40% (Figure 12a). Under these situations, the 95% confidence limits for DSR estimates are large and the estimated values would be consistently less than the actual survival rates (Figure 9). Under these circumstances, increasing the sample sizes would not result in a more accurate estimate of the DSR.

## DISCUSSION

The application of quantitative CH analysis methods to the problem of age-grading mosquitoes represents a significant advance in vector survival research. This technique was successfully applied to an Australian strain of *Ae. aegypti*, and also to *An. farauti*, an important malaria vector in the Australasian region. In addition, whereas previous studies focused on individual mosquitoes,^{25}^{–}^{27}^{,}^{40} this study is the first to critically evaluate the reliability of survival estimates for mosquito populations based on estimates of the population age structure. The addition of *Oc. vigilax* and *An. farauti* in this investigation brings to four the number of mosquito species for which CH age-related changes have been investigated.

Quantitative analysis of CHs showed different hydrocarbon abundance profiles from three mosquito genera. Signature hydrocarbon profiles were obtained for each species from individuals at the same age, with greater similarity between *Ae. aegypti* and *Oc. vigilax* than between either species and *An. farauti*. These observations may reflect the taxonomic similarity of *Ae. aegypti* and *Oc. vigilax* within the subfamily Culicinae and the more distant separation of *An. farauti* within the Anophelinae. However, both *An. farauti* and *Ae. aegypti* exhibited age-dependent increases in C29 abundance, although the increase was curvilinear relative to other hydrocarbons for *An. farauti* and linear for *Ae. aegypti*. A curvilinear increase in relative C29 abundance was the predominant age-related change observed from *Cx. quinquefasciatus* hydrocarbons.^{24} In contrast to *An. farauti* and *Ae. aegypti*, there were no significant patterns in the abundance of hydrocarbons with age from *Oc. vigilax*. Differences in CH dynamics may occur between species because of ecologic or behavioral differences. For instance, they may reflect differences in the suitability of the laboratory environment for the species. Certain insects are known to regulate hydrocarbon quantities in response to changes in their environment.^{41} The absence of CH abundance changes may be because certain critical stimuli in the natural environment are missing from the laboratory environment. The next step in the evaluation of CH analysis is to apply the technique on mosquitoes maintained in the field, preferably on marked-released-recaptured specimens. Other *Ochlerotatus* species need to be studied to determine whether the absence of CH variation in *Oc. vigilax* reflects a generic trend.

An important difference between this and previous applications of CHs to predict mosquito ages is that age categories were chosen based on the ability of CHs to differentiate them. The characteristic points of change in the CH abundance variables determined the boundaries between age groups. In this way, age predictions were made with greater accuracy and reduced bias than when predictions were made into regularly spaced age categories. The curvilinear change in the CH variable for *An. farauti* facilitated the dichotomous separation of < 5- and ≥ 5-day-old mosquitoes. However, the linear change in CH abundances for *Ae. aegypti* facilitated the differentiation of an additional age class (≥ 9 days of age). Differentiating between more than three age classes could not be achieved without reducing the accuracy of the age predictions. The predictor variables used in the logistic models for *Ae. aegypti* were similar to the predictor variables used in linear regression age-predicting models developed for the Thailand and the Puerto Rican strains of *Ae. aegypti.*^{26} This indicates that the models are probably generally applicable to *Ae. aegypti*.

Using simulation techniques, we applied CH age estimates to the estimation of mosquito population age structure and survival rates. The simulations demonstrated that the survival rates of *An. farauti* can be estimated without bias from the proportion of a sample of mosquitoes estimated to be ≥ 5 days of age. However, it is more appropriate to estimate the survival rates of *Ae. aegypti* from the proportion ≥ 9 days of age because there were large inaccuracies in *Ae. aegypti* survival rate estimates based on the proportion ≥ 5 days of age. Estimates of survival rates based on the estimated proportion ≥ 9 days of age were without bias, a result of the greater accuracy of predictions of mosquitoes into < 9-day-old and ≥ 9-day-old groups.

The proposed method for estimating mosquito survival rates from the proportions of mosquitoes in age categories shares similarities with the parous rate method of survival rate estimation.^{28} Both methods require data on the proportion of mosquitoes that have survived beyond a given event and the time required to reach that event. In the case of the parous rate method, the two parameters are completion of the first oviposition and the length of the gonotrophic cycle. In the case of CH-based survival rate estimates, the event is survival to a critical age on a chronologic time scale; therefore, estimates of survival rates are independent of the gonotrophic cycle length. Although parous and nulliparous females can be differentiated with considerable accuracy,^{42} the gonotrophic cycle length is variable in response to climatic, host, and habitat influences.^{43} Investigations of *An. farauti* in Papua New Guinea have shown that the gonotrophic cycle length of this species varies with the phase of the lunar cycle and distance of adult females from the point of emergence.^{44} The gonotrophic cycle length can be estimated from cross-correlation analysis of time-series parous rate data,^{30}^{,}^{45} However, data sets were not always suitable for cross correlation analysis in these studies. Additionally, estimates of survival rates from the parous rate method are inappropriate for estimates of vectorial capacity if mosquito species require more than one blood meal within a single gonotrophic cycle.^{31} In contrast, CH analysis provides more reliable estimates of age on a chronologic scale, leading to more precise survival rate estimates. Changes in abundances of hydrocarbons on which age prediction analyses are based have been shown to be robust to changes in laboratory temperature and larval rearing conditions.^{25} As this work has shown, more accurate estimation of age at the individual mosquito level results in more accurate estimation of mosquito population survival rates.

Currently, sequential sampling protocols are predominantly designed to classify insect abundance into broad categories. Hypothesis tests based on the sequential probability ratio test^{46} and Monte Carlo models^{47} have been adapted for the purpose. Hypothesis tests were used to determine probabilities that individual *An. stephensi* were > 12 days of age (and therefore have survived the extrinsic incubation period of *Plasmodium* spp.) based on the ratio of C29 to hentriacontane (C_{31}H_{64}).^{27} However, the appropriate sample size required to estimate mosquito population survival rates using CH analysis has not previously been determined. An empiric approach was used in the present study to generate sequential sampling stop lines by performing simulations based on a randomized model. The outcome has been the generation of objective sampling plans for survival rate estimation for *An. farauti* and *Ae. aegypti*. A prominent feature of the sampling plans is that when individuals in the category of interest are scarce (in this case female mosquitoes older than the critical ages), larger sample sizes are required to estimate survival rates to equivalent accuracy. Similar conclusions were drawn after the application of fixed-precision sequential sampling plans based on the Taylor power function^{48} to estimate the abundance of wheat pests.^{34} This study demonstrates that considerable gains can be made by incorporating sequential sampling plans in protocols for estimating mosquito survival rates.

The assumption that mosquito survival rate was independent of age enabled simulations to be based on the exponential survival function. The exponential function has been criticized as an oversimplification of survival rates,^{49} and evidence has been provided that survival rates vary with age for some mosquito species and most often decrease.^{50} However, recent mark-release-recapture experiments demonstrated a constant survival rate for a strain of *Ae. aegypti* from Thailand, although the survival rate was lower for an older cohort than a younger cohort from strain from Puerto Rico.^{51} Additional field-based investigations of survival rates using techniques such as mark-release-recapture experiments are required to determine the predominant survivorship strategies of these species and the applicability of the survival rate estimation techniques proposed in this investigation.

The assumption of a stable age distribution is more appropriate for some mosquito species than for others. In particular, temperate, brooded species are subject to periodic bursts of recruitment causing instability in the population age structure. Although constant recruitment is also an assumption of the parous rate method, adjustments have been made to account for variable population growth.^{29}^{,}^{30}^{,}^{43}^{,}^{52} The next step in the evaluation of these simulations is to apply CH analysis to estimate the survival rates of field populations and compare estimates with independently obtained survival rate estimates. Depending on the outcome of these tests, adjustments may have to be made to the method of survivorship estimation to account for population growth and other confounding factors.

Quantitative CH analysis has provided valuable estimates of mosquito age on a chronologic scale. Given that hydrocarbons are constituents of the cuticle of all insects, there is a large potential that similar methods may be used to predict the ages and survival characteristics of other mosquitoes and insects outside the Culicidae. This has particular significance for investigations into the dynamics of various vector-borne diseases, for which vector survival is a fundamental defining variable.

Hydrocarbons (*n*-alkanes) and corresponding molecular ions (MIs) subjected to analysis

Hydrocarbon | Designation | MI |
---|---|---|

* Internal standard for analysis. | ||

Octadecane, C_{18}H_{38}* | C18 | 254 |

Pentacosane, C_{25}H_{52} | C25 | 352 |

Hexacosane, C_{26}H_{54} | C26 | 366 |

Heptacosane, C_{27}H_{56} | C27 | 380 |

Octacosane, C_{28}H_{58} | C28 | 394 |

Nonacosane, C_{29}H_{60} | C29 | 408 |

Gas chromatography/mass spectroscopy chromatograms showing relative hydrocarbon abundance in the legs of individual three-day-old female mosquitoes. **a**, *Anopheles farauti*, **b**, *Aedes aegypti*, **c**, *Ochlerotatus vigilax*. Chromatograms are of the 57 ions common to all hydrocarbons. The peaks of specific *n*-alkanes are labeled by the number of carbon atoms.

Citation: The American Journal of Tropical Medicine and Hygiene Am J Trop Med Hyg 74, 3; 10.4269/ajtmh.2006.74.462

Gas chromatography/mass spectroscopy chromatograms showing relative hydrocarbon abundance in the legs of individual three-day-old female mosquitoes. **a**, *Anopheles farauti*, **b**, *Aedes aegypti*, **c**, *Ochlerotatus vigilax*. Chromatograms are of the 57 ions common to all hydrocarbons. The peaks of specific *n*-alkanes are labeled by the number of carbon atoms.

Citation: The American Journal of Tropical Medicine and Hygiene Am J Trop Med Hyg 74, 3; 10.4269/ajtmh.2006.74.462

Gas chromatography/mass spectroscopy chromatograms showing relative hydrocarbon abundance in the legs of individual three-day-old female mosquitoes. **a**, *Anopheles farauti*, **b**, *Aedes aegypti*, **c**, *Ochlerotatus vigilax*. Chromatograms are of the 57 ions common to all hydrocarbons. The peaks of specific *n*-alkanes are labeled by the number of carbon atoms.

Citation: The American Journal of Tropical Medicine and Hygiene Am J Trop Med Hyg 74, 3; 10.4269/ajtmh.2006.74.462

Boxplots showing variation in relative cuticular hydrocarbon abundance over all age samples for female mosquitoes. **a**, *Anopheles farauti* (n = 108), **b**, *Aedes aegypti* (n = 124), **c**, *Ochlerotatus vigilax* (n = 85). The relative abundance of each hydrocarbon was determined by dividing the abundance of the molecular ion by the total abundance of all five molecular ions. The upper and lower ends of the center box indicate the 75th and 25th percentiles, respectively. The line inside the box indicates the median and the bars indicate 1.5 times the distance of the interquartile range from the median. Dots mark potential outliers.

Boxplots showing variation in relative cuticular hydrocarbon abundance over all age samples for female mosquitoes. **a**, *Anopheles farauti* (n = 108), **b**, *Aedes aegypti* (n = 124), **c**, *Ochlerotatus vigilax* (n = 85). The relative abundance of each hydrocarbon was determined by dividing the abundance of the molecular ion by the total abundance of all five molecular ions. The upper and lower ends of the center box indicate the 75th and 25th percentiles, respectively. The line inside the box indicates the median and the bars indicate 1.5 times the distance of the interquartile range from the median. Dots mark potential outliers.

Boxplots showing variation in relative cuticular hydrocarbon abundance over all age samples for female mosquitoes. **a**, *Anopheles farauti* (n = 108), **b**, *Aedes aegypti* (n = 124), **c**, *Ochlerotatus vigilax* (n = 85). The relative abundance of each hydrocarbon was determined by dividing the abundance of the molecular ion by the total abundance of all five molecular ions. The upper and lower ends of the center box indicate the 75th and 25th percentiles, respectively. The line inside the box indicates the median and the bars indicate 1.5 times the distance of the interquartile range from the median. Dots mark potential outliers.

Age-dependent patterns in the abundances of cuticular hydrocarbons from individual female *Anopheles farauti* mosquitoes (▴). **a**, Abundance of nonacosane (as determined from the ratio of the 408 ion to the internal standard molecular ion, 254). **b**, Variable *far1*.

Age-dependent patterns in the abundances of cuticular hydrocarbons from individual female *Anopheles farauti* mosquitoes (▴). **a**, Abundance of nonacosane (as determined from the ratio of the 408 ion to the internal standard molecular ion, 254). **b**, Variable *far1*.

Age-dependent patterns in the abundances of cuticular hydrocarbons from individual female *Anopheles farauti* mosquitoes (▴). **a**, Abundance of nonacosane (as determined from the ratio of the 408 ion to the internal standard molecular ion, 254). **b**, Variable *far1*.

Age predictions of *Anopheles farauti* female mosquitoes into two age groups by nominal logistic regression based on the variable *far1*.

Age predictions of *Anopheles farauti* female mosquitoes into two age groups by nominal logistic regression based on the variable *far1*.

Age predictions of *Anopheles farauti* female mosquitoes into two age groups by nominal logistic regression based on the variable *far1*.

Age-dependent patterns in the abundances of cuticular hydrocarbons from individual female *Aedes aegypti* mosquitoes (▴). **a**, Variable *aeg1*, **b**, Variable *aeg2*.

Age-dependent patterns in the abundances of cuticular hydrocarbons from individual female *Aedes aegypti* mosquitoes (▴). **a**, Variable *aeg1*, **b**, Variable *aeg2*.

Age-dependent patterns in the abundances of cuticular hydrocarbons from individual female *Aedes aegypti* mosquitoes (▴). **a**, Variable *aeg1*, **b**, Variable *aeg2*.

Age predictions of *Aedes aegypti* females based on the variables *aeg1* and *aeg2*. **a**, Age predictions of individual mosquitoes (▴) at two-day age intervals using multiple-variable linear regression analysis. The slope of the regression line is significantly different from the slope of the predicted equals actual line. **b**, Age predictions of individual mosquitoes into three age groups using nominal logistic regression analysis.

Age predictions of *Aedes aegypti* females based on the variables *aeg1* and *aeg2*. **a**, Age predictions of individual mosquitoes (▴) at two-day age intervals using multiple-variable linear regression analysis. The slope of the regression line is significantly different from the slope of the predicted equals actual line. **b**, Age predictions of individual mosquitoes into three age groups using nominal logistic regression analysis.

Age predictions of *Aedes aegypti* females based on the variables *aeg1* and *aeg2*. **a**, Age predictions of individual mosquitoes (▴) at two-day age intervals using multiple-variable linear regression analysis. The slope of the regression line is significantly different from the slope of the predicted equals actual line. **b**, Age predictions of individual mosquitoes into three age groups using nominal logistic regression analysis.

Confidence limits (CLs) for daily survival rate estimates for *Anopheles farauti* based on the estimated proportion of the sample ≥ 5 days of age and sample sizes of 20, 50, 100, 200, and 500 mosquitoes.

Confidence limits (CLs) for daily survival rate estimates for *Anopheles farauti* based on the estimated proportion of the sample ≥ 5 days of age and sample sizes of 20, 50, 100, 200, and 500 mosquitoes.

Confidence limits (CLs) for daily survival rate estimates for *Anopheles farauti* based on the estimated proportion of the sample ≥ 5 days of age and sample sizes of 20, 50, 100, 200, and 500 mosquitoes.

Confidence limits (CLs) for daily survival rate estimates for *Aedes aegypti* based on the estimated proportion of the sample ≥ 5 days of age and sample sizes of 20, 50, 100, 200, and 500 mosquitoes.

Confidence limits (CLs) for daily survival rate estimates for *Aedes aegypti* based on the estimated proportion of the sample ≥ 5 days of age and sample sizes of 20, 50, 100, 200, and 500 mosquitoes.

Confidence limits (CLs) for daily survival rate estimates for *Aedes aegypti* based on the estimated proportion of the sample ≥ 5 days of age and sample sizes of 20, 50, 100, 200, and 500 mosquitoes.

Confidence limits (CLs) for daily survival rate estimates for *Aedes aegypti* based on the estimated proportion of the sample ≥ 9 days of age and sample sizes of 20, 50, 100, 200, and 500 mosquitoes.

Confidence limits (CLs) for daily survival rate estimates for *Aedes aegypti* based on the estimated proportion of the sample ≥ 9 days of age and sample sizes of 20, 50, 100, 200, and 500 mosquitoes.

Confidence limits (CLs) for daily survival rate estimates for *Aedes aegypti* based on the estimated proportion of the sample ≥ 9 days of age and sample sizes of 20, 50, 100, 200, and 500 mosquitoes.

Sequential sampling guidelines for estimating *Anopheles farauti* survival rates based on the estimated proportion of a sample ≥ 5 days of age. Lines represent minimal sample sizes needed to estimate survivorship to a given accuracy with 95% confidence. Areas to the right of the lines are zones of acceptance for survivorship estimates at a given accuracy (j, ± 0.075; k, ± 0.050; l, ± 0.025). *DSR* = daily survival rate.

Sequential sampling guidelines for estimating *Anopheles farauti* survival rates based on the estimated proportion of a sample ≥ 5 days of age. Lines represent minimal sample sizes needed to estimate survivorship to a given accuracy with 95% confidence. Areas to the right of the lines are zones of acceptance for survivorship estimates at a given accuracy (j, ± 0.075; k, ± 0.050; l, ± 0.025). *DSR* = daily survival rate.

Sequential sampling guidelines for estimating *Anopheles farauti* survival rates based on the estimated proportion of a sample ≥ 5 days of age. Lines represent minimal sample sizes needed to estimate survivorship to a given accuracy with 95% confidence. Areas to the right of the lines are zones of acceptance for survivorship estimates at a given accuracy (j, ± 0.075; k, ± 0.050; l, ± 0.025). *DSR* = daily survival rate.

Sequential sampling guidelines for estimating *Aedes aegypti* survival rates based on the estimated proportion of a sample older than a given age. **a**, Estimated proportion ≥ 5 days of age. **b**, Estimated proportion ≥ 9 days of age. Lines represent minimal sample sizes needed to estimate survival rates to a given accuracy with 95% confidence. Areas to the right of the lines are zones of acceptance for survivorship estimates at a given accuracy (i, ± 0.100; j, ± 0.075; k, ± 0.050; l, ± 0.025). *DSR* = daily survival rate.

Sequential sampling guidelines for estimating *Aedes aegypti* survival rates based on the estimated proportion of a sample older than a given age. **a**, Estimated proportion ≥ 5 days of age. **b**, Estimated proportion ≥ 9 days of age. Lines represent minimal sample sizes needed to estimate survival rates to a given accuracy with 95% confidence. Areas to the right of the lines are zones of acceptance for survivorship estimates at a given accuracy (i, ± 0.100; j, ± 0.075; k, ± 0.050; l, ± 0.025). *DSR* = daily survival rate.

Sequential sampling guidelines for estimating *Aedes aegypti* survival rates based on the estimated proportion of a sample older than a given age. **a**, Estimated proportion ≥ 5 days of age. **b**, Estimated proportion ≥ 9 days of age. Lines represent minimal sample sizes needed to estimate survival rates to a given accuracy with 95% confidence. Areas to the right of the lines are zones of acceptance for survivorship estimates at a given accuracy (i, ± 0.100; j, ± 0.075; k, ± 0.050; l, ± 0.025). *DSR* = daily survival rate.

Address correspondence to Leon E. Hugo, Mosquito Control Laboratory, Queensland Institute of Medical Research, Herston, Queensland 4006, Australia. E-mail: leon.hugo@qimr.edu.au

^{}

Authors’ addresses: Leon E. Hugo, Brian H. Kay, and Peter A. Ryan, Mosquito Control Laboratory, Queensland Institute of Medical Research, Herston, Queensland 4006, Australia, Telephone: 61-7-3362-0354, Fax: 61-7-3362-0106, E-mails: leon.hugo@qimr.edu.au, brian.kay@qimr.edu.au, and peter.ryan@qimr.edu.au. Geoff K. Eaglesham and Neil Holling, Pathology and Scientific Services, Queensland Health, Brisbane, Queensland 4000, Australia., E-mails: geoff_eaglesham@health.qld.gov.au and neil_holling@health.qld.gov.au.

Acknowledgments: We thank Lieutenant-Colonel Robert Cooper (Australian Army Malaria Institute) and Dr. Scott Ritchie (Tropical Public Health Unit, Queensland Health) for providing *An. farauti* and *Ae. aegypti* mosquitoes, respectively.

Financial support: This study was supported by the Mosquito and Arbovirus Research Committee, Australia.

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