# Exploring the potential of computer vision analysis of pupae size dimorphism for adaptive sex sorting systems of various vector mosquito species

Mario Zacares, Gustavo Salvador-Herranz, David Almenar, Carles Tur, Rafael Argiles, Kostas Bourtzis, Herve Bossin, Ignacio Pla

<figure><img src="image_1.png" /></figure>

## To cite this version:

Mario Zacares, Gustavo Salvador-Herranz, David Almenar, Carles Tur, Rafael Argiles, et al., Exploring the potential of computer vision analysis of pupae size dimorphism for adaptive sex sorting systems of various vector mosquito species. Parasites & Vectors, 2018, 11 (2), 10.1186/s13071-018-3221-x. hal-02003902

HAL Id: hal-02003902

https://hal.science/hal-02003902

Submitted on 28 Oct 2019

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_2.png" /></figure>
RESEARCH

Open Access

<figure><img src="image_3.png" /></figure>

CrossMark

# Exploring the potential of computer vision analysis of pupae size dimorphism for adaptive sex sorting systems of various vector mosquito species

Mario Zacarés¹, Gustavo Salvador-Herranz<fnref n="2" />, David Almenar³, Carles Tur³*, Rafael Argilés⁴, Kostas Bourtzis⁴, Hervé Bossin⁵,⁶ and Ignacio Pla³

## Abstract

**Background:** Several mosquito population suppression strategies based on the rearing and release of sterile males have provided promising results. However, the lack of an efficient male selection method has hampered the expansion of these approaches into large-scale operational programmes. Currently, most of these programmes targeting *Aedes* mosquitoes rely on sorting methods based on the sexual size dimorphism (SSD) at the pupal stage. The currently available sorting methods have not been developed based on biometric analysis, and there is therefore potential for improvement. We applied an automated pupal size estimator developed by Grupo Tragsa with laboratory samples of *Anopheles arabiensis*, *Aedes albopictus*, *Ae. polynesiensis*, and three strains of *Ae. aegypti*. The frequency distribution of the pupal size was analyzed. We propose a general model for the analysis of the frequency distribution of mosquito pupae in the context of SSD-sorting methods, which is based on a Gaussian mixture distribution functions, thus making possible the analysis of performance (% males recovery) and purity (% males on the sorted sample).

**Results:** For the three *Aedes* species, the distribution of the pupae size can be modeled by a mixture of two Gaussian distribution functions and the proposed model fitted the experimental data. For a given population, each size threshold is linked to a specific outcome of male recovery. Two dimensionless parameters that measure the suitability for SSD-based sorting of a specific batch of pupae are provided. The optimal sorting results are predicted for the highest values of SSD and lowest values of intra-batch variance. Rearing conditions have a strong influence in the performance of the SSD-sorting methods and non-standard rearing can lead to increase pupae size heterogeneity.

(Continued on next page)

<figure><img src="image_4.png" /></figure>

BMC

© The Author(s). 2018 **Open Access** This is an open access article distributed under the terms of the Creative Commons Attribution IGO License (https://creativecommons.org/licenses/by/3.0/igo/), which permits unrestricted use, distribution, and reproduction in any medium, provided appropriate credit to the original author(s) and the source is given.

<footnote>* Correspondence: ctur@tragsa.es</footnote>

<footnote n="2">²Grupo Tragsa, Avda. de la Industria 26, 46980 Paterna, Valencia, Spain</footnote>

<footnote>Full list of author information is available at the end of the article</footnote>
(Continued from previous page)

**Conclusions:** Sex sorting of pupae based on size dimorphism can be achieved with a high performance (% males recovery) and a reasonably high purity (% males on the sorted sample) for the different *Aedes* species and strains. The purity and performance of a sex sorting operation in the tested *Aedes* species are linked parameters whose relation can be modeled. The conclusions of this analysis are applicable to all the existing SSD-sorting methods. The efficiency of the SSD-sorting methods can be improved by reducing the heterogeneity of pupae size within rearing containers. The heterogeneity between batches does not strongly affect the quality of the sex sorting, as long as a specific separation threshold is not pre-set before the sorting process. For new developments, we recommend using adaptive and precise threshold selection methods applied individually to each batch or to a mix of batches. Adaptive and precise thresholds will allow the sex-sorting of mixed batches in operational conditions maintaining the target purity at the cost of a reduction in performance. We also recommend a strategy whereby an acceptable level of purity is pre-selected and remains constant across the different batches of pupae while the performance varies from batch to batch to fit with the desired purity.

**Keywords:** Sterile insect technique, Biometrical analysis, Morphometrics frequency distribution models, Sexual size dimorphism, Sex sorting methods, *Aedes aegypti*, *Aedes albopictus*, *Aedes polynesiensis*, *Anopheles arabiensis*

## Background

There is a global renewed interest in area-wide integrated mosquito management strategies based on the mass production and release of sterile males to suppress target populations [1–4]. These techniques are usually referred to as genetic control methods and include, among others, the sterile insect technique (SIT), the incompatible insect technique (IIT) and the release of insects carrying a dominant lethal gene (RIDL) [1, 4–7]. Several small-scale projects have demonstrated the high potential of these strategies to suppress mosquito populations [6, 8–10]. The scaling-up of these projects from pilot to operational has been hampered by several problems, the most significant one being the lack of an efficient sex-sorting method [1, 11, 12]. Given that only the female mosquitoes bite and transmit the human pathogens, those methods must be capable of ensuring a predefined acceptable level of female contamination while maximizing the male pupae recovery.

The successful use of genetic sexing strains (GSS) for the sex sorting of *Ceratitis capitata* and other fruit fly species [13–17] has encouraged researchers to develop similar GSS strains for mosquitoes. GSS strains that can be sex-sorted at early developmental stages (eggs or L1) are generally accepted to be the optimal solution for mass-scale SIT and related techniques [11, 12]. A genetic sexing strain based on the tolerance to dieldrin has been developed for *Anopheles arabiensis*; however, this strain presents several problems and has limited potential for SIT applications [18, 19]. In addition, several transgenic genetic sexing strains developed for different mosquito vector species are also of limited applied potential due to either lack of stability, low male performance or subject to extensive regulation [11, 12].

The current lack of a functional GSS has led to the mosquito population suppression projects to use alternative ways in the sex-sorting process. For the mosquito species with strong sexual size dimorphism (SSD), mainly *Aedes*

and *Culex* species, mechanical methods have been generally adopted for sorting [6, 8, 20]. Although several designs and proposals for sex sorting on a mass scale have been suggested in the past [21, 22], all mosquito genetic control programmes currently use either plate separators [23] or sieves [8] for sex sorting that have been devised for small-scale rearing conditions. The development of new designs with automation capability for unattended sorting would increase the efficiency of those projects and allow their upgrade to large operational programmes [12, 24].

The efficiency of SSD-sorting methods in terms of male recovery, female contamination and speed depends on technical and biological factors. The technical features basically affect the rate of separation per time unit, and differ between methods. The main biological determinant is the size distribution between sexes and their overlap as well as the effect of rearing conditions on this characteristic. All the SSD-sorting methods rely on the same principle: the separation in two samples by a threshold size. It should be noted that an analysis of the biological determinants of the distribution of size will in principle be applicable to all SSD-sorting methods

In order to improve the performance of new designs of sex-sorting methods based on SSD, a previous biometric analysis is required, specifically dealing with the analysis of the frequency distribution of the size of sexes. However, there is scarce information regarding the distribution of size in mosquitoes. Usually, the scope of the biometric studies in mosquitoes has been to find correlations between the body size and other biological traits [25–29], providing only point and variance estimates, and only a limited number of studies have included detailed frequency distributions [30–32]. For insects, most of the frequency distributions of the size can fit to normal probability functions. When a strong SSD is present, each sex can fit to an independent normal curve [33]. SSD is generally assumed as a species-specific (or
population-specific) trait with a narrow degree of variation
caused by complex interactions of factors [34–37].

Several experiments have shown that variations in the
mosquito larval rearing conditions can increase or
reduce the average size of the resulting pupae [38–41].
The SSD is slightly influenced by intraspecific competi-
tion [40, 42], but not by food availability [38] or the pol-
lution by conspecifics [43] as size of both sexes is
equally affected by these parameters and the difference
between the average size of each sex remains constant.
The objective of the present study is to optimize the
utilization of the SSD-sorting methods through the
understanding of the frequency distribution in the pupal
size of different mosquito species and strains, with the
ultimate goal to: (i) understand the performance of the
current sex-sorting methods in different conditions; (ii)
assess the relationship between the parameters of im-
portance for sex-sorting devices: female contamination
and male recovery; (iii) evaluate the suitability of
size-based sex sorting methods for different species and
strains of mosquitoes; and (iv) propose features that will
optimize the performance of SSD-sorting methods.

To achieve these objectives, we developed a general
model for the size distribution of mosquito at the pupal
stage. The frequency distribution can be modelled as a
mixture of two normal probability density functions. We
analyzed the frequency distribution in size of four
important mosquito vector species that are currently the
target of area-wide integrated vector control projects using
SIT-based methods: *Aedes aegypti*, *Ae. albopictus*, *Ae. polynesiensis* and *Anopheles arabiensis*. The intraspecific
variation is also evaluated for *Ae. aegypti*, since three differ-
ent laboratory strains were included in the analysis. The
use of an automated pupae size estimator system based on
artificial vision developed by Grupo Tragsa, Spain, allowed
the collection of a large amount of size measurements thus
facilitating the achievement of our objective.

**Methods**

Laboratory strains

The *Aedes aegypti* Sri Lanka strain originates from mos-
quitoes collected from the Narahenpita area, District of
Colombo, Western Province, Sri Lanka. This strain was
kindly provided by Ms. Asha Wijegunawardana (Univer-
sity of Kelaniya, Sri Lanka) and has been maintained in
the Insect Pest Control Laboratory of the Joint Food and
Agriculture Organization and International Atomic En-
ergy Agency (IPCL-Joint FAO/IAEA) laboratories since
2017. F28 mosquitoes from this strain were analyzed in
the present study.

The *Ae. aegypti* GSS has been developed by classical
genetic approaches and has been maintained in the
IPCL-Joint FAO/IAEA since 2017. F₅ mosquitoes from
this strain were used in the present study.

The *Ae. aegypti* WB2 line was recently generated by
transfer of *Wolbachia* wAlbB from *Aedes albopictus* into
*Aedes aegypti* via embryonic microinjection at Michigan
State University (personal communication, Zhiyong Xi),
and has been maintained in the IPCL laboratories since
2016. This strain was introgressed into the genomic back-
ground of an *Ae. aegypti* strain from Brazil, provided by
Professor Margareth Capurro (University of Sao Paolo,
Brazil), through a series of seven backcrosses using in
every generation *Wolbachia*-infected females mated with
*Ae. aegypti* Brazil males. This resulted in the construction
of the *Ae. aegypti* WB2-BRA strain used. F₁₂ mosquitoes
from this strain were analyzed in the present study.

The incompatible *Ae. polynesiensis* "Aito" (BC9) strain
carries *Wolbachia* B from *Ae. riversi*. This strain was gener-
ated through multiple backcrosses between *Aedes riversi*
females and *Aedes polynesiensis* aposymbiotic males
(Hapairai, 2013). This strain which has been maintained at
Institut Louis Malardè (ILM), Tahiti since 2010 was recently
used in a pilot IIT field study on the atoll of Tetiaroa,
French Polynesia (Bossin et al. manuscript in preparation).

The *Ae. albopictus* Rimini strain was originated from
field collections in northern Italy. It has been maintained
in the IPCL since 2010.

The *An. arabiensis* Dongola strain was originated from the
Northern State of Sudan. It has been maintained in the IPCL
since 2005. It is also available at the Malaria Research and
Reference Reagent Resource Center, MR4, as MRA-856.

Mosquito rearing

Standard rearing conditions have been used for the main-
tenance of experimental colonies, egg collection and
hatching of *Ae. albopictus* and *Ae. aegypti* [44, 45], *Ae.
polynesiensis* [39], and *An. arabiensis* [46, 47] colonies.

Pupae production

For each species or strain, three larval containers were
prepared for pupae production as described below. These
three replicates represented a random sample of the differ-
ent rearing units found in a mass rearing facility.

For *Ae. aegypti* and *Ae. albopictus*, 2000 first-instar larvae
were introduced in white acrylonitrile-butadiene-styrene
(ABS) plastic trays (41 × 30 × 8 cm) with 1.5 l of deionized
water. Since larvae of *Ae. polynesiensis* must be reared
under lower densities [39], 1200 first-instar larvae were in-
troduced in 40 × 60 × 15 cm containers with 4 l of
water. The larvae were fed with the standard *Aedes*
IPCL diet [48, 49] at a concentration of 75 g per liter of
diet. The diet regime ranged from 0.2 mg of dry weight
per larvae on the first day to 0.8 mg on the last days.

Different batches of eggs of *Ae. arabiensis* were hatched
in white plastic trays (41 × 30 × 8 cm). Two days after the
hatching, approximately 500-1000 larvae were visually iso-
lated in the same kind of trays with 1.5 l of deionized water.
The larvae were fed with the standard *Anopheles* IPCL diet [46], in a concentration of 10 g/l ranging from 5ml on the first day to 20 ml on the last days.

All pupae in each container were collected on a daily basis starting at 24 hours from the beginning of the pupation. A batch of pupae was defined as all the pupae produced in 24 hours for a specific species/strain and replicate(s). The selected batches were sex-sorted under a binocular microscope. All the pupae in a batch were classified into males and females groups, and the resulting samples are referred to as batch-sex groups. The batch where the proportion of male and female was closer to 50%, usually on the 2nd or 3rd day from the beginning of pupation, was selected for the analysis.

## Measurement of pupal size

The lateral profile area of the pupae was automatically measured by means of a computer vision system (Fig. 1), which comprises: (i) a translucent rigid surface with circular uniform movement, acting as conveyor on which the mosquito pupae are arranged; (ii) a uniform and high intensity led white light backlight system and (iii) a high resolution/high speed camera placed in top position. In this way, the mosquito pupae pass continuously under the camera while being backlit by the lighting system. The backlighting of the pupae allows photograph of them with a high contrast, which facilitates their subsequent extraction and isolation from the background (segmentation). In order to increase the precision and accuracy of the measurement of the areas, avoiding errors due to the effects of refraction of light by water droplets, the size of the pupae was measured in dry conditions for each session.

A factor of special importance is that the backlight system must guarantee an illuminated area with a uniform intensity, at least in the interest area of capture of the camera. This is because the light intensity directly

affects the size of the areas extracted in the segmentation process, and variations in the intensity could result in errors in the relative measurements. However, even with a uniform backlighting system, minor errors may occur in the measurement due to the position of each pupa with respect to the position of the camera (different projected areas) and electrical noise in the silicone sensor of the camera. To minimise these phenomena, several pictures of each pupa are recorded while in the camera capture area (around 15 shots per pupa), and then the median of all the measurements of each individual is chosen as the value of size. So, each individual has to be identified and its path has to be tracked. For this task, we have developed a predictive tracking algorithm, based on Kalman filters [50], which is able to identify and track individuals in their rotational displacement under the field of view of the camera. Additionally, the algorithm is robust enough to follow the characteristic rapid movements of the pupae in dry conditions, which are quite active.

The median size in square pixels is then transformed to a unidimensional parameter by the square root to linearize the measure of size. The measure of size presented in this study is then the square root of the pixel area. The outcome of the analysis is scale-independent, and the conclusions are valid regardless of the actual value of this magnitude. Since the pupae were sex sorted manually, we assume that a certain degree of identification error occured. Errors in the manual sex identification can affect the estimation of the statistical parameters, especially those pupae with size far larger or smaller than the corresponding sex average value. In order to minimize this effect, we considered each value that exceeded two standard deviations from the average as an error in sex identification. These values were subsequently excluded from the analysis.

## Model for the frequency distribution of size

The proposed model relies on the basic assumption that the probability density function for the pupal size of each sex follows a Gaussian distribution, with the mean and standard deviation as the characteristic parameters. The mixture distribution for this situation is:

$$f(x) = \alpha_m N(x; \mu_m, \sigma_m) + \alpha_f N(x; \mu_f, \sigma_f) \quad (1)$$

where $N(x; \mu_i, \sigma_i)$ is the normal probability density function for size (x), with mean $\mu_i$ and standard deviation $\sigma_i$. The scalars $\alpha_i$ are the proportions of each sex in the model, being $\alpha_m + \alpha_f = 1$. The subscripts m and f denote males and females respectively.

<figure><img src="image_5.png" /></figure>
## Predictions from the model

One of the goals of our model is to provide a statistical tool to estimate the theoretical outcomes of male recovery and female contamination. In order to quantify them we introduce the performance (PER) and purity (PUR) functions defined as follows:

$$ PER(x) = \frac{\text{recovered males from the original sample for a given } x}{\text{males in the original sample}} \times 100 \quad (2) $$

$$ PUR(x) = \frac{\text{recovered males from the original sample for a given } x}{\text{recovered pupae from the original sample for a given } x} \times 100 \quad (3) $$

For any given size threshold (x), PER provides the male recovery percentage and PUR the percentage of males on the sorted sample. Assuming the model given by Equation 1, it is easy to show that both functions can be estimated in terms of the normal distribution function:

$$ PER(x) = \Phi\left(\frac{x-\mu_m}{\sigma_m}\right) \times 100 \quad (4) $$

$$ PUR(x) = \frac{\alpha_m \Phi\left(\frac{x-\mu_m}{\sigma_m}\right)}{\alpha_m \Phi\left(\frac{x-\mu_m}{\sigma_m}\right) + (1-\alpha_m)\Phi\left(\frac{x-\mu_f}{\sigma_f}\right)} \times 100 \quad (5) $$

where Φ denotes the standard normal cumulative distribution function. In order to determine both functions, the parameters {α_m, μ_i, σ_i} of the model must be known. Purity and performance are inversely linked. A decrease in female contamination can be achieved by reducing the value of the threshold, but this unavoidably produces

a reduction in the performance (Fig. 2). The features of PER(x) and PUR(x) depend on the chosen set of parameters. However many sets give rise to functions that are related by simple symmetry transformations like translations or scaling. As long as both functions are transformed in the same way, the purity versus performance curve remains invariant (Fig. 2c). Therefore, parameters {α_i, μ_i, σ_i} are not suitable to classify unequivocally the different samples as they can lead to the same purity-performance curve. In order to find a more appropriate space parameter, we introduce two new dimensionless parameters: the sexual dimorphism index (SDI) and the sexual homoscedasticity index (SHI) defined by

$$ SDI = \frac{\mu_f - \mu_m}{2\sqrt{\sigma_m \sigma_f}} \quad (6) $$

$$ SHI = \sqrt{\frac{\sigma_m}{\sigma_f}} \quad (7) $$

Combining definitions (6) and (7) with Equations 4 and 5, we can rewrite performance and purity functions as

$$ PER(z) = \Phi\left(\frac{z + SDI}{SHI}\right) \times 100 \quad (8) $$

$$ PUR(z) = \frac{\alpha_m \Phi\left(\frac{z + SDI}{SHI}\right)}{\alpha_m \Phi\left(\frac{z + SDI}{SHI}\right) + (1-\alpha_m)\Phi\left(\frac{z - SDI}{SHI^{-1}}\right)} \times 100 \quad (9) $$

z being a dimensionless variable defined by $z = \frac{x - \frac{\mu_m + \mu_f}{2}}{\sqrt{\sigma_m \sigma_f}}$

Equations 8 and 9 reveal that PER(z) and PUR(z) only depend on three dimensionless parameters: α_m, SDI and SHI. In other words, given α_m, all combinations of the

<figure><img src="image_6.png" /><figcaption>**Fig. 2** Depiction of the purity-performance relationship under a mixture of two Gaussian distributions applied to the analysis of sex sorting by size. The graphs consider α_m = 0.5 and three different sets of parameters s = {μ_m, σ_m, μ_f, σ_f}, s1 = {10, 1, 11, 1}, s2 = {8, 1, 9, 1} and s3 = {12, 2, 14, 2}. The performance of sets 2 and 3 is obtained by translating and scaling the performance of set 1: PER2(x) = PER1(x + 2), PER3(x) = PER1(x - 2/2). The same transformations are applied to purity functions. **a** Purity versus size (X). **b** Performance versus size (X). **c** Purity versus performance</figcaption></figure>
original parameters {μ<sub>m</sub>, μ<sub>f</sub>, σ<sub>m</sub>, σ<sub>f</sub>} giving the same pair {SDI, SHI} have exactly the same performance and purity functions in terms of the dimensionless variable z. Consequently, the dimensionless parameters {SDI, SHI} are more suitable than classical measures of center and spread to classify unequivocally different pupae samples with regard to purity and performance.

Basic statistics and model fit

The mean and standard deviation was estimated for every batch-sex group dataset, and its deviation from the normal distribution was tested by means of the Shapiro-Wilk test. The fit of the data to the probability density function of the mixture model was tested by means of the Kolmogornov-Smirnov test. All the statistic computations were done using the *base* package of R [51]. The significance level was set to α = 0.05.

Partitioning of the variance

A number of pupae equal to the minimal sample size was randomly selected for each batch-sex group per species/strain. This was performed in order to get a balanced factorial design dataset. A linear model was fit for each batch by means of ordinary least squares. The model included sex and batch as fixed factors, and their interaction. The partitioning of variance was assessed through ANOVA. All statistical analyses were done using the *base* package of R [51].

Results

Table 1 summarizes the statistics of the pupal size of the species and strains used in the present study. In total, 7733 pupae were analyzed. The majority of the batches were not significantly different from a normal distribution, and the mixture of two Gaussian distributions fited well to all batches of all the species/strains used when male and female pupae data are combined. Table 2 presents the significance of the goodness-of-fit between the models and the data. None of the samples was significantly different from a Gaussian mixture distribution. Only two batches separated by sex showed significant departures from normality: *An. arabiensis* females of the batch 3, and *Ae. albopictus* Rimini males of batch 3.

Figure 3 shows the histograms and fitted models for the three batches of each species/strain studied. After the parameters of the model have been estimated, the purity-performance characteristic curve is computed and the quality of sorting can be analyzed theoretically. Each value of pupal size is linked to a pair of purity and performance values, which are inversely related (Fig. 4). The fitted models allow simulating the output of SSD-sorting methods under different circumstances. Table 3 shows the main descriptors for the predicted output from the fitted model for each batch in the

experimental data. These results should not be consid-
ered as a general prediction of how a particular strain
will perform with SSD-sorting methods, since they are
only applicable for the specific rearing conditions of this
experiment. However, they show the potential of
SSD-based sex-sorting procedures when standard
rearing procedures are applied. Table 4 provides exam-
ples for one of the strains of Ae. aegypti (GSS) of how
the performance-purity output varies under different
simulated conditions. The simulation *a* describes the
performance when the three batches are mixed and a
threshold size is determined by keeping constant the
level of purity of 99.5 %. It is shown how SDI takes
lower values than any of the individual batches, and an
average reduction of 17 % in performance is predicted
for the same level of purity (male recovery of 74.5 %
with a female contamination of 0.5 % after mixing the
three batches). Simulations *b* and *c* assess the effect in
the performance of the size heterogeneity and the
variations in the SSD respectively. For simulation *b* the
variance of both sexes is scaled by the same factor while
the distance between means remains constant. Taking
batch 1 as a reference, the standard deviation of both
sexes is multiplied by 0.8 and 1.2 respectively. For simu-
lation *c*, taking again batch 1 as reference, the average
size of males and females is increased or decreased by
0.5 √pixels but the standard deviations are not modified
in this case. It is worth mentioning that the variation of
the statistical parameters in simulations *b* and *c* only
affect the dimensionless parameter SDI, while SHI
remains unaltered. Results show that changes in size het-
erogeneity and SSD have contrary effects in the perform-
ance; an increase in intra-batch variance produces a
significant drop in performance whereas an increase in
SSD improves the quality of sorting. Simulation *d*
describes how the output of SSD-sorting systems vary
with the election of a predefined constant threshold for
all the batches.

The contribution of different factors to the variability
in size has been assessed by means of ANOVA. The re-
sults for the partitioning of the variance are shown in
Table 5. For all the *Aedes* species, the biggest source of
variation is the SSD. For *An. arabiensis*, there are signifi-
cant differences in size between sexes, but this factor
explained only a relatively small portion of the total
variance.

Discussion

For all the species and strains examined in this study,
the joint frequency distribution of pupal size included an
area of overlap between the individual male and female
distributions. This essentially means that a complete
separation of sexes according to a given threshold of size
is not possible, and every threshold that separates the
<table><caption>**Table 1** Descriptive statistics for the batches of pupae</caption><thead><tr><th>Batch</th><th>Sex</th><th>N</th><th>Proportion ± SE</th><th>Mean size ± SE</th><th>SD ± SE</th></tr></thead><tbody><tr><td colspan="6"><em>Anopheles arabiensis</em> - Dongola</td></tr><tr><td>1</td><td>Males</td><td>24</td><td>0.48 ± 0.10</td><td>13.23 ± 0.21</td><td>1.02 ± 0.15</td></tr><tr><td>1</td><td>Females</td><td>26</td><td>0.52 ± 0.10</td><td>14.40 ± 0.19</td><td>0.99 ± 0.14</td></tr><tr><td>2</td><td>Males</td><td>24</td><td>0.53 ± 0.10</td><td>13.23 ± 0.20</td><td>0.98 ± 0.15</td></tr><tr><td>2</td><td>Females</td><td>21</td><td>0.47 ± 0.11</td><td>13.41 ± 0.23</td><td>1.03 ± 0.16</td></tr><tr><td>3</td><td>Males</td><td>32</td><td>0.46 ± 0.09</td><td>13.98 ± 0.18</td><td>1.03 ± 0.13</td></tr><tr><td>3</td><td>Females</td><td>38</td><td>0.54 ± 0.08</td><td>14.16 ± 0.16</td><td>0.98 ± 0.11</td></tr><tr><td>Total</td><td>Males</td><td>80</td><td>0.48 ± 0.06</td><td>13.53 ± 0.12</td><td>1.07 ± 0.08</td></tr><tr><td>Total</td><td>Females</td><td>85</td><td>0.52 ± 0.05</td><td>14.05 ± 0.11</td><td>1.06 ± 0.08</td></tr><tr><td colspan="6"><em>Aedes albopictus</em> - Rimini</td></tr><tr><td>1</td><td>Males</td><td>337</td><td>0.53 ± 0.03</td><td>18.66 ± 0.05</td><td>0.85 ± 0.03</td></tr><tr><td>1</td><td>Females</td><td>303</td><td>0.47 ± 0.03</td><td>21.9 ± 0.05</td><td>0.87 ± 0.04</td></tr><tr><td>2</td><td>Males</td><td>407</td><td>0.60 ± 0.02</td><td>17.73 ± 0.04</td><td>0.72 ± 0.03</td></tr><tr><td>2</td><td>Females</td><td>277</td><td>0.40 ± 0.03</td><td>21.26 ± 0.05</td><td>0.78 ± 0.03</td></tr><tr><td>3</td><td>Males</td><td>434</td><td>0.62 ± 0.02</td><td>18.46 ± 0.04</td><td>0.84 ± 0.03</td></tr><tr><td>3</td><td>Females</td><td>261</td><td>0.38 ± 0.03</td><td>21.62 ± 0.05</td><td>0.78 ± 0.03</td></tr><tr><td>Total</td><td>Males</td><td>1178</td><td>0.58 ± 0.01</td><td>18.26 ± 0.03</td><td>0.90 ± 0.02</td></tr><tr><td>Total</td><td>Females</td><td>841</td><td>0.42 ± 0.02</td><td>21.6 ± 0.03</td><td>0.85 ± 0.02</td></tr><tr><td colspan="6"><em>Aedes polynesiensis</em> - Aito (BC9)</td></tr><tr><td>1</td><td>Males</td><td>164</td><td>0.41 ± 0.04</td><td>17.13 ± 0.05</td><td>0.66 ± 0.04</td></tr><tr><td>1</td><td>Females</td><td>239</td><td>0.59 ± 0.03</td><td>21.09 ± 0.05</td><td>0.72 ± 0.03</td></tr><tr><td>2</td><td>Males</td><td>202</td><td>0.49 ± 0.04</td><td>16.03 ± 0.05</td><td>0.72 ± 0.04</td></tr><tr><td>2</td><td>Females</td><td>210</td><td>0.51 ± 0.03</td><td>19.84 ± 0.05</td><td>0.69 ± 0.03</td></tr><tr><td>3</td><td>Males</td><td>195</td><td>0.48 ± 0.04</td><td>17.03 ± 0.04</td><td>0.56 ± 0.03</td></tr><tr><td>3</td><td>Females</td><td>214</td><td>0.52 ± 0.03</td><td>20.72 ± 0.05</td><td>0.67 ± 0.03</td></tr><tr><td>Total</td><td>Males</td><td>561</td><td>0.46 ± 0.02</td><td>16.70 ± 0.03</td><td>0.82 ± 0.02</td></tr><tr><td>Total</td><td>Females</td><td>663</td><td>0.54 ± 0.02</td><td>20.57 ± 0.03</td><td>0.87 ± 0.02</td></tr><tr><td colspan="6"><em>Aedes aegypti</em> - GSS</td></tr><tr><td>1</td><td>Males</td><td>246</td><td>0.47 ± 0.03</td><td>17.34 ± 0.05</td><td>0.76 ± 0.03</td></tr><tr><td>1</td><td>Females</td><td>272</td><td>0.53 ± 0.03</td><td>20.31 ± 0.04</td><td>0.73 ± 0.03</td></tr><tr><td>2</td><td>Males</td><td>117</td><td>0.51 ± 0.05</td><td>18.20 ± 0.07</td><td>0.75 ± 0.05</td></tr><tr><td>2</td><td>Females</td><td>113</td><td>0.49 ± 0.05</td><td>22.16 ± 0.07</td><td>0.75 ± 0.05</td></tr><tr><td>3</td><td>Males</td><td>496</td><td>0.44 ± 0.02</td><td>18.04 ± 0.03</td><td>0.72 ± 0.02</td></tr><tr><td>3</td><td>Females</td><td>635</td><td>0.56 ± 0.02</td><td>22.24 ± 0.04</td><td>0.95 ± 0.03</td></tr><tr><td>Total</td><td>Males</td><td>859</td><td>0.46 ± 0.02</td><td>17.86 ± 0.03</td><td>0.81 ± 0.02</td></tr><tr><td>Total</td><td>Females</td><td>1020</td><td>0.54 ± 0.02</td><td>21.72 ± 0.04</td><td>1.22 ± 0.03</td></tr><tr><td colspan="6"><em>Aedes aegypti</em> - Sri Lanka</td></tr><tr><td>1</td><td>Males</td><td>314</td><td>0.56 ± 0.03</td><td>16.41 ± 0.06</td><td>1.08 ± 0.04</td></tr><tr><td>1</td><td>Females</td><td>245</td><td>0.44 ± 0.03</td><td>19.58 ± 0.08</td><td>1.29 ± 0.06</td></tr><tr><td>2</td><td>Males</td><td>309</td><td>0.55 ± 0.03</td><td>16.36 ± 0.06</td><td>0.99 ± 0.04</td></tr><tr><td>2</td><td>Females</td><td>249</td><td>0.45 ± 0.03</td><td>20.01 ± 0.08</td><td>1.26 ± 0.06</td></tr><tr><td>3</td><td>Males</td><td>153</td><td>0.5 ± 0.04</td><td>16.36 ± 0.08</td><td>0.98 ± 0.06</td></tr><tr><td>3</td><td>Females</td><td>156</td><td>0.5 ± 0.04</td><td>19.85 ± 0.09</td><td>1.13 ± 0.06</td></tr><tr><td>Total</td><td>Males</td><td>776</td><td>0.54 ± 0.02</td><td>16.38 ± 0.04</td><td>1.03 ± 0.03</td></tr></tbody></table>
<table><caption>**Table 1** Descriptive statistics for the batches of pupae (Continued)</caption><thead><tr><th>Batch</th><th>Sex</th><th>N</th><th colspan="2">Proportion ± SE</th><th colspan="2">Mean size ± SE</th><th colspan="2">SD ± SE</th></tr></thead><tbody><tr><td>Total</td><td>Females</td><td>650</td><td>0.46</td><td>±</td><td>0.02</td><td>19.81</td><td>±</td><td>0.05</td><td>1.25</td><td>±</td><td>0.03</td></tr><tr><td colspan="11"><em>Aedes aegypti</em> - WB2-BRA</td></tr><tr><td>1</td><td>Males</td><td>270</td><td>0.68</td><td>±</td><td>0.03</td><td>17.65</td><td>±</td><td>0.04</td><td>0.70</td><td>±</td><td>0.03</td></tr><tr><td>1</td><td>Females</td><td>129</td><td>0.32</td><td>±</td><td>0.04</td><td>21.23</td><td>±</td><td>0.07</td><td>0.83</td><td>±</td><td>0.05</td></tr><tr><td>2</td><td>Males</td><td>86</td><td>0.44</td><td>±</td><td>0.05</td><td>18.39</td><td>±</td><td>0.07</td><td>0.66</td><td>±</td><td>0.05</td></tr><tr><td>2</td><td>Females</td><td>111</td><td>0.56</td><td>±</td><td>0.05</td><td>22.37</td><td>±</td><td>0.09</td><td>0.99</td><td>±</td><td>0.07</td></tr><tr><td>3</td><td>Males</td><td>160</td><td>0.38</td><td>±</td><td>0.04</td><td>19.12</td><td>±</td><td>0.06</td><td>0.74</td><td>±</td><td>0.04</td></tr><tr><td>3</td><td>Females</td><td>264</td><td>0.62</td><td>±</td><td>0.03</td><td>23.15</td><td>±</td><td>0.06</td><td>0.95</td><td>±</td><td>0.04</td></tr><tr><td>Total</td><td>Males</td><td>516</td><td>0.51</td><td>±</td><td>0.02</td><td>18.23</td><td>±</td><td>0.04</td><td>0.96</td><td>±</td><td>0.03</td></tr><tr><td>Total</td><td>Females</td><td>504</td><td>0.49</td><td>±</td><td>0.02</td><td>22.48</td><td>±</td><td>0.05</td><td>1.22</td><td>±</td><td>0.04</td></tr></tbody></table>

Batch, number of the batch, corresponding to a rearing container; N, number of pupae; Proportion, proportion of pupae; Mean size (√pixel) for the group; SD, Standard deviation; SE, standard error

sample in two will leave a certain proportion of each sex in the batch of the other group: smaller females in the male group and/or bigger males in the female group. This limitation of the SSD-based sorting methods is commonly recognized, altogether with the general observation that rearing conditions have a strong effect over

<table><caption>**Table 2** Results for the goodness-of-fit of the data to a probability distribution function. *P*-values are provided for each test</caption><thead><tr><th rowspan="3">Species/Strain</th><th rowspan="3">Batch</th><th colspan="2">S-W</th><th>K-S</th></tr><tr><th>Males</th><th>Females</th><th>Mixture</th></tr><tr><th><em>P</em>-value</th><th><em>P</em>-value</th><th><em>P</em>-value</th></tr></thead><tbody><tr><td rowspan="3">An. arabiensis Dongola</td><td>1</td><td>0.7334</td><td>0.7329</td><td>0.9094</td></tr><tr><td>2</td><td>0.7290</td><td>0.2108</td><td>0.7998</td></tr><tr><td>3</td><td>0.9345</td><td>0.0102*</td><td>0.4434</td></tr><tr><td rowspan="3">Ae. albopictus Rimini</td><td>1</td><td>0.1545</td><td>0.3109</td><td>0.9730</td></tr><tr><td>2</td><td>0.0526</td><td>0.6420</td><td>0.6992</td></tr><tr><td>3</td><td>0.0021*</td><td>0.3856</td><td>0.8665</td></tr><tr><td rowspan="3">Ae. polynesiensis (Aito (BC9))</td><td>1</td><td>0.3576</td><td>0.0488</td><td>0.9371</td></tr><tr><td>2</td><td>0.7452</td><td>0.3139</td><td>0.9556</td></tr><tr><td>3</td><td>0.6154</td><td>0.5026</td><td>0.7538</td></tr><tr><td rowspan="3">Ae. aegypti GSS</td><td>1</td><td>0.6916</td><td>0.2393</td><td>0.7966</td></tr><tr><td>2</td><td>0.1250</td><td>0.9713</td><td>0.9872</td></tr><tr><td>3</td><td>0.4354</td><td>0.7882</td><td>0.9726</td></tr><tr><td rowspan="3">Ae. aegypti Sri Lanka</td><td>1</td><td>0.4785</td><td>0.5730</td><td>0.9305</td></tr><tr><td>2</td><td>0.6273</td><td>0.8647</td><td>0.976</td></tr><tr><td>3</td><td>0.7664</td><td>0.3403</td><td>0.9897</td></tr><tr><td rowspan="3">Ae. aegypti WB2-BRA</td><td>1</td><td>0.1064</td><td>0.1099</td><td>0.7892</td></tr><tr><td>2</td><td>0.3019</td><td>0.1325</td><td>0.9840</td></tr><tr><td>3</td><td>0.6914</td><td>0.0480</td><td>0.5103</td></tr></tbody></table>

Abbreviations: S-W, Shapiro-Wilk test for the test of normality of the distributions of each sex; K-S, Kolmogorov-Smirnov test for the fit to a mixture of normal distributions

the performance of the methods [8, 20–22, 52]. However, the mechanisms under these observations have not been investigated in depth, which may affect the optimization of new sorting methods based on SSD.

For the four species analyzed, including the three *Ae. aegypti* laboratory strains, the distribution of the size of each sex considered apart followed a normal distribution, as commonly observed in insects [33]. For the three *Ae. aedes* species studied here, the joint frequency distribution for both sexes is noticeably bimodal, and can be modeled through a mixture of two normal probability density functions. This model is rather simple, with only five parameters that can be easily estimated directly from a population sample. It is likely that this approach can be generalized to other *Aedes* species as well as to culicine mosquitoes with a marked dimorphism in size [31, 38, 53]. In addition, this method of analysis could be generally applied to all known SSD-based sorting methods, since all of them rely on separating batches of pupae in two groups through the definition of a threshold size.

The features of the distribution in sizes of the individuals determine the differences between samples/ strains/ species in the suitability for any SSD-sorting method. These differences are reflected in two main parameters: the performance (% males recovery) and sample purity (% males on the sorted sample). Both can be predicted from the probability density function. For a given set of the model parameters ($\alpha_m$; $\mu_i$, $\sigma_i$), each size threshold has a pair of values of performance and purity associated. Under these model assumptions, purity and performance in each sample of pupae are unequivocally linked; each value of purity corresponds to a single value of performance. Since the evaluation of the quality of a given sorting through the predicted values of purity-performance depends on the chosen value of threshold, the relationship of both parameters in a dimensionless space has been analyzed theoretically. This analysis has provided two useful indices that
<figure><img src="image_7.png" /><figcaption>**Fig. 3** Frequency distribution of size (√pixel) for pupae of different mosquito species and strains reared under small-scale laboratory conditions. Males are represented in blue and females in red. Three replicates are presented for each mosquito species/strain</figcaption></figure>

describe the applicability of SSD-sorting methods for a given sample of pupae, i.e. the quality of the biological material and the rearing conditions. As SDI increases, the purity-performance function becomes more optimal (better performance with higher purity). The SDI index has two components, the SSD and the sample variance. Consequently, an increase in SSD and a reduction in variance increase the efficiency of any SSD-sorting method, as will be discussed later. Index SHI modifies the slope of the curve. The higher the SHI value, the more flattened purity-performance curve is obtained. This parameter describes the difference in variance between males and females, which is difficult to control during the rearing process. SDI and SHI can be used for long-term monitoring of the quality control of the sorting process.

The purity and performance are inversely correlated. From the applied point of view, any sorting system must choose a size threshold considering the trade-off

between performance and purity. From Equations 8 and 9, it is possible to estimate, for a given sample, the threshold of size needed to obtain a desired value of purity or performance. Unfortunately, it is not possible to calculate a single constant size threshold for sex sorting that keeps constant the purity and performance levels across different batches. It is known that there is heterogeneity in size in the production units (rearing containers) that affects the outcome of the sorting methods [7, 19, 20, 30]. For instance, the three *Ae. aegypti* GSS SSD batches varied in purity (99.2-100%) and performance (66-94%) when separated by the same threshold value (see Table 4).

Keeping the purity as a constant parameter, and assuming heterogeneity in size, the outcome of the sorting will have a variable percent recovery of males. Since this heterogeneity is important in the output of the sex sorting, we analyzed and quantified the sources of variation in size in the experimental sample. Then, we used the
<figure><img src="image_8.png" /><figcaption>**Fig. 4** Depiction of the SSD-sorting methods functioning simulated by a mixture of two normal distribution functions. Different threshold of sizes separates the sample in two subsamples. The subsample of smaller size has a different male proportion depending on the chosen threshold. Purity = % males on the sorted sample. Performance = % males recovery. The dotted lines depict a value of threshold. **a** Probability density function of male and female pupal size. **b** Purity versus performance</figcaption></figure>

parameters directly estimated from the samples to predict the expected values of purity and performance for each batch of pupae. Changing the value of these parameters in the fitted models allowed us to simulate the outcome of SSD-sorting methods under different scenarios. The partitioning of variance showed two different patterns of relative importance in respect to the source of heterogeneity in size. For the *Aedes* species, the main source of variation was the sexual difference, followed by the residual, the differences between batches and finally the interaction sex-batch. For *Anopheles*, the effect of sex was of less importance, and the residual accounted for most of the variation.

The SSD, as the absolute difference between mean size of each sex, is the main factor that explains the interspecific differences in the applicability of SSD-sorting methods. A higher SSD will produce higher performance independently of the scale, and for all the size thresholds considered, yielding a higher SDI. The two species with higher SSD (*Ae. aegypti* and *Ae. polynesiensis*) are known to yield better results than *Ae. albopictus* when separated with plate separators. On the other hand, *An. arabiensis*, as expected [11, 12], showed a poor suitability for the SSD-sorting methods. The experimental samples of *An. arabiensis* showed an average SSD of 0.52 √pixels, while the *Aedes* species ranged from 3.3

to 3.9 √pixels. Likely, even achieving a reduction in the heterogeneity would not be enough to make SSD-sorting methods suitable for *An. arabiensis* or related species. For example, a SSD-sorting method was used to sort *An. albi-manus* in a trial in El Salvador [54], and resulted in 14% of female contamination in the released mosquitoes which would be currently unacceptable.

The residual variance is the second important source of variation in the *Aedes* group. It accounts for the unexplained variation due to other factors, mainly the natural heterogeneity in size that can be found in any pupal batch. The heterogeneity in size in a given batch (rearing container) has a strong effect on the performance. As an example, our simulations (Table 4) with the GSS strain predict that a 20 % increase in the standard deviation of the experimental value reduces the performance by about 17 %. Conversely, a reduction of the same magnitude produces an increase in male recovery of 7.6 %. The heterogeneity in size could be due to genetic and/or environmental factors [55, 56]. It is not expected that the genetic heterogeneity of laboratory populations has a major effect given that it has been drastically reduced by the colonization process [55]. On the other hand, it is known that intraspecific asymmetric density-dependent factors can increase the variability in
<table><caption>**Table 3** Predictions of the fitted models with the experimental parameters for different measures of suitability to sexual size dimorphism sorting methods. Performance (% males recovery) at different levels of purity (% males in the sorted sample)</caption><thead><tr><th rowspan="2">Species/Strain</th><th rowspan="2">Batch</th><th rowspan="2">SDI</th><th rowspan="2">SHI</th><th colspan="3">Performance</th></tr><tr><th>Purity = 99.9</th><th>Purity = 99.5</th><th>Purity = 99.0</th></tr></thead><tbody><tr><td rowspan="4">An. arabiensis Dongola</td><td>1</td><td>0.58</td><td>1.01</td><td>&lt;0.01</td><td>0.04</td><td>0.23</td></tr><tr><td>2</td><td>0.09</td><td>0.98</td><td>-</td><td>-</td><td>-</td></tr><tr><td>3</td><td>0.09</td><td>1.02</td><td>&lt;0.01</td><td>&lt;0.01</td><td>-</td></tr><tr><td>Total</td><td>0.24</td><td>1.00</td><td>&lt;0.01</td><td>&lt;0.01</td><td>-</td></tr><tr><td rowspan="4">Ae. albopictus Rimini</td><td>1</td><td>1.89</td><td>0.99</td><td>73.09</td><td>88.45</td><td>92.96</td></tr><tr><td>2</td><td>2.35</td><td>0.96</td><td>95.12</td><td>98.78</td><td>99.45</td></tr><tr><td>3</td><td>1.95</td><td>1.04</td><td>83.92</td><td>93.55</td><td>96.19</td></tr><tr><td>Total</td><td>1.91</td><td>1.02</td><td>78.97</td><td>91.13</td><td>94.62</td></tr><tr><td rowspan="4">Ae. polynesiensis Aito (BC9)</td><td>1</td><td>2.87</td><td>0.96</td><td>99.41</td><td>99.89</td><td>99.96</td></tr><tr><td>2</td><td>2.69</td><td>1.03</td><td>98.93</td><td>99.74</td><td>99.88</td></tr><tr><td>3</td><td>3.00</td><td>0.92</td><td>99.78</td><td>99.97</td><td>99.99</td></tr><tr><td>Total</td><td>2.29</td><td>0.97</td><td>91.41</td><td>97.25</td><td>98.55</td></tr><tr><td rowspan="4">Ae. aegypti GSS</td><td>1</td><td>2.00</td><td>1.02</td><td>80.28</td><td>91.51</td><td>94.74</td></tr><tr><td>2</td><td>2.65</td><td>1.00</td><td>98.65</td><td>99.68</td><td>99.86</td></tr><tr><td>3</td><td>2.54</td><td>0.87</td><td>95.17</td><td>99.03</td><td>99.61</td></tr><tr><td>Total</td><td>1.94</td><td>0.81</td><td>33.75</td><td>74.51</td><td>86.43</td></tr><tr><td rowspan="4">Ae. aegypti Sri Lanka</td><td>1</td><td>1.35</td><td>0.92</td><td>5.54</td><td>31.16</td><td>48.47</td></tr><tr><td>2</td><td>1.63</td><td>0.89</td><td>24.63</td><td>60.80</td><td>75.26</td></tr><tr><td>3</td><td>1.67</td><td>0.93</td><td>37.38</td><td>67.23</td><td>78.52</td></tr><tr><td>Total</td><td>1.51</td><td>0.90</td><td>15.66</td><td>48.85</td><td>64.99</td></tr><tr><td rowspan="4">Ae. aegypti WB2-BRA</td><td>1</td><td>2.35</td><td>0.92</td><td>95.69</td><td>99.15</td><td>99.67</td></tr><tr><td>2</td><td>2.46</td><td>0.82</td><td>89.46</td><td>97.94</td><td>99.21</td></tr><tr><td>3</td><td>2.40</td><td>0.89</td><td>89.61</td><td>97.23</td><td>98.69</td></tr><tr><td>Total</td><td>1.96</td><td>0.89</td><td>63.59</td><td>86.67</td><td>92.77</td></tr></tbody></table>

Abbreviations: SDI, SHI, dimensionless parameters, characteristic of each batch

<table><caption>**Table 4** Predicted values for the descriptive parameters of the sex sorting of the *Ae. aegypti* GSS strain simulated under different conditions</caption><thead><tr><th>Sim.</th><th>Conditions</th><th>Group</th><th>μ<sub>m</sub></th><th>μ<sub>r</sub></th><th>σ<sub>m</sub></th><th>σ<sub>r</sub></th><th>SDI</th><th>SHI</th><th>Performance</th><th>Purity</th></tr></thead><tbody><tr><td rowspan="3">a</td><td rowspan="3">Experimental</td><td>Batch1</td><td>17.34</td><td>20.31</td><td>0.76</td><td>0.73</td><td>2.00</td><td>1.02</td><td>91.51</td><td>99.5</td></tr><tr><td>Batch 2</td><td>18.20</td><td>22.16</td><td>0.75</td><td>0.75</td><td>2.65</td><td>1.00</td><td>99.68</td><td>99.5</td></tr><tr><td>Batch 3</td><td>18.04</td><td>22.24</td><td>0.95</td><td>0.72</td><td>2.54</td><td>0.87</td><td>99.03</td><td>99.5</td></tr><tr><td></td><td>Combination of batches</td><td>Total</td><td><strong>17.86</strong></td><td><strong>21.72</strong></td><td><strong>1.22</strong></td><td><strong>0.81</strong></td><td>1.94</td><td>0.81</td><td>74.51</td><td>99.5</td></tr><tr><td rowspan="2">b</td><td rowspan="2">Differences in intra-batch variance.</td><td>Batch 1</td><td>17.34</td><td>20.31</td><td>0.76</td><td>0.73</td><td>2.00</td><td>1.02</td><td>91.51</td><td>99.5</td></tr><tr><td>sd* 1.2</td><td>17.34</td><td>20.31</td><td><strong>0.91</strong></td><td><strong>0.87</strong></td><td>1.66</td><td>1.02</td><td>74.38</td><td>99.5</td></tr><tr><td rowspan="3">c</td><td rowspan="3">Differences in SSD</td><td>Batch 1</td><td>17.34</td><td>20.31</td><td>0.76</td><td>0.73</td><td>2.00</td><td>1.02</td><td>91.51</td><td>99.5</td></tr><tr><td>SSD-0.5</td><td><strong>17.59</strong></td><td><strong>20.06</strong></td><td>0.76</td><td>0.73</td><td>1.66</td><td>1.02</td><td>74.14</td><td>99.5</td></tr><tr><td>Constant</td><td>SSD+0.5</td><td><strong>17.09</strong></td><td><strong>20.56</strong></td><td>0.76</td><td>0.73</td><td>2.33</td><td>1.02</td><td>97.99</td><td>99.5</td></tr><tr><td rowspan="3">d</td><td rowspan="3">Fixed threshold</td><td>Batch1</td><td>17.34</td><td>20.31</td><td>0.76</td><td>0.73</td><td>2.00</td><td>1.02</td><td>93.69</td><td>99.22</td></tr><tr><td>Batch 2</td><td>18.20</td><td>22.16</td><td>0.75</td><td>0.75</td><td>2.65</td><td>1.00</td><td>65.54</td><td>100.00</td></tr><tr><td>Batch 3</td><td>18.04</td><td>22.24</td><td>0.95</td><td>0.72</td><td>2.54</td><td>0.87</td><td>73.80</td><td>99.99</td></tr></tbody></table>

Abbreviations: Sim, reference for the simulation; Group, specific simulation for the group; μ<sub>m</sub>, μ<sub>r</sub>, σ<sub>m</sub>, σ<sub>r</sub>, parameters of the model; SDI, SHI, dimensionless parameters;

Performance, % males recovery; Purity, % males on the sorted sample

Simulations: a, effects of sex-sorting after combining the three batches; b, effects of increase/decrease the variance; c, effects of increase/decrease the difference in means between sexes; d, effects of sex-sorting three batches with a predefined size threshold. For each simulation, the parameters that are modified from the experimental data (first 3 rows) are highlighted in bold style
<table><caption>**Table 5** ANOVA tables for each species/strain. The factors included are batch (rearing container) and sex (male or female)</caption><thead><tr><th>Species/Strain</th><th></th><th>df</th><th>SS</th><th>MS</th><th>F</th><th>P</th><th></th></tr></thead><tbody><tr><td rowspan="4">An. arabiensis Dongola</td><td>Batch</td><td>2</td><td>9.6</td><td>4.798</td><td>5.298</td><td>0.006</td><td>***</td></tr><tr><td>Sex</td><td>1</td><td>6.81</td><td>6.807</td><td>7.515</td><td>0.007</td><td>***</td></tr><tr><td>Batch:Sex</td><td>2</td><td>10.29</td><td>5.145</td><td>5.681</td><td>0.004</td><td>***</td></tr><tr><td>Residuals</td><td>120</td><td>108.69</td><td>0.906</td><td></td><td></td><td></td></tr><tr><td rowspan="4">Ae. albopictus Rimini</td><td>Batch</td><td>2</td><td>174</td><td>87</td><td>133.646</td><td>&lt;0.001</td><td>***</td></tr><tr><td>Sex</td><td>1</td><td>4281</td><td>4281</td><td>6565.183</td><td>&lt;0.001</td><td>***</td></tr><tr><td>Batch:Sex</td><td>2</td><td>10</td><td>5</td><td>7.864</td><td>&lt;0.001</td><td>***</td></tr><tr><td>Residuals</td><td>1560</td><td>1017</td><td>1</td><td></td><td></td><td></td></tr><tr><td rowspan="4">Ae. polynesiensis Aito (BC9)</td><td>Batch</td><td>2</td><td>263</td><td>131</td><td>295.618</td><td>&lt;0.001</td><td>***</td></tr><tr><td>Sex</td><td>1</td><td>3625</td><td>3625</td><td>8155.481</td><td>&lt;0.001</td><td>***</td></tr><tr><td>Batch:Sex</td><td>2</td><td>4</td><td>2</td><td>4.289</td><td>0.014</td><td>*</td></tr><tr><td>Residuals</td><td>978</td><td>435</td><td>0</td><td></td><td></td><td></td></tr><tr><td rowspan="4">Ae. aegypti GSS</td><td>Batch</td><td>2</td><td>278.2</td><td>139.1</td><td>223.99</td><td>&lt;0.001</td><td>***</td></tr><tr><td>Sex</td><td>1</td><td>2306.3</td><td>2306.3</td><td>3713.93</td><td>&lt;0.001</td><td>***</td></tr><tr><td>Batch:Sex</td><td>2</td><td>32.9</td><td>16.4</td><td>26.45</td><td>&lt;0.001</td><td>***</td></tr><tr><td>Residuals</td><td>672</td><td>417.3</td><td>0.6</td><td></td><td></td><td></td></tr><tr><td rowspan="4">Ae. aegypti Sri Lanka</td><td>Batch</td><td>2</td><td>11.8</td><td>5.9</td><td>4.587</td><td>0.0104</td><td>*</td></tr><tr><td>Sex</td><td>1</td><td>2764.1</td><td>2764.1</td><td>2152.107</td><td>&lt;0.001</td><td>***</td></tr><tr><td>Batch:Sex</td><td>2</td><td>10</td><td>5</td><td>3.892</td><td>0.020</td><td>*</td></tr><tr><td>Residuals</td><td>912</td><td>1171.4</td><td>1.3</td><td></td><td></td><td></td></tr><tr><td rowspan="4">Ae. aegypti WB2-BRA</td><td>Batch</td><td>2</td><td>260.3</td><td>130.2</td><td>208.85</td><td>&lt;0.001</td><td>***</td></tr><tr><td>Sex</td><td>1</td><td>1926.1</td><td>1926.1</td><td>3090.347</td><td>&lt;0.001</td><td>***</td></tr><tr><td>Batch:Sex</td><td>2</td><td>8.3</td><td>4.1</td><td>6.627</td><td>0.001</td><td>**</td></tr><tr><td>Residuals</td><td>510</td><td>317.9</td><td>0.6</td><td></td><td></td><td></td></tr></tbody></table>

Abbreviations: df, degrees of freedom; SS, sum of squares; MS, mean sum of squares; F, F-statistics; P, P-value for the F-statistics

size in other insects which have an aquatic larval developmental stage [57, 58]. Given that the mosquito larvae are usually kept at high densities in the artificial rearing containers, the heterogeneity in size could potentially be reduced by adjusting the larval density.

The variance between rearing containers is also an important factor to consider in SSD-sorting. In a real mass production context, there is variation in size between batches that is present in our experiments as well. This variation affected mainly the average size of the pupae, but also at some extent the absolute SSD magnitude (Table 5, Interaction term Batch:Sex). It has been reported that the food availability or the water pollution by conspecifics does not affect the absolute SSD magnitude in *Aedes* [38, 43] while larval competition could produce some degree of sexual alometry in size [40, 42]. The intraspecific variation in SSD is a complex issue [35–37] out of the scope of this article, but worth to be investigated in mosquitoes in the context of SSD-sorting methods. The variability between rearing containers is of major applied significance because the threshold of size needed to obtain a desired degree of purity is specific for each batch. The use of a common fixed threshold for all

the production batches would produce a variable output in respect to purity and performance, and it is therefore not recommended (Table 4). In a mass production context, it can be sometimes useful to mix the pupae production of different rearing containers before the sex sorting, but this would likely increase the size heterogeneity. This is clearly shown in the simulations presented in Tables 3 and 4. For example, mixing the *Ae. aegypti* GSS pupae production from three rearing trays reduced the performance in about 17% (with purity level of 99.5%).

Two main strategies are presently used for SSD sorting methods. First, sieves [8], rows of slots [21] or openings between plates [22], which are based on fixed size thresholds, were developed through a trial and error process. This means that the purity and performance are not controlled and they entirely depend on the rearing conditions. On the other hand, plate separators [23], which rely on a visual adaptive size threshold election system, exhibit better performance [52] at the expense of productivity [21]. Both strategies can be optimized using the appropriate analytical tool. For the fixed threshold methods, a more optimal threshold based on
the actual range of variation in size between batches of pupae may be required. The plate separator could be optimized by the determination of less subjective threshold election criteria. Finally, the analytical framework proposed here can be integrated in large scale mechanized sex-sorters of high precision.

## Conclusions

The distribution of size in mosquito pupae can be modeled by a mixture of two Gaussian distribution functions. This approach, combined with the parameters obtained from laboratory samples, can be useful to understand and optimize the mechanisms of the SSD-sorting methods. Purity and performance, which are the most relevant features of sex sorting devices, can be directly calculated from the presented model. Two additional dimensionless parameters, SDI and SHI, which are good descriptors of the suitability of a species/strain under given rearing conditions for its sorting with SSD-based methods are proposed. This approach can be applied to all the SSD-sorting methods. The output of the SSD-sorting methods can be improved by reducing the heterogeneity in size within the rearing containers. The heterogeneity between batches can affect the quality of sex sorting when different batches are mixed before the sorting or when a common separation threshold is determined for a series of batches. For new designs of sex-sorting devices based on SSD, we recommend the following: (i) use of an adaptive and precise threshold selection method based on automatic measurement systems and the proposed formulas; and (ii) a specific threshold size for each batch to maintain the purity at a constant level. In this way, the heterogeneity in size will be resulting to a variable male recovery (performance). From the practical point of view, this study shows that enhanced SSD-based sex sorting methods can be applied to *Aedes* mosquito mass-rearing facilities that depend on lateral area to distinguish sexes to efficiently produce batches of male-only pupae with a male recovery ranging between 70% and 99% and female contamination under 0.5%, with the lower values of male recovery being obtained when different batches are mixed or when larval rearing conditions are not standardized.

## Abbreviations

**GSS**: Genetic sexing strain; **IIT**: Incompatible insect technique; **RIDL**: Release of insects carrying a dominant lethal; **SDI**: Sexual dimorphism index; **SHI**: Sexual homoscedasticity index; **SIT**: Sterile insect technique; **SSD**: Sexual size dimorphism

## Acknowledgements

We would like to thank the staff members of the Insect Pest Control Laboratory of the Joint FAO/IAEA Division, Antonios Augustinos, Nanwintoum S. Bimbile-Somda, Danilo Carvalho, Anna Konczal, Hamidou Maïga, Wadaka Mamai, Gulizar Pillwax and Asha Wijegunawardana, for their great support during the preparation of the samples used in this study. We are particularly grateful to Angela Aguado and José Félix Descalzo for their essential assistance. We thank to Enrique Torrente and Jose Antonio Herrador their indispensable support to carry

out this research. This study was supported by the International Atomic Energy research contact no. 17939 as part of the Coordinated Research Project "Exploring genetic, molecular, mechanical and behavioural methods of sex separation in mosquitoes". MZ acknowledges support from Universidad Católica de Valencia "San Vicente Mártir" (grant 2018-253-002)

## Funding

This research was financially supported by GRUPO TRAGSA. Publication costs for this study was provided by the International Atomic Energy Agency as part of the Coordinated Research Project "Exploring genetic, molecular, mechanical and behavioural methods of sex separation in mosquitoes".

## Availability of data and materials

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

## About this supplement

This article has been published as part of *Parasites & Vectors* Volume 11 Supplement 2, 2018: *Exploring genetic molecular, mechanical and behavioural methods of sex separation in mosquitoes*. The full contents of the supplement are available online at https://parasitesandvectors.biomedcentral.com/articles/supplements/volume-11-supplement-2.

## Authors' contributions

MZ, GS, DA, CT, RA, IP designed the study. HB and KB provided the strains. GS designed and built the acquisition data system based on artificial vision. DA and CT performed the data collection. DA and MZ analyzed the data and wrote the manuscript. MZ proposed the theoretical model for data analysis. GS, CT, RA, IP and KB contributed to the manuscript drafting. All authors read and approved the final manuscript.

## Ethics approval and consent to participate

Not applicable.

## Consent for publication

Not applicable.

## Competing interests

The authors declare that they have no competing interests.

## Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Author details

¹Departamento de Ciencias Experimentales y Matemáticas, Universidad Católica de Valencia "San Vicente Mártir", C/Guillem de Castro 94, 46003 Valencia, Spain. ²Departamento de Expresión Gráfica, Proyectos y Urbanismo, Universidad CEU Cardenal Herrera, Valencia, Spain. ³Grupo Tragsa, Avda. de la Industria 26, 46980 Paterna, Valencia, Spain. ⁴Insect Pest Control Section, Joint FAO/IAEA Division of Nuclear Techniques in Food and Agriculture, Wagramerstrasse 5, PO Box 100, A-1400 Vienna, Austria. ⁵Laboratoire d'Entomologie Médicale, Institut Louis Malardé, BP 30, 98713 Papeete, Tahiti, French Polynesia. ⁶IRD, AP-HM, SSA, VITROME, IHU-Méditerranée infection, Univ. Aix Marseille, Marseille, France.

Published: 24 December 2018

## References

1. Lees RS, Gilles JR, Hendrichs J, Vreysen MJ, Bourtzis K. Back to the future: the sterile insect technique against mosquito disease vectors. Curr Opin Insect Sci. 2015;10:156-62.

2. Benedict MQ, Robinson AS. The first releases of transgenic mosquitoes: an argument for the sterile insect technique. Trends Parasitol. 2003;19:349-55.

3. Alphey L, Benedict M, Bellini R, Clark GG, Dame DA, Service MW, et al. Sterile-insect methods for control of mosquito-borne diseases: an analysis. Vector Borne Zoonotic Dis. 2010;10:295-311.

4. Bourtzis K, Lees RS, Hendrichs J, Vreysen MJB. More than one rabbit out of the hat: Radiation, transgenic and symbiont-based approaches for sustainable management of mosquito and tsetse fly populations. Acta Trop. 2016;157:115-30.
5. Dyck VA, Hendrichs J, Robinson AS. Sterile insect technique: principles and practice in area-wide integrated pest management. Dordrecht: Springer, 2006.

6. Harris AF, McKemey AR, Nimmo D, Curtis Z, Black J, Morgan SA, et al. Successful suppression of a field mosquito population by sustained release of engineered male mosquitoes. Nat Biotechnol. 2012;30:828-30.

7. Alphey L. Genetic control of mosquitoes. Annu Rev Entomol. 2014;59:205-24.

8. Bellini R, Medici A, Puggioli A, Balestrino F, Carrieri M. Pilot field trials with *Aedes albopictus* irradiated sterile males in Italian urban areas. J Med Entomol. 2013;50:317-25.

9. Carvalho DO, McKemey AR, Garziera L, Lacroix R, Donnelly CA, Alphey L, et al. Suppression of a field population of *Aedes aegypti* in Brazil by sustained release of transgenic male mosquitoes. PLoS Negl Trop Dis. 2015;9:e0003864.

10. Mains JW, Brelsfoard CL, Rose RI, Dobson SL. Female adult *Aedes albopictus* suppression by Wolbachia-infected male mosquitoes. Sci Rep. 2016;6:33846.

11. Gilles JRL, Schetelig MF, Scolari F, Marec F, Curapur ML, Franz G, et al. Towards mosquito sterile insect technique programmes: exploring genetic, molecular, mechanical and behavioural methods of sex separation in mosquitoes. Acta Trop. 2014;132:S178-87.

12. Papathanos PA, Bossin HC, Benedict MQ, Catteruccia F, Malcolm CA, Alphey L, et al. Sex separation strategies: past experience and new approaches. Malar J. 2009;8 Suppl 2:S5.

13. Caceres C. Mass rearing of temperature sensitive genetic sexing strains in the Mediterranean fruit fly (Ceratitida capitata). Genetica 2002;116:107-116.

14. Robinson A, Franz G, Fisher K. Genetic sexing strains in the medfly, *Ceratititis capitata*: development, mass rearing and field application. Trends Entomol. 1999;2:81-104.

15. McCombs SD, Saul SH. Translocation-based genetic sexing system for the oriental fruit fly (Diptera: Tephritidae) based on pupal color dimorphism. Ann Entomol Soc Am. 1995;88:695-8.

16. Zepeda-Cisneros CS, Meza Hernández JS, García-Martínez V, Ibañez-Palacios J, Zacharopoulou A, Franz G. Development, genetic and cytogenetic analyses of genetic sexing strains of the Mexican fruit fly, *Anastrepha ludens* Loew (Diptera: Tephritidae). BMC Genet. 2014;15:S1.

17. Augustinos AA, Targovska A, Cancio-Martinez E, Schorn E, Franz G, Cáceres C, et al. *Ceratitis capitata* genetic sexing strains: laboratory evaluation of strains from mass-rearing facilities worldwide. Entomol Exp Appl. 2017;164:305-17.

18. Yamada H, Benedict MQ, Malcolm CA, Oliva CF, Soliban SM, Gilles JR. Genetic sex separation of the malaria vector, *Anopheles arabiensis*, by exposing eggs to dieldrin. Malar J. 2012;11:208.

19. Yamada H, Jandric Z, Chhem-Kieth S, Vreysen MJB, Rathor MN, Gilles JRL, et al. *Anopheles arabiensis* egg treatment with dieldrin for sex separation leaves residues in male adult mosquitoes that can bioaccumulate in goldfish (*Carassius auratus auratus*). Environ Toxicol Chem. 2013;32:2786-91.

20. Carvalho DO, Nimmo D, Naish N, McKemey AR, Gray P, Wilke ABB, et al. Mass production of genetically modified *Aedes aegypti* for field releases in Brazil. J Vis Exp JoVE. 2014. https://doi.org/10.3791/3579.

21. Mcrray EMJ. A mechanical device for the rapid sexing of *Aedes aegypti*. J Econ Entomol. 1961;54:4-819.

22. Gerberg E, Hopkins TM, Gentry JW. others. Mass rearing of *Culex pipiens* L. Mosq News. 1969;29:382-5.

23. Focks DA. An improved separator for the developmental stages, sexes and species of mosquitoes (Diptera, Culicidae). J Med Entomol. 1980;17:567-8.

24. Benedict MQ, Knols BG, Bossin HC, Howell PI, Mialhe E, Caceres C, et al. Colonisation and mass rearing: learning from others. Malar J. 2009;8:S4.

25. Steinwascher K. Relationship between pupal mass and adult survivorship and fecundity for *Aedes aegypti*. Environ Entomol. 1982;11:150-3.

26. Armbruster P, Hutchinson RA. Pupal mass and wing length as indicators of fecundity in *Aedes albopictus* and *Aedes geniculatus* (Diptera: Culicidae). J Med Entomol. 2002;39:699-704.

27. Blackmore MS. Lord CC. The relationship between size and fecundity in *Aedes albopictus*. J Vector Ecol. 2000;25:212-7.

28. Alto BW, Reiskind MH, Lounibos LP. Size alters susceptibility of vectors to dengue virus infection and dissemination. Am J Trop Med Hyg. 2008;79:688-95.

29. Lyimo EO, Koella JC. Relationship between body size of adult *Anopheles gambiae* s.l. and infection with the malaria parasite *Plasmodium falciparum*. Parasitology. 1992;104:233-7.

30. Schneider JR, Morrison AC, Astete H, Scott TW, Wilson ML. Adult size and distribution of *Aedes aegypti* (Diptera: Culicidae) associated with larval habitats in Iquitos. Peru. J Med Entomol. 2004;41:634-42.

31. Virginio F, Oliveira Vidal P, Suesdek L. Wing sexual dimorphism of pathogen-vector culicids. Parasit Vectors. 2015;8:159.

32. Lardeux F, Tetuanui A. Larval growth of *Aedes polynesiensis* and *Aedes aegypti* (Diptera: Culicidae). Mosq Syst. 1995;27:118-24.

33. Gouws EJ, Gaston KJ, Chown SL. Intraspecific body size frequency distributions of insects. PLOS ONE. 2011;6:e16606.

34. Stamps J. Sexual size dimorphism in species with asymptotic growth after maturity. Biol J Linn Soc. 1993;50:123-45.

35. Fairbairn DJ, Blanckenhorn WU, Székely T. Sex, size and gender roles: evolutionary studies of sexual size dimorphism. New York: Oxford University Press; 2007.

36. Teder T, Tammaru T. Sexual size dimorphism within species increases with body size in insects. Oikos. 2005;108:321-34.

37. Blanckenhorn WU, Meier R, Teder T. Rensch's rule in insects: patterns among and within species. In: Fairbairn, D Blanckenhorn W, Székely T, editors. Sex, size and gender roles. Oxford: Oxford University Press; 2007. p. 60-70.

38. Wormington JD, Juliano SA. Sexually dimorphic body size and development time plasticity in *Aedes mosquitoes* (Diptera: Culicidae). Evol Ecol Res. 2014;16:223-34.

39. Hapairai LK, Marie J, Sinkins SP, Bossin HC. Effect of temperature and larval density on *Aedes polynesiensis* (Diptera: Culicidae) laboratory rearing productivity and male characteristics. Acta Trop. 2014;132:S108-15.

40. Bedhomme S, Agnew P, Sidobre C, Michalakis Y. Sex-specific reaction norms to intraspecific larval competition in the mosquito *Aedes aegypti*. J Evol Biol. 2003;16:721-30.

41. Lyimo EO, Takken W, Koella JC. Effect of rearing temperature and larval density on larval survival, age at pupation and adult size of *Anopheles gambiae*. Entomol Exp Appl. 1992;63:265-71.

42. Agnew P, Haussy C, Michalakis Y. Effects of density and larval competition on selected life history traits of *Culex pipiens quinquefasciatus* (Diptera: Culicidae). J Med Entomol. 2000;37:732-5.

43. Bédhomme S, Agnew P, Sidobre C, Michalakis Y. Pollution by conspecifics as a component of intraspecific competition among *Aedes aegypti* larvae. Ecol Entomol. 2005;30:1-7.

44. Yamada H, Parker A, Oliva C, Balestrino F, Gilles J. X-ray-induced sterility in *Aedes albopictus* (Diptera: Culicidae) and male longevity following irradiation. J Med Entomol. 2014;51:811-6.

45. Zheng M-L, Zhang D-J, Damiens DD, Lees RS, Gilles JRL. Standard operating procedures for standardized mass rearing of the dengue and chikungunya vectors *Aedes aegypti* and *Aedes albopictus* (Diptera: Culicidae) - II - Egg storage and hatching. Parasit Vectors. 2015;8:348.

46. Damiens D, Benedict MQ, Wille M, Gilles JRL. An inexpensive and effective larval diet for *Anopheles arabiensis* (Diptera: Culicidae): eat like a horse, a bird, or a fish? J Med Entomol. 2012;49:1001-11.

47. Soma DD, Maiga H, Mamai W, Bimbile-Somda NS, Venter N, Ali AB, et al. Does mosquito mass-rearing produce an inferior mosquito? Malar J. 2017;16:357.

48. Balestrino F, Puggioli A, Gilles JRL, Bellini R. Validation of a new larval rearing unit for *Aedes albopictus* (Diptera: Culicidae) mass rearing. PLOS ONE. 2014;9:e91914.

49. Puggioli A, Balestrino F, Damiens D, Lees RS, Soliban SM, Madakacherry O, et al. Efficiency of three diets for larval development in mass rearing *Aedes albopictus* (Diptera: Culicidae). J Med Entomol. 2013;50:819-25.

50. Szeliski R. Computer vision: algorithms and applications. London: Springer Science & Business Media; 2010.

51. R Core Team. R: A Language and Environment for Statistical Computing. Vienna: R Foundation for Statistical Computing; 2017. https://www.R-project.org/

52. Zhang D, Zhang M, Wu Y, Gilles JRL, Yamada H, Wu Z, et al. Establishment of a medium-scale mosquito facility: optimization of the larval mass-rearing unit for *Aedes albopictus* (Diptera: Culicidae). Parasit Vectors. 2017;10:569.

53. Brust RA. Weight and development time of different stadia of mosquitoes reared at various constant temperatures. Can Entomol. 1967;99:986-93.

54. Lofgren CS, Dame DA, Breeland SG, Weidhaas DE, Jeffery G, Kaiser R, et al. Release of chemosterilized males for the control of *Anopheles albimanus* in El Salvador. Am J Trop Med Hyg. 1974;23:288-97.

55. Schneider JR, Chadee DD, Mori A, Romero-Severson J, Severson DW. Heritability and adaptive phenotypic plasticity of adult body size in the mosquito *Aedes aegypti* with implications for dengue vector competence. Infect Genet Evol J Mol Epidemiol Evol Genet Infect Dis. 2011;11:11-6.

56. Lehmann T, Dalton R, Kim EH, Dahl E, Diabate A, Dabire R, et al. Genetic contribution to variation in larval development time, adult size, and longevity of starved adults of *Anopheles gambiae*. Infect Genet Evol. 2006;6:410-6.

57. Peckarsky BL, Cowan CA. Consequences of larval intraspecific competition to stonefly growth and fecundity. Oecologia. 1991;88:277-88.

58. Gribbin SD, Thompson DJ. Asymmetric intraspecific competition among larvae of the damselfly *Ischnura elegans* (Zygotera: Coenagrionidae). Ecol Entomol. 1990;15:37-42.