# Comparison of Model Predictions and Laboratory Observations of Transgene Frequencies in Continuously-Breeding Mosquito Populations

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## Abstract

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## 1. Introduction

^{TM}[14], persistence is neither intended nor expected, due to the phenotype of the transgene. Such transgenes have been referred to as “self-limiting” [2], reflecting their expected disappearance from wild populations. An incremental step-by-step process of developing self-limiting approaches prior to persistent transgenes is recommended for development of genetically-modified mosquitoes [2], in part so that predictive tools can be devised and tested experimentally to ensure that the modified-mosquito behaviors expected actually occur or, if deviations from the models occur, whether these present greater risk than what was expected prior to the observations.

## 2. Materials and Methods

#### 2.1. Modelling

_{e}, load on egg batch size, and L

_{l}, load on adult longevity) from a prior distribution. Second, a time series of transgene proportion was simulated using the model with the given parameters, for each of the initial conditions applicable to the transgenic strain. Finally, the parameter set was ‘accepted’ if the sum of square distances between the simulated and actual time-series was below a tolerance threshold. The estimated joint posterior distribution is the set of all accepted parameter sets, and we calculated the overall load on genetic fitness by the product 1 − (1 − L

_{e})(1 − L

_{l}). We used a uniform prior distribution by selecting the load on egg batch size from U (0, 1) and load on longevity from U (0, 0.7) (the restriction to less than 0.7 prevents the possibility that all females die in the first week of the simulation). We used a tolerance level equal to the 1% quantile of the sum of square distance samples, which was judged to give a satisfactory balance between the number of posterior samples (which increases with tolerance) and the concentration of posterior density (which reduces with tolerance [25]). This produced 100 posterior points out of 10,000 prior samples.

#### 2.2. Laboratory Experiments

#### 2.2.1. Mosquito Strains

#### 2.2.2. Study Protocol

#### 2.3. Statistical Analysis

## 3. Results

^{2}= 5.65, d.f. = 3, p = 0.13) nor as a function of oviposition number (χ

^{2}= 0.18, d.f. = 1, p = 0.68).

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Adult longevity and duration of pupation used for the model. (

**A**) illustrates adult longevity data (black markers) of [23] that was used to fit a Weibull curve for survival (solid line delimiting gray area fitted by maximizing likelihood). In addition to the data which was available for 24 days, we assumed all adults died before day 30; and (

**B**) the distribution of pupal development times used for model parameterization is shown, based on summarized data [22].

**Figure 2.**The simulation algorithm. The females in the population on day d are described by the variables $({{A}_{W}}_{i,d},{{A}_{T}}_{i,d})$ (adults, i denotes age) and $({{E}_{W}}_{d},{{E}_{T}}_{d})$ (juveniles), where the subscript W or T denotes wildtype or transgenic. The parameter ${\mu}_{i}$ is the probability an adult female dies at age i (derived from the survivorship function shown in Figure 1A), and ${\mathsf{\Phi}}_{W}$ and ${\mathsf{\Phi}}_{T}$ are the probability vectors of pupation after one, two, or three days (Figure 1B). The probability that a given egg is transgenic is half the fraction of transgenic individuals in the adult female population because all transgenic females are hemizygous (their fathers are non-transgenic), and Mendelian inheritance of the transgene has been confirmed experimentally [13,22].

**Figure 3.**Restocking of Ag(DSM)1 cages. The actual numbers of pupae returned each week and the totals are represented. Three frequencies of seeding of hemizygous transgenic females were made: 20%, 50%, and 100% (

**A**–

**C**, respectively). Transgenic males (⚫), transgenic females (☐), non-trangenic males (▲), non-transgenic females (⚪), and the total (◇). Arrows indicate weeks in which no GM mosquitoes were detected.

**Figure 4.**Restocking of Ag(DSM)2 cages. The actual numbers of pupae returned each week and the totals are represented. Two frequencies of seeding of hemizygous transgenic females were made: 20% (

**A**–

**C**), 50% (

**D**–

**F**). Transgenic males (⚫), transgenic females (☐), non-trangenic males (▲), non-transgenic females (⚪), and the total (◇). Arrows indicate weeks in which no GM mosquitoes were detected.

**Figure 5.**Model predictions and observations of transgene frequency in unselected populations. The modeled frequency expected of the transgene in the experimental populations when seeded at different frequencies and the observations for either GMM line. The gray bands show the 95% central quantile intervals of the model trajectories. The dashed and solid black lines represent the experimental results for three replicates of two treatments with Ag(DSM)2 (

**A**,

**B**) and the single experiments at three treatment levels with Ag(DSM)1 (

**C**–

**E**).

**Table 1.**The log ratio and likelihood of the experimental data conforming to the predictions of the disappearance model as a function of the initial release density and transgenic line.

Strain | Initial Release Level | L Ratio | d.f. | p |
---|---|---|---|---|

Ag(DSM)1 | 100% | 34.47 | 5,6 | <0.001 |

50% | 21.07 | 6,7 | <0.001 | |

20% | 4.62 | 6,7 | <0.05 | |

Ag(DSM)2 | 50% | 32.93 | 6,7 | <0.001 |

20% | 9.39 | 6,7 | <0.01 |

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**MDPI and ACS Style**

Valerio, L.; North, A.; Collins, C.M.; Mumford, J.D.; Facchinelli, L.; Spaccapelo, R.; Benedict, M.Q. Comparison of Model Predictions and Laboratory Observations of Transgene Frequencies in Continuously-Breeding Mosquito Populations. *Insects* **2016**, *7*, 47.
https://doi.org/10.3390/insects7040047

**AMA Style**

Valerio L, North A, Collins CM, Mumford JD, Facchinelli L, Spaccapelo R, Benedict MQ. Comparison of Model Predictions and Laboratory Observations of Transgene Frequencies in Continuously-Breeding Mosquito Populations. *Insects*. 2016; 7(4):47.
https://doi.org/10.3390/insects7040047

**Chicago/Turabian Style**

Valerio, Laura, Ace North, C. Matilda Collins, John D. Mumford, Luca Facchinelli, Roberta Spaccapelo, and Mark Q. Benedict. 2016. "Comparison of Model Predictions and Laboratory Observations of Transgene Frequencies in Continuously-Breeding Mosquito Populations" *Insects* 7, no. 4: 47.
https://doi.org/10.3390/insects7040047