The survival of adult female

Here we apply generalised additive models to data from 351 published adult

Our results indicate that adult

Our results support the importance of producing site-specific mosquito survival estimates. By including fluctuating temperature regimes, our models provide insight into seasonal patterns of

Survival of arthropod vectors is one of the most important components of transmission of a vector-borne pathogen [

Adult female

Reconciling the expected difference between laboratory and field survival estimates has been complicated by the lack of precision of available field techniques and the limited temperature ranges over which field experiments have been undertaken. In mosquito cages in the laboratory, conditions can be controlled and the effects of temperature quantified accurately, but additional causes of mortality experienced in the field, such as predation or disease are absent. The most commonly used method for observing

Using laboratory estimates of survival to predict field survival is complicated by the different mortality risks in the two settings, unknown importance of senescence in the field, and the transition from constant laboratory to fluctuating natural temperature regimes. It has long been assumed that the high rate of mortality in the field, due to external causes, ensures few mosquitoes live long enough to experience age-dependent mortality [

Observations from temperature-controlled laboratory experiments have produced a range of candidate parametric functions that are suitable for modelling age-dependent mortality, such as the Gompertz and Logistic functions [

In this study we compiled published observations from a variety of studies and modelled the effect of temperature on survival of adult female

Relevant publications were collected by searching the databases of PubMed, Google Scholar and the Armed Forces Pest Management Board Literature Retrieval System using the search terms

Literature searches for MRR field experiments were completed independently under a parallel project to investigate mosquito movement (Guerra

Where available, the initial number of mosquitoes (for laboratory experiments) and number of deaths/recaptures on each subsequent day of observation (for MRR experiments) were extracted. Where only graphical summaries were available, these observations were recreated using GetData Graph Digitizer [

Summary of laboratory and field data

Number of experiments | 210 | 9 | 141 | 50 |

Mean temperature (^{o}C) (±SD) | 25.9 (22.3-29.5) | 20.3 (17.0-23.7) | 25.5 (21.9-29.1) | 25.5 (22.9-28.3) |

Minimum/Maximum temperature (^{o}C) | 15/35 | 16.7/26 | 10/35 | 20.7/30.1 |

Median number of mosquitoes observed/released (IQR) | 29 (15–40) | 552 (249–1007) | 70 (25–382) | 602 (493–798) |

Dietary regime (%) | Blood: 7.1 | - | Blood: 3.0 | - |

Sugar: 1.0 | Sugar: 38.2 | |||

Blood + Sugar: 91.9 | Blood + Sugar: 58.8 | |||

Age at release (Days) (±SD) | - | 3.2 (0.6-5.8) | - | 3.6 (1.3-5.9) |

SD = Standard deviation, IQR = Interquartile range, MRR = Mark-release-recapture.

A range of parametric equations have been used to model the survival function of laboratory and field adult mosquitoes. For field data, the exponential function, adjusted for recapture number, was the most frequently used model [

The relative likelihood values for each model were averaged for experiments of equivalent temperature to give a balanced estimate of the each model’s suitability at different temperatures.

As the distribution of survival times may undergo complex changes across a range of temperatures we also chose to construct a non-parametric model that would not share the same restrictions as the aforementioned parametric models. For this we chose regression spline generalised additive models (GAMs) which apply a smoothing variable to the explanatory variables in order to model the response variable [

To evaluate the improvement of using GAMs over the parametric alternatives, we fitted parametric and GAM models to each laboratory experiment and calculated the difference in AIC between parametric and non-parametric models across all experiments.

A second GAM was then formulated to use the data from all experiments in one model to recreate the relationship between survival, time and temperature. The GAM was formulated as follows:

_{
ij
} = number of mosquitoes surviving at observation

_{
ij
} = number of mosquitoes at start of time step at

_{
ij
} = survival probability for a mosquito at

_{
i
} = day of observation

_{
i
} = temperature of observation

_{
j
} = random error term for experiment

_{
d
} = random error term for mosquito diet

_{
j
}^{
2
} = variance across experiments

_{
d
}^{
2
} = variance across mosquito diets

Smoothing parameters were selected by restricted maximum likelihood with a data-driven basis dimension choice of _{
D
} _{
T
} = 5 and 5 for

For the model to fit biologically appropriate responses, additional data defining the limits of prediction were required. Observations from Christophers [

Because MRR data was too limited to fit models over a range of temperatures as we did for the laboratory mosquitoes, we used the laboratory-based models above to estimate temperature and age-matched expected mortality rates for mosquitoes in the field and compared those estimates to observed field mortality estimates from MRR data. To simulate the realistic effects of temperature in the field, in contrast to the constant temperatures of the laboratory, we recreated 59 separate daily fluctuating temperature regimes using the maximum and minimum temperatures of each MRR experiment and assumed sinusoidal progression in the day with a decreasing exponential curve at night [

Of the four parametric models tested, no one model was consistently most suitable across the range of temperatures tested (Figure

When non-parametric GAMs were used to fit the same data, both the overall model likelihood and the number of experiments for which it was optimal increased (Table

Evaluation of parametric and non-parametric model fit to laboratory data

Log-Logistic | 320.40/22.620 | 4.4/1.5 |

Gompertz | 304.83/0.005 | 2.2/21.9 |

Exponential | 302.89/2.969 | 1.5/13.8 |

Weibull | 302.90/0.023 | 0.7/13.3 |

GAM | - | 91.1/49.5 |

AIC = Akaike information criterion, GAM = Generalised additive model.

The non-parametric GAM model allowed us to quantify the effects of age and temperature on mortality whilst still taking into account the random effects at the experiment and mosquito diet level. Figures

The greatest uncertainty around these predictions occurs around the 50% survival time (Figure

To estimate longevity in the field, the daily mortality in the laboratory model was compared to field observations of mortality from MRR experiments where other, external factors may contribute to mortality. For

Clear differences in survival can be observed between laboratory models (Figure

When field data uncertainty was incorporated with the existing laboratory model uncertainty, overall uncertainty was reduced due to the higher value of external mortality and the lower uncertainty in estimating this parameter (Figure

In this study we used data from 410

It is also worth considering the scope of the model we developed. While it may suggest that adult survival is possible even at low temperatures, factors limiting the development of the immature stages may preclude the establishment of an adult population. For adult

Here we have shown that GAMs captured more of the variation in survival between different experiments than conventional, parametric models of mosquito mortality, including the Gompertz and logistic models which previously provided the best fit of the options examined [

The relative fit of the GAM indicated the presence of age-dependent survival. This age-related effect may be related to senescence or other factors, but appears to be less important in the wild. On average we found that mortality due to external causes was significantly greater (4.5 times for

The greater tolerance of lower temperatures observed for

The seasonal variation and geographic limits of

Given that dengue is a disease that affects over half the world’s population [

We created an explicit model of

DENV: Dengue virus; MRR: Mark-release-recapture; AIC: Akaike’s information criterion; RL: Relative likelihood; GAM: Generalised additive model.

Disclaimer: The findings and conclusions are those of the authors and do not necessarily represent the official position of the Centers for Disease Control and Prevention.

OJB designed the experiment, wrote the manuscript and collected and analysed the data. MAJ, DLS, TWS, PWG and SIH also helped conceive and design the experiments. MAJ, SB, NG, DMP, DLS and TWS helped with data analysis and interpretation. CAG, HD, MGG, PL, RM and LMS collected data. All authors were involved in drafting and revising the manuscript and all authors approved the final version.

Data bibliography and summary statistics.

Click here for file

We would like to thank Lauren Carrington, Louis Lambrechts, Dalva Wanderley, Maria Macoris, Ephantus J. Muturi and Barry Alto for kindly sharing primary survival data.

O.J.B. is funded by a BBSRC studentship. DMP is funded by a Sir Richard Southwood Graduate Scholarship from the Department of Zoology at the University of Oxford. P.W.G is a Medical Research Council (UK) Career Development Fellow (#K00669X) and receives support from the Bill and Melinda Gates Foundation (#OPP1068048) which also supports S.B. N.G. is funded by a grant from the Bill & Melinda Gates Foundation (OPP1053338). S.I.H. is funded by a Senior Research Fellowship from the Wellcome Trust (095066). This study was partially funded by EU grant 21803 IDAMS (