A climate-driven mechanistic population model of Aedes albopictus with diapause
© Jia et al. 2016
Received: 7 July 2015
Accepted: 12 March 2016
Published: 24 March 2016
The mosquito Aedes albopitus is a competent vector for the transmission of many blood-borne pathogens. An important factor that affects the mosquitoes’ development and spreading is climate, such as temperature, precipitation and photoperiod. Existing climate-driven mechanistic models overlook the seasonal pattern of diapause, referred to as the survival strategy of mosquito eggs being dormant and unable to hatch under extreme weather. With respect to diapause, several issues remain unaddressed, including identifying the time when diapause eggs are laid and hatched under different climatic conditions, demarcating the thresholds of diapause and non-diapause periods, and considering the mortality rate of diapause eggs.
Here we propose a generic climate-driven mechanistic population model of Ae. albopitus applicable to most Ae. albopictus-colonized areas. The new model is an improvement over the previous work by incorporating the diapause behaviors with many modifications to the stage-specific mechanism of the mosquitoes’ life-cycle. monthly Container Index (CI) of Ae. albopitus collected in two Chinese cities, Guangzhou and Shanghai is used for model validation.
The simulation results by the proposed model is validated with entomological field data by the Pearson correlation coefficient r 2 in Guangzhou (r 2 = 0.84) and in Shanghai (r 2 = 0.90). In addition, by consolidating the effect of diapause-related adjustments and temperature-related parameters in the model, the improvement is significant over the basic model.
The model highlights the importance of considering diapause in simulating Ae. albopitus population. It also corroborates that temperature and photoperiod are significant in affecting the population dynamics of the mosquito. By refining the relationship between Ae. albopitus population and climatic factors, the model serves to establish a mechanistic relation to the growth and decline of the species. Understanding this relationship in a better way will benefit studying the transmission and the spatiotemporal distribution of mosquito-borne epidemics and eventually facilitating the early warning and control of the diseases.
Aedes albopitus (Skuse), also known as the Asian tiger mosquito, is a competent vector for the transmission of many blood-borne epidemics such as dengue fever, West Nile virus infections and Chikungunya fever [1–5]. Ae. albopictus is a species native to the tropical areas of Southeast Asia; and during the last century, it has rapidly invaded countries throughout the world. Now the species is pervasively found in the subtropical and temperate climate areas of East Asia, Europe, Africa, the Middle East and the Americas [1, 2]. The extensive spreading of Ae. albopictus is not only prompted by the increasing trend of international trade and travel [3–5] but is also mediated by climate change in a global context . It has been corroborated that the growth of Ae. albopictus is constrained by the changing nature of physical environment; as a result, their population density is extrinsically impinged by a series of climatic factors including temperature, precipitation and photoperiod . Because of this link to climate change, modeling the population dynamics of Ae. albopictus based on climatic factors serves a critical role for further identifying the causal relation to the transmission and control of mosquito-borne pathogens .
Within the realm of quantitative modeling, the climate-driven dynamics of the mosquito has been explored by two types of models: the statistical population model and the mechanistic population model . The statistical population model aims to establish a mathematical correlation between the population abundance and climatic factors using data solicited from controlled experiments or field observations [10–12]. Although these statistical relationships are relatively straightforward and can be easily understood, they are flawed in describing the intrinsic biological mechanism of how the morphology of pathogen carriers is mediated by the environment. Another overlooked facet in the statistical population model pertains to the limited coverage of the species’ life-cycle stages; for example, the majority of mosquito models have only differentiated between the aquatic period and the aerial period, while other sub-stages (e.g. eggs, larvae, pupae) have been less emphasized . When climatic factors are involved in promoting or inhibiting the development, the influence on each sub-stage of the life-cycle is a critical aspect that must be further scrutinized [14, 15]. To overcome these limitations, the mechanistic population model explores the fluctuation of population by factoring in a priori established development process in a context constrained by environment . For the study of Ae. albopictus, this type of model and its variations have been applied to specific geographic regions and have been modified for extensions to other Aedes spp. [16–22]. One important work in this area is attributed to Erickson et al. , who developed a stage-structured population model consisting of six ordinary differential equations to correspond to different stages of Ae. albopictus’ life-cycle, with each equation measuring the mortality rate and growth rate dependent on a stage-specific temperature variable. Thereafter, Cailly et al.  established a generic temperature-driven model that extended the application to different mosquito species. This model served a more general purpose to represent the complete life-cycle with ten model compartments and temperature-driven mortality rate and growth rate [25, 26]. In a follow-up study, Tran et al.  optimized the parameters and transition functions in Cailly’s model to estimate the population dynamics of Ae. albopictus with improved accuracy and a better fit to field observations.
An overlooked area in the formulation of the mechanistic population model is the phenomenon of diapause. Diapause refers to the physiological mechanism within certain species that inhibits the development of organism as a strategy to survive unfavorable environmental conditions, such as extreme weather [28, 29]. Diapause is observed among Ae. albopictus in selected subtropical areas and temperate climate areas where the relatively cold season of a year makes the mosquito eggs become dormant and unable to hatch [7, 30]. The delay in development can only be remedied when the eggs are exposed to enough warmth or a long photoperiod [1, 7]. Many entomologists previously associated Ae. albopictus diapause with environmental conditions using controlled experiments. For example, Wang  and Imai & Maeda  discovered that the intervening factors of diapause included low temperatures and short photoperiods; and this conclusion was later confirmed by a series of controlled experiments [1, 7, 30, 33]. In addition, comparative studies identified that the unique mechanism of diapause greatly improved the survival rate of Ae. albopictus under extreme desiccation and cold-stress conditions [34, 35]. These findings, however, have been rarely incorporated in the mechanistic population model . Two exceptions are the models proposed by Cailly et al.  and Tran et al. , where diapause was quantified as a piecewise function dichotomizing the development into diapause period, say last September through early March, and that of non-diapause for the rest of year. Compared with Erickson et al. , accounting for diapause greatly improved the model performance and generated a close approximation of the field observation. However, the adjustment was based on a relative empirical assumption that diapause occurs in the same time period over different years as well as does not manifest regional differences. As diapause is a dynamic process primarily dictated by degrees of temperature and lengths of photoperiod [31, 32], it is more reasonable to assume diapause as a temperature- and photoperiod-driven phenomenon in a general way to consolidate the effect of temporal as well as regional differences.
Along the line of existing mechanistic population models [23, 24, 27], this paper, proposes a generic model to study Ae. albopictus population by considering diapause as a dynamic process conditional on the change of temperature and photoperiod. By restructuring the model and tuning the parameters, the study strictly captures the stage-specific mechanism of the mosquitoes’ life-cycle. In addition, the model has been validated by field data collected in two Chinese cities over a five-year span where the phenomenon of diapause was introduced by seasonality. The proposed model aims to: (i) define a fine-tuned relationship between major climatic variables (temperature and photoperiod) and diapause-related events in Ae. albopictus’s development cycle; (ii) explicitly quantify the effect of temperature on the population dynamics during the aquatic period based on controlled laboratory experiments and related literature.
The paper is organized as follows. The Methods section first presents the two sets of field observations in Chinese cities, which are employed as evidence for model validation. Then the new model is proposed based on two existing mechanistic population models. The Results section demonstrates simulation results, which are further compared and validated with field observations. The Discussion section discusses the improvement of the model over the original model as well as the sensitivity of non-climatic variables in the model. Lastly, the Conclusions section summarizes the contribution of the study and proposes directions for future research.
Study areas and data
To validate the model, we firstly conducted rigorous field experiments to collect Ae. albopictus larval samples. Field observations on the Ae. albopictus population were conducted in two southern Chinese cities, Guangzhou and Shanghai, over a respective period of five years. The two study areas both belong to the subtropical climate zone with a humid and hot summer and an arid and cold winter. Compared to Guangzhou, the weather in Shanghai exhibits a higher degree of seasonality with a colder spring, autumn and winter.
Monthly CI (in %) of Ae. albopictus larvae in Guangzhou and in Shanghai over a respective five-year period
To correspond to the CI data for each city, we collected daily mean temperature and precipitation data from China Meteorological Data Sharing Service System. We also derived photoperiod data using an existing source . These datasets included Guangzhou over 2007–2011 and Shanghai over 2009–2013.
Basic mechanistic population model
Parameters dependent of climatic variables in the model
Egg hatching rate (day-1)
Larval development rate (day-1)
Dependent of T 
Pupal development rate (day-1)
Dependent of T 
Larval mortality rate (day-1)
Dependent of T 
Pupal mortality rate (day-1)
Dependent of T 
Adult mortality rate (day-1)
Dependent of T 
Oviposition rate by each female (day-1)
Dependent of T 
Gestating adult development rate (day-1)
Environmental carrying capacity for larvae (ha-1)
Environmental carrying capacity for pupae (ha-1)
Parameters independent of climatic variables in the model
Standard environmental carrying capacity for larvae (ha-1)
Standard environmental carrying capacity for pupae (ha-1)
Percentage of females at emergence stage
Egg mortality rate (day-1)
Emerging adult mortality rate (day-1)
Adult mortality rate related to seeking behavior (day-1)
Emerging adult development rate (day-1)
Blood feeding adult development rate (day-1)
Ovipositing adult development rate (day-1)
This proposed basic model is still in need of further scrutiny, in that it overlooks two important mechanistic facets. First, as noted by Cailly et al. [24, 27] and Tran et al. , diapause characterized only by a single binary variable (z dia) appears to be flawed. When applied for a different region, this model is less effective by assuming a static diapause period, say late September through early March (z dia = 0), and the rest of the year as the non-diapause period (z dia = 1) . As diapause is a climate-driven phenomenon that differs across geographic regions and arises on different days , a model that considers the temporal variation of diapause needs to be considered and validated for all life-cycle stages of Ae. albopictus. Secondly, when the effect of diapause is incorporated, the role of climate-dependent parameters (Table 2) needs to be further scrutinized toward a better model performance. To address these two concerns, we propose an improved mechanistic population model that aims to adjust asterisked parameters in Table 2.
Improved mechanistic population model
In this section, we focus on improving the basic model (Equation 2) from two perspectives: model structure and model parameters. First, we integrate the confirmed relationship between diapause-related effects and climatic variables (temperature and photoperiod); and then we restructured the model by quantifying the conditions when the diapause arises. Secondly, we adjust several model parameters, such as development rates, mortality rates and oviposition rate (see asterisked parameters in Table 2).
Model structure: relationship between diapause and climate
During the diapause period (t begin < t < t end), on average Ae. albopictus adults succumb to a temperature of under 9.5 °C (γ Aem = γ Ag = γ Ar = 0 when T aver < 9.5 °C) .To survive such extreme conditions, egg diapause occurs as an adaptive strategy to improve survival rate compared with non-diapause egg [7, 34, 35]. However, the mortality rate and development rate of diapause eggs are less explored by existing literature; and therefore we denote these two parameters as m dia and f dia respectively in Equation 5 and conduct their sensitivity analysis in Results section. In addition to Equation 4, the hatching of diapause eggs is subject to other environmental factors, such as water and food availability [32, 44, 45]. In accordance with Tran et al. , we consider that the hatching is also dependent on the first precipitation event in spring (P week > P 0, where P 0 = 0 mm).
Model parameters: temperature-driven mechanism
Development lengths and mortality rates of Ae. albopictus under different temperatures
Egg hatching length (days)
Larval development length (days)
Pupal development length (days)
Larval survival rate (%)b
Pupal survival rate (%)b
Adult survival length (days) e,c
The scientific significance of the proposed model can only be corroborated by rigorous validation with respect to field data. To prepare for validation, we aimed to derive the simulation results first with an initial population of 106 eggs and a starting time t 0 of January 1st. Then the model was discretized using the Euler Method in MatLab 2015 . Specifically, multiple rounds of simulations were conducted on a daily basis over six years in Guangzhou (2006–2011) and Shanghai (2008–2013). The results derived for the first year (i.e. 2006 for Guangzhou and 2008 for Shanghai) were not used for comparison, as they were strongly dependent on the initial setting [24, 27].
We then compared larva abundance between the monthly observed CI (Table 1) and the monthly simulated results (L R, which is relative to the maximum simulated value over the entire study period) using the Pearson’s correlation coefficient (r). In this case, the study period is 2007–2011 for Guangzhou and 2009–2013 for Shanghai.
Simulated diapause periods
Simulated population abundance
Simulated favorable development period (DOY: F LP or F A >1%) at the larval-pupal stage (L + P) and at the adult stage (A b + A o)
Larval-pupal (F LP > 1%)
Adult (F A > 1%)
Larval-pupal (F LP > 1%)
Adult (F A > 1%)
Figure 6 is the comparison between the observed CI and the simulated L R over a five-year period in Guangzhou and that in Shanghai (Fig. 6). The simulated population is highly consistent with the field observations (CI), with r equals to 0.84 for Guangzhou (Fig. 6a) and 0.90 for Shanghai (Fig. 6b). However, a good match with field data does not fully capture the fluctuation of population, leading to underestimations (green dots) and overestimations (red dots) for certain months. Four apparent underestimations are Oct 2008, May 2010 for Guangzhou and Jun 2011, Jun 2013 for Shanghai.
Figure 7 shows the r 2 for the comparison within each single year. Generally, over a five-year period, Shanghai (Fig. 7l) has a better fit than Guangzhou (Fig. 7f) in terms of r 0 2. Specifically, in Shanghai, the simulation result is overall very satisfactory with the best fit appearing in 2012 (r 0 2 = 0.91, Fig. 7j); in Guangzhou, the simulation result in 2007 is considerably underestimated (r 0 2 = 0.67 compared to the average r 0 2 = 0.71 in Fig. 7f).
These results share similar findings with other case studies in Shanghai [55, 56] and Guangzhou [57, 58]. Specifically, the predicted population growth periods in Shanghai (i.e. F LP > 1 %, March-November; F A > 1 %, April-November, Table 6) parallel with existing studies [55, 56].
It can be seen from Fig. 8 that the change of r introduced by the single-factor sensitivity analysis is generally minor. The overall improvement of r ranges from 0.004 to 0.017 (or 0.4–2.0 %) in Guangzhou and from 0 to 0.016 (0–1.7 %) in Shanghai. The greatest change is observed on parameter σ in the case of Guangzhou and m E in Shanghai. This analysis provides compelling evidence that the proposed model is relatively robust and is not sensitive to non-climatic variables, corroborating the applicability of the model.
This section evaluates the improvement of the new model based on several adjustments to the original model and discusses the difference in model performance between the two study areas.
The results above corroborate the model’s potential in simulating Ae. albopictus population. However, compared to Shanghai (31.2°N), the performance in Guangzhou (23.1°N) seems to be less satisfactory (i.e. curve fitting rate is 90 % for Shanghai and 84 % for Guangzhou, Fig. 6). This regional difference could be explained in two very different respects.
First, the effect of the diapause in the low-latitude area is of arguable existence . Guangzhou is located further south and has comparatively warm and humid winters. The mild climatic conditions could be favorable for certain Ae. albopictus to sustain and develop without taking the strategy of diapause. For example, our field experiments showed evidence that during winter times there were still a very low number of larvae, pupae and adults (Fig. 5) in Guangzhou that could circumvent the process of diapause. This observation was supported by Liu et al.  that found in the same region a small proportion of Ae. albopictus larvae hatched after mid-November could still survive the extreme weather and grow into non-ovipositing adults. A separate evidence could be found in Fig. 9 that applying the diapause-related structural adjustment is less effective in Guangzhou (r: 0.72 → 0.80) than in Shanghai (r: 0.42 → 0.75).
Secondly, the seasonality of Ae. albopictus is relatively complex in tropical climate areas. In an annual development cycle, Ae. albopictus population showed one peak in subtropical climate areas and two peaks with different magnitudes in tropical climate areas . As Guangzhou is located in close vicinity to tropical climate areas, our field observations of CI show interchangeable patterns (i.e. 2007, 2010 and 2011 have two peaks, while 2008 and 2009 have one peak, Fig. 6a). This dynamic pattern created a certain degree of uncertainty for validation and eventually degraded model performance for cases in Guangzhou. Comparatively, Shanghai with an apparent single-peak pattern in the years of study yielded better simulation results (Fig. 6b).
The phenomenon of diapause among Ae. albopictus has been confirmed in most temperate climate areas and is of arguable existence in subtropical climate areas . Generally, low temperatures and short photoperiods create an unfavorable condition for Ae. albopcitus to develop. To survive the extreme conditions, especially during winter times, egg diapause occurs as an adaptive strategy to lower mortality rates [1, 7]. This climate-driven mechanism of diapause has only been explored in a limited manner [24, 27].
This paper proposes a climate-driven mechanistic population model of Ae. albopictus that accounts for the biological phenomenon of diapause. The model is a natural extension of two existing mechanistic population models [24, 27] with emphasis on the climate-driven diapause conditions and stage-specific moderating variables. Although the former models also considered diapause, several issues remained unaddressed, such as identifying the time when diapause eggs are laid and hatched, demarcating the thresholds of diapause and non-diapause periods, and incorporating the mortality rate and the hatching rate of diapause eggs. To remedy these flaws, an improved generic model is proposed, capturing the multifaceted climate-driven mechanism of diapause-related effects. The formation of the model and the attribution of parameters are fine-tuned to existing research and field data collected in two Chinese cities over a respective five-year period. Overall, the simulation results are relatively compelling and fit the majority of our field observations. The study also confirms the respective as well as the joint effects of model structure and temperature-driven parameters, corroborating findings from other mechanistic models [23, 24, 27].
Admittedly, the proposed model is methodologically flawed in several aspects. First, the parameter of precipitation was included but was not closely examined in our model. Existing studies have identified either a positive , a negative , or no influence of precipitation on population abundance . The actual effect of precipitation should be carefully weighted through rigorous field observations before any attempt to quantify the variable in the model. Secondly, in the study only the Container Index was used for model validation and could not fully represent the multifaceted population growth of Ae. albopictus. Future research should explore other monitoring indices, such as the Breteuil Index (BI) and the Housing Index (HI) to generate a solid and robust conclusion. Thirdly, the sensitivity analysis on the non-climatic variables (Table 3) is exclusive of other variables, while the joint effect of multiple variables is not evaluated. In the future the extension of the assessment should include multivariate analysis methods, such as the Fourier amplitude sensitivity testing [59, 61].
Lastly, a promising direction to extend the study considers the incorporation with other non-mechanistic ecological models, such as the GARP  model and the CLIMEX model  and the correlation with epidemic models, such as the SIR model [64, 65] to describe the mechanistic transmission and the spatiotemporal distribution of mosquito-borne epidemics. For example, one such an attempt is the work conducted by Erickson et al.  that integrated the research on Ae. albopcitus population  with an SEIR model . To this end, better understanding the mechanism and variables effecting the Ae. albopictus population growth and improving the model performance will eventually contribute to proactive strategies to predict and prevent contingent mosquito-borne epidemics.
The research was financially supported by National Key Basic Research and Development Plan (2012CB955501) of China Ministry of Science and Technology.
The research was financially supported by National Natural Science Foundation of China (81273139) of China Ministry of Science and Technology.
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