Predicting Culex pipiens/restuans population dynamics by interval lagged weather data
© Lebl et al.; licensee BioMed Central Ltd. 2013
Received: 11 February 2013
Accepted: 30 April 2013
Published: 2 May 2013
Culex pipiens/restuans mosquitoes are important vectors for a variety of arthropod borne viral infections. In this study, the associations between 20 years of mosquito capture data and the time lagged environmental quantities daytime length, temperature, precipitation, relative humidity and wind speed were used to generate a predictive model for the population dynamics of this vector species.
Mosquito population in the study area was represented by averaged time series of mosquitos counts captured at 6 sites in Cook County (Illinois, USA). Cross-correlation maps (CCMs) were compiled to investigate the association between mosquito abundances and environmental quantities. The results obtained from the CCMs were incorporated into a Poisson regression to generate a predictive model. To optimize the predictive model the time lags obtained from the CCMs were adjusted using a genetic algorithm.
CCMs for weekly data showed a highly positive correlation of mosquito abundances with daytime length 4 to 5 weeks prior to capture (quantified by a Spearman rank order correlation of r S = 0. 898) and with temperature during 2 weeks prior to capture (r S = 0. 870). Maximal negative correlations were found for wind speed averaged over 3 week prior to capture (r S = − 0. 621). Cx. pipiens/restuans population dynamics was predicted by integrating the CCM results in Poisson regression models. They were used to simulate the average seasonal cycle of the mosquito abundance. Verification with observations resulted in a correlation of r S = 0. 899 for daily and r S = 0. 917 for weekly data. Applying the optimized models to the entire 20-years time series also resulted in a suitable fit with r S = 0. 876 for daily and r S = 0. 899 for weekly data.
The study demonstrates the application of interval lagged weather data to predict mosquito abundances with a feasible accuracy, especially when related to weekly Cx. pipiens/restuans populations.
KeywordsCulex pipiens Culex restuans Cross-correlation map Mosquito vector Population dynamics Predictive model Seasonal cycle
Culex pipiens (Diptera: Culicidae), the northern house mosquito, is widely distributed all over the world except Australia and Antarctica. Cx. restuans is rather similar in morphological characteristics and breeding habitat preferences but exclusively distributed in North America. Both are important vectors for arthropod borne viral infections affecting the health of humans, domestic and wild animals. They transmit diseases like West Nile fever, St. Louis encephalitis, Japanese encephalitis, Western equine encephalitis, and Rift Valley fever[1, 3, 4]. As mosquitoes are poikilothermic animals investigating the Cx. pipiens/restuans population dynamics in relation to factors like ambient temperature and rainfall could help to predict the population dynamics of this species, which is an essential requirement for an efficient vector control.
Previous studies have already confirmed that population densities vary strongly with temperature[5, 6]. This is due to the temperature dependence of the development rates of eggs, larvae and pupae, survival rates of immatures as well as imagos. Temperature also influences the length of the gonotrophic cycle[7–10]. Furthermore, during winter Cx. pipiens/restuans undergo reproductive diapause controlled not only by temperature, but also by daytime length[11, 12].
Also precipitation has already been identified as another important factor influencing Cx. pipiens/restuans population dynamics, as high rainfall occurring several weeks before a capture event was positively correlated with the mosquito abundance[5, 6]. The accurate mechanisms behind this relationship however are less well understood. It has been suggested that rainfall increases the water surface area and therefore possible oviposition sites[6, 13]. Precipitation may also negatively affect mosquito capture, as the immature stages might get washed away by heavy rainfall. Geery recorded a partial flushing of larvae (22–34% reduction) from catch basins in Cook County by rain events < 25 mm and an up to 91% reduction for strong rainfall of > 100 mm. Furthermore, precipitation may also decrease adult activity levels[15, 16].
One of the classical approaches to investigate the relation between mosquito population dynamics and weather data is to correlate their time series[13, 17]. In 2005 Curriero et al. introduced cross-correlation maps (CCMs) as a tool to study the influence of environmental conditions during a time lagged interval (instead of using point lags, i.e., the conditions at a certain time point prior to the capture event) on the abundance of Ochlerotatus sollicitans, another Culicidae species. They demonstrated that lagged time intervals are better adapted to describe the mosquito abundance than point lags. Since then CCMs have been used to illustrate the correlations between various environmental factors and population size of Aedes sollicitans, Ae. vexans, Cx. pipiens, Cx. restuans and Cx. salinarius[5, 19, 20].
The aim of this study is to use interval lagged correlations between environmental factors and observed Cx. pipiens/restuans abundance, gained from CCMs, to develop a predictive model of mosquito population dynamics. This mosquito model should be able to simulate the seasonal cycle of Cx. pipiens/restuans populations and help uncover the temporal scale influences on model performance by comparing daily versus weekly predictions. Such a model would be immensely useful for risk assessment studies i.e. of such arboviral diseases as mentioned above. An analogous study using CCMs and simulated population dynamics of midges was recently presented by the authors for Bluetongue disease in Austria. In this study a mosquito model developed for a spatial scale representative for a major part of Cook County, and not for specific localized capture sites, is introduced. Such models encompassing larger areas are important tools for investigating mosquito born disease outbreaks and their intervention strategies.
Cx. pipiens/restuans capture data
To create a predictive model valid for the whole year, it was necessary to generate a continuous time series of the capture data. As Culex mosquitoes are not active at low temperatures, the mosquito control agency did not operate their traps during winter time. Mosquito counts for winter time, i.e. when no traps were set up, were assumed to be zero (21. Oct. - 30. April). Remaining missing values (6.9%) were replaced by corresponding values of the averaged annual course of the Cx. pipiens/restuans catches (averaged over all years and locations).
For the generation of the predictive model the data set was divided into training and test data. To archive a uniform distribution of the test data over the 20 years the data were split in even and odd years. The odd years were selected by a random process to be the test data set.
In this model the environmental conditions at the capture event (X i ) were also included, as they could affect mosquito activity and thus the capture rate. Please note that j and k for the lags of the five parameters do not necessarily have the same values. Non-relevant terms from this full model were removed in a stepwise procedure to identify the model with the lowest AIC (Akaike’s Information Criterion). The resulting model (CCM) was used to predict the mosquito abundance.
Parameters of the regression models
D 0, 0
D lag 1,lag 2
T 0, 0
T lag 1,lag 2
P 0, 0
P lag 1,lag 2
H 0, 0
H lag 1,lag 2
W 0, 0
W lag 1,lag 2
r S - training
r S - test
RMSE - training
RMSE - test
To test whether those regression models can be used to predict Cx. pipiens/restuans population dynamics we calculated Spearman’s rank correlation coefficient r S (as the data were non-Gaussian distributed) and the root mean square error RMSE between the model predictions and the observations. All statistical analyses were conducted with the freely available statistical computing environment R. The package genalg was used to conduct the genetic algorithm.
The Cx. pipiens/restuans capture rates were positively correlated with daytime length, temperature and precipitation (Figure 3). Humidity and wind speed were negatively correlated with mosquito abundance. The highest correlation was found for daytime length averaged from the fifth and fourth week prior the capture event with r S (5, 4) = 0. 898 (daily r S (39, 28) = 0. 873). Mosquito abundances were highly correlated with the mean temperature of the 2 weeks prior a capture event resulting in r S (2, 1) = 0. 870. The highest daily correlation was estimated for the average temperature calculated from the last 18 days prior the capture day with r S (18, 1) = 0. 853. Of the tested environmental quantities precipitation showed the weakest association with mosquito abundance. The highest correlation for this quantity was found for precipitation averaged over the 10 weeks prior to capture with r S (10, 1) = 0. 487 (daily data: r S (76, 1) = 0. 474). Interestingly, although precipitation was positively correlated with mosquito capture rates, humidity showed to be negatively correlated with mosquito capture rates. The highest effect was found for the humidity averaged over the time period of 15 to 2 weeks prior capture resulting in r S (15, 2) = − 0. 561 (daily data: r S (106, 23) = − 0. 562). A maximum negative correlation of r S (3, 1) = − 0. 621 (daily r S (23, 1) = − 0. 647) was found for wind speed averaged over 3 weeks (23 days) prior to capture.
The OPT model obtained by the genetic algorithm included similar environmental quantities (Table 1).
D 0, 0
D 85, 85
T 0, 0
T 12, 1
P 0, 0
P 51, 16
H 0, 0
H 38, 1
W 119, 86
D 0, 0
D 13, 13
T 0, 0
T 1, 1
P 7, 3
H 4, 1
W 17, 12
Both, the CCM and the OPT model, were able to predict the beginning and the end of the seasonal cycle as well as the inter-annual differences in the amplitude correctly. However, the models produced by the genetic algorithm are better adapted to predict mosquito abundances during mid-summer as they could reproduce the bimodal seasonal peak abundance of some of the years. The advantage of using the optimized time lags obtained by the genetic algorithm compared to implementing the results from the CCMs directly into a regression model is shown by the higher correlation coefficient and lower RMSE (both for the training as well as the test data sets) and by a significantly improved AIC (Table 1).
Temperature dependent life expectancy and development rates make it difficult to distinctly assign the time lags influencing mosquito capture rates to the different developmental stages. Under summer field conditions adult Culex spp. have a mean lifespan of about 1 week[30, 31]. Weather conditions within this period therefore have their main impact on adult mosquitoes. The duration of the aquatic stages also varies with temperature, and weather conditions from about 8 to 20 days prior to capture presumably affect the aquatic stage; weather conditions from about 20 to 28 days affect the adult stage of the parent generation. Previous studies with CCMs considered a time period of about 4 weeks, which approximately represents the lifetime of a mosquito, inclusive all aquatic stages[5, 18, 19]. The results of this study however show that environmental factors have to be considered further back in time. As this exceeds the mean mosquito lifespan, it is likely that weather conditions occurring far back in time do not affect the current population directly, but affect previous generations. Due to exponential growth rates even small effects of weather conditions on a mosquito population could therefore result in vast effects in future generations.
Daytime length may be the most important factor generating the seasonal pattern of mosquito abundance as it regulates - together with temperature - the incidence of diapause. The conditions occurring during pupal development have been shown to determine whether the adult female undergoes diapause[11, 32]. The results of the regression models revealed that maximum mosquito abundance was reached 4 weeks after the longest daytime length. This is also reflected by the results of the CCMs. The shift of 4 weeks between the photoperiod and the mosquito abundance peak may indicate that effects on the pupal stage of the parent generation may be more influential than effects on the current generation.
The time with the strongest effect of ambient temperature was at the time of the capture and the time shortly before this event, indicating that mostly adult mosquitoes were affected. Mosquito capture rates increased with increasing temperature, as already shown in previous studies[5, 6]. Furthermore, it has been demonstrated that considerable changes in the temperature at the capture event compared to the previous days affect the number of captured mosquitoes. Chuang et al. found a similar temperature effect for Cx. tarsalis and Ae. vexans as the authors described a positive influence of temperature at the week of the capture and a lesser negative effect of temperature with a 2 week lag. Thus it seems that female Cx. pipiens/restuans are strongly influenced by temperature changes. This might indicate that they delay flight activities (e.g. host searching) until more favorable temperature conditions occur and considerably decrease their activities at a sudden temperature drops. Sudden temperature changes could not only affect their activity, but could also possibly influence their survival rates.
Capture rates were influenced by rainfall accumulated over long time periods exceeding the typical mosquito life span. This indicates that the amount of precipitation during the previous generation had a stronger effect on the capture rates than the rain falling during the lifespan of the captured mosquitoes. As many of the potential breeding sites, such as shallow temporal ponds, only exist after a certain amount of rainfall, the increased number of breeding sites after rainfall had a positive effect on the number of captured mosquitoes weeks later. Those pools need to be sustained by rainfall for several weeks to ensure the survival of the aquatic stages. At our study site, the suburban area of Chicago, catch basins represent an important breeding site for mosquitoes[14, 33]. In temporary as well as in stagnant water bodies rainfall increases the water volume. This causes a decreasing larval density, which results in increased development rates and decreased mortality rates[34, 35]. Previous studies have shown that high amounts of rainfall decrease the number of mosquito larvae in catch basins dramatically[14, 36]. Interestingly, this negative effect of precipitation on the larvae was not visible in our study where the effects of previous rainfall on the number of adult mosquitoes was investigated. It is possible that this negative effect on larvae, which is noticeable for about 4 days, was overlain by the subsequent longer lasting positive effects mentioned above.
In contradiction to the results from the CCMs, a high relative humidity in the month prior the capture event had a positive effect on mosquito capture rates. This shows that interrelations between environmental quantities may shroud the effect of one quantity on the mosquito capture rates when it is considered without others (as it was done in the CCMs). The regression analysis on the contrary allows to control for the effect of the other quantities included in the model. This positive effect of relative humidity was also found for several Culicidae species, showing that relative humidity influences mosquito activity patterns and the dynamics of oviposition[15, 37].
Experiments by Hoffmann indicate that a high wind speed does not reduce flight activity in mosquitoes, but rather impairs the mosquito orientation by deluding attracting stimuli like CO2 and thus reducing capture rates. The results of this study indicate that the effects of wind on the parent generation may have a more important effect on the capture rates than on the current generation. The negative effect of elevated wind speed in the several weeks prior to the capture event may be caused by a lower chance for a blood meal during this time period.
Mosquito larvae control strategies conducted by the mosquito control agency in the study area were not accounted for in this study. Those strategies have been changed over the course of 20 years in the methods used as well as in efficiency. Aberrations of our model results from the observation data could thus be caused by changes in the used mosquito larvae control strategies. For further applications of the presented models one has to keep in mind that they represent a “managed” Cx. pipiens/restuans population. This is on the one hand a benefit, as in many inhabited areas (in the U.S.A.) there is some kind of mosquito control, especially in endemic areas of mosquito borne diseases like WNV. On the other hand, one has to be careful when adopting this model for other regions.
Cross-correlation maps have been proven to be useful tools in investigating time lagged associations between vector abundance and environmental factors[5, 18–20]. However, as pointed out by Cohnstaedt, there are two major disadvantages of CCMs. First, they do not consider that fact that adults at one time period are a function of the number of adults from the previous generation. And second, that lagged weather variables by a fixed time period ignores the temperature dependence of developmental rates. The first argument concurs with the results of this study. By extending in this study the maximum time lag we were able to reveal that environmental effects on previous generations are likely more important factors describing the number of captured mosquitoes than the effect of those variables on the current generation. With our analyses we are not able to counter the second argument, we can just be careful when interpreting the results found regarding their association to different developmental stages.
The final question is, whether the information gained from CCMs could be used to predict Cx. pipiens/restuans population dynamics. The applicability of the models for daily and weekly predictions depends of course on ones expectations. On both time scales the models resulted in a good predictability of the seasonal cycle. Interannual differences in the mosquito abundance could in large part be reproduced. Especially the optimized model for the weekly data allowed to predict the mosquito abundances to a high degree, and could be of practical use, e.g. planning of mosquito control strategies and simulation of mosquito borne diseases.
We are grateful to Paul Geery from the Desplaines Valley Mosquito Abatement District for providing the mosquito capture data. The study was financed by the Postdoc program of the University of Veterinary Medicine Vienna.
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