Environ Ecol StatDOI 10.1007/s10651-014-0273-8

Clustering of the abundance of West Nile virus vectormosquitoes in Peel Region, Ontario, Canada

Xiaogang Wang · Jiafeng Wang · Curtis Russell ·Paul Proctor · Richard Bello · Kaz Higuchi ·Huaiping Zhu

Received: 22 September 2012 / Revised: 6 January 2014© Springer Science+Business Media New York 2014

Abstract Understanding the spatial–temporal distribution of vector mosquitoes isessential in designing an efficient mosquito control strategy to reduce the risk of themosquito-borne disease. In this paper, we apply a non-parametric clustering method,CLUES, to the surveillance data of West Nile virus vector mosquitoes collected bylight traps in Peel Region, Ontario, during the mosquito seasons in 2004–2010. Inorder to obtain robust and reliable results, a statistical smoothing procedure LOWESSis applied to the original time series data. It was found that the mosquito trap sitescan be clustered into three groups. The weather impact on the mosquito abundance

Handling Editor: Pierre Dutilleul.

This work was supported by an Early Researcher Award of Ontario, the Pilot Infectious Disease Impactand Response Systems Program of Public Health Agency of Canada (PHAC), Natural Sciences andEngineering Research Council (NSERC) of Canada and Canadian Foundation of Innovations (CFI).

X. Wang · J. Wang · H. Zhu (B)LAMPS, Department of Mathematics and Statistics, York University, Toronto, ON, Canadae-mail: Huaiping@mathstat.yorku.ca

C. RussellEnteric, Zoonotic and Vector-Borne Diseases, Public Health Ontario, Toronto, ON, Canada

P. ProctorEnvironmental Health, Vector-Borne Diseases Team, Region of Peel, ON, Canada

R. BelloDepartment of Geography, York University, Toronto, ON, Canada

K. HiguchiFaculty of Environmental Studies, York University, Toronto, ON, Canada

K. HiguchiAdaptation and Impacts Research Section, Environment Canada, Toronto, ON, Canada

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of each clustered group are similar, while the interannual variability and the highestabundance and peak time in each mosquito season are different. The impact of weatherfactors on this clustering is investigated.

Keywords Abundance · Automatic clustering · Culex pipiens/restuans mosquitoes ·k-Nearest neighbors · Local shrinking · Precipitation · Temperature

1 Introduction

Mosquitoes can carry many diseases, such as malaria, dengue fever, Rift valley fever,West Nile virus (WNV), yellow fever, etc.. To reduce the risk of an outbreak, mos-quito abundance is monitored in the interested areas during the mosquito season by asurveillance program.

WNV is a mosquito-borne infection that first made its appearance in North Americain 1999. It is a human, horse and bird neuropathogen that can result in encephalitis,meningitis and sometimes lead to death. A female mosquito can acquire the virus byobtaining a blood meal from an infected bird and after a few days can then pass thevirus into another host (birds, horses, humans or other domestic animals) when it takesa blood meal. Higher temperature can shorten the virus extrinsic incubation period inthe vector and increase the probability of transmission (Kilpatrick et al. 2008; Richardset al. 2007).

The purpose of mosquito surveillance program is to monitor mosquito popula-tions associated with WNV, determine the level of WNV activity and the virus riskamong these species and use this information to make decisions regarding the riskfor transmission to humans and the need to implement mosquito control plans (PeelPublic Health 2002). Surveillance data of birds and mosquitoes provides an earlywarning of risk to human health and helps to guide education and control interven-tions. In the Region of Peel, Ontario, Canada, WNV was first detected in birds andmosquitoes in 2001, with cases of locally acquired human illness occurring for thefirst time in 2002. In 2002, Peel health unit conducted surveillance activities in theRegion involving dead birds, adult mosquitoes, larval mosquitoes and human cases.Around 40 species of mosquitoes were found in the Region of Peel. Culex pipiensand C. restuans are the primary vectors of WNV, as they prefer to feed on birds, themain reservoir of WNV; and are effective transmitters of the virus. Culex mosquitoesare more common in urban and suburban area using standing water as primary habi-tat. They breed quickly, producing as many as four generations in their life span sothat their numbers can greatly increase in summer when the weather conditions areappropriate.

Since the mosquito abundance in a region is closely related to environmental con-ditions, such as weather and landscape, in order to optimize prevention capabilities,the actions of mosquito control should be designed according to the related environ-mental factors (Patz et al. 2008). Therefore it is important to investigate the spatial andtemporal distribution of vector mosquitoes by which we hope to find a way to studyand determine hot spots and peak times of mosquito abundance in mosquito season;and provide useful information for efficient mosquito control and risk assessment of

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WNV. Understanding the spatial features of mosquito abundance in Peel Region willalso allow us to generalize the modeling studies to other regions in southern Ontario,Canada.

Spatial–temporal clustering is well applied in analyzing data of surveillance pro-grams and epidemiological data of infectious diseases (Mostashari et al. 2003; Artz2011). Its application on the study of mosquito abundance has been seen in design-ing sampling routines for entomological evaluation of vector control (Magbity andLines 2002); grouping the trap-collected mosquitoes (Zhong et al. 2003); classifyingspecies according to breeding habitat (Devi and Jauhari 2007); assessing the mosquitodistribution in qualitative and quantitative ways (Balakrishnan et al. 2011).

In this paper we use a non-parametric clustering technique, CLUES, to analyzethe mosquito abundance data collected under the WNV surveillance program in PeelRegion, Ontario, Canada, to cluster the mosquito traps by similarity in temporal vari-ations. Since the data are time series in natural and vary greatly through the summer,we apply a widely used smoothing technique called Locally Weighted ScatterplotSmoothing (LOWESS) to smooth the data in order to obtain reliable and robust clus-tering results. The attributes of weather, represented by temperature and precipitation,on the spatial–temporal variation in the trapped mosquitoes in Peel Region, is alsoinvestigated.

2 Data: mosquito surveillance and weather

Our study area is Peel Region, Ontario, Canada, which is located in the Greater TorontoArea (GTA),consisting of the City of Mississauga, the City of Brampton, and theTown of Caledon. Peel Region has the second-largest population in Ontario afterToronto. Its geographical span is about 20 km (west to east) by 50 km (south tonorth), extending from Lake Ontario lakeshore in Mississauga to Oak Ridges Moraine.Its central location is around 43.6N and 79.7W and the climate belongs to humidcontinental climate zone with four seasons. The regional topography slopes fromnorthwest to southeast towards Lake Ontario. The topographic elevations range from300 meters above sea level (masl) at the northwestern corner to about 80 masl near LakeOntario. Credit River, Etobicoke Creek, Mimico Creek, and West Humber River runacross the region. The Region can be roughly described as predominately urban andcharacterized by comparatively new large-tract suburban developments, although thenorthern portion (Caledon) of the region is predominately rural agricultural (Drackleyet al. 2011).

2.1 Mosquito surveillance program in Region of Peel, ON

The WNV surveillance program in Peel Region was initiated by the Government ofOntario in 2001. The data on mosquito, dead bird and human infection cases werecollected during the mosquito season from June to September. The adult mosquitoeswere captured by CDC (Center of Disease Control and Prevention) light traps, whichcontained dry ice (CO2) to attract blood-seeking mosquitoes. The mosquitoes werecollected one night a week from each trap location. The trap was set in the late afternoon

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Fig. 1 Positions of mosquito trap sites and weather station in Peel Region, Ontario, Canada

and picked up the next morning. Then the mosquito samples were immobilized byfreezing and sent to a biological lab for species identification and viral testing. In theearly years, the setup of mosquito traps followed human infection cases, so there wasno continuous observation for a fixed location. Since 2004, all mosquito traps werepermanent traps with fixed trap sites, under the rule that at least one trap existed ineach ward (Fig. 1). Therefore the data from 2004 to 2010 was used in this study. Thereare 29 traps having complete data in the past 7 years, two more traps were set up inlater years.

From Fig. 1, we can see that most traps are located in the south (the City of Missis-sauga, 16 traps), and the central areas (the City of Brampton, 9 traps). Only four trapsare in the northern rural area (the Town of Caledon). The average distance betweenall the trap sites is 6.6 km.

The main vectors for WNV in Peel Region are C. pipiens and C. restuans (PeelPublic Health 2002). They are found in similar habitats, prefer water with high organicmatter, and are found in urban environments. They also have close morphologicalfeatures, making it difficult to separate them from the trapped samples because theymay lose their morphological identification features in the capture process. Due tothe time limit for virus monitoring, the majority of C. pipiens and C. restuans are

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Fig. 2 Abundance curves for two separate mosquito traps from Peel Region

combined as C. pipiens/restuans in the adult mosquito data collected for public healthapplication. Earlier studies (DeGaetano 2005; Trawinski and MacKay 2008; Wanget al. 2011) also grouped C. pipiens/restuans to represent WNV vector mosquitoesin the study area. For each trap, the original count was smoothed over preceding andsucceeding weeks to reduce random effects, such as moonlight, on capture probabilities(Service 1993). The collected mosquito counts can vary largely according to time anddifferent mosquito trap sites. Figure 2 shows the mosquito abundance curves in twotraps as example.

2.2 Weather conditions and index

Temperature and precipitation are two major related weather factors to be used to studythe mosquito abundance. The warmer weather can accelerate the aquatic stages of thedevelopment of mosquitoes and rich precipitation can create more standing waterfor mosquitoes to lay their eggs. The weather data recorded at the weather stationabutting Pearson International Airport (See Fig. 1), is the only station with completetemperature and precipitation records in Peel Region during the study period. The dailymean temperature and precipitation data for the region were obtained from NationalClimate Data Archive (http://climate.weatheroffice.gc.ca/Welcome_e.html).

Considering the Culex mosquito biology, a temperature derivative, the degree day(DD) based on a reference temperature of 9 ◦C (Madder et al. 1983), was used torepresent the lower temperature limit for mosquito development:

DD ={

T − 9, if T > 9,

0, if T ≤ 9.

The weekly mean daily temperature and precipitation for each mosquito season in2004–2010 are displayed in Fig. 3.

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Fig. 3 Weekly mean daily temperature (◦C) and precipitation amount (mm) recorded at Pearson Airport

3 Clustering using smoothed data

3.1 Nonparametric clustering

Clustering is the process of partitioning a set of objects into subsets based on somemeasure of similarity (or dissimilarity) between pairs of objects. For many clusteringalgorithms, such as K-means (MacQueen 1967; Hartigan and Wong 1979) and PAM(Kaufman and Rousseeuw 1990), the number of clusters or sub-populations needs tobe specified by the user. The determination of the number of clusters is one of the mostdifficult problems in cluster analysis. One of the most widely used methods for estimat-ing the number of clusters or sub-population is based on optimizing a certain measureof strength of the clusters (Tibshirani et al. 2000; Fraley and Raftery 2002). A non-parametric alternative is to dynamically move data points toward cluster centers and usethe number of convergence points as a natural estimate of the number of clusters. Thekey issue here is how to move data points toward their cluster centers. One approach,gravitational clustering (Wright 1977; Kundu 1999; Sato 2000; Wang and Rau 2001)can be interpreted from the point of view of field theory in physics: each data pointis considered as a particle of unit mass with zero velocity which is gradually movingtoward the cluster center due to gravitation. Another approach, mean-shift cluster-ing (Fukunaga and Hostetler 1975; Cheng 1995; Comaniciu and Meer 1999, 2000,2001, 2002) originates from the ideas in kernel density estimation: data points aretransformed toward denser regions by using kernel functions.

Wang et al. (2006) proposed an automatic clustering algorithm that determines thenumber of clusters and the partition without any input parameter except the conver-gence criterion. In their algorithm, however, the shrinking process is determined bythe K-nearest neighbour approach (Mack and Rosenblatt 1979) instead of kernel func-tions. It can be very adaptive to the local topological structure of the sample space andwell suited for dealing with high-dimensional sparse samples. This property leads tobetter clustering especially when the clusters are of irregular shapes. Since this cluster-ing algorithm is dictated by the K-nearest neighbor approach and the final partition is a

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function of K, one would ask how this value should be determined. Wang et al. (2006)resolved this issue by maximizing an objective function that can measure the qualityof any partition associated with each particular choice of K. To be more specific, theiralgorithm starts from a small K and gradually increases the size of K until a measureof the strength of clusters, such as the CH index or the Silhouette index, is optimized.The estimation of the number of clusters and the ultimate partition are then obtainedsimultaneously based on the optimal K.

Let the underlying probability distribution function G(x), x = (x1, x2, . . . , xn) ∈Rn , be a non-negative continuous function, where n is the dimensionality. We choosethe norm, ||·||, to be Euclidean distance. Then, for any given α, x̄ = (x̄1, x̄2, . . . , x̄n) ∈Rn , define a set

B (x̄, d) = {x ∈ Rn : ||x − x̄|| < d} ⊂ Rn (1)

such that ∫B(x̄,d)

G(y)dy = α. (2)

where the radius d of the set B (x̄, d) depends on the value of α. If α is set to 0, thenB (x̄, d) is a singleton set. To avoid this trivial case, we assume that α is positive inthe sequel. It is obvious that the value of α is bounded by αM = ∫

RnG(x)dx > 0.

From the previous approximation xk with parameter α > 0 and radius parameterd > 0 obtained from (3) with x̄ = xk , the new step approximation of the optima isdefined as

xk+1 = 1

α

∫

B(xk ,d)

yG(y)dy, (3)

with initial guess x0 being given. The new position xk+1 is the ratio of the first-ordermoment over the zero-order moment on the local region. It is clear that the iterationat each step k > 0 only depends on the local integration over B(xk, d). If G(x) is aprobability density function, then xk+1 represents the conditional mean on B(xk, d).Meanwhile, the new approximation xk+1 also depends the choice of the parametersα and d. However, the true underlying probability distribution is unknown. An non-parametric estimation is defined as

xk+1i = median

x[t]j ∈NK

(x[t]

i

)x[t]j , (4)

where NK (x[t]i ) is the smallest sphere that contains K nearest neighbors of the data

point x[t]i .

This dynamic procedure is iterated unless a pre-specified convergence criterion issatisfied. The clusters formed in this process including memberships and number ofclusters are then determined automatically after the convergence is observed. Detaileddescription of the CLUES algorithm can be found in Wang et al. (2006). A freecomputer package CLUES in R is available together with detailed descriptions andinstructions on how to use it. Instruction manual can be found at http://cluescran.r-project.org/web/packages/clues/index.html

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3.2 Smoothing data using LOWESS

It can be seen from Fig. 2 that the number of observations could change drastically from1 week to the next. It presents a significant challenge for any clustering algorithm sincethey all must employ a distance function in order to form homogenous groups. Anyanomaly would introduce distortions into the clustering process due to its dominatingpresence in the computation required for a proper partition. Furthermore, the main goalof clustering is not to predict the weekly outcome. Instead, the main goal of clusteringis to partition the sites with similar patterns together in order to build area-specificmathematical or statistical model.

To achieve a reliable and robust clustering result, some data preprocessing is neces-sary. We employ a smoothing technique called LOWESS to exact complicated patternby reducing the impact of random noise. This smoothing technique has been proposedby Cleveland (1979) and widely used in data analysis, see Simonoff (1993). It is anon-parametric local regression for smoothing data.

The underlying model in LOWESS for weighted local regression is given by

E(Yi ) = g(ti ) + εi , (5)

where the Yi are the actual of counts and ti are the observation times. The function gis assumed to be unknown. The model is represented by two parts: the deterministicpart g which represented an unknown underlying non-random process and the randompart εi which represents noise or the impact of unknown factors involved in the dataobserving process.

Since the deterministic part is assumed to be unknown, it is often approximatedlocally by a polynomial. For a given order of polynomial, the coefficients βk of apolynomial at a given time point t is determined by minimizing the following lossfunction:

minβ0,β1,··· ,βp

n∑i=1

w

(ti − t

h

) (yi −

p∑k=0

βk tki

)2

, (6)

where w is a weight function and h is the bandwidth which controls the magnitude ofsmoothing. Confidence interval can also be obtained for the local regression. Detaileddiscussions can be found in Cleveland and Devlin (1988).

Since the LOWESS estimates the mean function by trying to remove the noise, wethen apply the CLUES algorithm to the smoothed data to partition the data accordingto the estimated mean functions. Results are presented in the next section.

4 Results

4.1 Clustering results

By applying the CLUES algorithm in conjunction with the LOWESS method describedin previous section, we obtained a partition of all traps and found three clusters. Cluster1 has thirteen trap sites, Cluster 2 has ten and Cluster 3 has six. The spatial distributionof of three clusters are displayed in Fig. 4.

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Fig. 4 Clusters of mosquitotraps in Peel Region

Fig. 5 Seasonal trends for three clusters with smoothing parameter of 10 %

It can be seen that 37.5 % of Mississauga traps (six), half in the north and half inthe south, one third of Brampton traps (three), and all traps in Caleton (four) belongto Cluster 1; over 40 % of traps in Mississauga (seven), mainly in the south (six), onethird in Brampton (three), locating in central Brampton, belong to Cluster 2; threetraps in Mississauga, at the corners of this region, and three in Brampton belong toCluster 3. The time series data of each cluster is analyzed in the following, by usingLOWESS procedure by using 10 % as smoothing parameter. The smoothing curvesrepresenting the deterministic patterns for these three clusters shown in the Fig. 5.

It can be seen that values in Cluster 1 was always the lowest among the three. Aminor upward trend can be seen due to the increased peak values in 2008–2010. In2004–2008, the levels in Cluster 2 and 3 are close, and the upward trend is clear in bothof them. After 2008, the upward trend in Cluster 3 continued, while the trend in Cluster2 turned down. Cluster 3 with the smallest number of traps (six traps), is the cluster

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Table 1 The weeks with peakmosquito abundance in eachcluster

2004 2005 2006 2007 2008 2009 2010

Cluster 1 31 29–30 31–32 29–30 31 33 32

Cluster 2 30 31 30 27–31 31–32 32–33 29

Cluster 3 32 31–32 27–29 29–31 32 27, 34 29

with the largest value of captured mosquitoes and the most volatility, which mainlyoccurred in the last 3 years. The highest value happened in 2010, and the averagedcount per trap night was over 70 C. pipiens/restuans mosquitoes.

Most of the peak values were reached in the middle of the season in Cluster 1,except a delay in 2009. A flat top in the time series is seen in 2007 in Cluster 2 whichrepresents a peak during that summer. The peak in 2009 was much earlier than otheryears. In cluster 3, the counts in 2009 and 2010 significantly exceeded the other twoclusters. The weeks with peak values in 2004–2010 are listed in Table 1.

The peak weeks of the three clusters are mostly overlapped, concentrating in weeksaround 29–31. In general, the peaks lasted 1–2 weeks, except in cluster 2 in 2007which lasted 5 weeks. In 2009, two peaks were seen in Cluster 3. In 2010, the peak inCluster 1 lagged 3 weeks behind clusters 2 and 3.

From Fig. 3, we can see that 2004 and 2009 had cooler summers while 2005’ssummer was the hottest. Furthermore, 2007 is the driest season and 2008 is the wettest.The precipitation in 2004–2006 was close to the 30-year average (1971–2000) and wellabove the normal in 2008–2010. It exceeded the normal by >50 % in 2008, while in thepreceding year 2007, the precipitation was only half of the historical average, whichwas almost the driest summer for the past 90 years according to meteorological records.The relationships between weekly mosquito abundance and the weather conditions inthe preceding week for each cluster are displayed in Fig. 6.

In Fig. 6, the x-axis is the accumulated degree days (ADD) for the precedingweek before mosquito sampling, the y-axis is the accumulated precipitation for thepreceding week. The contour line is the averaged mosquito abundance per trap in eachcluster. In Cluster 1, the range of abundance is around 1–10 mosquitoes per trap, themost favorable weather for mosquito abundance is 70–100 ◦C ADD, and 50–70 mmaccumulated precipitation. A second favorable weather condition could be 50–60 ◦CADD and 20–30 mm in precipitation. It is a relatively cooler and drier condition, andthe abundance level is about the half of the abundance when compared with the mostfavorable weather conditions.

In Cluster 2, the range of abundance is 3–30 mosquitoes per trap, which is higherthan that of Cluster 1. Two favorable weather conditions can be seen: (1) 75–90 degreedays and 50–65 mm of accumulated precipitation; (2) 80–90 degree days and 25–35mm of precipitation. The temperature conditions are close, while there is a big gapin precipitation. The 80–90 ◦C is at the historical average of the weekly accumulateddegree days in July and August. In addition, the weekly total precipitation around60 mm deviates from the amount under a normal weather which is 70–80 mm forJune to September. The contour also shows that the warm and wet conditions canresult in more mosquitoes, since the level ’25’ curve extends to the top right corner.

In Cluster 3, the maximal abundance is even higher than that of cluster 2; the rangeof abundance is 5–50 mosquitoes per trap. There are several centers with high values

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Fig. 6 Mosquito abundance andweather (temperature andprecipitation)

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with the dominant two are seen under such weather conditions: (1) 80–110 degree daysand > 50 mm precipitation; (2) 90–110 degree days and about 10 mm precipitation.The fact that the high level of contour curve extends to both low and high temperatureconditions in the upper pattern implies that the high precipitation can prompt mosquitoabundance consistently.

Among the three clusters, the most favorable warm conditions are almost identical:the temperature of July and August. This might explain the similar weather patternsin all three clusters: the peaks are seen in the middle of the mosquito season, as shownin Fig. 5. This also explains the high mosquito abundance in 2008–2010, since thesethree summers had plenty of rainfall. While, the impacts of precipitation are diverseamong the clusters (see Fig. 5): For the wettest summer in 2008, its abundance iscomparable to the following 2 years (2009 and 2010) in Cluster 1. The highest valueis seen in Cluster 2; and the abundance in 2009 and 2010 are even higher than that of2008 in Cluster 3. It is interesting to see that in the driest year, 2007, the abundancein Cluster 2 is not low when compared with other years. This might be due to the factthat a warm and dry condition could also be helpful to mosquito capture, as displayedat bottom right in Fig. 6.

Since there are significant differences in abundance under the same temperatureand precipitation, it suggests that other weather factors, such as wind, or other envi-ronmental factors, such as land surface cover, may also influence mosquito abundance.

The smoothed curves together with their corresponding 95 % CI are plotted for theclusters (Fig. 7). It is expected that large observations is always accompanied by widerconfidence intervals. Intuitively, this makes sense since the level of variation of countsmight be proportional to the average level of response.

Figure 7 presents the time series and confidence intervals produced by LOWESSwith smoothing parameter of 10 %. We observe that the confidence interval is notsymmetric with the upper half wider than the lower portion in general.

5 Concluding remarks

The trap sites of WNV vector mosquitoes in Peel Region, Ontario, Canada are found toform three groups according to their temporal variation patterns. The impact of weatherconditions on the mosquito abundance in each group are similar while the variabilitiesand the maximum values in each mosquito season are different. By comparing thetemperature and precipitation, patterns in the three mosquito abundance time seriescan be explained. The warm weather condition in July and August is favorable tomosquito abundance. We believe that this is the reason for observing the peak values inthe middle of the season. Precipitation is also known to affect the mosquito abundance.We would like to point out that the relationship is not linear, since the highest rainfall in2008 did not generate highest abundance. In Cluster 2, both the wet and dry conditionscan prompt mosquito abundance. The high values are seen in summer of both 2007and 2008, one with extreme dryness and the other with extreme wetness. The differentresponse to the precipitation may be attributed to the different landscape compositionaround the trap sites, such as woods, grass, slope, or soil characteristics, etc, whichcan modulate the weather impacts. For example, water from the rainfall can last for a

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Fig. 7 LOWESS confidence interval for cluster 1–3

longer time at a lower or shaded area, which can turn into a mosquito development site.In the drier years, there was lots of sunshine and the permanent water could be easilywarmed up to accelerate the mosquito development. Additionally, in drier years, thereis less precipitation to wash-out urban catch basins; which are good development sites

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for C. pipiens/restuans. Since these catch basins are not exposed to direct sunlight,they may retain accumulated water over the mosquito season. In years with heavyprecipitation, the catch basins can be flushed out and result in removal of immaturemosquitoes. The landscape in the trap sites of Cluster 1 may reduce the effects ofweather conditions. We believe that this is the main reason for the fact that the bothvariability in cluster 1 and the magnitude are small. The time series associated withCluster 2 and 3 ran close in 2004–2008, while they deviate from each other in 2009–2010. We observe that the high precipitation continuously increased the abundance inCluster 3 while decreased the abundance in Cluster 2. This difference in abundancemay also be attributed to the landscape features. We believe that the observed temporalvariation might be related to warmer weather, while the magnitude is modulated byprecipitation and landscape features which might be the cause of spatial variations.

In this paper, our clustering technique is used to study the impact of weather con-ditions on mosquito abundance, which is one of the first few steps towards the devel-opment of a toolkit for public health for control and prevention of WNV. We expectthat these results can be used for improving the efficiency in mosquito control byconsidering the spatial–temporal variations among different trap clusters. The resultscould also be helpful for building a mathematical or statistical model for mosquitodensities by clusters. To improve the simulation of vector mosquito populations, bothweather and landscape factors should be considered in the modeling. The traps inthe same cluster can be grouped together to increase the sample size for developingmosquito population models for a finer spatial scale, such as community level relatedto an individual mosquito trap. We leave this as our future work when the landscapeinformation around each trap site in the region becomes available.

Acknowledgments The authors would like to thank the editor, the associated editor and two reviewersfor their valuable comments and suggestions that greatly improve the quality and presentation of the paper.The opinions, results and conclusions reported in this paper are those of the authors. No endorsement bythe Ontario Agency for Health Protection and Promotion is intended or should be inferred.

References

Artz M (2011) Surveillance and epidemiology of infectious diseases using spatial and temporal cluster-ing methods. Integrated series in information systems, 1, vol 27. Infectious disease informatics andbiosurveillance. Part 2, pp 207–234

Balakrishnan S, Srinivasan M, Elumalai K (2011) A survey on mosquito diversity in Parangipettai coast,southeast coast of Tamilnadu, India. J Entomol 8:259–266

Cheng Y (1995) Mean shift, mode seeking, and clustering. IEEE Trans Pattern Anal Mach Intell 17:790–799Cleveland WS (1979) Robust locally weighted regression and smoothing scatterplots. J Am Stat Assoc

74:829–836Cleveland WS, Devlin SJ (1988) Locally weighted regression: an approach to regression analysis by local

fitting. J Am Stat Assoc 83:596–610Comaniciu D, Meer P (1999) Mean shift analysis and applications. In: Proceedings of the seventh interna-

tional conference on computer vision, pp 1197–1203Comaniciu D, Meer P (2000) Real-time tracking of non-rigid objects using mean ahift. In: Proceedings of

IEEE conference on computer vision and pattern recognition (CVPR’00). vol 2, pp 142–149Comaniciu D, Meer P (2001) The variable bandwidth mean shift and data-driven scale selection. In: Pro-

ceedings of the eighth international conference on computer vision, vol 1, pp 438–445Comaniciu D, Meer P (2002) Mean shift: a robust approach toward feature space analysis. IEEE Trans

Pattern Anal Mach Intell 24:603–619

123

Environ Ecol Stat

DeGaetano AT (2005) Meteorological effects on adult mosquito (Culex) population in metropolitan NewJersey. Int J Biometeorol 49:345–353

Devi NP, Jauhari RK (2007) Mosquito species associated within some western Himalayas phytogeographiczones in the Garhwal region of India. J Insect Sci 7:32

Drackley A, Newbold KB, Taylor C (2011) Defining social-based spatial boundaries in the Region of Peel,Ontario, Canada. Int J Health Geogr 10:38

Fraley C, Raftery AE (2002) Model-based clustering, discriminant analysis, and density estimation. J AmerStat Assoc 97:611–631

Fukunaga K, Hostetler LD (1975) The estimation of the Gradient of a density function, with applicationsin pattern recognition. IEEE Trans Inf Theory 21:32–40

Hartigan JA, Wong MA (1979) A K-means clustering algorithm. Appl Stat 28:100–108Kaufman L, Rousseeuw PJ (1990) Finding groups in data: an introduction to cluster analysis. Wiley, New

YorkKilpatrick AM, Meola MA, Moudy RM, Kramer LD (2008) Temperature, viral genetics, and the transmis-

sion of West Nile virus by Culex pipiens mosquitoes. PLoS Pathog 4:e1000092. doi:10.1371/journal.ppat.1000092

Kundu S (1999) Gravitational clustering: a new approach based on the spatial distribution of the points.Pattern Recognit 32:1149–1160

Mack YP, Rosenblatt M (1979) Multivariate k-nearest neighbor density estimates. J Multivar Anal 9:1–15MacQueen JB (1967) Some methods for classification and analysis of multivariate observations. In: Proceed-

ings of 5th Berkeley symposium on mathematical statistics and probability, vol 1, Berkeley. Universityof California Press, CA, pp 281–297

Madder DJ, Surgeoner GA, Helson BV (1983) Number of generations, egg production, and developmentaltime of Culex pipiens and Culex restuans (Diptera: Culicidae) in Southern Ontario. J Med Entomol20:275–287

Magbity EB, Lines JD (2002) Spatial and temporal distribution of Anopheles Gambiae s.l. (Diptera: Culi-cidae) in two Tanzanian villages: implication for designing mosquito sampling routines. Bull EntomolRes 92:483–488

Mostashari F, Kulldorff M, Hartman JJ, Miller JR, Kulasekera V (2003) Dead bird clustering: a potentialearly warning system for West Nile virus activity. Emerg Infect Dis 9:641–646

Patz JA, Olson SH, Uejio CK, Gibbs HK (2008) Disease emergence from global climate and land usechange. Med Clin N Am 92:1473–1491

Peel Public Health (2002) West Nile virus. http://www.peelregion.ca/health/vbd/whatis-WNV.htmRichards SL, Mores CN, Lord CC, Tabachnick WJ (2007) Impact of extrinsic incubation temperature and

virus exposure on vector competence of Culex pipiens quinquefasciatus Say (Diptera: Culicidae) forWest Nile virus. Vector Borne Zoonotic Dis 7:629–636

Sato Y (2000) An autonomous clustering technique. In: Kiers, ALH, Rasson, J-P, Groenen, PJE, Schader,M (eds) Data analysis, classification, and related methods. Springer, Berlin

Service MW (1993) Mosquito ecology: field sampling methods, 2nd edn. Chapman and Hall, LondonSimonoff JS (1993) Smoothing methods in statistics. Springer, BerlinTibshirani R, Walther G, Hastie T (2000) Estimating the number of clusters in a dataset via the gap statistic.

Technical report 208, Dept of Statistics, Stanford UnivTrawinski, MacKay DS (2008) Meteorologically conditioned time-series predictions of West Nile virus

vector mosquitoes. Vector-Borne Zoonotic Dis 8:505–521Wang J, Ogden NH, Zhu H (2011) The impact of weather conditions on Culex pipiens and Culex restuans

mosquito abundance: a case study in Peel Region. J Med Entomol 48:468–475Wang JH, Rau JD (2001) VQ-agglomeration: a novel approach to clustering. IEE Proc-Vis Image Signal

Process 148:36–44Wang X, Qiu W, Zamar RH (2006) CLUES: a non-parametric clustering method based on local shrinking.

Comput Stat Data Anal 52:286–298Wright WE (1977) Gravitational clustering. Pattern Recognit 9:151–166Zhong H, Yan Z, Jones F, Brock C (2003) Ecological analysis of mosquito light trap collections from west

central Florida. Environ Entomol 32:807–815

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Xiaogang Wang is currently an Associate Professor in Statistics at the Department of Mathematics andStatistics of York University. He obtained his Ph.D. in Statistics from University of British Columbia in2001. His research interests include statistical learning and likelihood inference. He has published paperson likelihood inference, clustering and optimization. He is currently working building statistical modelsfor spatial and temporal data.

Jiafeng Wang , Ph.D. in atmospheric science from Institute of Atmospheric Physics, Chinese Academyof Sciences, Beijing, China. He was awarded an NSERC visiting fellowship at Climate Research Branch(CRB), Environment Canada (EC) and now a postdoctoral fellow at Department of Mathematics and Sta-tistics, York University working on the project “Modeling climate and environmental change on vector-borne disease”, under the supervision of Prof. Huaiping Zhu. The interdisciplinary project involves variousexpertise and tools, such as dynamical system, data mining and analysis, statistical modeling, geographi-cal information system (GIS), climate change downscaling, etc.

Curtis Russell received his Ph.D. in biology from Brock University focusing on mosquitoes and theirpotential to vector West Nile Virus to humans. Curtis works for Public Health Ontario where he is aprogram consultant within the Enteric, Zoonotic, and Vector-Borne Diseases section. There he providesexpert consultation to Ontario’s heath units on vector-borne diseases such as West Nile Virus and Lymedisease.

Paul Proctor, the supervisor of the Vector-Borne Disease Team and Environmental Health of Peel Region,Ontario. He has been in charge of the mosquito surveillance program in Peel Region since 2001.

Richard Bello, Ph.D. 1982 McMaster, Associate Professor, Department of Geography, York Universityspecializing in boundary layer climates, plant-atmosphere interactions and evapotranspiration.

Kaz Higuchi, Ph.D. in atmospheric physics from University of Toronto, now adjunct professor in envi-ronmental studies. His research interest includes Complex systems and agent-based modelling, climatechange science and climate change adaptation strategy development. He has contributed towards (a)enhanced understanding of the dynamics of atmospheric low-frequency variability modes (particularly,the North Atlantic Oscillation) and their impacts; (b) development of inverse modelling strategies forglobal estimation of carbon sources and sinks, and, (c) enhanced understanding of the contribution ofatmospheric transport to the measurements of carbon dioxide.

Huaiping Zhu, Ph.D. in mathematics from Montreal in 2000, now an associate professor in the Depart-ment of Mathematics and Statistics. His research interest includes dynamical systems, bifurcation the-ory and applications, Hilbert’s 16th Problem; modelling and analysis in ecology and epidemiology.Regional climate modeling, dynamics of climate impact and vector-borne diseases, mosquito-borne dis-eases, malaria, dengue and West Nile virus. Currently he is the Project leader of the “Modeling and RiskAssessment of West Nile Virus Transmission under Global Warming”, Canada’s Clean Air Agenda: PilotInfectious Disease Impact and Response Systems (PIDIRS) Program, Public Health Agency of Canada(PHAC). His research and his team have been supported by NSERC, Mathematics of Information Tech-nology and Complex Systems (MITACS), Canadian Foundation of Innovation (CFI), Ontario Ministry ofEnvironment and an Early Researcher Award (ERA) of Ministry of Research and Innovation, Ontario.

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