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J Appl Ecol. 2019;56:2225–2235. wileyonlinelibrary.com/journal/jpe

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© 2019 The Authors. Journal of Applied Ecology
© 2019 British Ecological Society
Received:12Augus t2018

Accepted:27April2019
DOI : 10.1111/136 52664.1345 4
RESEARCH ARTICLE
Applying the N‐mixture model approach to estimate mosquito
population absolute abundance from monitoring data
Mattia Manica1,2  Beniamino Caputo2  Alessia Screti2  Federico Filipponi2 
Roberto Rosà1,3  Angelo Solimini2  Alessandra della Torre2  Marta Blangiardo4
1Department of Biodiversity and Molecular
Ecology, Research and Innovation
Centre, Fondazione Edmund Mach, San
Michele all'Adige, Italy
2Dipar timento di Sanit à Pubblica e
Malattie Infet tive, L aboratory affiliated to
Istitu to Paste ur Italia – Fondazione Cen ci
Bolognetti, Sapienza University of Rome,
Rome, Italy
3Center Agriculture Food
Environment, University of Trento, San
Michele all’Adige, Italy
4MRC Centr e for Environment a nd
Health, Department of Epidemiology and
Biostatisti cs, School of Public Hea lth,
Faculty of Medicine, Imperial College
London, London, UK
Correspondence
Marta Blangiardo
Email: m.blangiardo@imperial.ac.uk
Handling Editor: Michael Pocock
Abstract
1. Estimating population abundance is a key objective of surveillance programmes,
particularly for vector species of public health interest. For mosquitos, which are
vectors of human pathogens, established methods to measure absolute population
abundance such as markreleaserecapture are difficult to implement and usually
spatially limited. Typically, regional monitoring schemes assess species relative
abundance (counting captured individuals) to prioritize control efforts and study
species distribution. However, assessing absolute abundance is crucial when the
focus is on pathogen transmission by contacts between vectors and hosts. Here,
we applied the Nmixture model approach to estimate mosquito abundance from
standard monitoring data.
2. We extended the Nmixture model approach in a Bayesian framework by consid
ering a betabinomial distribution for the detection process. We ran a simulation
study to explore model performance under a low detection probability, a time
varying population and different sets of independent variables.
3. When informative priors were used and the model was well specified, estimates
by Nmixture model well correlated (>0.9) with synthetic data and had a mean
absolute deviation of about 20%. Correlation decreased and biased increased with
uninformative priors or model misspecification.
4. When fed with field monitoring data to estimate the absolute abundance of the
mosquito arbovirus vector Aedes albopictus within the metropolitan city of Rome
(Italy), the Nmixture model showed higher population size in residential neigh
bourhoods than in large green areas and revealed that traps located adjacent to
vegetated sites have a higher probability of capturing mosquitoes.
5. Synthesis and applications. Our results show that, if supported by a good knowl
edge of the target species biology and by informative priors (e.g. from previous
studies of capture rates), the Nmixture model represents a valuable tool to ex
ploit field monitoring data to estimate absolute abundance of disease vectors and
to assess vectorrelated health risk on a wide spatial and temporal scale. For mos
quitoes specifically, it is also valuable to invest in increased efficiency of trapping
devices to improve estimates of absolute abundance from the models.
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1  INTRODUCTION
Estimating the absolute abundance of animal populations is an ex
tremely challenging task. A tradeoff exists between sampling ef
forts, analy tical tools and information gathered. On the other hand,
estimates of relative abundance or indexes of abundance are more
easily achievable, especially when dealing with arthropod popula
tions. These approaches rely on the assumption that “the higher
the number of collected specimens, the higher the population abun
dance” and does not take into account differences in detectability
and/or trap performance, de facto providing biased estimates when
factors influencing the detection are not controlled for (Joseph, Elkin,
Martin, & Possingham, 2009).
In the case of insect species of public health relevance, such mos
quito vectors of malaria parasites or of arboviruses, absolute abun
dance is a cru cial parameter to infer the vector to host contact ratio and
inform models aimed at estimating risk of pathogen transmission and
effectiveness of vector control interventions. However, MarkRelease
Recapture experiments – which are considered the gold standard to
estimate size of animal populations – are not only very laborious and
challenging to implement in the field, but also raise ethical concerns
due to the need to release large number of potential vectors, which
may contribute to disease transmission. For this reason, only few stud
ies have been carried out so far (Cianci et al., 2013; Gouagna, Dehecq,
Fontenille,Dumont, & Boyer, 2015; Villela etal., 2017,2015) toesti
mate the absolute abundance of mosquito vec tors which cause millions
of infections and thousands of deaths every year (WHO, 2016).
The Nmixture model approach is a statistical method exploited
in ecological studies to estimate absolute population abundance
from observed field data (Kéry & Royle, 2016; Royle & Dorazio,
2009). This method treats data as the observable outcome of two
linked components: an observation and a population process.
Therefore, this approach takes simultaneously into account the
underlying ecological process and the mechanism by which obser
vations are sampled. Nowadays, it has been extended to deal with:
nonindependent detection that may occur when individuals show
correlated behaviour (Martin et al., 2011), spatiotemporal varia
tion (Hostetler & Chandler, 2015); species uncertainty that may
occur when it is difficult to exactly identify captured individuals
(Chambert, Hossack, Fishback, & Davenport, 2016); and density de
pendence and environmental stochasticity (Bellier, Kéry, & Schaub,
2016). In recent years, it has been applied to various animal species
(Belant et al., 2016;Hunter,Nibbelink,&Cooper,2017;Kéry etal.,
2009), but it is still considered an emerging method (Dénes, Silveira,
& Beissinger, 2015) and its reliability and robustness have been
questioned (Barker,Schofield, Link,& Sauer,2017;Link, Schofield,
Barker, & Sauer, 2018).
We here proposed and tested the Nmixture model to estimate
absolute mosquito abundance exploiting monitoring data routinely
gathered in surveillance schemes carried out in areas where mosqui
toes represent either a public health risk or a severe nuisance.
Firstly, we tested how well the Nmix ture approach performs to
estimate a set of parameters and population absolute abundances
from synthetic trap data under realistic scenarios of environmen
tal conditions. We addressed how robust the approach is against
the typical constraints of a mosquito field monitoring scheme (i.e.
low detection/capture rate, repeated multiple sampling dates and
violation of the assumption of closed population) and developed a
comprehensive simulation study to assess the robustness of the ap
proach against (a) the introduction of additional unexplained varia
tion, and (b) underparametrization of the model by not considering
relevant covariates in the obser vation or in the population process.
Secondly, we applied the Nmixture model approach to a case
study to investigate whether the abundance of the tiger mosquito
Aedes albopictus differs in different ecological context s within the
city of Rome (Italy) and to explore the implications for vector con
trol. In recent decades, this aggressive daytime biting species has
become a global public health threat due to its invasive potential
which extended worldwide from Asia and to its c apacity to transmit
a large number of arbovirus (such as Chikungunya, Dengue and Zika;
Gratz, 2004). The species has been well established in Italy for more
than 20 years and has been responsible for two Chikungunya out
breakscausing250and500cases(IstitutoSuperiorediSanità,2017;
Manicaetal.,2017;Rezzaetal.,2007).
2  MATERIALS AND METHODS
2.1  N‐mixture model approach
The model we proposed is framed in a Bayesian hierarchical per
spective, which allows extreme flexibilit y and could accommodate
further extension of the Nmixture model including spatial depend
ency or nonlinear effects.
We consider specimen counts nijt collected in the trap i of
site j at time of collection t, sampled from a Binomial distribution
nijt ~ Binomial(πijt, Njt), where:
(i) πijt is the capture/detection probability of trap i within site j at
time of collection t that is assumed to come from a Beta distri
bution πijt ~ Beta(aijt, bijt);
(ii) Njt is the unobserved population absolute abundance present
within site j at time of collection t, that is assumed to be a dis
crete number sampled from a Poisson distribution with mean λjt,
i.e. Njt ~ Poisson(λjt).
KEY WORDS
abundance, Bayesian model, disease vector, Nmixture model, tiger mosquito, trap efficiency,
vectorborne pathogens

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MANIC A et Al.
Therefore, we assume that repeated observations from the same
site j and time t are drawn from the same subpopulation Njt. The
mean of the Beta distribution represents the average capture/de
tection probability and is indicated as Pijt.. The means of the Poisson
and Beta distribution could be modelled as a function of covariates.
Specifically, for the Poisson distribution we assume that
log(λjt) = Yβ + εj, where Y is a matrix whose elements are the covari
ate values, β is the vector of estimated parameter and εj ~ Norm(0,
σ2) are sitedependent residuals.
For the Beta distribution, we use the following parametrization:
aijt = ϑPijt and bijt = ϑ(1−Pijt). Under this parametrization the mean of
the Beta distribution is equal to Pijt. Then it is easy to specify a linear
model on Pijt through the logit transformation so that logit(Pijt) = X γ
where logit(Pijt) = log(Pijt/(1− Pijt)), X is the covariates matrix, which
can impact trap performances and therefore the detection process,
and γ is the vector of estimated parameter.
A Multivariate Normal distribution (MVNorm(0, 1000*I) was
chosen as minimally informative prior for the parameters of the pop
ulation process (β) and for the covariates of the detec tion process.
On the other hand, informative priors were chosen for the in
tercepts of the detection processes (γ0 ~ Norm (−7,0.1)) as well as
for the parameter ϑ of the Beta distribution: ϑ ~ Gamma(60,0.1).
Parameters values for the informative priors were based upon es
timates obtained in a MarkReleaseRecapture experiment on Aedes
albopictus in Rome (Marini, Caputo, Pombi, Tarsitani, & Della Torre,
2010) where the same traps (ST) were used (see Appendix S1).
Finally a HalfCauchy distribution σ was consi dered (σ ~ Nor m(0,1)/
Norm(0,25)) for the standard deviation of the Normal distribution
used to account for unexplained variation among sites (i.e. random ef
fects). Bayesian inference was carried out using Markov Chain Monte
Carlo (MCMC) simulative approach using r version 3.4.0 (R Core Team,
2017)andJagsversion4.2.0(Plummer,2003;Su&Yajima,2015).
2.2  Creating synthetic data
We generated synthetic data for the covariates and applied the pre
vious model to obtain synthetic data of trap mosquito collections.
At first, we considered three covariates (Table 1) for the population
abundance process (Y) and two for the detection/capture process
(X) considering five traps (i = 1, …, 5) for each of the 12 sites ( j = 1, …,
12) at 12 weeks of collections (t = 1, …, 12).
In order to simulate a mosquito population temporal profile, re
alistic temperature and precipitation data (see section Applying N‐
mixture model to obser ved data for details) were used as a basis for
creating synthetic data for the following two covariates of the pop
ulation process:
(i) weekly mean Land Surface Temperature (LST ) recorded from
15 July 2013 to 30 September 2013 in Rome to which we added
a site dependent and a collection dependent noise drawn from
two Normal distributions of mean 0 and standard deviation 2
and 1, respectively;
(ii) cumulative precipitation in the previous 4 weeks of collection
recorded from 15 July 2013 to 30 September 2013 in Rome as
suggested in Manic a et al. (2016).
The third c ovariate was sample d from a Uniform dist ribution (min = 0.2 ,
max = 0.8) and kept const ant over collection to represent a physical
characteristic of the site.
Similarly, realistic data related to residual water level in trap was
used to create synthetic data for one of the covariates related to the
detection process. The weekly mean residual water level in trap (mea
sured in millilitre, see section Applying N‐mixture model to observed
data for details) recorded from 15 July 2013 to 30 September 2013
in Rome, was used, adding a trap and a collectiondependent noise
drawn from two Normal distributions: Norm(0, 20) and Norm(0, 50)
respectively.
The other covariate of the detection process was sampled from
a Uniform distribution (min = 0, max = 1) and kept constant over col
lections to characterize the ecological features of the trapping area.
The parameters values for the population process (β) were cho
sen as follows: β0 = 0, β1 = 1.5, β2 =0.75,β3=−0.75.Valuesfor the
sitedependent residuals
𝜀j
were sampled from a Normal distribution
Norm(0, σ = 0.5).
Process
Model
parameter
Parameter
value Variable Description of synthetic dat a
Population β00 Intercept of population process
β11.5 Y1Derived from land surface temperature
data
β20.75 Y2Derived from precipit ation data
β3−0.75 Y3Sampled from Uniform distribution
σ0.5 Standard deviation for sitedependent
noise
Detection γ0−6. 5 Intercept of detection process
γ10.5 X1Derived from residual water level in
trap
γ2−0.5 X2Sampled from Uniform distribution
ϑ500 Gamma distribution parameter
TABLE 1 Model variables and
parameters used in the simulation of field
monitoring of mosquito abundance
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MANIC A et Al.
Parameter values for the detection process (γ) were chosen as
follows: γ0=−6.5,γ1 = 0.5, γ2=−0.5,whileϑ was set at 50 0.
All variables were standardized (subtracted their mean and di
vided by their standard deviation) to help mixing of chains and inter
pretation of result s (Schielzeth, 2010) wit h the exception of Y1 (weekly
mean LST), which was centred around 13°C and then divided by its
standard deviation to impose a biological constrain on the effect of
temperature on population abundance, as 13°C is the lower tem
perature threshold for emerging Ae. albopictus females (Roiz, Rosà,
Arnoldi, & Rizzoli, 2010). Therefore, we fitted the model for synthetic
data without intercept, forcing the regression line to go through the
origin at 13°C in adherence to Ae. albopictus mosquito biology.
Given the defined parameter and covariate values for the pop
ulation process, we obtained the population absolute abundance
present within site j at time of collection t (Njt) by sampling from a
Poisson distribution (see section N‐mixture model approach).
Specimen counts data (nijt) were obtained sampling from the
Binomial distribution, describing the detection process. Then, to ac
count for random variation in the detection process, the specimen
counts sampling was repeated 100 times, thus obtaining 100 dif
ferent datasets mimicking different monitoring outcomes from the
same population.
2.3  Simulation study on synthetic data
A set of simulations was carried out in order to test the robustness
of the chosen Nmixture model approach under the following as
sumption: extremely low detection/capture rate and timevarying
population abundance.
We fitted the Nmixture model to 100 synthetic dataset s in order to
estimate population abundance (N) along with all parameters for both
the detec tion and the population process. Precisely, we computed for
each parameter: the distribution of the mean of the 100 posterior dis
tributions, the coverage, i.e. the proportion of posterior distributions
where 95% credible interval contains the synthetic parameter values
(see Table 1) and the root mean squared error (RMSE). For each of the
100 simulation runs, three parallel MCMC chains were run, each with
40,000 iterations. The first 10,000 were discarded as burnin. A thin
ning rate of one on 10 was applied resulting in 9,000 iterations.
In addition, we investigated how the Nmix ture model would
perform under different model specifications (Knape & Korner
Nievergelt, 2015; Link et al., 2018):
(i) when the population process is underparametrized, so not all the
covariates used to simulate population abundance are included in
the model (i.e. discarding the second and third covariate in turn),
(ii) when the detection process is underparametrized, so not all the
covariates used to simulate specimen counts are included in the
model (i.e. discarding one covariate in turn),
(iii) when additional variation sampled from Norm(0,0.1) is used
to simulate specimen counts but is not accounted for in the
Nmixture model used to estimate parameters and population
abundances,
(iv) when noninformative priors are chosen for the γ and ϑ parame
ter of the detection process.
2.4  Applying N‐mixture model to observed data
Mosquito collections were carried out weekly from 1 July 2013 to 20
November 2013 (t = 1, …, 22 weeks). Twelve sites ( j = 1,…, 12) were
identified inside the metropolitan area of Rome (Italy) and clustered
in four zones (named S1, S2, S3, S4). Three sites were selected within
each zone. Each site encloses a circular area of 300 m radius likely
representing three different ecological habitats for Aedes albopictus.
We arbitrarily defined the three habitats as:
1. “Vegetated” characterized by urban green spaces with high
presence of grasslands (>50%) and trees (from 30% to 40%),
few buildings or roads and scarcely inhabited;
2. “Mixed”characterizedbypresenceofbuildings(from19%to27%)
and trees (from 23% to 30%);
3. “Residential” with similar characteristics to “Mixed” but more
densely populated (Figure S1).
Ecological habitats were identified by visual inspection of a qualified
medical entomologist (author BC) and by quantitative assessment
carried out both from population census data (ISTAT, 2011) and from
a series of spatial datasets. Descriptive meteorological and land cover
variables were recorded both at site level (300 m circular buffer) and
at trap level (20 m circular buffer), using the methodology described
in Manica et al. (2016). Land Surface Temperature (LST ) recorded at
each site has been extracted from reconstructed temporal series of
MODIS satellite data, collected by NASA (http://modis.gsfc.nasa.gov)
and proce ssed as described in Metz, Rocchini, a nd Neteler (2014). The
cumulated mm of precipitation at each trap location was derived from
the spatial interpolation of mm of daily precipitation data recorded at
46 meteorological sampling stations, collected by the Hydrographic
Service of Lazio Region and disseminated through the hydrographic
annals (http://www.idrog rafico.regio ne.lazio.it/annal i/index.htm).
StickyTraps(ST)(Facchinellietal.,2007)werelocatedinthefour
zones (S1–S4) and within the three different habitats (Vegetated,
Mixed, Residential) as shown in Figure 1. Five STs (i = 1,…,5) were lo
cated within each site (15 traps per zone) and equipped with 500 ml
of tap water and sticky sheets. Every week, the residual trap water
level (ml) was recorded and mosquito collected, screened for spe
cies and gender and counted. Afterwards, STs were replenished with
500 ml of tap water and equipped with new sticky sheets.
The weekly number of captured adult Ae. albopictus females in
each ST (Figure 2) was used as response variable in the model.
The covariates we considered for the capture/detection process
were percent of trees within the 20 m circular buffer and the weekly
residual water in STs (mm). For the population abundance process
we considered habitat type and climatic covariates (e.g. temperature
and precipitation) preceding the sampling week, to take into account
the effect of climate on the development of mosquito immature

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MANIC A et Al.
stages (Roiz et al., 2010). Specifically, the climatic covariates were
the mean L ST recorded within the time window including the 3rd
and 4th weeks prior to the collec tion, its quadratic term (to account
for a nonlinear relationship) and the cumulated precipitation (mm)
in the previous two weeks. Within two “Vegetated” sites for t wo
weeks (34th and 35th), all STs were found deac tivated, meaning that
both mosquito data and residual water level were missing (Figure 2).
To overcome this issue, for those weeks and sites we simulated a
single ST assigning the average covariate values recorded on active
STs in the same weeks. Finally, we assumed that the capture rate of
the traps is an average value over a monitored area defined by mos
quito flight range. Then we used the estimate of mosquito absolute
abundance produced by the Nmixture model to compute mosquito
density (per hec tare) over the monitored area.
All quantitative variables were standardized (subtracted their
mean and divided by their standard deviation) to help chains mixing
and ease interpretation of results (Schielzeth, 2010). The model fea
tured a burnin of 250,0 00 iterations, a thinning rate of 150, three
chains and a total number of 500,00 0 iterations, resulting in 5,001
iterations per parameter for each posterior distribution. From the
estimated mosquito absolute abundance, we computed the vector
to host ratio, dividing mosquito abundance by the resident human
population (ISTAT, 2011) in a 300metre buffer.
Asses sment of mixing of chain s and model stati stical assumpt ions
was carried out by graphical analysis of residuals and simulations
from model estimated parameters (Zuur, Ieno, & Freckleton, 2016).
Finally, to fur ther assess model performance we compared model
posterior predictive distribution to observed data.
3  RESULTS
3.1  Simulation study on synthetic data
Fitting the Nmixture model to synthetic data we showed that all
parameters for both the detection and the population process are
within the 95% CI of the distribution of the mean estimated values
except for γ2 (Table 2). All the parameters for the population abun
dance process had >98% coverage while coverage was lower for the
detection process, especially for γ2(71%).
The synthetic population data are consistently within the 95%
credible interval of the estimated population, leading to a coverage
above 90% for each site, although for a few sites (Site2, Site10,
Site11) the estimated population abundance is slightly higher than
the created synthetic value (Figure 3).
Regarding the covariates for the population absolute abundance,
failing to include Y3, a covariate representing a physical ch aracteristic
of the site that was kept constant over time, did not af fect greatly th e
results. However, not including the spatiotemporal covariate in the
population process (precipitation) leads to a worse representation of
the population dynamics and to more biased estimates of absolute
FIGURE 1 Location of the four
sampling zones in the metropolitan area
of the city of Rome (red square in central
panel) and the Stick y Traps (cross circles)
for the 12 sampling sites (circles) over the
different land cover classes
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Journal of Applied Ecology
MANIC A et Al.
abundance that for some site were consistently outside the 95%
credible interval; for some sites this happens as frequently as 99% of
outputs (Appendix S2, simulation II). Fitting the same model consid
ering also the intercept in the model specification (with vague prior)
leads to comparable results. Moreover, even if the model computed
reasonable estimates of the population absolute abundance, exclud
ing the spatiotemporal variables in the detection/capture process
led to extremely biased model parameters (“true” value never within
the credible inter val in the 100 simulation runs). A similar but less
strong pattern could be observed when neglecting the spatiotem
poral covariate in the capture/detection process (water). Finally,
failing to include the covariate in the capture/detection process that
was kept constant over time had a negative effect only in few sites
without affecting the estimation of model parameters (Appendix S2,
simulation IV, V). In our simulation study, the main consequences of
adding unaccounted random noise in the detection/capture process
were a reduc tion in the accuracy of the es timation of γ0, the overes ti
mation of the mosquito population on average and an increase of the
RMSE in some sites (Appendix S2, simulation VIX). This behaviour
is consistent with that observed elsewhere (Link et al., 2018) and
may constitute one of the major drawbacks of the Nmixture model
approach given that misspecification and unaccounted variance
FIGURE 2 Weekly trap collection
(black dot s), in each sampling zone (panel
S1–S4) for each habitat (Residential,
Mixed and Vegetated) in Rome, Italy. Each
panel represents one of the twelve sites
considered in the analysis. The xaxis
shows the week of collec tion, while the y
axis shows the counts of Aedes albopictus
females trapped in each of five Sticky
Tra p s
TABLE 2 Result of simulation of the model including all covariates and no additional noise
Process Parameter Synthetic value
Estimated value from simulation s
Coverage (%) RMSEMean 0.025% CI 0 .975% CI
Population β11.50 1. 517 1.442 1.591 99 0.035
β20.75 0.734 0. 612 0 .851 98 0.051
β3−0.75 −0 .618 −0.796 −0.4 49 100 0.14 0
σ0.50 0.483 0.304 0 .678 10 0 0.076
Detection γ0−6. 50 −6. 698 −6.923 −6.424 90 0. 211
γ10.50 0.598 0.496 0.722 91 0.10 0
γ2−0.50 −0.625 −0.721 −0. 523 71 0.1 26
ϑ500 596. 55 565.49 6 32.10 99 96 .55

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Journal of Applied Ecology
MANIC A et Al.
are likely to occur in realcase studies. However, the proportion of
times the synthetic values of the population absolute abundance fell
within the 95% was not considerably af fected, at least for the simu
lated intensity of the noise.
3.2  N‐mixture model results on observed data
In the case study a total of 2,504 Aedes albopictus females were col
lected, the Nmixture model showed a quadratic relationship of the
mosquito population abundance with L ST, with a peak at about 25°C
(Table 3). On the other hand, the cumulative precipitation in the two
weeks preceding the collections showed a negative association with
population absolute abundance. Vegetated habitat had statistic ally
lower infestation than the other two habitats, while the effect of
Mixed and Residential habitat on Ae. albopictus population absolute
abundance was comparable.
Regarding the detec tion process, water evaporation in ST (as
assessed by weekly measures of residual water) was negatively
associated to mosquito counts, while the higher abundance of
vegetated habitats had a positive effect size. The low value of the
intercept for the detection/capture process indicates a very low
capture rate of STs (Table 3). The estimated capture rate on av
erage was 0.022%(95%ci: 0.017%–0.026%)which islower than
previously observed in a MarkReleaseRecapture study (mean
capture rates of three releases: 0.082%, 0.093% and 0.059%, num
ber of traps = 55, Figure S2).
Estimates of population absolute abundance provided mean
values ranging from 9.6 to 816.9 female mosquitoes/hectare over
all, and from 22 to 800, 20.8 to 816.9, and 9.6 to 251 in residential,
mixed and vegetated habitats respec tively (Figure 4).
Model validation indicated that the proposed model complied
with underlying statistical assumptions and simulated data from the
model reasonably resembled observed data (Figures S3–S5).
4  DISCUSSION
Results show that the Nmixture model is a promising framework
to estimate absolute mosquito abundance based on data from rou
tinely monitoring activities, so far only exploited to estimate relative
abundance. This could lead to a novel way to obtain more realistic
estimates of vectorhost ratio needed to predict the risk of pathogen
transmission, as well as of effectiveness of control interventions, at a
local level.
FollowingtherecommendationofBarkeretal.(2017)andKéry
(2018), the model incorporated informative priors on capture rate
(Marini et al., 2010) and mosquito biology (Roiz et al., 2010) to
overcome the inherent biases linked to the Nmixture approach
as discussed in Link et al. (2018) and Duarte, Adams, and Peterson
(2018). It should be noted that choice of priors does have an im
pact on the final estimates and should be informed by evidence. In
particular, the intercept of the detection/capture process may be
FIGURE 3 Population absolute
abundance comparison: synthetic and
fitted by the Nmix ture model. Dot s
represent the synthetic population
absolute abundance, the solid line
represents the posterior mean population
absolute abundance estimated from the
model and averaged over the 100 runs,
grey areas represent the 95% credible
interval. The xaxis shows the synthetic
time of collections, while the yaxis shows
the absolute population abundance; note
that each panel has a different yaxis
range to ease visualization
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Journal of Applied Ecology
MANIC A et Al.
difficult to estimate as fluctuating together with other covariates;
despite assuming a ver y informative prior may help identifiability,
nevertheless it may also force a specific result. Our results show
that running the model with these informative priors produced
less biased estimates of mosquito population absolute abundance
with respect to using noninformative priors and that neglecting
some important covariates could lead to biased estimates (see
Appendix S2, section Simulation Result). Therefore, although in
principle the Nmixture approach could be applicable in any areas
based on routine mosquito monitoring data, the need of clear as
sumptions on prior distributions and model specification (Knape &
KornerNievergelt, 2015) reduce its application in the realworld.
TABLE 3 Nmixture model result on the Aedes albopictus case study. LST = Land Temperature Surface, Vegetated, Mixed and Residential
refer to Habitat Type
Process Covariate Mean SE 2. 5% 97.5%
Population Mixed (intercept) 9.4 28 0.26 8.91 9.939
LST 2.523 0.646 1.238 3. 74
LST2−2. 2 51 0.636 −3. 46 −0.982
Precipitation −0.375 0.055 −0 .476 −0. 27
Vegetated −0.93 0.343 −1 .636 − 0.241
Residential 0.054 0.348 −0. 659 0.74 6
Difference between
Residential and
Vegetated
0.984 0.349 0.289 1.70 0
σ0.441 0 .147 0. 248 0.808
Detection Intercept −8.447 0 .112 −8 .659 −8.2 55
Residual Water 0.119 0.04 0.04 0.198
Tre e (% ) 0.118 0.04 0.035 0.197
ϑ4,360.55 489.13 3,516.56 5,381.98
FIGURE 4 Case study result s of Aedes
albopictus population density estimated by
the Nmixture model in the t welve sites
(300 m radius buf fer), in each sampling
zone (panel S1–S4) for each habitat
(Residential, Mixed, Vegetated) in Rome,
Italy. Each panel represents one of the
twelve sites considered in the analysis.
The xaxis shows the week of collection,
while the yaxis shows the estimated
density per hectare of Aedes albopictus
females. The solid lines represent the
mean value of the posterior distribution
of the absolute abundance divided per the
site area, the dashed lines represent the
95% credible interval

2233
Journal of Applied Ecology
MANIC A et Al.
Additionally, separating the effect of variables between the pop
ulation and the detection/capture process could represent an ad
ditional challenge.
We are aware that the Nmixture model is available in a frequen
tist framework through sof tware packages like un m ark ed (Fiske &
Chandler, 2011). However, this specification may lead to unrealistic
(large) estimate of detection probability as the model tends to miss
estimates of detection rate near the boundaries (0 or 1), which re
sults in biases when it is known that the detection rate is very low.
We were able to overcome the issue by using a Bayesian perspec
tive, tailoring the prior distribution of the detection/capture rate
parameter on previous results obtained in MarkReleaseRecapture
experiments and taking into account mosquito biology to specif y the
model. This approach could be extended to other settings, mosquito
vector species or trap devices, but ef forts should be made to cor
rectly specif y the model, to assess trap performances and its priors
distribution given the emerging evidences that Nmixture model
misspecification will result in low accuracy and poor reliabilit y com
pared tostandard regression (Barkeret al.,2017,Linketal.,2018).
The Nmixture model has been very recently implemented in the
IntegratedNested LaplaceApproximations (Rue etal.,2017)which
mightreducecomputationtime(Meehan, Michel,&Rue,2017) and
make it more appealing to a broader audience.
The analysis of our case study showed that absolute Ae. al‐
bopictus abundance was higher in densely populated areas (i.e.
Residential and Mixed Habitats) than in highly vegetated and less
populated ones. Our estimate of Ae. albopictus densities is relatively
lowerthan those estimated byManicaet al. (2017) in the same re
gion. However, a crude comparison may not be appropriate due to
spatial and temporal heterogeneities arising from different sam
pling locations. Whenever feasible, it would be beneficial to set
up a MarkReleaseRecapture experiment in the monitored area
to compare and calibrate the model estimate produced by the N
mixture model approach. However, it is important to note that low
and heterogenic capture rates among traps may represent a limiting
factor for the exploitation of Nmixture model for mosquito sur
veillance ( Veech, Ott, & Troy, 2016). In fact, the stick y traps used
in the analysed case study were not highly effective in capturing a
great fraction of adult mosquito population (Marini et al., 2010) and
a great variation of capture rate was obser ved among traps, likely
due to Ae. albopictus’ great adaptability and plasticity in the ovipo
sition behaviour (Hawley, 1988) and to the unrecorded presence of
other factors af fecting oviposition habitat selection (Fader & Juliano,
2014). Improved trap performance both in terms of capture rate
and data collection would make Nmixture model estimates more
reliable. Nevertheless, these variations in capture/detection pro
cess could be explicitly modelled in a BetaBinomial process within
the Nmixture approach. BetaBinomial capture/detection process
results showed that Ae. albopictus is mainly captured in traps posi
tioned near small vegetated area, consistent with the species’ pref
erence for green spot as resting and oviposition sites (BartlettHealy
et al., 2012; Crepeau et al., 2013; Manic a et al., 2016). The amount of
water in the trap also resulted associated with the capture/detec tion
probability as oviposition and consequently the probability of ap
proaching the trap is expec ted to be lower when the trap water level
is low (Unlu, Farajollahi, Strickman, & Fonseca, 2013).
In conclusion, this study represent s one of the first applications
of the Nmixture approach to species of epidemiological relevance.
Public Health authorities would benefit from the introduction of
novel statistical method for the estimation of mosquito population
absolute abundance. Shifting the perspective from methods that
estimate relative vector abundance to methods that focus on ab
solute abundance could help fill the gap between simple counts of
mosquito collected in a monitoring perspective and inference capa
bility of the actual biting population, in order to assess the actual
risk of pathogen transmission, as well as the effectiveness of control
interventions.
AUTHORS' CONTRIBUTIONS
M.M., A .S.o., F.F., B.C., A.d.T. and M.B. conceived the ideas and
designed methodology; B.C., F.F., A.S.o. and A.S.c. collected the
data; M.M., F.F. and M.B. analysed and interpreted data; M.M.,
A.d.T., M.B. and R.R. wrote the manuscript; B.C. and A. S.o. criti
cally revised the manuscript. All authors gave final approval for
publication.
DATA AVA ILAB ILITY STATE MEN T
Data available via the Figshare Repository https ://doi.org/10.6084/
m9.figsh are.81180 35.v1 (Manica et al., 2019). Jags code available
from the Figshare Repositor y. To access the project, go to https
://figsh are.com/proje cts/Apply ing_the_Nmixtu re_model_appro
ach_to_estim ate_mosqu ito_popul ation_abund ance_from_monit
oring_data/61355 .
ORCID
Mattia Manica https://orcid.org/0000000337091199
Marta Blangiardo https://orcid.org/000000021621704X
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SUPPORTING INFORMATION
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How to cite this article: Manica M, Caputo B, Screti A, et al.
Applying the Nmixture model approach to estimate mosquito
population absolute abundance from monitoring data. J Appl
Ecol. 2019;56:2225–2235. ht tp s ://doi.org/10 .1111/
13652664.13454