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Applying the N‐mixture model approach to estimate mosquito population absolute abundance from monitoring data

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Journal of Applied Ecology
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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 mark‐release‐recapture 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 N‐mixture model approach to estimate mosquito abundance from standard monitoring data. We extended the N‐mixture model approach in a Bayesian framework by considering a beta‐binomial 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. When informative priors were used and the model was well specified, estimates by N‐mixture 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. 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 N‐mixture model showed higher population size in residential neighbourhoods than in large green areas and revealed that traps located adjacent to vegetated sites have a higher probability of capturing mosquitoes. Synthesis and applications. Our results show that, if supported by a good knowledge of the target species biology and by informative priors (e.g. from previous studies of capture rates), the N‐mixture model represents a valuable tool to exploit field monitoring data to estimate absolute abundance of disease vectors and to assess vector‐related health risk on a wide spatial and temporal scale. For mosquitoes 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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J Appl Ecol. 2019;56:2225–2235. wileyonlinelibrary.com/journal/jpe  
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 2225
© 2019 The Authors. Journal of Applied Ecology
© 2019 British Ecological Society
Received:12Augus t2018 
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Accepted:27April2019
DOI : 10.1111/136 5-2664.1345 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 mark-release-recapture 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 N-mixture model approach to estimate mosquito abundance from
standard monitoring data.
2. We extended the N-mixture model approach in a Bayesian framework by consid-
ering a beta-binomial 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 N-mixture 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 N-mixture 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 N-mixture model represents a valuable tool to ex-
ploit field monitoring data to estimate absolute abundance of disease vectors and
to assess vector-related 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 trade-off 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, Mark-Release-
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 etal., 2017,2015) toesti-
mate the absolute abundance of mosquito vec tors which cause millions
of infections and thousands of deaths every year (WHO, 2016).
The N-mixture 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:
non-independent detection that may occur when individuals show
correlated behaviour (Martin et al., 2011), spatio-temporal 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 etal.,
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 N-mixture 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 N-mix 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) under-parametrization of the model by not considering
relevant covariates in the obser vation or in the population process.
Secondly, we applied the N-mixture 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 day-time 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-
breakscausing250and500cases(IstitutoSuperiorediSanità,2017;
Manicaetal.,2017;Rezzaetal.,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 N-mixture 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, N-mixture model, tiger mosquito, trap efficiency,
vector-borne pathogens
    
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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 site-dependent 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 Mark-Release-Recapture 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 Half-Cauchy 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)andJagsversion4.2.0(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 collection-dependent 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.Valuesfor the
site-dependent 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 site-dependent
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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Parameter values for the detection process (γ) were chosen as
follows: γ0=−6.5,γ1 = 0.5, γ2=−0.5,whileϑ 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 N-mixture model approach under the following as-
sumption: extremely low detection/capture rate and time-varying
population abundance.
We fitted the N-mixture 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 burn-in. A thin-
ning rate of one on 10 was applied resulting in 9,000 iterations.
In addition, we investigated how the N-mix ture model would
perform under different model specifications (Knape & Korner-
Nievergelt, 2015; Link et al., 2018):
(i) when the population process is under-parametrized, 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 under-parametrized, 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
N-mixture model used to estimate parameters and population
abundances,
(iv) when non-informative 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”characterizedbypresenceofbuildings(from19%to27%)
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).
StickyTraps(ST)(Facchinellietal.,2007)werelocatedinthefour
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 N-mixture 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 burn-in 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 300-metre 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 N-mixture 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 (Site-2, Site-10,
Site-11) 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 spatio-temporal 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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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 spatio-temporal 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 spatio-tem-
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 VI-X). This behaviour
is consistent with that observed elsewhere (Link et al., 2018) and
may constitute one of the major drawbacks of the N-mixture 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 x-axis
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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MANIC A et Al.
are likely to occur in real-case 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 N-mixture 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 islower than
previously observed in a Mark-Release-Recapture 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 N-mixture 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 vector-host ratio needed to predict the risk of pathogen
transmission, as well as of effectiveness of control interventions, at a
local level.
FollowingtherecommendationofBarkeretal.(2017)andKéry
(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 N-mixture 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 N-mix 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 x-axis shows the synthetic
time of collections, while the y-axis shows
the absolute population abundance; note
that each panel has a different y-axis
range to ease visualization
2232 
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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 non-informative priors and that neglecting
some important covariates could lead to biased estimates (see
Appendix S2, section Simulation Result). Therefore, although in
principle the N-mixture 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 &
Korner-Nievergelt, 2015) reduce its application in the real-world.
TABLE 3 N-mixture 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 N-mixture 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 x-axis shows the week of collection,
while the y-axis 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 N-mixture 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 Mark-Release-Recapture
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 N-mixture model
misspecification will result in low accuracy and poor reliabilit y com-
pared tostandard regression (Barkeret al.,2017,Linketal.,2018).
The N-mixture model has been very recently implemented in the
IntegratedNested LaplaceApproximations (Rue etal.,2017)which
mightreducecomputationtime(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
lowerthan those estimated byManicaet 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 Mark-Release-Recapture 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 N-mixture 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 N-mixture model estimates more
reliable. Nevertheless, these variations in capture/detection pro-
cess could be explicitly modelled in a Beta-Binomial process within
the N-mixture approach. Beta-Binomial 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 (Bartlett-Healy
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 N-mixture 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_N-mixtu re_model_appro
ach_to_estim ate_mosqu ito_popul ation_abund ance_from_monit
oring_data/61355 .
ORCID
Mattia Manica https://orcid.org/0000-0003-3709-1199
Marta Blangiardo https://orcid.org/0000-0002-1621-704X
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SUPPORTING INFORMATION
Additional supporting information may be found online in the
Suppor ting Information section at the end of the article.
How to cite this article: Manica M, Caputo B, Screti A, et al.
Applying the N-mixture 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/
1365-2664.13454
... Here we present an independent evaluation of WIM releases for the suppression of Ae. aegypti. Additionally, we describe, and test, the abundance estimation approach we used (N-Mixture Bayesian hierarchical model [18]); this approach is relatively novel in mosquito ecology, being used previously to estimate the abundance of Ae. albopictus [19], and Ae. aegypti, but with a Mark Release Recapture Component [20] (MRR). ...
... This approach has been previously used in mosquito ecology and has potential applications in analyzing mosquito surveillance data and guide control actions. It was used to estimate the abundance of Ae. albopictus [19], and Ae. aegypti in a Mark Release Recapture (MRR) study [20]. ...
... We discovered during data validation that the trapping time of the first trapping (first day of week 28), in both areas, was statistically different from other weeks. The mean trapping time during the first trapping was 27 (26,27) hrs., and 18 (18,19) hrs. in the UA, and TA respectively. In comparison, the mean trapping time on other days was 23 (23,24) hrs. ...
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Among disease vectors, Aedes aegypti (L.) (Diptera: Culicidae) is one of the most insidious species in the world. The disease burden created by this species has dramatically increased in the past 50 years, and during this time countries have relied on pesticides for control and prevention of viruses borne by Ae. aegypti. The small number of available insecticides with different modes of action had led to increases in insecticide resistance, thus, strategies, like the “Incompatible Insect Technique” using Wolbachia’s cytoplasmic incompatibility are desirable. We evaluated the effect of releases of Wolbachia infected Ae. aegypti males on populations of wild Ae. aegypti in the metropolitan area of Houston, TX. Releases were conducted by the company MosquitoMate, Inc. To estimate mosquito population reduction, we used a mosquito abundance Bayesian hierarchical estimator that accounted for inefficient trapping. MosquitoMate previously reported a reduction of 78% for an intervention conducted in Miami, FL. In this experiment we found a reduction of 93% with 95% credibility intervals of 86% and 96% after six weeks of continual releases. A similar result was reported by Verily Life Sciences, 96% [94%, 97%], in releases made in Fresno, CA.
... N-mixture models have already been applied to a wide range of wildlife species (e.g. Belant et al., 2016;Hunter, Nibbelink & Cooper, 2017;Kéry, 2018;Kidwai et al., 2019;Manica et al., 2019;Romano et al., 2017;Ward et al., 2017), but are still considered as an emerging framework with ongoing extensions to original parameterizations (Barker et al., 2018;Bötsch, Jenni & Kéry, 2019;Denes, Silveira & Beissinger, 2015;. ...
... Allowing for the separate estimation of abundance and detection probabilities from replicated counts of unmarked individuals (e.g. Zipkin et al., 2014), N-mixture models have in recent years become applied to taxa ranging from mosquitoes to megafaunal mammals (Kidwai et al., 2019;Manica et al., 2019). In the present study, we applied a set of such models to spotlight count data for C. moreletii in southern Yucatan, where it inhabits particularly dynamic waterbodies and serves as an important flagship species for a large expanse of protected forest. ...
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Estimates of animal abundance provide essential information for population ecological studies. However, the recording of individuals in the field can be challenging, and accurate estimates require analytical techniques which account for imperfect detection. Here, we quantify local abundances and overall population size of Morelet's crocodiles (Crocodylus moreletii) in the region of Calakmul (Campeche, Mexico), comparing traditional approaches for crocodylians (Minimum Population Size-MPS; King's Visible Fraction Method-VFM) with binomial N-mixture models based on Poisson, zero-inflated Poisson (ZIP) and negative binomial (NB) distributions. A total of 191 nocturnal spotlight surveys were conducted across 40 representative locations (hydrologically highly dynamic aquatic sites locally known as aguadas) over a period of 3 years (2017-2019). Local abundance estimates revealed a median of 1 both through MPS (min-max: 0-89; first and third quartiles, Q 1-Q 3 : 0-7) and VFM (0-112; Q 1-Q 3 : 0-9) non-hatchling C. moreletii for each aguada, respectively. The ZIP based N-mixture approach shown overall superior confidence over Poisson and NB, and revealed a median of 6 ± 3 individuals (min = 0; max = 120 ± 18; Q 1 = 0; Q 3 = 18 ± 4) jointly with higher detectabilities in drying aguadas with low and intermediate vegetation cover. Extrapolating these inferences across all waterbodies in the study area yielded an estimated~10,000 (7,000-11,000) C. moreletii present, highlighting Calakmul as an important region for this species. Because covariates enable insights into population responses to local environmental conditions, N-mixture models applied to spotlight count data result in particularly insightful estimates of crocodylian detection and abundance.
... With absolute abundance estimates, it becomes possible to quantify the total contribution of species to ecosystem functioning and ecosystem services, such as those based on estimates of biomass (e.g., [31,55,56]). Absolute abundance can also help quantify the transmission of diseases or parasites (e.g., the abundance of mosquitos [57]), which is relevant for public health impacts or the impact of pest species (e.g., feral cats [58]). ...
... N-mixture models have been applied to a wide range of wildlife species ranging from invertebrates to large mammals (Paudel et al., 2015;Kidwai et al., 2019;Manica et al., 2019;Searle et al., 2020;Than et al. 2020;Barão-Nóbrega et al., 2022), that explicitly allow for assessing abundance estimates and detection probability from a repeated count data of unmarked individuals (Kéry and Royle, 2015;Bötsch et al., 2020). N-mixture model is cost effective and widely used to estimate the abundance of population from count data with both spatial and temporal replications while accounting for imperfect detection (Royle, 2004;Joseph et al., 2009). ...
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Globally, the river ecosystems are threatened due to human-driven exploitation and indiscriminate resource use. The rate of species loss is a magnitude higher in these ecosystems, hence, identifying conservation priority areas as refugia, using the flagship-cum-indicator species approach can aid in long-term conservation of multiple species and ensure uninterrupted functioning of ecological processes. For effective conservation planning, we derived the site occupancy and abundance of Gangetic dolphin (Platanista gangetica) as a flagship species in the Ganga River Basin, and modelled their distribution vis-à-vis river conditions for identifying Conservation Priority Stretches (CPS). The study incorporates the first-ever basin-wide (4635 km river) Gangetic dolphin (GD) sightings to estimate range decline, abundance, and identify CPS of select rivers in the Basin. A total of 2151 sightings of surfacing dolphins with mean encounter rate of 0.55 ± 0.09 sightings/km of the river was observed from the surveyed stretch. The GD encounter rate varied significantly across the surveyed rivers (Analysis of Variance, F = 3.08, p
... An analogous relationship between urban habitats and distribution was found for another alien insect, the Asian tiger mosquito (Aedes albopictus (Skuse, 1894) (Diptera: Culicidae)). This species has rapidly adapted to the newly invaded areas but has never been observed using spontaneous trees as oviposition sites because it prefers sub-pots or tires that are typical cavities in the urban areas [55]. The strong connection between C. marshalli and its food plant was confirmed by the high contribution of the pel_abu variable in explaining both C. marshalli occurrence and egg abundance, even with low levels of Pelargonium abundance. ...
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Simple Summary Cacyreus marshalli is strictly dependent on its host plant (Pelargonium spp.), which is widely cultivated as an ornamental plant in mountain areas. An experiment demonstrated that the butterfly is able to develop on some wild geraniums, too, making mountain areas highly at risk for a potential expansion to natural habitats. We therefore decided to carry out research in a protected mountain area (Gran Paradiso National Park), focusing on the drivers which determine the distribution of C. marshalli using data provided by either an opportunistic approach or a rigorous survey protocol. The data collected via the planned survey were more informative than the opportunistic observations, which were few and narrow. We suggest investing more in citizen science projects and combining them with a designed protocol according to an integrated approach. We observed that C. marshalli distribution is strictly linked to host plant availability but is constrained by cold temperatures, although Pelargonium spp. are abundant. The temperature increase scenario showed an increase of butterfly abundance, but halving of the host plant population could drive the rate of infestation to return to what it was previously, excluding a countertrend in some high-altitude sites. It is therefore important to test management actions designed to control alien species before implementing them. Abstract Cacyreus marshalli is the only alien butterfly in Europe. It has recently spread in the Gran Paradiso National Park (GPNP), where it could potentially compete with native geranium-consuming butterflies. Our study aimed to (1) assess the main drivers of its distribution, (2) evaluate the potential species distribution in GPNP and (3) predict different scenarios to understand the impact of climate warming and the effect of possible mitigations. Considering different sampling designs (opportunistic and standardised) and different statistical approaches (MaxEnt and N-mixture models), we built up models predicting habitat suitability and egg abundance for the alien species, testing covariates as bioclimatic variables, food plant (Pelargonium spp.) distribution and land cover. A standardised approach resulted in more informative data collection due to the survey design adopted. Opportunistic data could be potentially informative but a major investment in citizen science projects would be needed. Both approaches showed that C. marshalli is associated with its host plant distribution and therefore confined in urban areas. Its expansion is controlled by cold temperatures which, even if the host plant is abundant, constrain the number of eggs. Rising temperatures could lead to an increase in the number of eggs laid, but the halving of Pelargonium spp. populations would mostly mitigate the trend, with a slight countertrend at high elevations.
... The results of the spatial analysis for the whole set of data ( Figure S4) show that (i) the no mosquito category is more frequent than the other categories at higher elevations, reflecting the less permissive eco-climatic situation beyond 500 m [24,25]; (ii) the high abundance categories are more frequent in areas without full artificial surface cover, in agreement with recognised hot-spots in small green areas within a highly urbanized environment in Italy [6,26]; (iii) the high abundance categories are more frequent in areas closer to the coastline; notably, although no entomological data are available to confirm this results, it is noteworthy that all outbreaks of chikungunya in Italy started in coastal sites [4]; (iv) lack of clear distribution patterns related to distance from inland water bodies. ...
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Mosquitoes represent a considerable nuisance and are actual/potential vectors of human diseases in Europe. Costly and labour-intensive entomological monitoring is needed to correct planning of interventions aimed at reducing nuisance and the risk of pathogen transmission. The widespread availability of mobile phones and of massive Internet connections opens the way to the contribution of citizen in complementing entomological monitoring. ZanzaMapp is the first mobile “mosquito” application for smartphones specifically designed to assess citizens’ perception of mosquito abundance and nuisance in Italy. Differently from other applications targeting mosquitoes, ZanzaMapp prioritizes the number of records over their scientific authentication by requesting users to answer four simple questions on perceived mosquito presence/abundance/nuisance and geo-localizing the records. The paper analyses 36,867 ZanzaMapp records sent by 13,669 devices from 2016 to 2018 and discusses the results with reference to either citizens’ exploitation and appreciation of the app and to the consistency of the results obtained with the known biology of main mosquito species in Italy. In addition, we provide a first small-scale validation of ZanzaMapp data as predictors of Aedes albopictus biting females and examples of spatial analyses and maps which could be exploited by public institutions and administrations involved in mosquito and mosquito-borne pathogen monitoring and control.
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We derive an asymptotic likelihood function for open-population N-mixture models and show that it has favorable computational complexity and accuracy when compared to the traditional likelihood function for large population sizes. We validate our asymptotic model with simulation studies and apply our model to estimate the population size of Ancient Murrelet chicks, comparing against results obtained using the traditional N-mixture likelihood and an alternative asymptotic model based on the multivariate normal distribution. For the Ancient Murrelet case study, our asymptotic model computes twice as fast as the traditional models, eleven times faster when parallel processing is used, and provides higher-precision estimates than the asymptotic multivariate normal model. We provide an open-source implementation of our methods in the quickNmix R package.Supplementary material to this paper is provided online.
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Mosquito surveillance data can be used for predicting mosquito distribution and dynamics as they relate to human disease. Often these data are collected by independent agencies and aggregated to state and national level portals to characterize broad spatial and temporal dynamics. These larger repositories may also share the data for use in mosquito and/or disease prediction and forecasting models. Assumed, but not always confirmed, is consistency of data across agencies. Subtle differences in reporting may be important for development and the eventual interpretation of predictive models. Using mosquito vector surveillance data from Arizona as a case study, we found differences among agencies in how trapping practices were reported. Inconsistencies in reporting may interfere with quantitative comparisons if the user has only cursory familiarity with mosquito surveillance data. Some inconsistencies can be overcome if they are explicit in the metadata while others may yield biased estimates if they are not changed in how data are recorded. Sharing of metadata and collaboration between modelers and vector control agencies is necessary for improving the quality of the estimations. Efforts to improve sharing, displaying, and comparing vector data from multiple agencies are underway, but existing data must be used with caution.
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Surveillance programs are needed to guide mosquito-control operations to reduce both nuisance and the spread of mosquito-borne diseases. Understanding the thresholds for action to reduce both nuisance and the risk of arbovirus transmission is becoming critical. To date, mosquito surveillance is mainly implemented to inform about pathogen transmission risks rather than to reduce mosquito nuisance even though lots of control efforts are aimed at the latter. Passive surveillance, such as digital monitoring (validated by entomological trapping), is a powerful tool to record biting rates in real time. High-quality data are essential to model the risk of arbovirus diseases. For invasive pathogens, efforts are needed to predict the arrival of infected hosts linked to the small-scale vector to host contact ratio, while for endemic pathogens efforts are needed to set up region-wide highly-structured surveillance measures to understand seasonal re-activation and pathogen transmission in order to carry out effective control operations.
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A large chikungunya outbreak is ongoing in Italy, with a main cluster in the Anzio coastal municipality. With preliminary epidemiological data, and a transmission model using mosquito abundance and biting rates, we estimated the basic reproduction number R0 at 2.07 (95% credible interval: 1.47–2.59) and the first case importation between 21 May and 18 June 2017. Outbreak risk was higher in coastal/rural sites than urban ones. Novel transmission foci could occur up to mid-November.
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Background Experiments involving mosquito mark-release-recapture (MRR) design are helpful to determine abundance, survival and even recruitment of mosquito populations in the field. Obstacles in mosquito MRR protocols include marking limitations due to small individual size, short lifespan, low efficiency in capturing devices such as traps, and individual removal upon capture. These limitations usually make MRR analysis restricted to only abundance estimation or a combination of abundance and survivorship, and often generate a great degree of uncertainty about the estimations. Methodology/Principal findings We present a set of Bayesian biodemographic models designed to fit data from most common mosquito recapture experiments. Using both field data and simulations, we consider model features such as capture efficiency, survival rates, removal of individuals due to capturing, and collection of pupae. These models permit estimation of abundance, survivorship of both marked and unmarked mosquitoes, if different, and recruitment rate. We analyze the accuracy of estimates by varying the number of released individuals, abundance, survivorship, and capture efficiency in multiple simulations. These methods can stand capture efficiencies as low as usually reported but their accuracy depends on the number of released mosquitoes, abundance and survivorship. We also show that gathering pupal counts allows estimating differences in survivorship between released mosquitoes and the unmarked population. Conclusion/Significance These models are important both to reduce uncertainty in evaluating MMR experiments and also to help planning future MRR studies.
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Successful management of wildlife populations requires accurate estimates of abundance. Abundance estimates can be confounded by imperfect detection during wildlife surveys. N-mixture models enable quantification of detection probability and often produce abundance estimates that are less biased. The purpose of this study was to demonstrate the use of the R-INLA package to analyze N-mixture models and to compare performance of R-INLA to two other common approaches -- JAGS (via the runjags package), which uses Markov chain Monte Carlo and allows Bayesian inference, and unmarked, which uses Maximum Likelihood and allows frequentist inference. We show that R-INLA is an attractive option for analyzing N-mixture models when (1) familiar model syntax and data format (relative to other R packages) are desired, (2) survey level covariates of detection are not essential, (3) fast computing times are necessary (R-INLA is 10 times faster than unmarked, 300 times faster than JAGS), and (4) Bayesian inference is preferred.
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A guide to data collection, modeling and inference strategies for biological survey data using Bayesian and classical statistical methods. This book describes a general and flexible framework for modeling and inference in ecological systems based on hierarchical models, with a strict focus on the use of probability models and parametric inference. Hierarchical models represent a paradigm shift in the application of statistics to ecological inference problems because they combine explicit models of ecological system structure or dynamics with models of how ecological systems are observed. The principles of hierarchical modeling are developed and applied to problems in population, metapopulation, community, and metacommunity systems. The book provides the first synthetic treatment of many recent methodological advances in ecological modeling and unifies disparate methods and procedures. The authors apply principles of hierarchical modeling to ecological problems, including * occurrence or occupancy models for estimating species distribution * abundance models based on many sampling protocols, including distance sampling * capture-recapture models with individual effects * spatial capture-recapture models based on camera trapping and related methods * population and metapopulation dynamic models * models of biodiversity, community structure and dynamics * Wide variety of examples involving many taxa (birds, amphibians, mammals, insects, plants) * Development of classical, likelihood-based procedures for inference, as well as Bayesian methods of analysis * Detailed explanations describing the implementation of hierarchical models using freely available software such as R and WinBUGS * Computing support in technical appendices in an online companion web site.
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N‐mixture models provide an appealing alternative to mark‐recapture models, in that they allow for estimation of detection probability and population size from count data, without requiring that individual animals be identified. There is, however, a cost to using the N‐mixture models: inference is very sensitive to the model's assumptions. We consider the effects of three violations of assumptions which might reasonably be expected in practice: double counting, unmodeled variation in population size over time, and unmodeled variation in detection probability over time. These three examples show that small violations of assumptions can lead to large biases in estimation. The violations of assumptions we consider are not only small qualitatively, but are also small in the sense that they are unlikely to be detected using goodness‐of‐fit tests. In cases where reliable estimates of population size are needed, we encourage investigators to allocate resources to acquiring additional data, such as recaptures of marked individuals, for estimation of detection probabilities. This article is protected by copyright. All rights reserved.
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Monitoring animal populations is central to wildlife and fisheries management, and the use of N-mixture models toward these efforts has markedly increased in recent years. Nevertheless, relatively little work has evaluated estimator performance when basic assumptions are violated. Moreover, diagnostics to identify when bias in parameter estimates from N-mixture models is likely is largely unexplored. We simulated count data sets using 837 combinations of detection probability, number of sample units, number of survey occasions, and type and extent of heterogeneity in abundance or detectability. We fit Poisson N-mixture models to these data, quantified the bias associated with each combination, and evaluated if the parametric bootstrap goodness-of-fit (GOF) test can be used to indicate bias in parameter estimates. We also explored if assumption violations can be diagnosed prior to fitting N-mixture models. In doing so, we propose a new model diagnostic, which we term the quasi-coefficient of variation (QCV). N-mixture models performed well when assumptions were met and detection probabilities were moderate (i.e., ≥0.3), and the performance of the estimator improved with increasing survey occasions and sample units. However, the magnitude of bias in estimated mean abundance with even slight amounts of unmodeled heterogeneity was substantial. The parametric bootstrap GOF test did not perform well as a diagnostic for bias in parameter estimates when detectability and sample sizes were low. The results indicate the QCV is useful to diagnose potential bias and that potential bias associated with unidirectional trends in abundance or detectability can be diagnosed using Poisson regression. This study represents the most thorough assessment to date of assumption violations and diagnostics when fitting N-mixture models using the most commonly implemented error distribution. Unbiased estimates of population state variables are needed to properly inform management decision making. Therefore, we also discuss alternative approaches to yield unbiased estimates of population state variables using similar data types, and we stress that there is no substitute for an effective sample design that is grounded upon well-defined management objectives.
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Binomial N-mixture models have proven very useful in ecology, conservation and monitoring: they allow estimation and modeling of abundance separately from detection probability using simple counts. Recently, doubts about parameter identifiability have been voiced. I conducted a large-scale screening test with 137 bird data sets from 2,037 sites. I found virtually no identifiability problems for Poisson and zero-inflated Poisson (ZIP) binomial N-mixture models, but negative-binomial (NB) models had problems in 25% of all data sets. The corresponding multinomial N-mixture models had no problems. Parameter estimates under Poisson and ZIP binomial and multinomial N-mixture models were extremely similar. Identifiability problems became a little more frequent with smaller sample sizes (267 and 50 sites), but were unaffected by whether the models did or did not include covariates. Hence, binomial N-mixture model parameters with Poisson and ZIP mixtures typically appeared identifiable. In contrast, NB mixtures were often unidentifiable, which is worrying since these were often selected by AIC. Identifiability of binomial N-mixture models should always be checked. If problems are found, simpler models, integrated models which combine different observation models or the use of external information via informative priors or penalized likelihoods may help. This article is protected by copyright. All rights reserved.
Article
N-mixture models describe count data replicated in time and across sites in terms of abundance N and detectability p. They are popular because they allow inference about N while controlling for factors that influence p without the need for marking animals. Using a capture-recapture perspective, we show that the loss of information that results from not marking animals is critical, making reliable statistical modeling of N and p problematic using just count data. One cannot reliably fit a model in which the detection probabilities are distinct among repeat visits as this model is overspecified. This makes uncontrolled variation in p problematic. By counter example, we show that even if p is constant after adjusting for covariate effects (the "constant p" assumption) scientifically plausible alternative models in which N (or its expectation) is non-identifiable or does not even exist as a parameter, lead to data that are practically indistinguishable from data generated under an N-mixture model. This is particularly the case for sparse data as is commonly seen in applications. We conclude that under the constant p assumption reliable inference is only possible for relative abundance in the absence of questionable and/or untestable assumptions or with better quality data than seen in typical applications. Relative abundance models for counts can be readily fitted using Poisson regression in standard software such as R and are sufficiently flexible to allow controlling for p through the use covariates while simultaneously modeling variation in relative abundance. If users require estimates of absolute abundance, they should collect auxiliary data that help with estimation of p.