^{1}

^{2}

^{3}

^{4}

^{5}

^{1}

^{3}

^{2}

The authors have declared that no competing interests exist.

Conceived and designed the experiments: GM PP SM AP RR. Performed the experiments: GM PP. Analyzed the data: GM PP MG AP SM RR. Wrote the paper: GM PP MG AP SM RR.

Zoonotic pathogens are believed to cause about three quarters of human emerging infectious diseases, many of which (22%) are spread by vectors such as mosquitoes [

The transmission of mosquito-borne diseases is largely driven by the abundance of the vector [

In the Piedmont region of Northwestern Italy, an extensive program of monitoring adult mosquitoes has been implemented, since 1997, by the Municipality of Casale Monferrato and the Istituto per le Piante da Legno e l’Ambiente (IPLA). The area is at risk for WNV, because of the presence of suitable vector and reservoir host populations, and the increasing numbers of human cases of WNV in adjacent areas [

The main goal of our work is to describe and interpret in a robust theoretical framework the high heterogeneity observed among different seasons for

In their work, Rosà and co-authors [

Density-dependence in mosquito population growth is another important factor in regulating

Diapause is a common mechanism adopted by mosquitoes to survive through winter. While other mosquitoes, for instance

We therefore develop a density-dependent stochastic model that describes temporal variations of

We follow a stochastic approach as deterministic models ignore the contribution of demographic stochasticity which is especially relevant when the vector population is low, for instance at the beginning and at the end of mosquito activity season. The proposed model explicitly accounts for the temporal variation of all immature stages, i.e. eggs, four larval instars and the pupal stage; it is assumed that the lengths of all mosquito life stages depend on temperature and that developmental rates of larval stages are density-dependent; finally, a diapausing mechanism is included in response to the photoperiod.

The effect of precipitation on survival and development of mosquito life stages is not explicitly accounted for, as, to the best of our knowledge, no reliable data on

Finally, extensive model simulations have been carried out in order to better understand the role played by different eco-climatic factors in shaping the seasonal specific vector dynamics and to forecast, under various illustrative scenarios, likely changes in

_{2} dry ice baited traps operated by Municipality of Casale Monferrato and the Istituto per le Piante da Legno e l’Ambiente (IPLA), under the regional program for mosquito surveillance, authorized by Regione Piemonte. The traps were dispersed over an area of 987 km^{2} in the Eastern Piedmont Region in North West of Italy (see Figure G in

The model for the dynamics of the abundance of the vector in seven life stages of _{1}, _{2}, _{3}, _{4}), pupae (_{E} is the number of eggs laid in one oviposition; _{A} is the length of the gonotrophic cycle; _{C} is a function of the time defined equal to 1 when the trap is open and 0 otherwise;

Daily mean temperature and precipitation records for the period and study area considered were obtained from ARPA Piedmont [

We actually adopted a discrete–time stochastic version of model _{0}(

Mortality and developmental rates across different vector life stages have been modeled as a function of temperature following the approach already proposed in [

To the best of our knowledge, data on adult mortality at different temperature are not available for _{E} per oviposition and the duration of the gonotrophic cycle _{A} in our simulations were chosen uniformly in the intervals [150,240] and [

Free model parameters to be estimated are the capture rate α, the increase of adult death rate in the wild β, the density-dependent factor _{0}. More specifically, we assumed α and β to be equal among all years considered, while the value of _{0} could be year-specific.

Model predictions for the dynamics of mosquito population during a specific season depend on the free parameters θ = (α, β, _{0}) but are also influenced by the intrinsic stochasticity of simulations and by the uncertainty on parameters defining the transition rates used in the model (e.g. the developmental and mortality rates for different mosquito life-stages). By denoting the latter set as _{{m,y}}(

In order to estimate the free parameters by taking into account both the stochasticity of the process and the uncertainty on parameter estimates defined by _{{m,y}}(

The posterior distributions of the free parameters θ were explored by Markov chain Monte Carlo (MCMC) sampling applied to the likelihood of observing the monthly number of trapped adults, averaged among the 24 considered sites. Assuming that for each month the number of observed trapped adult mosquitoes follows a Poisson distribution with mean obtained from the model, the likelihood of the observed data over the twelve simulated years has been defined as
_{{m,y}} is the observed average number of trapped adults over the 24 sites at month _{0}(

The posterior distribution of θ was obtained by using random-walk Metropolis-Hastings sampling approach [

Model predictions associated with the estimated posterior distributions of model parameters for the different seasons (from 2000 to 2011) were analyzed in terms of

Finally, we applied the model to assess the influence of the temperature on the population dynamics. To this aim, we simulated each year

The proposed model can well reproduce the number of weekly captures of adult mosquitoes reported between May and September for all the twelve years of observation (2000–2011). In particular, more than 90% of the weekly trap records lie within the 2.5–97.5% quantile of model predictions. The model shows the ability of reproducing both the strong seasonality characterizing the adult population dynamics within different years and the high heterogeneity observed among different seasons in terms of mosquito density (see

Average number of weekly captured

In agreement with collected data (see

Boxplot (2.5%, 25%, 75% and 97.5% quantile and median) of predicted onset (lower orange bars in panel a) and offset (higher orange bars in panel a), defined as the week of the year when the 5% and the 95% of the cumulative captures are reached respectively; week of the year associated with peak (highest) capture (red bars in panel b); total annual captures, i.e. the sum of the 20 weekly captures (green bars in panel c); peak capture, i.e. maximum number of trapped adults in a single capture session (purple bars in panel d). Blue boxplots represent the distributions of the observed site-specific values. Distributions of the observed peak capture were obtained by computing the maximum of 3-point moving average of weekly captures.

The highest capture is predicted to occur, on average, between the 27^{th} and 31^{st} week of the year (corresponding to the month of July) in good agreement with observed values (see

The 2.5–97.5% quantile of the predicted offsets are between the 34^{th} and 37^{th} week (mid-August—mid-September) in each year, like the observed captures (see ^{st} and the 23^{rd} week (end of May–beginning of June), a few weeks earlier than what observed (median values between 24^{th}-27^{th} week, June).

In [

Furthermore, the median predicted season length is positively correlated (y = −2.00 + 0.80⋅x, p-value<0.01) with the average temperature recorded between mid-April and the end of June, which varies from 18.5°C in 2004 to 21.5°C in 2003.

The model accounts for the observed heterogeneous dynamics of the mosquito population among different seasons thanks to the explicit inclusion of two seasonal factors. The first one is the dependence of developmental and mortality rates of different mosquito stages on temperature. The second one is represented by the assumption of a year specific density-dependent factor for larval stages, which may reflect possible differences in the availability of breeding sites in different years.

The estimated posterior distribution of the initial number of adults (namely A_{0}) spans a wide range, between approximately 1 and 1,000 in each season (see

Boxplot (2.5%, 25%, 75% and 97.5% quantile and median) of posterior distributions of parameters _{0} (panel a) and

Conversely, estimated posterior distributions of the density-dependent factor are remarkably different among years (see

The capture rate α is estimated to be on average 11.35% (10% median, see

The estimated posterior distribution of β, the increase in adult mortality rate in the wild relatively to lab conditions, is also very wide (95% CI 1.09,23.98, see

Undoubtedly, independent estimates on a subset of our free parameters would allow providing more robust estimates of these specific biological quantities. However, the MCMC approach represents a suitable statistical technique to handle uncertainties about parameters, as it takes into account all possible parameters’ configurations compliant with patterns observed in the data. Simulations were run also by assuming seasonal dependent α and β. The two different modeling assumptions result in qualitatively similar predictions about the abundance of the mosquito among different years (see

Temperature plays a crucial role in shaping the population dynamics of

Boxplots (2.5%, 25%, 75% and 97.5% quantile and median) of predicted annual synthetic indexes associated with different temperature inputs (x-axis, from -2.5°C to +2.5°C with respect to actual records). Panel (a) shows the effect on the duration of the breeding season, defined as the difference between the week of the year when the 95% and the 5% of the cumulative captures are reached; panels (b) and (c) show respectively the effect on the timing and the value of the peak capture; panel (d) shows the effect on the total annual captures.

Hotter seasons might also reduce the maximal abundance of adult mosquitoes (about -25% for the +2.5°C scenario) but produce only negligible effects on the overall number of captured adults during the whole season. This apparent contradiction can be explained by the observation that higher temperatures increase mosquito populations during spring and decrease them during summer (see

On the other hand, changes in the larval carrying capacity produce proportional effects on mosquito abundance during the whole breeding season. For instance, our analysis shows that a 30% reduction of the density-dependent factor

Boxplots (2.5%, 25%, 75% and 97.5% quantile and median) of predicted annual synthetic indexes associated with different values of

In this paper, we investigated which are the main drivers of the observed high heterogeneity characterizing the

Overall, this work provides useful indications about the dynamics of

The data also exhibit a large degree of spatial heterogeneity, as trap captures vary in abundance and temporal patterns. Investigating these patterns would require detailed information on habitat utilization and related mosquito movement, which are not available and are beyond the scope of the present work. Instead, data coming from different traps were aggregated in order to strengthen the investigation of seasonal heterogeneity, by reducing the influence of climatic condition characterizing single specific days.

In this work,

(XLSX)

(PDF)

The fieldwork was realized by the technicians of the "Istituto per le Piante da Legno e l'Ambiente" operative center of Casale Monferrato. The authors especially acknowledge Andrea Mosca for useful discussions on fieldwork data. We thank the anonymous reviewers for their helpful and constructive comments that contributed to improve the final version of the manuscript.