Ecology

Experimental designData collection took place in different sites disseminated along the mainland French coastline in sectors dedicated to Pacific oyster farming. Over the years, the number of sites monitored varied from 43 sites until 2009, to 13 between 2009 and 2013, and finally to 8 sites since 2015. Here, we focus on 13 sites (Fig. 1 & Table 1) that were almost continuously monitored since 1993. All these sites stand in tidal areas except Marseillan, located in the Mediterranean Thau lagoon, for which tidal variations are only tenuous and Men-er-Roué which is in subtidal deep-water oyster culture area in the Bay of Quiberon. Sentinel oysters were reared in plastic meshed bags fixed on iron tables, mimicking the oyster farmers practices. In Marseillan, half-grown oysters were cemented onto vertical ropes (from 1993 to 2007 and from 2015 to 2018), reared in Australian baskets (from 2008 to 2011), or put in bags fixed on iron tables (2012, 2013, 2014). As for spat oysters, they were reared in pearl-nets between 2008 and 2011 or put in bags since 2012.Fig. 1Site locations (coordinates in WGS84) along the French coastline. The site numbers refer to Table 1.Full size imageTable 1 Site identification and coordinates in WGS84.Full size tableDuring the 1993–2013 period, at the beginning of each annual campaign, one batch of diploid spat (three in 2012 and 2013) and one batch of diploid half-grown oysters were bought from an oyster farmer (i.e., wild-caught individuals) and then deployed simultaneously on all sites of the monitoring network. Here, the term “batch” designates a group of oysters born from the same reproductive event (spatfall or hatchery cohort), having experienced strictly the same zootechnical route. One batch could eventually be reared in several different bags (up to 3) deployed in the same site. Different batches were never mixed in the same bag.During the 2009–2013 period, up to three additional batches of triploid spat were bought in commercial hatcheries and included in the survey strategy (for a maximum of 6 batches of spat per site in 2012 and 2013). In 2009, the batches that were bought had already been exposed to a first wave of mortality before being followed by the network. Thus, the data collected this year should be interpreted with caution. Since 2014, the origin of spat and half-grown oysters has changed notably to better control the initial health status of oysters (no contact with the natural environment before deployment in all sites). The hatchery facility of Ifremer-Argenton now produces the sentinel diploid spat used in the monitoring network (one batch for all sites per campaign), whereas, the half-grown oysters was composed of spat reared on the same location the previous year but not monitored.Data collectionAfter the deployment of the different batches at the beginning of the campaign (seeding dates from February to April depending on the year), growth and mortality were longitudinally monitored yearly. Until 1999, annual campaigns usually ended in the winter of the year the monitoring began (i.e. in December), whereas, during the period 2000–2018, all sites frequently extended the campaign to end in the winter (February to March) of the following year.Observations were collected on each site quarterly until 2008 but then monthly to bimonthly depending on the season. At each sampling date, local operators carefully emptied each bag in separate baskets, counted the dead individuals (those with open or empty shells) and alive ones, and removed the dead individuals. Then local operators weighed all alive individuals in each basket (mass taken at the bag level, protocol mainly used between 1993 and 1998 and since 2004) and/or collected 30 individuals to individually weigh them in the laboratory (mass taken at the individual level, protocol used between 1995 and 2010 for spat and since 1996 for half-grown oysters).Data cleaningDuring the 2009–2013 period, several batches of spat were monitored per site and campaign. Some had a similar background to the batches monitored before 2009 (i.e., wild-caught spat from natural spatfall collected in the bay of Arcachon). To ensure the continuity of the time-series, we thus decided to remove all mass and mortality data of spat that did not originate from natural spatfall in the Bay of Arcachon, as well as triploid spat bought in hatcheries (see Table 2 for the origin and number of batches kept per site and campaign). To ensure that the life-cycle indicators are as comparable as possible between campaign and site (i.e. estimated in a common restricted time window), we removed data collected after December 31 of the year the monitoring began, as well as the site × campaign combinations when monitoring ended before October because the growth or mortality could still be in the exponential phase during this end-of-follow-up periods26. As the protocol of mass data collection changed over the years, we could not only use the mass data taken at the bag level or that at the individual level without greatly breaking the continuity of the time-series. We thus kept data taken at the individual level until 2008 and those taken at the bag level since 2009. We then checked for nonsense or missing data (e.g., the mass of a bag was equal to 0 or missing although they were still alive oysters in the bag), duplicated values and removed data for bags not part of the protocols or incorrectly identified. Finally, we removed site × campaign combinations for which we had fewer than four mass or mortality data because more data is necessary to study the temporal pattern of growth and mortality.Table 2 Origins of the different oyster batches retained after data cleaning.Full size tableData processing and analysisAt this point, the available data were, therefore, the number of living individuals per bag, the number of dead individuals since the last visit, the individual mass (g) of oysters (until 2008) and the total mass (g) of the living individuals per bag (since 2009).For mass data collected until 2008, we calculated the mean of the individual mass per date × site × age class combination by averaging the mass of the individuals. In other cases (mass data collected since 2009), we calculated the mean mass of individuals for each bag × date × site × age class combination by dividing the total mass of living oysters by the number of living individuals and then averaged data by date × site × age class combination. Our mass data, hereafter called mean mass data, is thus composed of the mean of the individual mass until 2008 and the mean mass of individuals since 2009.For mortality data, we could not calculate a cumulative mortality per bag × date × site × age class combination as (1-frac{number;of;alive;oysters;at;sampling;date}{number;of;oysters;at;previous;sampling;date}) because the total number of oysters (dead and alive) on a specific date often differed from the number of alive oysters at the previous date (e.g., because oysters were lost from the bags, or were sampled for complementary analyses such as pathogen detection). We thus took into account changes in oyster numbers between visits and calculated cumulative mortality using the following formula: CMt = 1 − ((1 − CMt-1) × (1 − IMt)). CMt = Cumulative mortality at time t; CMt-1 = Cumulative mortality at time t-1; IMt = Mortality rate at time t. IMt was obtained by dividing the number of dead oysters by the sum of alive and dead oysters at time t. When several bags were followed, we then averaged the cumulative mortality per date × site × age class combinations.We modeled the evolution of the mean mass and cumulative mortality data as a function of time to cope with changes in data frequency acquisition during annual monitoring campaigns. According to previous studies, annual mortality and growth curves in C. gigas follow a sigmoid curve11,26. Therefore, we fitted a logistic model, Eq. (1), and a Gompertz model, Eq. (2), which correspond to the most commonly used sigmoid models for growth and other data27, to describe Yt = mean mass (in grams) and cumulative mortality at time t.$${Y}_{t}=frac{a}{left(1+{e}^{left(-btimes left(t-cright)right)}right)}$$
(1)
$${Y}_{t}=atimes {e}^{left(-eleft(-btimes left(t-cright)right)right)}$$
(2)
These equations estimate three parameters: the upper asymptote (a), the slope at inflection (b), and the time of inflection (c).As the mean mass of half-grown individuals at the beginning of the campaign was higher than 0, we also fitted a four-parameter version of the logistic model, Eq. (3), and Gompertz model, Eq. (4), which is commonplace in the growth-curve analysis of bacterial counts27, and estimated (d) which represents the lowest asymptote of the curve. This parameter also moves the model curve vertically without changing its shape. The upper asymptote thus becomes equal to d + a.$${Y}_{t}=d+frac{a}{left(1+{e}^{left(-btimes left(t-cright)right)}right)}$$
(3)
$${Y}_{t}=d+atimes {e}^{left(-eleft(-btimes left(t-cright)right)right)}$$
(4)
Model fitting was carried out using non-linear least squares regressions (R package nls.multstrat28). This method allows running 5000 iterations of the fitting process with start parameters drawn from a uniform distribution and retaining the fit with the lowest score of Akaike Information Criterion (AIC). The sigmoid curve (i.e. logistic or Gompertz) with the lowest mean AIC of all models was selected as the best curve describing the data (see technical validation section). More

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GRIIS and the Country CompendiumThe Global Register of Introduced and Invasive Species (GRIIS) arose following recognition of the need for a product of this nature in discussions on implementation of the Convention on Biological Diversity (CBD). In 2011, a joint work programme to strengthen information services on invasive alien species as a contribution towards Aichi Biodiversity Target 9 was developed19. The Global Invasive Alien Species Information Partnership (GIASI Partnership) was then established to assist Parties to the CBD, and others, to implement Article 8(h) and Target 9 of the Aichi Biodiversity Targets. The Conference of Parties (COP-11) welcomed the development of the GIASI Partnership and requested the Executive Secretary to facilitate its implementation (paragraph 22 of decision XI/28). In 2013, the development of GRIIS was identified as a key priority to be led by the IUCN ISSG and Partners built on a prototype initiated almost a decade earlier (Item 4, Report of the Global Invasive Alien Species Information Partnership, Steering Committee, 1st meeting Montreal, 15 October 2013)20.GRIIS is a database of discrete checklists of alien species that are present in specified geographic units (including not only countries, but also as yet unpublished checklists of islands, offshore territories, and protected areas) (Fig. 1). The GRIIS Country Compendium is a collation and key product that derives and is updatable from the working GRIIS Research Database that underpins this and other GRIIS products (Fig. 1). Individual checklists are published to GBIF through an installation of the Integrated Publishing Toolkit21 (IPT) and hosted by the GBIF Secretariat. Exceptions include the Belgium (hosted by the Research Institute for Nature and Forest) and U.S.A checklists (hosted by the United States Geological Survey). Data are published as Darwin Core (dwc namespace) Archive files and the terms and structure follow that standard exchange format22.The GRIIS Country Compendium is an aggregation of 196 GRIIS country checklists of which 82% have been verified by Country Editors (see13), along with revised and additional fields that enable global level analysis and country and taxon comparisons (Tables 2, 3). Checklists for the 196 countries were combined into a single file (Table 3). A field was added to indicate which country the checklist belonged to, and the ISO 3116-1 Alpha-2 and Alpha-3 country codes are included to facilitate dataset integration (see ‘Usage notes’) (Table 2). A field was also added to indicate the verification status of each checklist (Table 2). The ID field was renamed (originally ‘taxonID’ and now ‘recordID’), as the data now represent a country-level occurrence dataset containing multiple records per species, rather than checklist-type data that contains one record per species. In total, the data now include 18 fields as described in Table 2, encompassing taxonomic, location, habitat, occurrence, introduced and invasive alien status (see also Table 1). This publication represents a versioned, citable snapshot of the Compendium (Fig. 1) that is ready for analysis and integration with other data sources (e.g. workflow23 and ‘Example applications of the Compendium’ outlined further below).Table 2 Fields and field terms in the GRIIS Country Compendium.Full size tableTable 3 Countries in the GRIIS Country Compendium and their review status.Full size tablePopulation of data fields in GRIISThe methods by which GRIIS is populated were described in 201813 and are summarised in brief here. A systematic decision-making process is used for each geographic unit by species record to designate non-native origin and evidence of impact (see Fig. 2 in Pagad et al.13). Comprehensive searches are undertaken for each country. Records are included from the earliest documented to the most recent accessed record prior to the date of the latest published checklist version. Information sources include peer-reviewed scientific publications, national checklists and databases, reports containing results of surveys of alien and invasive alien species, general reports (including unpublished government reports), and datasets held by researchers and practitioners13. A log of the changes to each checklist is available on the GBIF IPT24, with the changes to the Belgium checklist available at the INBO IPT25. The most up to date version of each checklist is thus available via GBIF.org, as is a list of all GRIIS checklists at GBIF.org24.Fig. 2Summary of data in the GRIIS Country Compendium. Number of invasive alien species by major taxonomic group (a) and habitat (b). Number of records per major taxonomic groups (c) and habitat (d). The number of species and records associated with invasion impact (i.e. isInvasive) are shown in black. Note different y-axis scales in each case.Full size imageIntroduced species of all taxonomic groups are considered for inclusion in GRIIS. Habitats include terrestrial, freshwater, brackish, marine and also host (i.e. for species that are not free-living) (Table 2, Pagad et al.13). The habitat information in GRIIS (Table 2) is sourced from taxon and region-specific databases such as WoRMS (World Register of Marine Species), FishBase, Pacific Island Ecosystems at Risk, and the USDA Plants Database. Typically, GRIIS records are at the species level, but in some cases, other ranks are more appropriate including infraspecies (including forms, varieties and subspecies). A separate field is provided for hybrids (Table 2). Where species are present and both native to parts of a country and alien in other parts of the country, their introduction status (dwc:establishmentMeans) is included as Native|Alien (Tables 1, 2)26. If there is limited knowledge about the Origin of the species, its introduction status (dwc:establishmentMeans) is included as Cryptogenic|Uncertain (Tables 1, 2).Two types of evidence are considered to assign a species by country record as invasive (Table 1, see also Pagad et al.13): (i) when any authoritative source (e.g. from the primary literature or unpublished reports from country/species experts), describe an environmental impact, and/or (ii) when any source determines the species to be widespread, spreading rapidly or present in high abundance (based on the assumption that cover, abundance, high rates of population growth or spread are positively correlated with impact)27,28. Each record is assigned either invasive or null in the isInvasive field to reflect the presence of evidence of impact, or absence of evidence of impact (note, not ‘evidence of absence of impact’), for that species by country record (Table 2). In the future this information may be supplemented with impact scores29,30,31. Finally, a draft checklist is sent to Country Editors for validation and revision (see Technical Validation).Taxonomic harmonization and normalizationThe use of different synonyms across countries to refer to the same taxonomic concept is frequent32. The species in each Country Checklist were thus harmonised against the GBIF Backbone Taxonomy33. The names in each checklist were matched using a custom script that integrates with the GBIF API34, and the accepted name, taxon rank, status and higher taxonomy (Table 2) were obtained at this stage. Spelling and other errors in assigning species authorship were corrected where appropriate.To validate the taxonomic harmonisation, every name variant present in the GRIIS Country Compendium was checked against the GBIF Backbone Taxonomy using the API33. A unique list of names (i.e. acceptedName Usage) was thus produced and the source name retained as ‘scientificName’ (that can differ across countries) (Table 2). Over 95% of names across all kingdoms matched exactly at 98% or greater confidence (Table 4). All names that were below 98% confidence or had a match type other than ‘Exact’ were checked and modified if appropriate to do so. Of the non-matches (n = 253, those with a match type of ‘None’), most were formulaic hybrid names of plants and animals (~62%), which are not officially supported by GBIF35. The remaining non-matches were names of mostly plants (17%), but also animals (8%), viruses (8%) and chromists (3%).Table 4 Taxonomic matching results (percentages) by Kingdom using the GBIF Backbone Taxonomy33.Full size tableData summaryThere are currently ~23 700 species represented by 101 000 taxon-country combination records, across 196 countries in the GRIIS Country Compendium. All raw numbers are provided to the nearest order of magnitude to reflect the taxonomic uncertainty and dynamic nature of GRIIS (see ‘Known data gaps and uncertainties’). The vast majority of records are at the species level (97.6%), with the remaining present as subspecies (1.7%), varieties (0.6%), genera (0.1%) and forms ( More

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Renewal processes represent development under variable conditionsThe consequence of a drastic environmental change can be demonstrated by introducing a shift in development time during the process. For demonstration, we consider a scenario where a group of individuals enter into a favourable environment reducing development time from (40pm 5) time units to (20pm 5).We show, in Fig. 1, that our dynamic pseudo-stage-structured MPM yields a gradual stage completion with an average development time of approximately (30pm 5) steps (solid dark lines) when conditions shift at ({tau }=20) (each step corresponds to 1 time unit). The target Erlang-distributed development trajectories without the shift are shown as dashed gray lines. The snapshots of the population structure, represented by the development indicator q, taken at each time step, show that half of the development is complete at the time of the switch and the switch accelerates the accumulation of q (Fig. S1).Figure 1Response to change in development time. The number of developing individuals is simulated by using the cumulative development process and compared to (a) the age-dependent development process, (b) an ODE representation, (c) an LCT representation, and (d) a DDE representation. Solid dark lines show the cumulative development and thick blue lines show the alternative models. Dashed gray lines mark the two target trajectories before and after the shift in development time (marked with red crosses).Full size imageIn age-dependent development, a sharp transition, instead of a gradual one, is observed at the (20^{th}) step (Fig. 1a). The switch results in the majority of individuals reaching target development age immediately at the time of switch. Previous work, reported in Erguler et al.59 and Erguler et al.55, aimed at modelling population dynamics under variable conditions, based on this dynamic age-dependent framework. Our results suggest that cumulative development might improve the fit to the data, prediction accuracy, and applicable geospatial range of these models.We see in Fig. 1b that the canonical ODE framework represents an exponentially distributed development time and a shift in rate at (t=20). The LCT extension to the framework helps to incorporate time dependence and represent the long and short development time distributions (Fig. 1c). The resulting model accommodates change in the rate parameter (gamma ) (Eq. 8), e.g doubling of (gamma ) changes development time from (40pm 5) to (20pm 2.5). However, to accommodate the required shift, the model needs to be transformed from a 66-dimensional system to an 18-dimensional one, which is beyond the scope of this work. We argue that in cases where development time distribution is fixed a priori (excluded from model calibration), the LCT framework provides a significant advantage over canonical ODEs. Although the framework has been used in the field of infectious disease epidemiology64,65, it has recently been applied to the modelling of vector population dynamics30.The DDE framework also yields a gradual development trajectory with an intermediate duration (Fig. 1d). However, the distribution tends towards the longer development trajectory compared to the one achieved with cumulative development. The canonical DDE framework assumes a homogenous cohort, where all individuals react in the same way to variations in development rate. The assumption gives rise to sharp stage transitions within a single generation if all individuals are introduced at the same time. As a potential workaround, it has been proposed to generate a plausible population history, through variable entry times, until the required (or observed) developmental variation builds up31,32. Variation in development rates then acts upon the population and results in the modification of the existing age-structure. It is worthwhile to mention that a recent extension to the DDE framework to accommodate trait variation in population dynamics34 might also accommodate changing development rates within a single stage; however, it has not yet been employed at this scale.Cumulative development is in agreement with the widely known degree-day (DD) framework, where development time is predicted by the heat accumulating in organisms46. Although the rate of accumulation in response to environmental conditions varies considerably, the DD framework implies that the combination of two different rates yields an average development time (also seen with cumulative development in Fig. 1). Experimental evaluation of this will be the topic of future research.It is worth mentioning that our dynamically structured renewal process-based MPM follows the assumption of random population heterogeneity9,11; namely, at the individual level, the future behaviour of an organism is not affected by its historical behaviour. However, trait variation within a population is prevalent in many species, and is known to impact population dynamics and species interactions34,66,67. Future development of our framework will consider improving upon this limitation.Environmental variation transformed into development timesSeveral non-linear relationships have been proposed to represent the temperature dependence of insect development68. A common feature is the presence of low and high temperature thresholds beyond which development is prohibitively slow. Often, there exists an optimum between the thresholds where the process is most efficient. A typical relationship between temperature and development rate, reported in Briere et al.50, is seen in Fig. 2a. Mean development time, given by the reciprocal of rate in Fig. 2b, exhibits the two thresholds and the optimum.Figure 2Development under environmental variation. In (a), development rate (Eq. 9) is shown with (alpha =1.5times 10^{-5}), (T_L=0^oC), and (T_H=50^oC). In (b), mean development time is shown together with the probability densities of three temperature regimes ((rho _L), (rho _M), and (rho _H)). In (c), the number of individuals completing development at each step are shown with respect to the three temperature regimes. Solid lines indicate the median, shaded areas indicate the (90%) range of 1000 simulations, and thick lines indicate simulations with the expected values of each regime.Full size imageTo investigate how temperature variation is transformed into cumulative development time, we assumed three variation regimes at relatively low, medium, and high temperatures ((rho _L), (rho _M), and (rho _H), respectively). Densities of the corresponding Gaussian probability distributions are plotted in Fig. 2b. Accordingly, each variation is transformed by a slightly different region of the rate function (Eq. 9). Eventually, the three development time distributions emerge as shown in Fig. 2c.We found that the output of (rho _H) is skewed towards longer durations compared to what we would otherwise obtain if we simulated the process under constant conditions with the mean of (rho _H). The impact of variation in the middle range, (rho _M), is similar to that of (rho _H), but less pronounced. Conversely, the output of (rho _L) is skewed towards shorter durations. Our results suggest that, when development is already highly efficient, variation in temperature causes frequent encounters of longer (but not shorter) development durations, eventually extending the overall duration of the process. In the low efficiency range, development takes long to complete, but frequent encounters of relatively short durations—especially as the process approaches its optimum duration—triggers completion earlier than in the case of no variation.Overall, our model predictions are in agreement with the rate summation effect, which states that the different outcomes obtained under constant and varying temperatures is due to the non-linear relationship between temperature and development rate (the Kaufmann effect)16. Furthermore, acceleration of development in insects subjected to varying high temperatures, its retardation at varying low temperatures, and low variability of development time in the linear range of the rate curve have been widely discussed69. Several groups have reported evidence in support of this effect, which is also in agreement with our results. For instance, Vangansbeke et al. (2015) reported for three insect species, Phytoseiulus persimilis, Neoseiulus californicus, and Tetranychus urticae, that varying temperatures with a lower mean yields faster development compared to the yield at mean constant temperatures70. However, observations of this phenomenon might result in different responses for different species at similar temperatures due to the difference in rate curves. Identification of the optimum temperature range may facilitate comparison. For instance, Carrington et al. (2013) assumed (26^oC) as optimum based on the high dengue incidence in Thailand, and showed that large variations around (26^oC) increases development time for the dengue vector, Aedes aegypti71. Wu et al. (2015) demonstrated that development is faster at around (26^oC) compared to (23^oC) for the fly, Megaselia scalaris, and found that varying temperatures at around (23^oC) accelerates the process47. Finally, in a modelling study employing DDs, Chen et al. (2013) reported that larger diurnal temperature ranges relate to additional DD accumulation and faster development in grape berry moth, Paralobesia viteana72. Under the realistic non-optimum field conditions, where these simulations had been performed, a decrease in development time is expected in response to varying temperatures according to our results.We note that the variation in development times is due to temperature since we ignore intrinsic stochasticity to demonstrate the impact of (rho ) in isolation. The deterministic setup removes the upper limit in the number of distinct pseudo-stage indicators: a different q emerges from each k, and a different k emerges from each (rho ). Since the number of pseudo-stages quickly exhausts the computational resources, we set the precision of q to the nearest 100(^{th}) decimal point, effectively capping the number of pseudo-stages at 100 (see Accuracy of the pseudo-stage approximation). As shown in Fig. S2, the approximation has a negligible impact on accuracy.Environmental dependency extracted from life tables under constant conditionsHaving discussed the importance of environmental variability in development, in this section, we employ a well-established experimental method to unravel the relationship between temperature and development time in a common mosquito species. In contrast to invasive vectors, which effectively render new territories suitable for disease transmission, Culex species pose an imminent threat with their wide distribution and ornitophilic (Cx. pipiens biotype pipiens), mamophilic (Cx. pipiens biotype molestus), and intermixed (their hybrids) blood feeding behaviour. Here, we investigate the temperature dependencies of mortality and development of Cx. quinquefasciatus, the southern house mosquito, which is an important disease vector, widely distributed across the tropics and sub-tropics73,74.To infer the dependencies, we used a generic temperature-driven insect development model, described in Methods, and the life history observations performed at five constant temperatures (15, 20, 23, 27, and (30,^{circ })C) under laboratory conditions60,61. As a result of the inverse modelling procedure, detailed in Methods, we found that the generic model yields an overall match between the simulations and observations. In Fig. 3a, we present a comparison of observed and simulated maximum production and the stage-emergence times for pupae and adults. Here, we define the stage-emergence time as the time taken from the beginning of an experiment to the time when half of the maximum production of a stage (pupa or adult) is observed. In addition, in Fig. S3, we present the comparison of time trajectories separately for each temperature.Figure 3Inverse modelling of Cx. quinquefasciatus environmental dependency. The comparison of observed and simulated maximum pupa (P) and adult (A) production and the corresponding stage-emergence times is given in (a). Observations are represented with dots and simulations with box plots. The environmental dependency of larva and pupa development time (b) and mortality (c), derived by the posterior mode sample (Theta _q), is shown in (b,c). Solid lines represent the median and shaded areas represent the (90%) range.Full size imageWe found that the generic model faithfully replicates the observed development times of larvae and pupae. On the other hand, stage mortalities are predicted well at three temperatures, but are overestimated at 20 or (27,^{circ })C. The impact of temperature on mortality might be more complex than it is captured by the quartic equation (Eq. 11). Optimum survival seen at (27,^{circ })C suggests that the relationship might be non-symmetrical or multimodal. In addition, the observed variability in mortality suggests that the mismatch could also be due to experimental error or the intrinsic stochasticity of the biological processes.We extracted the functional forms of temperature dependence from the posterior samples, shown in Fig. 3b, c, and found that the data inform the model as expected within the temperature range of the experiments ((15{-}30,^{circ })C). Stage durations are well informed, and reflect the low variability seen in the data (the standard deviation is less than 1.5 days at all temperatures for both stages). Accordingly, pupae develop in less than 4 days, which is much shorter than the larva development time (between 10 and 20 days above (20,^{circ })C). The model predicts that the minimum temperature at which development occurs (from the larva stage) is (10.5,^{circ })C, which is close to (10.9,^{circ })C, reported in Grech et al.75.The observed variability in pupa and adult production suggests that survival is a highly stochastic process regardless of the controlled laboratory conditions. A deterministic model, such as the one used in this context, represents the mean of such processes but does not capture their variability. The simulated variability is a result of the uncertainty in parameter estimates. Model parameters contribute unequally to the output as a result of the model structure and the functional forms of temperature dependence, and the data inform certain parameters better than others76,77. For instance, daily mortality, shown in Fig. 3c, is more constrained for larva than pupa, which is likely due to the short duration of the pupa stage—changes in daily mortality have larger consequences as development time increases.We note that a well-informed model yields predictions in the form of verifiable hypotheses; however, these are not necessarily accurate predictions. Model accuracy is assessed when such hypotheses are experimentally tested as part of the cyclic process of model development78. Here, we demonstrated that our modelling framework can be used to derive biologically meaningful inferences and to help improve the understanding of the temperature dependence of Cx. quinquefasciatus.Greater information content of semi-field experimentsThe number of experiments required to test a range of conditions, including different combinations of multiple drivers, may quickly exhaust available resources. Moreover, variable conditions may have a previously unaccounted impact on development and mortality. In this section, we demonstrate that observations performed under variable conditions are valuable sources of information for our modelling framework, which is capable of representing the dynamics under such conditions.Cx. pipiens, the northern house mosquito, is a competent disease vector, widely distributed across the temperate countries in North America, Europe, Asia, and North and East Africa74,79. Unlike Cx. quinquefasciatus, Cx. pipiens biotype pipiens is known to enter a reproductive diapause phase, where adult females arrest oogenesis during harsh winter conditions80,81. When larvae are exposed to short photoperiods and low temperatures during development, they emerge as adults destined to diapause. Although Cx. pipiens biotype molestus has lost the ability to diapause, its immature stages have been reported to retain metabolic sensitivity to photoperiod82,83.To reveal the environmental dependence of the molestus biotype, we exposed its eggs to variable temperatures in semi-field conditions until adult emergence (or loss of cohort). The numbers of viable larvae, pupae, and adults observed in different experimental batches are given in Fig. S4. We employed the extended model with both temperature and photoperiod dependence (see Methods), and calibrated the model against seven of the semi-field experiments, performed in March, May, June, July, August, and September (Fig. S4(a), (b), (d), (f), (g), (i) and (j)).As a result, we found that the model replicates the patterns of abundance emerging in the observations, e.g. stage timing and maximum adult production, reasonably well in most of the experiments, regardless of the times during which they were performed (Figs. S5 and S6). Quantitative evaluation of the agreement reveals that the observed and simulated adult emergence times are less than a week apart (Table 1).Table 1 Comparison of observed and simulated adult emergence time and the total number of adults produced. Simulation output is given in terms of the median and (90%) range.Full size tableOn the other hand, we found that egg and larva mortalities, and also, pupa and adult production are highly variable in the observations (see Fig. S4(c), (f), and (g)). Spikes of larva mortality are seen in Spring and Autumn (especially in May, September, and October). Despite this variability, the difference between the predicted and observed adult production was around 11 or less, except in the case of the experiment E7, which unexpectedly yielded only one pupa and no adults.We obtain relatively large mismatches when predicting larva abundances, specifically where egg mortality is not predicted well (E5, E7, E8, E10, E11, E12). We hypothesise that the stress associated with rearing lab-grown specimens under variable conditions might elevate egg mortality, induce premature hatching, or affect the survival of the larvae produced. Since egg development starts inside gravid females, i.e. under the optimum conditions of the laboratory, the observable part of development subjected to variable conditions remains mainly the hatching behaviour. Consequently, we observed rapid and synchronous completion of the egg stage in all experiments (see Figs. S5 and S6). Being exposed to a narrow range of temperatures, relatively less information can be obtained on the environmental dependency of the egg stage. As a potential improvement, we recommend that future adaptations of the semi-field experiments consider using field-captured adult female mosquitoes as the source of eggs.In addition to egg mortality, we observed spikes of larva mortality in May (E3), July (E8), and in Autumn (E14, E15, and E16). A likely cause of such transient high mortality is brief temperature shifts towards the extremes. However, the rarity of such events prevents the inverse modelling procedure from adequately capturing their impacts on life processes. As a potential improvement, we recommend that the experiments are performed in overlapping time frames, increasing the likelihood of observing the impact of an extreme event at different times during development. We note that the early decline in larva abundance seen in Autumn could be a result of insufficient food supply due to the increased nutritional requirements. According to the proposed metabolic response to short photoperiods, larvae would require additional food to accumulate fat reserves in preparation for diapause, the state where adult females endure several months without feeding. This implies that development takes longer than it would at long photoperiods when subjected to similar temperature regimes.Using the extended model and the semi-field data, we identified the environmental dependencies shown in Fig. 4. The data informed about the temperature dependency of each life stage as well as the photoperiod dependency of larvae. As expected, the overall variability in the inferred dependencies is higher for Cx. pipiens compared to Cx. quinquefasciatus (Fig. 3). We found that the larva and pupa development times closely match the observations reported by Spanoudis et al.62 at long photoperiods (see Fig. S7). However, the development times reported in Kiarie-Makara et al.84 at short photoperiods and moderate temperatures do not suggest a significant impact of daylight, which could be due to the particular strain of Cx. pipiens used in these experiments. As expected, the temperature dependency of egg development was not well informed by the data in the current configuration of the model and the functional forms of environmental dependence.Figure 4Environmental dependency of Cx. pipiens development and mortality inferred from semi-field life table experiments. Solid lines represent the median and shaded areas represent the (90%) range.Full size imageWe found that the photoperiod dependency is significantly non-linear with an average threshold of 13.7 hours of daylight (Fig. 4c). Photoperiod-driven extension in development time (about 1.7 times more at 13:11 h L:D than at 15:9 h L:D) contributes to improving the accuracy of predictions at the end of the high season (Fig. S8). The critical photoperiod (CPP) agrees well with the ones identified for Cx. pipiens biotype pipiens85,86. For instance, Sanburg and Larsen reported that there is an exponential relationship between follicle sizes in adult females (signifying commitment to diapause) and the photoperiods they were exposed to during immature stages85. We inferred a similar (but reverse) gradient between photoperiod and the extension of larva development time from 15 to 12 hours of daylight (Fig. 4c).Risk assessment with annual development profilesWe extrapolated the development dynamics of Cx. pipiens over the calendar year by setting up a hypothetical experiment at the beginning of each week. We simulated the subsequent development dynamics and obtained the annual development profile as shown in Fig. 5. Accordingly, the immature stages begin development from late February and the first adults emerge in May (adults emerging late in May start developing in the experiments set up late in March). The profile is consistent with the regular Cx. pipiens high season in the region.Figure 5Annual development profile of Cx. pipiens in Petrovaradin, Serbia, in 2017. The outcome of each hypothetical semi-field experiment is plotted vertically along the y-axis at the date when the experiment is initiated. The maximum number of adults produced is given in blue, and the time it takes (from the date indicated on the x-axis) to produce half of the maximum is given in green. Solid lines represent the median and shaded areas represent the 90% range of model predictions. Outcomes of the semi-field experiments (dots) are plotted together with the model predictions. The time points marked with circles indicate the experiments used to calibrate the model. Estimated time of first adult emergence is given in the inset.Full size imageAs seen in Fig. 5, predicted adult emergence times agree well with the observations throughout the high season. However, there is a greater variation in the maximum number of adults than the times of emergence (extending to almost (40%) of the possible outcomes in early August). A greater variability (almost (80%) in August) is seen in the corresponding observations, which we transformed into the percentage of eggs emerging as adults (where available) to facilitate comparison. According to the model, variation in adult production is associated with the variation in both development times and mortality during immature stages. We recall that the uncertainty in the informed environmental dependencies is high around relatively less frequently encountered values—especially the lower and higher temperature extremes (Fig. 4). Specifically, egg development times cannot be identified precisely, but immediate hatching of the larvae is predicted between 20 and 25 °C. Consequently, we found that frequent exposure to temperatures outside the well-informed range have a significant impact on the variation in adult production (Fig. S9).We adopt the time of first adult emergence as a proxy of the first generation of adults in the season. According to our model, early adult emergence is a result of shorter development times and higher success rates, which indicates that the temperature conditions allow for an early first generation of adults. An early first generation greatly contributes to an early peak of adult abundance, which may increase the risk of vector-borne disease transmission in humans. For instance, an early peak of abundance may cause an early start of West Nile virus circulation and amplification in Culex pipiens and their avian hosts, which increases the likelihood of virus spillover to humans51,87. Anecdotal evidence shows that the anomalously hot April and May that occurred in 2018 in Serbia shifted the peak of Cx. pipiens abundance forward by more than one month (Petrić et al., unpublished). Similarly, 2018 was the year with the largest number of autochthonous West Nile virus infections throughout Europe (more than the total of the previous seven years together)88,89.In summary, our results showed that the semi-field experiments, when used in combination with our dynamic pseudo-stage-structured MPM, help to develop predictive models and inform over a wide range of environmental conditions. We developed a predictive model of Cx. pipiens biotype molestus development and gained insights into the specifics of temperature and photoperiod dependencies by reducing the need of extensive laboratory data. We used life history observations from 7 experiments performed under semi-field conditions and employed a generic model structure, largely uninformed on the specific environmental dependencies of the species. The cumulative development framework we introduced applies broadly to poikilotherms subjected to highly variable environmental conditions. Although the generic model structure helps to develop exploratory models and identify potential environmental dependencies, accuracy can be improved by customising the models for the known dependencies of particular species. With a straightforward extension of the development model to cover the complete life cycle (with egg laying and density dependence), it is possible to incorporate field observations of eggs or adult mosquitoes, and develop an environment-driven population dynamics model. More