Introduction

In Europe and North America, most wild ungulate populations are managed through hunting (Solberg et al. 1999; Apollonio et al. 2010). Hunting mortality rates often exceed natural mortality rates and can limit population abundance (Solberg et al. 1999; Allendorf et al. 2008; Keuling et al. 2013). However, despite several million animals being culled every year in Europe (Massei et al. 2015; Linnell et al. 2020), some ungulate populations continue expanding both numerically and spatially, such as red deer (Cervus elaphus), roe deer (Capreolus capreolus) and wild boar (Sus scrofa; Morelle et al. 2016; Linnell et al. 2020). The increase in ungulate populations sizes, in particular wild boar, has potentially negative consequences for both the economy and the environment, e.g., zoonoses (Gortázar et al. 2006; Wu et al. 2011; Podgórski and Śmietanka 2018), crop damage (Schley and Roper 2003; Geisser and Reyer 2004), damage to timber production (Côté et al. 2004; Burrascano et al. 2015), or road accidents (Langbein et al. 2011; Thurfjell et al. 2015). Maintaining wild ungulate populations at “acceptable” levels is therefore an important management goal (Apollonio et al. 2010; Massei et al. 2015; Linnell et al. 2020).

To control population abundance, several management policies have been implemented, including the establishment of minimum quota systems (i.e., minimum number of individuals to be culled at the end of the hunting season; Vajas et al. 2020). A quota is reached by adjusting the hunting effort, i.e. number of hunters, during the hunting trip (Hilborn 1985; Maillard et al. 2010; Vajas et al. 2020). It becomes, however, increasingly difficult to reach these quotas in the current context of a global decline in the number of hunters translating into a decline in hunting effort (Massei et al. 2015). This raises the issue of trying to increase hunting efficiency (more culled animals for the same effort; Vajas et al. 2023). Moreover, the relationship between the effort invested by hunters and the probability that it results in a cull is generally non-linear and depends on hunting conditions and timing during the hunting season (Walters 2003; Maunder et al. 2006; Vajas et al. 2021).

Fisheries science provides an analytical framework for separating the fishing process into two key components: effort and catchability. Fishing effort refers to the amount of investment in fishing activities while catchability corresponds to the probability of catching a fish by deploying a unit of effort and is influenced by fishing method and species biology (Hilborn et al. 1992; Arreguin-Sánchez 1996; Vajas et al. 2021). Translated to the hunting context, hunting effort corresponds to the amount of labor provided by hunters (Vajas et al. 2020) and "cullability" (catchability adapted to the cull) allows us to understand the places, times and best conditions in which the same hunting effort would lead to more culled individuals (Vajas et al. 2023). Consequently, the success of hunting can be quantified in terms of the number of animals culled, data provided and associated with a hunting effort quantity within the collected hunting bag. The cullability of the animals represents this binding probability that needs to be brought out.

Cullability can vary in space and time depending on animal behavior and conditions affecting hunters (Salthaug and Aanes 2003; Wilberg et al. 2009; Thurfjell et al. 2017; Vajas et al. 2021). In space, visibility for hunters can vary with vegetation cover and progression can be impaired by topography (terrain ruggedness), possibly reducing hunting success (Lebel et al. 2012; Wszola et al. 2019; Vajas et al. 2021). Hunters’ skills may also improve over the hunting season, leading to an increased hunting success during the season to reach a plateau and in some cases, followed by a decline in effectiveness, i.e. less culling for the same effort (Milner-Gulland et al. 2008; Diekert et al. 2016; Vajas et al. 2020, 2021). Habitat can also change with season: e.g., in autumn, trees losing their leaves facilitates game tracking (Mysterud and Østbye 1999; Rivrud et al. 2014; Vajas et al. 2020). On a daily scale, weather conditions can also affect cullability in a more sudden and less controllable way. Bad weather conditions can decrease cullability by degrading hunting conditions and by changing animal movement behavior as well as their detectability (Keuling et al. 2008; Thurfjell et al. 2013). It also reduces hunter’s motivation, and therefore the effort involved (Rivrud et al. 2014; Diekert et al. 2016).

In this study, we address the following two questions: (i) is success of wild boar hunting, shown through cullability variations, affected by the weather cullability variation on a daily basis, and if so, to what extent? and (ii) does hunting effort, i.e., simplified by the number of hunters present during the hunt party, during a wild boar drive hunt vary according to the weather conditions on a daily basis, and if so, to what extent ? For this purpose, our study relies on daily hunting log data records (daily hunting bags) for two southern departments in France, as well as daily meteorological data from national weather stations from 2005 to 2016. Although it seems that "bad weather" reduces hunting success and effort, in the absence of biological a priori for the exact effect of each weather variable (Tredennick et al. 2021), we performed model selection across multiple biologically realistic models within an initial global exploratory approach. The aim is to address the aforementioned yes/no questions on the weather effects at large scale. In a subsequent process-based approach, in which analyses are conducted under controlled conditions, the aim is to estimate the range of these effects.

Materials & methods

Study area & hunting process

The study areas are located in the departments of Ardèche and Hérault in south of France (Fig. 1). Ardèche is characterized by a wide range of weather conditions due to its topography and North–South extension. The area is divided into three bio-geoclimatic regions: plateaus to the north (between 350 and 850 m), the Cévennes mountain to the west (up to over 1000 m), and Mediterranean lowland in the south. Hérault stretches from the Mediterranean Sea to the southern Cévennes moutains, reaching an altitude of up to 1000 m. The climate is Mediterranean with a temperate continental influence in the mountainous areas. The southern Ardèche and Hérault are typified by Mediterranean habitats comprising oak and garrigue, which provide a refuge and concealment for wild boar (Fournier-Chambrillon et al. 1995; Acevedo et al. 2006; Vajas et al. 2024). Biogeographical description of habitats and topography, as well as associated climatic conditions, is given in an earlier study (see Vajas 2020) and illustrated in appendix A (A.1 for Ardèche and A.2 for Hérault). Departments are divided into Management Units (MUs), defined according to biogeographical factors (Maillard et al. 1999), which group several municipalities together. Ardèche is divided into 28 MUs and Hérault into 23 MUs (Fig. 1).

Fig. 1
figure 1

Location of the two departments in France (red polygons). Ardèche (left) is made up of 28 hunting Management Units (MUs) constituting the territories of the full dataset, and 3 × 2 MUs in controlled dataset in three key habitats: “deciduous valley”, “mountain slope woodland”, and “central mountain plateau”. Hérault (right) is composed of 23 MUs constituting the full dataset territories and 2 × 2 MUs in the controlled dataset in two key habitats: “mediterranean mid-mountain” and “mediterranean mixed-scrubland”. Note: the colours follow the graphical abstract

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Both in Ardèche and Hérault, wild boar hunting occurs from September to February. Hunting is organized mainly as drive hunts (Vajas 2020), involving long-legged hunting dogs able to run for several kilometers, between 2 and 5 unarmed people (beaters) who “drives” game out of cover or “drive” dogs, and hunters armed with rifle posted at strategic points (Vajas 2020). The number of hunting dogs depends on the number of lead-dog beaters, each of them accompanied by one pack of half a dozen dogs.

Hunting logbooks and weather data

Hunting logbook data management

Hunting teams (one per municipality) are assigned a hunting logbook by their respective department’s hunting federation. Date and location of each hunting trip, number of hunters involved, and number of wild boars culled are recorded in these logbooks, for 11 hunting seasons in Ardèche (2006–2007 to 2016–2017) and 12 seasons in Hérault (2005–2006 to 2016–2017), covering 527 municipalities, 337,910 hunting trips, and 287,861 culled wild boars (Table 1, table B.1, and table B.2).

Table 1 Summary statistics for study areas, hunting logbooks and weather data for the full data set and the controlled dataset (homogeneous sub-sampling)
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We first ran our variable selection model (exploratory approach) on the full dataset to answer the first question ‘does the weather have an effect’ – yes or no – at large scale. Second, we ran our variable selection model (process-based approach) and used the selected model on a subsampling dataset to estimate the intercepts value to answer the second question ‘to what extent’ under controlled dataset condition. This second approach is driven by three key considerations: (i) to limit the biases set out in the conceptual framework for cullability (success ~ f(effort, cullability, density)), i.e. to control (a) density variance and (b) habitat variance (habitat cullability proxy) within a framework as homogenous as possible – (ii) to offer greater interpretability of the results i.e. attributed the cullability estimated variations only to weather variations (see appendix C for MU scale modelling) – (iii) to improve modelling efficiency (better chain convergence and clearer select variable results, see results section).

Thus for (a) we used wild boar density data estimated in a previous study on the catchability framework (Vajas et al. 2021) at the MU and year scale to ordered MU with the less density variance over time (variance analyses on years median density value at MU scale, appendix D.1), (b) we used public landcover habitat data (IGN data see description in appendix A), and checked multifactorial habitat analysis on forest composition diversity as proportion of deciduous trees, conifers, lands, forest fruit trees (appendix A) at municipalities within MU (10 ± 4 municipalities per MU) to ordered MU with the less habitat variance over space (variance analyses from each PCA row, see appendix D.2; Dray and Dufour 2007; Kassambara and Mundt 2020). As a final step, a map of large meteorological areas clusters (spatial clustering methods apply to group MU together, appendix D.3; Charrad et al. 2014; Galili 2015) was used to identify five MU pairs that exhibited a common weather pattern and low density and habitat variances (appendix D.4).

Therefore, we focused our model estimation on 5 mains emblematic territories corresponding to “Deciduous valley”, “Mountain slope woodland”, “Central Mountain plateau”, “Mediterranean mid-mountain” and “Mediterranean mixed-scrubland” (see Fig. 1). This represents 107 municipalities selected (appendix E), covering 75,348 hunting trips for 58,407 wild boars culled (see Table 1 and appendix B, table B.1 and B.2).

Weather data management

Daily meteorological data used in this study were collected from Météo France public service (https://donneespubliques.meteofrance.fr). For each hunting day, we extracted information on precipitation (mm), temperature (degree Celsius), snowfall (cm), and the duration of freezing during the hunting day (minutes per day; Table 1). As weather data at the scale of municipalities and hunting trips were not directly available, we imputed the data from the closest weather station sharing the same landscape and climate type to each municipality in which the hunt took place. A summary is presented in Table 1 and all-weather stations are shown on figure F.1 (R script F.2). The collinearity of weather variables was checked using principal component analysis (PCA), correlation matrix analysis ade4, Factoextra, corrplot r package (Dray and Dufour 2007; Wei et al. 2017; Kassambara and Mundt 2020). Collinearity of the variables was <|0.70| (Dormann et al. 2013), and we therefore retained all weather variables in the analysis (appendix G, figures G.1–4 & tables G.1–4). All weather continuous data were discretized into 3 modalities: null (baseline), medium and high (see Table 2, for more statistics see appendix G table G.5) to capture potential non-linear effect and facilitate the interpretation of output estimates in relation to the null effect and each other level modality (low versus high).

Table 2 Modality level definitions for daily weather variables
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Hunting success modelling

Let \({S}_{i}\) be the observed hunting success indicator variable such that for a drive hunt party i it takes the value 1 if at least one wild boar was culled and 0 otherwise (the 50th quantile is characterized by 0 culls). Therefore, we assumed that hunting success is a random draw from a Bernouilli distribution with success probability \({P}_{i}\). Hunting success obviously depends on the number of hunters \({E}_{i}\) so it was used as an offset in the model described below. Furthermore, in addition to using the categorical weather variables at the drive hunts scale, we added calendar month to account for possible changing cullability during the hunting season (Vajas et al. 2021), due to e.g. changes in hunter efficiency, habitats and weather conditions from September to February. Hunting seasons (corresponding to the years) and municipalities were added as random effects.

The hunting success probability \({P}_{i}\) for drive hunt i was modelled by the following logit-linear model

$${\text{logit}(P}_{i})={\text{log}(E}_{i})+\text{a}+{\sum }_{j=1}^{K}{b}_{j,l}{x}_{i, j}+{m}_{i }+ {h}_{i}+{\mu }_{i}+{\gamma }_{i}+ {\varepsilon }_{i}$$
(1)

where \({E}_{i}\) is the effort offset, “a” the intercept, \({b}_{j,l}\) the coefficient for explanatory variables \({x}_{j}\) (j: temperature, rain, frost, snow) for each “l” main habitat types index (see previous section), \({m}_{i}\) month effect, \({h}_{i}\) main habitat types effect, \({\mu }_{i}\) and \({\gamma }_{i}\) normal random effects for municipalities and hunting season (variance \({\sigma }_{\mu }^{2}\) and\({\sigma }_{\gamma }^{2}\)), and \({\varepsilon }_{i}\) residuals. We used a Bayesian approach for fitting the model with uninformative priors. We examined the goodness-of-fit of our model using a posterior predictive check after having checked the correct mixing of the MCMC chains and convergence.

Hunting effort modelling

For our second question, which focuses on the hunting human dimension, the aim is to understand and anticipate hunters’ behavior (see Bourdaud et al. 2019 for an example in fisheries). Thus, hunting effort \({E}_{i}\) in drive hunt party i was modelled with a Poisson distribution \(Poisson({\lambda }_{i})\) with expectation \({\lambda }_{i}\). The same explanatory variables and random effects as for hunting success were included in the model. In this case, calendar month represents the effect of variations in hunter investment during the hunting season (Vajas et al. 2020, 2021). The log-linear model for hunting effort is therefore:

$$\text{log}\left({\lambda }_{i}\right)=\text{a}+{\sum }_{j=1}^{K}{b}_{j,l}{x}_{i, j}+{m}_{i}+{h}_{i}+{\mu }_{i}+{\gamma }_{i}+ {\varepsilon }_{i}$$
(2)

The same Bayesian model fitting and checking procedure as well as uninformative priors were used.

Variable and model selection

We used a Bayesian variable selection procedure to identify the variables with the greatest impact on hunting success (Eq. 1) and hunting effort (Eq. 2) both for explanatory (full dataset) and process-based approach (controlled dataset) analyses. We followed the approach developed by Kuo and Mallick (1998) to select relevant explanatory variables and to provide the probability estimates for each explanatory variable of being part of the most relevant model. We further estimated the probability of each possible combination of variables being in the final true model, following O’Hara et al. (2009).

For this, a binary coefficient g is added in each model Eqs. (1 and 2) for all explanatory variables (\({\sum }_{j=1}^{K}{{g}_{j}b}_{j,l}{x}_{i, j}+{g^{\prime}h}_{i}+{g^{\prime \prime}m}_{i}+g^{\prime \prime \prime}{\mu }_{i}+g^{\prime \prime \prime \prime}{\gamma }_{i}\)). These coefficients can take the value of 0 or 1 and are assumed to be the realization of a Bernoulli draw with probability \({p}_{j}\) that explanatory variable \({x}_{j}\) is in the true model. If \(g\) = 0, the corresponding variable does not have any effect in the model. The joint posterior distribution of \(g= \text{1,0},\text{1,1}\dots k\) provides the probabilities of apparition of each variable and combinations of each explanatory variable in the final model.

Implementation and computing

Bayesian inference was carried out using the Markov Chain Monte Carlo (MCMC) approach and implemented the Nimble package (de Valpine et al. 2017, 2022) in the R programming environment (R Core Team 2023). The full set of R and Nimble codes are available in appendix H (for hunting success & hunting effort fig H.1 & H.2) and I for variable selection models (for hunting success & hunting effort fig I.1 & I.2).

For fitting the models and variable selection, both for hunting success and hunting effort (based on full dataset), we ran 4 MCMC chains for 1,000,000 iterations with a burn-in period of 500,000, and thinning of 100. The good mixing of the chains was checked a posteriori (see posterior predictive check).

For fitting the models with controlled dataset for both hunting success and hunting effort, 4 MCMC chains were run with 2,000,000 iterations, a burn-in period of 1,500,000 and thinning of 100. As this data set was smaller, a larger number of iterations could be carried out and stored. The correct mixing of the chains was checked a posteriori (see posterior predictive check).

Results

Variable and model selection

All the putative explanatory variables have a probability of belonging in the true model from 75 to 100%, for hunting success and hunting effort, both on the full dataset and controlled dataset (Table 3). All the variables were selected for hunting success on the full dataset (90%, 9 times higher than the second selected model) and controlled dataset (91%, almost 20 times higher than the second selected model, Table 4). However, the result is equiprobable to 25% for the model explaining hunting effort on the full dataset scale. At the scale of the full dataset, although a clear effect of weather variables is highlighted, it is not possible to choose the "best model" based on this equiprobable set of results. However, the influence of meteorological variables on hunting effort was clear and supported the controlled dataset results in which all variables are selected. Thus, with regard to the first question, weather variables have an effect on hunting success (Table 4).

Table 3 Variable posterior probabilities for both full dataset model and controlled dataset model and both success and effort response variable. Each column corresponds to all explanatory variables, i.e., MU for management Unit, temperature, rain, snow, frost, month and two random variable hunting season (year) and Municipality ID (unique code corresponding to a unique municipality). The values are expressed as percentages and correspond to the probability that the variable is selected in the model
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Table 4 Posterior probabilities of model selection for full and controlled datasets for both hunting success and hunting effort modelling. Each column corresponds to all explanatory variables, i.e., MU for management Unit, temperature, rain, snow, frost, month and two random variable hunting season (year) and Municipality ID (unique code corresponding to a unique municipality). 1 means that the variable is in the model, 0 that it is not in the model. Expressed as a percentage of the probability of selection, in red the most likely model to be the true model and in orange equiprobable probability
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Posterior predictive check

We assessed the posterior predictive checks of the hunting success and effort models applied to controlled dataset to check the good fit between predictions and observed data (appendices J). We performed a posterior check on a sample of 300 simulated points per chain, i.e., 1200 points for each observed point in the dataset.

The hunting success model provides binary values, “0” (unsuccessful hunt predicted) or “1” (successful hunt predicted). The posterior predictive check then seeks to calculate distributions of percentages of correct values. When examining the overall performance of the model, it predicts the correct outcome for 61.5% of the observed data. However, if we specifically focus on the success and unsuccess predictions, the model shows a lower fit with success (predict success) 41.58% and a higher fit with unsuccess (predict unsuccess) 69.58%. The model exhibits a conservative tendency in predicting success, but it demonstrates a high accuracy rate when a success is predicted (when a harvest is observed a success is also predicted by our model). This pattern likely stems from the infrequent occurrence of success observations within our dataset, while unsuccessful hunts are predominantly represented in the dataset and correctly predicted by the model (appendices J.1, figure J.1.1). For more information see appendices J.1, for the different dataset scales, i.e., by territories, by hunting season, by month (figure J.1.2), and also at the successful and unsuccessful modalities (figure J.1.3–4-5–6).

The hunting effort model predicts a number of hunters (appendices J.2). The posterior predictive check consists of assessing the median of the observed data within the simulated posterior distribution at the scales: all posterior, by territories, by month and by hunting season (appendices J.2, figure J.2.1). The number of observed hunters is systematically close to the medians of all the distributions, indicating a perfectly fitted model. All the verification figures and descriptions are available in the appendices (J.2).

Hunting success

Inspection of the significance of the different variables selected (within the 90% credibility interval) by the model shows significant differences between at least one modality level within each variable, supporting the variable selection result as estimated. In other words, all the variables in the model have a significant effect, but this is not observed across all the variable modalities level across all the territories (see Fig. 2 & appendix K). Results can be split into two groups of variables:—the variables describing hunting variability considered by the model but not of primary importance – territories, hunting months, hunting seasons and municipality ID –, results description available in appendix K.1, and—the weather explanatory variables main focus of the study – temperature, rain, snow, frost – (see Fig. 2).

Fig. 2
figure 2

For each main habitat types, multipanel plot of weather explanatory variables on hunting success at 90% CI, i.e. a) temperature, b) rain, c) snow, d) frost. x-axis represents modality level (low or high modality) and y-axis represents intercept estimate for each of the weather variables. The baseline effect is represented by a red dotted line at 0, the red box plot indicates the absence of significant differences at 0, the green box plot indicates a significant difference at 0 and between them, and the orange box plot indicate a significant difference at 0 but not between the modality levels

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For weather results, the "temperature" variable had a significant effect on the hunting success (different from 0 in CI 90%) in all the main habitat types with a negative effect of low temperatures in “Deciduous valley”, “Mediterranean mid-mountain”, “Mediterranean mixed-scrubland”, a positive effect of low temperatures in “Central mountain plateau”, a negative effect of high temperatures in “Mountain slope woodland”, “Mediterranean mid-mountain”, “Mediterranean mixed-scrubland” and a positive effect of high temperatures in “Deciduous valley” (Fig. 2a). The "rain" variable was significant for “Deciduous valley” and “Mountain slope woodland” with a negative effect of heavy rainfall on success (Fig. 2b). The "snow" variable was significant in “Central Mountain plateau” with a positive effect (better success) in modalities “medium” and “high” different from 0 but not different from each other (Fig. 2c). Finally, the "frost" variable was significant for “Central Mountain plateau” and “Mediterranean mid-mountain” respectively on modality “high” and “medium” with a positive effect (Fig. 2d). Half a day of frost “Mediterranean mid-mountain” or days of frost for “Central Mountain plateau” increases hunting success.

Here, to illustrate these differences on hunting success, we have simulated under fixed conditions (median value of posterior distribution of y-intercepts, month, hunting season, and municipality ID, and null effect of weather variables not considered), the only two significant additive effects of weather conditions in this main manuscript (Fig. 3), while all simple effects are presented in appendices (see appendix K figure K.1.2). For example, in the "Deciduous valley" territory, for 30 hunters, the prediction of success fell from 0.42 under neutral conditions to 0.30 during episodes of heavy rain and low temperatures, representing a 20% decrease in success (Fig. 3a). In the "Central Mountain Plateau", under neutral conditions, the probability of success was 0.45 compared with around 0.62 under conditions of low temperature, frost and snow cover, representing a 37% increase in success (Fig. 3b).

Fig. 3
figure 3

Multipanel graph with x-axis fixed number of hunters and y-axis predicted success (between 0 and 1) illustrating the results of success model simulation. Lines represent the median values of the simulation, while the coloured shapes represent the 90% CI. Both panels illustrating the importance of the changes in hunting success prediction according to the significant additive effects of the weather conditions in a) the "deciduous valley" territory with low temperature and heavy rainfall and in b) the "central moutain plateau" territory with low temperature, a long period of frost and heavy snow cover

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Hunting effort

As for hunting success models, inspection of the significance of the different variables selected (within the 90% CI) by the model shows significant differences between at least one modality within each variable (see Fig. 4 and appendix K.2). In the same way for the effort models, we can be split into two groups of variables: the variables describing—hunting variability – MU types, hunting months, hunting seasons and municipality ID, results description available in appendix K.2—and the 2- weather variables—temperature, rain, snow, frost – (see Fig. 4).

Fig. 4
figure 4

For each Main habitat types, multipanel plot of weather explanatory variables on hunting effort at 90% CI, i.e. a) temperature, b) rain, c) snow, d) frost. x-axis represents modality level (low or high modality) and y-axis represents intercept estimate for each of the weather variables. The baseline effect is represented by a red dotted line at 0, the red box plot indicates the absence of significant differences at 0, the green box plot indicates a significant difference at 0 and between them, and the orange box plots indicate a significant difference at 0 but not between the modality levels

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For weather results, the “temperature” variable was significant (different from 0 in CI 90%), hunting effort in all territories with a negative effect of low temperature and a positive effect of high temperature in “Deciduous valley”, “Mountain slope woodland” and “Central mountain plateau” (all in Ardèche) and a strictly negative effect of low and high temperature in “Mediterranean mid-mountain” and “Mediterranean mixed-scrubland” (all in Hérault, see Fig. 4a). The “rain” variable was significant in all the territories with a negative effect for the high modality in “Deciduous valley”, “Central mountain plateau” and “Mediterranean mid-mountain”, for the low and high modalities in “Mountain slope woodland” and “Mediterranean mixed-scrubland”, and finally a positive effect of the low modality in “Mediterranean mid-mountain” (see Fig. 4b). The “snow” variable was significant in all the territories, with a negative main effect on hunting effort, differing in intensity between the modalities of “Mountain slope woodland” and “Mediterranean mid-mountain” between low and high and undifferentiated between these modalities for “Deciduous valley” and “Mediterranean mixed-scrubland” (Fig. 4c). The low modality is not significantly different from 0 in “Central mountain plateau”, although the high modality is significantly different (Fig. 4c). Finally, the “frost” variable is also significant for all main habitat types, with a negative significant effect for the high modality for all territories, with the low modality for “Mountain slope woodland” and “Deciduous valley” without distinction of modality for the latter (Fig. 4d). Finally, for “Mediterranean mid-mountain”, low modality had a significant positive effect on hunting effort (Fig. 4d).

In order to illustrate these differences on hunting success, we have simulated under fixed conditions (median value of posterior distribution of y-intercepts, month, hunting season, and municipality ID, and null effect of weather variables not considered), the only three significant additive effects of weather conditions in this main manuscript (Fig. 5), while all simple effects are presented in appendices (see appendix K, figure K.2.2 for all simulation). All patterns show a decrease in hunter investment in three groups of results, deciduous valley and Central Mountain (Fig. 5.a), mountain slope woodland (Fig. 5.b) and Mediterranean mid-mountain & mixed-scrubland (Fig. 5.c), with a decrease of between 16 and 23% approximately in the number of hunters (respectively from 11 to 9 hunters, 12 to 10 hunters, and 17 to 13 hunters).

Fig. 5
figure 5

Multipanel graph with in x-axis on the left the mean and standard deviation of the number of hunters expected under neutral conditions (in yellow) and on the right the effect of significant additive meteorological conditions (low temperature + rain in red and low temperature + long frost period + snow cover in blue) on the number of hunters in y-axis represented by the mean values simulated in the effort model associated with their sd. Although there are 5 territories in our analysis, similar results allowed us to group "deciduous valley" & "central mountain plateau" in a), "Mountain slope woodland" in b) and Mediterranean "mid-moutain" and "mixed scrubland" in c)

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Discussion

All-weather predictors appeared to influence both hunting success and hunting effort both at the large scale and in the controlled dataset scale (Table 3 & 4, Fig. 2 & 4). Guided by the cullability conceptual framework, the controlled dataset has been designed to limit the influence of confounding factors. This has been achieved through the use of a dataset with controlled density variance (from Vajas et al. 2021) and habitat variance (proxy for small-scale cullability), in addition to the inclusion of temporal (monthly and annual) and spatial (communal) variations to have the purest estimate and easiest interpretation of weather variables effects on hunting success and hunting effort. Thus, warm temperatures have a negative effect on success, whereas depending on the main habitat type, they can have a positive effect (in central territories) and a negative effect on effort (in the Mediterranean territories). Rain could have a negative effect both on hunting success and effort, while snow and frost increased hunting success in the mountainous areas of Ardèche, reducing the hunting effort during these periods. Thus, the combination of poor weather conditions leads to a reduction in both hunting success (Fig. 2) and hunting effort (Fig. 5), whereas the combination of snow and frost leads to greater success for the same amount of effort invested (Fig. 4) but leads to a reduction in investment (Fig. 5).

Cullability, hunting success: Weather influence

Cullability allows the identification of the determinants of the cull, i.e. hunting success (Hilborn et al. 1992; Arreguin-Sánchez 1996). Cullability therefore typically varies in time and space (Wilberg et al. 2009), and is determined by two sets of factors related to the animal hunted, and the human hunter, respectively, and develops a whole range of glossary terms to facilitate the interpretation of the results and highlight discussion, adapted here to a hunting context. The animal factor includes, for example, the presence of the animal in the hunting area (accessibility) and the behavior of the animal related to environmental conditions and predation risk (vulnerability). The human factor, on the other hand, accounts for the difficulty of the hunt like visibility or practicability (habitat density, visibility, topography), the experience of the hunter (knowledge of the area, the species, equipment skills), and possibly also the ability and skills of the hunting dogs (Grignolio et al. 2011; Godwin et al. 2013; Vajas et al. 2020).

Two main findings emerge regarding hunting success. Firstly, there is a negative impact of low temperatures and rainfall on hunting success (Fig. 3a). Secondly, there is a positive effect of low temperature, frost and snow on hunting success in mountainous territories in Ardèche (Fig. 3b). On the other hand, rainfall can have several adverse consequences on hunting success. Rain may reduce visibility, thereby hindering the ability of posted shooters to take accurate shots (Rivrud et al. 2014). Furthermore, the quality of hunting conditions, especially for beaters, may be compromised due to the reduced practicability of the hunting ground. Weather conditions can also affect hounds’ tracking abilities. The ability of dogs and other predators to detect odours plays a crucial role in their ability to find and track prey (Conover 2007; Dahlgren et al. 2012). Both dry soil and a warm atmosphere, as well as wet soil and heavy rainfall, can reduce the ability to pick up odours and decrease tracking efficiency (Shivik 2002; Conover 2007). Conversely, wet, frozen, and snowy soil can preserve odours and enhance tracking. In this way, low humidity or frost could improve the track as we can see in the "Mediterranean mid-mountain" territory. Snow-covered ground can assist beaters in detecting animal tracks (Baur et al. 2021). However, heavy snowfall can significantly impede movement while hunting, although this is likely less common in Europe compared to North America, for example (Curtis 1971).

Nevertheless, while the aforementioned findings were highlighted by the analysis, the amplitude and diversity of the meteorological conditions were not sufficiently elucidated. For example, a rainy day can encompass a range of scenarios, such as short bursts of precipitation, continuous drizzle throughout the day, or nighttime rainfall. In Mediterranean territories, "Cévénole” episodes are characterized by brief and heavy rainfall, with the potential for total millimeters of precipitation to be recorded within an hour. These episodes may coincide with or be completely missing the hunting party, affecting hunting in different ways. Moreover, the occurrence of consecutive days of poor weather can have a detrimental effect hunting success due to the accumulation of negative effects over time (Hansen et al. 1986). One hypothesis associated with meteorological changes in our study concerns the potential impact of changes in the practicability of hunting grounds and consecutive poor weather days may not be sufficiently approximated by daily data. For instance, the impact of frost, which is characterized by alternating cycles of freezing and thawing, whether they occur in a single day or over several days, can be significant, particularly regarding activities such as dog tracking. This is due to the degradation of odours, which is a consequence of the freezing and thawing cycles (Conover 2007). Or else, the effect of the same amount of precipitation on hunting may vary according to habitat, hunting conditions may already be difficult in areas such as steep slopes (Lebel et al. 2012; Wszola et al. 2019).

Weather conditions also influence animal behavior and decision-making. For example, for an animal, poor weather may affect the trade-off between conserving energy (by stay hiding), or go in quest of more calories against energy depletion (Parker and Robbins 2018; Parker 1988). Thus, in theory, spatial behavioral responses to meteorological conditions could influence animal accessibility. However, the interpretation of this phenomenon is not straightforward. It can be assumed that an animal in movement would be less detectable to hunters (Lone et al. 2014). In our case, wild boar appears to adopt an energy conservation strategy in poor weather episodes, such as rain, frost or snow, by reducing their movements (Keuling et al. 2008; Thurfjell et al. 2014). However, these are the most successful conditions. It is possible that the benefits of these conditions for hunters outweigh the loss of success associated with the absence of movement.

Hunting effort allocation: Weather influence

Hunting effort can be understood as a set of labor involved both during hunting and during all series of investment decisions made over time (Laloë 1995). It may be divided into two components: nominal effort, which encompasses all the economic resources required to embark on a hunting expedition, such as travelling to the hunting ground by vehicle for example; and effective effort, which is the effort that can or does directly transform into the harvested quantity (for example the distance travelled by car does not affect the yield; Rist et al. 2008, 2010). Consequently, while the first can be employed for investment decision-making or economic optimization, the second offers a more comprehensive synthesis of information on the mortality rates associated with hunting.

Therefore, weather can influence the nominal hunting effort by reducing hunters’ investment in their leisure activity. This can be illustrated by Baur et al. (2021), who notes that weather can affect the time and effort required to prepare equipment and drive for instance. In our case, we only know to the number of hunters at the start of the hunt. This is our measure of effective effort, which is already the result of a previous variation in nominal effort. In the Ardèche territories (central territories), low temperatures had a negative effect on the investment of hunters, while high temperatures had a positive effect. In the Hérault territories (Mediterranean territories), both excessively low and high temperatures had a negative impact on hunting effort by reducing hunters’ investment compared with mild temperatures. Calendar months enable us to capture this fluctuation of the hunter’s investment trend during hunting season. Thus, investment at the beginning of the season is a significant contributing factor, with milder temperatures in the north encouraging investment, while high temperatures, including heatwaves, discourage hunters in the south (it should be noted that the temperature can be considerable at the beginning of the hunting season.). Overall, rain, snow, or frost had a negative effect on hunters’ investment, consistent with previous studies (Peterson and Unit 1969; Curtis 1971; Rivrud et al. 2014; Diekert et al. 2016).

Study limitations and perspectives

The study is subject to factors that remain uncertain and unpredictable. These can be grouped into three main categories: (i) weather data and dynamics; (ii) animal behavior; and (iii) hunters’ motivation and skills.

First, other relevant weather variables than the ones included in our analyses could affect either success or effort, such as sunshine or wind (Baur et al. 2021). Wind is a complex meteorological component that is difficult to account for at a small spatial scale. The interplay of wind microvariations, particularly those associated with lateral vegetation cover, is of great importance for odor capture by animals (Conover 2007). Considering habitat structure would help understanding the small-scale prey-hunter relationships at play (Burrascano et al. 2015; Vajas et al. 2024). Regarding the meteorological data, they have undergone an imputation process, making them non-exclusive and non-specific to all our areas (see Appendix F).

Second, previous works have shown that animal behavior plays a crucial role in hunting success (Ciuti et al. 2012; Thurfjell et al. 2017; Fattebert et al. 2019). To some extent, we did include some behaviors in our model, e.g. the effect of learning across calendar months variable. But other behavioral traits related to escape dynamics and the landscape of fear are also potentially important (Sodeikat and Pohlmeyer 2003; Thurfjell et al. 2013). The landscape of fear (Brown et al. 1999; Laundré et al. 2001), which reflects how animals perceive and respond to hunting as a form of predation risk, can vary with age and season (Grignolio et al. 2011; Ciuti et al. 2012; Thurfjell et al. 2017; Wevers et al. 2020). This variability influences the likelihood of flight and, consequently, hunting success (e.g., whether an animal remains in a hunting area or leaves it). Furthermore, shifts in habitat use and selection are important trade-offs for animals exposed to predation or hunting risk (Acevedo et al. 2011; Lone et al. 2015, 2016; Wevers et al. 2020). Such shifts can alter potential predator–prey encounters, including those with human hunters, further complicating hunting outcomes. Non-lethal disturbances, such as recreational activities (e.g. hiking or cycling) that occur within hunting areas can also alter land use and diel patterns, increasing unpredictability in frequently visited (Ohashi et al. 2013; Gruas et al. 2020). Finally, differential vulnerability to hunting based on life stage may provide further insights (Bunnefeld et al. 2009, 2011; Bergqvist 2022). Combined with hunting bag data, these factors could provide a novel perspective on hunting dynamics, including the learning curve of prey over time (Thurfjell et al. 2017).

Third, previous work has highlighted the co-existence of different groups of hunters with different motivations and skills (von Essen et al. 2019; Connally et al. 2021; Vajas et al. 2023), with consequences on hunting success (Keuling et al. 2016, 2021). Hunters are a heterogeneous group characterized by different identities and motivations that determine their hunting efficiency. Thus, they may adopt different hunting practices in a contrasting cultural landscape. Professional hunters will be more successful (Doerr et al. 2001; Connally et al. 2021), while the concept of success in recreational hunting may be more secondary (von Essen and Tickle 2020). This may be exacerbated by a split in hunting motivation between former local hunters, who are aware of local problems, and new urban hunters who wish to practice multiple hunting methods on multiple game species throughout the national territory (Vajas et al. 2023).

Management implication

From the perspective of wildlife game management, our study provides several pieces of information that can be used to control the population of wild boar. Firstly, the initial findings indicate a need to include variance factors associated with cullability and meteorological conditions to ascertain the influence of these factors on future studies. Secondly, the findings may then be employed to facilitate an examination into the potential for optimizing the hunting process, i.e. best yield for the same invest hunting effort (Vajas et al. 2023). Our results identify optimal time windows during which hunting success is the highest, as well as periods during which investment decreases.

However, our results should also be seen in the light of future changes in hunting practices. Indeed, hunting may be subject to major legislative changes that will restrict its activity (see Vajas et al. 2023), but it is also part of a changing environment. In this respect, Baur et al. (2021) propose a discussion on the relationship between climate change and hunting practices. Regardless of the effects of these changes on wild boar populations (see Touzot et al. 2020), they can alter hunting habits and quality. For example, in our case, too-hot hunting periods at the start of the hunting season (September–October) have known reduced hunting investment in Mediterranean territories. These are periods that will be warmer in the future, and they are also the periods with the lowest cullability and hunting effort (Vajas et al. 2021). This raises questions about the use of these periods to fill the hunting quota. Periods of heavy (extreme) rainfall will become more intense in all areas, which will reduce success and even make the main habitat type less or impracticable for a longer period. In addition, snow cover and ground frost tend to decrease, whereas this was not only a favorable period for hunting, but also one of the weather conditions that limited the dynamics of wild boar populations (e.g., frozen soil limit resource access, Thurfjell et al. 2014). Hunting efficiency and periods of greater investment could therefore change the optimal hunting periods. Thus, the practice of recreational hunting to support management efforts in a changing and uncontrollable environment raises the question of the ability of the current hunting methods to address wild boar management issues and requires a balanced approach that takes into account both ecological and socio-cultural factors in the search for sustainable hunting practices.

Conclusion

Our analysis of the variability of the relationship between hunting effort and success under unpredictable and sudden changes in weather conditions demonstrates the complexity of relying on recreational hunting in the context of wildlife management. Weather conditions affect both hunting success and hunting effort, but discrepancies between the effort allocated and the potential success under the same conditions exist. This raises the question of the perception of potential hunting success by hunters, who might intuitively dismiss weather conditions perceived as unfavorable for hunting, contrary to the actual outcome. Baur et al. (2021) raises the discussion of the “self-fulfilling prophecy”, i.e. a reduction in investment when conditions are assumed to be less favorable (see also Johnston et al. 2010 for recreational fishery). The hunting effort modelling sheds light on this point. In the absence of a field survey, it is quite possible that the estimate of hunting success favors or discourages hunter investment. However, an alternative example is presented here, low temperatures, snow cover and a long period of frost result in a lower investment in terms of the number of hunters, but success is significantly greater. Such discrepancies underline that the fact that hunting is primarily a leisure activity with a multitude of motivations (von Essen and Tickle 2020), including the enjoyment of an outdoor experience, social interaction and the symbiosis with their dogs, rather than the harvest an animal (Hammitt et al. 1990; Tynon 1997). These considerations prompt questions regarding the controllability of management measures proposed or imposed to regulate hunting effort to achieve a specific harvest quota (Vajas et al. 2023). This in turn raises the question of hunters' ability to manage wild boar populations solely through their investments. Indeed, recreational hunting, like recreational fishing, differs from other forms of harvest (commercial or subsistence) by its low yield, with a high level of effort invested for a low number of individuals culled (Hilborn 1985; Milner-Gulland et al. 2008). While we identified optimal conditions and periods during which hunting success is the highest and therefore effort should be highest when the aim is to control or limit populations, these periods for adaptive allocation of effort might change under changing climate. This calls for considering the revision of hunting methods alone to achieve management goals.