Relating national levels of crop damage to the abundance of large grazing birds: Implications for management

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2019 The Authors. Journal of Applied Ecology published by John Wiley & Sons Ltd on behalf of British Ecological Society 1Grimsö Wildlife Research Station, Department of Ecology, Swedish University of Agricultural Sciences, Riddarhyttan, Sweden 2Department of Ecology, Swedish University of Agricultural Sciences, Uppsala, Sweden 3Arctic Ecology Department, Norwegian Institute for Nature Research, The Fram Centre, Tromsø, Norway


| INTRODUC TI ON
Wildlife damage on human livelihoods can unfold into conflicts between human interests such as conservation, agriculture and forestry (Redpath et al., 2013). When managing conflicts arising from human-wildlife interactions, knowledge about the relationship between damage levels and population size is fundamental to understand possible outcomes of different interventions and management strategies, as well as to set relevant goals (Conover, 2002;Madsen et al., 2017).
The need for interventions to mitigate damage by large grazing birds (geese, swans and cranes) on agricultural fields, has recently been accentuated . Many populations of large grazing birds have increased from threatened to superabundant in Europe during at least five decades  due to conservation efforts and agricultural intensification (Ebbinge, 1991;Fox, Elmberg, Tombre, & Hessel, 2017;Gauthier, Giroux, Reed, Bechet, & Belanger, 2005) and a warmer climate (Jensen, Madsen, Johnson, & Tamstorf, 2014;Mason, Keane, Redpath, & Bunnefeld, 2018). The increasing numbers of large grazing birds and their preference for agricultural fields over their natural foraging habitats -because crops provide higher quality food (Fox & Abraham, 2017) -cause a loss in harvest yield for the farmers . For example, in Islay, Scotland, spring grazing barnacle geese reduced harvests on spring grasslands by up to 82% (Perceival & Houston, 1992). Also, annual economic compensation for harvest losses due to barnacle geese ranged from 5,000 euros in Belgium to more than 5 million euros in the Netherlands in recent years . As the impact of foraging large grazing birds on agricultural landscapes increases, it fuels the conflict between farming and conservation objectives (Stroud, Madsen, & Fox, 2017). While it is reasonable to assume that agricultural yield losses depend on the number of birds and their grazing pressure (Parrott & McKay, 2001), the annual variation in yields caused by factors other than grazing birds (e.g. weather, soil, crop-type) make specific quantification of damage difficult to assess (Anon, 1970;McKenzie & Shaw, 2017). For instance, plants may compensate for grazing (Van der Graaf, Stahl, & Bakker, 2005;McNaughton, 1979) and under certain conditions intermediate grazing may stimulate plant growth (McNaughton, 1979). Few studies have been able to evaluate the relationship between bird numbers and damage levels and this link has often simply been assumed to be linear (Cusack et al., 2018;McKenzie & Shaw, 2017), especially at the national scale where most political and strategic management decisions are conducted .
Increasing populations of large grazing birds and damage to agricultural fields have led to recent initiatives to establish adaptive flyway management plans. All states along the flyway for these birds need to reach a consensus in agreeing their goals and measures to tackle this issue Stroud et al., 2017). Several measures to mitigate the damage and conservation conflicts exist and have been suggested within the plans for example, set-aside areas, bird-scaring and population control . However, the current lack of data linking crop damage with population size creates a challenge when it comes to (a) predicting outcomes of proposed interventions, (b) allocating money for compensation costs and (c) adapt any subsequent goals and recommendations for monitoring and compensation strategies.
In Sweden, farmers can report crop damage caused by large grazing birds to acquire economic compensation from an accredited government compensatory scheme. Reported damages must be approved, species involved identified and yield losses estimated by authorized government inspectors before economic compensations are paid. In addition, estimates of population numbers of large grazing birds are conducted as part of the national monitoring schemes (Nilsson, 2013). We use this available data to (a) investigate the relative importance of the species reported to cause crop damage in Sweden; (b) describe temporal and large scale spatial patterns of damage; (c) reveal the relationships between estimated national population numbers and levels of crop damage across 16 years (2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015) and whether these relationships differ among the species; and (d) explore the relationship between the amount of damage, yield loss and compensation costs incurred.

| Crop damage data
In 1995, the Swedish Government launched a system to compensate farmers for crop damage caused by large grazing birds. Since then, all farmers can report crop damage to the County Administrative Boards (CABs) to receive compensation. All reported damages are verified according to a standardized procedure by trained and authorized inspectors from the CABs (Månsson et al., 2011). The specific methodology varies slightly between crop types (e.g. potato, cereals, hay) but is in general based on a comparison between damaged and undamaged parts of the same field (or a field in close proximity if the whole field is damaged) to estimate yield loss. If damage occurs during an early stage, the field is visited twice: first immediately after the damage occurs to geo-tag the affected area and to identify the species responsible and then a second time just before harvest, to estimate the yield loss. The inspectors verify the affected crops and identify the species responsible based on established protocols (Månsson et al., 2011). Because the first inspection takes place immediately after the farmer contacts the CAB, we expect the identification of the culprit species to be accurate. Harvest loss due to other factors such as drought, flooding or other wildlife (e.g. wild boar Sus scrofa) is also estimated and deducted from the total loss (Månsson et al., 2011). Once the damage is registered, the CABs calculate the economical compensations due to be paid, based on the annual crop market price. allowed to perform lethal scaring as soon as greylag geese were feeding on unharvested crops independent of season (Månsson, 2017). As a consequence, the CABs decided to cease compensation for crop damage caused by greylag geese (see Figure S1), except for in regions of high concentration of geese like Scania (the southernmost Swedish province) and local areas where shooting was prohibited to avoid disturbance, for example in the vicinity of wetland reserves.
We used three indices to quantify damage level: the number of approved reports of damage (damage reports), registered kilos of yield loss (yield loss) and the amount of compensation paid (compensation costs). Information about the compensatory scheme was spread by information campaigns via CABs and farmer associations.
It is reasonable to assume that the awareness about the compensation scheme among farmers was low immediately after it was introduced. To decrease the risk of such a bias, we excluded the first 5 years of data before the year 2000 (n 1995-1999 = 21 damage reports).
Since geese often occur in mixed flocks (Table S1), one damage report may include several species. When investigating species-specific crop damage, we included all damage reports (i.e.

| National indices of bird numbers
We used the total number of birds registered during the annual national autumn counts in September for greylag geese, and October for barnacle and bean geese (Nilsson & Haas, 2016).
These counts are conducted mainly by volunteers in the vicinity of roosting sites, mainly in southern Sweden (<61° North) and are designed to cover all main stopover sites (Nilsson, 2013).
The number of surveyed sites has basically been constant for the October counts, whereas the range of September counts has expanded as greylag geese have been found further north (Nilsson, 2013). For common crane, we used the maximum number of birds counted during the second half of September at the four major autumn stopover sites: lakes Tåkern, Hjälstaviken, Kvismaren and Hornborgasjön (Lundin, 2005;Nilsson, 2016). The timing of the crane and geese monitoring periods match the species' peak numbers at Swedish autumn staging sites. These estimates of population numbers should be viewed as estimates of national numbers and do not provide detailed information about local abundances and within-year variation (Nilsson, 2013). Autumn counts for whooper swan involved very poor coverage (<200 individuals/ year) and were not analysed.

| Crop availability and market prices
Since 2000, ley is the most abundant crop in Sweden (40% of the agricultural land) followed by wheat (14%) and barley (13%) (84% of wheat corresponds to winter crops while 92% of barley, to spring crops; Anon, 2018a). The south and central areas of Sweden have an agricultural-dominated landscape fragmented with urban settlements and boreonemoral forests. Ley is the major crop (>37%), followed by wheat (15%), barley (14%) and a mosaic of rapeseed, potatoes, legumes, carrots and beets (<5%).
In the north, forest cover increases and agricultural heterogeneity decreases with ley and barley as the major crops (c. 70% and 12% respectively). The availability of crops at the national scale did not show any distinct trends from 2000 until 2015 ( Figure   S2). Similarly, market prices (corrected for inflation), did not show any tendency over the study period either ( Figure S3). There is considerable variation in the market price between crops, for example, higher for rapeseed and potato (14-34 euros/100 kg) and lower for barley and wheat (8-17 euros/100 kg) (Anon, 2018a(Anon, , 2018b).

| Modelling relationships between population indices and damage levels
To analyse the broad relationship between damage reports and population indices we fitted, for each species, a Negative Binomial We accounted for temporal autocorrelation by assuming that regression residuals follow a random walk (i.e. Rw1) process. Our model for damage reports is expressed as. and the models for yield loss and compensation costs are expressed as.
(1) where, mu^ refers to the mean; D t the number of damage reports in year t; P t population index (×1,000 birds) in year t; Y t yield loss (in metric tonnes) in year t; and C t compensation costs (×1,000 euros) in year t. u t is the Rw1 residual defined by the formula u t = u t−1 + Ѵ t ; where u t is the trend of the response variable at time t; u t−1 the trend at time t − 1; and Ѵ t the noise component. Ѵ t follows a Normal distribution (Ѵ t ~ N (0, σ Ѵ 2 )) and σ Ѵ 2 is the variance of the noise component. The same applies for the Rw1 residuals z t and w t in Models 2 and 3 respectively. These models refer to the broad association (over the study period) between covariates and response due to a common trend. All three models are log-log models. Hence, the relationship between covariates will be a power law of the type P^ β 1 (Model 1), P^ ζ 1 (Model 2) and P^ δ 1 (Model 3) and linear if β 1 (ζ 1 or δ 1 ) = 1.
To evaluate how inter-annual fluctuations of population indices are related to inter-annual fluctuations of damage reports, yield loss and compensation costs, we ran Models 1, 2 and 3 including a drift term into the random walk. A random walk Rw1 with a drift term is equivalent to a non-drift random walk plus a linear effect of time, which can be simply added as an ordinary covariate. This is a modelbased variant of detrending the response and covariate to examine the annual association between the variables when trends in both variables are accounted for. Our models are expressed as.
where, drift term = t − RT and RT is a reference time, accounting for the first year of our dataset (i.e. 2000). So, if time variable t is a vector from year 2000, 2001… to 2015, the drift term will be a vector 0, 1, 2… to 15. These are also log-log models and, therefore, the relationships between covariates will also be a power law of the type P^ β 2 (Model 4), P^ ζ 2 (Model 5) and P^ δ 2 (Model 6); linear if β 2 (ζ 2 or δ 2 ) = 1.
Bean goose was excluded from the analysis because of the

| Diffuse priors
Because we used a Bayesian approach, priors are required for the parameters in the models: the size of the NegBin distribution (k) for Models 1 and 4; precision of the Gamma distribution (Ø) for

| Crop damage in Sweden
Between 2000  About 90% of all damages were caused by common cranes, barnacle and greylag geese ( Table 1). The remaining 8% was due to whooper swans and bean geese. Barley, ley (hay and pastures) and wheat were the most reported crops to be damaged (41%, 27% and 14% respectively) while rapeseed, potatoes and legumes were less often reported (5%, 3% and 2% respectively). All other crops represented <2% of the total damage reports. (4) log (mu ∧ C t ) = Intercept + 2 × log (P t ) + w t + 1 × drift term TA B L E 1 Number of damage reports, yield loss (metric tonnes T), compensation costs (euros) and percentages (in parentheses) for five species of large grazing birds in Sweden from 2000 to 2015 (see Table S2 for detailed damage levels in North, mid and South Sweden)  (Figure 1a). A similar temporal pattern was found for yield loss (Figure 1b) and compensation costs (Figure 1c). However, there was a mismatch between peaks of compensation costs and those for damage reports and yield loss.
More damage reports were registered in southern than northern Sweden. Similarly, yield losses and compensation costs were higher in the south and involved more species and crops (Figure 2). South Sweden showed a bimodal pattern of damage, with peaks during spring and late summer to autumn. In mid and northern Sweden damage was concentrated in late summer and autumn. (Figure 2b). In southern Sweden, 64% of the spring damage was due to barnacles (two thirds on ley and 16% on barley), 25% to greylags (half on ley, 20% on barley and wheat and 9% in rapeseed) and 7% to cranes (half on barley, a quarter on wheat and 12% on legumes). From the autumn damage reported in south Sweden, 42% was caused by greylags in July (half on barley, 14% on leguminous, 12% on wheat and 7% on ley, beets and carrots) and 46% by cranes in August (two-thirds on barley and 18% on wheat). As for mid Sweden, 75% of the autumn damage was due to cranes (twothirds on barley, 13% on wheat and potatoes and 7% on leguminous) and 18% to greylags (half on barley, 15% on wheat and 12% on leguminous and carrots). In northern Sweden, 74% of all registered damage was due to cranes foraging on barley fields (Figure 2).

| Relationships between population indices and damage levels
Damage levels (damage reports, yield loss and compensation costs) were positively related to population indices for common crane, barnacle and greylag goose (Figure 3). However, the broad relationships contained a high level of uncertainty (Table 2). Linear relationships could not be ruled out for common crane and greylag goose (Table 2). However, a nonlinear relationship appeared to fit best for greylag goose (Figure 3). Under the log-log model, a linear relationship (beta = 1) did not appear compatible with the data for barnacle goose ( Table 2).
As population indices and damage levels displayed a general increase during the study period (Figure 1), we also investigated whether annual changes in population indices were associated with annual changes in crop damage (detrended data). We found no evident relationship between annual estimates of population indices and damage levels when data was detrended (Figure 4;

| D ISCUSS I ON
Knowledge about the relationship between population size and damage levels is crucial for wildlife damage management (Conover, 2002;Madsen et al., 2017). However, this knowledge is lacking for large grazing birds, especially at large spatial scales , and the relationship is often assumed to be linear (Cusack et al., 2018;McKenzie & Shaw, 2017). In this manuscript we investigated this important knowledge gap in the ecology of wildlife damage management. We assessed the relationship between national numbers of staging large grazing birds and national levels of reported crop damage, yield loss and compensation costs in Sweden, described how national temporal patterns of damage differs across the country and discussed how further information about spatiotemporal patterns of damage is crucial to provide guidance for when and where preventive actions should be prioritized and how to monitor the system.
We showed that crop damage has increased in Sweden since 2000. Common crane, barnacle and greylag goose caused the majority of yield losses and costs for compensation (c. 90%). It is reasonable to assume that damage levels are related to bird numbers and grazing pressures (Parrott & McKay, 2001). Our results broadly supported this assertion as when estimated populations sizes of large grazing birds increased, so did the levels of crop damage. We also showed that relationships between population numbers and damage levels seem to differ among species. Although a linear relationship could not be ruled out for common crane and greylag goose, barnacle goose showed a curvilinear relationship with all three damage level indicators (damage reports, yield loss and compensation costs) increasing at a lower rate when population numbers increase. For barnacles, this pattern could be explained by a tendency for the flocks to aggregate more than the other two species (Nilsson, 2013), that is concentrating the impact of damage. This is further supported by an observed increase of yield loss per reported damage at higher population indices ( Figure 5). For greylag goose we found no such increase, suggesting that more fields could be damaged when population index increase.
However, the lowered, but still increasing rates of yield loss as barna-  Regardless of the shape of the relationships, compensation costs seemed on average proportional to yield loss. However, annual peaks of yield loss did not always mirror annual peaks of compensation costs, which seems consistent with the variability of crop types that are damaged ( Figure S3). As large grazing birds tend to concentrate in big numbers around wetlands, foraging on the surrounding agricultural landscape (Jankowiak et al., 2015), individual farmers in areas of high concentrations of large grazing birds may be disproportionately affected .
Our study demonstrated a high degree of uncertainty around the predicted estimates of the relationships between damage levels and population indices. In addition, annual changes in population indices did not relate to detrended inter-annual changes of damage levels.
There are several possible reasons. Firstly, national indices of population size were based on monitoring data restricted to specific staging sites during a few weeks in autumn. It is reasonable to assume that the autumn staging monitoring provides a reasonable index of national Therefore, the results rely on the farmer's willingness to report. We have no information about any variation in willingness to report, but this may depend on crop type (as they differ in provided income), revenue of the farms themselves and any previous experience of damage.
Since availability of different crops and market prices has been stable over the study period ( Figures S2 and S3), we assume that willingness to report within crop types, has not changed. Yet, it is reasonable to suspect that willingness to report may increase with increasing levels of damage, that is, tolerance to damage levels may have changed across time and space. Thirdly, the opportunistic foraging behaviour of large grazing birds can lead to sudden bursts of crop damage when local food availability and foraging conditions change (Béchet, Giroux, Gauthier, Nichols, & Hines, 2003;Clausen & Madsen, 2015;Tombre et al., 2008). This spatio-temporal mismatch together with local damage peaks is hard to detect with the coarse data at our disposal.
Wildlife damage depends not only on the presence of species causing damage, but also on resource availability (Conover, 2002), both of which vary across Sweden. The most damage was reported in southern Sweden, with peaks during spring and autumn, comprising a greater diversity of bird species and crop types. In northernmost Sweden, damage was concentrated in late summer and early autumn, three quarters of which took place on barley fields by common cranes. Although barley and wheat had similar availability, barley was more reported than wheat by all species (e.g. in southern and mid Sweden, autumn greylag reports on barley and wheat were 2:1; while crane reports were 3:1). Barley was also more reported than ley for cranes (<7% damage reports on ley even though its availability was four times higher than barley). Ley, the most abundant crop overall in Sweden and suitable throughout spring until late summer, was the most reported crop damaged by geese in spring in southernmost Sweden. Strategies for crop protection, therefore, need to be adapted to regional and seasonal conditions and the species involved.

| Management implications
Management under uncertainty is a major challenge in all natural systems. Recently developed adaptive goose flyway management plans in Europe suggest population control to reduce damage and conservation conflicts: see for example the adaptive management F I G U R E 5 Scatterplot of the ratios yield loss (metric tonnes) and compensation costs (thousands of euros) per damage reports versus population indices (thousands of individuals), for three main species of large grazing birds causing crop damage in Sweden from 2000 to 2015. Red dots in the greylag goose graphs represent the data after 2009 when compensation rules changed for this species plan for the pink-footed goose (Madsen and Williams 2012), and the current work to establish management plans to control the superabundant numbers of barnacle and greylag geese Powolny et al. 2018). The present study suggests that population control may be one possible tool to mitigate damage on a long-term basis (>15 years), especially when populations of large grazing birds continue to increase and crop damage levels are positively related to bird numbers. However, interpretation and guidance should be made with caution as this is a very complex and dynamic system both in time and space. The degree of uncertainty in our estimation demonstrates the difficulty to quantitatively predict specific outcomes of such management actions. Clearly, we need to address the uncertainty around damage-population size relationships and to do so, we need to design monitoring schemes that capture the site-specific variation of crop damage and abundance of wildlife. A possible way to increase the spatiotemporal resolution of data may be to include opportunistic citizen science data or to include observers in new bird monitoring programs in relation to crop protection. Such effort is also compatible with an increased cooperation with farmers, to build upon trust and to increase the understanding of attitudes and effectiveness for managing conservation conflicts (Josefsson, Pärt, Berg, Lokhorst, & Eggers, 2018;Mishra, Young, Fiechter, Rutherford, & Redpath, 2017;Young et al., 2016). Where there are possibilities to receive economical compensation for crop damage (as in Sweden), farmers should be actively encouraged to report damages together with, for example, participation in citizen science-based monitoring of large grazing birds promoted by local conservation organizations. Tjernberg for authorizing the use of the common crane counts.

ACK N OWLED G EM ENTS
David Flumm for the English proof review. Henrik Andrén, Matthew Low, Steve Redpath and three anonymous reviewers whose comments highly improved this manuscript.