How climate change and wildlife management affect population structure in wild boars

Global climate change affects many species and contributes to the exceptional population growth of wild boar populations and thus to increasing human-wildlife conflicts. To investigate the impact of climate change on wild boar populations we extended existing models on population dynamics. We included for the first time different juvenile conditions to account for long-lasting effects of juvenile body mass on adult body mass and reproductive success. Our analysis shows that incorporating phenotypes, like body mass differences within age classes, has strong effects on projected population growth rates, population structures and the relative importance of certain vital rates. Our models indicated that an increase in winter temperatures and food availability will cause a decrease in mean body mass and litter size within Central European wild boar populations. We further analysed different hunting regimes to identify their effects on the population structure as well as their efficiency in limiting population growth. While targeting juveniles had the lowest effect on population structure, such strategies are, however, rather ineffective. In contrast, culling predominantly yearlings seems very effective. Despite being equally effective, only focusing on adults will not result in a reduction of population size due to their low proportion within populations.

Differences in the number of offspring depending on maternal juvenile body mass were not available from the literature. The same was true for the relative contribution to light (LJ) and heavy juveniles (HJ) by LAJ and HAJ females, respectively. These proportions were therefore calculated from our own data on reproductive success of semi-naturally kept yearling and adult females collected in 2013 and 2015, respectively (for details on the two study populations and their housing condition see 7 ). Due to limited supplementary feeding representing intermediate food availability in 2014 7 , data from this year were not considered in the present analysis. Food availability in 2013 and 2015 corresponded to favourable environmental conditions in the present study (for details see 7 ). To calculate the mean number of offspring produced LAJ and HAJ females as well as their respective proportional contribution to LJ and HJ, F0-females of the cohort 2011 were classified according their median juvenile body mass at around 8 months of age (31.2 kg).
In 2013, when F0-females reproduced as yearlings, females classified as yearlings light as juveniles (YLAJ, n = 20) produced 15.7 % less offspring than the overall mean in 2013 (2.14). Females identified as yearlings heavy as juveniles (YHAJ, n = 21) produced 16.5 % more offspring compared to the overall average. In 2015, when F0-females reproduced as adults, females classified as adults light as juveniles (ALAJ, n = 23) produced 6.5 % less offspring than the overall mean in 2015 (2.65). Females heavy as juveniles (AHAJ, n = 20) produced 9.0 % more compared to the average. For juveniles the same percentages were assumed as those found in yearlings due to a lack of data 7 .
The proportional production of light or heavy juveniles by LAJ and HAJ females was calculated from the same data 7 . Offspring of F0-females (F1 born in 2013 and 2015) were classified as light and heavy juveniles based on the median of juvenile body mass of piglets born in 2015 (21.5 kg; i.e., piglets born by adult sows). This threshold was used to classify F1juveniles from both years to exclude the effect of mother´s young age in 2013. This was necessary as piglets born by yearlings were on average lighter compared with those born by adult sows (mean ± sd = 18.8 ± 5.1 kg (n = 112) and 21.7 ± 5.3 kg (n = 112) in 2013 and 2015, respectively; t = 4.19, P < 0.001). A different threshold was used compared with the median body mass from F0-females because F1-piglets in 2013 and 2015 were weighed as young as six months and thus about two months earlier than the F0-females in 2011. In 2013, when F0females were yearlings, 35.7 % and 26.2 % of offspring of F0-females light (YLAJ) or heavy (YHAJ) as juveniles were classified as heavy juveniles, respectively (Supporting Table S2). In 2015, when F0-females were adults 28.0 % and 73.9 % of the offspring of adult F0-females light (ALAJ) or heavy (AHAJ) as juveniles were classified as heavy juveniles, respectively. Given that females reproduce earlier in mast years and that body mass gain during the first year of life is linear 3 , it is plausible to assume that females contribute in higher proportions to heavy juveniles under favourable conditions. Therefore, a 20 % divergence from the computed values in favour to the production of light juveniles was assumed under unfavourable conditions.

Survival
Annual survival rates were taken from Briedermann 3 as those were based on a large database collected over several decades and provide survival data for different environmental scenarios. Seasonal survival rates of yearling and adult female wild boars were not available from the literature. The main natural cause of death among older wild boar classes is starvation 8 , which occurs mostly in winter when food availability is lowest. Consequently, a high summer survival of 95 % was assumed for yearlings and adults. Validation of this assumption revealed no major effect on the model outcome (see Results and Supplementary Information 2). For juveniles some studies report postnatal or summer survival rates. Excluding the artificial enclosure situation reported in Martys 9 and the exceptionally high mortality rate found in an Hungarian population 3,10 , we used the juvenile summer survival rate of 73 % as reported by Fruzinski 11 for Polish juveniles. The Polish population studied by Fruzinski 11 in fact is geographically close and thus very similar to the East German population reported in Briedermann 3 .
Further, no literature data were available regarding the differences in survival in relation to juvenile body mass. Due to a lower body surface to volume ratio and the resulting higher energy demands for thermoregulation, LJ are more susceptible to cold temperatures 12,13 . Although it has never been shown explicitly for wild boars that body mass affects survival of juveniles, it nevertheless seems plausible that LJ have lower survival rates than HJ. Thus, winter survival was assumed to be 10 % higher and lower for HJ and LJ, respectively, compared to the averages under favourable and unfavourable conditions. The effect of this assumption was also tested by altering this percentage ( Supplementary Information 2). Again, the models were found to be very robust towards changes in this percentage, except for the unlikely scenario that heavy and light juveniles would not differ in their survival rates under unfavourable environmental conditions (Supplementary Information 2). Again, only under unfavourable conditions was the proportion of LAJ and HAJ females also affected by altering the difference in survival between HJ and LJ (Supplementary Information 2). Neither of these, however, affected the conclusions we drew from the model outcome (see also main text).
With increasing body size, relative difference in the surface to volume ratio, and thus the differences in energy demands for thermoregulation 12 , diminish. Therefore, no difference in survival of yearlings and adults based on their juvenile body mass was assumed. Although potential long-term effects of juvenile body mass on survival, as found for reproduction 7 , cannot be excluded finally, it seems plausible that the reduced reproductive effort in females which have been light as juveniles (see above) results from a trade-off between survival and reproduction 14 and thus causes no long-term effect of juvenile body mass on survival.
Because winter conditions are more strongly affected by climate change in temperate regions 15,16 compared to summer conditions, the two different parameterisations of the model (i.e., favourable and unfavourable) refer only to winter conditions. Therefore, identical summer survival rates of all classes were used in both models. This is in line with a very weak and so far negligible negative effect of increasing summer temperatures on wild boar population growth 17 . Winter survival rates were calculated from annual and summer survival rates (Swinter = Sannual / Ssummer).

Supplementary Information 2
Validating the effect of model assumptions that had to be drawn due to a lack of empirical data Two major assumptions had to be drawn during the model construction due to the lack of empirical data: (i) on the summer survival of yearlings and adults, which was set to 95 % (see main article) and (ii) on the difference in annual survival rates of light (LJ) and heavy juveniles (HJ), which was set to 20 %. In order to test for the effect of these assumptions on the results, and thus on the conclusions from the population modelling, these percentages were varied and the different model outcomes were compared with respect to sensitivities, elasticities, and stable stage distributions.

Varying summer survival of yearlings and adults
For validation of the assumed summer survival rates of yearling and adults this rate was modified from 85 % to 100 % (model assumption: 95 %).

Sensitivities
Varying summer survival among yearlings and adults had virtually no effect on sensitivities, neither under favourable nor under unfavourable conditions. With decreasing summer survival of adults and yearlings, the sensitivity of juvenile survival increased only slightly ( Fig. S1 and Fig. S2) and no changes regarding the ranking of sensitivities were caused.

Figure S1
Sensitivities under favourable conditions with varying summer survival rates of yearlings and adults. Vital rates are survival (S) and fecundity (F) of the age classes in brackets: heavy juveniles (HJ), light juveniles (LJ), yearlings heavy (Y_hj) and light as juveniles (Y_lj), and adults heavy (A_hj) and light as juveniles (A_lj). Yearlings and adults can contribute to both heavy and light juveniles; the contribution is signed by a hyphen (e.g., Y_lj-HJ).

Figure S2
Sensitivities under unfavourable conditions with varying summer survival rates of yearlings and adults. Vital rates are survival (S) and fecundity (F) of the age classes in brackets: heavy juveniles (HJ), light juveniles (LJ), yearlings heavy (Y_hj) and light as juveniles (Y_lj), and adults heavy (A_hj) and light as juveniles (A_lj). Yearlings and adults can contribute to both heavy and light juveniles; the contribution is signed by a hyphen (e.g., Y_lj-HJ). Sensitivities under unfavourable conditions 85% 90% 95% 100%

Elasticities
Elasticities were even less affected than sensitivities by varying summer survival among yearlings and adults, regardless of environmental conditions ( Fig. S3 and Fig. S4).

Figure S3
Elasticities under favourable conditions with varying summer survival rates of yearlings and adults. Vital rates are survival (S) and fecundity (F) of the age classes in brackets: heavy juveniles (HJ), light juveniles (LJ), yearlings heavy (Y_hj) and light as juveniles (Y_lj), and adults heavy (A_hj) and light as juveniles (A_lj). Yearlings and adults can contribute to both heavy and light juveniles; the contribution is signed by a hyphen (e.g., Y_lj -HJ). Elasticities under unfavourable conditions 85% 90% 95% 100%

Population structure
Finally, there was also only a minor effect on population structure of varying the rate of summer survival of yearlings and adults. Decreasing their summer survival caused only slight increases in the proportion of juveniles (both classes) whereas the proportion of yearlings and adults slightly decreased under both conditions ( Fig. S5 and Fig. S6).  Varying differences in winter survival rates of juveniles For validation, the assumed difference in winter survival rates between HJ and LJ was varied from ± 0 % to ± 15 % in steps of 5 % (model assumption: ± 10 % from the overall mean for HJ and LJ, respectively; see main article).

Sensitivities
Varying differences in survival rates between LJ and HJ did not notably affect the sensitivities under favourable conditions and thus the conclusions drawn from the models. The higher the differences in survival rates between HJ and LJ the more importance heavy juveniles gained under unfavourable conditions. This, however, did not affect the conclusions as the survival of light juveniles always had the highest sensitivity, irrespective of the difference in survival between the two juvenile classes (Fig. S7). Also, under unfavourable conditions, varying the difference in annual survival between HJ and LJ only caused minor differences on the sensitivities. Except for the assumption that there is no difference (i.e., ± 0 %), in which case survival of LJ showed the highest sensitivity, survival of adults heavy as juveniles (A_hj) always showed the highest sensitivity (Fig. S8). Arguably, under unfavourable environmental conditions with cold winters and low food availability a lower body mass is especially detrimental 21 . Therefore, the assumption that HJ and LJ do not differ in their survival seems highly unlikely so that also under unfavourable conditions the main conclusions drawn from the model results remain largely unaffected. Elasticities Similar to sensitivities, increasing the difference in annual survival between HJ and LJ increased the importance of individuals heavy as juveniles with respect to elasticities. Again, these changes did not majorly affect the conclusions drawn from the models as the class with the highest elasticity did not change under both favourable (i.e., survival of both juvenile classes) and unfavourable (i.e., survival of A_hj) conditions. As with sensitivities, the only exception was the unlikely assumption of no difference in annual survival between HJ and LJ under unfavourable environmental conditions ( Fig. S9 and Fig. S10).

Figure S9
Elasticities under favourable conditions of versions, varying the differences in yearly survival rates between heavy and light juveniles from 0 % to 15 %. Vital rates are survival (S) and fecundity (F) of the age classes in brackets: heavy juveniles (HJ), light juveniles (LJ), yearlings heavy (Y_hj) and light as juveniles (Y_lj), and adults heavy (A_hj) and light as juveniles (A_lj). Yearlings and adults can contribute to both heavy and light juveniles; the contribution is signed by a hyphen (e.g., Y_lj-HJ).

Figure S10
Elasticities under unfavourable conditions with varying the differences in yearly survival rates between heavy and light juveniles. Vital rates are survival (S) and fecundity (F) of the age classes in brackets: heavy juveniles (HJ), light juveniles (LJ), yearlings heavy (Y_hj) and light as juveniles (Y_lj), and adults heavy (A_hj) and light as juveniles (A_lj). Yearlings and adults can contribute to both heavy and light juveniles; the contribution is signed by a hyphen (e.g., Y_lj-HJ). Elasticities under favourable conditions 0% 10% 20% 30%

Population structure
The age structure of the asymptotic population, as well as the stable stage structure within the age classes, also remained largely unaffected by varying the difference in annual survival of HJ and LJ. The proportion of individuals light as juveniles increased slightly with decreasing survival differences (Fig. S11) but no qualitative changes could be observed and all age classes were dominated by individuals light as juveniles under favourable conditions. Under unfavourable conditions, however, this effect was stronger and caused qualitative changes. If the assumed difference in survival was below 20 % all age classes were again dominated by individuals light as juveniles. Otherwise older classes (i.e., yearlings and adults) were dominated by individuals heavy as juveniles (Fig. S12).

Figure S11
Stable stage distribution under favourable conditions with varying differences in yearly survival rates between heavy and light juveniles. Heavy juveniles (HJ), light juveniles (LJ), yearlings heavy (Y_hj) and light as juveniles (Y_lj), and adults heavy (A_hj) and light as juveniles (A_lj).

Figure S12
Stable stage distribution under unfavourable conditions with varying differences in yearly survival rates between heavy and light juveniles. Heavy juveniles (HJ), light juveniles (LJ), yearlings heavy (Y_hj) and light as juveniles (Y_lj), and adults heavy (A_hj) and light as juveniles (A_lj).  The calculation was based on the survival sensitivities of the respective age classes weighed by the proportion of the classes within the stable age population, respectively. The classes are light (LJ) and heavy juveniles (HJ), yearlings light (YLAJ) and heavy as juveniles (YHAJ) as well as adults light (ALAJ) and heavy as juveniles (AHAJ). Weighted sensitivities were additionally corrected for discriminability as follows: For LJ and HJ weighed sensitivities were divided by 2 as distinguishing between male and female piglets is difficult and one needs to assume that by chance only every second animal shot is a female; for yearlings and adults weighed sensitivities were averaged across individuals that have been light or heavy at juveniles as those are might not easily distinguishable anymore in these age classes.