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Accepted Article
Tables and Figures
Table 1. Assignment of ibex age to the penalty variable, which was created to describe if hunters face a penalty for shooting an individual of the adjacent smaller or larger age-class.
Lower and upper limit assign each age to the lower or upper age range of each age-class, assuming selection of longer horns close to the lower limit and selection of shorter horns or indifference close to the upper limit. Note that we collapsed the age-classes 1–2 and 2–3 due to an overlap for 2-year-old animals.
Age-classes 1-2 / 2-3 4-5 6-10 ≥11
Hunting age 1 2 3 4 5 6 7 8 9 10 ≥11
Penalty lower limit lower
limit upper limit lower
limit upper limit lower
limit lower limit lower
limit upper limit upper
limit lower limit
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Table 2. Statistical parameter of the selected additive logistic regression model fitted to the conditional harvesting probability (CHP). The influence of stHL was significant for both penalty conditions (upper and lower limit). The confounding age variable accounts for the sampling scheme. Random effects on the intercept were assigned for individuals nested within hunting units (u) and for calendar years (v).
Parametric coefficient:
Estimate Std. Error Z-value p-value
Intercept -1.095 6.202 -0.177 0.86
Approximate significance of smooth terms:
edf Ref.df Chi-square p-value
slower limit(stHL) 3.400 4.330 34.190 1.22e-06 ***
supper limit(stHL) 3.600 4.510 32.250 4.99e-06 ***
s(age) 8.815 8.978 1050.030 < 2e-16 ***
u 5.975 7 734.550 2.33e-05 ***
v 23.917 24 364.850 < 2e-16 ***
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Fig. 1. (A) Characteristic age trend in Alpine ibex horn growth, and (B) corresponding indices after standardization by age-specific mean and standard deviation values.
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Fig. 2. (A) Accumulated total horn length (y-axis) at different harvesting ages (x-axis; from young to old ibex males from left to right). Black dots refer to total horn length at different harvesting ages, whereas grey dots show the length of the corresponding horn growth increments of animals that were harvested at later ages. Dashed grey lines are linear trends, with R2 ranging from 0.49 at age-class 9 to 0.94 and 0.97 at age-class 2 and 14, respectively.
(B) Differences in the total horn length of harvested animals and the accumulated length of the same number of horn increments of those male ibexes that were harvested at later ages.
Grey-dashed frames show age-classes in which hunters are allowed to harvest. The outermost, first increment has been removed in this data (see Fig. S5 for more details).
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Fig. 3. Partial effects of standardized horn length (stHL) and age on the conditional harvesting probability (CHP) with 0.95 confidence intervals from the mixed additive logistic regression model. The effect of stHL on CHP is shown for two penalty conditions (Table 1):
Close to the lower limit of each age class, hunters favoured longer horns; close to the upper limit, hunters tended to shoot animals with average horn length. Note that the increasing effect of age on CHP does not imply that hunters favour older ibex, but rather that age must be included in the hunting model to control for the confounding effect of the sampling scheme.
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Fig. 4. Predicted conditional harvesting probabilities (CHP) with 0.95-confidence intervals from the mixed additive logistic regression model. Predictions are shown for different standardized horn lengths (stHL) and ages, exemplarily for adult ibex males in hunting unit 8 in calendar year 1990. Each panel corresponds to one of the age-classes assigned to the hunters. Light (lower limit) and dark grey (dark limit) shadings refer to the penalty-term in the model, with the corresponding right-side numbers indicating the ibex age.