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... thresholds. The model f(p(x i ) = l + b log (x i /t)) if x i >t (2) has been previously proposed together with a likelihood maximisation method for estimate the threshold and its confidence interval =-=[1]-=-. Modifications and further developments on such threshold value models can be found in [2,3]. A useful alternative to these parametric approaches is provided by isotonic regression. The main advantag...

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...sity of altitudes and aspects (Mysterudset al . 2001a). STATISTICAL ANALYSES To estimate objectively the start of mass loss, peak of mass loss and end dates of mass loss, we applied threshold models (=-=Ulm 1989-=-; for an application see Lambin & Yoccoz 2001) with one or two breaking points ( φ 1 , orsφ 1sandsφ 2swhensφ 2swas estimable) on the predicted body mass from generalized additive model (GAM) fits (Has...

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...and τ2 are the threshold values defining the dates for which the proportion of mixed groups starts and peaks, respectively. We used profile likelihood to estimate the onset and the peak of rut dates (=-=Ulm 1989-=-). Peak of rut (τ2) was estimated first by using the complete dataset. We estimated the onset of rut (τ1) by using a subset of the data ranging from Julian date 150 (May 30; from when group compositio...

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...ues may not correspond to a strict biological process. They were calculated using profileslikelihoods on the best model selected for each trait, a methodology commonly used in toxicologysand ecology (=-=Ulm 1989-=-).sThe threshold methodology allowed getting AIC values for all combination of models and thresholdsson each trait (QAICc for survival and detection). Since an important number of models were obtained...

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...ues may not correspond to a strict biological process. They were calculated using profileslikelihoods on the best model selected for each trait, a methodology commonly used in toxicologysand ecology (=-=Ulm 1989-=-).sThe threshold methodology allowed getting AIC values for all combination of models and thresholdsson each trait (QAICc for survival and detection). Since an important number of models were obtained...

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...eproduction, survival would not be equal to 1. We therefore fitted models that allowed for a threshold value below or above which there was no relationship between survival and explanatory variables (=-=Ulm 1989-=-, 1991; see also (Grenfellset al . 1992) ). Below (for number of pups) or above (for age) the threshold (TH), survival is constant and equal to the mortality with no costs present. This mortality coul...

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...ld animals. When using a threshold effect, we iteratively fitted threshold functions (with one breaking point, f1) while minimizing the residual sum of squares (analogous to using profile likelihood; =-=Ulm, 1989-=-) to estimate the age or date when rumen fill dropped (or increased) suddenly (Lambin & Yoccoz, 2001; Loe et al., 2005). All analyses were conducted for each sex separately. To control for possible be...