Ecological Archives E089-046-A1

Bård-Jørgen Bårdsen, Per Fauchald, Torkild Tveraa, Knut Langeland, Nigel Gilles Yoccoz, and Rolf Anker Ims. 2008. Experimental evidence of a risk-sensitive reproductive allocation in a long-lived mammal. Ecology 89:829–837.

Appendix A. Model selection and the pool of candidate models.

TABLE A1. The relative evidence for each candidate model (i) in Table 1 (Long-term feeding) and Table 3 (Experiment I and II) was assessed by rescaling and ranking models relative to the value of the model with the lowest Akaike’s Information Criterion value (Δi; the model in bold were selected and used for inference in each analysis as its Δi equals zero). The models were fitted by maximum likelihood (ML) as the restricted maximum likelihood (REML) fit used in the Table 1 and 3 are not recommended when several models are compared to each other (Pinheiro and Bates 2000). The predictors included in the different models are marked with an "x".


i 		 

Manipulation†

Season†

Manip. × seas.†

Year

Initial body mass
(IBM)

Manip. × IBM

Manip. × Year

df

  

Female body mass, Δi

      

Calf body mass, Δi

    
   

Long-term
feeding

 

Experiment I

 

Experiment II

     

Long-term
feeding

 

Experiment I

 

Experiment II

   
                     
                                                   

1.

  

x

x

x

x

x

x

x

12

  

2.20

  

3.51

  

0.73

      

1.80

  

2.85

  

0.89

    

2.

  

x

x

x

x

x

x

 

11

  

0.37

  

1.70

  

0.00

      

0.00

  

1.43

  

0.00

    

3.

  

x

x

x

x

x

   

10

  

0.00

  

0.00

  

4.02

      

2.90

  

0.00

  

0.35

    

4.

  

x

x

x

x

      

7

  

85.08

  

53.26

  

66.85

      

10.39

  

12.42

  

2.14

    

5.

  

x

x

x

       

6

  

89.12

  

68.81

  

67.87

      

37.10

  

31.43

  

26.14

    
                                                   

† The three predictors in bold were kept in all models based on our a priori expectations of the experimental translocation of animals in the three seasons of interest, i.e., we aimed at estimating the effect of experimental manipulation in the three different seasons.


TABLE A2. The relative evidence for each candidate model (i) in Table 2 was assessed by rescaling and ranking models relative to the value of the model with the lowest Akaike’s Information Criterion value (Δi; the model in bold were selected and used for inference in each analysis as its Δi equals zero). Season was not included as a predictor in these analyses as updated calf presence in the autumn was used as a proxy for production throughout all seasons. The predictors included in the different models are marked with an "x".


i 		 

Manipulation†

Year

Initial body mass
(IBM)

Manip. × Year

Manip. × IBM

df

  

Calf production, Δi

  
   

Long-term
feeding‡

  

Experiment I‡

  

Experiment II

  
         
                             

1.

  

x

(x)

x

(x)

x

6(4)

  

1.65

  

2.73

  

3.13

  

2.

  

x

(x)

x

(x)

 

5

  

__

 

__

 

1.15

  

3.

  

x

(x)

x

   

4(3)

  

1.99

 

1.91

  

0.43

 

4.

  

x

(x)

     

3

  

__

 

__

 

0.00

  

5.

  

x

        

2

  

0.00

  

0.00

  

0.23

  
                             

† The predictor in bold was kept in all models based on our a priori expectations of the experimental translocation of animals, i.e., we aimed at estimating the effect of experimental manipulation.
‡ Data from the year 2004 was removed from two analyses as a dog intruded the calf paddock killing at least two calves in one of the experimental groups. Consequently, the terms including year were not included in these models (the markings not included as well as the degrees of freedom for these analyses are given in parentheses).

LITERATURE CITED

Pinheiro, J. C., and D. M. Bates. 2000. Mixed effect models in S and S-PLUS. Springer, New York, USA.


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