Calculations shown in Appendix C.
Ecological Archives A016-001-S1.
Authors
File list (downloads)
Description
N. Thompson Hobbs
Natural Resource Ecology Laboratory
Colorado State University
Fort Collins, CO 80523-1499
E-mail: nthobbs@nrel.colostate.edu
Hobbs_Hilborn_supplement1.txt -- Contains data collected at Isle Royal National Park (Michigan, USA) during the winter (January and February) from 1971–2001 and prey dependent model predictions and calculations.
Hobbs_Hilborn_supplement2.txt -- Contains data collected at Isle Royal National Park (Michigan, USA) during the winter (January and February) from 1971–2001 and ratio dependent model predictions and calculations.
Hobbs_Hilborn_supplement3.txt -- Contains data collected at Isle Royal National Park (Michigan, USA) during the winter (January and February) from 1971–2001 and predator dependent model predictions and calculations.
Hobbs_Hilborn_supplement4.txt -- Contains estimates of model selection statistics for the prey dependent, ratio dependent, and predator dependent models.
Hobbs_Hilborn_supplement.xls -- A spreadsheet showing details of the computation. The data files listed above can be downloaded into a spreadsheet of your choice.
Hobbs_Hilborn_supplement1.txt contains data collected at Isle Royal National Park (Michigan, USA) during the winter (January and February) from 1971–2001 and prey dependent model predictions and calculations.
The file is tab delimited and contains 8 columns and 94 rows. The columns correspond to the variables listed below, and each row corresponds to a yearly observation, prey dependent model prediction, or calculation.
Hobbs_Hilborn_supplement1
Column
Variable name
Description
1
Years
Years of data collection – 1971-2001
2
Number of Moose
Number of moose in IsleRoyalNational Park
3
Number of Wolves
Number of wolves in IsleRoyalNational Park
4
Kill Rate
Number of kills made by a wolf pack divided by the number of wolves in that pack divided by the number of days during which that pack was observed
5
Model Prediction
Prey dependent model prediction
6
Observation-Prediction
Difference between observations and model predictions
7
Likelihood
The value of a normal probability density function with column 6 as one argument (mu – xbar) and sigma (see below) as the other argument.
8
Log(likelihood)
Natural log of column 7
To make sure the file was downloaded properly, compare the column sums to the following figures:
1
186816
2
103882
3
2160
4
89
5
89
6
0.03
7
65
8
-49
There are also calculations based on the data that are indexed in a column to their left (2 columns, 7 rows). These indices and the calculations they index are:
a
Maximum likelihood estimate of model parameter a.
h
Maximum likelihood estimate of model parameter h
n
Number of data points
K
Number of parameters estimated from the data, including the standard deviation
sigma
Estimate of the standard deviation
sum log likelihoods
Sums of the log likelihoods for the maximum likelihood estimates of model parameters
AICc
Akaike’s information criterion adjusted for small samples
Hobbs_Hilborn_supplement2.txt contains data collected at IsleRoyalNational Park (Michigan, USA) during the winter (January and February) from 1971–2001 and ratio dependent model predictions and calculations.
The file is tab delimited and contains 9 columns and 94 rows. The columns correspond to the variables listed below, and each row corresponds to a yearly observation, ratio dependent model prediction, or calculation.
Hobbs_Hilborn_supplement2
Column
Variable name
Description
1
Years
Years of data collection – 1971–2001
2
Number of Moose
Number of moose in IsleRoyalNational Park
3
Number of Wolves
Number of wolves in IsleRoyalNational Park
4
Kill Rate
Number of kills made by a wolf pack divided by the number of wolves in that pack divided by the number of days during which that pack was observed
5
Ratio (wolves/moose)
Number of wolves divided by number of moose
6
Model Prediction
Ratio dependent model prediction
7
Observation-Prediction
Difference between observations and model predictions
8
Likelihood
The value of a normal probability density function with column 7 as one argument (mu – xbar) and sigma (see below) as the other argument.
9
Log(likelihood)
Natural log of column 8
To make sure the file was downloaded properly, compare the column sums to the following figures:
1
186816
2
103882
3
2160
4
89
5
5952
6
88
7
0
8
74
9
-38
There are also calculations based on the data that are indexed in a column to their left (2 columns, 7 rows). These indices and the calculations they index are:
a
Maximum likelihood estimate of model parameter a.
h
Maximum likelihood estimate of model parameter h
n
Number of data points
K
Number of parameters estimated from the data, including the standard deviation
sigma
Estimate of the standard deviation
sum log likelihoods
Sums of the log likelihoods for the maximum likelihood estimates of model parameters
AICc
Akaike’s information criterion adjusted for small samples
Hobbs_Hilborn_supplement3.txt contains data collected at IsleRoyalNational Park (Michigan, USA) during the winter (January and February) from 1971–2001 and predator dependent model predictions or calculations.
The file is tab delimited and contains 10 columns and 94 rows. The columns correspond to the variables listed below, and each row corresponds to a yearly observation, predator dependent model prediction, or calculation.
Hobbs_Hilborn_supplement3
Column
Variable name
Description
1
Years
Years of data collection – 1971–2001
2
Number of Moose
Number of moose in IsleRoyalNational Park
3
Number of Wolves
Number of wolves in IsleRoyalNational Park
4
Kill Rate
Number of kills made by a wolf pack divided by the number of wolves in that pack divided by the number of days during which that pack was observed
5
Ratio (wolves/moose)
Number of wolves divided by number of moose
6
Model Prediction
Predator dependent model prediction
7
Observation-Prediction
Difference between observations and model predictions
8
(obs-pred)^2
Difference between observations and model predictions squared
9
Likelihood
The value of a normal probability density function with column 7 as one argument (mu – xbar) and sigma (see below) as the other argument.
10
Log(likelihood)
Natural log of column 9
To make sure the file was downloaded properly, compare the column sums to the following figures:
1
186816
2
103882
3
2160
4
89
5
5952
6
88
7
1
8
130228770
9
75
10
-38
There are also calculations based on the data that are indexed in a column to their left (2 columns, 7 rows. These indices and the calculations they index are:
a
Maximum likelihood estimate of model parameter a.
h
Maximum likelihood estimate of model parameter h
n
Number of data points
K
Number of parameters estimated from the data, including the standard deviation
sigma
Estimate of the standard deviation
sum log likelihoods
Sums of the log likelihoods for the maximum likelihood estimates of model parameters
AICc
Akaike’s information criterion adjusted for small samples
Hobbs_Hilborn_supplement4.txt contains estimates of model selection statistics for the prey dependent, ratio dependent, and predator dependent models.
The file is tab delimited and contains 5 columns and 4 rows. The columns correspond to the variables listed below, and each row corresponds to a model type.
Hobbs_Hilborn_supplement4
Column
Variable name
Description
1
Model, Mi
Model type
2
AICc
Akaike’s information criterion adjusted for small sample
3
Δr
The difference between the AICc value of the model and the model with the lowest AICc value
4
L(Mi|Y)
The likelihood of the model given the data.
5
wr
The Akaike weight
To make sure the file was downloaded properly, compare the column sums to the following figures:
1
n/a
2
269.99
3
22.03
4
1.54
5
1.00
Instructions
To reproduce the results presented in the paper, see the descriptions of the indexed calculations shown above. To obtain the parameter estimates, use a nonlinear optimization routine to find the values of model parameters that maximize the sum of the log likelihoods.
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