Ecological Archives A016-005-A1

Charles D. Canham and María Uriarte. 2006. Analysis of neighborhood dynamics of forest ecosystems using likelihood methods and modeling. Ecological Applications 16:62–73.

Appendix A. True and estimated parameter values for six hypothetical seed dispersal data sets.

We tested for tradeoffs among parameters in an exponential seed dispersal function using six hypothetical data sets (A–F) generated from a hypothetical 1 km2 source area of trees and 200 1-m2 quadrats distributed in two transects through a central 1 ha portion of the source area.  Simulated seed rain was generated as a Poisson process, with mean seed rain specified by:

where dbhi and disti are the size and distance to i = 1..n trees within a 50 m radius of a seed trap, and is a normalizer that equals the arcwise integration of the dispersal kernel.  We generated six data sets (A–F) with different combinations of parameters (Table 1). We then used maximum-likelihood estimation with simulated annealing to test our ability to accurately estimate the underlying parameter values [A(est.) – F(est.)].   We also report 2-unit support intervals (SI) as measures of the strength of evidence for the parameter estimates. The shapes of the true and estimated dispersal functions are illustrated in Fig. 1 of the manuscript.

TABLE A1.  Parameter values used to generate datasets A–F, and the values estimated using maximum likelihood methods [A(est.) – F(est.)], along with 2-unit support intervals (SI) as a measure of the strength of evidence for the parameter estimates.

Parameters

Data set

A

alpha

B

beta

A (est)

990.9

1.02

3630.3

0.87

2-unit SI

946.3 - 1035.5

0.97 - 1.07

3430.6 - 3830.0

0.85 - 0.89

A

1000

1

2500

1

B (est)

965.6

2.04

3062.4

0.93

2-unit SI

936.6 - 994.6

2.01 - 2.07

2955.2 - 3169.5

0.92 - 0.94

B

1000

2

2500

1

C (est)

962.8

3.04

2830.8

0.96

C

1000

3

2500

1

2-unit SI

943.5 - 982.1

3.01 - 3.07

2774.1 - 2887.4

0.95 - 0.97

D (est)

981.9

1.04

2075.6

0.90

2-unit SI

937.7 - 1026.1

0.98 - 1.09

1899.1 - 2252.0

0.88 - 0.93

D

1000

1

1500

1

E (est)

1023.8

0.97

414.0

1.80

2-unit SI

982.8 - 1069.8

0.91 - 1.02

387.1 - 442.9

1.77 - 1.83

E

1000

1

250

2

F (est)

1043.9

0.94

75.7

2.82

2-unit SI

997.0 - 1090.9

0.89 - 0.99

70.4 - 81.0

2.78 - 2.86

F

1000

1

50

3

 



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