growtrans: Growth Transition Matrix for a Size-Structured Population...
In fishmethods: Fishery Science Methods and Models
Description
Usage
Arguments
Details
Value
Note
Author(s)
References
Examples
Description
Generates a growth transition matrix from parameters of the von Bertalanffy growth
equation following Chen et al. (2003)
Usage
1
2
Arguments
Lmin
Mid-point of starting size class.
Lmax
Mid-point of end size class. This should be one increment larger than Linf.
Linc
Size class increment.
Linf
L-infinity parameter of the von Bertalanffy growth equation.
SELinf
Standard error of Linf.
K
Growth parameter of the von Bertalanffy growth equation.
SEK
Standard error of K.
rhoLinfK
Correlation between Linf and K. Usually from a parameter correlation matrix.
Details
Transition probabilities are calculated by using formulae 3-9 and procedures
in Chen et al. (2003). Negative growth increments result if Lmax is beyond
Linf, so the transition matrix is truncated at Linf. The last size class acts as
a plus group and has a probability of 1.
Value
A matrix of dimensions n size classes x n size classes.
Note
This function is based on an example EXCEL spreadsheet provided by Yong Chen.
Author(s)
Gary A. Nelson, Massachusetts Division of Marine Fisheries [email protected]
References
Chen, Y., M. Hunter, R. Vadas, and B. Beal. 2003. Developing a growth-transition matrix for stock assessment
of the green sea urchin (Strongylocentrotus droebachiensis) off Maine. Fish. Bull. 101: 737-744.
Examples
1
2
# For Chen et al. 2003
growtrans(Lmin=40,Lmax=101,Linc=1,Linf=100,SELinf=15,K=0.100588,SEK=0.04255,rhoLinfK=0.94)
Example output
Loading required package: MASS
Loading required package: boot
Loading required package: bootstrap
Loading required package: lme4
Loading required package: Matrix
Loading required package: numDeriv
40 41 42 43 44 45
40 0.04227017 0.05954389 0.07885564 0.09777030 0.11298681 0.12112573
41 0.00000000 0.04346235 0.06124743 0.08102541 0.10019329 0.11527674
42 0.00000000 0.00000000 0.04470453 0.06301867 0.08327025 0.10267739
43 0.00000000 0.00000000 0.00000000 0.04599936 0.06486083 0.08559271
44 0.00000000 0.00000000 0.00000000 0.00000000 0.04734971 0.06677725
45 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.04875858
46 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
47 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
48 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
49 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
50 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
51 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
52 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
53 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
54 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
55 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
56 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
57 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
58 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
59 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
60 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
61 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
62 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
63 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
64 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
65 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
66 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
67 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
68 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
69 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
70 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
71 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
72 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
73 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
74 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
75 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
76 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
77 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
78 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
79 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
80 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
81 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
82 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
83 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
84 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
85 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
86 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
87 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
88 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
89 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
90 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
91 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
92 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
93 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
94 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
95 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
96 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
97 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
98 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
99 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
100 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
46 47 48 49 50 51
40 0.11984998 0.10886579 0.09026074 0.06788811 0.04601802 0.02791633
41 0.12280034 0.12048668 0.10827646 0.08859193 0.06557711 0.04361650
42 0.11758619 0.12443085 0.12101381 0.10753792 0.08678022 0.06317415
43 0.10522267 0.11991121 0.12600940 0.12142208 0.10664370 0.08482546
44 0.08799533 0.10782894 0.12224733 0.12752749 0.12170191 0.10558767
45 0.06877147 0.09048070 0.11049576 0.12458952 0.12897602 0.12184346
46 0.05022922 0.07084719 0.09305138 0.11322235 0.12693210 0.13034521
47 0.00000000 0.05176505 0.07300830 0.09570996 0.11600759 0.12926871
48 0.00000000 0.00000000 0.05336973 0.07525886 0.09845895 0.11884993
49 0.00000000 0.00000000 0.00000000 0.05504716 0.07760314 0.10130085
50 0.00000000 0.00000000 0.00000000 0.00000000 0.05680152 0.08004560
51 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.05863723
52 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
53 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
54 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
55 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
56 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
57 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
58 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
59 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
60 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
61 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
62 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
63 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
64 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
65 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
66 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
67 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
68 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
69 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
70 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
71 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
72 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
73 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
74 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
75 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
76 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
77 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
78 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
79 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
80 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
81 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
82 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
83 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
84 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
85 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
86 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
87 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
88 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
89 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
90 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
91 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
92 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
93 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
94 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
95 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
96 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
97 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
98 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
99 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
100 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
52 53 54 55 56 57
40 0.01504289 0.007142768 0.002963051 0.001064045 0.0003275327 8.551464e-05
41 0.02587781 0.013589354 0.006263874 0.002511776 0.0008678707 2.557451e-04
42 0.04119507 0.023880884 0.012207727 0.005455412 0.0021114792 7.007730e-04
43 0.06068579 0.038763592 0.021933986 0.010901936 0.0047168720 1.759362e-03
44 0.08272847 0.058119548 0.036332413 0.020045290 0.0096752175 4.047114e-03
45 0.10436414 0.080491033 0.055483986 0.033912281 0.0182226047 8.530061e-03
46 0.12183668 0.102967973 0.078116085 0.052788662 0.0315142359 1.647325e-02
47 0.13162462 0.121671378 0.101394696 0.075607736 0.0500441235 2.914950e-02
48 0.13159227 0.132803154 0.121337311 0.099640642 0.0729713822 4.726187e-02
49 0.12174736 0.133894905 0.133869038 0.120824258 0.0977030838 7.021377e-02
50 0.10423806 0.124697373 0.136167897 0.134809835 0.1201221385 9.558038e-02
51 0.08259092 0.107272885 0.127696852 0.138401628 0.1356124744 1.192211e-01
52 0.06055905 0.085243987 0.110407475 0.130742032 0.1405855206 1.362633e-01
53 0.00000000 0.062572046 0.088009889 0.113643814 0.1338284179 1.427080e-01
54 0.00000000 0.000000000 0.064681632 0.090893941 0.1169836576 1.369507e-01
55 0.00000000 0.000000000 0.000000000 0.066893601 0.0939016763 1.204285e-01
56 0.00000000 0.000000000 0.000000000 0.000000000 0.0692141508 9.703884e-02
57 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 7.164991e-02
58 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
59 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
60 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
61 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
62 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
63 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
64 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
65 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
66 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
67 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
68 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
69 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
70 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
71 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
72 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
73 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
74 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
75 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
76 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
77 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
78 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
79 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
80 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
81 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
82 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
83 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
84 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
85 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
86 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
87 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
88 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
89 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
90 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
91 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
92 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
93 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
94 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
95 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
96 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
97 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
98 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
99 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
100 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
58 59 60 61 62
40 1.872406e-05 3.396680e-06 5.038863e-07 6.027492e-08 5.726729e-09
41 6.357022e-05 1.317218e-05 2.246465e-06 3.110608e-07 3.445944e-08
42 1.973089e-04 4.659063e-05 9.113045e-06 1.457027e-06 1.877139e-07
43 5.598662e-04 1.503084e-04 3.363803e-05 6.194564e-06 9.257192e-07
44 1.452350e-03 4.423002e-04 1.129815e-04 2.390465e-05 4.132996e-06
45 3.444395e-03 1.187151e-03 3.453028e-04 8.373160e-05 1.670558e-05
46 7.468160e-03 2.906399e-03 9.603177e-04 2.662187e-04 6.113314e-05
47 1.480395e-02 6.490376e-03 2.430287e-03 7.683106e-04 2.025434e-04
48 2.682932e-02 1.322071e-02 5.596723e-03 2.012752e-03 6.075652e-04
49 4.445427e-02 2.456487e-02 1.172867e-02 4.786361e-03 1.650093e-03
50 6.734308e-02 4.163452e-02 2.236702e-02 1.033209e-02 4.057618e-03
51 9.327211e-02 6.436893e-02 3.881648e-02 2.024622e-02 9.034165e-03
52 1.181118e-01 9.077927e-02 6.130245e-02 3.601458e-02 1.821231e-02
53 1.367480e-01 1.167854e-01 8.810439e-02 5.815625e-02 3.324363e-02
54 1.447564e-01 1.370519e-01 1.152337e-01 8.525170e-02 5.494441e-02
55 1.401026e-01 1.467169e-01 1.371599e-01 1.134495e-01 8.222727e-02
56 1.239794e-01 1.432771e-01 1.485747e-01 1.370566e-01 1.114270e-01
57 1.003114e-01 1.276373e-01 1.464656e-01 1.503136e-01 1.367262e-01
58 7.420799e-02 1.037255e-01 1.314022e-01 1.496587e-01 1.519164e-01
59 0.000000e+00 7.689598e-02 1.072876e-01 1.352740e-01 1.528456e-01
60 0.000000e+00 0.000000e+00 7.972203e-02 1.110041e-01 1.392517e-01
61 0.000000e+00 0.000000e+00 0.000000e+00 8.269489e-02 1.148818e-01
62 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 8.582391e-02
63 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
64 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
65 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
66 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
67 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
68 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
69 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
70 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
71 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
72 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
73 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
74 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
75 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
76 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
77 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
78 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
79 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
80 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
81 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
82 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
83 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
84 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
85 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
86 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
87 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
88 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
89 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
90 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
91 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
92 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
93 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
94 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
95 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
96 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
97 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
98 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
99 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
100 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
63 64 65 66 67
40 4.251863e-10 2.424059e-11 1.041257e-12 3.310665e-14 8.306328e-16
41 3.006161e-09 2.030235e-10 1.042122e-11 3.985401e-13 1.116958e-14
42 1.918925e-08 1.530872e-09 9.361789e-11 4.304536e-12 1.456503e-13
43 1.105924e-07 1.039276e-08 7.549612e-10 4.160359e-11 1.704162e-12
44 5.754715e-07 6.352327e-08 5.465467e-09 3.598769e-10 1.777942e-11
45 2.703722e-06 3.495864e-07 3.552038e-08 2.786104e-09 1.654831e-10
46 1.146961e-05 1.732230e-06 2.072462e-07 1.930515e-08 1.374162e-09
47 4.393319e-05 7.728510e-06 1.085587e-06 1.197274e-07 1.018085e-08
48 1.519505e-04 3.104806e-05 5.105316e-06 6.646156e-07 6.729842e-08
49 4.745531e-04 1.123132e-04 2.155613e-05 3.302291e-06 3.969297e-07
50 1.338286e-03 3.658421e-04 8.171825e-05 1.468722e-05 2.088925e-06
51 3.408020e-03 1.073079e-03 2.781490e-04 5.847283e-05 9.809468e-06
52 7.837026e-03 2.834349e-03 8.500718e-04 2.083868e-04 4.110488e-05
53 1.627434e-02 6.741655e-03 2.332720e-03 6.648110e-04 1.537018e-04
54 3.051865e-02 1.444039e-02 5.747874e-03 1.898665e-03 5.128772e-04
55 5.168244e-02 2.785465e-02 1.271739e-02 4.854342e-03 1.527244e-03
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81 2.295726e-01 1.758788e-01 1.030034e-01 4.475652e-02 1.395644e-02
82 2.435462e-01 2.319938e-01 1.716863e-01 9.593583e-02 3.921241e-02
83 2.141550e-01 2.519041e-01 2.338582e-01 1.667569e-01 8.861087e-02
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85 6.378825e-05 3.051440e-06 7.703537e-08 9.482009e-10 5.200992e-12
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87 6.674038e-11 1.839564e-13 1.522818e-16
88 2.999142e-09 1.500708e-11 2.805090e-14
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92 3.672455e-04 1.661246e-05 3.469640e-07
93 2.873494e-03 2.152709e-04 7.822677e-06
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98 4.943186e-01 3.529896e-01 1.526917e-01
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100 0.000000e+00 0.000000e+00 1.000000e+00
fishmethods documentation built on Nov. 21, 2018, 1:04 a.m.
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Description Usage Arguments Details Value Note Author(s) References Examples
Description
Generates a growth transition matrix from parameters of the von Bertalanffy growth equation following Chen et al. (2003)
Usage
1 2 |
Arguments
Lmin |
Mid-point of starting size class. |
Lmax |
Mid-point of end size class. This should be one increment larger than Linf. |
Linc |
Size class increment. |
Linf |
L-infinity parameter of the von Bertalanffy growth equation. |
SELinf |
Standard error of Linf. |
K |
Growth parameter of the von Bertalanffy growth equation. |
SEK |
Standard error of K. |
rhoLinfK |
Correlation between Linf and K. Usually from a parameter correlation matrix. |
Details
Transition probabilities are calculated by using formulae 3-9 and procedures in Chen et al. (2003). Negative growth increments result if Lmax is beyond Linf, so the transition matrix is truncated at Linf. The last size class acts as a plus group and has a probability of 1.
Value
A matrix of dimensions n size classes x n size classes.
Note
This function is based on an example EXCEL spreadsheet provided by Yong Chen.
Author(s)
Gary A. Nelson, Massachusetts Division of Marine Fisheries [email protected]
References
Chen, Y., M. Hunter, R. Vadas, and B. Beal. 2003. Developing a growth-transition matrix for stock assessment of the green sea urchin (Strongylocentrotus droebachiensis) off Maine. Fish. Bull. 101: 737-744.
Examples
1 2 | # For Chen et al. 2003
growtrans(Lmin=40,Lmax=101,Linc=1,Linf=100,SELinf=15,K=0.100588,SEK=0.04255,rhoLinfK=0.94)
|
Example output
Loading required package: MASS
Loading required package: boot
Loading required package: bootstrap
Loading required package: lme4
Loading required package: Matrix
Loading required package: numDeriv
40 41 42 43 44 45
40 0.04227017 0.05954389 0.07885564 0.09777030 0.11298681 0.12112573
41 0.00000000 0.04346235 0.06124743 0.08102541 0.10019329 0.11527674
42 0.00000000 0.00000000 0.04470453 0.06301867 0.08327025 0.10267739
43 0.00000000 0.00000000 0.00000000 0.04599936 0.06486083 0.08559271
44 0.00000000 0.00000000 0.00000000 0.00000000 0.04734971 0.06677725
45 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.04875858
46 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
47 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
48 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
49 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
50 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
51 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
52 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
53 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
54 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
55 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
56 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
57 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
58 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
59 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
60 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
61 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
62 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
63 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
64 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
65 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
66 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
67 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
68 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
69 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
70 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
71 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
72 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
73 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
74 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
75 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
76 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
77 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
78 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
79 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
80 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
81 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
82 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
83 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
84 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
85 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
86 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
87 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
88 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
89 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
90 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
91 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
92 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
93 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
94 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
95 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
96 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
97 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
98 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
99 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
100 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
46 47 48 49 50 51
40 0.11984998 0.10886579 0.09026074 0.06788811 0.04601802 0.02791633
41 0.12280034 0.12048668 0.10827646 0.08859193 0.06557711 0.04361650
42 0.11758619 0.12443085 0.12101381 0.10753792 0.08678022 0.06317415
43 0.10522267 0.11991121 0.12600940 0.12142208 0.10664370 0.08482546
44 0.08799533 0.10782894 0.12224733 0.12752749 0.12170191 0.10558767
45 0.06877147 0.09048070 0.11049576 0.12458952 0.12897602 0.12184346
46 0.05022922 0.07084719 0.09305138 0.11322235 0.12693210 0.13034521
47 0.00000000 0.05176505 0.07300830 0.09570996 0.11600759 0.12926871
48 0.00000000 0.00000000 0.05336973 0.07525886 0.09845895 0.11884993
49 0.00000000 0.00000000 0.00000000 0.05504716 0.07760314 0.10130085
50 0.00000000 0.00000000 0.00000000 0.00000000 0.05680152 0.08004560
51 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.05863723
52 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
53 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
54 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
55 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
56 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
57 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
58 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
59 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
60 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
61 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
62 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
63 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
64 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
65 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
66 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
67 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
68 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
69 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
70 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
71 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
72 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
73 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
74 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
75 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
76 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
77 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
78 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
79 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
80 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
81 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
82 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
83 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
84 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
85 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
86 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
87 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
88 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
89 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
90 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
91 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
92 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
93 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
94 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
95 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
96 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
97 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
98 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
99 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
100 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
52 53 54 55 56 57
40 0.01504289 0.007142768 0.002963051 0.001064045 0.0003275327 8.551464e-05
41 0.02587781 0.013589354 0.006263874 0.002511776 0.0008678707 2.557451e-04
42 0.04119507 0.023880884 0.012207727 0.005455412 0.0021114792 7.007730e-04
43 0.06068579 0.038763592 0.021933986 0.010901936 0.0047168720 1.759362e-03
44 0.08272847 0.058119548 0.036332413 0.020045290 0.0096752175 4.047114e-03
45 0.10436414 0.080491033 0.055483986 0.033912281 0.0182226047 8.530061e-03
46 0.12183668 0.102967973 0.078116085 0.052788662 0.0315142359 1.647325e-02
47 0.13162462 0.121671378 0.101394696 0.075607736 0.0500441235 2.914950e-02
48 0.13159227 0.132803154 0.121337311 0.099640642 0.0729713822 4.726187e-02
49 0.12174736 0.133894905 0.133869038 0.120824258 0.0977030838 7.021377e-02
50 0.10423806 0.124697373 0.136167897 0.134809835 0.1201221385 9.558038e-02
51 0.08259092 0.107272885 0.127696852 0.138401628 0.1356124744 1.192211e-01
52 0.06055905 0.085243987 0.110407475 0.130742032 0.1405855206 1.362633e-01
53 0.00000000 0.062572046 0.088009889 0.113643814 0.1338284179 1.427080e-01
54 0.00000000 0.000000000 0.064681632 0.090893941 0.1169836576 1.369507e-01
55 0.00000000 0.000000000 0.000000000 0.066893601 0.0939016763 1.204285e-01
56 0.00000000 0.000000000 0.000000000 0.000000000 0.0692141508 9.703884e-02
57 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 7.164991e-02
58 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
59 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
60 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
61 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
62 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
63 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
64 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
65 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
66 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
67 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
68 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
69 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
70 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
71 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
72 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
73 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
74 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
75 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
76 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
77 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
78 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
79 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
80 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
81 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
82 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
83 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
84 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
85 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
86 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
87 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
88 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
89 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
90 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
91 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
92 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
93 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
94 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
95 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
96 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
97 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
98 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
99 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
100 0.00000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000e+00
58 59 60 61 62
40 1.872406e-05 3.396680e-06 5.038863e-07 6.027492e-08 5.726729e-09
41 6.357022e-05 1.317218e-05 2.246465e-06 3.110608e-07 3.445944e-08
42 1.973089e-04 4.659063e-05 9.113045e-06 1.457027e-06 1.877139e-07
43 5.598662e-04 1.503084e-04 3.363803e-05 6.194564e-06 9.257192e-07
44 1.452350e-03 4.423002e-04 1.129815e-04 2.390465e-05 4.132996e-06
45 3.444395e-03 1.187151e-03 3.453028e-04 8.373160e-05 1.670558e-05
46 7.468160e-03 2.906399e-03 9.603177e-04 2.662187e-04 6.113314e-05
47 1.480395e-02 6.490376e-03 2.430287e-03 7.683106e-04 2.025434e-04
48 2.682932e-02 1.322071e-02 5.596723e-03 2.012752e-03 6.075652e-04
49 4.445427e-02 2.456487e-02 1.172867e-02 4.786361e-03 1.650093e-03
50 6.734308e-02 4.163452e-02 2.236702e-02 1.033209e-02 4.057618e-03
51 9.327211e-02 6.436893e-02 3.881648e-02 2.024622e-02 9.034165e-03
52 1.181118e-01 9.077927e-02 6.130245e-02 3.601458e-02 1.821231e-02
53 1.367480e-01 1.167854e-01 8.810439e-02 5.815625e-02 3.324363e-02
54 1.447564e-01 1.370519e-01 1.152337e-01 8.525170e-02 5.494441e-02
55 1.401026e-01 1.467169e-01 1.371599e-01 1.134495e-01 8.222727e-02
56 1.239794e-01 1.432771e-01 1.485747e-01 1.370566e-01 1.114270e-01
57 1.003114e-01 1.276373e-01 1.464656e-01 1.503136e-01 1.367262e-01
58 7.420799e-02 1.037255e-01 1.314022e-01 1.496587e-01 1.519164e-01
59 0.000000e+00 7.689598e-02 1.072876e-01 1.352740e-01 1.528456e-01
60 0.000000e+00 0.000000e+00 7.972203e-02 1.110041e-01 1.392517e-01
61 0.000000e+00 0.000000e+00 0.000000e+00 8.269489e-02 1.148818e-01
62 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 8.582391e-02
63 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
64 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
65 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
66 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
67 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
68 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
69 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
70 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
71 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
72 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
73 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
74 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
75 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
76 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
77 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
78 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
79 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
80 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
81 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
82 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
83 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
84 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
85 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
86 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
87 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
88 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
89 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
90 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
91 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
92 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
93 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
94 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
95 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
96 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
97 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
98 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
99 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
100 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
63 64 65 66 67
40 4.251863e-10 2.424059e-11 1.041257e-12 3.310665e-14 8.306328e-16
41 3.006161e-09 2.030235e-10 1.042122e-11 3.985401e-13 1.116958e-14
42 1.918925e-08 1.530872e-09 9.361789e-11 4.304536e-12 1.456503e-13
43 1.105924e-07 1.039276e-08 7.549612e-10 4.160359e-11 1.704162e-12
44 5.754715e-07 6.352327e-08 5.465467e-09 3.598769e-10 1.777942e-11
45 2.703722e-06 3.495864e-07 3.552038e-08 2.786104e-09 1.654831e-10
46 1.146961e-05 1.732230e-06 2.072462e-07 1.930515e-08 1.374162e-09
47 4.393319e-05 7.728510e-06 1.085587e-06 1.197274e-07 1.018085e-08
48 1.519505e-04 3.104806e-05 5.105316e-06 6.646156e-07 6.729842e-08
49 4.745531e-04 1.123132e-04 2.155613e-05 3.302291e-06 3.969297e-07
50 1.338286e-03 3.658421e-04 8.171825e-05 1.468722e-05 2.088925e-06
51 3.408020e-03 1.073079e-03 2.781490e-04 5.847283e-05 9.809468e-06
52 7.837026e-03 2.834349e-03 8.500718e-04 2.083868e-04 4.110488e-05
53 1.627434e-02 6.741655e-03 2.332720e-03 6.648110e-04 1.537018e-04
54 3.051865e-02 1.444039e-02 5.747874e-03 1.898665e-03 5.128772e-04
55 5.168244e-02 2.785465e-02 1.271739e-02 4.854342e-03 1.527244e-03
56 7.903917e-02 4.838713e-02 2.526639e-02 1.111101e-02 4.058587e-03
57 1.091614e-01 7.569756e-02 4.507650e-02 2.276813e-02 9.625493e-03
58 1.361533e-01 1.066498e-01 7.221480e-02 4.176955e-02 2.037337e-02
59 1.533644e-01 1.353224e-01 1.038910e-01 6.860549e-02 3.848608e-02
60 1.560138e-01 1.546381e-01 1.342185e-01 1.008863e-01 6.488654e-02
61 1.433335e-01 1.591496e-01 1.557165e-01 1.328272e-01 9.763911e-02
62 1.189275e-01 1.475167e-01 1.622372e-01 1.565775e-01 1.311352e-01
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