Overview

Six models are used to forecast each major age class of sockeye salmon in the major rivers of Bristol Bay. Five of these models are linear regressions and the sixth is a 5-year running average of the age class under consideration.

Forecast models

This document covers output from five linnear regression models run against four major age classes in this river. Three regressions are variations of the sibling relationship with the age being forecast (Table 1). The first regression (sibling) uses observed forecast age and the brood year younger sibling return. The second regression (ln.sibling) uses a natural log transformation of both the forecasted age and the sibling return. The third regression (lnY.sibling) uses the sibling age return and a natural log transformation of the forecasted age. Two linnear regression models based on forecasted age return and total spawning escapment. The first of these (lnS.lnR) is the natural log of the forecasted age class regressed against the natural log of the spawning escapement. The second forecast method that relies on the relationship between the forecasted age and the spawning escapement is a linnear transformation of the Ricker relationship.

Table 1. Forecast ages and the sibling age class used for forecasting.

Forecast Age Sibling
Age.12 Age.11
Age.22 Age.21
Age.13 Age.12
Age.23 Age.22

Output

Each model output consists of a table and two graphs. The table shows the most recent 10 years of observed returns for the age being forecast (‘Observed Return’) and the relevant sibling return (‘Sibling Return’) shown in bold black text. Brood and return years are shown in blue text. Two regression model statistics (R-squared and P-value of the slope) are shown in red. Model forecasted returns are shown in bold black text with a yellow highlight. Error measurements are shown in green text. Error measurements shown are absolute deviation (AD), absolute percent error (APE), percent error (PE) and arc tan percent error (AAPE).

After the table summarizing the model output for the most recenet ten years, two graphs are shown for each of the linnear regression models. The first graph is a scatter plot of the data with a linnear regression superimposed. The second graph is a plot of the residuals of the regression analysis.

Absolute deviation (AD) is defined as

\[\ AD = O - F\] where

O = Observed Return

F = Forecasted Return

Percent error (PE) is defined as

\[\ PE = (F - O)/O\] Absolute Percent error (APE) is defined as

\[\ APE = |(F - O)/O|\]

Arctangent percent error (AAPE) is defined (Kim and Kim, 2016) as \[\ AAPE = arctan(|((O - F)/O)|)\]

At the end of the model output section for each age class, a performance table is presented that contains the mean absolute deviation (MAD), neam absolute percent error (MAPE), mean percent error (MPE) and mean arctanget percent error (MAAPE). These performance metrics are calculated and presented across the most recent three and five years. Color bars show the relative size of each metric.

age.12

Below are model outputs using data from 1972

sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2008 580,028 23,087 0.168 0.008 1,276,412 696,384 0.55 0.55 0.88
2013 2009 457,370 5,413 0.148 0.011 804,643 347,273 0.43 0.43 0.65
2014 2010 3,219,167 97,693 0.148 0.010 3,008,571 210,596 0.07 -0.07 0.07
2015 2011 2,215,847 82,387 0.337 0.000 2,745,198 529,351 0.19 0.19 0.23
2016 2012 2,391,537 11,745 0.372 0.000 941,479 1,450,058 1.54 -1.54 0.55
2017 2013 2,742,095 61,369 0.345 0.000 2,137,610 604,486 0.28 -0.28 0.22
2018 2014 2,955,138 32,824 0.398 0.000 1,512,491 1,442,647 0.95 -0.95 0.45
2019 2015 5,261,676 38,702 0.404 0.000 1,725,634 3,536,042 2.05 -2.05 0.59
2020 2016 2,623,245 1,205 0.370 0.000 779,395 1,843,850 2.37 -2.37 0.61
2021 2017 NA 57,773 0.333 0.000 2,476,650 NA NA NA NA

ln.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2008 580,028 23,087 0.238 0.002 966,499 386,471 0.40 0.40 0.59
2013 2009 457,370 5,413 0.228 0.002 807,460 350,090 0.43 0.43 0.65
2014 2010 3,219,167 97,693 0.218 0.002 1,060,096 2,159,071 2.04 -2.04 0.59
2015 2011 2,215,847 82,387 0.253 0.001 1,127,872 1,087,974 0.96 -0.96 0.46
2016 2012 2,391,537 11,745 0.278 0.000 938,680 1,452,857 1.55 -1.55 0.55
2017 2013 2,742,095 61,369 0.289 0.000 1,189,200 1,552,896 1.31 -1.31 0.52
2018 2014 2,955,138 32,824 0.310 0.000 1,150,112 1,805,026 1.57 -1.57 0.55
2019 2015 5,261,676 38,702 0.326 0.000 1,226,497 4,035,179 3.29 -3.29 0.65
2020 2016 2,623,245 1,205 0.340 0.000 803,047 1,820,198 2.27 -2.27 0.61
2021 2017 NA 57,773 0.330 0.000 1,426,292 NA NA NA NA

lnY.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2008 580,028 23,087 0.199 0.004 1,029,147 449,119 0.44 0.44 0.66
2013 2009 457,370 5,413 0.187 0.004 586,960 129,590 0.22 0.22 0.28
2014 2010 3,219,167 97,693 0.188 0.004 8,896,080 5,676,913 0.64 0.64 1.05
2015 2011 2,215,847 82,387 0.253 0.001 3,431,651 1,215,804 0.35 0.35 0.50
2016 2012 2,391,537 11,745 0.289 0.000 666,330 1,725,207 2.59 -2.59 0.62
2017 2013 2,742,095 61,369 0.273 0.000 1,991,404 750,692 0.38 -0.38 0.27
2018 2014 2,955,138 32,824 0.314 0.000 1,104,668 1,850,470 1.68 -1.68 0.56
2019 2015 5,261,676 38,702 0.327 0.000 1,317,708 3,943,969 2.99 -2.99 0.64
2020 2016 2,623,245 1,205 0.346 0.000 561,959 2,061,286 3.67 -3.67 0.67
2021 2017 NA 57,773 0.312 0.000 2,256,662 NA NA NA NA

lnS.lnR

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2008 580,028 2,472,690 0.106 0.029 905,559 325,531 0.36 0.36 0.51
2013 2009 457,370 1,169,466 0.099 0.032 548,511 91,141 0.17 0.17 0.20
2014 2010 3,219,167 1,463,928 0.102 0.029 628,782 2,590,384 4.12 -4.12 0.68
2015 2011 2,215,847 1,177,074 0.093 0.033 570,217 1,645,630 2.89 -2.89 0.64
2016 2012 2,391,537 900,312 0.077 0.046 503,272 1,888,264 3.75 -3.75 0.67
2017 2013 2,742,095 938,160 0.049 0.089 554,057 2,188,039 3.95 -3.95 0.67
2018 2014 2,955,138 1,474,428 0.027 0.151 726,220 2,228,918 3.07 -3.07 0.65
2019 2015 5,261,676 1,920,954 0.028 0.147 849,058 4,412,618 5.20 -5.20 0.70
2020 2016 2,623,245 1,691,910 0.040 0.103 847,011 1,776,233 2.10 -2.10 0.60
2021 2017 NA 1,899,972 0.045 0.088 932,497 NA NA NA NA

ricker

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2008 580,028 2,472,690 0.001 0.320 913,437 333,409 0.37 0.37 0.52
2013 2009 457,370 1,169,466 0.011 0.247 557,243 99,873 0.18 0.18 0.21
2014 2010 3,219,167 1,463,928 0.010 0.248 649,800 2,569,367 3.95 -3.95 0.67
2015 2011 2,215,847 1,177,074 0.009 0.252 580,908 1,634,939 2.81 -2.81 0.64
2016 2012 2,391,537 900,312 0.016 0.208 497,362 1,894,175 3.81 -3.81 0.67
2017 2013 2,742,095 938,160 0.032 0.135 550,344 2,191,751 3.98 -3.98 0.67
2018 2014 2,955,138 1,474,428 0.047 0.090 763,553 2,191,585 2.87 -2.87 0.64
2019 2015 5,261,676 1,920,954 0.044 0.093 874,952 4,386,724 5.01 -5.01 0.69
2020 2016 2,623,245 1,691,910 0.027 0.146 877,752 1,745,493 1.99 -1.99 0.59
2021 2017 NA 1,899,972 0.023 0.161 949,284 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2012 2008 580,028.0 1,900,142 1,320,114 0.69 0.69 1.16
2013 2009 457,370.2 1,277,740 820,370 0.64 0.64 1.06
2014 2010 3,219,167.0 1,171,891 2,047,276 1.75 -1.75 0.57
2015 2011 2,215,846.9 1,555,140 660,707 0.42 -0.42 0.29
2016 2012 2,391,536.7 1,666,861 724,675 0.43 -0.43 0.29
2017 2013 2,742,095.4 1,772,790 969,306 0.55 -0.55 0.34
2018 2014 2,955,138.0 2,205,203 749,935 0.34 -0.34 0.25
2019 2015 5,261,676.4 2,704,757 2,556,920 0.95 -0.95 0.45
2020 2016 2,623,244.7 3,113,259 490,014 0.16 0.16 0.18
2021 2017 NA 3,194,738 NA NA NA NA

Performance summary

Average is clear winner in the performance department and gives 3.2m forecast. Recent similar returns have returned 2.9 and 5.2m so this feels ok.

model range MAD MAPE MPE MAAPE
sibling 5 years 1,775,416 143.83% -143.83% 0.48
sibling 3 years 2,274,180 178.96% -178.96% 0.55
ln.sibling 5 years 2,133,231 199.59% -199.59% 0.57
ln.sibling 3 years 2,553,468 237.54% -237.54% 0.60
lnY.sibling 5 years 2,066,325 226.05% -226.05% 0.55
lnY.sibling 3 years 2,618,575 277.87% -277.87% 0.62
lnS.lnR 5 years 2,498,814 361.29% -361.29% 0.66
lnS.lnR 3 years 2,805,923 345.44% -345.44% 0.65
ricker 5 years 2,481,946 353.27% -353.27% 0.65
ricker 3 years 2,774,601 329.08% -329.08% 0.64
average 5 years 1,098,170 48.49% -42.19% 0.30
average 3 years 1,265,623 48.09% -37.60% 0.30

age.22

Below are model outputs using data from 1972

sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2007 645,106 1,861,895 -0.023 0.639 683,826 38,720 0.06 0.06 0.06
2013 2008 360,663 580,028 -0.022 0.612 756,012 395,349 0.52 0.52 0.83
2014 2009 396,324 457,370 -0.022 0.642 750,445 354,121 0.47 0.47 0.73
2015 2010 1,371,814 3,219,167 -0.023 0.682 610,096 761,718 1.25 -1.25 0.51
2016 2011 864,072 2,215,847 -0.025 0.811 769,672 94,399 0.12 -0.12 0.11
2017 2012 616,530 2,391,537 -0.024 0.766 782,936 166,407 0.21 0.21 0.26
2018 2013 228,372 2,742,095 -0.024 0.823 774,299 545,927 0.71 0.71 1.17
2019 2014 240,535 2,955,138 -0.025 0.916 707,794 467,259 0.66 0.66 1.10
2020 2015 285,200 5,261,676 -0.020 0.679 570,597 285,396 0.50 0.50 0.79
2021 2016 NA 2,623,245 -0.007 0.403 621,512 NA NA NA NA

ln.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2007 645,106 1,861,895 -0.027 0.762 594,843 50,263 0.08 -0.08 0.08
2013 2008 360,663 580,028 -0.026 0.736 558,760 198,097 0.35 0.35 0.50
2014 2009 396,324 457,370 -0.025 0.728 544,309 147,985 0.27 0.27 0.36
2015 2010 1,371,814 3,219,167 -0.024 0.708 610,932 760,882 1.25 -1.25 0.51
2016 2011 864,072 2,215,847 -0.013 0.486 647,077 216,994 0.34 -0.34 0.25
2017 2012 616,530 2,391,537 -0.009 0.422 667,976 51,446 0.08 0.08 0.08
2018 2013 228,372 2,742,095 -0.008 0.416 675,005 446,633 0.66 0.66 1.10
2019 2014 240,535 2,955,138 -0.018 0.605 621,129 380,594 0.61 0.61 1.01
2020 2015 285,200 5,261,676 -0.023 0.798 587,151 301,951 0.51 0.51 0.81
2021 2016 NA 2,623,245 -0.024 0.995 537,957 NA NA NA NA

lnY.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2007 645,106 1,861,895 -0.019 0.544 491,170 153,936 0.31 -0.31 0.23
2013 2008 360,663 580,028 -0.020 0.575 577,744 217,082 0.38 0.38 0.54
2014 2009 396,324 457,370 -0.020 0.594 576,708 180,383 0.31 0.31 0.43
2015 2010 1,371,814 3,219,167 -0.020 0.614 437,107 934,707 2.14 -2.14 0.60
2016 2011 864,072 2,215,847 -0.027 0.951 570,107 293,965 0.52 -0.52 0.33
2017 2012 616,530 2,391,537 -0.025 0.850 594,278 22,251 0.04 -0.04 0.04
2018 2013 228,372 2,742,095 -0.024 0.834 603,134 374,762 0.62 0.62 1.02
2019 2014 240,535 2,955,138 -0.024 0.888 535,354 294,819 0.55 0.55 0.89
2020 2015 285,200 5,261,676 -0.019 0.646 418,551 133,351 0.32 0.32 0.44
2021 2016 NA 2,623,245 -0.007 0.407 469,301 NA NA NA NA

lnS.lnR

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2007 645,106 2,945,304 -0.007 0.393 697,907 52,802 0.08 0.08 0.08
2013 2008 360,663 2,472,690 -0.006 0.379 659,147 298,484 0.45 0.45 0.69
2014 2009 396,324 1,169,466 -0.011 0.446 530,620 134,296 0.25 0.25 0.33
2015 2010 1,371,814 1,463,928 -0.010 0.426 555,170 816,644 1.47 -1.47 0.54
2016 2011 864,072 1,177,074 -0.009 0.418 538,607 325,465 0.60 -0.60 0.36
2017 2012 616,530 900,312 -0.010 0.432 512,565 103,964 0.20 -0.20 0.17
2018 2013 228,372 938,160 -0.010 0.441 521,933 293,562 0.56 0.56 0.91
2019 2014 240,535 1,474,428 -0.004 0.362 568,366 327,831 0.58 0.58 0.94
2020 2015 285,200 1,920,954 -0.005 0.377 595,951 310,751 0.52 0.52 0.83
2021 2016 NA 1,691,910 -0.009 0.430 563,815 NA NA NA NA

ricker

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2007 645,106 2,945,304 0.105 0.032 578,245 66,861 0.12 -0.12 0.10
2013 2008 360,663 2,472,690 0.118 0.023 624,465 263,802 0.42 0.42 0.63
2014 2009 396,324 1,169,466 0.140 0.013 562,862 166,538 0.30 0.30 0.40
2015 2010 1,371,814 1,463,928 0.137 0.013 597,388 774,426 1.30 -1.30 0.51
2016 2011 864,072 1,177,074 0.136 0.012 570,293 293,779 0.52 -0.52 0.33
2017 2012 616,530 900,312 0.141 0.010 512,145 104,385 0.20 -0.20 0.17
2018 2013 228,372 938,160 0.148 0.008 527,360 298,988 0.57 0.57 0.92
2019 2014 240,535 1,474,428 0.133 0.010 608,399 367,864 0.60 0.60 0.99
2020 2015 285,200 1,920,954 0.129 0.010 617,522 332,321 0.54 0.54 0.86
2021 2016 NA 1,691,910 0.137 0.008 598,842 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2012 2007 645,105.8 599,192 45,914 0.08 -0.08 0.07
2013 2008 360,662.7 678,075 317,412 0.47 0.47 0.72
2014 2009 396,324.2 700,786 304,462 0.43 0.43 0.66
2015 2010 1,371,813.9 584,238 787,576 1.35 -1.35 0.52
2016 2011 864,071.6 698,316 165,756 0.24 -0.24 0.19
2017 2012 616,529.7 727,596 111,066 0.15 0.15 0.18
2018 2013 228,371.8 721,880 493,509 0.68 0.68 1.14
2019 2014 240,535.0 695,422 454,887 0.65 0.65 1.08
2020 2015 285,200.4 664,264 379,064 0.57 0.57 0.93
2021 2016 NA 446,942 NA NA NA NA

Performance summary

None of these relationships look good here and the running average performs even wors. This is a case of picking the least offensive model. We picked ln.sibling and lnY.sibling for a forecast of 266,000.

model range MAD MAPE MPE MAAPE
sibling 5 years 311,878 44.01% 39.11% 0.69
sibling 3 years 432,861 62.18% 62.18% 1.02
ln.sibling 5 years 279,524 44.02% 30.61% 0.65
ln.sibling 3 years 376,392 59.62% 59.62% 0.97
lnY.sibling 5 years 223,830 40.87% 18.75% 0.54
lnY.sibling 3 years 267,644 49.69% 49.69% 0.78
lnS.lnR 5 years 272,314 49.36% 17.07% 0.64
lnS.lnR 3 years 310,714 55.36% 55.36% 0.89
ricker 5 years 279,467 48.57% 19.82% 0.65
ricker 3 years 333,058 56.99% 56.99% 0.92
average 5 years 320,856 45.97% 36.47% 0.70
average 3 years 442,487 63.61% 63.61% 1.05

age.13

Below are model outputs using data from 1972

sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2007 1,538,885 1,861,895 0.419 0.000 4,043,064 2,504,179 0.62 0.62 1.02
2013 2008 1,594,896 580,028 0.374 0.000 1,793,982 199,086 0.11 0.11 0.12
2014 2009 889,419 457,370 0.376 0.000 1,591,688 702,269 0.44 0.44 0.67
2015 2010 2,291,469 3,219,167 0.381 0.000 6,023,160 3,731,691 0.62 0.62 1.02
2016 2011 1,311,129 2,215,847 0.297 0.000 3,851,542 2,540,412 0.66 0.66 1.09
2017 2012 2,012,814 2,391,537 0.254 0.001 3,831,542 1,818,728 0.47 0.47 0.73
2018 2013 3,315,115 2,742,095 0.231 0.001 4,028,173 713,058 0.18 0.18 0.21
2019 2014 3,159,370 2,955,138 0.235 0.001 4,160,210 1,000,839 0.24 0.24 0.31
2020 2015 7,133,088 5,261,676 0.234 0.001 6,254,035 879,054 0.14 -0.14 0.12
2021 2016 NA 2,623,245 0.349 0.000 3,836,650 NA NA NA NA

ln.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2007 1,538,885 1,861,895 0.441 0 3,471,994 1,933,109 0.56 0.56 0.90
2013 2008 1,594,896 580,028 0.413 0 1,579,747 15,149 0.01 -0.01 0.01
2014 2009 889,419 457,370 0.413 0 1,363,565 474,146 0.35 0.35 0.49
2015 2010 2,291,469 3,219,167 0.415 0 4,564,118 2,272,649 0.50 0.50 0.78
2016 2011 1,311,129 2,215,847 0.400 0 3,371,063 2,059,934 0.61 0.61 1.00
2017 2012 2,012,814 2,391,537 0.363 0 3,267,714 1,254,900 0.38 0.38 0.56
2018 2013 3,315,115 2,742,095 0.355 0 3,381,396 66,281 0.02 0.02 0.02
2019 2014 3,159,370 2,955,138 0.369 0 3,510,530 351,160 0.10 0.10 0.11
2020 2015 7,133,088 5,261,676 0.380 0 4,693,411 2,439,677 0.52 -0.52 0.33
2021 2016 NA 2,623,245 0.425 0 3,392,497 NA NA NA NA

lnY.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2007 1,538,885 1,861,895 0.383 0 3,367,740 1,828,855 0.54 0.54 0.87
2013 2008 1,594,896 580,028 0.357 0 1,377,029 217,867 0.16 -0.16 0.14
2014 2009 889,419 457,370 0.356 0 1,277,813 388,394 0.30 0.30 0.41
2015 2010 2,291,469 3,219,167 0.362 0 7,670,272 5,378,803 0.70 0.70 1.17
2016 2011 1,311,129 2,215,847 0.314 0 3,329,295 2,018,166 0.61 0.61 0.99
2017 2012 2,012,814 2,391,537 0.279 0 3,349,699 1,336,885 0.40 0.40 0.59
2018 2013 3,315,115 2,742,095 0.270 0 3,764,349 449,234 0.12 0.12 0.13
2019 2014 3,159,370 2,955,138 0.286 0 4,093,649 934,278 0.23 0.23 0.29
2020 2015 7,133,088 5,261,676 0.296 0 11,198,096 4,065,007 0.36 0.36 0.52
2021 2016 NA 2,623,245 0.349 0 3,207,907 NA NA NA NA

lnS.lnR

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2007 1,538,885 2,945,304 0.189 0.005 3,127,727 1,588,842 0.51 0.51 0.80
2013 2008 1,594,896 2,472,690 0.168 0.008 2,542,279 947,382 0.37 0.37 0.54
2014 2009 889,419 1,169,466 0.159 0.008 1,435,654 546,235 0.38 0.38 0.55
2015 2010 2,291,469 1,463,928 0.163 0.007 1,667,432 624,037 0.37 -0.37 0.27
2016 2011 1,311,129 1,177,074 0.164 0.006 1,432,692 121,563 0.08 0.08 0.09
2017 2012 2,012,814 900,312 0.166 0.005 1,173,363 839,451 0.72 -0.72 0.40
2018 2013 3,315,115 938,160 0.155 0.006 1,239,518 2,075,597 1.67 -1.67 0.56
2019 2014 3,159,370 1,474,428 0.132 0.010 1,739,945 1,419,426 0.82 -0.82 0.42
2020 2015 7,133,088 1,920,954 0.133 0.009 2,104,353 5,028,735 2.39 -2.39 0.61
2021 2016 NA 1,691,910 0.145 0.006 2,008,508 NA NA NA NA

ricker

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2007 1,538,885 2,945,304 -0.012 0.450 2,888,545 1,349,660 0.47 0.47 0.72
2013 2008 1,594,896 2,472,690 0.008 0.264 2,422,687 827,791 0.34 0.34 0.48
2014 2009 889,419 1,169,466 0.019 0.199 1,484,127 594,708 0.40 0.40 0.59
2015 2010 2,291,469 1,463,928 0.015 0.217 1,714,941 576,528 0.34 -0.34 0.25
2016 2011 1,311,129 1,177,074 0.017 0.209 1,477,005 165,876 0.11 0.11 0.13
2017 2012 2,012,814 900,312 0.017 0.206 1,193,062 819,752 0.69 -0.69 0.39
2018 2013 3,315,115 938,160 0.025 0.163 1,262,245 2,052,870 1.63 -1.63 0.55
2019 2014 3,159,370 1,474,428 0.037 0.117 1,796,701 1,362,670 0.76 -0.76 0.41
2020 2015 7,133,088 1,920,954 0.037 0.114 2,111,961 5,021,127 2.38 -2.38 0.61
2021 2016 NA 1,691,910 0.023 0.164 2,039,766 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2012 2007 1,538,885 3,413,485 1,874,600 0.55 0.55 0.88
2013 2008 1,594,896 2,984,527 1,389,631 0.47 0.47 0.72
2014 2009 889,419 1,793,999 904,580 0.50 0.50 0.79
2015 2010 2,291,469 1,641,449 650,020 0.40 -0.40 0.28
2016 2011 1,311,129 1,648,583 337,454 0.20 0.20 0.25
2017 2012 2,012,814 1,525,160 487,654 0.32 -0.32 0.24
2018 2013 3,315,115 1,619,945 1,695,169 1.05 -1.05 0.47
2019 2014 3,159,370 1,963,989 1,195,381 0.61 -0.61 0.36
2020 2015 7,133,088 2,417,979 4,715,109 1.95 -1.95 0.58
2021 2016 NA 3,386,303 NA NA NA NA

Performance summary

Sibling models look much better than spawner models or average. A basket of sibling models gives a forecast of 3.5m which is very similar to the last time we had ~2.5m siblings.

model range MAD MAPE MPE MAAPE
sibling 5 years 1,390,418 33.85% 28.23% 0.49
sibling 3 years 864,317 18.60% 9.23% 0.21
ln.sibling 5 years 1,234,390 32.69% 11.90% 0.40
ln.sibling 3 years 952,373 21.31% -13.34% 0.15
lnY.sibling 5 years 1,760,714 34.32% 34.32% 0.50
lnY.sibling 3 years 1,816,173 23.69% 23.69% 0.31
lnS.lnR 5 years 1,896,954 113.61% -110.21% 0.42
lnS.lnR 3 years 2,841,253 162.67% -162.67% 0.53
ricker 5 years 1,884,459 111.23% -106.74% 0.42
ricker 3 years 2,812,222 158.74% -158.74% 0.53
average 5 years 1,686,154 82.59% -74.40% 0.38
average 3 years 2,535,220 120.17% -120.17% 0.47

age.23

Below are model outputs using data from 1972

sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2006 498,857 717,671 0.229 0.002 851,510 352,653 0.41 0.41 0.62
2013 2007 524,055 645,106 0.228 0.002 796,045 271,989 0.34 0.34 0.48
2014 2008 688,521 360,663 0.229 0.002 609,544 78,977 0.13 -0.13 0.11
2015 2009 157,958 396,324 0.231 0.002 635,180 477,222 0.75 0.75 1.25
2016 2010 399,927 1,371,814 0.240 0.001 1,243,409 843,483 0.68 0.68 1.13
2017 2011 571,249 864,072 0.203 0.002 888,496 317,247 0.36 0.36 0.51
2018 2012 369,748 616,530 0.199 0.002 736,292 366,545 0.50 0.50 0.78
2019 2013 157,853 228,372 0.201 0.002 499,515 341,662 0.68 0.68 1.14
2020 2014 113,926 240,535 0.215 0.001 489,939 376,013 0.77 0.77 1.28
2021 2015 NA 285,200 0.229 0.001 500,375 NA NA NA NA

ln.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2006 498,857 717,671 0.455 0 800,267 301,410 0.38 0.38 0.54
2013 2007 524,055 645,106 0.445 0 745,573 221,518 0.30 0.30 0.40
2014 2008 688,521 360,663 0.439 0 544,176 144,345 0.27 -0.27 0.21
2015 2009 157,958 396,324 0.436 0 576,177 418,219 0.73 0.73 1.21
2016 2010 399,927 1,371,814 0.408 0 1,078,819 678,893 0.63 0.63 1.04
2017 2011 571,249 864,072 0.362 0 808,591 237,342 0.29 0.29 0.39
2018 2012 369,748 616,530 0.356 0 676,154 306,406 0.45 0.45 0.69
2019 2013 157,853 228,372 0.347 0 407,292 249,438 0.61 0.61 1.01
2020 2014 113,926 240,535 0.367 0 397,928 284,001 0.71 0.71 1.19
2021 2015 NA 285,200 0.378 0 412,706 NA NA NA NA

lnY.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2006 498,857 717,671 0.389 0 682,954 184,098 0.27 0.27 0.35
2013 2007 524,055 645,106 0.388 0 637,067 113,012 0.18 0.18 0.21
2014 2008 688,521 360,663 0.389 0 499,333 189,188 0.38 -0.38 0.27
2015 2009 157,958 396,324 0.383 0 521,273 363,316 0.70 0.70 1.16
2016 2010 399,927 1,371,814 0.376 0 1,159,935 760,009 0.66 0.66 1.09
2017 2011 571,249 864,072 0.323 0 720,306 149,056 0.21 0.21 0.26
2018 2012 369,748 616,530 0.321 0 588,529 218,782 0.37 0.37 0.53
2019 2013 157,853 228,372 0.321 0 426,700 268,847 0.63 0.63 1.04
2020 2014 113,926 240,535 0.339 0 410,420 296,493 0.72 0.72 1.20
2021 2015 NA 285,200 0.350 0 402,959 NA NA NA NA

lnS.lnR

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2006 498,857 1,953,228 -0.011 0.427 755,527 256,670 0.34 0.34 0.48
2013 2007 524,055 2,945,304 -0.014 0.469 800,224 276,169 0.35 0.35 0.49
2014 2008 688,521 2,472,690 -0.019 0.558 745,941 57,420 0.08 0.08 0.08
2015 2009 157,958 1,169,466 -0.018 0.560 668,483 510,526 0.76 0.76 1.27
2016 2010 399,927 1,463,928 -0.014 0.489 664,995 265,069 0.40 0.40 0.59
2017 2011 571,249 1,177,074 -0.014 0.493 632,363 61,114 0.10 0.10 0.11
2018 2012 369,748 900,312 -0.013 0.481 602,002 232,254 0.39 0.39 0.56
2019 2013 157,853 938,160 -0.008 0.408 592,993 435,140 0.73 0.73 1.22
2020 2014 113,926 1,474,428 0.004 0.289 631,694 517,767 0.82 0.82 1.35
2021 2015 NA 1,920,954 -0.002 0.346 647,160 NA NA NA NA

ricker

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2006 498,857 1,953,228 0.167 0.010 795,790 296,934 0.37 0.37 0.54
2013 2007 524,055 2,945,304 0.178 0.007 700,856 176,801 0.25 0.25 0.33
2014 2008 688,521 2,472,690 0.219 0.002 728,934 40,413 0.06 0.06 0.06
2015 2009 157,958 1,169,466 0.232 0.002 702,738 544,781 0.78 0.78 1.29
2016 2010 399,927 1,463,928 0.188 0.004 717,601 317,674 0.44 0.44 0.67
2017 2011 571,249 1,177,074 0.183 0.004 658,796 87,547 0.13 0.13 0.15
2018 2012 369,748 900,312 0.183 0.003 577,989 208,241 0.36 0.36 0.51
2019 2013 157,853 938,160 0.176 0.004 579,145 421,291 0.73 0.73 1.21
2020 2014 113,926 1,474,428 0.140 0.008 675,348 561,421 0.83 0.83 1.37
2021 2015 NA 1,920,954 0.120 0.013 689,292 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2012 2006 498,856.8 639,799 140,942 0.22 0.22 0.28
2013 2007 524,055.4 587,308 63,252 0.11 0.11 0.12
2014 2008 688,520.9 650,284 38,237 0.06 -0.06 0.06
2015 2009 157,957.6 664,934 506,977 0.76 0.76 1.27
2016 2010 399,926.5 563,435 163,509 0.29 0.29 0.39
2017 2011 571,249.2 453,863 117,386 0.26 -0.26 0.20
2018 2012 369,747.8 468,342 98,594 0.21 0.21 0.26
2019 2013 157,853.5 437,480 279,627 0.64 0.64 1.06
2020 2014 113,926.5 331,347 217,420 0.66 0.66 1.09
2021 2015 NA 322,541 NA NA NA NA

Performance summary

Average is best performing model and gives us a forecast of 322,000.

model range MAD MAPE MPE MAAPE
sibling 5 years 448,990 59.69% 59.69% 0.97
sibling 3 years 361,406 64.98% 64.98% 1.07
ln.sibling 5 years 351,216 54.04% 54.04% 0.86
ln.sibling 3 years 279,948 59.31% 59.31% 0.96
lnY.sibling 5 years 338,637 51.73% 51.73% 0.82
lnY.sibling 3 years 261,374 57.47% 57.47% 0.93
lnS.lnR 5 years 302,269 48.69% 48.69% 0.77
lnS.lnR 3 years 395,054 64.64% 64.64% 1.05
ricker 5 years 319,235 49.89% 49.89% 0.78
ricker 3 years 396,985 63.97% 63.97% 1.03
average 5 years 175,307 41.09% 30.75% 0.60
average 3 years 198,547 50.20% 50.20% 0.80