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
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 2,594,705 1,205 0.370 0.000 779,395 1,815,310 2.33 -2.33 0.61
2021 2017 4,144,547 57,140 0.334 0.000 2,458,263 1,686,284 0.69 -0.69 0.39
2022 2018 NA 27,451 0.383 0.000 1,670,614 NA NA NA NA

ln.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
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 2,594,705 1,205 0.340 0.000 803,047 1,791,658 2.23 -2.23 0.60
2021 2017 4,144,547 57,140 0.330 0.000 1,423,684 2,720,864 1.91 -1.91 0.58
2022 2018 NA 27,451 0.347 0.000 1,342,543 NA NA NA NA

lnY.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
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 2,594,705 1,205 0.346 0.000 561,959 2,032,746 3.62 -3.62 0.66
2021 2017 4,144,547 57,140 0.312 0.000 2,222,925 1,921,622 0.86 -0.86 0.43
2022 2018 NA 27,451 0.349 0.000 1,127,676 NA NA NA NA

lnS.lnR

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
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 2,594,705 1,691,910 0.040 0.103 847,011 1,747,694 2.06 -2.06 0.59
2021 2017 4,144,547 1,899,972 0.045 0.088 932,192 3,212,355 3.45 -3.45 0.66
2022 2018 NA 2,221,152 0.055 0.064 1,079,255 NA NA NA NA

ricker

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
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 2,594,705 1,691,910 0.027 0.146 877,752 1,716,953 1.96 -1.96 0.58
2021 2017 4,144,547 1,899,972 0.023 0.161 949,014 3,195,533 3.37 -3.37 0.66
2022 2018 NA 2,221,152 0.013 0.211 1,060,144 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
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 2,594,705.0 3,113,259 518,554 0.17 0.17 0.20
2021 2017 4,144,547.4 3,189,030 955,517 0.30 -0.30 0.23
2022 2018 NA 3,539,632 NA NA NA NA

Performance summary

The average model is the best performing and produces a believable ~3.5 million.

model range MAD MAPE MPE MAAPE
sibling 5 years 1,816,954 126.02% -126.02% 0.45
sibling 3 years 2,345,879 168.81% -168.81% 0.53
ln.sibling 5 years 2,381,124 206.15% -206.15% 0.58
ln.sibling 3 years 2,849,234 247.74% -247.74% 0.61
lnY.sibling 5 years 2,099,900 190.54% -190.54% 0.51
lnY.sibling 3 years 2,632,779 249.16% -249.16% 0.58
lnS.lnR 5 years 2,757,925 354.50% -354.50% 0.65
lnS.lnR 3 years 3,124,222 356.88% -356.88% 0.65
ricker 5 years 2,736,509 343.79% -343.79% 0.65
ricker 3 years 3,099,737 344.57% -344.57% 0.65
average 5 years 1,150,046 45.97% -39.30% 0.29
average 3 years 1,343,663 47.05% -35.95% 0.29

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
2013 2008 360,663 13,074 0.177 0.006 789,780 429,117 0.54 0.54 0.87
2014 2009 396,324 5,754 0.170 0.007 649,648 253,323 0.39 0.39 0.57
2015 2010 1,371,814 37,948 0.173 0.005 1,211,368 160,446 0.13 -0.13 0.12
2016 2011 864,072 41,341 0.208 0.002 1,296,280 432,209 0.33 0.33 0.46
2017 2012 616,530 5,727 0.192 0.003 641,896 25,366 0.04 0.04 0.04
2018 2013 228,372 0 0.194 0.002 545,995 317,623 0.58 0.58 0.95
2019 2014 240,535 2,346 0.206 0.002 573,100 332,565 0.58 0.58 0.94
2020 2015 282,087 1 0.213 0.001 520,975 238,888 0.46 0.46 0.70
2021 2016 418,590 0 0.223 0.001 511,861 93,270 0.18 0.18 0.22
2022 2017 NA 7,207 0.228 0.001 637,842 NA NA NA NA

ln.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2013 2008 360,663 13,074 0.394 0 772,193 411,531 0.53 0.53 0.85
2014 2009 396,324 5,754 0.376 0 658,748 262,424 0.40 0.40 0.58
2015 2010 1,371,814 37,948 0.369 0 875,140 496,674 0.57 -0.57 0.35
2016 2011 864,072 41,341 0.382 0 906,054 41,983 0.05 0.05 0.05
2017 2012 616,530 5,727 0.387 0 657,179 40,649 0.06 0.06 0.07
2018 2013 228,372 0 0.387 0 162,553 65,819 0.40 -0.40 0.28
2019 2014 240,535 2,346 0.402 0 572,237 331,702 0.58 0.58 0.94
2020 2015 282,087 1 0.390 0 182,086 100,001 0.55 -0.55 0.34
2021 2016 418,590 0 0.394 0 177,242 241,348 1.36 -1.36 0.52
2022 2017 NA 7,207 0.372 0 669,370 NA NA NA NA

lnY.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2013 2008 360,663 13,074 0.169 0.007 608,934 248,271 0.41 0.41 0.60
2014 2009 396,324 5,754 0.165 0.007 485,107 88,782 0.18 0.18 0.22
2015 2010 1,371,814 37,948 0.167 0.006 1,234,037 137,777 0.11 -0.11 0.10
2016 2011 864,072 41,341 0.194 0.003 1,385,086 521,014 0.38 0.38 0.54
2017 2012 616,530 5,727 0.192 0.003 481,842 134,687 0.28 -0.28 0.22
2018 2013 228,372 0 0.191 0.003 414,564 186,192 0.45 0.45 0.68
2019 2014 240,535 2,346 0.203 0.002 432,450 191,915 0.44 0.44 0.67
2020 2015 282,087 1 0.211 0.001 396,081 113,994 0.29 0.29 0.38
2021 2016 418,590 0 0.219 0.001 390,984 27,607 0.07 -0.07 0.07
2022 2017 NA 7,207 0.221 0.001 484,787 NA NA NA NA

lnS.lnR

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
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 282,087 1,920,954 -0.005 0.377 595,951 313,864 0.53 0.53 0.84
2021 2016 418,590 1,691,910 -0.009 0.431 563,623 145,033 0.26 0.26 0.33
2022 2017 NA 1,899,972 -0.009 0.440 573,507 NA NA NA NA

ricker

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
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 282,087 1,920,954 0.129 0.010 617,522 335,434 0.54 0.54 0.87
2021 2016 418,590 1,691,910 0.137 0.008 598,666 180,076 0.30 0.30 0.41
2022 2017 NA 1,899,972 0.139 0.007 596,721 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
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 282,087.1 664,264 382,177 0.58 0.58 0.93
2021 2016 418,590.4 446,319 27,729 0.06 0.06 0.07
2022 2017 NA 357,223 NA NA NA NA

Performance summary

Blending all sibling models here produces a forecast of ~0.6 million fish.

model range MAD MAPE MPE MAAPE
sibling 5 years 201,542 36.85% 36.85% 0.57
sibling 3 years 221,574 40.70% 40.70% 0.62
ln.sibling 5 years 155,904 59.15% -33.49% 0.43
ln.sibling 3 years 224,350 83.02% -44.37% 0.60
lnY.sibling 5 years 130,879 30.62% 16.61% 0.40
lnY.sibling 3 years 111,172 26.74% 22.03% 0.37
lnS.lnR 5 years 236,851 42.52% 34.41% 0.64
lnS.lnR 3 years 262,243 45.36% 45.36% 0.70
ricker 5 years 257,349 44.39% 36.24% 0.67
ricker 3 years 294,458 48.29% 48.29% 0.76
average 5 years 293,874 42.56% 42.56% 0.68
average 3 years 288,264 43.05% 43.05% 0.70

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
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 7,055,601 5,261,676 0.234 0.001 6,254,035 801,566 0.13 -0.13 0.11
2021 2016 1,996,358 2,594,705 0.347 0.000 3,796,768 1,800,410 0.47 0.47 0.73
2022 2017 NA 4,144,547 0.327 0.000 5,206,872 NA NA NA NA

ln.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
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 7,055,601 5,261,676 0.380 0 4,693,411 2,362,190 0.50 -0.50 0.32
2021 2016 1,996,358 2,594,705 0.424 0 3,369,373 1,373,015 0.41 0.41 0.60
2022 2017 NA 4,144,547 0.414 0 4,173,778 NA NA NA NA

lnY.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
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 7,055,601 5,261,676 0.296 0 11,198,096 4,142,495 0.37 0.37 0.53
2021 2016 1,996,358 2,594,705 0.347 0 3,165,434 1,169,076 0.37 0.37 0.53
2022 2017 NA 4,144,547 0.340 0 5,749,786 NA NA NA NA

lnS.lnR

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
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 7,055,601 1,920,954 0.133 0.009 2,104,353 4,951,248 2.35 -2.35 0.61
2021 2016 1,996,358 1,691,910 0.145 0.006 2,007,829 11,471 0.01 0.01 0.01
2022 2017 NA 1,899,972 0.146 0.006 2,180,814 NA NA NA NA

ricker

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
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 7,055,601 1,920,954 0.037 0.114 2,111,961 4,943,640 2.34 -2.34 0.61
2021 2016 1,996,358 1,691,910 0.023 0.163 2,039,169 42,811 0.02 0.02 0.02
2022 2017 NA 1,899,972 0.024 0.158 2,180,513 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
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 7,055,601 2,417,979 4,637,621 1.92 -1.92 0.58
2021 2016 1,996,358 3,370,806 1,374,448 0.41 0.41 0.60
2022 2017 NA 3,507,852 NA NA NA NA

Performance summary

Blending everything but the ricker model gives us a forecast of ~4.2 million.

model range MAD MAPE MPE MAAPE
sibling 5 years 1,226,920 29.89% 24.77% 0.42
sibling 3 years 1,200,939 28.10% 19.55% 0.38
ln.sibling 5 years 1,081,509 28.29% 8.16% 0.32
ln.sibling 3 years 1,362,122 33.69% 0.14% 0.35
lnY.sibling 5 years 1,606,394 29.72% 29.72% 0.41
lnY.sibling 3 years 2,081,950 32.25% 32.25% 0.45
lnS.lnR 5 years 1,859,439 111.29% -111.06% 0.40
lnS.lnR 3 years 2,127,382 105.81% -105.43% 0.35
ricker 5 years 1,844,349 108.67% -107.83% 0.40
ricker 3 years 2,116,374 104.01% -102.61% 0.35
average 5 years 1,878,055 86.01% -69.70% 0.45
average 3 years 2,402,484 97.81% -70.63% 0.52

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
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 112,679 240,535 0.215 0.001 489,939 377,260 0.77 0.77 1.28
2021 2015 409,328 282,087 0.229 0.001 498,386 89,058 0.18 0.18 0.21
2022 2016 NA 418,590 0.235 0.001 580,096 NA NA NA NA

ln.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
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 112,679 240,535 0.367 0 397,928 285,248 0.72 0.72 1.19
2021 2015 409,328 282,087 0.378 0 409,965 637 0.00 0.00 0.00
2022 2016 NA 418,590 0.382 0 512,227 NA NA NA NA

lnY.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
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 112,679 240,535 0.339 0 410,420 297,741 0.73 0.73 1.21
2021 2015 409,328 282,087 0.350 0 401,624 7,703 0.02 -0.02 0.02
2022 2016 NA 418,590 0.354 0 455,095 NA NA NA NA

lnS.lnR

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
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 112,679 1,474,428 0.004 0.289 631,694 519,015 0.82 0.82 1.36
2021 2015 409,328 1,920,954 -0.002 0.346 646,972 237,645 0.37 0.37 0.53
2022 2016 NA 1,691,910 -0.005 0.377 618,239 NA NA NA NA

ricker

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
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 112,679 1,474,428 0.140 0.008 675,348 562,668 0.83 0.83 1.37
2021 2015 409,328 1,920,954 0.120 0.013 689,120 279,792 0.41 0.41 0.60
2022 2016 NA 1,691,910 0.127 0.010 664,094 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
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 112,679.2 331,347 218,668 0.66 0.66 1.09
2021 2015 409,327.7 322,291 87,036 0.27 -0.27 0.21
2022 2016 NA 324,171 NA NA NA NA

Performance summary

The average model at 0.32 million fish appears most compelling here.

model range MAD MAPE MPE MAAPE
sibling 5 years 298,354 49.75% 49.75% 0.78
sibling 3 years 269,327 54.42% 54.42% 0.88
ln.sibling 5 years 215,814 41.55% 41.55% 0.66
ln.sibling 3 years 178,441 44.36% 44.36% 0.73
lnY.sibling 5 years 188,426 39.07% 38.30% 0.61
lnY.sibling 3 years 191,430 45.82% 44.54% 0.76
lnS.lnR 5 years 297,033 48.10% 48.10% 0.75
lnS.lnR 3 years 397,266 64.09% 64.09% 1.04
ricker 5 years 311,908 49.20% 49.20% 0.77
ricker 3 years 421,251 65.55% 65.55% 1.06
average 5 years 160,262 40.77% 19.62% 0.56
average 3 years 195,110 52.31% 34.30% 0.79

Forecast summary

A preliminary look at the models for this river leads us to an initial forecast of ~8.6 million broken down as follows:

Table 2. Preliminary Forecast.

age forecast
1.2 3.50
2.2 0.59
1.3 4.20
2.3 0.32