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 132,092 0 -0.028 0.850 200,161 68,070 0.34 0.34 0.48
2014 2010 567,609 0 -0.027 0.857 198,301 369,308 1.86 -1.86 0.58
2015 2011 507,840 0 -0.026 0.817 208,126 299,714 1.44 -1.44 0.53
2016 2012 364,112 0 -0.024 0.786 215,892 148,220 0.69 -0.69 0.39
2017 2013 906,913 0 -0.023 0.768 219,636 687,277 3.13 -3.13 0.65
2018 2014 734,904 1,766 -0.022 0.726 55,454 679,449 12.25 -12.25 0.75
2019 2015 233,249 0 0.054 0.073 232,002 1,247 0.01 -0.01 0.01
2020 2016 555,165 851 0.054 0.070 420,176 134,988 0.32 -0.32 0.24
2021 2017 1,013,997 2,073 0.085 0.029 743,055 270,942 0.36 -0.36 0.26
2022 2018 NA 0 0.248 0.000 230,949 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 132,092 0 -0.025 0.718 112,881 19,211 0.17 -0.17 0.14
2014 2010 567,609 0 -0.024 0.717 113,374 454,235 4.01 -4.01 0.67
2015 2011 507,840 0 -0.024 0.755 118,414 389,426 3.29 -3.29 0.65
2016 2012 364,112 0 -0.024 0.787 123,035 241,077 1.96 -1.96 0.58
2017 2013 906,913 0 -0.024 0.810 126,503 780,410 6.17 -6.17 0.71
2018 2014 734,904 1,766 -0.024 0.854 164,657 570,247 3.46 -3.46 0.66
2019 2015 233,249 0 0.001 0.318 132,195 101,054 0.76 -0.76 0.41
2020 2016 555,165 851 0.000 0.321 292,966 262,199 0.89 -0.89 0.44
2021 2017 1,013,997 2,073 0.023 0.162 393,427 620,570 1.58 -1.58 0.55
2022 2018 NA 0 0.063 0.051 133,637 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 132,092 0 -0.025 0.718 113,202 18,890 0.17 -0.17 0.14
2014 2010 567,609 0 -0.024 0.717 113,680 453,928 3.99 -3.99 0.67
2015 2011 507,840 0 -0.024 0.749 118,649 389,191 3.28 -3.28 0.65
2016 2012 364,112 0 -0.024 0.776 123,205 240,907 1.96 -1.96 0.58
2017 2013 906,913 0 -0.024 0.795 126,623 780,290 6.16 -6.16 0.71
2018 2014 734,904 1,766 -0.024 0.832 245,721 489,183 1.99 -1.99 0.59
2019 2015 233,249 0 0.017 0.198 131,942 101,307 0.77 -0.77 0.41
2020 2016 555,165 851 0.016 0.198 278,010 277,154 1.00 -1.00 0.46
2021 2017 1,013,997 2,073 0.037 0.109 1,041,422 27,425 0.03 0.03 0.03
2022 2018 NA 0 0.086 0.027 134,480 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 132,092 514,188 -0.029 0.991 115,111 16,980 0.15 -0.15 0.13
2014 2010 567,609 518,040 -0.028 0.980 115,758 451,851 3.90 -3.90 0.67
2015 2011 507,840 421,380 -0.026 0.864 121,998 385,842 3.16 -3.16 0.65
2016 2012 364,112 193,326 -0.025 0.803 120,637 243,475 2.02 -2.02 0.59
2017 2013 906,913 387,036 -0.025 0.869 129,259 777,654 6.02 -6.02 0.71
2018 2014 734,904 340,590 -0.023 0.810 134,934 599,970 4.45 -4.45 0.68
2019 2015 233,249 651,172 -0.023 0.788 147,524 85,725 0.58 -0.58 0.35
2020 2016 555,165 469,230 -0.021 0.740 146,356 408,809 2.79 -2.79 0.63
2021 2017 1,013,997 578,700 -0.019 0.673 155,961 858,036 5.50 -5.50 0.70
2022 2018 NA 770,772 -0.014 0.546 175,507 NA NA NA NA

ricker

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
2013 2009 132,092 514,188 0.326 0 146,996 14,904 0.10 0.10 0.11
2014 2010 567,609 518,040 0.328 0 146,239 421,370 2.88 -2.88 0.64
2015 2011 507,840 421,380 0.314 0 156,272 351,568 2.25 -2.25 0.61
2016 2012 364,112 193,326 0.308 0 127,919 236,193 1.85 -1.85 0.58
2017 2013 906,913 387,036 0.314 0 164,791 742,122 4.50 -4.50 0.69
2018 2014 734,904 340,590 0.303 0 169,289 565,615 3.34 -3.34 0.66
2019 2015 233,249 651,172 0.299 0 155,421 77,828 0.50 -0.50 0.32
2020 2016 555,165 469,230 0.298 0 177,609 377,555 2.13 -2.13 0.60
2021 2017 1,013,997 578,700 0.290 0 172,351 841,646 4.88 -4.88 0.69
2022 2018 NA 770,772 0.269 0 153,386 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2013 2009 132,091.5 264,771 132,680 0.50 0.50 0.79
2014 2010 567,608.9 171,948 395,661 2.30 -2.30 0.61
2015 2011 507,839.9 220,199 287,641 1.31 -1.31 0.52
2016 2012 364,111.9 284,171 79,941 0.28 -0.28 0.22
2017 2013 906,913.0 324,865 582,048 1.79 -1.79 0.57
2018 2014 734,903.9 495,713 239,191 0.48 -0.48 0.31
2019 2015 233,249.0 616,276 383,027 0.62 0.62 1.02
2020 2016 555,164.6 549,404 5,761 0.01 -0.01 0.01
2021 2017 1,013,997.0 558,868 455,129 0.81 -0.81 0.42
2022 2018 NA 688,846 NA NA NA NA

Performance summary

Although the sibling models appear to perform well, there is insufficient data to forecast from those models. The best models seem to be ricker and average models. Weighting these with proportional MAAPE gives us a forecast of ~0.45 million fish.

model range MAD MAPE MPE MAAPE
sibling 5 years 354,781 321.46% -321.46% 0.38
sibling 3 years 135,726 23.04% -23.04% 0.17
ln.sibling 5 years 466,896 257.38% -257.38% 0.55
ln.sibling 3 years 327,941 107.89% -107.89% 0.47
lnY.sibling 5 years 335,072 198.88% -197.83% 0.44
lnY.sibling 3 years 135,295 59.70% -57.95% 0.30
lnS.lnR 5 years 546,039 386.77% -386.77% 0.62
lnS.lnR 3 years 450,856 295.86% -295.86% 0.56
ricker 5 years 520,953 307.09% -307.09% 0.59
ricker 3 years 432,343 250.33% -250.33% 0.54
average 5 years 333,031 74.41% -49.55% 0.47
average 3 years 281,305 48.21% -6.78% 0.49

age.22

ln.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2013 2008 38,397 0 0.191 0.004 12,460 25,937 2.08 -2.08 0.59
2014 2009 56,113 0 0.183 0.005 12,877 43,236 3.36 -3.36 0.66
2015 2010 500 0 0.172 0.006 13,427 12,927 0.96 0.96 1.53
2016 2011 11,165 0 0.157 0.007 12,260 1,096 0.09 0.09 0.10
2017 2012 4,050 0 0.158 0.006 12,230 8,179 0.67 0.67 1.11
2018 2013 678 0 0.160 0.006 11,881 11,203 0.94 0.94 1.51
2019 2014 5,345 0 0.153 0.006 11,044 5,699 0.52 0.52 0.82
2020 2015 8,177 1 0.155 0.005 14,683 6,506 0.44 0.44 0.67
2021 2016 11,612 0 0.153 0.005 10,712 900 0.08 -0.08 0.08
2022 2017 NA 0 0.154 0.004 10,733 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 38,397 0 0.096 0.037 13,481 24,916 1.85 -1.85 0.58
2014 2009 56,113 0 0.092 0.038 13,886 42,227 3.04 -3.04 0.65
2015 2010 500 0 0.086 0.041 14,430 13,929 0.97 0.97 1.53
2016 2011 11,165 0 0.078 0.047 13,188 2,024 0.15 0.15 0.18
2017 2012 4,050 0 0.079 0.044 13,131 9,081 0.69 0.69 1.15
2018 2013 678 0 0.080 0.040 12,745 12,067 0.95 0.95 1.51
2019 2014 5,345 0 0.077 0.042 11,852 6,507 0.55 0.55 0.88
2020 2015 8,177 1 0.078 0.039 11,637 3,460 0.30 0.30 0.40
2021 2016 11,612 0 0.079 0.036 11,530 83 0.01 -0.01 0.01
2022 2017 NA 0 0.080 0.034 11,531 NA NA NA NA

Below are model outputs using data from 1972

lnS.lnR

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
2013 2008 38,397 1,054,704 -0.015 0.492 19,909 18,488 0.93 -0.93 0.45
2014 2009 56,113 514,188 -0.007 0.390 17,691 38,422 2.17 -2.17 0.60
2015 2010 500 518,040 -0.001 0.333 18,575 18,075 0.97 0.97 1.54
2016 2011 11,165 421,380 -0.016 0.533 15,471 4,307 0.28 0.28 0.37
2017 2012 4,050 193,326 -0.016 0.537 13,160 9,109 0.69 0.69 1.15
2018 2013 678 387,036 -0.013 0.482 14,732 14,054 0.95 0.95 1.52
2019 2014 5,345 340,590 -0.017 0.568 13,262 7,917 0.60 0.60 0.98
2020 2015 8,177 651,172 -0.016 0.575 14,599 6,422 0.44 0.44 0.67
2021 2016 11,612 469,230 -0.017 0.608 13,467 1,855 0.14 0.14 0.16
2022 2017 NA 578,700 -0.017 0.609 13,864 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 38,397 1,054,704 0.086 0.046 20,121 18,277 0.91 -0.91 0.44
2014 2009 56,113 514,188 0.083 0.047 22,397 33,716 1.51 -1.51 0.54
2015 2010 500 518,040 0.079 0.048 23,069 22,569 0.98 0.98 1.55
2016 2011 11,165 421,380 0.077 0.049 19,323 8,159 0.42 0.42 0.63
2017 2012 4,050 193,326 0.077 0.046 12,192 8,141 0.67 0.67 1.11
2018 2013 678 387,036 0.071 0.051 17,912 17,233 0.96 0.96 1.53
2019 2014 5,345 340,590 0.062 0.062 15,563 10,218 0.66 0.66 1.09
2020 2015 8,177 651,172 0.060 0.062 18,825 10,648 0.57 0.57 0.92
2021 2016 11,612 469,230 0.066 0.050 17,088 5,476 0.32 0.32 0.44
2022 2017 NA 578,700 0.068 0.047 17,828 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2013 2008 38,397.443 16,464 21,934 1.33 -1.33 0.52
2014 2009 56,112.745 23,740 32,373 1.36 -1.36 0.52
2015 2010 500.258 31,563 31,062 0.98 0.98 1.55
2016 2011 11,164.587 25,928 14,763 0.57 0.57 0.92
2017 2012 4,050.314 24,461 20,410 0.83 0.83 1.37
2018 2013 678.268 22,045 21,367 0.97 0.97 1.54
2019 2014 5,345.267 14,501 9,156 0.63 0.63 1.04
2020 2015 8,176.851 4,348 3,829 0.88 -0.88 0.44
2021 2016 11,612.419 5,883 5,729 0.97 -0.97 0.46
2022 2017 NA 5,973 NA NA NA NA

Performance summary

None of the models are very compelling so we take the average and forecast ~0.005 million fish

model range MAD MAPE MPE MAAPE
sibling 5 years 22,326 78.54% 78.54% 1.28
sibling 3 years 19,308 69.59% 69.59% 1.15
ln.sibling 5 years 6,497 53.10% 49.74% 0.84
ln.sibling 3 years 4,368 34.77% 29.17% 0.52
lnY.sibling 5 years 6,239 49.84% 49.55% 0.79
lnY.sibling 3 years 3,350 28.45% 27.97% 0.43
lnS.lnR 5 years 7,871 56.42% 56.42% 0.90
lnS.lnR 3 years 5,398 39.15% 39.15% 0.60
ricker 5 years 10,343 63.45% 63.45% 1.02
ricker 3 years 8,781 51.42% 51.42% 0.82
average 5 years 12,098 85.79% 11.61% 0.97
average 3 years 6,238 82.87% -40.77% 0.65

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 513,077 52,672 0.328 0 403,565 109,513 0.27 -0.27 0.21
2014 2009 751,758 132,092 0.327 0 505,536 246,222 0.49 -0.49 0.32
2015 2010 1,132,845 567,609 0.320 0 1,040,968 91,877 0.09 -0.09 0.08
2016 2011 1,460,188 507,840 0.351 0 977,593 482,594 0.49 -0.49 0.32
2017 2012 312,468 364,112 0.387 0 825,684 513,216 0.62 0.62 1.02
2018 2013 1,180,877 906,913 0.358 0 1,500,167 319,290 0.21 0.21 0.26
2019 2014 1,115,187 734,904 0.375 0 1,220,280 105,093 0.09 0.09 0.09
2020 2015 647,133 233,249 0.393 0 629,309 17,823 0.03 -0.03 0.03
2021 2016 931,734 555,165 0.393 0 1,000,326 68,593 0.07 0.07 0.07
2022 2017 NA 1,013,997 0.400 0 1,520,428 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 513,077 52,672 0.399 0 330,252 182,825 0.55 -0.55 0.34
2014 2009 751,758 132,092 0.390 0 484,681 267,078 0.55 -0.55 0.34
2015 2010 1,132,845 567,609 0.389 0 878,766 254,080 0.29 -0.29 0.22
2016 2011 1,460,188 507,840 0.407 0 854,374 605,813 0.71 -0.71 0.39
2017 2012 312,468 364,112 0.427 0 766,559 454,091 0.59 0.59 0.97
2018 2013 1,180,877 906,913 0.399 0 1,067,053 113,824 0.11 -0.11 0.10
2019 2014 1,115,187 734,904 0.418 0 987,514 127,673 0.13 -0.13 0.11
2020 2015 647,133 233,249 0.432 0 621,623 25,509 0.04 -0.04 0.04
2021 2016 931,734 555,165 0.434 0 888,292 43,442 0.05 -0.05 0.05
2022 2017 NA 1,013,997 0.442 0 1,140,685 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 513,077 52,672 0.254 0.001 332,176 180,901 0.54 -0.54 0.34
2014 2009 751,758 132,092 0.247 0.001 399,078 352,680 0.88 -0.88 0.44
2015 2010 1,132,845 567,609 0.237 0.001 990,494 142,351 0.14 -0.14 0.13
2016 2011 1,460,188 507,840 0.263 0.000 888,315 571,873 0.64 -0.64 0.37
2017 2012 312,468 364,112 0.292 0.000 676,653 364,185 0.54 0.54 0.86
2018 2013 1,180,877 906,913 0.274 0.000 2,053,656 872,779 0.42 0.42 0.64
2019 2014 1,115,187 734,904 0.287 0.000 1,289,894 174,707 0.14 0.14 0.16
2020 2015 647,133 233,249 0.305 0.000 491,381 155,752 0.32 -0.32 0.24
2021 2016 931,734 555,165 0.304 0.000 907,263 24,470 0.03 -0.03 0.03
2022 2017 NA 1,013,997 0.314 0.000 2,161,743 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 513,077 1,054,704 -0.009 0.407 558,389 45,311 0.08 0.08 0.09
2014 2009 751,758 514,188 -0.007 0.397 497,487 254,271 0.51 -0.51 0.33
2015 2010 1,132,845 518,040 -0.003 0.355 506,449 626,396 1.24 -1.24 0.51
2016 2011 1,460,188 421,380 0.003 0.294 503,652 956,536 1.90 -1.90 0.58
2017 2012 312,468 193,326 0.008 0.258 446,380 133,912 0.30 0.30 0.40
2018 2013 1,180,877 387,036 0.012 0.233 507,804 673,073 1.33 -1.33 0.52
2019 2014 1,115,187 340,590 0.015 0.212 505,338 609,849 1.21 -1.21 0.50
2020 2015 647,133 651,172 0.016 0.204 592,558 54,575 0.09 -0.09 0.08
2021 2016 931,734 469,230 0.018 0.187 553,737 377,997 0.68 -0.68 0.39
2022 2017 NA 578,700 0.022 0.164 589,989 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 513,077 1,054,704 0.353 0 486,740 26,337 0.05 -0.05 0.05
2014 2009 751,758 514,188 0.378 0 635,221 116,538 0.18 -0.18 0.15
2015 2010 1,132,845 518,040 0.378 0 638,734 494,111 0.77 -0.77 0.41
2016 2011 1,460,188 421,380 0.371 0 627,963 832,225 1.33 -1.33 0.52
2017 2012 312,468 193,326 0.363 0 441,995 129,527 0.29 0.29 0.39
2018 2013 1,180,877 387,036 0.360 0 621,043 559,834 0.90 -0.90 0.44
2019 2014 1,115,187 340,590 0.357 0 602,454 512,733 0.85 -0.85 0.43
2020 2015 647,133 651,172 0.355 0 673,369 26,236 0.04 0.04 0.04
2021 2016 931,734 469,230 0.360 0 669,552 262,182 0.39 -0.39 0.27
2022 2017 NA 578,700 0.358 0 685,374 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2013 2008 513,077.4 970,159 457,082 0.47 0.47 0.73
2014 2009 751,758.3 818,069 66,311 0.08 0.08 0.09
2015 2010 1,132,845.1 727,959 404,886 0.56 -0.56 0.34
2016 2011 1,460,187.6 720,563 739,624 1.03 -1.03 0.47
2017 2012 312,467.8 856,140 543,673 0.64 0.64 1.05
2018 2013 1,180,877.0 834,067 346,810 0.42 -0.42 0.29
2019 2014 1,115,187.1 967,627 147,560 0.15 -0.15 0.13
2020 2015 647,132.7 1,040,313 393,180 0.38 0.38 0.55
2021 2016 931,733.7 943,170 11,437 0.01 0.01 0.01
2022 2017 NA 837,480 NA NA NA NA

Performance summary

The sibling models (sibling, ln.sibling, lnY.sibling) perform best. Weighting a basket of these models gives us a forecast of ~1.5 million fish.

model range MAD MAPE MPE MAAPE
sibling 5 years 204,803 20.35% 19.22% 0.30
sibling 3 years 63,836 6.10% 4.21% 0.06
ln.sibling 5 years 152,908 18.37% 5.33% 0.25
ln.sibling 3 years 65,542 7.31% -7.31% 0.07
lnY.sibling 5 years 318,379 28.85% 15.09% 0.38
lnY.sibling 3 years 118,310 15.98% -6.95% 0.14
lnS.lnR 5 years 369,881 72.14% -60.14% 0.38
lnS.lnR 3 years 347,474 66.05% -66.05% 0.32
ricker 5 years 298,103 49.52% -36.24% 0.32
ricker 3 years 267,051 42.72% -40.12% 0.25
average 5 years 288,532 31.87% 9.14% 0.40
average 3 years 184,059 18.09% 7.92% 0.23

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 7,949 16,128 0.130 0.019 26,226 18,277 0.70 0.70 1.16
2014 2008 56,710 38,397 0.133 0.016 35,067 21,644 0.62 -0.62 0.36
2015 2009 1,805 56,113 0.134 0.015 43,163 41,358 0.96 0.96 1.53
2016 2010 13,439 500 0.127 0.016 18,838 5,398 0.29 0.29 0.38
2017 2011 3,088 11,165 0.130 0.014 23,070 19,982 0.87 0.87 1.42
2018 2012 0 4,050 0.134 0.012 19,459 19,459 1.00 1.00 1.57
2019 2013 3,254 678 0.139 0.009 17,363 14,109 0.81 0.81 1.34
2020 2014 0 5,345 0.144 0.008 18,892 18,892 1.00 1.00 1.57
2021 2015 59,052 8,177 0.149 0.006 19,551 39,502 2.02 -2.02 0.59
2022 2016 NA 11,612 0.141 0.007 22,142 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 7,949 16,128 0.283 0.001 20,542 12,592 0.61 0.61 1.01
2014 2008 56,710 38,397 0.274 0.001 27,748 28,962 1.04 -1.04 0.47
2015 2009 1,805 56,113 0.284 0.000 33,069 31,264 0.95 0.95 1.51
2016 2010 13,439 500 0.173 0.005 5,955 7,484 1.26 -1.26 0.51
2017 2011 3,088 11,165 0.161 0.007 17,219 14,131 0.82 0.82 1.36
2018 2012 0 4,050 0.154 0.007 12,112 12,112 1.00 1.00 1.57
2019 2013 3,254 678 0.027 0.154 912 2,343 2.57 -2.57 0.62
2020 2014 0 5,345 0.027 0.152 4,556 4,556 1.00 1.00 1.57
2021 2015 59,052 8,177 0.027 0.147 2,780 56,272 20.24 -20.24 0.76
2022 2016 NA 11,612 0.026 0.149 4,211 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 7,949 16,128 0.138 0.016 17,267 9,318 0.54 0.54 0.86
2014 2008 56,710 38,397 0.142 0.014 19,975 36,735 1.84 -1.84 0.57
2015 2009 1,805 56,113 0.139 0.013 23,547 21,743 0.92 0.92 1.49
2016 2010 13,439 500 0.094 0.034 14,653 1,214 0.08 0.08 0.09
2017 2011 3,088 11,165 0.097 0.030 15,758 12,670 0.80 0.80 1.33
2018 2012 0 4,050 0.102 0.025 14,207 14,207 1.00 1.00 1.57
2019 2013 3,254 678 0.005 0.284 5,064 1,810 0.36 0.36 0.51
2020 2014 0 5,345 0.006 0.271 5,396 5,396 1.00 1.00 1.57
2021 2015 59,052 8,177 0.011 0.235 2,376 56,676 23.85 -23.85 0.76
2022 2016 NA 11,612 0.009 0.244 2,829 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 7,949 415,452 -0.030 0.966 19,859 11,910 0.60 0.60 0.98
2014 2008 56,710 1,054,704 -0.029 0.901 18,733 37,978 2.03 -2.03 0.59
2015 2009 1,805 514,188 -0.027 0.847 20,465 18,660 0.91 0.91 1.47
2016 2010 13,439 518,040 -0.028 0.924 18,551 5,112 0.28 0.28 0.36
2017 2011 3,088 421,380 -0.027 0.893 18,433 15,345 0.83 0.83 1.37
2018 2012 0 193,326 -0.025 0.803 18,274 18,274 1.00 1.00 1.57
2019 2013 3,254 387,036 -0.022 0.707 14,546 11,292 0.78 0.78 1.29
2020 2014 0 340,590 -0.022 0.736 13,740 13,740 1.00 1.00 1.57
2021 2015 59,052 651,172 -0.024 0.862 11,603 47,450 4.09 -4.09 0.68
2022 2016 NA 469,230 -0.022 0.775 11,962 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 7,949 415,452 0.221 0.003 27,010 19,061 0.71 0.71 1.18
2014 2008 56,710 1,054,704 0.218 0.002 21,296 35,415 1.66 -1.66 0.56
2015 2009 1,805 514,188 0.202 0.003 28,355 26,550 0.94 0.94 1.50
2016 2010 13,439 518,040 0.190 0.004 26,152 12,713 0.49 0.49 0.76
2017 2011 3,088 421,380 0.193 0.003 24,639 21,551 0.87 0.87 1.43
2018 2012 0 193,326 0.181 0.004 15,925 15,925 1.00 1.00 1.57
2019 2013 3,254 387,036 0.025 0.163 17,966 14,712 0.82 0.82 1.35
2020 2014 0 340,590 0.025 0.162 16,120 16,120 1.00 1.00 1.57
2021 2015 59,052 651,172 0.002 0.308 16,944 42,109 2.49 -2.49 0.62
2022 2016 NA 469,230 -0.001 0.329 15,659 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2013 2007 7,949.202 26,857 18,908 0.70 0.70 1.17
2014 2008 56,710.256 26,085 30,625 1.17 -1.17 0.50
2015 2009 1,804.625 29,642 27,837 0.94 0.94 1.51
2016 2010 13,439.104 26,273 12,834 0.49 0.49 0.76
2017 2011 3,088.118 18,624 15,536 0.83 0.83 1.37
2018 2012 0.000 16,598 16,598 1.00 1.00 1.57
2019 2013 3,254.474 15,008 11,754 0.78 0.78 1.30
2020 2014 0.000 4,317 4,317 1.00 1.00 1.57
2021 2015 59,052.373 3,956 55,096 13.93 -13.93 0.75
2022 2016 NA 13,079 NA NA NA NA

Performance summary

Blending all significant regressions produces a forecast of ~0.013 million fish.

model range MAD MAPE MPE MAAPE
sibling 5 years 22,389 113.98% 33.17% 1.30
sibling 3 years 24,168 127.77% -6.93% 1.17
ln.sibling 5 years 17,883 512.60% -399.77% 1.18
ln.sibling 3 years 21,057 793.64% -726.98% 0.99
lnY.sibling 5 years 18,152 540.32% -413.86% 1.15
lnY.sibling 3 years 21,294 840.39% -749.90% 0.95
lnS.lnR 5 years 21,220 153.97% -9.62% 1.30
lnS.lnR 3 years 24,161 195.53% -77.11% 1.18
ricker 5 years 22,083 123.57% 24.17% 1.31
ricker 3 years 24,313 143.47% -22.21% 1.18
average 5 years 20,660 350.87% -206.17% 1.31
average 3 years 23,722 523.64% -404.76% 1.21

Forecast summary

A preliminary look at the models for this river leads us to an initial forecast of ~2 million broken down as follows:

Table 2. Preliminary Forecast.

age forecast
1.2 0.450
2.2 0.005
1.3 1.500
2.3 0.013