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 1973

sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2008 630,133 317 0.310 0.000 479,110 151,023 0.32 -0.32 0.24
2013 2009 305,157 5,484 0.310 0.000 791,384 486,227 0.61 0.61 1.01
2014 2010 537,386 10,189 0.301 0.000 1,053,669 516,284 0.49 0.49 0.77
2015 2011 444,756 36,528 0.287 0.000 2,519,055 2,074,299 0.82 0.82 1.36
2016 2012 1,977,511 38,199 0.134 0.012 1,712,523 264,989 0.15 -0.15 0.13
2017 2013 2,859,582 162,141 0.213 0.002 5,990,543 3,130,961 0.52 0.52 0.83
2018 2014 2,156,591 102,286 0.314 0.000 2,280,139 123,548 0.05 0.05 0.06
2019 2015 11,553,434 295,278 0.368 0.000 5,388,805 6,164,629 1.14 -1.14 0.49
2020 2016 1,796,941 29,391 0.799 0.000 1,376,208 420,733 0.31 -0.31 0.23
2021 2017 NA 184,024 0.799 0.000 6,208,196 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 630,133 317 0.310 0 429,287 200,846 0.47 -0.47 0.31
2013 2009 305,157 5,484 0.312 0 750,428 445,271 0.59 0.59 0.97
2014 2010 537,386 10,189 0.300 0 803,308 265,922 0.33 0.33 0.46
2015 2011 444,756 36,528 0.299 0 991,549 546,793 0.55 0.55 0.89
2016 2012 1,977,511 38,199 0.290 0 942,094 1,035,417 1.10 -1.10 0.48
2017 2013 2,859,582 162,141 0.314 0 1,290,593 1,568,989 1.22 -1.22 0.50
2018 2014 2,156,591 102,286 0.346 0 1,268,327 888,264 0.70 -0.70 0.39
2019 2015 11,553,434 295,278 0.369 0 1,620,512 9,932,922 6.13 -6.13 0.71
2020 2016 1,796,941 29,391 0.409 0 1,174,460 622,481 0.53 -0.53 0.33
2021 2017 NA 184,024 0.420 0 1,775,849 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 630,133 317 0.127 0.020 273,107 357,026 1.31 -1.31 0.52
2013 2009 305,157 5,484 0.121 0.021 416,578 111,421 0.27 0.27 0.35
2014 2010 537,386 10,189 0.121 0.020 589,649 52,263 0.09 0.09 0.10
2015 2011 444,756 36,528 0.124 0.017 4,277,555 3,832,799 0.90 0.90 1.46
2016 2012 1,977,511 38,199 0.075 0.051 1,814,695 162,816 0.09 -0.09 0.08
2017 2013 2,859,582 162,141 0.116 0.018 781,963,766 779,104,184 1.00 1.00 1.57
2018 2014 2,156,591 102,286 0.106 0.021 2,067,943 88,647 0.04 -0.04 0.04
2019 2015 11,553,434 295,278 0.142 0.008 65,928,506 54,375,072 0.82 0.82 1.36
2020 2016 1,796,941 29,391 0.245 0.000 519,452 1,277,489 2.46 -2.46 0.62
2021 2017 NA 184,024 0.244 0.000 4,521,509 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 630,133 1,259,568 -0.028 0.773 354,316 275,817 0.78 -0.78 0.41
2013 2009 305,157 1,146,276 -0.027 0.760 354,308 49,151 0.14 0.14 0.16
2014 2010 537,386 927,054 -0.026 0.756 339,921 197,464 0.58 -0.58 0.35
2015 2011 444,756 961,200 -0.025 0.778 347,497 97,260 0.28 -0.28 0.22
2016 2012 1,977,511 1,233,900 -0.025 0.786 363,534 1,613,978 4.44 -4.44 0.68
2017 2013 2,859,582 1,113,630 -0.024 0.762 373,215 2,486,367 6.66 -6.66 0.72
2018 2014 2,156,591 1,382,466 -0.024 0.786 405,647 1,750,943 4.32 -4.32 0.68
2019 2015 11,553,434 2,160,792 -0.022 0.718 466,426 11,087,008 23.77 -23.77 0.76
2020 2016 1,796,941 1,837,260 -0.004 0.361 560,844 1,236,096 2.20 -2.20 0.60
2021 2017 NA 2,600,982 0.004 0.283 736,921 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 630,133 1,259,568 0.039 0.133 376,216 253,917 0.67 -0.67 0.38
2013 2009 305,157 1,146,276 0.039 0.128 378,036 72,879 0.19 0.19 0.23
2014 2010 537,386 927,054 0.040 0.124 357,789 179,597 0.50 -0.50 0.32
2015 2011 444,756 961,200 0.044 0.109 367,273 77,483 0.21 -0.21 0.17
2016 2012 1,977,511 1,233,900 0.047 0.100 384,946 1,592,565 4.14 -4.14 0.68
2017 2013 2,859,582 1,113,630 0.045 0.101 397,025 2,462,558 6.20 -6.20 0.71
2018 2014 2,156,591 1,382,466 0.047 0.094 418,677 1,737,914 4.15 -4.15 0.68
2019 2015 11,553,434 2,160,792 0.040 0.108 375,196 11,178,238 29.79 -29.79 0.77
2020 2016 1,796,941 1,837,260 -0.005 0.380 542,850 1,254,091 2.31 -2.31 0.61
2021 2017 NA 2,600,982 -0.010 0.459 632,834 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2012 2008 630,133.1 1,088,538 458,405 0.42 0.42 0.63
2013 2009 305,157.0 817,574 512,417 0.63 0.63 1.03
2014 2010 537,385.9 320,809 216,576 0.68 -0.68 0.38
2015 2011 444,756.3 334,141 110,615 0.33 -0.33 0.24
2016 2012 1,977,511.3 394,104 1,583,407 4.02 -4.02 0.68
2017 2013 2,859,582.1 778,989 2,080,593 2.67 -2.67 0.63
2018 2014 2,156,590.7 1,224,879 931,712 0.76 -0.76 0.41
2019 2015 11,553,433.8 1,595,165 9,958,269 6.24 -6.24 0.71
2020 2016 1,796,940.7 3,798,375 2,001,434 0.53 0.53 0.84
2021 2017 NA 4,068,812 NA NA NA NA

Performance summary

The sibling relationship looks so so but performs ok. If we take that model alone we get 6.2m. If we toss out the two worst performing models (ricker and lnS.lnR) and take a basket approach we get 4.3m. This is an age class that could make a difference of greater than a million.

model range MAD MAPE MPE MAAPE
sibling 5 years 2,020,972 43.63% -20.55% 0.35
sibling 3 years 2,236,303 50.13% -46.52% 0.26
ln.sibling 5 years 2,809,614 193.49% -193.49% 0.48
ln.sibling 3 years 3,814,555 245.33% -245.33% 0.48
lnY.sibling 5 years 167,001,642 88.26% -15.42% 0.73
lnY.sibling 3 years 18,580,403 110.90% -55.91% 0.67
lnS.lnR 5 years 3,634,878 827.85% -827.85% 0.69
lnS.lnR 3 years 4,691,349 1009.69% -1009.69% 0.68
ricker 5 years 3,645,073 931.88% -931.88% 0.69
ricker 3 years 4,723,414 1208.48% -1208.48% 0.69
average 5 years 3,311,083 284.38% -263.30% 0.65
average 3 years 4,297,138 251.01% -215.88% 0.65

age.22

Below are model outputs using data from 1973

sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2007 3,376,161 53,088 -0.031 0.962 3,620,429 244,268 0.07 0.07 0.07
2013 2008 1,104,563 630,133 -0.030 0.971 3,593,805 2,489,242 0.69 0.69 1.15
2014 2009 2,761,971 305,157 -0.029 0.978 3,530,481 768,510 0.22 0.22 0.27
2015 2010 5,985,044 537,386 -0.029 0.997 3,503,422 2,481,621 0.71 -0.71 0.39
2016 2011 3,901,938 444,756 -0.028 0.976 3,572,631 329,307 0.09 -0.09 0.08
2017 2012 4,775,925 1,977,511 -0.027 0.971 3,545,323 1,230,603 0.35 -0.35 0.25
2018 2013 467,780 2,859,582 -0.026 0.918 3,743,149 3,275,369 0.88 0.88 1.43
2019 2014 1,280,264 2,156,591 -0.021 0.663 3,190,733 1,910,468 0.60 0.60 0.98
2020 2015 1,005,735 11,553,434 -0.014 0.510 -243,430 1,249,165 5.13 5.13 0.89
2021 2016 NA 1,796,941 0.007 0.258 3,225,257 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 3,376,161 53,088 0.031 0.163 1,960,302 1,415,859 0.72 -0.72 0.40
2013 2008 1,104,563 630,133 0.022 0.193 2,908,649 1,804,086 0.62 0.62 1.02
2014 2009 2,761,971 305,157 0.015 0.223 2,561,045 200,926 0.08 -0.08 0.07
2015 2010 5,985,044 537,386 0.016 0.217 2,763,979 3,221,064 1.17 -1.17 0.49
2016 2011 3,901,938 444,756 0.019 0.199 2,754,700 1,147,237 0.42 -0.42 0.29
2017 2012 4,775,925 1,977,511 0.020 0.190 3,412,757 1,363,169 0.40 -0.40 0.28
2018 2013 467,780 2,859,582 0.029 0.150 3,684,979 3,217,199 0.87 0.87 1.43
2019 2014 1,280,264 2,156,591 -0.007 0.406 3,037,066 1,756,802 0.58 0.58 0.94
2020 2015 1,005,735 11,553,434 -0.014 0.515 3,214,351 2,208,617 0.69 0.69 1.14
2021 2016 NA 1,796,941 -0.023 0.835 2,593,968 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 3,376,161 53,088 -0.020 0.556 2,455,393 920,768 0.37 -0.37 0.27
2013 2008 1,104,563 630,133 -0.021 0.584 2,666,241 1,561,678 0.59 0.59 0.96
2014 2009 2,761,971 305,157 -0.020 0.578 2,505,037 256,934 0.10 -0.10 0.09
2015 2010 5,985,044 537,386 -0.019 0.578 2,581,092 3,403,951 1.32 -1.32 0.52
2016 2011 3,901,938 444,756 -0.020 0.597 2,614,338 1,287,600 0.49 -0.49 0.32
2017 2012 4,775,925 1,977,511 -0.020 0.610 3,098,153 1,677,773 0.54 -0.54 0.34
2018 2013 467,780 2,859,582 -0.013 0.484 3,665,653 3,197,873 0.87 0.87 1.43
2019 2014 1,280,264 2,156,591 -0.023 0.755 2,423,838 1,143,573 0.47 0.47 0.73
2020 2015 1,005,735 11,553,434 -0.018 0.594 964,898 40,837 0.04 -0.04 0.04
2021 2016 NA 1,796,941 0.012 0.223 2,356,816 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 3,376,161 1,432,500 0.161 0.011 3,206,266 169,896 0.05 -0.05 0.05
2013 2008 1,104,563 1,259,568 0.164 0.009 2,861,450 1,756,887 0.61 0.61 1.01
2014 2009 2,761,971 1,146,276 0.153 0.010 2,561,139 200,831 0.08 -0.08 0.07
2015 2010 5,985,044 927,054 0.154 0.009 2,126,345 3,858,698 1.81 -1.81 0.57
2016 2011 3,901,938 961,200 0.135 0.013 2,274,718 1,627,219 0.72 -0.72 0.40
2017 2012 4,775,925 1,233,900 0.129 0.014 2,844,118 1,931,807 0.68 -0.68 0.38
2018 2013 467,780 1,113,630 0.129 0.013 2,646,700 2,178,920 0.82 0.82 1.36
2019 2014 1,280,264 1,382,466 0.118 0.016 3,043,443 1,763,178 0.58 0.58 0.94
2020 2015 1,005,735 2,160,792 0.108 0.019 4,275,257 3,269,522 0.76 0.76 1.27
2021 2016 NA 1,837,260 0.068 0.050 3,394,818 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 3,376,161 1,432,500 -0.028 0.748 3,222,933 153,228 0.05 -0.05 0.05
2013 2008 1,104,563 1,259,568 -0.027 0.746 2,882,402 1,777,839 0.62 0.62 1.01
2014 2009 2,761,971 1,146,276 -0.026 0.747 2,580,260 181,711 0.07 -0.07 0.07
2015 2010 5,985,044 927,054 -0.025 0.741 2,132,814 3,852,229 1.81 -1.81 0.57
2016 2011 3,901,938 961,200 -0.021 0.630 2,292,541 1,609,396 0.70 -0.70 0.39
2017 2012 4,775,925 1,233,900 -0.018 0.578 2,877,599 1,898,326 0.66 -0.66 0.38
2018 2013 467,780 1,113,630 -0.018 0.575 2,678,650 2,210,870 0.83 0.83 1.36
2019 2014 1,280,264 1,382,466 -0.021 0.660 3,071,478 1,791,214 0.58 0.58 0.95
2020 2015 1,005,735 2,160,792 -0.019 0.621 4,204,956 3,199,221 0.76 0.76 1.27
2021 2016 NA 1,837,260 0.002 0.301 3,325,692 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2012 2007 3,376,161.3 2,699,660 676,501 0.25 -0.25 0.20
2013 2008 1,104,563.4 3,164,756 2,060,192 0.65 0.65 1.08
2014 2009 2,761,970.8 3,000,387 238,416 0.08 0.08 0.09
2015 2010 5,985,043.6 2,348,185 3,636,859 1.55 -1.55 0.55
2016 2011 3,901,937.6 2,971,953 929,984 0.31 -0.31 0.23
2017 2012 4,775,925.4 3,425,935 1,349,990 0.39 -0.39 0.28
2018 2013 467,779.9 3,705,888 3,238,108 0.87 0.87 1.43
2019 2014 1,280,264.2 3,578,531 2,298,267 0.64 0.64 1.06
2020 2015 1,005,734.8 3,282,190 2,276,455 0.69 0.69 1.15
2021 2016 NA 2,286,328 NA NA NA NA

Performance summary

The sibling model performs poorly and is largely dependant on a single data point. The Ricker relationship is not significant. Tossing those two models leaves us with a basket forecasting 3.5m.

model range MAD MAPE MPE MAAPE
sibling 5 years 1,598,982 140.89% 123.32% 0.73
sibling 3 years 2,145,001 220.18% 220.18% 1.10
ln.sibling 5 years 1,938,605 59.09% 26.45% 0.81
ln.sibling 3 years 2,394,206 71.29% 71.29% 1.17
lnY.sibling 5 years 1,469,531 48.41% 5.36% 0.57
lnY.sibling 3 years 1,460,761 46.22% 43.40% 0.73
lnS.lnR 5 years 2,154,129 71.24% 15.46% 0.87
lnS.lnR 3 years 2,403,873 72.25% 72.25% 1.19
ricker 5 years 2,141,805 70.62% 16.15% 0.87
ricker 3 years 2,400,435 72.31% 72.31% 1.19
average 5 years 2,018,561 58.33% 30.05% 0.83
average 3 years 2,604,277 73.65% 73.65% 1.21

age.13

Below are model outputs using data from 1973

sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2007 429,303 53,088 0.652 0 369,612 59,692 0.16 -0.16 0.14
2013 2008 1,090,637 630,133 0.657 0 1,172,113 81,476 0.07 0.07 0.07
2014 2009 488,704 305,157 0.657 0 719,568 230,863 0.32 0.32 0.44
2015 2010 671,706 537,386 0.660 0 1,034,503 362,797 0.35 0.35 0.50
2016 2011 1,095,740 444,756 0.659 0 895,619 200,122 0.22 -0.22 0.18
2017 2012 1,278,331 1,977,511 0.659 0 3,032,654 1,754,323 0.58 0.58 0.94
2018 2013 1,945,681 2,859,582 0.602 0 3,947,205 2,001,525 0.51 0.51 0.80
2019 2014 2,005,941 2,156,591 0.541 0 2,745,564 739,622 0.27 0.27 0.35
2020 2015 12,434,897 11,553,434 0.537 0 12,462,803 27,906 0.00 0.00 0.00
2021 2016 NA 1,796,941 0.867 0 2,294,063 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 429,303 53,088 0.752 0 149,431 279,873 1.87 -1.87 0.58
2013 2008 1,090,637 630,133 0.732 0 1,081,550 9,086 0.01 -0.01 0.01
2014 2009 488,704 305,157 0.733 0 622,160 133,456 0.21 0.21 0.27
2015 2010 671,706 537,386 0.733 0 952,103 280,397 0.29 0.29 0.40
2016 2011 1,095,740 444,756 0.731 0 816,098 279,642 0.34 -0.34 0.25
2017 2012 1,278,331 1,977,511 0.730 0 2,564,832 1,286,500 0.50 0.50 0.79
2018 2013 1,945,681 2,859,582 0.723 0 3,218,912 1,273,231 0.40 0.40 0.58
2019 2014 2,005,941 2,156,591 0.724 0 2,514,192 508,251 0.20 0.20 0.25
2020 2015 12,434,897 11,553,434 0.728 0 8,361,073 4,073,824 0.49 -0.49 0.32
2021 2016 NA 1,796,941 0.762 0 2,241,169 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 429,303 53,088 0.564 0 306,090 123,213 0.40 -0.40 0.28
2013 2008 1,090,637 630,133 0.565 0 656,476 434,160 0.66 -0.66 0.38
2014 2009 488,704 305,157 0.561 0 437,697 51,007 0.12 -0.12 0.10
2015 2010 671,706 537,386 0.563 0 592,629 79,077 0.13 -0.13 0.12
2016 2011 1,095,740 444,756 0.563 0 527,788 567,953 1.08 -1.08 0.48
2017 2012 1,278,331 1,977,511 0.554 0 3,824,512 2,546,180 0.67 0.67 1.11
2018 2013 1,945,681 2,859,582 0.535 0 9,722,220 7,776,539 0.80 0.80 1.33
2019 2014 2,005,941 2,156,591 0.503 0 3,253,962 1,248,020 0.38 0.38 0.56
2020 2015 12,434,897 11,553,434 0.509 0 48,015,539,350 48,003,104,452 1.00 1.00 1.57
2021 2016 NA 1,796,941 0.363 0 1,086,193 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 429,303 1,432,500 -0.013 0.456 759,571 330,268 0.43 0.43 0.66
2013 2008 1,090,637 1,259,568 -0.014 0.474 709,584 381,053 0.54 -0.54 0.34
2014 2009 488,704 1,146,276 -0.013 0.461 693,449 204,744 0.30 0.30 0.40
2015 2010 671,706 927,054 -0.012 0.453 634,158 37,548 0.06 -0.06 0.06
2016 2011 1,095,740 961,200 -0.011 0.447 644,117 451,623 0.70 -0.70 0.39
2017 2012 1,278,331 1,233,900 -0.012 0.463 716,085 562,246 0.79 -0.79 0.41
2018 2013 1,945,681 1,113,630 -0.011 0.450 700,288 1,245,393 1.78 -1.78 0.57
2019 2014 2,005,941 1,382,466 -0.011 0.458 775,508 1,230,433 1.59 -1.59 0.55
2020 2015 12,434,897 2,160,792 -0.008 0.419 946,440 11,488,457 12.14 -12.14 0.75
2021 2016 NA 1,837,260 0.019 0.185 1,058,768 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 429,303 1,432,500 0.025 0.185 776,083 346,780 0.45 0.45 0.68
2013 2008 1,090,637 1,259,568 0.028 0.170 742,548 348,089 0.47 -0.47 0.31
2014 2009 488,704 1,146,276 0.028 0.164 731,039 242,334 0.33 0.33 0.46
2015 2010 671,706 927,054 0.028 0.162 665,775 5,931 0.01 -0.01 0.01
2016 2011 1,095,740 961,200 0.030 0.153 676,662 419,078 0.62 -0.62 0.37
2017 2012 1,278,331 1,233,900 0.034 0.135 747,887 530,444 0.71 -0.71 0.39
2018 2013 1,945,681 1,113,630 0.034 0.131 736,328 1,209,353 1.64 -1.64 0.56
2019 2014 2,005,941 1,382,466 0.037 0.120 792,317 1,213,624 1.53 -1.53 0.54
2020 2015 12,434,897 2,160,792 0.033 0.128 789,432 11,645,465 14.75 -14.75 0.75
2021 2016 NA 1,837,260 -0.007 0.411 1,026,195 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2012 2007 429,303.4 1,734,058 1,304,755 0.75 0.75 1.25
2013 2008 1,090,636.5 1,379,298 288,661 0.21 0.21 0.26
2014 2009 488,704.5 1,087,094 598,390 0.55 0.55 0.89
2015 2010 671,705.9 492,982 178,724 0.36 -0.36 0.26
2016 2011 1,095,740.2 586,857 508,883 0.87 -0.87 0.43
2017 2012 1,278,331.3 755,218 523,113 0.69 -0.69 0.39
2018 2013 1,945,681.0 925,024 1,020,657 1.10 -1.10 0.48
2019 2014 2,005,941.5 1,096,033 909,909 0.83 -0.83 0.43
2020 2015 12,434,897.2 1,399,480 11,035,417 7.89 -7.89 0.73
2021 2016 NA 3,752,118 NA NA NA NA

Performance summary

The three sibling models are performing well here. A basket of those gives us 2.1m.

model range MAD MAPE MPE MAAPE
sibling 5 years 944,699 31.61% 22.67% 0.46
sibling 3 years 923,018 25.96% 25.96% 0.39
ln.sibling 5 years 1,484,290 38.58% 5.39% 0.44
ln.sibling 3 years 1,951,769 36.16% 3.68% 0.38
lnY.sibling 5 years 9,603,048,629 78.50% 35.46% 1.01
lnY.sibling 3 years 16,004,043,004 72.77% 72.77% 1.15
lnS.lnR 5 years 2,995,631 339.80% -339.80% 0.53
lnS.lnR 3 years 4,654,761 516.79% -516.79% 0.62
ricker 5 years 3,003,593 385.09% -385.09% 0.52
ricker 3 years 4,689,481 597.53% -597.53% 0.62
average 5 years 2,799,596 227.57% -227.57% 0.49
average 3 years 4,321,994 327.30% -327.30% 0.54

age.23

Below are model outputs using data from 1973

sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2006 1,369,945 1,632,027 0.536 0 1,344,524 25,420 0.02 -0.02 0.02
2013 2007 2,456,691 3,376,161 0.541 0 2,420,290 36,401 0.02 -0.02 0.01
2014 2008 943,044 1,104,563 0.541 0 1,021,809 78,765 0.08 0.08 0.08
2015 2009 785,912 2,761,971 0.548 0 2,040,167 1,254,255 0.61 0.61 1.01
2016 2010 2,345,584 5,985,044 0.547 0 4,003,666 1,658,082 0.41 0.41 0.62
2017 2011 3,275,009 3,901,938 0.532 0 2,662,106 612,904 0.23 -0.23 0.19
2018 2012 1,137,567 4,775,925 0.532 0 3,207,471 2,069,904 0.65 0.65 1.07
2019 2013 495,689 467,780 0.512 0 575,603 79,915 0.14 0.14 0.16
2020 2014 200,712 1,280,264 0.523 0 1,056,121 855,408 0.81 0.81 1.34
2021 2015 NA 1,005,735 0.532 0 854,753 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 1,369,945 1,632,027 0.528 0 1,324,747 45,198 0.03 -0.03 0.03
2013 2007 2,456,691 3,376,161 0.531 0 2,211,690 245,001 0.11 -0.11 0.10
2014 2008 943,044 1,104,563 0.532 0 1,010,155 67,111 0.07 0.07 0.07
2015 2009 785,912 2,761,971 0.542 0 1,922,844 1,136,932 0.59 0.59 0.97
2016 2010 2,345,584 5,985,044 0.522 0 3,236,542 890,958 0.28 0.28 0.36
2017 2011 3,275,009 3,901,938 0.519 0 2,364,658 910,351 0.38 -0.38 0.27
2018 2012 1,137,567 4,775,925 0.522 0 2,751,218 1,613,652 0.59 0.59 0.96
2019 2013 495,689 467,780 0.494 0 548,664 52,975 0.10 0.10 0.11
2020 2014 200,712 1,280,264 0.527 0 1,080,397 879,685 0.81 0.81 1.35
2021 2015 NA 1,005,735 0.507 0 846,539 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 1,369,945 1,632,027 0.527 0 1,211,038 158,907 0.13 -0.13 0.12
2013 2007 2,456,691 3,376,161 0.529 0 1,781,486 675,205 0.38 -0.38 0.27
2014 2008 943,044 1,104,563 0.527 0 1,096,272 153,228 0.14 0.14 0.16
2015 2009 785,912 2,761,971 0.536 0 1,564,588 778,677 0.50 0.50 0.78
2016 2010 2,345,584 5,985,044 0.530 0 3,129,219 783,636 0.25 0.25 0.32
2017 2011 3,275,009 3,901,938 0.528 0 1,956,764 1,318,245 0.67 -0.67 0.38
2018 2012 1,137,567 4,775,925 0.524 0 2,402,053 1,264,486 0.53 0.53 0.84
2019 2013 495,689 467,780 0.505 0 926,582 430,893 0.47 0.47 0.72
2020 2014 200,712 1,280,264 0.523 0 1,070,109 869,396 0.81 0.81 1.34
2021 2015 NA 1,005,735 0.505 0 935,531 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 1,369,945 1,465,158 0.168 0.010 2,324,571 954,627 0.41 0.41 0.61
2013 2007 2,456,691 1,432,500 0.160 0.011 2,233,569 223,122 0.10 -0.10 0.09
2014 2008 943,044 1,259,568 0.163 0.009 2,007,545 1,064,501 0.53 0.53 0.85
2015 2009 785,912 1,146,276 0.156 0.010 1,813,894 1,027,982 0.57 0.57 0.92
2016 2010 2,345,584 927,054 0.152 0.010 1,480,665 864,919 0.58 -0.58 0.35
2017 2011 3,275,009 961,200 0.146 0.010 1,551,082 1,723,927 1.11 -1.11 0.48
2018 2012 1,137,567 1,233,900 0.135 0.012 1,942,502 804,935 0.41 0.41 0.62
2019 2013 495,689 1,113,630 0.132 0.012 1,765,144 1,269,455 0.72 0.72 1.20
2020 2014 200,712 1,382,466 0.125 0.013 2,037,641 1,836,928 0.90 0.90 1.46
2021 2015 NA 2,160,792 0.081 0.037 2,648,781 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 1,369,945 1,465,158 -0.029 0.740 2,347,976 978,031 0.42 0.42 0.62
2013 2007 2,456,691 1,432,500 -0.026 0.695 2,260,155 196,536 0.09 -0.09 0.08
2014 2008 943,044 1,259,568 -0.025 0.696 2,028,596 1,085,552 0.54 0.54 0.86
2015 2009 785,912 1,146,276 -0.025 0.695 1,828,561 1,042,649 0.57 0.57 0.92
2016 2010 2,345,584 927,054 -0.025 0.730 1,472,878 872,706 0.59 -0.59 0.36
2017 2011 3,275,009 961,200 -0.023 0.672 1,549,475 1,725,534 1.11 -1.11 0.48
2018 2012 1,137,567 1,233,900 -0.019 0.599 1,967,693 830,126 0.42 0.42 0.63
2019 2013 495,689 1,113,630 -0.019 0.597 1,780,713 1,285,024 0.72 0.72 1.20
2020 2014 200,712 1,382,466 -0.020 0.659 2,071,519 1,870,806 0.90 0.90 1.46
2021 2015 NA 2,160,792 -0.017 0.586 2,690,446 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2012 2006 1,369,944.7 1,827,008 457,063 0.25 0.25 0.32
2013 2007 2,456,691.1 1,689,176 767,515 0.45 -0.45 0.30
2014 2008 943,044.1 2,078,222 1,135,178 0.55 0.55 0.88
2015 2009 785,911.5 1,817,652 1,031,740 0.57 0.57 0.92
2016 2010 2,345,583.8 1,621,309 724,275 0.45 -0.45 0.30
2017 2011 3,275,009.2 1,580,235 1,694,774 1.07 -1.07 0.48
2018 2012 1,137,566.6 1,961,248 823,681 0.42 0.42 0.63
2019 2013 495,688.9 1,697,423 1,201,734 0.71 0.71 1.18
2020 2014 200,712.5 1,607,952 1,407,240 0.88 0.88 1.43
2021 2015 NA 1,490,912 NA NA NA NA

Performance summary

Things look similar across models with the exception of the ricker which isn’t convincing at all. Taking the remaining models in a weighted basket approach gives us 1.3m.

model range MAD MAPE MPE MAAPE
sibling 5 years 1,055,243 44.77% 35.56% 0.67
sibling 3 years 1,001,742 53.14% 53.14% 0.86
ln.sibling 5 years 869,524 43.15% 27.75% 0.61
ln.sibling 3 years 848,770 49.91% 49.91% 0.80
lnY.sibling 5 years 933,331 54.56% 27.61% 0.72
lnY.sibling 3 years 854,925 60.13% 60.13% 0.97
lnS.lnR 5 years 1,300,033 74.61% 6.79% 0.82
lnS.lnR 3 years 1,303,773 67.84% 67.84% 1.09
ricker 5 years 1,316,839 75.06% 6.81% 0.83
ricker 3 years 1,328,652 68.22% 68.22% 1.10
average 5 years 1,170,341 70.45% 9.68% 0.80
average 3 years 1,144,218 66.77% 66.77% 1.08