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 1975

lnS.lnR

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
2013 2009 97,897 484,149 -0.022 0.587 120,677 22,779 0.19 0.19 0.23
2014 2010 203,018 468,696 -0.021 0.594 120,469 82,549 0.69 -0.69 0.39
2015 2011 206,794 428,191 -0.018 0.548 125,250 81,545 0.65 -0.65 0.38
2016 2012 486,258 432,438 -0.015 0.492 127,796 358,462 2.80 -2.80 0.64
2017 2013 3,586,571 894,148 -0.006 0.387 108,841 3,477,730 31.95 -31.95 0.77
2018 2014 1,124,541 618,477 -0.025 0.790 133,380 991,160 7.43 -7.43 0.72
2019 2015 504,880 796,684 -0.025 0.809 137,196 367,684 2.68 -2.68 0.63
2020 2016 1,701,542 680,512 -0.025 0.902 144,625 1,556,917 10.77 -10.77 0.74
2021 2017 8,582,944 2,852,308 -0.025 0.973 150,831 8,432,112 55.90 -55.90 0.78
2022 2018 NA 1,247,460 0.032 0.131 259,015 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 97,897 484,149 0.337 0.000 114,966 17,069 0.15 0.15 0.17
2014 2010 203,018 468,696 0.337 0.000 112,611 90,407 0.80 -0.80 0.42
2015 2011 206,794 428,191 0.341 0.000 109,730 97,064 0.88 -0.88 0.44
2016 2012 486,258 432,438 0.345 0.000 112,646 373,611 3.32 -3.32 0.66
2017 2013 3,586,571 894,148 0.342 0.000 142,483 3,444,088 24.17 -24.17 0.77
2018 2014 1,124,541 618,477 0.246 0.001 147,016 977,525 6.65 -6.65 0.72
2019 2015 504,880 796,684 0.231 0.001 163,448 341,432 2.09 -2.09 0.59
2020 2016 1,701,542 680,512 0.222 0.001 163,368 1,538,174 9.42 -9.42 0.74
2021 2017 8,582,944 2,852,308 0.200 0.002 65,471 8,517,472 130.10 -130.10 0.78
2022 2018 NA 1,247,460 0.020 0.179 266,957 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2013 2009 97,897.27 170,586 72,689 0.43 0.43 0.64
2014 2010 203,017.83 151,247 51,771 0.34 -0.34 0.25
2015 2011 206,794.30 120,018 86,776 0.72 -0.72 0.40
2016 2012 486,257.72 140,429 345,829 2.46 -2.46 0.62
2017 2013 3,586,570.85 231,504 3,355,067 14.49 -14.49 0.75
2018 2014 1,124,540.62 916,108 208,433 0.23 -0.23 0.18
2019 2015 504,879.85 1,121,436 616,556 0.55 0.55 0.88
2020 2016 1,701,541.75 1,181,809 519,733 0.44 -0.44 0.30
2021 2017 8,582,943.51 1,480,758 7,102,185 4.80 -4.80 0.69
2022 2018 NA 3,100,095 NA NA NA NA

Performance summary

This is another strange one. This age class has increased dramatically in recent years. That plus the performance of the average model lead us to take that as the forecast, giving us a forecast of ~3.1 million fish.

model range MAD MAPE MPE MAAPE
sibling 5 years 2,662,734 701.79% -697.70% 0.54
sibling 3 years 3,136,129 663.85% -657.03% 0.50
ln.sibling 5 years 2,825,491 1077.67% -1077.67% 0.65
ln.sibling 3 years 3,274,721 946.42% -946.42% 0.61
lnY.sibling 5 years 2,870,166 1406.67% -1406.67% 0.67
lnY.sibling 3 years 3,356,377 1500.69% -1500.69% 0.64
lnS.lnR 5 years 2,965,121 2174.66% -2174.66% 0.73
lnS.lnR 3 years 3,452,238 2311.65% -2311.65% 0.72
ricker 5 years 2,963,738 3448.41% -3448.41% 0.72
ricker 3 years 3,465,693 4719.99% -4719.99% 0.70
average 5 years 2,360,395 410.12% -388.13% 0.56
average 3 years 2,746,158 192.86% -156.21% 0.62

age.22

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 4,818 492,546 0.005 0.282 2,516 2,302 0.92 -0.92 0.45
2014 2009 4,713 484,149 0.007 0.274 2,608 2,105 0.81 -0.81 0.42
2015 2010 2,101 468,696 0.008 0.265 2,741 640 0.23 0.23 0.30
2016 2011 3,339 428,191 0.008 0.259 2,989 350 0.12 -0.12 0.10
2017 2012 52,482 432,438 0.009 0.251 2,968 49,515 16.68 -16.68 0.76
2018 2013 13,702 894,148 0.012 0.232 1,467 12,234 8.34 -8.34 0.73
2019 2014 65,787 618,477 0.008 0.255 2,323 63,464 27.32 -27.32 0.77
2020 2015 9,783 796,684 0.006 0.267 1,966 7,817 3.98 -3.98 0.67
2021 2016 179,558 680,512 0.005 0.278 2,400 177,159 73.83 -73.83 0.78
2022 2017 NA 2,852,308 0.001 0.309 750 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 4,818 492,546 -0.023 0.647 2,261 2,558 1.13 -1.13 0.49
2014 2009 4,713 484,149 -0.022 0.635 2,283 2,430 1.06 -1.06 0.48
2015 2010 2,101 468,696 -0.021 0.623 2,277 176 0.08 0.08 0.08
2016 2011 3,339 428,191 -0.020 0.618 2,124 1,215 0.57 -0.57 0.35
2017 2012 52,482 432,438 -0.019 0.607 2,168 50,314 23.20 -23.20 0.76
2018 2013 13,702 894,148 -0.017 0.569 3,654 10,048 2.75 -2.75 0.63
2019 2014 65,787 618,477 -0.017 0.581 3,107 62,680 20.17 -20.17 0.76
2020 2015 9,783 796,684 -0.016 0.575 3,850 5,933 1.54 -1.54 0.55
2021 2016 179,558 680,512 -0.016 0.577 3,610 175,948 48.73 -48.73 0.78
2022 2017 NA 2,852,308 -0.016 0.584 4,522 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2013 2008 4,818.235 3,958 860 0.22 -0.22 0.18
2014 2009 4,712.672 4,922 209 0.04 0.04 0.04
2015 2010 2,100.985 4,712 2,611 0.55 0.55 0.89
2016 2011 3,339.269 3,383 44 0.01 0.01 0.01
2017 2012 52,482.214 2,994 49,488 16.53 -16.53 0.76
2018 2013 13,701.714 13,491 211 0.02 -0.02 0.02
2019 2014 65,786.948 15,267 50,520 3.31 -3.31 0.65
2020 2015 9,783.418 27,482 17,699 0.64 0.64 1.07
2021 2016 179,558.490 29,019 150,540 5.19 -5.19 0.70
2022 2017 NA 64,263 NA NA NA NA

Performance summary

This one is another one for carefull consideration given the unprecedented return last year. It’s hard to trust anything other than the average giving us a forecast of ~0.06 million fish.

model range MAD MAPE MPE MAAPE
sibling 5 years 49,032 190.37% -163.43% 0.61
sibling 3 years 71,240 268.73% -223.83% 0.79
ln.sibling 5 years 64,197 98567.52% -98567.52% 0.78
ln.sibling 3 years 84,958 108501.93% -108501.93% 0.78
lnY.sibling 5 years 63,824 1639915771.03% -1639915771.03% 0.78
lnY.sibling 3 years 84,316 10560.50% -10560.50% 0.78
lnS.lnR 5 years 62,038 2602.88% -2602.88% 0.74
lnS.lnR 3 years 82,813 3504.01% -3504.01% 0.74
ricker 5 years 60,984 1927.97% -1927.97% 0.70
ricker 3 years 81,520 2348.23% -2348.23% 0.69
average 5 years 53,691 513.68% -487.92% 0.64
average 3 years 72,919 304.69% -261.76% 0.81

age.13

Below are model outputs using data from 1975

sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2013 2008 1,834,254 163,553 0.299 0.001 1,329,918 504,336 0.38 -0.38 0.27
2014 2009 1,139,868 97,897 0.298 0.001 1,063,686 76,183 0.07 -0.07 0.07
2015 2010 2,223,153 203,018 0.299 0.000 1,515,556 707,597 0.47 -0.47 0.31
2016 2011 2,060,682 206,794 0.301 0.000 1,553,278 507,404 0.33 -0.33 0.24
2017 2012 4,407,860 486,258 0.303 0.000 2,784,394 1,623,465 0.58 -0.58 0.35
2018 2013 8,286,002 3,586,571 0.388 0.000 18,663,317 10,377,315 0.56 0.56 0.90
2019 2014 3,630,434 1,124,541 0.619 0.000 3,526,212 104,222 0.03 -0.03 0.03
2020 2015 1,871,660 504,880 0.634 0.000 2,176,603 304,943 0.14 0.14 0.16
2021 2016 6,221,196 1,701,542 0.634 0.000 4,784,360 1,436,836 0.30 -0.30 0.23
2022 2017 NA 8,582,944 0.682 0.000 20,969,160 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 1,834,254 163,553 0.275 0.001 1,199,260 634,994 0.53 -0.53 0.33
2014 2009 1,139,868 97,897 0.279 0.001 968,088 171,781 0.18 -0.18 0.15
2015 2010 2,223,153 203,018 0.279 0.001 1,345,256 877,897 0.65 -0.65 0.38
2016 2011 2,060,682 206,794 0.288 0.000 1,383,595 677,087 0.49 -0.49 0.32
2017 2012 4,407,860 486,258 0.296 0.000 2,087,296 2,320,563 1.11 -1.11 0.48
2018 2013 8,286,002 3,586,571 0.337 0.000 6,044,667 2,241,335 0.37 -0.37 0.26
2019 2014 3,630,434 1,124,541 0.440 0.000 3,611,784 18,650 0.01 -0.01 0.01
2020 2015 1,871,660 504,880 0.467 0.000 2,375,554 503,894 0.21 0.21 0.26
2021 2016 6,221,196 1,701,542 0.469 0.000 4,394,301 1,826,895 0.42 -0.42 0.29
2022 2017 NA 8,582,944 0.514 0.000 10,915,845 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 1,834,254 163,553 0.276 0.001 1,021,069 813,185 0.80 -0.80 0.42
2014 2009 1,139,868 97,897 0.271 0.001 861,082 278,786 0.32 -0.32 0.24
2015 2010 2,223,153 203,018 0.268 0.001 1,170,841 1,052,312 0.90 -0.90 0.44
2016 2011 2,060,682 206,794 0.268 0.001 1,206,795 853,887 0.71 -0.71 0.39
2017 2012 4,407,860 486,258 0.270 0.001 2,761,737 1,646,122 0.60 -0.60 0.36
2018 2013 8,286,002 3,586,571 0.329 0.000 44,855,937,677 44,847,651,675 1.00 1.00 1.57
2019 2014 3,630,434 1,124,541 0.251 0.001 2,242,280 1,388,155 0.62 -0.62 0.37
2020 2015 1,871,660 504,880 0.279 0.000 1,445,692 425,968 0.29 -0.29 0.22
2021 2016 6,221,196 1,701,542 0.282 0.000 3,681,916 2,539,280 0.69 -0.69 0.39
2022 2017 NA 8,582,944 0.339 0.000 1,157,057,193 NA NA NA NA

lnS.lnR

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
2013 2008 1,834,254 492,546 0.013 0.243 1,108,714 725,540 0.65 -0.65 0.38
2014 2009 1,139,868 484,149 0.018 0.214 1,136,898 2,970 0.00 0.00 0.00
2015 2010 2,223,153 468,696 0.019 0.205 1,150,350 1,072,803 0.93 -0.93 0.45
2016 2011 2,060,682 428,191 0.027 0.170 1,221,702 838,980 0.69 -0.69 0.39
2017 2012 4,407,860 432,438 0.035 0.137 1,245,536 3,162,323 2.54 -2.54 0.62
2018 2013 8,286,002 894,148 0.049 0.096 931,541 7,354,461 7.89 -7.89 0.73
2019 2014 3,630,434 618,477 0.010 0.249 1,175,609 2,454,826 2.09 -2.09 0.59
2020 2015 1,871,660 796,684 0.008 0.258 1,106,961 764,699 0.69 -0.69 0.39
2021 2016 6,221,196 680,512 0.005 0.279 1,187,190 5,034,005 4.24 -4.24 0.68
2022 2017 NA 2,852,308 -0.001 0.334 799,718 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 1,834,254 492,546 0.397 0 1,020,206 814,048 0.80 -0.80 0.42
2014 2009 1,139,868 484,149 0.399 0 1,032,205 107,664 0.10 -0.10 0.09
2015 2010 2,223,153 468,696 0.402 0 1,019,351 1,203,801 1.18 -1.18 0.50
2016 2011 2,060,682 428,191 0.402 0 998,503 1,062,179 1.06 -1.06 0.48
2017 2012 4,407,860 432,438 0.405 0 1,028,248 3,379,611 3.29 -3.29 0.65
2018 2013 8,286,002 894,148 0.395 0 1,313,507 6,972,495 5.31 -5.31 0.70
2019 2014 3,630,434 618,477 0.344 0 1,302,571 2,327,864 1.79 -1.79 0.57
2020 2015 1,871,660 796,684 0.337 0 1,411,815 459,845 0.33 -0.33 0.24
2021 2016 6,221,196 680,512 0.336 0 1,382,175 4,839,020 3.50 -3.50 0.66
2022 2017 NA 2,852,308 0.317 0 535,178 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2013 2008 1,834,254 1,151,918 682,336 0.59 -0.59 0.36
2014 2009 1,139,868 1,210,244 70,376 0.06 0.06 0.06
2015 2010 2,223,153 1,143,393 1,079,760 0.94 -0.94 0.45
2016 2011 2,060,682 1,392,956 667,726 0.48 -0.48 0.31
2017 2012 4,407,860 1,601,650 2,806,210 1.75 -1.75 0.57
2018 2013 8,286,002 2,333,163 5,952,839 2.55 -2.55 0.62
2019 2014 3,630,434 3,623,513 6,921 0.00 0.00 0.00
2020 2015 1,871,660 4,121,626 2,249,966 0.55 0.55 0.88
2021 2016 6,221,196 4,051,328 2,169,868 0.54 -0.54 0.34
2022 2017 NA 4,883,430 NA NA NA NA

Performance summary

Blending the sibling and ln.sibling models seem most credible here. Blending those gives us a forecast of ~11.3 million fish. Dropping the average model gives us a forecast of ~15.3 million fish. THIS IS AN AGE CLASS TO BE DISCUSSED.

model range MAD MAPE MPE MAAPE
sibling 5 years 2,769,356 32.18% -4.34% 0.33
sibling 3 years 615,334 15.67% -6.33% 0.14
ln.sibling 5 years 1,382,267 42.31% -33.83% 0.26
ln.sibling 3 years 783,146 21.10% -6.96% 0.18
lnY.sibling 5 years 8,970,730,240 63.99% -23.99% 0.58
lnY.sibling 3 years 1,451,134 53.45% -53.45% 0.33
lnS.lnR 5 years 3,754,063 349.06% -349.06% 0.60
lnS.lnR 3 years 2,751,177 233.97% -233.97% 0.55
ricker 5 years 3,595,767 284.18% -284.18% 0.57
ricker 3 years 2,542,243 187.13% -187.13% 0.49
average 5 years 2,637,161 107.74% -85.90% 0.48
average 3 years 1,475,585 36.11% 0.28% 0.40

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 6,508 0 0.294 0 18,173 11,664 0.64 0.64 1.06
2014 2008 12,279 4,818 0.297 0 20,403 8,124 0.40 0.40 0.58
2015 2009 0 4,713 0.300 0 20,095 20,095 1.00 1.00 1.57
2016 2010 3,717 2,101 0.303 0 18,061 14,344 0.79 0.79 1.32
2017 2011 36,731 3,339 0.306 0 18,314 18,416 1.01 -1.01 0.46
2018 2012 97,089 52,482 0.304 0 45,744 51,345 1.12 -1.12 0.49
2019 2013 59,617 13,702 0.305 0 25,667 33,950 1.32 -1.32 0.52
2020 2014 13,477 65,787 0.302 0 55,203 41,726 0.76 0.76 1.26
2021 2015 34,029 9,783 0.294 0 23,553 10,476 0.44 -0.44 0.30
2022 2016 NA 179,558 0.294 0 115,799 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 6,508 0 0.031 0.159 24 6,484 269.21 -269.21 0.78
2014 2008 12,279 4,818 0.019 0.202 2,531 9,748 3.85 -3.85 0.67
2015 2009 0 4,713 0.021 0.193 2,620 2,620 1.00 1.00 1.57
2016 2010 3,717 2,101 0.003 0.298 887 2,830 3.19 -3.19 0.65
2017 2011 36,731 3,339 0.004 0.291 1,116 35,615 31.92 -31.92 0.77
2018 2012 97,089 52,482 0.005 0.283 3,846 93,243 24.24 -24.24 0.77
2019 2013 59,617 13,702 0.009 0.252 2,454 57,163 23.29 -23.29 0.76
2020 2014 13,477 65,787 0.011 0.235 5,428 8,050 1.48 -1.48 0.54
2021 2015 34,029 9,783 0.013 0.219 2,382 31,647 13.29 -13.29 0.75
2022 2016 NA 179,558 0.015 0.207 9,675 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 6,508 0 0.009 0.262 865 5,643 6.52 -6.52 0.71
2014 2008 12,279 4,818 0.009 0.262 1,022 11,257 11.01 -11.01 0.74
2015 2009 0 4,713 0.008 0.263 1,101 1,101 1.00 1.00 1.57
2016 2010 3,717 2,101 0.011 0.243 467 3,251 6.96 -6.96 0.72
2017 2011 36,731 3,339 0.011 0.242 511 36,219 70.82 -70.82 0.78
2018 2012 97,089 52,482 0.010 0.248 1,797 95,292 53.03 -53.03 0.78
2019 2013 59,617 13,702 0.012 0.233 803 58,814 73.25 -73.25 0.78
2020 2014 13,477 65,787 0.011 0.236 2,995 10,483 3.50 -3.50 0.66
2021 2015 34,029 9,783 0.012 0.223 841 33,188 39.45 -39.45 0.77
2022 2016 NA 179,558 0.012 0.226 46,401 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 6,508 518,041 0.000 0.322 8,209 1,701 0.21 0.21 0.26
2014 2008 12,279 492,546 0.001 0.315 8,475 3,804 0.45 -0.45 0.30
2015 2009 0 484,149 0.002 0.307 8,675 8,675 1.00 1.00 1.57
2016 2010 3,717 468,696 -0.007 0.397 6,940 3,223 0.46 0.46 0.71
2017 2011 36,731 428,191 -0.007 0.395 7,266 29,465 4.06 -4.06 0.68
2018 2012 97,089 432,438 -0.005 0.374 7,552 89,538 11.86 -11.86 0.74
2019 2013 59,617 894,148 -0.003 0.349 4,696 54,921 11.69 -11.69 0.74
2020 2014 13,477 618,477 -0.006 0.395 6,647 6,830 1.03 -1.03 0.47
2021 2015 34,029 796,684 -0.006 0.393 5,716 28,313 4.95 -4.95 0.69
2022 2016 NA 680,512 -0.008 0.417 6,669 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 6,508 518,041 -0.008 0.394 8,520 2,012 0.24 0.24 0.30
2014 2008 12,279 492,546 -0.007 0.389 8,207 4,072 0.50 -0.50 0.32
2015 2009 0 484,149 -0.006 0.378 8,221 8,221 1.00 1.00 1.57
2016 2010 3,717 468,696 -0.015 0.501 6,193 2,476 0.40 0.40 0.59
2017 2011 36,731 428,191 -0.014 0.499 5,732 30,999 5.41 -5.41 0.70
2018 2012 97,089 432,438 -0.012 0.472 6,093 90,996 14.93 -14.93 0.75
2019 2013 59,617 894,148 -0.010 0.439 9,558 50,059 5.24 -5.24 0.70
2020 2014 13,477 618,477 -0.011 0.457 8,523 4,954 0.58 -0.58 0.35
2021 2015 34,029 796,684 -0.010 0.450 9,744 24,285 2.49 -2.49 0.62
2022 2016 NA 680,512 -0.010 0.455 9,325 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2013 2007 6,508.40 15,185 8,677 0.57 0.57 0.93
2014 2008 12,278.89 14,513 2,234 0.15 0.15 0.18
2015 2009 0.00 12,517 12,517 1.00 1.00 1.57
2016 2010 3,717.37 9,418 5,701 0.61 0.61 0.99
2017 2011 36,730.58 5,979 30,752 5.14 -5.14 0.70
2018 2012 97,089.27 11,847 85,242 7.20 -7.20 0.72
2019 2013 59,616.89 29,963 29,654 0.99 -0.99 0.46
2020 2014 13,477.24 39,431 25,954 0.66 0.66 1.09
2021 2015 34,028.84 42,126 8,097 0.19 0.19 0.23
2022 2016 NA 48,189 NA NA NA NA

Performance summary

Blending all significant models gives us a forecast of ~0.047 million fish.

model range MAD MAPE MPE MAAPE
sibling 5 years 31,183 93.03% -62.79% 0.61
sibling 3 years 28,717 84.11% -33.72% 0.69
ln.sibling 5 years 45,144 1884.64% -1884.64% 0.72
ln.sibling 3 years 32,287 1268.82% -1268.82% 0.68
lnY.sibling 5 years 46,799 4801.01% -4801.01% 0.75
lnY.sibling 3 years 34,161 3873.20% -3873.20% 0.74
lnS.lnR 5 years 41,813 671.76% -671.76% 0.67
lnS.lnR 3 years 30,021 589.20% -589.20% 0.64
ricker 5 years 40,258 573.05% -573.05% 0.62
ricker 3 years 26,432 277.02% -277.02% 0.56
average 5 years 35,940 283.57% -249.56% 0.64
average 3 years 21,235 61.34% -4.64% 0.60

age.14

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 54,919 750,292 0.187 0.005 62,162 7,243 0.12 0.12 0.13
2014 2008 142,193 1,834,254 0.190 0.005 102,681 39,513 0.38 -0.38 0.27
2015 2009 25,693 1,139,868 0.196 0.004 77,543 51,851 0.67 0.67 1.11
2016 2010 16,030 2,223,153 0.196 0.003 117,721 101,691 0.86 0.86 1.41
2017 2011 103,138 2,060,682 0.171 0.005 107,112 3,974 0.04 0.04 0.04
2018 2012 70,631 4,407,860 0.174 0.004 191,313 120,682 0.63 0.63 1.04
2019 2013 38,718 8,286,002 0.129 0.012 276,789 238,071 0.86 0.86 1.41
2020 2014 23,053 3,630,434 0.026 0.158 103,667 80,614 0.78 0.78 1.29
2021 2015 38,864 1,871,660 0.014 0.213 80,774 41,909 0.52 0.52 0.82
2022 2016 NA 6,221,196 0.014 0.213 123,192 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 54,919 750,292 0.355 0 4,917 50,002 10.17 -10.17 0.74
2014 2008 142,193 1,834,254 0.355 0 56,874 85,319 1.50 -1.50 0.54
2015 2009 25,693 1,139,868 0.358 0 16,460 9,233 0.56 -0.56 0.34
2016 2010 16,030 2,223,153 0.359 0 99,300 83,270 0.84 0.84 1.38
2017 2011 103,138 2,060,682 0.358 0 76,214 26,923 0.35 -0.35 0.26
2018 2012 70,631 4,407,860 0.361 0 580,737 510,106 0.88 0.88 1.43
2019 2013 38,718 8,286,002 0.360 0 2,759,736 2,721,019 0.99 0.99 1.56
2020 2014 23,053 3,630,434 0.353 0 255,798 232,745 0.91 0.91 1.47
2021 2015 38,864 1,871,660 0.351 0 43,924 5,059 0.12 0.12 0.13
2022 2016 NA 6,221,196 0.352 0 903,661 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 54,919 750,292 0.046 0.114 1,876 53,043 28.28 -28.28 0.77
2014 2008 142,193 1,834,254 0.044 0.117 17,404 124,789 7.17 -7.17 0.72
2015 2009 25,693 1,139,868 0.047 0.105 4,748 20,944 4.41 -4.41 0.68
2016 2010 16,030 2,223,153 0.047 0.101 41,932 25,902 0.62 0.62 1.02
2017 2011 103,138 2,060,682 0.048 0.097 29,219 73,919 2.53 -2.53 0.62
2018 2012 70,631 4,407,860 0.051 0.087 3,122,201 3,051,570 0.98 0.98 1.55
2019 2013 38,718 8,286,002 0.048 0.090 1,193,803,786 1,193,765,068 1.00 1.00 1.57
2020 2014 23,053 3,630,434 0.023 0.168 63,823 40,771 0.64 0.64 1.06
2021 2015 38,864 1,871,660 0.024 0.163 10,550 28,315 2.68 -2.68 0.63
2022 2016 NA 6,221,196 0.025 0.156 805,040 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 54,919 518,041 0.158 0.010 19,327 35,592 1.84 -1.84 0.58
2014 2008 142,193 492,546 0.158 0.010 17,940 124,254 6.93 -6.93 0.72
2015 2009 25,693 484,149 0.155 0.009 18,340 7,352 0.40 -0.40 0.28
2016 2010 16,030 468,696 0.155 0.008 17,324 1,294 0.07 0.07 0.08
2017 2011 103,138 428,191 0.156 0.007 14,377 88,760 6.17 -6.17 0.71
2018 2012 70,631 432,438 0.151 0.008 15,503 55,128 3.56 -3.56 0.66
2019 2013 38,718 894,148 0.148 0.008 68,656 29,938 0.44 0.44 0.66
2020 2014 23,053 618,477 0.148 0.007 32,423 9,370 0.29 0.29 0.39
2021 2015 38,864 796,684 0.148 0.006 52,966 14,102 0.27 0.27 0.35
2022 2016 NA 680,512 0.149 0.006 38,489 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 54,919 518,041 -0.023 0.641 21,809 33,110 1.52 -1.52 0.54
2014 2008 142,193 492,546 -0.022 0.626 21,557 120,636 5.60 -5.60 0.70
2015 2009 25,693 484,149 -0.020 0.601 22,496 3,197 0.14 -0.14 0.12
2016 2010 16,030 468,696 -0.020 0.593 22,024 5,994 0.27 0.27 0.36
2017 2011 103,138 428,191 -0.019 0.592 20,322 82,815 4.08 -4.08 0.68
2018 2012 70,631 432,438 -0.017 0.563 21,476 49,155 2.29 -2.29 0.61
2019 2013 38,718 894,148 -0.016 0.541 36,050 2,667 0.07 -0.07 0.07
2020 2014 23,053 618,477 -0.015 0.536 28,861 5,808 0.20 0.20 0.25
2021 2015 38,864 796,684 -0.015 0.531 33,696 5,168 0.15 -0.15 0.13
2022 2016 NA 680,512 -0.014 0.527 30,684 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2013 2007 54,919.10 99,088 44,169 0.45 0.45 0.68
2014 2008 142,193.49 96,408 45,786 0.47 -0.47 0.31
2015 2009 25,692.75 81,559 55,866 0.68 0.68 1.14
2016 2010 16,030.00 70,822 54,792 0.77 0.77 1.29
2017 2011 103,137.54 66,608 36,530 0.55 -0.55 0.34
2018 2012 70,631.02 68,395 2,236 0.03 -0.03 0.03
2019 2013 38,717.89 71,537 32,819 0.46 0.46 0.70
2020 2014 23,052.63 50,842 27,789 0.55 0.55 0.88
2021 2015 38,864.44 50,314 11,449 0.23 0.23 0.29
2022 2016 NA 54,881 NA NA NA NA

Performance summary

lnS.lnR, ricker and average models perform best but ricker is not significant. Blending the other two gives us a forecast of ~0.05 million fish.

model range MAD MAPE MPE MAAPE
sibling 5 years 97,050 56.49% 56.49% 0.92
sibling 3 years 120,198 71.89% 71.89% 1.17
ln.sibling 5 years 699,170 64.85% 50.72% 0.97
ln.sibling 3 years 986,274 67.03% 67.03% 1.05
lnY.sibling 5 years 239,391,928 156.60% -51.95% 1.09
lnY.sibling 3 years 397,944,718 144.09% -34.84% 1.09
lnS.lnR 5 years 39,459 214.41% -174.76% 0.55
lnS.lnR 3 years 17,803 33.04% 33.04% 0.46
ricker 5 years 29,123 135.85% -127.80% 0.35
ricker 3 years 4,548 14.29% -0.87% 0.15
average 5 years 22,165 36.28% 13.04% 0.45
average 3 years 24,019 41.10% 41.10% 0.62

Forecast summary

A preliminary look at the models for this river leads us to an initial forecast of ~18.6 million broken down as follows:

Table 2. Preliminary Forecast.

age forecast
1.2 3.10
2.2 0.06
1.3 15.30
2.3 0.05
1.4 0.05