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
2012 2008 163,553 492,546 -0.024 0.615 118,836 44,717 0.38 -0.38 0.27
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 1,722,458 680,512 -0.025 0.902 144,625 1,577,833 10.91 -10.91 0.74
2021 2017 NA 2,852,308 -0.025 0.974 150,917 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 163,553 492,546 0.333 0.000 114,486 49,067 0.43 -0.43 0.29
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 1,722,458 680,512 0.222 0.001 163,368 1,559,091 9.54 -9.54 0.74
2021 2017 NA 2,852,308 0.200 0.002 65,489 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2012 2008 163,553.37 215,599 52,046 0.24 0.24 0.31
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 1,722,458.39 1,181,809 540,650 0.46 -0.46 0.30
2021 2017 NA 1,484,941 NA NA NA NA

Performance summary

The two credible models (5-year average, ricker) produce a forecast of 858,000.

model range MAD MAPE MPE MAAPE
sibling 5 years 1,112,687 406.01% -401.92% 0.51
sibling 3 years 624,964 127.40% -120.58% 0.40
ln.sibling 5 years 1,259,456 684.20% -684.20% 0.63
ln.sibling 3 years 829,757 290.75% -290.75% 0.58
lnY.sibling 5 years 1,277,228 724.08% -724.08% 0.64
lnY.sibling 3 years 859,696 353.78% -353.78% 0.60
lnS.lnR 5 years 1,354,574 1115.56% -1115.56% 0.70
lnS.lnR 3 years 978,892 700.70% -700.70% 0.70
ricker 5 years 1,339,149 915.40% -915.40% 0.69
ricker 3 years 959,349 609.38% -609.38% 0.68
average 5 years 1,013,307 363.80% -341.81% 0.55
average 3 years 455,213 41.16% -4.51% 0.46

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
2012 2007 0 518,041 0.012 0.246 2,987 2,987 1.00 1.00 1.57
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 9,896 796,684 0.006 0.267 1,966 7,929 4.03 -4.03 0.68
2021 2016 NA 680,512 0.005 0.278 2,400 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 0 518,041 -0.020 0.568 2,975 2,975 1.00 1.00 1.57
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 9,896 796,684 -0.016 0.575 3,850 6,045 1.57 -1.57 0.55
2021 2016 NA 680,512 -0.016 0.577 3,611 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2012 2007 0.000 10,017 10,017 1.00 1.00 1.57
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 9,895.501 27,482 17,587 0.64 0.64 1.06
2021 2016 NA 29,041 NA NA NA NA

Performance summary

No regressions are significant so we take a 5-year moving average forecast of 29,000.

model range MAD MAPE MPE MAAPE
sibling 5 years 23,576 92.06% -29.83% 0.76
sibling 3 years 21,065 83.66% -39.00% 0.62
ln.sibling 5 years 28,980 58135.43% -58135.43% 0.78
ln.sibling 3 years 29,731 58247.97% -58247.97% 0.78
lnY.sibling 5 years 28,889 1639914236.45% -1639914236.45% 0.78
lnY.sibling 3 years 29,572 2733034533.37% -2733034533.37% 0.78
lnS.lnR 5 years 26,698 1129.77% -1129.77% 0.61
lnS.lnR 3 years 27,876 1322.87% -1322.87% 0.72
ricker 5 years 26,060 965.31% -965.31% 0.61
ricker 3 years 26,257 816.37% -816.37% 0.65
average 5 years 23,570 410.10% -383.99% 0.50
average 3 years 22,772 132.15% -89.49% 0.58

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
2012 2007 750,292 30,883 0.292 0.001 762,655 12,364 0.02 0.02 0.02
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 1,894,955 504,880 0.634 0.000 2,176,603 281,648 0.13 0.13 0.15
2021 2016 NA 1,722,458 0.634 0.000 4,831,224 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 750,292 30,883 0.275 0.001 560,493 189,798 0.34 -0.34 0.25
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 1,894,955 504,880 0.467 0.000 2,375,554 480,599 0.20 0.20 0.25
2021 2016 NA 1,722,458 0.470 0.000 4,427,136 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 750,292 30,883 0.272 0.001 695,748 54,543 0.08 -0.08 0.07
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 1,894,955 504,880 0.279 0.000 1,445,692 449,263 0.31 -0.31 0.23
2021 2016 NA 1,722,458 0.282 0.000 3,744,351 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 750,292 518,041 0.015 0.235 1,104,937 354,646 0.32 0.32 0.44
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 1,894,955 796,684 0.008 0.258 1,106,961 787,994 0.71 -0.71 0.39
2021 2016 NA 680,512 0.005 0.280 1,187,608 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 750,292 518,041 0.400 0 1,056,600 306,309 0.29 0.29 0.39
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 1,894,955 796,684 0.337 0 1,411,815 483,140 0.34 -0.34 0.25
2021 2016 NA 680,512 0.336 0 1,382,591 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2012 2007 750,291.5 1,354,561 604,270 0.45 0.45 0.68
2013 2008 1,834,254.1 1,151,918 682,336 0.59 -0.59 0.36
2014 2009 1,139,868.4 1,210,244 70,376 0.06 0.06 0.06
2015 2010 2,223,152.7 1,143,393 1,079,760 0.94 -0.94 0.45
2016 2011 2,060,681.7 1,392,956 667,726 0.48 -0.48 0.31
2017 2012 4,407,859.5 1,601,650 2,806,210 1.75 -1.75 0.57
2018 2013 8,286,002.1 2,333,163 5,952,839 2.55 -2.55 0.62
2019 2014 3,630,434.4 3,623,513 6,921 0.00 0.00 0.00
2020 2015 1,894,954.9 4,121,626 2,226,671 0.54 0.54 0.87
2021 2016 NA 4,055,987 NA NA NA NA

Performance summary

Two possible basket of models seem equally plausible. Both [lnY.sibling + sibling + ln.sibling] or [sibling + ln.sibling]. Both give a forecast of 4.1m. Really shouldn’t be using lnY.sibling since there is one datapoint that is clearly driving that relationship.

model range MAD MAPE MPE MAAPE
sibling 5 years 2,578,811 32.49% -5.08% 0.33
sibling 3 years 3,587,729 23.83% 21.86% 0.36
ln.sibling 5 years 1,147,647 43.59% -35.50% 0.26
ln.sibling 3 years 913,528 19.28% -5.79% 0.17
lnY.sibling 5 years 8,970,397,820 64.67% -24.67% 0.58
lnY.sibling 3 years 14,949,829,698 64.32% 2.33% 0.72
lnS.lnR 5 years 2,919,717 278.41% -278.41% 0.54
lnS.lnR 3 years 3,532,427 356.50% -356.50% 0.57
ricker 5 years 2,845,058 235.76% -235.76% 0.53
ricker 3 years 3,261,166 247.92% -247.92% 0.51
average 5 years 2,332,073 106.50% -84.89% 0.47
average 3 years 2,728,811 103.12% -67.10% 0.50

age.23

Below are model outputs using data from 1972

sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2006 7,390 5,282 0.291 0.001 21,498 14,108 0.66 0.66 1.09
2013 2007 6,508 0 0.294 0.000 18,173 11,664 0.64 0.64 1.06
2014 2008 12,279 4,818 0.297 0.000 20,403 8,124 0.40 0.40 0.58
2015 2009 0 4,713 0.300 0.000 20,095 20,095 1.00 1.00 1.57
2016 2010 3,717 2,101 0.303 0.000 18,061 14,344 0.79 0.79 1.32
2017 2011 36,731 3,339 0.306 0.000 18,314 18,416 1.01 -1.01 0.46
2018 2012 97,089 52,482 0.304 0.000 45,744 51,345 1.12 -1.12 0.49
2019 2013 59,617 13,702 0.305 0.000 25,667 33,950 1.32 -1.32 0.52
2020 2014 13,646 65,787 0.302 0.000 55,203 41,557 0.75 0.75 1.25
2021 2015 NA 9,896 0.294 0.000 23,617 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 7,390 5,282 0.029 0.167 2,351 5,039 2.14 -2.14 0.60
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 13,646 65,787 0.011 0.235 5,428 8,219 1.51 -1.51 0.54
2021 2015 NA 9,896 0.013 0.219 2,395 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 7,390 5,282 0.009 0.263 902 6,488 7.19 -7.19 0.72
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 13,646 65,787 0.011 0.236 2,995 10,651 3.56 -3.56 0.66
2021 2015 NA 9,896 0.012 0.223 844 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 7,390 548,410 -0.001 0.330 7,875 485 0.06 0.06 0.07
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 13,646 618,477 -0.006 0.395 6,647 6,999 1.05 -1.05 0.47
2021 2015 NA 796,684 -0.006 0.394 5,717 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 7,390 548,410 -0.008 0.401 8,844 1,454 0.16 0.16 0.19
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 13,646 618,477 -0.011 0.457 8,523 5,123 0.60 -0.60 0.36
2021 2015 NA 796,684 -0.010 0.450 9,747 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2012 2006 7,389.681 18,549 11,159 0.60 0.60 0.99
2013 2007 6,508.400 15,185 8,677 0.57 0.57 0.93
2014 2008 12,278.890 14,513 2,234 0.15 0.15 0.18
2015 2009 0.000 12,517 12,517 1.00 1.00 1.57
2016 2010 3,717.370 9,418 5,701 0.61 0.61 0.99
2017 2011 36,730.580 5,979 30,752 5.14 -5.14 0.70
2018 2012 97,089.270 11,847 85,242 7.20 -7.20 0.72
2019 2013 59,616.887 29,963 29,654 0.99 -0.99 0.46
2020 2014 13,646.131 39,431 25,785 0.65 0.65 1.08
2021 2015 NA 42,160 NA NA NA NA

Performance summary

The only statistically viable option (sibling) gives us a forecast of 23,000.

model range MAD MAPE MPE MAAPE
sibling 5 years 31,923 99.96% -38.08% 0.81
sibling 3 years 42,284 106.60% -56.41% 0.75
ln.sibling 5 years 39,414 1683.31% -1683.31% 0.70
ln.sibling 3 years 52,875 1635.06% -1635.06% 0.69
lnY.sibling 5 years 40,846 4152.45% -4152.45% 0.74
lnY.sibling 3 years 54,919 4327.91% -4327.91% 0.74
lnS.lnR 5 years 36,829 582.48% -563.90% 0.67
lnS.lnR 3 years 50,486 820.14% -820.14% 0.65
ricker 5 years 35,930 531.60% -515.61% 0.62
ricker 3 years 48,726 692.40% -692.40% 0.60
average 5 years 35,427 291.75% -241.38% 0.79
average 3 years 46,894 294.63% -251.03% 0.76

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
2012 2006 94,203 1,017,214 0.188 0.006 71,480 22,723 0.32 -0.32 0.24
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 23,339 3,630,434 0.026 0.158 103,667 80,328 0.77 0.77 1.29
2021 2015 NA 1,894,955 0.014 0.212 81,017 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 94,203 1,017,214 0.355 0 10,373 83,829 8.08 -8.08 0.73
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 23,339 3,630,434 0.353 0 255,798 232,459 0.91 0.91 1.47
2021 2015 NA 1,894,955 0.351 0 45,332 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 94,203 1,017,214 0.047 0.114 2,869 91,334 31.83 -31.83 0.77
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 23,339 3,630,434 0.023 0.168 63,823 40,484 0.63 0.63 1.05
2021 2015 NA 1,894,955 0.024 0.163 10,799 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 94,203 548,410 0.158 0.011 20,813 73,390 3.53 -3.53 0.66
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 23,339 618,477 0.148 0.007 32,423 9,084 0.28 0.28 0.37
2021 2015 NA 796,684 0.148 0.006 52,983 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 94,203 548,410 -0.025 0.657 21,809 72,394 3.32 -3.32 0.66
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 23,339 618,477 -0.015 0.536 28,861 5,522 0.19 0.19 0.23
2021 2015 NA 796,684 -0.015 0.531 33,706 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2012 2006 94,202.80 131,754 37,551 0.29 0.29 0.38
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 23,338.92 50,842 27,503 0.54 0.54 0.87
2021 2015 NA 50,371 NA NA NA NA

Performance summary

Three models perform reasonably: lnS.lnR, ricker, and average. The ricker relationship is unconvincing. A basket of the remaining two models forecasts 52,000.

model range MAD MAPE MPE MAAPE
sibling 5 years 108,949 63.33% 63.33% 1.04
sibling 3 years 146,361 75.53% 75.53% 1.25
ln.sibling 5 years 714,755 79.30% 65.17% 1.22
ln.sibling 3 years 1,154,528 92.44% 92.44% 1.49
lnY.sibling 5 years 239,391,389 115.18% 13.99% 1.16
lnY.sibling 3 years 398,952,374 87.06% 87.06% 1.39
lnS.lnR 5 years 36,841 210.41% -178.77% 0.50
lnS.lnR 3 years 31,383 142.40% -94.65% 0.56
ricker 5 years 29,231 138.03% -119.49% 0.39
ricker 3 years 19,115 85.14% -72.38% 0.30
average 5 years 30,776 47.09% 23.84% 0.65
average 3 years 20,853 34.41% 32.23% 0.53