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
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 1,774,510 29,391 0.799 0.000 1,376,208 398,302 0.29 -0.29 0.22
2021 2017 3,755,663 181,714 0.799 0.000 6,135,300 2,379,637 0.39 0.39 0.56
2022 2018 NA 297,033 0.778 0.000 8,936,926 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 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 1,774,510 29,391 0.409 0 1,174,460 600,050 0.51 -0.51 0.33
2021 2017 3,755,663 181,714 0.420 0 1,769,750 1,985,913 1.12 -1.12 0.49
2022 2018 NA 297,033 0.443 0 2,075,070 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 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 1,774,510 29,391 0.245 0.000 519,452 1,255,058 2.42 -2.42 0.62
2021 2017 3,755,663 181,714 0.244 0.000 4,377,506 621,843 0.14 0.14 0.16
2022 2018 NA 297,033 0.282 0.000 20,427,361 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 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 1,774,510 1,837,260 -0.004 0.361 560,844 1,213,666 2.16 -2.16 0.60
2021 2017 3,755,663 2,600,982 0.004 0.284 736,208 3,019,455 4.10 -4.10 0.68
2022 2018 NA 1,608,357 0.026 0.148 600,151 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 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 1,774,510 1,837,260 -0.005 0.380 542,850 1,231,661 2.27 -2.27 0.61
2021 2017 3,755,663 2,600,982 -0.010 0.458 632,001 3,123,662 4.94 -4.94 0.69
2022 2018 NA 1,608,357 -0.021 0.758 611,469 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
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 1,774,510.3 3,798,375 2,023,865 0.53 0.53 0.85
2021 2017 3,755,662.7 4,064,326 308,663 0.08 0.08 0.08
2022 2018 NA 4,419,956 NA NA NA NA

Performance summary

The sibling model looks best here giving us a forecast of ~7.9 million. This is the largest believable forecast option. Dropping the largest model (lnY.sibling) shaves ~2 million from this forecast.

model range MAD MAPE MPE MAAPE
sibling 5 years 2,439,416 47.96% -9.37% 0.43
sibling 3 years 2,980,856 60.71% -34.85% 0.43
ln.sibling 5 years 2,995,228 193.57% -193.57% 0.48
ln.sibling 3 years 4,172,962 258.75% -258.75% 0.51
lnY.sibling 5 years 167,088,961 88.44% -9.92% 0.75
lnY.sibling 3 years 18,750,658 112.76% -48.31% 0.71
lnS.lnR 5 years 3,911,488 820.28% -820.28% 0.69
lnS.lnR 3 years 5,106,710 1001.18% -1001.18% 0.68
ricker 5 years 3,946,806 947.16% -947.16% 0.69
ricker 3 years 5,177,854 1233.48% -1233.48% 0.69
average 5 years 3,060,620 205.66% -181.31% 0.54
average 3 years 4,096,932 228.39% -187.80% 0.55

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
2013 2008 1,104,563 58,244 0.330 0.000 4,371,812 3,267,248 0.75 0.75 1.24
2014 2009 2,761,971 122,169 0.304 0.000 6,835,047 4,073,076 0.60 0.60 0.97
2015 2010 5,985,044 274,064 0.248 0.001 11,509,128 5,524,084 0.48 0.48 0.75
2016 2011 3,901,938 532,979 0.204 0.003 14,751,053 10,849,116 0.74 0.74 1.23
2017 2012 4,775,925 353,152 0.057 0.077 5,887,732 1,111,807 0.19 0.19 0.23
2018 2013 467,780 88,059 0.059 0.071 3,750,029 3,282,249 0.88 0.88 1.43
2019 2014 1,280,264 73,755 0.053 0.079 3,566,920 2,286,656 0.64 0.64 1.06
2020 2015 993,181 66,999 0.052 0.079 3,465,241 2,472,060 0.71 0.71 1.19
2021 2016 2,173,717 168,097 0.051 0.078 4,113,344 1,939,628 0.47 0.47 0.73
2022 2017 NA 370,147 0.044 0.093 5,348,587 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 1,104,563 58,244 0.323 0.000 3,840,433 2,735,870 0.71 0.71 1.19
2014 2009 2,761,971 122,169 0.282 0.001 4,702,994 1,941,024 0.41 0.41 0.61
2015 2010 5,985,044 274,064 0.271 0.001 5,925,300 59,743 0.01 -0.01 0.01
2016 2011 3,901,938 532,979 0.291 0.000 7,398,007 3,496,070 0.47 0.47 0.73
2017 2012 4,775,925 353,152 0.281 0.000 5,967,170 1,191,245 0.20 0.20 0.24
2018 2013 467,780 88,059 0.289 0.000 3,840,225 3,372,446 0.88 0.88 1.43
2019 2014 1,280,264 73,755 0.212 0.001 3,375,552 2,095,287 0.62 0.62 1.02
2020 2015 993,181 66,999 0.194 0.002 3,187,315 2,194,135 0.69 0.69 1.15
2021 2016 2,173,717 168,097 0.173 0.003 3,891,135 1,717,419 0.44 0.44 0.67
2022 2017 NA 370,147 0.163 0.004 4,576,331 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 1,104,563 58,244 0.231 0.002 3,291,218 2,186,655 0.66 0.66 1.10
2014 2009 2,761,971 122,169 0.207 0.003 6,233,166 3,471,195 0.56 0.56 0.90
2015 2010 5,985,044 274,064 0.184 0.005 23,282,457 17,297,414 0.74 0.74 1.24
2016 2011 3,901,938 532,979 0.168 0.006 65,834,149 61,932,211 0.94 0.94 1.51
2017 2012 4,775,925 353,152 0.070 0.056 5,875,414 1,099,489 0.19 0.19 0.23
2018 2013 467,780 88,059 0.081 0.041 2,880,960 2,413,180 0.84 0.84 1.38
2019 2014 1,280,264 73,755 0.064 0.060 2,657,356 1,377,092 0.52 0.52 0.82
2020 2015 993,181 66,999 0.063 0.060 2,568,996 1,575,815 0.61 0.61 1.01
2021 2016 2,173,717 168,097 0.061 0.061 3,212,118 1,038,401 0.32 0.32 0.45
2022 2017 NA 370,147 0.057 0.065 5,065,222 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 1,104,563 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 993,181 2,160,792 0.108 0.019 4,275,257 3,282,076 0.77 0.77 1.28
2021 2016 2,173,717 1,837,260 0.068 0.050 3,391,930 1,218,213 0.36 0.36 0.51
2022 2017 NA 2,600,982 0.063 0.056 4,137,500 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 1,104,563 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 993,181 2,160,792 -0.019 0.621 4,204,956 3,211,775 0.76 0.76 1.27
2021 2016 2,173,717 1,837,260 0.002 0.299 3,322,252 1,148,536 0.35 0.35 0.49
2022 2017 NA 2,600,982 0.009 0.245 3,608,755 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
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 993,180.7 3,282,190 2,289,009 0.70 0.70 1.16
2021 2016 2,173,716.8 2,283,818 110,101 0.05 0.05 0.05
2022 2017 NA 1,938,173 NA NA NA NA

Performance summary

The lnY.sibling and the average model looks to be the best of a poor lot here suggesting a forecast of ~3.5 million.

model range MAD MAPE MPE MAAPE
sibling 5 years 2,218,480 57.80% 57.80% 0.93
sibling 3 years 2,232,781 60.87% 60.87% 0.99
ln.sibling 5 years 2,114,106 56.57% 56.57% 0.90
ln.sibling 3 years 2,002,280 58.35% 58.35% 0.95
lnY.sibling 5 years 1,500,795 49.59% 49.59% 0.78
lnY.sibling 3 years 1,330,436 48.50% 48.50% 0.76
lnS.lnR 5 years 2,074,839 64.17% 37.00% 0.89
lnS.lnR 3 years 2,087,823 56.87% 56.87% 0.91
ricker 5 years 2,052,144 63.56% 37.17% 0.89
ricker 3 years 2,050,508 56.42% 56.42% 0.90
average 5 years 1,857,095 53.11% 37.35% 0.80
average 3 years 1,565,792 46.26% 46.26% 0.76

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
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 12,280,096 11,553,434 0.537 0 12,462,803 182,708 0.01 0.01 0.01
2021 2016 466,899 1,774,510 0.864 0 2,258,270 1,791,371 0.79 0.79 1.32
2022 2017 NA 3,755,663 0.846 0 4,228,674 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 1,090,637 630,133 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 12,280,096 11,553,434 0.728 0 8,361,073 3,919,022 0.47 -0.47 0.31
2021 2016 466,899 1,774,510 0.762 0 2,218,250 1,751,351 0.79 0.79 1.31
2022 2017 NA 3,755,663 0.723 0 3,535,492 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 1,090,637 630,133 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 12,280,096 11,553,434 0.509 0 48,015,539,350 48,003,259,254 1.00 1.00 1.57
2021 2016 466,899 1,774,510 0.362 0 1,075,426 608,527 0.57 0.57 0.92
2022 2017 NA 3,755,663 0.353 0 2,294,748 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 1,090,637 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 12,280,096 2,160,792 -0.008 0.419 946,440 11,333,656 11.98 -11.98 0.75
2021 2016 466,899 1,837,260 0.019 0.185 1,057,870 590,971 0.56 0.56 0.90
2022 2017 NA 2,600,982 0.013 0.216 1,241,703 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 1,090,637 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 12,280,096 2,160,792 0.033 0.128 789,432 11,490,663 14.56 -14.56 0.75
2021 2016 466,899 1,837,260 -0.007 0.408 1,025,136 558,237 0.54 0.54 0.87
2022 2017 NA 2,600,982 -0.001 0.331 1,039,829 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
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 12,280,095.5 1,399,480 10,880,616 7.77 -7.77 0.73
2021 2016 466,899.2 3,721,158 3,254,259 0.87 0.87 1.43
2022 2017 NA 3,595,390 NA NA NA NA

Performance summary

The sibling and ln.sibling look most attractive here. Weighting with proportional MAAPE gives us a mixed model forecast of ~3.5 million.

model range MAD MAPE MPE MAAPE
sibling 5 years 1,293,910 43.26% 43.26% 0.68
sibling 3 years 904,567 35.91% 35.91% 0.56
ln.sibling 5 years 1,747,671 47.15% 28.40% 0.65
ln.sibling 3 years 2,059,541 48.68% 17.43% 0.62
lnY.sibling 5 years 9,603,087,704 68.30% 68.30% 1.09
lnY.sibling 3 years 16,001,705,267 64.97% 64.97% 1.01
lnS.lnR 5 years 2,992,540 333.68% -311.33% 0.64
lnS.lnR 3 years 4,385,020 470.68% -433.43% 0.73
ricker 5 years 3,000,464 379.67% -357.89% 0.62
ricker 3 years 4,420,842 554.40% -518.09% 0.72
average 5 years 3,317,711 225.51% -190.53% 0.69
average 3 years 5,014,928 315.98% -257.68% 0.86

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
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 198,214 1,280,264 0.523 0 1,056,121 857,907 0.81 0.81 1.34
2021 2015 662,088 993,181 0.532 0 847,059 184,970 0.22 0.22 0.27
2022 2016 NA 2,173,717 0.539 0 1,554,004 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 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 198,214 1,280,264 0.527 0 1,080,397 882,183 0.82 0.82 1.35
2021 2015 662,088 993,181 0.507 0 838,355 176,267 0.21 0.21 0.26
2022 2016 NA 2,173,717 0.519 0 1,471,826 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 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 198,214 1,280,264 0.523 0 1,070,109 871,895 0.81 0.81 1.35
2021 2015 662,088 993,181 0.504 0 932,245 270,157 0.29 0.29 0.39
2022 2016 NA 2,173,717 0.515 0 1,218,339 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 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 198,214 1,382,466 0.125 0.013 2,037,641 1,839,427 0.90 0.90 1.46
2021 2015 662,088 2,160,792 0.081 0.038 2,647,365 1,985,277 0.75 0.75 1.25
2022 2016 NA 1,837,260 0.048 0.085 2,138,333 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 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 198,214 1,382,466 -0.020 0.659 2,071,519 1,873,305 0.90 0.90 1.47
2021 2015 662,088 2,160,792 -0.017 0.586 2,689,084 2,026,996 0.75 0.75 1.26
2022 2016 NA 1,837,260 0.004 0.288 2,144,633 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
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 198,213.8 1,607,952 1,409,738 0.88 0.88 1.43
2021 2015 662,088.1 1,490,412 828,324 0.56 0.56 0.90
2022 2016 NA 1,153,713 NA NA NA NA

Performance summary

Blending all The sibling models and the average gives us a forecast of ~1.4 million.

model range MAD MAPE MPE MAAPE
sibling 5 years 761,120 40.90% 31.69% 0.61
sibling 3 years 374,264 38.98% 38.98% 0.59
ln.sibling 5 years 727,086 41.90% 26.50% 0.59
ln.sibling 3 years 370,475 37.44% 37.44% 0.57
lnY.sibling 5 years 831,135 55.39% 28.45% 0.73
lnY.sibling 3 years 524,315 52.32% 52.32% 0.82
lnS.lnR 5 years 1,524,604 77.95% 33.50% 1.00
lnS.lnR 3 years 1,698,053 79.06% 79.06% 1.30
ricker 5 years 1,548,197 78.30% 33.76% 1.01
ricker 3 years 1,728,442 79.32% 79.32% 1.31
average 5 years 1,191,650 72.66% 29.76% 0.92
average 3 years 1,146,599 71.35% 71.35% 1.17

Forecast summary

A preliminary look at the models for this river leads us to an initial forecast of ~16.4 million broken down as follows:

Table 2. Preliminary Forecast.

age forecast
1.2 8.0
2.2 3.5
1.3 3.5
2.3 1.4