Overview

Six models are used to forecast each major age class of sockeye salmon in the major rivers of Bristol Bay. Five of these models are linear regressions and the sixth is a 5-year running average of the age class under consideration.

Forecast models

This document covers output from five linnear regression models run against four major age classes in this river. Three regressions are variations of the sibling relationship with the age being forecast (Table 1). The first regression (sibling) uses observed forecast age and the brood year younger sibling return. The second regression (ln.sibling) uses a natural log transformation of both the forecasted age and the sibling return. The third regression (lnY.sibling) uses the sibling age return and a natural log transformation of the forecasted age. Two linnear regression models based on forecasted age return and total spawning escapment. The first of these (lnS.lnR) is the natural log of the forecasted age class regressed against the natural log of the spawning escapement. The second forecast method that relies on the relationship between the forecasted age and the spawning escapement is a linnear transformation of the Ricker relationship.

Table 1. Forecast ages and the sibling age class used for forecasting.

Forecast Age Sibling
Age.12 Age.11
Age.22 Age.21
Age.13 Age.12
Age.23 Age.22

Output

Each model output consists of a table and two graphs. The table shows the most recent 10 years of observed returns for the age being forecast (‘Observed Return’) and the relevant sibling return (‘Sibling Return’) shown in bold black text. Brood and return years are shown in blue text. Two regression model statistics (R-squared and P-value of the slope) are shown in red. Model forecasted returns are shown in bold black text with a yellow highlight. Error measurements are shown in green text. Error measurements shown are absolute deviation (AD), absolute percent error (APE), percent error (PE) and arc tan percent error (AAPE).

After the table summarizing the model output for the most recenet ten years, two graphs are shown for each of the linnear regression models. The first graph is a scatter plot of the data with a linnear regression superimposed. The second graph is a plot of the residuals of the regression analysis.

Absolute deviation (AD) is defined as

\[\ AD = O - F\] where

O = Observed Return

F = Forecasted Return

Percent error (PE) is defined as

\[\ PE = (F - O)/O\] Absolute Percent error (APE) is defined as

\[\ APE = |(F - O)/O|\]

Arctangent percent error (AAPE) is defined (Kim and Kim, 2016) as \[\ AAPE = arctan(|((O - F)/O)|)\]

At the end of the model output section for each age class, a performance table is presented that contains the mean absolute deviation (MAD), neam absolute percent error (MAPE), mean percent error (MPE) and mean arctanget percent error (MAAPE). These performance metrics are calculated and presented across the most recent three and five years. Color bars show the relative size of each metric.

age.12

Below are model outputs using data from 1972

sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2013 2009 88,287 328 0.036 0.135 144,288 56,001 0.39 0.39 0.57
2014 2010 130,232 0 0.035 0.135 130,363 131 0.00 0.00 0.00
2015 2011 166,292 1,478 0.036 0.129 186,310 20,018 0.11 0.11 0.12
2016 2012 176,979 1,219 0.038 0.120 174,234 2,745 0.02 -0.02 0.02
2017 2013 298,803 671 0.043 0.102 154,646 144,157 0.93 -0.93 0.45
2018 2014 583,074 1,149 0.053 0.078 178,605 404,469 2.26 -2.26 0.61
2019 2015 292,933 841 0.098 0.023 187,552 105,381 0.56 -0.56 0.35
2020 2016 191,935 202 0.111 0.016 149,397 42,538 0.28 -0.28 0.22
2021 2017 483,443 4,517 0.110 0.015 434,963 48,480 0.11 -0.11 0.10
2022 2018 NA 197 0.259 0.000 149,737 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 88,287 328 0.124 0.019 153,832 65,545 0.43 0.43 0.64
2014 2010 130,232 0 0.110 0.024 92,022 38,210 0.42 -0.42 0.29
2015 2011 166,292 1,478 0.105 0.025 168,292 2,000 0.01 0.01 0.01
2016 2012 176,979 1,219 0.113 0.019 165,535 11,444 0.07 -0.07 0.06
2017 2013 298,803 671 0.122 0.014 158,491 140,312 0.89 -0.89 0.44
2018 2014 583,074 1,149 0.143 0.008 172,336 410,738 2.38 -2.38 0.61
2019 2015 292,933 841 0.176 0.003 180,748 112,185 0.62 -0.62 0.37
2020 2016 191,935 202 0.194 0.002 160,260 31,675 0.20 -0.20 0.16
2021 2017 483,443 4,517 0.199 0.001 222,844 260,599 1.17 -1.17 0.49
2022 2018 NA 197 0.235 0.000 166,652 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 88,287 328 0.044 0.112 117,570 29,283 0.25 0.25 0.32
2014 2010 130,232 0 0.044 0.110 104,831 25,401 0.24 -0.24 0.19
2015 2011 166,292 1,478 0.043 0.109 169,756 3,464 0.02 0.02 0.02
2016 2012 176,979 1,219 0.051 0.087 155,822 21,157 0.14 -0.14 0.12
2017 2013 298,803 671 0.060 0.066 131,610 167,193 1.27 -1.27 0.51
2018 2014 583,074 1,149 0.069 0.051 159,916 423,158 2.65 -2.65 0.63
2019 2015 292,933 841 0.103 0.020 153,683 139,250 0.91 -0.91 0.44
2020 2016 191,935 202 0.115 0.014 118,706 73,229 0.62 -0.62 0.36
2021 2017 483,443 4,517 0.112 0.014 803,124 319,681 0.40 0.40 0.58
2022 2018 NA 197 0.172 0.002 120,180 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 88,287 313,946 -0.024 0.694 108,122 19,835 0.18 0.18 0.22
2014 2010 130,232 188,298 -0.022 0.645 114,552 15,680 0.14 -0.14 0.12
2015 2011 166,292 190,970 -0.021 0.637 114,717 51,575 0.45 -0.45 0.30
2016 2012 176,979 203,148 -0.020 0.625 114,791 62,188 0.54 -0.54 0.34
2017 2013 298,803 128,118 -0.019 0.624 123,844 174,959 1.41 -1.41 0.53
2018 2014 583,074 151,934 -0.011 0.465 125,726 457,348 3.64 -3.64 0.67
2019 2015 292,933 218,700 -0.003 0.350 119,872 173,061 1.44 -1.44 0.53
2020 2016 191,935 200,046 -0.005 0.379 125,434 66,501 0.53 -0.53 0.33
2021 2017 483,443 190,098 -0.005 0.377 128,339 355,104 2.77 -2.77 0.63
2022 2018 NA 511,770 -0.004 0.373 100,861 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 88,287 313,946 0.285 0 106,293 18,006 0.17 0.17 0.20
2014 2010 130,232 188,298 0.299 0 123,300 6,932 0.06 -0.06 0.05
2015 2011 166,292 190,970 0.300 0 123,468 42,824 0.35 -0.35 0.25
2016 2012 176,979 203,148 0.302 0 124,024 52,955 0.43 -0.43 0.29
2017 2013 298,803 128,118 0.302 0 118,218 180,585 1.53 -1.53 0.54
2018 2014 583,074 151,934 0.321 0 128,230 454,844 3.55 -3.55 0.66
2019 2015 292,933 218,700 0.322 0 130,682 162,251 1.24 -1.24 0.51
2020 2016 191,935 200,046 0.314 0 136,089 55,846 0.41 -0.41 0.28
2021 2017 483,443 190,098 0.314 0 138,317 345,126 2.50 -2.50 0.62
2022 2018 NA 511,770 0.306 0 54,457 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2013 2009 88,287 171,720 83,433 0.49 0.49 0.76
2014 2010 130,232 168,118 37,886 0.23 0.23 0.28
2015 2011 166,292 133,689 32,603 0.24 -0.24 0.19
2016 2012 176,979 134,807 42,172 0.31 -0.31 0.23
2017 2013 298,803 137,456 161,347 1.17 -1.17 0.50
2018 2014 583,074 172,119 410,955 2.39 -2.39 0.61
2019 2015 292,933 271,076 21,857 0.08 -0.08 0.07
2020 2016 191,935 303,616 111,681 0.37 0.37 0.53
2021 2017 483,443 308,745 174,698 0.57 -0.57 0.35
2022 2018 NA 370,038 NA NA NA NA

Performance summary

The average model performs best here and gives us a forecast of ~0.37 million fish.

model range MAD MAPE MPE MAAPE
sibling 5 years 149,005 83.10% -83.10% 0.34
sibling 3 years 65,466 31.94% -31.94% 0.22
ln.sibling 5 years 191,102 105.13% -105.13% 0.42
ln.sibling 3 years 134,820 66.26% -66.26% 0.34
lnY.sibling 5 years 224,502 116.75% -100.83% 0.51
lnY.sibling 3 years 177,387 64.03% -37.50% 0.46
lnS.lnR 5 years 245,395 195.82% -195.82% 0.54
lnS.lnR 3 years 198,222 158.03% -158.03% 0.50
ricker 5 years 239,730 184.44% -184.44% 0.52
ricker 3 years 187,741 138.24% -138.24% 0.47
average 5 years 176,108 91.51% -76.80% 0.41
average 3 years 102,745 33.81% -9.29% 0.32

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 3,072 205,680 -0.018 0.537 25,858 22,786 0.88 0.88 1.44
2014 2009 25,841 313,946 -0.019 0.577 27,110 1,269 0.05 0.05 0.05
2015 2010 9,047 188,298 -0.018 0.570 23,848 14,801 0.62 0.62 1.02
2016 2011 16,663 190,970 -0.017 0.551 23,328 6,665 0.29 0.29 0.38
2017 2012 9,337 203,148 -0.016 0.541 23,504 14,167 0.60 0.60 0.99
2018 2013 4,547 128,118 -0.016 0.543 20,401 15,854 0.78 0.78 1.29
2019 2014 4,843 151,934 -0.005 0.378 19,940 15,097 0.76 0.76 1.26
2020 2015 3,175 218,700 0.002 0.305 22,252 19,077 0.86 0.86 1.41
2021 2016 1,791 200,046 -0.003 0.356 20,467 18,676 0.91 0.91 1.48
2022 2017 NA 190,098 -0.005 0.383 18,996 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 3,072 205,680 0.060 0.080 27,272 24,200 0.89 0.89 1.44
2014 2009 25,841 313,946 0.048 0.103 27,370 1,529 0.06 0.06 0.06
2015 2010 9,047 188,298 0.052 0.090 24,899 15,852 0.64 0.64 1.05
2016 2011 16,663 190,970 0.047 0.100 24,324 7,661 0.31 0.31 0.43
2017 2012 9,337 203,148 0.046 0.099 24,630 15,293 0.62 0.62 1.02
2018 2013 4,547 128,118 0.043 0.102 19,227 14,680 0.76 0.76 1.27
2019 2014 4,843 151,934 0.026 0.156 19,898 15,055 0.76 0.76 1.26
2020 2015 3,175 218,700 0.015 0.207 23,144 19,969 0.86 0.86 1.41
2021 2016 1,791 200,046 0.014 0.212 21,189 19,398 0.92 0.92 1.48
2022 2017 NA 190,098 0.008 0.252 19,496 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2013 2008 3,072 40,818 37,746 0.92 0.92 1.49
2014 2009 25,841 39,810 13,969 0.35 0.35 0.50
2015 2010 9,047 35,514 26,467 0.75 0.75 1.24
2016 2011 16,663 24,243 7,580 0.31 0.31 0.43
2017 2012 9,337 18,577 9,240 0.50 0.50 0.78
2018 2013 4,547 12,792 8,245 0.64 0.64 1.07
2019 2014 4,843 13,087 8,244 0.63 0.63 1.04
2020 2015 3,175 8,887 5,712 0.64 0.64 1.06
2021 2016 1,791 7,713 5,922 0.77 0.77 1.28
2022 2017 NA 4,739 NA NA NA NA

Performance summary

None of the models here seem compelling so we go with and average forecast of ~0.005 million fish.

model range MAD MAPE MPE MAAPE
sibling 5 years 31,443 86.73% 86.73% 1.41
sibling 3 years 33,156 90.77% 90.77% 1.47
ln.sibling 5 years 21,176 79.60% 79.60% 1.30
ln.sibling 3 years 24,635 86.10% 86.10% 1.40
lnY.sibling 5 years 39,380 80.20% 80.20% 1.31
lnY.sibling 3 years 54,975 87.11% 87.11% 1.41
lnS.lnR 5 years 16,574 78.14% 78.14% 1.28
lnS.lnR 3 years 17,617 84.23% 84.23% 1.38
ricker 5 years 16,879 78.39% 78.39% 1.29
ricker 3 years 18,141 84.50% 84.50% 1.38
average 5 years 7,473 63.65% 63.65% 1.05
average 3 years 6,626 68.02% 68.02% 1.13

age.13

Below are model outputs using data from 1972

sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2013 2008 469,887 125,488 0.306 0 427,193 42,694 0.10 -0.10 0.09
2014 2009 364,308 88,287 0.305 0 369,385 5,077 0.01 0.01 0.01
2015 2010 338,788 130,232 0.308 0 435,766 96,978 0.22 0.22 0.28
2016 2011 538,658 166,292 0.308 0 490,593 48,065 0.10 -0.10 0.09
2017 2012 357,182 176,979 0.311 0 508,962 151,780 0.30 0.30 0.40
2018 2013 756,364 298,803 0.303 0 696,373 59,991 0.09 -0.09 0.08
2019 2014 983,763 583,074 0.331 0 1,159,142 175,379 0.15 0.15 0.18
2020 2015 418,533 292,933 0.398 0 667,679 249,146 0.37 0.37 0.54
2021 2016 469,036 191,935 0.375 0 513,222 44,186 0.09 0.09 0.09
2022 2017 NA 483,443 0.374 0 914,701 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 469,887 125,488 0.423 0 410,370 59,517 0.15 -0.15 0.13
2014 2009 364,308 88,287 0.424 0 340,469 23,839 0.07 -0.07 0.07
2015 2010 338,788 130,232 0.424 0 420,959 82,171 0.20 0.20 0.24
2016 2011 538,658 166,292 0.421 0 477,471 61,187 0.13 -0.13 0.11
2017 2012 357,182 176,979 0.426 0 495,804 138,622 0.28 0.28 0.37
2018 2013 756,364 298,803 0.417 0 648,413 107,951 0.17 -0.17 0.14
2019 2014 983,763 583,074 0.436 0 941,193 42,570 0.05 -0.05 0.04
2020 2015 418,533 292,933 0.471 0 650,852 232,319 0.36 0.36 0.51
2021 2016 469,036 191,935 0.457 0 508,145 39,109 0.08 0.08 0.08
2022 2017 NA 483,443 0.457 0 824,192 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 469,887 125,488 0.329 0 366,149 103,738 0.28 -0.28 0.22
2014 2009 364,308 88,287 0.326 0 319,171 45,137 0.14 -0.14 0.12
2015 2010 338,788 130,232 0.326 0 376,953 38,165 0.10 0.10 0.11
2016 2011 538,658 166,292 0.326 0 432,001 106,657 0.25 -0.25 0.20
2017 2012 357,182 176,979 0.328 0 453,029 95,847 0.21 0.21 0.26
2018 2013 756,364 298,803 0.325 0 718,843 37,521 0.05 -0.05 0.05
2019 2014 983,763 583,074 0.348 0 2,173,242 1,189,479 0.55 0.55 0.88
2020 2015 418,533 292,933 0.359 0 629,497 210,964 0.34 0.34 0.47
2021 2016 469,036 191,935 0.347 0 451,049 17,987 0.04 -0.04 0.04
2022 2017 NA 483,443 0.348 0 1,103,171 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 469,887 205,680 -0.010 0.423 392,096 77,791 0.20 -0.20 0.16
2014 2009 364,308 313,946 -0.009 0.414 429,699 65,391 0.15 0.15 0.18
2015 2010 338,788 188,298 -0.010 0.430 385,641 46,853 0.12 0.12 0.14
2016 2011 538,658 190,970 -0.009 0.420 385,370 153,288 0.40 -0.40 0.28
2017 2012 357,182 203,148 -0.009 0.423 393,266 36,084 0.09 0.09 0.10
2018 2013 756,364 128,118 -0.008 0.418 359,454 396,910 1.10 -1.10 0.48
2019 2014 983,763 151,934 -0.017 0.567 383,798 599,965 1.56 -1.56 0.55
2020 2015 418,533 218,700 -0.021 0.702 409,944 8,589 0.02 -0.02 0.02
2021 2016 469,036 200,046 -0.020 0.698 406,865 62,171 0.15 -0.15 0.13
2022 2017 NA 190,098 -0.020 0.694 406,275 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 469,887 205,680 0.275 0.001 416,736 53,151 0.13 -0.13 0.11
2014 2009 364,308 313,946 0.275 0.001 410,770 46,462 0.11 0.11 0.13
2015 2010 338,788 188,298 0.288 0.000 410,028 71,240 0.17 0.17 0.21
2016 2011 538,658 190,970 0.286 0.000 409,097 129,561 0.32 -0.32 0.24
2017 2012 357,182 203,148 0.288 0.000 417,007 59,825 0.14 0.14 0.17
2018 2013 756,364 128,118 0.288 0.000 356,627 399,737 1.12 -1.12 0.49
2019 2014 983,763 151,934 0.307 0.000 395,830 587,933 1.49 -1.49 0.54
2020 2015 418,533 218,700 0.314 0.000 435,070 16,537 0.04 0.04 0.04
2021 2016 469,036 200,046 0.314 0.000 432,648 36,388 0.08 -0.08 0.08
2022 2017 NA 190,098 0.315 0.000 430,876 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2013 2008 469,887 569,904 100,017 0.18 0.18 0.21
2014 2009 364,308 519,166 154,858 0.30 0.30 0.40
2015 2010 338,788 495,365 156,577 0.32 0.32 0.43
2016 2011 538,658 488,699 49,959 0.10 -0.10 0.09
2017 2012 357,182 473,326 116,144 0.25 0.25 0.31
2018 2013 756,364 413,765 342,599 0.83 -0.83 0.43
2019 2014 983,763 471,060 512,703 1.09 -1.09 0.48
2020 2015 418,533 594,951 176,418 0.30 0.30 0.40
2021 2016 469,036 610,900 141,864 0.23 0.23 0.29
2022 2017 NA 596,976 NA NA NA NA

Performance summary

The sibling models (sibling, ln.sibling, lnY.sibling) seem to perform best here. Blending those gives us a forecast of ~0.8 million fish.

model range MAD MAPE MPE MAAPE
sibling 5 years 136,096 19.90% 16.45% 0.26
sibling 3 years 156,237 20.35% 20.35% 0.27
ln.sibling 5 years 112,114 18.50% 10.04% 0.23
ln.sibling 3 years 104,666 15.97% 12.96% 0.21
lnY.sibling 5 years 310,360 23.72% 20.04% 0.34
lnY.sibling 3 years 472,810 30.74% 28.09% 0.46
lnS.lnR 5 years 220,744 58.66% -54.99% 0.26
lnS.lnR 3 years 223,575 57.90% -57.90% 0.23
ricker 5 years 220,084 57.44% -50.18% 0.26
ricker 3 years 213,619 53.58% -51.05% 0.22
average 5 years 257,946 53.81% -22.85% 0.38
average 3 years 276,995 53.90% -18.66% 0.39

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 27,737 38,261 0.489 0 46,094 18,357 0.40 0.40 0.58
2014 2008 8,282 3,072 0.486 0 17,972 9,690 0.54 0.54 0.86
2015 2009 8,630 25,841 0.497 0 35,490 26,860 0.76 0.76 1.26
2016 2010 2,908 9,047 0.497 0 21,290 18,382 0.86 0.86 1.41
2017 2011 3,523 16,663 0.505 0 26,685 23,162 0.87 0.87 1.42
2018 2012 9,653 9,337 0.509 0 19,916 10,263 0.52 0.52 0.82
2019 2013 2,776 4,547 0.516 0 15,568 12,792 0.82 0.82 1.36
2020 2014 559 4,843 0.525 0 15,269 14,710 0.96 0.96 1.53
2021 2015 313 3,175 0.533 0 13,270 12,957 0.98 0.98 1.55
2022 2016 NA 1,791 0.541 0 11,566 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 27,737 38,261 0.274 0.001 40,698 12,961 0.32 0.32 0.44
2014 2008 8,282 3,072 0.270 0.001 12,531 4,249 0.34 0.34 0.47
2015 2009 8,630 25,841 0.319 0.000 33,201 24,571 0.74 0.74 1.23
2016 2010 2,908 9,047 0.295 0.000 19,296 16,388 0.85 0.85 1.40
2017 2011 3,523 16,663 0.306 0.000 24,276 20,753 0.85 0.85 1.40
2018 2012 9,653 9,337 0.288 0.000 16,730 7,077 0.42 0.42 0.63
2019 2013 2,776 4,547 0.301 0.000 10,892 8,116 0.75 0.75 1.24
2020 2014 559 4,843 0.343 0.000 10,086 9,527 0.94 0.94 1.51
2021 2015 313 3,175 0.368 0.000 6,026 5,713 0.95 0.95 1.52
2022 2016 NA 1,791 0.413 0.000 2,814 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 27,737 38,261 0.333 0 33,405 5,668 0.17 0.17 0.20
2014 2008 8,282 3,072 0.333 0 20,525 12,243 0.60 0.60 0.98
2015 2009 8,630 25,841 0.352 0 27,134 18,504 0.68 0.68 1.13
2016 2010 2,908 9,047 0.344 0 20,510 17,602 0.86 0.86 1.41
2017 2011 3,523 16,663 0.339 0 21,316 17,793 0.83 0.83 1.38
2018 2012 9,653 9,337 0.331 0 17,787 8,134 0.46 0.46 0.70
2019 2013 2,776 4,547 0.341 0 16,019 13,243 0.83 0.83 1.36
2020 2014 559 4,843 0.348 0 14,946 14,387 0.96 0.96 1.53
2021 2015 313 3,175 0.326 0 12,656 12,343 0.98 0.98 1.55
2022 2016 NA 1,791 0.311 0 10,554 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 27,737 269,646 -0.028 0.811 32,660 4,923 0.15 0.15 0.18
2014 2008 8,282 205,680 -0.027 0.787 33,296 25,014 0.75 0.75 1.25
2015 2009 8,630 313,946 -0.026 0.775 30,644 22,014 0.72 0.72 1.20
2016 2010 2,908 188,298 -0.019 0.575 31,521 28,613 0.91 0.91 1.47
2017 2011 3,523 190,970 -0.021 0.655 29,521 25,998 0.88 0.88 1.44
2018 2012 9,653 203,148 -0.022 0.705 27,690 18,037 0.65 0.65 1.08
2019 2013 2,776 128,118 -0.022 0.702 29,074 26,298 0.90 0.90 1.47
2020 2014 559 151,934 -0.025 0.965 25,474 24,915 0.98 0.98 1.55
2021 2015 313 218,700 -0.021 0.697 23,887 23,574 0.99 0.99 1.56
2022 2016 NA 200,046 -0.023 0.832 21,264 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 27,737 269,646 0.170 0.008 35,089 7,352 0.21 0.21 0.26
2014 2008 8,282 205,680 0.175 0.006 35,952 27,670 0.77 0.77 1.28
2015 2009 8,630 313,946 0.160 0.008 31,656 23,026 0.73 0.73 1.21
2016 2010 2,908 188,298 0.187 0.004 33,604 30,696 0.91 0.91 1.48
2017 2011 3,523 190,970 0.143 0.010 31,375 27,852 0.89 0.89 1.44
2018 2012 9,653 203,148 0.116 0.018 29,689 20,036 0.67 0.67 1.12
2019 2013 2,776 128,118 0.110 0.019 25,875 23,099 0.89 0.89 1.45
2020 2014 559 151,934 0.071 0.049 24,981 24,422 0.98 0.98 1.55
2021 2015 313 218,700 0.025 0.155 25,324 25,011 0.99 0.99 1.56
2022 2016 NA 200,046 0.017 0.196 22,291 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2013 2007 27,737 23,001 4,736 0.21 -0.21 0.17
2014 2008 8,282 24,815 16,533 0.67 0.67 1.11
2015 2009 8,630 23,799 15,169 0.64 0.64 1.05
2016 2010 2,908 17,599 14,691 0.83 0.83 1.38
2017 2011 3,523 11,805 8,282 0.70 0.70 1.17
2018 2012 9,653 10,216 563 0.06 0.06 0.06
2019 2013 2,776 6,599 3,823 0.58 0.58 0.94
2020 2014 559 5,498 4,939 0.90 0.90 1.46
2021 2015 313 3,884 3,571 0.92 0.92 1.48
2022 2016 NA 3,365 NA NA NA NA

Performance summary

The average model performs best giving us a forecast of ~0.005 million fish.

model range MAD MAPE MPE MAAPE
sibling 5 years 14,777 82.90% 82.90% 1.33
sibling 3 years 13,486 92.05% 92.05% 1.48
ln.sibling 5 years 10,237 78.31% 78.31% 1.26
ln.sibling 3 years 7,785 87.93% 87.93% 1.42
lnY.sibling 5 years 13,180 81.13% 81.13% 1.30
lnY.sibling 3 years 13,324 92.15% 92.15% 1.48
lnS.lnR 5 years 23,764 88.03% 88.03% 1.42
lnS.lnR 3 years 24,929 95.65% 95.65% 1.52
ricker 5 years 24,084 88.41% 88.41% 1.42
ricker 3 years 24,177 95.27% 95.27% 1.52
average 5 years 4,236 63.08% 63.08% 1.02
average 3 years 4,111 79.90% 79.90% 1.29

Forecast summary

A preliminary look at the models for this river leads us to an initial forecast of ~1.2 million broken down as follows:

Table 2. Preliminary Forecast.

age forecast
1.2 0.300
2.2 0.005
1.3 0.800
2.3 0.003