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 1,382,656 1,790 0.263 0.001 1,884,441 501,785 0.27 0.27 0.35
2014 2010 4,795,481 41,816 0.266 0.001 4,614,988 180,494 0.04 -0.04 0.04
2015 2011 2,666,595 10,407 0.330 0.000 2,468,617 197,978 0.08 -0.08 0.07
2016 2012 3,133,423 77,219 0.331 0.000 7,140,675 4,007,252 0.56 0.56 0.91
2017 2013 9,677,410 207,823 0.229 0.001 10,906,524 1,229,114 0.11 0.11 0.13
2018 2014 20,246,492 163,321 0.539 0.000 8,215,683 12,030,809 1.46 -1.46 0.54
2019 2015 8,064,807 0 0.635 0.000 1,776,346 6,288,461 3.54 -3.54 0.66
2020 2016 5,724,076 87,518 0.572 0.000 7,360,047 1,635,971 0.22 0.22 0.28
2021 2017 11,137,673 36,289 0.574 0.000 4,126,439 7,011,235 1.70 -1.70 0.56
2022 2018 NA 8,525 0.534 0.000 2,585,601 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 1,382,656 1,790 0.131 0.016 1,917,457 534,801 0.28 0.28 0.37
2014 2010 4,795,481 41,816 0.128 0.016 2,449,155 2,346,326 0.96 -0.96 0.46
2015 2011 2,666,595 10,407 0.149 0.009 2,263,442 403,154 0.18 -0.18 0.15
2016 2012 3,133,423 77,219 0.155 0.007 2,712,414 421,010 0.16 -0.16 0.13
2017 2013 9,677,410 207,823 0.165 0.005 2,987,285 6,690,125 2.24 -2.24 0.60
2018 2014 20,246,492 163,321 0.203 0.002 3,188,627 17,057,865 5.35 -5.35 0.70
2019 2015 8,064,807 0 0.239 0.001 919,852 7,144,955 7.77 -7.77 0.72
2020 2016 5,724,076 87,518 0.156 0.005 3,199,953 2,524,123 0.79 -0.79 0.42
2021 2017 11,137,673 36,289 0.172 0.003 3,029,556 8,108,117 2.68 -2.68 0.63
2022 2018 NA 8,525 0.188 0.002 2,748,864 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 1,382,656 1,790 0.142 0.012 1,489,608 106,952 0.07 0.07 0.08
2014 2010 4,795,481 41,816 0.144 0.011 4,933,155 137,674 0.03 0.03 0.03
2015 2011 2,666,595 10,407 0.181 0.004 1,921,674 744,922 0.39 -0.39 0.27
2016 2012 3,133,423 77,219 0.183 0.003 14,378,160 11,244,737 0.78 0.78 1.30
2017 2013 9,677,410 207,823 0.144 0.008 94,244,080 84,566,670 0.90 0.90 1.46
2018 2014 20,246,492 163,321 0.192 0.002 9,522,728 10,723,764 1.13 -1.13 0.49
2019 2015 8,064,807 0 0.316 0.000 1,585,561 6,479,246 4.09 -4.09 0.68
2020 2016 5,724,076 87,518 0.279 0.000 4,772,659 951,417 0.20 -0.20 0.16
2021 2017 11,137,673 36,289 0.300 0.000 2,586,349 8,551,324 3.31 -3.31 0.65
2022 2018 NA 8,525 0.295 0.000 1,892,966 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 1,382,656 1,319,232 0.123 0.019 1,747,823 365,167 0.21 0.21 0.26
2014 2010 4,795,481 1,804,344 0.122 0.018 2,144,550 2,650,931 1.24 -1.24 0.50
2015 2011 2,666,595 1,098,006 0.135 0.012 1,558,431 1,108,164 0.71 -0.71 0.39
2016 2012 3,133,423 764,211 0.130 0.013 1,228,177 1,905,246 1.55 -1.55 0.55
2017 2013 9,677,410 1,183,348 0.108 0.020 1,711,846 7,965,564 4.65 -4.65 0.69
2018 2014 20,246,492 2,764,614 0.090 0.030 3,036,640 17,209,852 5.67 -5.67 0.70
2019 2015 8,064,807 1,941,474 0.143 0.007 2,730,838 5,333,969 1.95 -1.95 0.58
2020 2016 5,724,076 1,309,707 0.158 0.004 2,046,543 3,677,533 1.80 -1.80 0.57
2021 2017 11,137,673 4,274,224 0.154 0.005 5,713,966 5,423,707 0.95 -0.95 0.45
2022 2018 NA 7,507,254 0.204 0.001 10,689,997 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 1,382,656 1,319,232 0.050 0.097 1,814,770 432,113 0.24 0.24 0.30
2014 2010 4,795,481 1,804,344 0.050 0.094 2,108,734 2,686,748 1.27 -1.27 0.51
2015 2011 2,666,595 1,098,006 0.040 0.116 1,633,474 1,033,121 0.63 -0.63 0.37
2016 2012 3,133,423 764,211 0.044 0.102 1,279,671 1,853,752 1.45 -1.45 0.53
2017 2013 9,677,410 1,183,348 0.059 0.068 1,791,395 7,886,015 4.40 -4.40 0.68
2018 2014 20,246,492 2,764,614 0.060 0.065 2,457,770 17,788,722 7.24 -7.24 0.72
2019 2015 8,064,807 1,941,474 0.003 0.299 2,665,338 5,399,469 2.03 -2.03 0.59
2020 2016 5,724,076 1,309,707 -0.005 0.380 2,090,074 3,634,002 1.74 -1.74 0.57
2021 2017 11,137,673 4,274,224 -0.004 0.366 4,114,751 7,022,923 1.71 -1.71 0.56
2022 2018 NA 7,507,254 -0.018 0.662 7,893,463 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2013 2009 1,382,656 2,749,597 1,366,941 0.50 0.50 0.78
2014 2010 4,795,481 2,243,552 2,551,929 1.14 -1.14 0.49
2015 2011 2,666,595 2,699,500 32,904 0.01 0.01 0.01
2016 2012 3,133,423 2,323,639 809,784 0.35 -0.35 0.25
2017 2013 9,677,410 2,656,958 7,020,452 2.64 -2.64 0.63
2018 2014 20,246,492 4,331,113 15,915,379 3.67 -3.67 0.67
2019 2015 8,064,807 8,103,880 39,073 0.00 0.00 0.00
2020 2016 5,724,076 8,757,745 3,033,669 0.35 0.35 0.49
2021 2017 11,137,673 9,369,242 1,768,432 0.19 -0.19 0.16
2022 2018 NA 10,970,092 NA NA NA NA

Performance summary

This is a difficult one. The sibling and average model seem to be the best performing models but return very different results. Blending the two gives us a forecast of ~7 million.

model range MAD MAPE MPE MAAPE
sibling 5 years 5,639,118 140.77% -127.37% 0.43
sibling 3 years 4,978,555 182.05% -167.23% 0.50
ln.sibling 5 years 8,305,037 376.44% -376.44% 0.61
ln.sibling 3 years 5,925,732 374.42% -374.42% 0.59
lnY.sibling 5 years 22,254,484 192.31% -156.42% 0.69
lnY.sibling 3 years 5,327,329 253.07% -253.07% 0.50
lnS.lnR 5 years 7,922,125 300.40% -300.40% 0.60
lnS.lnR 3 years 4,811,737 156.65% -156.65% 0.54
ricker 5 years 8,346,226 342.22% -342.22% 0.62
ricker 3 years 5,352,131 182.38% -182.38% 0.57
average 5 years 5,555,401 137.14% -123.09% 0.39
average 3 years 1,613,725 18.00% 5.42% 0.22

age.22

sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2013 2008 47,795 0 0.379 0.000 135,413 87,618 0.65 0.65 1.07
2014 2009 208,956 1,627 0.382 0.000 336,275 127,319 0.38 0.38 0.55
2015 2010 214,853 1,237 0.374 0.000 281,675 66,822 0.24 0.24 0.30
2016 2011 105,680 2,946 0.372 0.000 485,680 380,000 0.78 0.78 1.30
2017 2012 56,376 0 0.300 0.000 130,255 73,879 0.57 0.57 0.92
2018 2013 57,517 0 0.304 0.000 128,013 70,496 0.55 0.55 0.89
2019 2014 340,940 3,535 0.308 0.000 495,681 154,741 0.31 0.31 0.43
2020 2015 38,542 4,771 0.306 0.000 590,028 551,486 0.93 0.93 1.50
2021 2016 429,370 0 0.181 0.002 134,816 294,554 2.18 -2.18 0.60
2022 2017 NA 3,526 0.161 0.004 373,714 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 47,795 0 0.287 0.000 75,760 27,965 0.37 0.37 0.53
2014 2009 208,956 1,627 0.293 0.000 349,869 140,913 0.40 0.40 0.59
2015 2010 214,853 1,237 0.295 0.000 313,488 98,635 0.31 0.31 0.43
2016 2011 105,680 2,946 0.299 0.000 359,531 253,851 0.71 0.71 1.18
2017 2012 56,376 0 0.272 0.000 74,838 18,463 0.25 0.25 0.32
2018 2013 57,517 0 0.277 0.000 74,116 16,599 0.22 0.22 0.28
2019 2014 340,940 3,535 0.282 0.000 328,874 12,066 0.04 -0.04 0.04
2020 2015 38,542 4,771 0.300 0.000 348,705 310,163 0.89 0.89 1.45
2021 2016 429,370 0 0.230 0.001 74,200 355,170 4.79 -4.79 0.69
2022 2017 NA 3,526 0.202 0.001 268,949 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 47,795 0 0.238 0.002 84,835 37,040 0.44 0.44 0.66
2014 2009 208,956 1,627 0.242 0.001 203,029 5,927 0.03 -0.03 0.03
2015 2010 214,853 1,237 0.249 0.001 164,218 50,635 0.31 -0.31 0.23
2016 2011 105,680 2,946 0.255 0.001 426,653 320,973 0.75 0.75 1.25
2017 2012 56,376 0 0.221 0.001 83,897 27,521 0.33 0.33 0.45
2018 2013 57,517 0 0.225 0.001 82,891 25,374 0.31 0.31 0.42
2019 2014 340,940 3,535 0.229 0.001 472,817 131,877 0.28 0.28 0.37
2020 2015 38,542 4,771 0.247 0.000 810,246 771,704 0.95 0.95 1.52
2021 2016 429,370 0 0.127 0.010 85,839 343,531 4.00 -4.00 0.67
2022 2017 NA 3,526 0.110 0.015 263,226 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 47,795 1,724,676 0.020 0.199 130,408 82,613 0.63 0.63 1.05
2014 2009 208,956 1,319,232 0.014 0.228 109,043 99,913 0.92 -0.92 0.45
2015 2010 214,853 1,804,344 0.015 0.221 130,671 84,182 0.64 -0.64 0.37
2016 2011 105,680 1,098,006 0.019 0.193 101,732 3,948 0.04 -0.04 0.04
2017 2012 56,376 764,211 0.020 0.187 83,610 27,234 0.33 0.33 0.45
2018 2013 57,517 1,183,348 0.026 0.157 104,895 47,378 0.45 0.45 0.69
2019 2014 340,940 2,764,614 0.027 0.150 168,226 172,714 1.03 -1.03 0.47
2020 2015 38,542 1,941,474 0.044 0.096 143,355 104,813 0.73 0.73 1.22
2021 2016 429,370 1,309,707 0.032 0.129 108,179 321,191 2.97 -2.97 0.64
2022 2017 NA 4,274,224 0.031 0.130 221,012 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 47,795 1,724,676 0.004 0.296 134,583 86,788 0.64 0.64 1.07
2014 2009 208,956 1,319,232 0.008 0.261 114,063 94,893 0.83 -0.83 0.43
2015 2010 214,853 1,804,344 0.010 0.252 134,243 80,609 0.60 -0.60 0.36
2016 2011 105,680 1,098,006 0.008 0.260 104,957 724 0.01 -0.01 0.01
2017 2012 56,376 764,211 0.009 0.252 81,599 25,223 0.31 0.31 0.42
2018 2013 57,517 1,183,348 0.007 0.262 108,690 51,173 0.47 0.47 0.73
2019 2014 340,940 2,764,614 0.006 0.269 153,247 187,693 1.22 -1.22 0.50
2020 2015 38,542 1,941,474 -0.002 0.343 146,029 107,487 0.74 0.74 1.23
2021 2016 429,370 1,309,707 0.005 0.273 112,261 317,109 2.82 -2.82 0.64
2022 2017 NA 4,274,224 0.007 0.263 157,849 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2013 2008 47,794.69 149,550 101,755 0.68 0.68 1.13
2014 2009 208,955.75 151,561 57,395 0.38 -0.38 0.27
2015 2010 214,852.73 170,778 44,074 0.26 -0.26 0.20
2016 2011 105,680.45 166,575 60,894 0.37 0.37 0.52
2017 2012 56,375.81 150,539 94,163 0.63 0.63 1.03
2018 2013 57,516.87 126,732 69,215 0.55 0.55 0.88
2019 2014 340,940.07 128,676 212,264 1.65 -1.65 0.56
2020 2015 38,541.97 155,073 116,531 0.75 0.75 1.25
2021 2016 429,369.92 119,811 309,559 2.58 -2.58 0.62
2022 2017 NA 184,549 NA NA NA NA

Performance summary

Nothing looks very compelling here so we go with the average for a forecast of ~0.18 million fish.

model range MAD MAPE MPE MAAPE
sibling 5 years 229,031 90.99% 3.60% 0.87
sibling 3 years 333,594 114.39% -31.27% 0.84
ln.sibling 5 years 142,492 123.67% -69.26% 0.55
ln.sibling 3 years 225,800 190.43% -131.13% 0.72
lnY.sibling 5 years 260,001 117.35% -42.73% 0.69
lnY.sibling 3 years 415,704 174.45% -92.36% 0.85
lnS.lnR 5 years 134,666 110.09% -49.74% 0.69
lnS.lnR 3 years 199,573 157.56% -108.82% 0.78
ricker 5 years 137,737 111.31% -50.67% 0.70
ricker 3 years 204,096 159.52% -110.45% 0.79
average 5 years 160,346 123.13% -46.20% 0.87
average 3 years 212,785 166.16% -116.06% 0.81

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 1,776,273 1,306,633 0.291 0.000 1,839,702 63,429 0.03 0.03 0.04
2014 2009 2,055,987 1,382,656 0.295 0.000 1,872,093 183,893 0.10 -0.10 0.09
2015 2010 1,989,184 4,795,481 0.295 0.000 3,434,047 1,444,863 0.42 0.42 0.63
2016 2011 2,859,737 2,666,595 0.256 0.001 2,406,154 453,583 0.19 -0.19 0.16
2017 2012 1,384,226 3,133,423 0.258 0.000 2,610,259 1,226,033 0.47 0.47 0.72
2018 2013 2,368,581 9,677,410 0.239 0.001 5,168,237 2,799,656 0.54 0.54 0.87
2019 2014 3,790,599 20,246,492 0.143 0.008 6,577,422 2,786,823 0.42 0.42 0.63
2020 2015 2,193,179 8,064,807 0.138 0.008 2,965,583 772,404 0.26 0.26 0.34
2021 2016 1,013,066 5,724,076 0.127 0.010 2,609,737 1,596,671 0.61 0.61 1.01
2022 2017 NA 11,137,673 0.105 0.017 3,184,870 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 1,776,273 1,306,633 0.461 0 1,696,830 79,444 0.05 -0.05 0.04
2014 2009 2,055,987 1,382,656 0.461 0 1,747,769 308,217 0.18 -0.18 0.15
2015 2010 1,989,184 4,795,481 0.460 0 3,258,927 1,269,743 0.39 0.39 0.57
2016 2011 2,859,737 2,666,595 0.441 0 2,382,354 477,383 0.20 -0.20 0.17
2017 2012 1,384,226 3,133,423 0.445 0 2,589,234 1,205,008 0.47 0.47 0.72
2018 2013 2,368,581 9,677,410 0.420 0 4,276,720 1,908,139 0.45 0.45 0.68
2019 2014 3,790,599 20,246,492 0.397 0 5,466,090 1,675,492 0.31 0.31 0.42
2020 2015 2,193,179 8,064,807 0.408 0 3,516,829 1,323,650 0.38 0.38 0.54
2021 2016 1,013,066 5,724,076 0.393 0 2,970,819 1,957,753 0.66 0.66 1.09
2022 2017 NA 11,137,673 0.329 0 3,565,455 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 1,776,273 1,306,633 0.354 0.000 1,542,696 233,578 0.15 -0.15 0.13
2014 2009 2,055,987 1,382,656 0.354 0.000 1,581,125 474,862 0.30 -0.30 0.23
2015 2010 1,989,184 4,795,481 0.349 0.000 3,747,762 1,758,578 0.47 0.47 0.72
2016 2011 2,859,737 2,666,595 0.319 0.000 2,145,349 714,388 0.33 -0.33 0.24
2017 2012 1,384,226 3,133,423 0.321 0.000 2,408,331 1,024,105 0.43 0.43 0.64
2018 2013 2,368,581 9,677,410 0.303 0.000 10,291,936 7,923,355 0.77 0.77 1.28
2019 2014 3,790,599 20,246,492 0.203 0.002 25,631,954 21,841,355 0.85 0.85 1.40
2020 2015 2,193,179 8,064,807 0.145 0.007 2,848,340 655,160 0.23 0.23 0.29
2021 2016 1,013,066 5,724,076 0.141 0.007 2,388,350 1,375,284 0.58 0.58 0.94
2022 2017 NA 11,137,673 0.116 0.013 3,230,118 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 1,776,273 1,724,676 0.008 0.262 2,100,043 323,769 0.15 0.15 0.18
2014 2009 2,055,987 1,319,232 0.008 0.266 1,956,977 99,010 0.05 -0.05 0.05
2015 2010 1,989,184 1,804,344 0.008 0.259 2,111,696 122,512 0.06 0.06 0.06
2016 2011 2,859,737 1,098,006 0.009 0.254 1,873,402 986,335 0.53 -0.53 0.33
2017 2012 1,384,226 764,211 0.007 0.267 1,745,461 361,235 0.21 0.21 0.26
2018 2013 2,368,581 1,183,348 0.013 0.225 1,915,642 452,939 0.24 -0.24 0.19
2019 2014 3,790,599 2,764,614 0.013 0.223 2,362,110 1,428,489 0.60 -0.60 0.36
2020 2015 2,193,179 1,941,474 0.030 0.137 2,232,509 39,330 0.02 0.02 0.02
2021 2016 1,013,066 1,309,707 0.031 0.130 1,995,988 982,922 0.49 0.49 0.77
2022 2017 NA 4,274,224 0.030 0.133 2,743,525 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 1,776,273 1,724,676 0.281 0.001 2,203,333 427,060 0.19 0.19 0.24
2014 2009 2,055,987 1,319,232 0.286 0.000 2,106,372 50,385 0.02 0.02 0.02
2015 2010 1,989,184 1,804,344 0.286 0.000 2,185,694 196,510 0.09 0.09 0.10
2016 2011 2,859,737 1,098,006 0.291 0.000 1,983,283 876,454 0.44 -0.44 0.30
2017 2012 1,384,226 764,211 0.296 0.000 1,692,777 308,552 0.18 0.18 0.22
2018 2013 2,368,581 1,183,348 0.295 0.000 2,044,441 324,140 0.16 -0.16 0.14
2019 2014 3,790,599 2,764,614 0.297 0.000 1,942,357 1,848,242 0.95 -0.95 0.45
2020 2015 2,193,179 1,941,474 0.274 0.000 2,278,401 85,222 0.04 0.04 0.04
2021 2016 1,013,066 1,309,707 0.278 0.000 2,133,926 1,120,860 0.53 0.53 0.84
2022 2017 NA 4,274,224 0.266 0.000 1,477,794 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2013 2008 1,776,273 2,974,225 1,197,951 0.40 0.40 0.59
2014 2009 2,055,987 2,767,418 711,431 0.26 0.26 0.33
2015 2010 1,989,184 2,405,095 415,911 0.17 0.17 0.21
2016 2011 2,859,737 2,030,916 828,821 0.41 -0.41 0.28
2017 2012 1,384,226 1,965,199 580,974 0.30 0.30 0.40
2018 2013 2,368,581 2,013,081 355,500 0.18 -0.18 0.15
2019 2014 3,790,599 2,131,543 1,659,056 0.78 -0.78 0.41
2020 2015 2,193,179 2,478,465 285,286 0.12 0.12 0.13
2021 2016 1,013,066 2,519,264 1,506,198 0.60 0.60 0.98
2022 2017 NA 2,149,930 NA NA NA NA

Performance summary

Blending the average, sibling, ln.sibling and ricker gives us a forecast of ~2.3 million fish.

model range MAD MAPE MPE MAAPE
sibling 5 years 1,836,317 46.15% 46.15% 0.71
sibling 3 years 1,718,633 43.20% 43.20% 0.66
ln.sibling 5 years 1,614,008 45.07% 45.07% 0.69
ln.sibling 3 years 1,652,298 44.73% 44.73% 0.68
lnY.sibling 5 years 6,563,852 57.06% 57.06% 0.91
lnY.sibling 3 years 7,957,267 55.27% 55.27% 0.88
lnS.lnR 5 years 652,983 31.16% -2.48% 0.32
lnS.lnR 3 years 816,914 37.16% -3.16% 0.38
ricker 5 years 737,403 37.10% -7.30% 0.34
ricker 3 years 1,018,108 50.47% -12.96% 0.44
average 5 years 877,403 39.27% 1.07% 0.41
average 3 years 1,150,180 49.71% -2.18% 0.51

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 34,600 175,413 0.108 0.030 133,102 98,502 0.74 0.74 1.23
2014 2008 67,122 47,795 0.109 0.028 88,242 21,120 0.24 0.24 0.30
2015 2009 68,016 208,956 0.112 0.024 140,877 72,862 0.52 0.52 0.82
2016 2010 58,421 214,853 0.112 0.023 140,896 82,474 0.59 0.59 0.95
2017 2011 1,099 105,680 0.111 0.022 102,758 101,659 0.99 0.99 1.56
2018 2012 0 56,376 0.115 0.018 83,306 83,306 1.00 1.00 1.57
2019 2013 52,030 57,517 0.121 0.015 80,857 28,827 0.36 0.36 0.51
2020 2014 11,853 340,940 0.124 0.013 177,121 165,267 0.93 0.93 1.50
2021 2015 75,577 38,542 0.113 0.016 71,707 3,870 0.05 -0.05 0.05
2022 2016 NA 429,370 0.114 0.014 200,074 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 34,600 175,413 0.280 0.001 102,202 67,601 0.66 0.66 1.10
2014 2008 67,122 47,795 0.261 0.001 55,794 11,329 0.20 -0.20 0.17
2015 2009 68,016 208,956 0.262 0.001 106,866 38,850 0.36 0.36 0.52
2016 2010 58,421 214,853 0.257 0.001 106,459 48,038 0.45 0.45 0.69
2017 2011 1,099 105,680 0.249 0.001 77,319 76,219 0.99 0.99 1.56
2018 2012 0 56,376 0.156 0.007 53,201 53,201 1.00 1.00 1.57
2019 2013 52,030 57,517 0.013 0.224 21,379 30,651 1.43 -1.43 0.53
2020 2014 11,853 340,940 0.013 0.223 88,175 76,321 0.87 0.87 1.42
2021 2015 75,577 38,542 0.010 0.239 16,067 59,510 3.70 -3.70 0.67
2022 2016 NA 429,370 0.009 0.248 94,398 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 34,600 175,413 0.174 0.007 79,198 44,597 0.56 0.56 0.91
2014 2008 67,122 47,795 0.172 0.007 60,219 6,903 0.11 -0.11 0.10
2015 2009 68,016 208,956 0.173 0.006 82,885 14,869 0.18 0.18 0.22
2016 2010 58,421 214,853 0.173 0.005 83,407 24,985 0.30 0.30 0.40
2017 2011 1,099 105,680 0.172 0.005 66,802 65,702 0.98 0.98 1.55
2018 2012 0 56,376 0.132 0.012 53,331 53,331 1.00 1.00 1.57
2019 2013 52,030 57,517 0.012 0.227 20,522 31,508 1.54 -1.54 0.54
2020 2014 11,853 340,940 0.012 0.227 69,499 57,646 0.83 0.83 1.37
2021 2015 75,577 38,542 0.011 0.236 19,187 56,390 2.94 -2.94 0.64
2022 2016 NA 429,370 0.010 0.241 93,420 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 34,600 1,528,086 0.044 0.118 91,946 57,345 0.62 0.62 1.03
2014 2008 67,122 1,724,676 0.038 0.133 95,032 27,910 0.29 0.29 0.39
2015 2009 68,016 1,319,232 0.036 0.136 81,450 13,434 0.16 0.16 0.20
2016 2010 58,421 1,804,344 0.036 0.131 95,494 37,072 0.39 0.39 0.57
2017 2011 1,099 1,098,006 0.032 0.141 72,965 71,865 0.98 0.98 1.56
2018 2012 0 764,211 0.026 0.160 52,520 52,520 1.00 1.00 1.57
2019 2013 52,030 1,183,348 0.050 0.085 49,792 2,237 0.04 -0.04 0.04
2020 2014 11,853 2,764,614 0.051 0.081 146,448 134,595 0.92 0.92 1.48
2021 2015 75,577 1,941,474 0.030 0.137 80,259 4,683 0.06 0.06 0.06
2022 2016 NA 1,309,707 0.031 0.130 53,147 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 34,600 1,528,086 0.067 0.073 94,105 59,504 0.63 0.63 1.04
2014 2008 67,122 1,724,676 0.068 0.068 94,405 27,283 0.29 0.29 0.39
2015 2009 68,016 1,319,232 0.072 0.059 85,966 17,950 0.21 0.21 0.26
2016 2010 58,421 1,804,344 0.072 0.057 93,586 35,165 0.38 0.38 0.54
2017 2011 1,099 1,098,006 0.078 0.047 78,026 76,927 0.99 0.99 1.56
2018 2012 0 764,211 0.022 0.180 54,209 54,209 1.00 1.00 1.57
2019 2013 52,030 1,183,348 -0.026 0.944 50,290 1,740 0.03 -0.03 0.03
2020 2014 11,853 2,764,614 -0.025 0.944 124,414 112,561 0.90 0.90 1.47
2021 2015 75,577 1,941,474 -0.022 0.765 73,033 2,544 0.03 -0.03 0.03
2022 2016 NA 1,309,707 -0.022 0.762 53,972 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2013 2007 34,600.432 82,903 48,303 0.58 0.58 0.95
2014 2008 67,122.121 81,456 14,334 0.18 0.18 0.21
2015 2009 68,015.752 77,474 9,458 0.12 0.12 0.14
2016 2010 58,421.461 63,627 5,206 0.08 0.08 0.09
2017 2011 1,099.204 56,219 55,120 0.98 0.98 1.55
2018 2012 0.000 45,852 45,852 1.00 1.00 1.57
2019 2013 52,029.967 38,932 13,098 0.34 -0.34 0.25
2020 2014 11,853.318 35,913 24,060 0.67 0.67 1.11
2021 2015 75,576.598 24,681 50,896 2.06 -2.06 0.59
2022 2016 NA 28,112 NA NA NA NA

Performance summary

Blending all significan regressions give us a forecast of ~0.11 million fish.

model range MAD MAPE MPE MAAPE
sibling 5 years 76,586 66.66% 64.50% 1.04
sibling 3 years 65,988 44.79% 41.19% 0.69
ln.sibling 5 years 59,180 159.78% -45.72% 1.15
ln.sibling 3 years 55,494 200.10% -142.40% 0.87
lnY.sibling 5 years 52,915 145.75% -33.23% 1.14
lnY.sibling 3 years 48,514 176.79% -121.49% 0.85
lnS.lnR 5 years 53,180 60.15% 58.35% 0.94
lnS.lnR 3 years 47,172 34.08% 31.08% 0.53
ricker 5 years 49,596 59.20% 56.42% 0.93
ricker 3 years 38,948 32.47% 27.84% 0.51
average 5 years 37,805 100.98% 5.04% 1.01
average 3 years 29,351 102.29% -57.62% 0.65

Forecast summary

A preliminary look at the models for this river leads us to an initial forecast of ~9.6 million broken down as follows:

Table 2. Preliminary Forecast.

age forecast
1.2 7.00
2.2 0.18
1.3 2.30
2.3 0.11