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 740,947 0 0.516 0 1,772,727 1,031,781 0.58 0.58 0.95
2014 2010 6,053,034 3,046 0.519 0 2,454,585 3,598,449 1.47 -1.47 0.54
2015 2011 2,846,209 4,589 0.501 0 2,909,401 63,192 0.02 0.02 0.02
2016 2012 8,590,994 21,302 0.501 0 6,804,771 1,786,223 0.26 -0.26 0.20
2017 2013 3,713,931 2,616 0.528 0 2,474,247 1,239,684 0.50 -0.50 0.32
2018 2014 4,484,066 9,832 0.525 0 4,229,603 254,463 0.06 -0.06 0.06
2019 2015 5,743,118 4,227 0.527 0 2,896,112 2,847,007 0.98 -0.98 0.46
2020 2016 2,659,891 3,011 0.517 0 2,671,640 11,749 0.00 0.00 0.00
2021 2017 6,161,217 1,511 0.518 0 2,313,672 3,847,545 1.66 -1.66 0.56
2022 2018 NA 12,704 0.496 0 5,042,798 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 740,947 0 0.375 0 804,680 63,733 0.08 0.08 0.09
2014 2010 6,053,034 3,046 0.389 0 2,825,989 3,227,045 1.14 -1.14 0.49
2015 2011 2,846,209 4,589 0.397 0 3,108,066 261,857 0.08 0.08 0.09
2016 2012 8,590,994 21,302 0.400 0 3,961,297 4,629,697 1.17 -1.17 0.49
2017 2013 3,713,931 2,616 0.420 0 2,923,050 790,881 0.27 -0.27 0.21
2018 2014 4,484,066 9,832 0.425 0 3,673,497 810,569 0.22 -0.22 0.18
2019 2015 5,743,118 4,227 0.433 0 3,215,880 2,527,238 0.79 -0.79 0.41
2020 2016 2,659,891 3,011 0.440 0 3,095,676 435,785 0.14 0.14 0.16
2021 2017 6,161,217 1,511 0.440 0 2,741,509 3,419,708 1.25 -1.25 0.51
2022 2018 NA 12,704 0.440 0 4,032,364 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 740,947 0 0.235 0.001 1,450,164 709,217 0.49 0.49 0.76
2014 2010 6,053,034 3,046 0.241 0.001 1,642,835 4,410,199 2.68 -2.68 0.63
2015 2011 2,846,209 4,589 0.225 0.001 1,829,663 1,016,546 0.56 -0.56 0.34
2016 2012 8,590,994 21,302 0.224 0.001 4,087,831 4,503,164 1.10 -1.10 0.48
2017 2013 3,713,931 2,616 0.255 0.000 1,703,331 2,010,600 1.18 -1.18 0.50
2018 2014 4,484,066 9,832 0.248 0.000 2,486,131 1,997,935 0.80 -0.80 0.42
2019 2015 5,743,118 4,227 0.252 0.000 1,906,743 3,836,375 2.01 -2.01 0.59
2020 2016 2,659,891 3,011 0.243 0.000 1,840,352 819,539 0.45 -0.45 0.30
2021 2017 6,161,217 1,511 0.241 0.000 1,722,603 4,438,613 2.58 -2.58 0.62
2022 2018 NA 12,704 0.225 0.001 3,068,670 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 740,947 2,266,140 0.219 0.002 1,539,324 798,378 0.52 0.52 0.82
2014 2010 6,053,034 4,207,410 0.223 0.002 2,086,585 3,966,449 1.90 -1.90 0.58
2015 2011 2,846,209 2,264,352 0.223 0.001 1,542,373 1,303,836 0.85 -0.85 0.43
2016 2012 8,590,994 4,164,444 0.217 0.001 2,167,135 6,423,860 2.96 -2.96 0.64
2017 2013 3,713,931 2,088,576 0.215 0.001 1,547,749 2,166,182 1.40 -1.40 0.53
2018 2014 4,484,066 4,458,540 0.204 0.002 2,372,479 2,111,587 0.89 -0.89 0.44
2019 2015 5,743,118 7,348,572 0.208 0.001 3,154,717 2,588,401 0.82 -0.82 0.42
2020 2016 2,659,891 4,462,728 0.220 0.001 2,458,869 201,022 0.08 -0.08 0.08
2021 2017 6,161,217 3,163,404 0.221 0.001 2,037,803 4,123,414 2.02 -2.02 0.59
2022 2018 NA 4,398,708 0.214 0.001 2,502,891 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 740,947 2,266,140 0.142 0.012 1,628,936 887,989 0.55 0.55 0.88
2014 2010 6,053,034 4,207,410 0.133 0.014 2,483,816 3,569,217 1.44 -1.44 0.53
2015 2011 2,846,209 2,264,352 0.132 0.013 1,623,202 1,223,007 0.75 -0.75 0.41
2016 2012 8,590,994 4,164,444 0.138 0.011 2,563,164 6,027,830 2.35 -2.35 0.61
2017 2013 3,713,931 2,088,576 0.134 0.011 1,598,306 2,115,626 1.32 -1.32 0.52
2018 2014 4,484,066 4,458,540 0.142 0.008 2,809,287 1,674,780 0.60 -0.60 0.36
2019 2015 5,743,118 7,348,572 0.141 0.007 3,573,279 2,169,839 0.61 -0.61 0.36
2020 2016 2,659,891 4,462,728 0.137 0.008 2,871,711 211,821 0.07 0.07 0.08
2021 2017 6,161,217 3,163,404 0.138 0.007 2,289,122 3,872,094 1.69 -1.69 0.56
2022 2018 NA 4,398,708 0.140 0.006 2,905,038 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2013 2009 740,946.6 2,787,520 2,046,573 0.73 0.73 1.22
2014 2010 6,053,033.8 1,976,136 4,076,898 2.06 -2.06 0.59
2015 2011 2,846,209.0 2,935,895 89,686 0.03 0.03 0.03
2016 2012 8,590,994.5 2,772,373 5,818,621 2.10 -2.10 0.60
2017 2013 3,713,931.2 4,182,068 468,137 0.11 0.11 0.13
2018 2014 4,484,066.2 4,389,023 95,043 0.02 -0.02 0.02
2019 2015 5,743,118.2 5,137,647 605,471 0.12 -0.12 0.11
2020 2016 2,659,890.6 5,075,664 2,415,773 0.48 0.48 0.74
2021 2017 6,161,216.5 5,038,400 1,122,816 0.22 -0.22 0.18
2022 2018 NA 4,552,445 NA NA NA NA

Performance summary

Blending the average model and the ln.sibling gives us a forecast of ~4.4 million fish.

model range MAD MAPE MPE MAAPE
sibling 5 years 1,640,090 64.23% -64.06% 0.28
sibling 3 years 2,235,434 88.35% -88.05% 0.34
ln.sibling 5 years 1,596,836 53.30% -47.67% 0.29
ln.sibling 3 years 2,127,577 72.47% -63.08% 0.36
lnY.sibling 5 years 2,620,613 140.36% -140.36% 0.49
lnY.sibling 3 years 3,031,509 167.80% -167.80% 0.50
lnS.lnR 5 years 2,238,121 104.31% -104.31% 0.41
lnS.lnR 3 years 2,304,279 97.52% -97.52% 0.36
ricker 5 years 2,008,832 85.85% -82.90% 0.38
ricker 3 years 2,084,585 79.08% -74.17% 0.33
average 5 years 941,448 19.00% 4.51% 0.23
average 3 years 1,381,354 27.22% 4.51% 0.34

age.22

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 1,247,528 2,520 0.624 0 2,775,711 1,528,184 0.55 0.55 0.89
2014 2009 9,725,832 11,611 0.626 0 3,460,694 6,265,137 1.81 -1.81 0.57
2015 2010 13,231,078 87,386 0.611 0 9,706,769 3,524,309 0.36 -0.36 0.26
2016 2011 2,573,729 43,953 0.617 0 6,328,002 3,754,273 0.59 0.59 0.97
2017 2012 397,153 3,702 0.612 0 2,980,939 2,583,787 0.87 0.87 1.42
2018 2013 38,269 2,155 0.614 0 2,780,356 2,742,086 0.99 0.99 1.56
2019 2014 71,802 4,883 0.615 0 2,924,316 2,852,514 0.98 0.98 1.55
2020 2015 119,279 0 0.617 0 2,446,659 2,327,380 0.95 0.95 1.52
2021 2016 577,057 0 0.619 0 2,382,002 1,804,945 0.76 0.76 1.26
2022 2017 NA 8,419 0.621 0 3,028,840 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 1,247,528 2,520 0.355 0 2,241,240 993,712 0.44 0.44 0.67
2014 2009 9,725,832 11,611 0.353 0 3,160,973 6,564,858 2.08 -2.08 0.59
2015 2010 13,231,078 87,386 0.359 0 5,341,752 7,889,326 1.48 -1.48 0.54
2016 2011 2,573,729 43,953 0.374 0 4,731,617 2,157,888 0.46 0.46 0.70
2017 2012 397,153 3,702 0.372 0 2,529,400 2,132,247 0.84 0.84 1.39
2018 2013 38,269 2,155 0.357 0 2,116,144 2,077,875 0.98 0.98 1.55
2019 2014 71,802 4,883 0.307 0 2,327,385 2,255,583 0.97 0.97 1.54
2020 2015 119,279 0 0.269 0 323,965 204,686 0.63 0.63 1.04
2021 2016 577,057 0 0.294 0 279,899 297,158 1.06 -1.06 0.48
2022 2017 NA 8,419 0.295 0 2,403,829 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 1,247,528 2,520 0.321 0 1,070,039 177,489 0.17 -0.17 0.14
2014 2009 9,725,832 11,611 0.322 0 1,218,442 8,507,389 6.98 -6.98 0.72
2015 2010 13,231,078 87,386 0.303 0 3,602,141 9,628,937 2.67 -2.67 0.63
2016 2011 2,573,729 43,953 0.313 0 2,076,519 497,210 0.24 -0.24 0.19
2017 2012 397,153 3,702 0.314 0 1,195,348 798,195 0.67 0.67 1.11
2018 2013 38,269 2,155 0.317 0 1,132,867 1,094,598 0.97 0.97 1.54
2019 2014 71,802 4,883 0.306 0 1,069,588 997,786 0.93 0.93 1.50
2020 2015 119,279 0 0.302 0 924,261 804,982 0.87 0.87 1.42
2021 2016 577,057 0 0.304 0 873,172 296,115 0.34 0.34 0.47
2022 2017 NA 8,419 0.307 0 982,061 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 1,247,528 2,757,912 0.467 0 1,378,939 131,412 0.10 0.10 0.10
2014 2009 9,725,832 2,266,140 0.468 0 1,066,406 8,659,426 8.12 -8.12 0.73
2015 2010 13,231,078 4,207,410 0.440 0 2,501,785 10,729,292 4.29 -4.29 0.68
2016 2011 2,573,729 2,264,352 0.436 0 1,181,809 1,391,920 1.18 -1.18 0.50
2017 2012 397,153 4,164,444 0.432 0 2,631,769 2,234,616 0.85 0.85 1.39
2018 2013 38,269 2,088,576 0.414 0 1,047,479 1,009,209 0.96 0.96 1.53
2019 2014 71,802 4,458,540 0.396 0 2,557,768 2,485,966 0.97 0.97 1.54
2020 2015 119,279 7,348,572 0.348 0 4,379,743 4,260,464 0.97 0.97 1.54
2021 2016 577,057 4,462,728 0.292 0 2,085,631 1,508,574 0.72 0.72 1.21
2022 2017 NA 3,163,404 0.285 0 1,351,173 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 1,247,528 2,757,912 0.012 0.244 1,281,089 33,561 0.03 0.03 0.03
2014 2009 9,725,832 2,266,140 0.013 0.235 1,021,967 8,703,864 8.52 -8.52 0.73
2015 2010 13,231,078 4,207,410 0.002 0.310 2,262,992 10,968,086 4.85 -4.85 0.69
2016 2011 2,573,729 2,264,352 0.000 0.325 1,157,502 1,416,227 1.22 -1.22 0.50
2017 2012 397,153 4,164,444 -0.002 0.344 2,389,722 1,992,569 0.83 0.83 1.37
2018 2013 38,269 2,088,576 -0.002 0.338 1,037,439 999,170 0.96 0.96 1.53
2019 2014 71,802 4,458,540 0.007 0.266 2,293,323 2,221,521 0.97 0.97 1.54
2020 2015 119,279 7,348,572 0.004 0.289 4,142,586 4,023,307 0.97 0.97 1.54
2021 2016 577,057 4,462,728 -0.008 0.429 1,957,603 1,380,546 0.71 0.71 1.17
2022 2017 NA 3,163,404 -0.008 0.424 1,271,156 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2013 2008 1,247,527.72 3,072,592 1,825,064 0.59 0.59 0.97
2014 2009 9,725,831.56 3,315,820 6,410,012 1.93 -1.93 0.58
2015 2010 13,231,077.52 4,734,101 8,496,977 1.79 -1.79 0.57
2016 2011 2,573,729.23 6,474,867 3,901,138 0.60 0.60 0.99
2017 2012 397,152.82 6,750,190 6,353,037 0.94 0.94 1.51
2018 2013 38,269.39 5,435,064 5,396,794 0.99 0.99 1.56
2019 2014 71,801.76 5,193,212 5,121,410 0.99 0.99 1.56
2020 2015 119,279.24 3,262,406 3,143,127 0.96 0.96 1.53
2021 2016 577,057.00 640,046 62,989 0.10 0.10 0.11
2022 2017 NA 240,712 NA NA NA NA

Performance summary

Blending the sibling, ln.sibling, and average models gives us a forecast of ~2.5 million fish.

model range MAD MAPE MPE MAAPE
sibling 5 years 2,462,143 90.75% 90.75% 1.46
sibling 3 years 2,328,280 89.48% 89.48% 1.44
ln.sibling 5 years 1,393,510 89.75% 47.28% 1.20
ln.sibling 3 years 919,142 88.75% 17.98% 1.02
lnY.sibling 5 years 798,335 75.54% 75.54% 1.21
lnY.sibling 3 years 699,628 71.43% 71.43% 1.13
lnS.lnR 5 years 2,299,766 89.61% 89.61% 1.44
lnS.lnR 3 years 2,751,668 88.93% 88.93% 1.43
ricker 5 years 2,123,423 88.84% 88.84% 1.43
ricker 3 years 2,541,791 88.17% 88.17% 1.42
average 5 years 4,015,472 79.64% 79.64% 1.25
average 3 years 2,775,842 68.27% 68.27% 1.07

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 1,930,847 2,679,158 0.300 0.000 1,266,532 664,315 0.52 -0.52 0.33
2014 2009 1,001,605 740,947 0.292 0.000 1,037,815 36,211 0.03 0.03 0.04
2015 2010 5,545,200 6,053,034 0.296 0.000 1,713,813 3,831,387 2.24 -2.24 0.60
2016 2011 2,168,999 2,846,209 0.244 0.001 1,399,643 769,356 0.55 -0.55 0.34
2017 2012 2,635,003 8,590,994 0.240 0.001 2,303,522 331,482 0.14 -0.14 0.13
2018 2013 2,789,274 3,713,931 0.264 0.000 1,562,926 1,226,348 0.78 -0.78 0.41
2019 2014 2,072,930 4,484,066 0.258 0.000 1,715,752 357,178 0.21 -0.21 0.17
2020 2015 7,068,371 5,743,118 0.261 0.000 1,927,285 5,141,086 2.67 -2.67 0.63
2021 2016 1,891,589 2,659,891 0.210 0.001 1,534,674 356,915 0.23 -0.23 0.19
2022 2017 NA 6,161,217 0.209 0.001 2,197,494 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 1,930,847 2,679,158 0.359 0 1,225,841 705,007 0.58 -0.58 0.35
2014 2009 1,001,605 740,947 0.362 0 649,860 351,744 0.54 -0.54 0.34
2015 2010 5,545,200 6,053,034 0.355 0 1,873,428 3,671,772 1.96 -1.96 0.58
2016 2011 2,168,999 2,846,209 0.380 0 1,345,773 823,227 0.61 -0.61 0.36
2017 2012 2,635,003 8,590,994 0.383 0 2,459,153 175,850 0.07 -0.07 0.07
2018 2013 2,789,274 3,713,931 0.400 0 1,578,049 1,211,225 0.77 -0.77 0.41
2019 2014 2,072,930 4,484,066 0.406 0 1,782,125 290,806 0.16 -0.16 0.14
2020 2015 7,068,371 5,743,118 0.412 0 2,052,431 5,015,940 2.44 -2.44 0.62
2021 2016 1,891,589 2,659,891 0.425 0 1,395,892 495,697 0.36 -0.36 0.26
2022 2017 NA 6,161,217 0.426 0 2,285,419 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 1,930,847 2,679,158 0.190 0.005 980,460 950,387 0.97 -0.97 0.46
2014 2009 1,001,605 740,947 0.185 0.005 809,420 192,184 0.24 -0.24 0.19
2015 2010 5,545,200 6,053,034 0.184 0.004 1,443,031 4,102,169 2.84 -2.84 0.64
2016 2011 2,168,999 2,846,209 0.202 0.002 1,057,343 1,111,656 1.05 -1.05 0.47
2017 2012 2,635,003 8,590,994 0.198 0.002 2,102,608 532,396 0.25 -0.25 0.20
2018 2013 2,789,274 3,713,931 0.218 0.001 1,199,550 1,589,724 1.33 -1.33 0.52
2019 2014 2,072,930 4,484,066 0.216 0.001 1,343,428 729,502 0.54 -0.54 0.34
2020 2015 7,068,371 5,743,118 0.220 0.001 1,583,734 5,484,637 3.46 -3.46 0.66
2021 2016 1,891,589 2,659,891 0.229 0.001 1,121,950 769,639 0.69 -0.69 0.39
2022 2017 NA 6,161,217 0.226 0.001 1,781,687 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 1,930,847 2,757,912 0.059 0.083 972,938 957,909 0.98 -0.98 0.46
2014 2009 1,001,605 2,266,140 0.056 0.086 944,457 57,148 0.06 -0.06 0.06
2015 2010 5,545,200 4,207,410 0.056 0.082 1,102,624 4,442,576 4.03 -4.03 0.68
2016 2011 2,168,999 2,264,352 0.057 0.077 981,287 1,187,713 1.21 -1.21 0.50
2017 2012 2,635,003 4,164,444 0.052 0.085 1,170,912 1,464,092 1.25 -1.25 0.51
2018 2013 2,789,274 2,088,576 0.054 0.077 1,000,231 1,789,043 1.79 -1.79 0.57
2019 2014 2,072,930 4,458,540 0.045 0.093 1,242,346 830,584 0.67 -0.67 0.38
2020 2015 7,068,371 7,348,572 0.048 0.084 1,428,340 5,640,030 3.95 -3.95 0.67
2021 2016 1,891,589 4,462,728 0.066 0.052 1,322,676 568,913 0.43 -0.43 0.29
2022 2017 NA 3,163,404 0.068 0.047 1,206,168 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 1,930,847 2,757,912 0.307 0 1,142,758 788,089 0.69 -0.69 0.39
2014 2009 1,001,605 2,266,140 0.312 0 1,021,691 20,086 0.02 0.02 0.02
2015 2010 5,545,200 4,207,410 0.314 0 1,453,279 4,091,921 2.82 -2.82 0.64
2016 2011 2,168,999 2,264,352 0.303 0 1,058,229 1,110,770 1.05 -1.05 0.47
2017 2012 2,635,003 4,164,444 0.309 0 1,526,764 1,108,240 0.73 -0.73 0.40
2018 2013 2,789,274 2,088,576 0.308 0 1,038,601 1,750,673 1.69 -1.69 0.56
2019 2014 2,072,930 4,458,540 0.314 0 1,627,946 444,984 0.27 -0.27 0.21
2020 2015 7,068,371 7,348,572 0.314 0 1,781,324 5,287,046 2.97 -2.97 0.64
2021 2016 1,891,589 4,462,728 0.288 0 1,688,647 202,943 0.12 -0.12 0.11
2022 2017 NA 3,163,404 0.288 0 1,436,755 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2013 2008 1,930,847 2,141,031 210,184 0.10 0.10 0.11
2014 2009 1,001,605 2,289,964 1,288,359 0.56 0.56 0.91
2015 2010 5,545,200 1,904,052 3,641,148 1.91 -1.91 0.58
2016 2011 2,168,999 2,606,403 437,403 0.17 0.17 0.20
2017 2012 2,635,003 2,499,803 135,200 0.05 -0.05 0.05
2018 2013 2,789,274 2,656,331 132,943 0.05 -0.05 0.05
2019 2014 2,072,930 2,828,016 755,086 0.27 0.27 0.35
2020 2015 7,068,371 3,042,281 4,026,090 1.32 -1.32 0.52
2021 2016 1,891,589 3,346,915 1,455,326 0.43 0.43 0.66
2022 2017 NA 3,291,433 NA NA NA NA

Performance summary

Blending the average, sibling and ln.sibling gives us a forecast of ~2.6 million fish.

model range MAD MAPE MPE MAAPE
sibling 5 years 1,482,602 80.74% -80.74% 0.31
sibling 3 years 1,951,727 103.61% -103.61% 0.33
ln.sibling 5 years 1,437,903 76.02% -76.02% 0.30
ln.sibling 3 years 1,934,147 98.74% -98.74% 0.34
lnY.sibling 5 years 1,821,179 125.41% -125.41% 0.42
lnY.sibling 3 years 2,327,926 156.40% -156.40% 0.46
lnS.lnR 5 years 2,058,533 161.73% -161.73% 0.48
lnS.lnR 3 years 2,346,509 168.24% -168.24% 0.45
ricker 5 years 1,758,777 115.46% -115.46% 0.38
ricker 3 years 1,978,324 112.05% -112.05% 0.32
average 5 years 1,300,929 42.59% -14.51% 0.32
average 3 years 2,078,834 67.51% -20.72% 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 2,379,818 6,972,782 0.328 0 774,961 1,604,857 2.07 -2.07 0.59
2014 2008 679,005 1,247,528 0.304 0 445,870 233,135 0.52 -0.52 0.33
2015 2009 1,396,254 9,725,832 0.302 0 1,006,296 389,958 0.39 -0.39 0.27
2016 2010 851,679 13,231,078 0.309 0 1,251,159 399,480 0.32 0.32 0.44
2017 2011 491,950 2,573,729 0.304 0 542,461 50,511 0.09 0.09 0.10
2018 2012 143,170 397,153 0.306 0 400,390 257,220 0.64 0.64 1.06
2019 2013 32,243 38,269 0.312 0 367,746 335,503 0.91 0.91 1.47
2020 2014 3,353 71,802 0.320 0 357,779 354,426 0.99 0.99 1.56
2021 2015 229,984 119,279 0.327 0 348,587 118,603 0.34 0.34 0.48
2022 2016 NA 577,057 0.332 0 375,309 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 2,379,818 6,972,782 0.515 0 731,258 1,648,561 2.25 -2.25 0.61
2014 2008 679,005 1,247,528 0.522 0 316,034 362,970 1.15 -1.15 0.49
2015 2009 1,396,254 9,725,832 0.515 0 933,312 462,942 0.50 -0.50 0.32
2016 2010 851,679 13,231,078 0.527 0 1,119,489 267,810 0.24 0.24 0.30
2017 2011 491,950 2,573,729 0.531 0 471,479 20,471 0.04 -0.04 0.04
2018 2012 143,170 397,153 0.532 0 179,092 35,922 0.20 0.20 0.25
2019 2013 32,243 38,269 0.539 0 52,380 20,137 0.38 0.38 0.56
2020 2014 3,353 71,802 0.578 0 68,933 65,581 0.95 0.95 1.52
2021 2015 229,984 119,279 0.585 0 71,725 158,260 2.21 -2.21 0.60
2022 2016 NA 577,057 0.571 0 192,430 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 2,379,818 6,972,782 0.281 0.001 402,779 1,977,039 4.91 -4.91 0.69
2014 2008 679,005 1,247,528 0.271 0.001 254,098 424,907 1.67 -1.67 0.56
2015 2009 1,396,254 9,725,832 0.260 0.001 552,312 843,941 1.53 -1.53 0.54
2016 2010 851,679 13,231,078 0.267 0.001 780,714 70,965 0.09 -0.09 0.08
2017 2011 491,950 2,573,729 0.275 0.000 301,398 190,552 0.63 -0.63 0.37
2018 2012 143,170 397,153 0.272 0.000 251,852 108,682 0.43 0.43 0.65
2019 2013 32,243 38,269 0.279 0.000 238,914 206,671 0.87 0.87 1.42
2020 2014 3,353 71,802 0.286 0.000 222,869 219,516 0.98 0.98 1.56
2021 2015 229,984 119,279 0.263 0.000 193,477 36,507 0.19 -0.19 0.16
2022 2016 NA 577,057 0.264 0.000 204,119 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 2,379,818 2,810,208 0.152 0.012 324,797 2,055,021 6.33 -6.33 0.71
2014 2008 679,005 2,757,912 0.136 0.015 340,259 338,746 1.00 -1.00 0.46
2015 2009 1,396,254 2,266,140 0.134 0.015 312,805 1,083,449 3.46 -3.46 0.66
2016 2010 851,679 4,207,410 0.121 0.018 448,519 403,160 0.90 -0.90 0.44
2017 2011 491,950 2,264,352 0.124 0.016 331,741 160,209 0.48 -0.48 0.31
2018 2012 143,170 4,164,444 0.122 0.015 458,212 315,042 0.69 0.69 1.14
2019 2013 32,243 2,088,576 0.115 0.017 314,153 281,910 0.90 0.90 1.46
2020 2014 3,353 4,458,540 0.119 0.015 439,829 436,477 0.99 0.99 1.56
2021 2015 229,984 7,348,572 0.065 0.055 491,029 261,045 0.53 0.53 0.85
2022 2016 NA 4,462,728 0.060 0.059 377,475 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 2,379,818 2,810,208 0.101 0.035 369,915 2,009,903 5.43 -5.43 0.70
2014 2008 679,005 2,757,912 0.106 0.030 388,301 290,703 0.75 -0.75 0.40
2015 2009 1,396,254 2,266,140 0.110 0.025 341,619 1,054,634 3.09 -3.09 0.65
2016 2010 851,679 4,207,410 0.118 0.020 541,218 310,461 0.57 -0.57 0.35
2017 2011 491,950 2,264,352 0.119 0.018 362,786 129,164 0.36 -0.36 0.26
2018 2012 143,170 4,164,444 0.123 0.015 548,920 405,750 0.74 0.74 1.23
2019 2013 32,243 2,088,576 0.117 0.016 332,663 300,420 0.90 0.90 1.46
2020 2014 3,353 4,458,540 0.091 0.030 520,834 517,481 0.99 0.99 1.56
2021 2015 229,984 7,348,572 0.058 0.065 573,695 343,711 0.60 0.60 0.98
2022 2016 NA 4,462,728 0.064 0.054 454,074 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2013 2007 2,379,818.218 639,106 1,740,712 2.72 -2.72 0.63
2014 2008 679,004.807 1,113,021 434,016 0.39 0.39 0.57
2015 2009 1,396,253.526 1,222,869 173,385 0.14 -0.14 0.12
2016 2010 851,679.142 1,391,156 539,477 0.39 0.39 0.56
2017 2011 491,949.803 1,210,679 718,730 0.59 0.59 0.97
2018 2012 143,170.081 1,159,741 1,016,571 0.88 0.88 1.43
2019 2013 32,242.898 712,411 680,169 0.95 0.95 1.52
2020 2014 3,352.858 583,059 579,706 0.99 0.99 1.57
2021 2015 229,984.301 304,479 74,495 0.24 0.24 0.31
2022 2016 NA 180,140 NA NA NA NA

Performance summary

THe ln.sibling performs best here and gives us a forecast of ~0.19 million fish.

model range MAD MAPE MPE MAAPE
sibling 5 years 223,253 59.57% 59.57% 0.94
sibling 3 years 269,511 74.77% 74.77% 1.17
ln.sibling 5 years 60,074 75.73% -14.27% 0.59
ln.sibling 3 years 81,326 118.08% -29.02% 0.89
lnY.sibling 5 years 152,386 62.05% 29.21% 0.83
lnY.sibling 3 years 154,231 67.96% 55.38% 1.04
lnS.lnR 5 years 290,936 71.84% 52.52% 1.07
lnS.lnR 3 years 326,477 80.71% 80.71% 1.29
ricker 5 years 339,305 71.82% 57.58% 1.10
ricker 3 years 387,204 83.19% 83.19% 1.34
average 5 years 613,934 73.28% 73.28% 1.16
average 3 years 444,790 73.12% 73.12% 1.13

Forecast summary

A preliminary look at the models for this river leads us to an initial forecast of ~8.4 million broken down as follows:

Table 2. Preliminary Forecast.

age forecast
1.2 4.40
2.2 1.20
1.3 2.50
2.3 0.19