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. Two of these models give us about 1 million and the other is 3 million.

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 376,195 8,822 0.019 0.203 1,147,993 771,797 0.67 0.67 1.12
2014 2010 578,974 10,043 0.018 0.206 1,147,764 568,790 0.50 0.50 0.78
2015 2011 2,738,603 64,031 0.017 0.209 2,051,479 687,124 0.33 -0.33 0.25
2016 2012 3,480,574 104,693 0.071 0.056 3,154,645 325,929 0.10 -0.10 0.09
2017 2013 3,860,507 29,906 0.172 0.005 1,615,735 2,244,772 1.39 -1.39 0.53
2018 2014 2,596,182 70,410 0.188 0.003 2,724,986 128,804 0.05 0.05 0.05
2019 2015 1,880,556 13,554 0.213 0.001 1,299,922 580,633 0.45 -0.45 0.30
2020 2016 3,018,963 53,838 0.212 0.001 2,308,219 710,744 0.31 -0.31 0.23
2021 2017 6,651,553 103,762 0.243 0.000 3,665,233 2,986,320 0.81 -0.81 0.42
2022 2018 NA 20,525 0.403 0.000 1,617,253 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 376,195 8,822 0.277 0.001 1,119,706 743,511 0.66 0.66 1.10
2014 2010 578,974 10,043 0.260 0.001 1,094,553 515,579 0.47 0.47 0.73
2015 2011 2,738,603 64,031 0.254 0.001 1,497,306 1,241,297 0.83 -0.83 0.43
2016 2012 3,480,574 104,693 0.275 0.000 1,712,704 1,767,870 1.03 -1.03 0.47
2017 2013 3,860,507 29,906 0.300 0.000 1,409,273 2,451,234 1.74 -1.74 0.57
2018 2014 2,596,182 70,410 0.316 0.000 1,761,730 834,453 0.47 -0.47 0.31
2019 2015 1,880,556 13,554 0.331 0.000 1,281,660 598,896 0.47 -0.47 0.31
2020 2016 3,018,963 53,838 0.338 0.000 1,732,327 1,286,636 0.74 -0.74 0.40
2021 2017 6,651,553 103,762 0.352 0.000 2,047,191 4,604,362 2.25 -2.25 0.61
2022 2018 NA 20,525 0.374 0.000 1,527,251 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 376,195 8,822 0.035 0.142 692,397 316,202 0.46 0.46 0.70
2014 2010 578,974 10,043 0.034 0.140 700,376 121,402 0.17 0.17 0.21
2015 2011 2,738,603 64,031 0.035 0.136 2,428,737 309,867 0.13 -0.13 0.11
2016 2012 3,480,574 104,693 0.070 0.058 6,683,723 3,203,149 0.48 0.48 0.74
2017 2013 3,860,507 29,906 0.108 0.022 1,037,138 2,823,369 2.72 -2.72 0.63
2018 2014 2,596,182 70,410 0.122 0.014 2,656,381 60,198 0.02 0.02 0.02
2019 2015 1,880,556 13,554 0.144 0.008 767,539 1,113,017 1.45 -1.45 0.53
2020 2016 3,018,963 53,838 0.143 0.007 1,886,301 1,132,662 0.60 -0.60 0.36
2021 2017 6,651,553 103,762 0.164 0.004 6,081,657 569,896 0.09 -0.09 0.09
2022 2018 NA 20,525 0.216 0.001 930,261 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 376,195 1,364,338 0.356 0 1,023,202 647,007 0.63 0.63 1.04
2014 2010 578,974 830,886 0.342 0 674,136 95,162 0.14 0.14 0.16
2015 2011 2,738,603 1,029,853 0.342 0 791,899 1,946,704 2.46 -2.46 0.62
2016 2012 3,480,574 670,578 0.339 0 586,877 2,893,697 4.93 -4.93 0.69
2017 2013 3,860,507 898,110 0.315 0 769,354 3,091,152 4.02 -4.02 0.68
2018 2014 2,596,182 640,158 0.305 0 615,985 1,980,198 3.21 -3.21 0.65
2019 2015 1,880,556 1,564,638 0.290 0 1,266,161 614,395 0.49 -0.49 0.32
2020 2016 3,018,963 1,635,270 0.297 0 1,329,076 1,689,887 1.27 -1.27 0.51
2021 2017 6,651,553 1,186,446 0.307 0 1,063,006 5,588,547 5.26 -5.26 0.70
2022 2018 NA 1,167,792 0.303 0 1,100,788 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 376,195 1,364,338 0.075 0.058 1,009,777 633,581 0.63 0.63 1.03
2014 2010 578,974 830,886 0.080 0.050 761,271 182,297 0.24 0.24 0.31
2015 2011 2,738,603 1,029,853 0.079 0.048 854,975 1,883,628 2.20 -2.20 0.60
2016 2012 3,480,574 670,578 0.077 0.048 676,075 2,804,499 4.15 -4.15 0.68
2017 2013 3,860,507 898,110 0.085 0.038 854,574 3,005,933 3.52 -3.52 0.66
2018 2014 2,596,182 640,158 0.085 0.036 720,912 1,875,270 2.60 -2.60 0.63
2019 2015 1,880,556 1,564,638 0.093 0.028 1,124,556 756,000 0.67 -0.67 0.38
2020 2016 3,018,963 1,635,270 0.089 0.029 1,154,914 1,864,049 1.61 -1.61 0.55
2021 2017 6,651,553 1,186,446 0.079 0.036 1,083,659 5,567,894 5.14 -5.14 0.70
2022 2018 NA 1,167,792 0.069 0.045 1,121,893 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2013 2009 376,195.4 1,116,807 740,612 0.66 0.66 1.10
2014 2010 578,973.6 928,150 349,176 0.38 0.38 0.54
2015 2011 2,738,603.2 868,700 1,869,903 2.15 -2.15 0.60
2016 2012 3,480,574.0 1,203,037 2,277,537 1.89 -1.89 0.58
2017 2013 3,860,506.7 1,644,222 2,216,284 1.35 -1.35 0.52
2018 2014 2,596,182.4 2,206,971 389,212 0.18 -0.18 0.15
2019 2015 1,880,555.7 2,650,968 770,412 0.29 0.29 0.39
2020 2016 3,018,963.0 2,911,284 107,679 0.04 -0.04 0.04
2021 2017 6,651,553.1 2,967,356 3,684,197 1.24 -1.24 0.51
2022 2018 NA 3,601,552 NA NA NA NA

Performance summary

Three models interest me here: Sibling lnY.sib and average. All are significant and produce forecasts between 0.9 and 3.6 million. This age class has been increasing in recent years so we might tend to believe the average (3.6m) over the others. Dropping the average gets us ~1.9 million.

model range MAD MAPE MPE MAAPE
sibling 5 years 1,330,255 60.12% -58.23% 0.31
sibling 3 years 1,425,899 52.31% -52.31% 0.32
ln.sibling 5 years 1,955,116 113.44% -113.44% 0.44
ln.sibling 3 years 2,163,298 115.30% -115.30% 0.44
lnY.sibling 5 years 1,139,828 97.78% -96.88% 0.33
lnY.sibling 3 years 938,525 71.48% -71.48% 0.33
lnS.lnR 5 years 2,592,836 284.93% -284.93% 0.57
lnS.lnR 3 years 2,630,943 233.80% -233.80% 0.51
ricker 5 years 2,613,829 270.86% -270.86% 0.58
ricker 3 years 2,729,314 247.48% -247.48% 0.54
average 5 years 1,433,557 61.87% -50.24% 0.32
average 3 years 1,520,763 52.31% -32.93% 0.31

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 332,158 1,655 0.365 0 750,379 418,221 0.56 0.56 0.90
2014 2009 144,293 2,519 0.371 0 770,092 625,799 0.81 0.81 1.34
2015 2010 441,803 6,938 0.376 0 931,114 489,311 0.53 0.53 0.84
2016 2011 1,304,626 41,290 0.376 0 2,339,606 1,034,980 0.44 0.44 0.67
2017 2012 653,764 5,117 0.349 0 835,659 181,895 0.22 0.22 0.27
2018 2013 56,488 978 0.351 0 674,248 617,760 0.92 0.92 1.48
2019 2014 53,209 0 0.358 0 615,738 562,528 0.91 0.91 1.48
2020 2015 321,080 6,554 0.365 0 852,009 530,929 0.62 0.62 1.03
2021 2016 846,586 5,883 0.365 0 812,747 33,840 0.04 -0.04 0.04
2022 2017 NA 3,289 0.366 0 711,814 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 332,158 1,655 0.602 0 665,718 333,560 0.50 0.50 0.79
2014 2009 144,293 2,519 0.597 0 744,378 600,085 0.81 0.81 1.33
2015 2010 441,803 6,938 0.569 0 972,388 530,584 0.55 0.55 0.88
2016 2011 1,304,626 41,290 0.560 0 1,635,401 330,775 0.20 0.20 0.25
2017 2012 653,764 5,117 0.564 0 855,869 202,105 0.24 0.24 0.30
2018 2013 56,488 978 0.563 0 514,029 457,541 0.89 0.89 1.45
2019 2014 53,209 0 0.528 0 60,514 7,305 0.12 0.12 0.14
2020 2015 321,080 6,554 0.561 0 870,465 549,385 0.63 0.63 1.04
2021 2016 846,586 5,883 0.549 0 818,367 28,219 0.03 -0.03 0.03
2022 2017 NA 3,289 0.551 0 686,297 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 332,158 1,655 0.231 0.002 408,023 75,865 0.19 0.19 0.22
2014 2009 144,293 2,519 0.235 0.002 421,602 277,309 0.66 0.66 1.09
2015 2010 441,803 6,938 0.241 0.001 501,965 60,162 0.12 0.12 0.14
2016 2011 1,304,626 41,290 0.242 0.001 2,576,752 1,272,125 0.49 0.49 0.77
2017 2012 653,764 5,117 0.244 0.001 456,555 197,209 0.43 -0.43 0.29
2018 2013 56,488 978 0.243 0.001 382,743 326,255 0.85 0.85 1.40
2019 2014 53,209 0 0.249 0.001 342,569 289,360 0.84 0.84 1.39
2020 2015 321,080 6,554 0.257 0.000 443,045 121,965 0.28 0.28 0.36
2021 2016 846,586 5,883 0.258 0.000 425,299 421,287 0.99 -0.99 0.46
2022 2017 NA 3,289 0.255 0.000 380,896 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 332,158 596,332 0.115 0.026 523,441 191,283 0.37 0.37 0.52
2014 2009 144,293 1,364,338 0.117 0.023 796,752 652,459 0.82 0.82 1.35
2015 2010 441,803 830,886 0.100 0.032 585,872 144,069 0.25 0.25 0.32
2016 2011 1,304,626 1,029,853 0.100 0.030 646,829 657,797 1.02 -1.02 0.47
2017 2012 653,764 670,578 0.103 0.026 531,895 121,869 0.23 -0.23 0.18
2018 2013 56,488 898,110 0.103 0.025 618,859 562,371 0.91 0.91 1.47
2019 2014 53,209 640,158 0.090 0.032 493,763 440,554 0.89 0.89 1.45
2020 2015 321,080 1,564,638 0.089 0.031 733,581 412,501 0.56 0.56 0.91
2021 2016 846,586 1,635,270 0.083 0.034 727,484 119,102 0.16 -0.16 0.14
2022 2017 NA 1,186,446 0.087 0.030 624,594 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 332,158 596,332 0.047 0.111 584,812 252,654 0.43 0.43 0.65
2014 2009 144,293 1,364,338 0.044 0.114 896,761 752,468 0.84 0.84 1.38
2015 2010 441,803 830,886 0.050 0.098 680,480 238,677 0.35 0.35 0.50
2016 2011 1,304,626 1,029,853 0.049 0.097 751,677 552,950 0.74 -0.74 0.40
2017 2012 653,764 670,578 0.050 0.092 597,615 56,149 0.09 -0.09 0.09
2018 2013 56,488 898,110 0.051 0.086 713,480 656,992 0.92 0.92 1.49
2019 2014 53,209 640,158 0.040 0.110 541,803 488,593 0.90 0.90 1.46
2020 2015 321,080 1,564,638 0.026 0.157 811,763 490,683 0.60 0.60 0.99
2021 2016 846,586 1,635,270 0.032 0.130 792,902 53,684 0.07 -0.07 0.06
2022 2017 NA 1,186,446 0.033 0.124 712,575 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2013 2008 332,158.15 816,119 483,960 0.59 0.59 0.97
2014 2009 144,293.15 875,419 731,126 0.84 0.84 1.38
2015 2010 441,803.28 656,652 214,849 0.33 0.33 0.45
2016 2011 1,304,626.36 510,170 794,456 1.56 -1.56 0.55
2017 2012 653,764.07 584,075 69,689 0.12 -0.12 0.11
2018 2013 56,487.63 575,329 518,841 0.90 0.90 1.46
2019 2014 53,209.32 520,195 466,986 0.90 0.90 1.46
2020 2015 321,079.83 501,978 180,898 0.36 0.36 0.51
2021 2016 846,586.29 477,833 368,753 0.77 -0.77 0.41
2022 2017 NA 386,225 NA NA NA NA

Performance summary

The ln.sibling model performs best here giving us a forecast of ~0.69 million.

model range MAD MAPE MPE MAAPE
sibling 5 years 385,390 54.25% 52.58% 0.86
sibling 3 years 375,766 52.61% 49.84% 0.85
ln.sibling 5 years 248,911 38.25% 36.87% 0.59
ln.sibling 3 years 194,970 26.21% 23.91% 0.40
lnY.sibling 5 years 271,215 67.90% 11.00% 0.78
lnY.sibling 3 years 277,537 70.35% 4.31% 0.74
lnS.lnR 5 years 331,279 55.12% 39.41% 0.83
lnS.lnR 3 years 324,052 53.94% 43.03% 0.83
ricker 5 years 349,220 51.77% 45.31% 0.82
ricker 3 years 344,320 52.47% 47.95% 0.84
average 5 years 321,033 61.02% 25.38% 0.79
average 3 years 338,879 67.66% 16.21% 0.79

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 1,728,705 1,046,765 0.153 0.012 1,202,802 525,903 0.44 -0.44 0.30
2014 2009 317,078 376,195 0.152 0.011 983,013 665,935 0.68 0.68 1.13
2015 2010 790,184 578,974 0.161 0.008 1,029,966 239,782 0.23 0.23 0.29
2016 2011 2,087,482 2,738,603 0.165 0.007 1,808,594 278,888 0.15 -0.15 0.13
2017 2012 1,582,991 3,480,574 0.184 0.004 2,110,120 527,129 0.25 0.25 0.32
2018 2013 2,008,451 3,860,507 0.180 0.004 2,173,399 164,948 0.08 0.08 0.08
2019 2014 1,576,519 2,596,182 0.195 0.002 1,716,729 140,209 0.08 0.08 0.09
2020 2015 1,598,528 1,880,556 0.198 0.002 1,466,584 131,944 0.09 -0.09 0.08
2021 2016 2,905,442 3,018,963 0.201 0.002 1,857,897 1,047,546 0.56 -0.56 0.35
2022 2017 NA 6,651,553 0.232 0.001 3,271,115 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 1,728,705 1,046,765 0.650 0 1,177,870 550,835 0.47 -0.47 0.31
2014 2009 317,078 376,195 0.652 0 488,477 171,399 0.35 0.35 0.50
2015 2010 790,184 578,974 0.654 0 702,796 87,388 0.12 -0.12 0.11
2016 2011 2,087,482 2,738,603 0.654 0 2,750,412 662,930 0.24 0.24 0.31
2017 2012 1,582,991 3,480,574 0.658 0 3,331,685 1,748,694 0.52 0.52 0.84
2018 2013 2,008,451 3,860,507 0.652 0 3,457,740 1,449,289 0.42 0.42 0.63
2019 2014 1,576,519 2,596,182 0.652 0 2,391,736 815,216 0.34 0.34 0.48
2020 2015 1,598,528 1,880,556 0.652 0 1,795,979 197,451 0.11 0.11 0.12
2021 2016 2,905,442 3,018,963 0.654 0 2,642,828 262,615 0.10 -0.10 0.09
2022 2017 NA 6,651,553 0.662 0 5,102,123 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 1,728,705 1,046,765 0.154 0.011 752,819 975,886 1.30 -1.30 0.51
2014 2009 317,078 376,195 0.152 0.011 543,219 226,141 0.42 0.42 0.62
2015 2010 790,184 578,974 0.159 0.008 592,197 197,987 0.33 -0.33 0.25
2016 2011 2,087,482 2,738,603 0.158 0.008 1,865,835 221,647 0.12 -0.12 0.11
2017 2012 1,582,991 3,480,574 0.171 0.005 2,793,809 1,210,818 0.43 0.43 0.65
2018 2013 2,008,451 3,860,507 0.173 0.004 3,139,713 1,131,262 0.36 0.36 0.51
2019 2014 1,576,519 2,596,182 0.181 0.003 1,595,324 18,805 0.01 0.01 0.01
2020 2015 1,598,528 1,880,556 0.187 0.002 1,127,752 470,776 0.42 -0.42 0.29
2021 2016 2,905,442 3,018,963 0.190 0.002 1,984,079 921,363 0.46 -0.46 0.31
2022 2017 NA 6,651,553 0.206 0.001 12,425,054 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 1,728,705 596,332 0.412 0 608,340 1,120,365 1.84 -1.84 0.58
2014 2009 317,078 1,364,338 0.401 0 1,311,229 994,151 0.76 0.76 1.26
2015 2010 790,184 830,886 0.378 0 810,606 20,423 0.03 0.03 0.03
2016 2011 2,087,482 1,029,853 0.378 0 975,757 1,111,725 1.14 -1.14 0.49
2017 2012 1,582,991 670,578 0.379 0 685,246 897,745 1.31 -1.31 0.52
2018 2013 2,008,451 898,110 0.373 0 902,486 1,105,965 1.23 -1.23 0.50
2019 2014 1,576,519 640,158 0.371 0 685,396 891,124 1.30 -1.30 0.51
2020 2015 1,598,528 1,564,638 0.365 0 1,517,635 80,894 0.05 -0.05 0.05
2021 2016 2,905,442 1,635,270 0.369 0 1,579,831 1,325,611 0.84 -0.84 0.43
2022 2017 NA 1,186,446 0.378 0 1,218,399 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 1,728,705 596,332 0.067 0.073 727,393 1,001,312 1.38 -1.38 0.53
2014 2009 317,078 1,364,338 0.076 0.057 1,216,888 899,810 0.74 0.74 1.23
2015 2010 790,184 830,886 0.081 0.049 914,306 124,122 0.14 0.14 0.16
2016 2011 2,087,482 1,029,853 0.081 0.046 1,027,323 1,060,159 1.03 -1.03 0.47
2017 2012 1,582,991 670,578 0.081 0.044 807,435 775,556 0.96 -0.96 0.46
2018 2013 2,008,451 898,110 0.087 0.036 989,668 1,018,783 1.03 -1.03 0.47
2019 2014 1,576,519 640,158 0.089 0.033 815,672 760,848 0.93 -0.93 0.45
2020 2015 1,598,528 1,564,638 0.095 0.027 1,274,913 323,615 0.25 -0.25 0.20
2021 2016 2,905,442 1,635,270 0.094 0.026 1,296,965 1,608,477 1.24 -1.24 0.51
2022 2017 NA 1,186,446 0.085 0.031 1,203,240 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2013 2008 1,728,705.0 1,489,575 239,130 0.16 -0.16 0.14
2014 2009 317,077.9 1,528,847 1,211,769 0.79 0.79 1.31
2015 2010 790,183.5 1,273,444 483,260 0.38 0.38 0.55
2016 2011 2,087,481.8 968,670 1,118,811 1.15 -1.15 0.49
2017 2012 1,582,990.7 1,170,680 412,311 0.35 -0.35 0.25
2018 2013 2,008,451.0 1,301,288 707,163 0.54 -0.54 0.34
2019 2014 1,576,519.5 1,357,237 219,283 0.16 -0.16 0.14
2020 2015 1,598,528.3 1,609,125 10,597 0.01 0.01 0.01
2021 2016 2,905,442.4 1,770,794 1,134,648 0.64 -0.64 0.37
2022 2017 NA 1,934,386 NA NA NA NA

Performance summary

The sibling model performs best giving us a forecast of ~3.3 million.

model range MAD MAPE MPE MAAPE
sibling 5 years 402,355 21.22% -4.93% 0.18
sibling 3 years 439,900 24.52% -19.07% 0.17
ln.sibling 5 years 894,653 29.88% 25.91% 0.43
ln.sibling 3 years 425,094 18.34% 11.71% 0.23
lnY.sibling 5 years 750,605 33.75% -1.53% 0.35
lnY.sibling 3 years 470,315 29.79% -29.00% 0.20
lnS.lnR 5 years 860,268 94.56% -94.56% 0.40
lnS.lnR 3 years 765,876 73.08% -73.08% 0.33
ricker 5 years 897,456 88.33% -88.33% 0.42
ricker 3 years 897,647 80.89% -80.89% 0.38
average 5 years 496,800 34.09% -33.83% 0.22
average 3 years 454,843 26.96% -26.52% 0.17

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 180,507 697,496 0.343 0 389,347 208,840 0.54 0.54 0.86
2014 2008 39,860 332,158 0.346 0 245,456 205,596 0.84 0.84 1.38
2015 2009 132,478 144,293 0.355 0 165,310 32,832 0.20 0.20 0.24
2016 2010 283,973 441,803 0.362 0 277,024 6,949 0.03 -0.03 0.02
2017 2011 495,528 1,304,626 0.365 0 605,844 110,315 0.18 0.18 0.22
2018 2012 84,332 653,764 0.364 0 355,569 271,237 0.76 0.76 1.27
2019 2013 31,764 56,488 0.367 0 119,420 87,656 0.73 0.73 1.22
2020 2014 28,826 53,209 0.376 0 113,921 85,095 0.75 0.75 1.24
2021 2015 229,746 321,080 0.385 0 213,688 16,058 0.08 -0.08 0.07
2022 2016 NA 846,586 0.388 0 417,527 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 180,507 697,496 0.676 0 316,697 136,190 0.43 0.43 0.65
2014 2008 39,860 332,158 0.671 0 174,203 134,343 0.77 0.77 1.28
2015 2009 132,478 144,293 0.656 0 85,596 46,882 0.55 -0.55 0.34
2016 2010 283,973 441,803 0.655 0 211,523 72,450 0.34 -0.34 0.25
2017 2011 495,528 1,304,626 0.654 0 499,738 4,210 0.01 0.01 0.01
2018 2012 84,332 653,764 0.657 0 290,095 205,763 0.71 0.71 1.18
2019 2013 31,764 56,488 0.640 0 41,258 9,494 0.23 0.23 0.29
2020 2014 28,826 53,209 0.661 0 38,410 9,584 0.25 0.25 0.32
2021 2015 229,746 321,080 0.680 0 157,830 71,916 0.46 -0.46 0.30
2022 2016 NA 846,586 0.679 0 345,428 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 180,507 697,496 0.487 0 190,227 9,719 0.05 0.05 0.05
2014 2008 39,860 332,158 0.489 0 133,697 93,837 0.70 0.70 1.17
2015 2009 132,478 144,293 0.495 0 105,498 26,981 0.26 -0.26 0.20
2016 2010 283,973 441,803 0.498 0 142,847 141,126 0.99 -0.99 0.46
2017 2011 495,528 1,304,626 0.491 0 337,791 157,737 0.47 -0.47 0.31
2018 2012 84,332 653,764 0.493 0 181,228 96,896 0.53 0.53 0.85
2019 2013 31,764 56,488 0.494 0 98,746 66,982 0.68 0.68 1.13
2020 2014 28,826 53,209 0.506 0 93,169 64,343 0.69 0.69 1.15
2021 2015 229,746 321,080 0.518 0 116,615 113,131 0.97 -0.97 0.46
2022 2016 NA 846,586 0.512 0 204,854 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 180,507 2,599,186 0.167 0.009 561,699 381,191 0.68 0.68 1.13
2014 2008 39,860 596,332 0.149 0.011 241,861 202,001 0.84 0.84 1.38
2015 2009 132,478 1,364,338 0.146 0.011 356,038 223,559 0.63 0.63 1.04
2016 2010 283,973 830,886 0.137 0.013 266,458 17,515 0.07 -0.07 0.06
2017 2011 495,528 1,029,853 0.138 0.011 297,981 197,548 0.66 -0.66 0.38
2018 2012 84,332 670,578 0.141 0.010 242,041 157,709 0.65 0.65 1.08
2019 2013 31,764 898,110 0.140 0.009 274,532 242,768 0.88 0.88 1.44
2020 2014 28,826 640,158 0.125 0.012 219,014 190,188 0.87 0.87 1.42
2021 2015 229,746 1,564,638 0.121 0.013 331,783 102,037 0.31 0.31 0.42
2022 2016 NA 1,635,270 0.120 0.012 334,932 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 180,507 2,599,186 0.050 0.105 446,150 265,643 0.60 0.60 0.97
2014 2008 39,860 596,332 0.085 0.047 283,740 243,880 0.86 0.86 1.41
2015 2009 132,478 1,364,338 0.065 0.069 400,663 268,185 0.67 0.67 1.11
2016 2010 283,973 830,886 0.070 0.059 316,280 32,307 0.10 0.10 0.11
2017 2011 495,528 1,029,853 0.071 0.056 350,284 145,244 0.41 -0.41 0.29
2018 2012 84,332 670,578 0.071 0.053 280,418 196,085 0.70 0.70 1.16
2019 2013 31,764 898,110 0.064 0.061 320,820 289,055 0.90 0.90 1.46
2020 2014 28,826 640,158 0.053 0.077 246,593 217,767 0.88 0.88 1.44
2021 2015 229,746 1,564,638 0.039 0.108 364,739 134,994 0.37 0.37 0.53
2022 2016 NA 1,635,270 0.043 0.094 362,140 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2013 2007 180,507.05 312,209 131,702 0.42 0.42 0.63
2014 2008 39,860.18 343,077 303,216 0.88 0.88 1.44
2015 2009 132,478.30 338,822 206,344 0.61 0.61 1.00
2016 2010 283,973.01 292,704 8,731 0.03 0.03 0.03
2017 2011 495,528.20 171,992 323,536 1.88 -1.88 0.58
2018 2012 84,332.12 226,469 142,137 0.63 0.63 1.04
2019 2013 31,764.35 207,234 175,470 0.85 0.85 1.39
2020 2014 28,825.83 205,615 176,789 0.86 0.86 1.41
2021 2015 229,745.68 184,885 44,861 0.24 -0.24 0.19
2022 2016 NA 174,039 NA NA NA NA

Performance summary

The ln.sibling model is the pretty clear favorite here looking at the performance and regression giving us a forecast of ~0.35 million.

model range MAD MAPE MPE MAAPE
sibling 5 years 114,072 50.02% 47.01% 0.81
sibling 3 years 62,936 51.87% 46.86% 0.85
ln.sibling 5 years 60,193 33.06% 14.83% 0.42
ln.sibling 3 years 30,331 31.18% 0.80% 0.30
lnY.sibling 5 years 99,818 66.81% 9.33% 0.78
lnY.sibling 3 years 81,485 77.97% 13.29% 0.91
lnS.lnR 5 years 178,050 67.50% 40.98% 0.95
lnS.lnR 3 years 178,331 68.67% 68.67% 1.09
ricker 5 years 196,629 65.36% 48.78% 0.98
ricker 3 years 213,939 71.81% 71.81% 1.14
average 5 years 172,559 89.16% 4.21% 0.92
average 3 years 132,373 64.97% 48.80% 1.00

Forecast summary

A preliminary look at the models for this river leads us to an initial forecast of ~5.9 million broken down as follows:

Table 2. Preliminary Ugashik Forecast.

age forecast
1.2 1.90
2.2 0.38
1.3 3.30
2.3 0.35