This document provides diagnostic plots for several spawner-recruit models that were used to characterize Canadian-origin Yukon Chinook salmon population dynamics at the Conservation Unit scale as described in:

Connors, B.M., O’Dell, A., Hunter, H., Glaser, D., Gill, J., Rossi, S., and Churchland, C. In review. Stock status and biological and fishery consequences of alternative harvest and rebuilding actions for Yukon River Chinook salmon (Oncorhynchus tshawytscha). DFO Can. Sci. Advis. Sec. Res. Doc. 2025/nnn. iv + 92 p.

Full details are provided in the document above but briefly, four state-space spawner-recruit models were fit: spawer-recruitment models with autoregressive recruitment residuals (labelled “AR1”), (2) spawner-recruitment models with time varying intrinsic productivity (labelled “TV”), (3) egg mass-recruitment models with AR1 recruitment residuals (labelled “AR1 egg mass”), and (4) egg mass-recruitment models with time varying intrinsic productivity (labelled “TV egg mass”). These models were fit to each of the nine Conservation Units for which we had data.

Diagnostics

We fit the spawner-recruitment model in a Bayesian estimation framework with Stan (Carpenter et al. 2017; Stan Development Team 2023), which implements the No-U-Turn Hamiltonian Markov chain Monte Carlo algorithm (Hoffman and Gelman 2014)) for Bayesian statistical inference to generate a joint posterior probability distribution of all unknowns in the model. The models can be found here.We sampled from 4 chains with 4,000 iterations each and discarded the first half as warm-up. We assessed chain convergence visually via trace plots and by ensuring that \(\hat{R}\) (potential scale reduction factor; Vehtari et al. 2021) was less than 1.01 and that the effective sample size was greater than 400. Posterior predictive checks were used to make sure the model returned known values, by simulating new datasets and checking how similar they were to our observed data.

Trace plots

These should be clearly mixed, with no single distribution deviating substantially from others (left column), and no chains exploring a strange space for a few iterations (right column).

Big.Salmon

MiddleYukonR.andtribs.

Nordenskiold

NorthernYukonR.andtribs.

Pelly

Stewart

UpperYukonR.

Whiteandtribs.

YukonR.Teslinheadwaters

ESS and \(\hat{R}\)

We aimed for minimum effective sample sizes that are greater than 2000 and \(\hat{R}\) values less than 1.05.

AR1 model:

CU ESS Rhat
Big.Salmon 267 1.023
MiddleYukonR.andtribs. 404 1.005
Nordenskiold 528 1.012
NorthernYukonR.andtribs. 456 1.013
Pelly 356 1.011
Stewart 380 1.009
UpperYukonR. 453 1.008
Whiteandtribs. 614 1.009
YukonR.Teslinheadwaters 498 1.007

Time varying (TV) model:

CU ESS Rhat
Big.Salmon 513 1.010
MiddleYukonR.andtribs. 419 1.009
Nordenskiold 688 1.005
NorthernYukonR.andtribs. 375 1.008
Pelly 468 1.006
Stewart 431 1.007
UpperYukonR. 507 1.006
Whiteandtribs. 403 1.008
YukonR.Teslinheadwaters 482 1.017

Egg mass AR1 model:

CU ESS Rhat
Big.Salmon 173 1.029
MiddleYukonR.andtribs. 277 1.009
Nordenskiold 237 1.032
NorthernYukonR.andtribs. 152 1.028
Pelly 216 1.008
Stewart 294 1.012
UpperYukonR. 257 1.014
Whiteandtribs. 262 1.019
YukonR.Teslinheadwaters 220 1.012

Time varying (TV) egg mass model:

CU ESS Rhat
Big.Salmon 260 1.013
MiddleYukonR.andtribs. 152 1.016
Nordenskiold 240 1.013
NorthernYukonR.andtribs. 286 1.015
Pelly 125 1.022
Stewart 302 1.015
UpperYukonR. 254 1.012
Whiteandtribs. 164 1.032
YukonR.Teslinheadwaters 249 1.011