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. 2025. 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 + 107 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”), and (3) egg mass-recruitment models with AR1 recruitment residuals (labelled “AR1 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 1.1 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). “D_scale” is the \(D\) term in equation C.4 in the research document and governs variability of age proportion vectors across cohorts.”Dir_alpha” refers to Dirichlet shape parameter for the gamma distribution used to generate vector of age-at-maturity proportions.

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 400 and \(\hat{R}\) values less than 1.1.The tables below summarize the lowest effective sample size (ESS) and largest \(\hat{R}\) across all estimated parameters for each CU and class of model.

AR1 model:

CU ESS Rhat
Big.Salmon 341 1.010
MiddleYukonR.andtribs. 277 1.033
Nordenskiold 1643 1.003
NorthernYukonR.andtribs. 575 1.008
Pelly 201 1.035
Stewart 533 1.009
UpperYukonR. 526 1.002
Whiteandtribs. 413 1.007
YukonR.Teslinheadwaters 475 1.011

Time varying (TV) model:

CU ESS Rhat
Big.Salmon 360 1.024
MiddleYukonR.andtribs. 259 1.018
Nordenskiold 697 1.005
NorthernYukonR.andtribs. 392 1.009
Pelly 432 1.009
Stewart 366 1.026
UpperYukonR. 603 1.003
Whiteandtribs. 475 1.008
YukonR.Teslinheadwaters 432 1.015

Egg mass AR1 model:

CU ESS Rhat
Big.Salmon 360 1.006
MiddleYukonR.andtribs. 527 1.011
Nordenskiold 1615 1.001
NorthernYukonR.andtribs. 547 1.005
Pelly 274 1.022
Stewart 529 1.005
UpperYukonR. 471 1.006
Whiteandtribs. 340 1.010
YukonR.Teslinheadwaters 471 1.003