# Identification of infectious agents in early chinook and marine coho salmon associated with cohort survival

*R*

^{2}= 0.81).

$$\text{Log}({S}_{I})={\beta}_{0,s(I)}+{\beta}_{1,s(I)}{\text{PDO}}_{I}+{\beta}_{2,s(I)}{\mathrm{DPI}}_{I}+{\gamma}_{\mathrm{there}(I)}+{\varepsilon}_{I}$$

(1)

where *S*_{I} is the cohort survival (SAR) for the observation *I* (an observation is a combination of CWT stock, season and year of ocean entry given a minimum sample size of ≥ 10 fish, to estimate pathogen prevalence; Supplementary Material 1, Tables S3, S4) , PDO_{I} is the Pacific Decadal Oscillation, IAP_{I} is the prevalence of infectious agents, *γ*_{there(I)} is a random effect representing the variation in survival between years of ocean entry (*there*), and the index *s* indicates among CWT stocks the variation in the influence of PDO and IAP on survival (i.e., random intercept and slope). We treated IAP_{I}our main predictor of interest, as a beta random variable to account for sampling error in the observations:

and

${\mathrm{NOT}}_{I}^{-}$ are the number of positive and negative screening results, respectively, for salmon from the stock *I*. Adding 1 to both values implies that this forward beta for IAP_{I} is actually an update of a flat conjugate beta prior B(1,1), with

as the number of binomial successes and

$({\mathrm{NOT}}_{I}^{+}+{\mathrm{NOT}}_{I}^{-})$ as the number of trials that provide information about the IAP_{I} (Bolker 2008). PDO is a representative variable of large-scale ocean temperature regimes that is often correlated with salmon marine survival (Rupp et al. 2012; Dale et al. 2017; Gosselin et al. 2018). The PDO has been standardized by centering and dividing by two standard deviations (Gelman 2008). We assumed a random slope for the PDO, varying by stock, because the PDO could have very different implications for a stock with marine culture in a relatively cold location (e.g., the west coast of Vancouver Island ) compared to another farm in a warm location (e.g., Strait of Georgia). We assumed a random slope for the prevalence of infectious agents, varying by stock, because evolution of the immune system and variation in resistance to certain pathogens is a known feature of local adaptation in salmonids (Ching 1984 Dionne et al. 2007; Wellband and Heath 2013). Note that for Chinook Salmon, we did not distinguish between oceanic and riverine life history types, but most CWT-CU pairings with adequate sample size (≥10 fish) were dominated by populations oceanic type (i.e. migrated seaward in their first year of life), except Atnarko, Nicola, Kitsumkalum and Stillaguamish (Fig. 1; Supplementary Material 1, Table S2 (all acronyms and names complete can be found here)). For coho, we assumed that all juveniles spent one year in fresh water before their first year at sea. A random interception for the stock was included to account for stock variation in survival (Zimmerman et al. 2015 ; Ruff et al. 2017) and a random intercept for the year of ocean entry was included to account for interannual variation in ocean conditions not represented by other model terms.

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