OPEN ACCESS | Article
Atlantic salmon survival at sea: temporal changes that
lack regional synchrony
Maria Tirronen a, Jeffrey A. Hutchingsb,c,d, Sebastián A. Pardob,e, and Anna Kuparinena
aDepartment of Biological and Environmental Science, University of Jyväskylä, FI-40014, Jyväskylä, Finland; bDepartment of Biology,
Dalhousie University, Halifax, NS B3H 4R2, Canada; cInstitute of Marine Research, Flødevigen Marine Research Station, His, N-4817,
Norway; dDepartment of Natural Sciences, University of Agder, Kristiansand, N-4604, Norway; eEcology Action Centre, Halifax, NS
B3K 4L3, Canada
Corresponding author: Maria Tirronen (email: maria.j.e.tirronen@jyu.fi)
Abstract
Spatial and temporal synchrony in abundance or survival trends can be indicative of whether populations are affected by
common environmental drivers. In Atlantic salmon (Salmo salar), return rates to natal rivers have generally been assumed to be
affected primarily by shared oceanic conditions, leading to spatially synchronous trends in mortality. Here, we investigated the
existence of parallel trends in salmon sea survival, using data on migrating smolts and returning adults from seven Canadian
populations presumed to share feeding grounds. We analysed sea survival, using a Bayesian change-point model capable of
detecting nonstationarity in time series data. Our results indicate that while salmon have experienced broadly comparable
patterns in survival, finer-scale temporal shifts are not synchronous among populations. Our findings are not consistent with
the hypothesis that salmon populations consistently share the same mortality-related stressors in the marine environment.
Although populations may have shared greater synchrony in survival patterns in the past, this synchrony may be breaking
down. It may be prudent to direct greater attention to smaller-scale regional and population-level correlates of survival.
Résumé
Le synchronisme spatial et temporel des tendances d’abondance ou de survie peut indiquer si différentes populations sont
influencées par les mêmes facteurs environnementaux. Il est généralement présumé que, chez les saumons atlantiques (Salmo
salar), les taux de retour aux rivières natales sont principalement influencés par des conditions océaniques communes, ce qui
mène à des tendances de mortalité synchrones dans l’espace. Nous examinons l’existence de tendances parallèles de survie en
mer des saumons en utilisant des données sur les saumoneaux migrants et les adultes retournant dans leur rivière natale de
sept populations canadiennes présumées avoir les mêmes aires d’alimentation. Nous analysons la survie en mer en utilisant
un modèle bayésien de points de changement pouvant détecter la présence de non-stationnarité dans les données de séries
chronologiques. Nos résultats indiquent que, bien que les saumons présentent des motifs de survie généralement semblables,
des changements temporels à échelle plus fine ne sont pas synchrones d’une population à l’autre. Nos résultats ne concordant
pas avec l’hypothèse voulant que les populations de saumons aient toujours en commun les mêmes facteurs de stress reliés à
la mortalité dans le milieu marin. Si les motifs de survie des populations peuvent avoir présenté un plus grand synchronisme
par le passé, ce synchronisme pourrait être en train de s’effriter. Il peut être prudent d’accorder plus d’attention aux corrélats
de la survie à des échelles régionales ou populationnelles plus fines. [Traduit par la Rédaction]
1. Introduction
dance or survival? If they are all declining, it would be sug-
The viability of a species depends on the resistance and re- gestive of a similarly shared threat. If abundance or survival
silience of its constituent populations to natural and human- trajectories differ in overall temporal sign (some increasing,
induced environmental change. Reduced viability reflects re- some declining, some remaining stable), it could be inferred
ductions in the abundance or survival of one or more of that the underlying causes of population change differ, pos-
these constituent populations. Under such circumstances, sibly giving rise to a “portfolio effect” that can underpin the
and when multiple populations are implicated, attempts to viability of some species (Schindler et al. 2010). For those shar-
understand and mitigate species’ threats lead to two funda- ing similar overall patterns of population decline, a second
mental questions. Firstly, to what extent do the separate pop- but related question is whether the beginning of the decline,
ulations share similar overall trends in trajectory in abun- and subsequent intermittent temporal changes in trajectory,
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occur simultaneously among populations. The former would ers hundreds (e.g., ICES 2017; Olmos et al. 2019, 2020). This
be suggestive of a common threat, the latter (depending on regional pooling of salmon data, particularly when the iden-
time lags) suggestive of different threats. tities of the specific constituent populations are not readily
Among vertebrates, particularly those of perceived ex- identifiable, can present challenges when trying to under-
ploitative or charismatic value, there are often sufficient data stand broad- and smaller-scale patterns in survival at the pop-
to monitor changes in at least one population for many ulation level. A second issue associated with data amalgama-
species (e.g., livingplanetindex.org). For some species, the tion can be the inclusion of populations that are sustained
data are comparatively rich, albeit highly variable in qual- by hatcheries into the regional or stock units, hatcheries
ity and temporal resolution. One of these is Atlantic salmon having rather well-documented, often unhelpful influences
(Salmo salar). The highest number of wild populations are when evaluating patterns of population survival (Fraser 2008;
found in Norway and in Canada (ICES 2021). Catch statistics of NASCO 2017).
salmon stocks in Norway peaked in the 1960s and 1970s and These challenges suggest utility in undertaking detailed
since then, catches have diminished (WWF 2001). Compared temporal analyses of salmon survival for which the support-
to the estimated abundance of wild Norwegian salmon (in- ing population data are as empirically strong as the best
cluding those caught by fishing) in the mid-1980s, numbers available information allows. There are seven Canadian pop-
were reduced by about half thereafter, and have been fairly ulations for which detailed information on the number of
stable since the early 1990s, excepting a short-term peak at outmigrating smolts and the number of returning adults ex-
the turn of the 21st century (SCSM 2019). A remarkably sim- ist. These populations are widely distributed throughout the
ilar pattern in overall pre-fishery abundance is evident for species’ Canadian range, extending from Newfoundland in
wild Canadian salmon (for which the earliest time series ex- the north to Nova Scotia in the south. For each of these
tend to the 1970s): high abundance until the mid-1980s fol- populations, Pardo et al. (2021) estimated survival of salmon
lowed by decline until the early 1990s and relative stability at sea, using a hierarchical Bayesian model that incorpo-
since (ICES 2021). rated Murphy’s (1952) maturity schedule model in conjunc-
Reasons for the initial abundance declines and subsequent tion with informative priors.
lack of recovery have been attributed to numerous addi- Here, we extended previous work (Olmos et al. 2019; Pardo
tive and interactive influences. For example, among the cur- et al. 2021) and examined whether population patterns in
rent stressors identified for wild Norwegian salmon, the top salmon marine survival are concordant or divergent at fine
five include farmed escapees and pathogens originating from temporal scales of resolution. Our approach involves applica-
salmon aquaculture, freshwater habitat alteration (e.g., bar- tion of the Bayesian online change-point detection (BOCPD)
riers to migration), acidification, and hydroelectric develop- method developed by Adams and MacKay (2007), combined
ment (SCSM 2019). Several studies provide support for the hy- with simulation-based filtering (Liu and West 2001; Perälä
pothesis that the initial decline of salmon in the late 1980s et al. 2017). This method, used previously to analyse tem-
and early 1990s was precipitated by increased mortality in poral changes in stock-recruitment parameters (Perälä et al.
the marine environment (e.g., Massiot-Granier et al. 2014). 2017; Tirronen et al. 2021) and Atlantic cod (Gadus morhua)
Questions related to the causes of this increased salmon abundance (Perälä et al. 2020), offers a procedure to detect
mortality can be addressed examining patterns of spatial and shifts in the parameters of the data-generating process. We
temporal coherence in population trajectories for survival. find that temporal shifts in survival at sea may not occur syn-
Olmos et al. (2019, 2020) reported a strong spatial coherence chronously nor be similar for populations in different rivers.
in temporal survival patterns among 13 “stock units” dis-
tributed in North America and southern Europe. Their find-
ings suggest that factors affecting salmon mortality at sea are 2. Materials and methods
temporally consistent at broad (North Atlantic) and smaller
(stock unit) spatial scales. 2.1. Data
One key data challenge when studying Atlantic salmon We analysed the time series of smolts and returning fish
mortality, and its potential spatial and temporal coherence of Atlantic salmon populations in seven rivers in eastern
among populations, is the near absence of empirical abun- Canada. These populations included Western Arm Brook
dance information on salmon prior to and during their mi- (WAB; Fig. 1) and the Campbellton and Conne rivers in
gration to the ocean (Olmos et al. 2019; ICES 2021). Perhaps Newfoundland and Labrador (NL), Rivière de la Trinité and
the most important developmental stage in this respect is the Rivière de la Saint-Jean in Quebec (QC), LaHave River in
smolt stage (the term “smolt” describes salmon during their Nova Scotia’s (NS) Southern Uplands, and Nashwaak River
downstream migration to the ocean; the term “post-smolt” in New Brunswick (NB). The numbers of emigrating smolts
typically encompasses the first 3–6 months of a salmon’s life were based on two methods. For Trinité, Saint-Jean, LaHave,
at sea). For example, of the 199 populations (stocks) of salmon Nashwaak, and Conne, smolt numbers were estimated from
for which spawning targets are evaluated in Norway, long- mark–recapture studies. For the WAB and Campbellton pop-
term data on smolts are available for two rivers, only one of ulations, smolt numbers were directly recorded at count-
which has been monitored since 2010 (SCSM 2019). ing fences during their seaward migration. The methods are
The variable quality of data at the population level has led fully cited by Pardo et al. (2021). The number of returning
to a tendency to amalgamate population-specific data into adults was based on direct counts of small (<63 cm) and large
stock units, some of which contain tens of populations, oth- (≥63 cm) salmon. Age determination from scales was done
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Fig. 1. Locations of the seven rivers in eastern Canada with temporal data of outmigrating smolts and returning adult Atlantic
salmon (adapted from the study by Pardo et al. 2021). The map uses a lat/long (geographic) projection and a WGS 84 datum.
for a subset of returns each year, which allowed for calcu- schedule model combined with an a priori unknown num-
lating the proportion of different age classes within the size ber of change points at which the model parameters, describ-
groups, and subsequently estimate the total proportion of ing survival and years at sea, shift. Marine survival of cohorts
each age class among the returning fish (Pardo et al. 2021). in different rivers were modelled separately. For years t =
Naturally, the true smolt abundances differ from the ob- 1, …,(T, where T is the length of the time series, the model
served smolt abundances. Pardo et al. (2021) used a hier- relates the obser)ved number of returning 1SW and 2SW fish,
archical Bayesian model to estimate the true abundances. R = R1SW, R2SW
t t t , in a given river, to the estimated number
To decrease bias in our results caused by measurement er- of smolts in that river (the posterior medians of the estimated
rors, we fitted our model using the medians of the poste- true smolt abundances; Pardo et al. 2021), St. For ease of no-
rior distributions of the true smolt abundances obtained by tation, we here use the same subscript for all abundance esti-
Pardo et al. (2021) as smolt abundance data. Similarly, the ob- mates corresponding to the 1SW fish count at year t, although
served returning fish abundances are likely to differ from the the smolt and 2SW fish counts were recorded at years t − 1
true numbers of returning fish. Pardo et al. (2021) estimated and t + 1, respectively. Moreover, the change points divide
these differences, the measurement errors, by bootstrapping. the data into I regimes, or segments, ρ = 1, 2, …, I. Given the
To consider the measurement errors in returning fish abun- position of a change point, the data before the change point
dance data in our model, we utilized the estimates by Pardo were assumed to be independent of the data after the change
et al. (2021). point.
For three rivers (LaHave, Saint-Jean, and Trinité), there The same underlying predictive model that relates Rt to St
was one or two missing years within their time series. For was assumed for the data in different segments so that only
those years, there had been no smolt count due to too much the values of the model parameters vary between segments.
water flow. In addition, in some years for one-sea-winter The model parameters of different segments, ηρ , ρ = 1, 2,
(1SW)-dominated populations, estimates of returning two- …, I, were assumed to be independent and identically dis-
sea-winter (2SW) fish were zero. These counts were included tributed. To estimate the parameter values, we applied the
in the analysis by adding a small quantity to enable log- BOCPD method, which processes data in a sequential man-
transformation. Given that the zero counts appeared only in ner, updating estimates for the parameter values and com-
1SW-dominated populations, small differences in the value of puting posterior probabilities for a change point after each
log 2SW returns are not likely to have a considerable impact data item. The approximation of ηρ at time t, inferred from a
on the marine survival estimates in the first year at sea. current run length rt, the time elapsed since the last change
point, is denoted by (r)
ηt . Moreover, given segmentation and
the corresponding parameter values, we assumed that the
2.2. Bayesian change-point model abundances of different cohorts are mutually independent.
We modelled marine survival of salmon by a Bayesian Such a simplifying assumption was also made by Pardo et al.
change-point model that consists of the Murphy’s maturity (2021).
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The Bayesian change-point model consists of the following the number of smolts and approximated model parameters.
probabil(ity distrib)utions: Such an assumption states that deviations from the predicted
number of returning fish by the Murphy’s maturity sched-
(1) p R (r)
( t |S)t, ηt , t = 1, ..., T ule model do not correlate between 1SW and 2SW fish. More
precisely, the logarithms of R1SW, R2SW were modelled as nor-
(2) p (0)
ηt mally distributed ra(ndo[m var]iables. )
(3) p (r |r − ) , t = 2, ..., T log (Ra ) ∼ N log R̂a (S) , ( 2 2
σ a ) + (εa )
t t 1 (7)
a = 1SW, 2SW
and
where σ a is the standard deviation of yearly variation of 1SW
(4) p (r1) and 2SW fish from the average relationship between smolts
The output distribution (eq. 1) is defined by the underlying and returning fish in log scale and εa describes yearly estima-
predictive model and (eq. 2) is the joint prior distribution of tion error (Pardo et al. 2021) in the (log-transformed) number
the model parameters. The transition probability (eq. 3) is the of 1SW and 2SW fish. With eq. 7, the abundances of 1SW and
change-point prior, which assumes that the run lengths r ∈ 2SW fish obey lognormal distributions with medians R̂1SW (S)
t 2SW
{0, 1, …, t − 1} form a Markov chain, and (eq. 4) defines the and R̂ (S), a√nd coefficients of variation.
initial run length distribution. [ ]
(8) CVa = exp ( a )2σ + (εa )2 − 1, a = 1SW, 2SW
2.3. Underlying predictive model Overall, the underlying predictive model has five param-
eters.
The average relationship between smolts and 1SW and ( )
2SW fish was represented by the Murphy’s (1952) maturity (9) η = s1SW, s2SW, p, σ 1SW, σ 2SW
schedule model.
(5) R̂1SW (S) = S · s1SW · p 2.4. Prior distributions
For the marine survival parameters s1SW and s2SW, we set
(6) R̂2SW (S) = S · s1SW · ( − p) · s2SW the same informative priors as Pardo et al. (2021). That is, for
1
the log-transformed at sea survival parameters (the instanta-
a a
where we omit t and (r) for ease of notation. Above, s1SW, s2SW neous mortality rates) z = −log (s ), a = 1SW, 2SW, we set
∈ [0, 1] denote the proportions of salmon surviving in their lognormal prior distributions:
first or second year at sea, respectively, and p ∈ [0, 1] is the pro-
1SW
portion of salmon that return to spawn after 1 year at sea. The (10) z ∼ lognormal (1, 0.22)
model (eqs. 5 and 6) assumes that salmon do not spend more
2SW
than 2 years at sea and that there are no repeat spawners. In (11) z ∼ lognormal (0.2, 0.3)
the populations we studied, age 3+ spawners (3SW+) comprise
a very small fraction of first-time spawners (Pardo et al. 2021). These priors favor such values of the marine survival param-
Nonetheless, accounting for 3SW+ fish would likely result in eters that Pardo et al. (2021) considered to be biologically re-
slightly higher estimates for overall survival at sea. alistic based on previous studies.
Following Pardo et al. (2021), we assumed that the number For the proportion of salmon that return to spawn after 1
of 1SW and 2SW fish are conditionally independent, given year at sea, we set
{
Normal (2.3, 0.4) for 1SW-dominated populations
(12) logit (p) ∼
Normal (0, 2.8) for non-1SW-dominated populations
For 1SW populations, this prior is concentrated to lower val- we carried out sensitivity analyses in terms of the hyperpa-
ues than the one used by Pardo et al. (2021) (Supplementary rameters σ a
reg and δa. While this prior does not limit the max-
Material, Figure S1a), while for 2SW populations, our prior is imum amount of random variation we assume to be present
somewhat less informative (Supplementary Material, Figure in the data, the hyperparameter σ a
reg defines the minimum
S1b). amount of random variation while δa controls the relative
The change-point inference may considerably depend on likelihood of the possible values of σ a. We first studied the
the amount of random variation that we assume to be present impact of δa on the change-point inference by setting δ1SW
in the empirical time series (Tirronen et al. 2021). Thus, the = δ2SW and using the values 0.5, 1, 2, 3, not bounding the
priors of σ a having been set to amount of random variation from below (σ a
reg = 0). Secondly,
( ) we tested the sensitivity of change-point inference in terms
of σ a
reg with δ1SW = δ2SW = 1. In this, we set σ 1SW = σ 1SW
reg reg , and
(13) σ a ∼ half-normal σ a a
reg, δ , a = 1SW, 2SW tested the values 0, 0.02, 0.03, 0.05, 0.1, 0.2 for all data sets
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(Supplementary Material, Table S2). For some rivers, we also posterior distribution of the model parameters). Particularly,
fitted the model using different values for σ 1SW 2SW
reg and σreg , we looked at the posterior distributions at the end of the seg-
when such a choice was assumed to result in a better fit to ments so that all the data in a segment contributed to the
the data (Supplementary Material, Table S3). In this, we also inferred parameter values in that segment. In addition to run-
used δa = 0.5 for some populations. specific estimates, the chosen approach provides full parame-
The conditional prior on the change point was defined us- ter posterior distributions which account for the uncertainty
ing a constant haza⎧rd function (Adams and MacKay 2007). related to the timing of the change points.
⎪⎪⎪ 1 When combined with simulation-based filtering, BOCPD is
⎨ if rt = 0 a stochastic method. Thus, there was some variation between
λ
(14) p (r |r ) = ⎪⎪⎪ 1 inferred change points and parameter values when fitting
t t−1 ⎩ 1 − if rt = rt−1 + 1
λ was repeated by using a different set of random samples in
0 otherwise the filter, although the priors of the variance parameters σ a
or the change-point prior were not changed. The amount of
for t = 2, …, T. With this model, the prior probability of variation was decreased when the number of samples was in-
a change point is 1/λ. Moreover, we assumed that a change creased. The stability of the results also depended on how
point occurred before the first data point, i.e., p(r1 = 0) = informative priors were used for the variance parameters.
1, and set a high prior probability of a change point, λ = To estimate the robustness of change-point inference with a
5, which is close to a single generation for salmon. As for chosen number of random samples in the filter, we repeated
the variance parameters, we carried out sensitivity analyses the model fitting twice using different random samples. In
in terms of λ by testing higher values (λ = 10, 20, 30) with this, we used 3 × 106 to 5 × 106 samples in the filter, which
σ a a
reg = 0 and δ = 1 (Supplementary Material, Table S1). resulted in sufficiently low variation in the inferred change
points. Moreover, for parameter estimates, we produced a
2.5. Change-point detection and parameter third replicate of the results.
inference
We fitted the change-point model to the empirical data
by applying the BOCPD method developed by Adams and 3. Results
MacKay (2007), combined with simulation-based filtering (Liu
and West 2001; Perälä et al. 2017). The method is sensitive to 3.1. Change points
changes in sequential data and provides a potential tool for Using the MLS method, our segmentation analysis detected
detecting temporal changes in the underlying processes that change points for all rivers except WAB (Table 1; Figs. 2
generate ecosystem data. It has been extensively validated for and 3). For all such rivers except Trinité, the number of in-
stock–recruitment models (Perälä et al. 2017; Tirronen et al. ferred change points was dependent on the prior distribu-
2021), and its performance in parameter inference in short tions of the variance parameters as well as the change-point
segments has also been found decent (Tirronen et al. 2021). prior (Supplementary Material, Tables S1–S3). Evidence of
The method processes data in a sequential manner, start- two change points was found for Saint-Jean, while for other
ing a new run at each time point, updating estimates for the rivers with inferred change points the results indicated a sin-
parameter values in the existing runs and computing poste- gle temporal shift in the parameters. However, the data of the
rior probabilities of the run lengths (Appendix A). In missing studied populations spanned across different time periods.
years, the parameter posteriors were assumed not to change Moreover, with some priors, MLS indicated two shifts in the
but a new run was started to account for the possibility of a parameters for Conne but the second change point was not
change point. In such years, the run length posteriors were supported by the posterior predictive distributions of 2SW
computed using one-step predictions (Perälä et al. 2017). fish, which suggested a better model fit to the data with two
The run length posterior probabilities obtained in filter- segments (Supplementary Material, Figures S10 and S11). Two
ing were used for computing smoothed run length probabil- change points were also inferred for LaHave, but the first seg-
ities (Discussion; Perälä et al. 2017), i.e., run length probabil- ment consisted of 1 year and was found only when the vari-
ities in retrospect, given the whole data. The smoothed run ance parameters were not bound below.
length probabilities are not affected by single outliers and Intriguingly, the results indicated different years of change
were used for dividing the data sets into segments. Following points for all rivers except two: Saint-Jean and Trinité, in QC.
Perälä et al. (2017), we looked for the most likely segmenta- While a change point was inferred for Trinité in 1993, the re-
tion (MLS) of each data set by maximizing the product of the sults suggested a shift in the marine survival parameters for
smoothed run length probabilities over all possible segmen- Saint-Jean in 1992 or 1993 (Supplementary Material, Tables
tations (Appendix A). In MLS, we set the maximum number S1–S3). However, for one of the analysed populations in NL,
of segments to five and considered only segments that con- Conne, the inferred year of a change point (1991) was close to
sisted of at least 3 years, except at the beginning and the end the timing of the change points for Saint-Jean and Trinité. For
of the time series, since the data cannot tell when the first the other two populations in NL, the Campbellton time series
segment started or the last one ended. did not include data before 1994, while for WAB, no change
In parameter inference, we considered the conditional points were inferred, although data were available already
probability distribution of the model parameters given the in 1974. Neither the LaHave population in NB nor the Nash-
data belonging to a given segment at time t (the run-specific waak population in NS had data before 1994. But, the years of
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Table 1. The SW dominance of each river studied, the years of change points inferred in the
most likely segmentation (MLS), the posterior medians of the Murphy’s maturity schedule
model parameters in the segments (the time period is shown in parenthesis) using river-specific
prior settings for the variance parameters (Supplementary Material, Table S3), and the hazard
rate λ = 5.
River Posterior medians in MLS
SW- Years of change
Name dominance points s1SW s2SW p
Campbellton 1 2005 0.055 (1994–2004) 0.012 0.934
0.083 (2005–2015) 0.068 0.949
Conne 1 1991 0.089 (1988–1990) 0.201 0.932
0.036 (1991–2015)∗ 0.142∗ 0.939
LaHave 2 2014 0.035 (1997–2013) 0.260 0.614
0.017 (2014–2017)∗ 0.223∗ 0.341∗
Nashwaak 2 2013 0.068 (1999–2013) 0.291 0.497
0.042 (2014–2017)∗ 0.269∗ 0.567
Saint-Jean 2 1992, 2009 0.056 (1990–1991) 0.301 0.096
0.036 (1992–2008)∗ 0.247∗ 0.120
0.060 (2009–2015) 0.291 0.109∗
Trinité 2 1993 0.049 (1985–1992) 0.274 0.413
0.027 (1993–2016)∗ 0.239∗ 0.330∗
Western Arm Brook 1 —— (1974–2015) —— ——
(WAB)
Note: The models were fitted using three different random sampes, which resulted in some differences in the estimates
(Supplementary Material, Tables S10–S12). The posteriors were estimated using 104 samples.
∗Indicates a decrease in a posterior median between two consecutive segments.
change points inferred later for LaHave and Nashwaak were Have. For both of the rivers, the timing of the change point
close to each other (2014 and 2013, respectively). On the other in the 2010s included a considerable amount of uncertainty.
hand, these two rivers were the only ones having data until Considering change-point detection, it should be noted,
2017, while for almost all other rivers, data were only avail- that the approximated measurement errors and the priors
able until 2015. Nonetheless, the year of change point in- set for the variance parameters may have played a consider-
ferred for Campbellton and also the second change point of able role since they together define the total amount of vari-
Saint-Jean were not close to any other inferred change point. ation around the average values. On average, the measure-
Naturally, there was some uncertainty included in the ment error of 2SW fish was high for all 1SW populations (the
change-point detection (Figs. 4 and 5). For Campbellton, both mean of ε2SW was 0.74 for Campbellton, 0.71 for WAB and
the filtered and smoothed run length probabilities clearly in- 0.55 for Conne, while it was <0.08 for all 2SW populations).
dicated a single temporal change in the marine survival pa- However, the measurement error of 1SW fish was low for all
rameters, with some uncertainty, while for Conne, there was populations except Campbellton (the mean of ε1SW was 0.21
more uncertainty included in the posterior run length prob- for Campbellton, and <0.07 for other populations). Moreover,
abilities. Particularly, between 2000 and 2010, the smoothed a high amount of scatter among successive years in the data
run length probabilities indicated the possibility of change can affect parameter inference and consequently, the accu-
points for Conne, although MLS did not include such change racy of change-point detection (Tirronen et al. 2021). Setting
points because of their low probability. Despite the differ- more informative priors for variance parameters may yield
ences in the patterns, there could have been approximate to more accurate parameter inference and change-point de-
synchrony around 2005 between Campbellton and Conne. tection. For some of the studied populations, tighter priors
Moreover, the filtered run length probabilities for WAB in- provided more evidence for change points (Supplementary
dicated the possibility of a change point at the beginning of Material, Table S2).
the 1990s and in 2010, but the smoothed run lengths did not
provide evidence for such change points. Among the popula-
tions in QC, the smoothed run length probabilities suggested 3.2. Parameter estimates
the possibility of a change point around 2000 for both Trinité Since the methods we used do not distinguish between
and Saint-Jean, in addition to the change points at the begin- changes in the model parameters, all the parameters could
ning of 1990s. However, such synchrony between these rivers contribute to the inferred change points. However, for all
seemed to have been vanished later. For the NB and NS rivers, rivers except Campbellton, due to the high amount of
there was more uncertainty about a change point at the be- uncertainty in the estimates of s2SW, the results more clearly
ginning of the recording period for Nashwaak, than for La- indicated shifts in s1SW than in s2SW (Fig. 6; Supplementary
1702 Can. J. Fish. Aquat. Sci. 79: 1697–1711 (2022) | dx.doi.org/10.1139/cjfas-2021-0302
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Fig. 2. The analysed time series of the returning 1SW and 2SW fish and the corresponding posterior predictive distributions
for the studied populations in NL (Fig. 1). The black solid lines correspond to the medians, while the coloured bars illustrate
the intervals between the 0.25th and 0.75th quantiles. The change-point model was fitted to the data sets with the hazard rate
λ = 5, using river-specific prior settings for the variance parameters (Supplementary Material, Table S3).
Material, Figure S7). Also, the estimates of p contained a high Nonetheless, among the NL populations, the posteriors
amount of uncertainty (Supplementary Material, Figure S6) suggested a steady decline in s1SW for Conne (also when two
and, compared to the posteriors of s1SW, shifts in p were more change points were inferred), increased at-sea survival for
uncertain for all rivers with change points except LaHave Campbellton and no stepwise change for WAB (Fig. 6). For
(Supplementary Material, Figure S6c). For 2SW populations, the rivers in QC, both Trinité and Saint-Jean experienced
the estimates of s1SW also contained rather high amount of a decline in s1SW at the beginning of the 1990s, but evi-
uncertainty, reflecting the less informative prior set for p for dence for another temporal change in at-sea survival was only
these populations. found for Saint-Jean, for which the posteriors suggested a
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Fig. 3. The analysed time series of the returning 1SW and 2SW fish and the corresponding posterior predictive distributions
for the studied populations in QC, NB, and NS (Fig. 1). The black solid lines correspond to the medians, while the coloured bars
illustrate the intervals between the 0.25th and 0.75th quantiles. The change-point model was fitted to the data sets with the
hazard rate λ = 5, using river-specific prior settings for the variance parameters (Supplementary Material, Table S3).
recovery approximately to the same level as s1SW was in the only during the second segment, after which s2SW increased
first segment. For Nashwaak (NB) and LaHave (NS), the pos- to the same level as it was in the first segment. The esti-
teriors suggested a decline in s1SW in 2013–2014. For Camp- mates of p suggested an increase in p for both NL populations
bellton, there was a considerable shift in the number of re- with change points; Campbellton and Conne. Such a change
turning 2SW fish between the segments (no 2SW fish in the was also suggested for Nashwaak and, during the second seg-
first segment except the last year, some 2SW fish in almost ment, for Saint-Jean. A decline in p was suggested for LaHave
every year in the second segment; Fig. 2) and the method also and Trinité.
estimated an increase in s2SW. For other rivers with inferred The full posterior distributions of s1SW, which take into ac-
change points, there could be a decrease in s2SW. However, for count the uncertainty of change points, resembled the ones
Saint-Jean, the posteriors suggested that s2SW was decreased by Pardo et al. (2021) for all rivers (Supplementary Material,
1704 Can. J. Fish. Aquat. Sci. 79: 1697–1711 (2022) | dx.doi.org/10.1139/cjfas-2021-0302
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Fig. 4. Posterior run length probabilities after filtering (left) and smoothing (right) for the studied populations in NL (Fig. 1).
Black corresponds to a probability of one, white corresponds to a probability of zero. The most likely segmentation is depicted
by a red line. The change-point model was fitted to the data sets with the hazard rate λ = 5, using river-specific prior settings
for the variance parameters (Supplementary Material, Table S3).
Section S2.1). For 2SW populations, the estimates of s2SW and ably low estimates for s2SW. For Campbellton, the number of
p also resembled the ones by Pardo et al. (2021) but for 1SW 2SW fish were zero in all years except the last one in the
populations, our estimates were lower, reflecting the differ- first inferred segment which yielded to extremely low esti-
ent prior used for p. Indeed, the posteriors we obtained for p mates for s2SW in the first segment. Regarding the differences
for 1SW populations were concentrated on lower values than in the posterior distributions, it should also be kept in mind
the ones obtained by Pardo et al. (2021) and, equivalently, the that, as we relied on the estimates of smolt abundances by
proportions of fish that stay 2 years at sea (1 − p) were esti- Pardo et al. (2021), there were some differences in the anal-
mated higher in our study, yielding to lower s2SW estimates. ysed smolt data between these studies.
However, all the differences in the parameter estimates were
not due to different prior settings, but the different struc- 4. Discussion
ture of the model and the accompanying method used for pa-
rameter estimation. Particularly, for Campbellton and WAB, Broad-scale environmental changes have been linked to
successive years of having zero 2SW fish (Fig. 2) did not re- broad-scale patterns in salmon productivity (Friedland et al.
markedly impact the estimates of p but produced consider- 2003, 2014; Olmos et al. 2019, 2020). Our analyses com-
Can. J. Fish. Aquat. Sci. 79: 1697–1711 (2022) | dx.doi.org/10.1139/cjfas-2021-0302 1705
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Fig. 5. Posterior run length probabilities after filtering (left) and smoothing (right) for the studied populations in QC, NB, and
NS (Fig. 1). Black corresponds to a probability of one, white corresponds to a probability of zero. The most likely segmentation
is depicted by a red line. The change-point model was fitted to the data sets with the hazard rate λ = 5, using river-specific
prior settings for the variance parameters (Supplementary Material, Table S3).
plement these efforts by drawing attention to the impor- outmigrating smolts and returning adults throughout the
tance of smaller-scale, possibly population-specific, influ- species’ North American range, we have identified differ-
ences on trends in Atlantic salmon survival (Pardo et al. 2021). ent temporal patterns in salmon mortality during the first
Supported by the strongest empirical data on numbers of year at sea. Populations differed in the number of survival
1706 Can. J. Fish. Aquat. Sci. 79: 1697–1711 (2022) | dx.doi.org/10.1139/cjfas-2021-0302
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Fig. 6. The marginal posterior distributions (the vertical axes) of the parameter s1SW (the proportion of salmon surviving in
their first year at sea) of the Murphy’s maturity schedule model with respect to time (the horizontal axes) inferred by the
Bayesian online change-point detection method. The shaded areas illustrate the prior distributions (grey) and the posterior
distributions according to the most likely segmentation (different colours), the latter ones inferred at the end of the segments.
The shaded areas correspond to the intervals between the 0.05th and the 0.95th percentiles while the solid lines correspond to
the medians of the posteriors. Similarly, the dashed lines show the 0.05th and 0.95th percentiles of the posterior distributions
and their medians after each time step, as inferred by the method. The change-point model was fitted to the data sets with the
hazard rate λ = 5, using river-specific prior settings for the variance parameters (Supplementary Material, Table S3).
change points, the timing of temporal changes, and direc- ery. Conne and Trinité experienced a single temporal change
tional trajectories in mortality. Among four populations for (a decline), whereas evidence for a change in at-sea survival
which data extended to at least 1990, Saint-Jean experi- for WAB was not found during 1974–2015. Among the three
enced two shifts in s1SW; first a decline and then a recov- populations for which data extended to the mid- or late
Can. J. Fish. Aquat. Sci. 79: 1697–1711 (2022) | dx.doi.org/10.1139/cjfas-2021-0302 1707
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1990s, all of them experienced single shifts in s1SW, declin- tor swamping from increased smolt abundance (Furey et al.
ing for two (LaHave and Nashwaak) and increasing for one 2016). Nonetheless, all hatchery fish were excluded from our
(Campbellton). smolt and adult salmon estimates. It is also instructive to
Given the widespread, empirically supported assumption observe that the most considerable declining shift in at-sea
that all salmon from North America migrate from their spe- survival was found for Conne River, the population with the
cific coastal areas to the Labrador Sea to feed (Olmos et al. closest proximity to salmon aquaculture operations, whose
2020), our work suggests that population differences in sur- negative consequences to wild salmon have been well docu-
vival at sea cannot be fully explained by shared environ- mented (McGinnity et al. 2003; Sylvester et al. 2019; Bradbury
mental conditions on these feeding grounds. One possibility et al. 2020). Potential mechanisms for the lack of synchrony
is that the strength of a shared, survival-based stressor has may also include freshwater carryover effects, such as the
waned over time, being more important in the early 1990s, impact of river acidification on marine survival (Thorstad
when three populations experienced a change point in at- et al. 2013) which suggest that among-river variability in
sea survival, than in the subsequent decades. This conclu- freshwater conditions, and not just estuarine/coastal differ-
sion would be consistent with the observation that relation- ences, could also explain the asynchrony we observed in
ships between North Pacific Ocean climate indices (Pacific survival at sea. Furthermore, growth rate at sea is known
Decadal Oscillation, North Pacific Gyre Oscillation) and re- to correlate with marine survival and can affect probabil-
gional physical and ecological processes have weakened over ity of returning as 1SW (Friedland et al. 1993). However,
time (Litzow et al. 2020). of particular importance could be the effect of freshwater
It is also likely that interpretative differences in the per- growth rate on smolt age and phenology, which then di-
ceived importance of broad- versus small-scale stressors on rectly impacts marine survival through size-dependent mor-
salmon survival can be attributed, in part, to differences tality and outmigration mismatch with optimal conditions,
in data sources. Olmos et al. (2020), for example, reported respectively (Russell et al. 2012; Jonsson et al. 2017; Gregory
that post-smolt survival trends for six North American and et al. 2018). The direct mechanisms behind these relation-
seven European “stock units” or SUs (ICES 2015, 2017) are ships (e.g., temporal differences in prey availability, preda-
synchronous and can be linked with sea surface tempera- tor avoidance) could be many but little is known about them
ture and primary production. Following ICES (2015, 2017), yet. Freshwater effects not only impact egg-to-smolt survival,
these SUs represent an amalgamation of data from an un- which is the life history trait with the highest variability
documented number of populations to estimate salmon sur- in their life cycle, but also influence what comes after, at
vival at large spatial scales (e.g., France, Newfoundland, Eng- sea.
land and Wales, USA). Rather than relying solely on smolt Although we studied marine survival on a smaller scale
and returning-adult abundance data, the SU-based estimates than Pardo et al. (2021), we recognize that changes may oc-
of salmon survival depend heavily on catch data, a source cur in even smaller temporal scale. The model we used de-
with biases that can prove problematic (e.g., Walters 2003). A scribes stepwise changes in the marine survival parameters,
third potential issue associated with the ICES’s data amalga- ignoring, e.g., continuous linear changes that can also be
mation is the inclusion of populations and stock units that present in the data (Pardo et al. 2021). Moreover, regarding
are solely sustained by hatcheries (e.g., US populations), a our results, it should be noted that the change-point prior
source of potential bias when evaluating patterns of popula- and the amount of random variation around the average re-
tion survival (Fraser 2008; NASCO 2017). Independently of the lationship between the number of smolts and returning fish,
data sources used to delineate the SUs, temporal synchrony that was assumed to be present in the data, may have had
is not a strong element that emerges from our analyses of a considerable impact on change-point inference (Tirronen
population-specific data associated with rivers located within et al. 2021). Nonetheless, we carried out sensitivity analyses in
four of the six North American SUs. terms of the priors of the variance parameters as well as the
The importance of small-scale, potentially population-level change-point prior, and the obtained posterior predictive dis-
processes has been previously recognized. Olmos et al. (2019, tributions suggest that the change points we reported yield
2020) noted that despite some broad-scale, spatial coher- a good model fit to the data (Supplementary Material, Sec-
ence in survival trends throughout the north Atlantic, un- tion S3). In addition, the priors set for the marine survival
explained annual and regional differences remain. Friedland parameters may have played a considerable role in param-
et al. (2014) hypothesized that southern North American pop- eter estimation. As the focus of this study was on change
ulations might be more susceptible to increased predator- points, we did not test alternative priors for the survival pa-
related mortality during the post-smolt period than north- rameters but, using a different prior for p than that of Pardo
ern populations. A combination of small salmon population et al. (2021), it was evident that the role of such priors can be
sizes (COSEWIC 2011) and increased abundance of highly considerable. Furthermore, with the priors we chose to use,
mobile mammalian predators (predation by grey seals (Hali- we could not infer temporal changes in s2SW or p, since the
choerus grypus) is related to a lack of recovery in several posterior distributions of these parameters contained a large
southern Canadian marine fishes; Swain and Benoît 2015; amount of uncertainty. In the previous study (Pardo et al.
Neuenhoff et al. 2019) lends credence to this hypothesis. 2021), the estimates obtained for s2SW and p were also highly
On the other hand, smolt-releases can have an impact on uncertain.
survival, since the releases may buffer predation of wild The present study suggests that a critical component in At-
salmon when they are coming out of the rivers, due to preda- lantic salmon life history, survival during the first sea win-
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ter, depends nontrivially on local or regional conditions. Our Author information
findings are not consistent with the hypothesis that salmon
populations consistently share the same mortality-related Author ORCIDs
stressors in the marine environment. Although populations Maria Tirronen https://orcid.org/0000-0001-6052-3186
may have shared greater synchrony in survival patterns in
the past, this synchrony may be breaking down, as reflected Author notes
by a lack of temporal concordance in survival change points. Jeffrey A. Hutchings is deceased.
Rather than focus primarily on putative large-scale stressors,
it may be prudent to direct greater attention to smaller-scale Author contributions
regional or population-level correlates of survival. This is fur- MT was responsible for formal analysis, methodology, soft-
ther supported by genomic data on the fine-scale metapopu- ware, visualization, writing —— original draft, writing —— re-
lation structuring and source–sink dynamics among nearby view and editing. JAH was responsible for conceptualization,
salmon rivers (Hindar et al. 2004; Kuparinen et al. 2010) as funding acquisition, writing —— original draft. SAP was re-
well as genetic and life history differentiation within salmon sponsible for conceptualization, methodology, writing——re-
river tributaries (e.g., Vähä et al. 2007). Although challeng- view and editing. AK was responsible for funding acquisition,
ing, the technology for population identification based on supervision, writing——original draft, writing——review and
genomic markers does exist (Vähä et al. 2016; Bernatchez editing.
et al. 2017). From the perspective of environmental manage-
ment, a focal shift from broad-scale oceanographic patterns Competing interests
to smaller-scale regional or local conditions implies a need The authors declare there are no competing interests.
to consider interactions among terrestrial and aquatic sys-
tems as well as human impacts on aquatic habitats. While the Funding information
present study takes a step towards understanding the timing
This work was funded by the Atlantic Salmon Conservation
and scale of drivers affecting salmon survival in the sea, lit-
Foundation and by the Academy of Finland (project grant
tle is still known about the underlying mechanisms and the
317495 to AK), Natural Sciences and Engineering Research
response times, particularly, how and when conditions expe-
Council of Canada (NSERC; Discovery Grants to JAH and AK),
rienced at egg, larval, and juveniles stages affect salmon later
and the European Research Council (COMPLEX-FISH 770884
in its life.
to AK).
Acknowledgements Supplementary material
We thank Yong Chen and two anonymous reviewers who Supplementary data are available with the article at https:
provided many helpful suggestions, which significantly im- //doi.org/10.1139/cjfas-2021-0302.
proved the manuscript. The present study reflects only the
authors’ view; the European Research Council is not respon-
sible for any use that may be made of the information it con- References
tains. Adams, R.P., and MacKay, D.J.C. 2007. Bayesian online changepoint detec-
tion. Technical report. Available from https://arxiv.org/abs/0710.3742.
Bernatchez, L., Wellenreuther, M., Araneda, C., Ashton, D., Barth, J.,
Article information Beacham, T., et al. 2017. Harnessing the power of genomics to secure
the future of seafood. Trends Ecol. Evol. 32:665–680. doi:10.1016/j.
History dates tree.2017.06.010.
Bradbury, I., Duffy, S., Lehnert, S.J., Jóhannsson, R., Fridriksson, J.H.,
Received: 5 November 2021 Castellani, M., et al. 2020. Model-based evaluation of the genetic im-
Accepted: 22 April 2022 pacts of farm-escaped Atlantic salmon on wild populations. Aquac.
Accepted manuscript online: 20 May 2022 Environ. Interact. 12: 45–59. doi: 10.3354/aei00346.
Version of record online: 27 September 2022 COSEWIC. 2011. COSEWIC assessment and status report on At-
lantic salmon Salmo salar in Canada. Committee on the Sta-
tus of Endangered Wildlife in Canada, Ottawa, Canada. Available
Copyright from https://wildlife-species.canada.ca/species-risk-registry/virtual_s
© 2022 The Author(s). This work is licensed under a Creative ara/files/cosewic/sr_Atlantic_Salmon_2011a_e.pdf.
Commons Attribution 4.0 International License (CC BY 4.0), Fraser, D. 2008. How well can captive breeding programs conserve biodi-
versity? A review of salmonids. Evol. Appl. 1: 535–586. doi:10.1111/j.
which permits unrestricted use, distribution, and reproduc- 1752-4571.2008.00036.x.
tion in any medium, provided the original author(s) and Friedland, K.D., Reddin, D.G., and Kocik, J.F. 1993. Marine survival of
source are credited. North American and European Atlantic salmon: effects of growth and
environment. ICES J. Mar. Sci. 50: 481–492. doi:10.1006/jmsc.1993.
1051.
Data availability Friedland, K.D., Reddind, D.G., and Castonguay, M. 2003. Ocean ther-
All data that support the plots and other findings in this paper mal conditions in the post-smolt nursery of North American Atlantic
are available from the corresponding author upon reasonable salmon. ICES J. Mar. Sci. 60: 343–355. doi:10.1016/S1054-3139(03)
00022-5.
request. Source data and code are available at https://doi.org/ Friedland, K.D., Shank, B.V., Todd, C.D., McGinnity, P., and Nye, J.A.
10.5061/dryad.9p8cz8wjg. 2014. Differential response of continental stock complexes of At-
Can. J. Fish. Aquat. Sci. 79: 1697–1711 (2022) | dx.doi.org/10.1139/cjfas-2021-0302 1709
Can. J. Fish. Aquat. Sci. Downloaded from cdnsciencepub.com by JYVASKYLAN YLIOPISTO on 10/11/22
For personal use only. 
Canadian Science Publishing
lantic salmon (Salmo salar) to the Atlantic Multidecadal Oscillation. Perälä, T., Olsen, E., and Hutchings, J. 2020. Disentangling conditional
J. Mar. Syst. 133: 77–87. doi: 10.1016/j.jmarsys.2013.03.003. effects of multiple regime shifts on Atlantic cod productivity. PLoS
Furey, N., Hinch, S., Bass, A., Middleton, C., Minke-Martin, V., and Lotto, ONE, 15(11):e0237414. doi:10.1371/journal.pone.0237414.
A. 2016. Predator swamping reduces predation risk during nocturnal Perälä, T.A., Swain, D.P., and Kuparinen, A. 2017. Examining nonstation-
migration of juvenile salmon in a high-mortality landscape. J. Anim. arity in the recruitment dynamics of fishes using Bayesian change
Ecol. 85: 948–959. doi:10.1111/1365-2656.12528. point analysis. Can. J. Fish. Aquat. Sci. 74(5): 751–765. doi:10.1139/
Gregory, S., Armstrong, J., and Britton, R. 2018. Is bigger really better? cjfas-2016-0177.
Towards improved models for testing how Atlantic salmon Salmo salar Russell, I.C., Aprahamian, M.W., Barry, J., Davidson, I.C., Fiske, P., Ib-
smolt size affects marine survival. J. Fish. Biol. 92: 579–592. doi:10. botson, A.T., et al. 2012. The influence of the freshwater environ-
1111/jfb.13550. ment and the biological characteristics of Atlantic salmon smolts on
Hindar, K., Tufto, J., Sættem, L.M., and Balstad, T. 2004. Conservation of their subsequent marine survival. ICES J. Mar. Sci. 69: 1563–1573.
genetic variation in harvested salmon populations. ICES J. Mar. Sci. doi:10.1093/icesjms/fsr208.
61(8): 1389–1397. doi:10.1016/j.icesjms.2004.08.011. Särkkä, S. 2013. Bayesian filtering and smoothing. Institute of Mathemat-
ICES. 2015. Report of the Working Group on North Atlantic Salmon (WG- ical Statistics Textbooks, Cambridge University Press. doi:10.1017/
NAS), 17–26 March. ICES CM 2015/ACOM:09. Moncton, Canada. Avail- CBO9781139344203.
able from https://www.ices.dk/sites/pub/Publication%20Reports/Expe Schindler, D., Hilborn, R., Chasco, B., Boatright, C., Quinn, T., Rogers, L.,
rt%20Group%20Report/acom/2015/WGNAS/wgnas_2015.pdf. and Webster, M. 2010. Population diversity and the portfolio effect in
ICES. 2017. Report of the Working Group on North Atlantic Salmon an exploited species. Nature, 465: 609–12. doi:10.1038/nature09060.
(WGNAS). ICES CM 2017/ACOM: 20. Copenhagen, Denmark. Avail- Scientific Council for Salmon Management. 2019. Status of wild Atlantic
able from https://www.ices.dk/sites/pub/Publication%20Reports/Expe salmon in Norway in 2019. Report from the Scientific Council for
rt%20Group%20Report/acom/2017/WGNAS/wgnas_2017.pdf. Salmon Management, No. 12. Full report is available from (in Norwe-
ICES. 2021. Working Group on North Atlantic Salmon. ICES Scientific gian) http://hdl.handle.net/11250/2619889. English summary is avail-
Reports, Vol. 3. doi: 10.17895/ices.pub.7923. able from https://www.vitenskapsradet.no/Portals/vitenskapsradet/P
Jonsson, B., Jonsson, M., and Jonsson, N. 2017. Influences of migration df/Status%20of%20wild%20Atlantic%20salmon%20in%20Norway.pdf.
phenology on survival are size dependent in juvenile Atlantic salmon Swain, D., and Benoît, H. 2015. Extreme increases in natural mortal-
(Salmo salar). Can. J. Zool. 95: 581–587. doi:10.1139/cjz-2016-0136. ity prevent recovery of collapsed fish populations in a Northwest
Kuparinen, A., Tufto, J., Consuegra, S., Hindar, K., Merilä, J., and Garcia Atlantic ecosystem. Mar. Ecol. Prog. Ser. 519: 165–182. doi:10.3354/
de Leaniz, C. 2010. Effective size of an Atlantic salmon (Salmo salar L.) meps11012.
metapopulation in northern Spain. Conserv. Genet. 11: 1559–1565. Sylvester, E.V.A., Wringe, B.F., Duffy, S.J., Hamilton, L.C., Fleming, I.A.,
doi:10.1007/s10592-009-9945-6. Castellani, M., et al. 2019. Estimating the relative fitness of escaped
Litzow, M., Hunsicker, M., Bond, N., Burke, B., Cunningham, C., Gosselin, farmed salmon offspring in the wild and modelling the consequences
J., et al. 2020. The changing physical and ecological meanings of north of invasion for wild populations. Evol. Appl. 12(4): 705–717. doi:10.
Pacific Ocean climate indices. Proc. Natl. Acad. Sci. U.S.A. 117: 7665– 1111/eva.12746.
7671. doi:10.1073/pnas.1921266117. Thorstad, E.B., Uglem, I., Finstad, B., Kroglund, F., Einarsdóttir, I.E.,
Liu, J., and West, M.A. 2001. Combined parameter and state estimation Kristensen, T., et al. 2013. Reduced marine survival of hatchery-
in simulation-based filtering. In Sequential Monte Carlo methods in reared Atlantic salmon post-smolts exposed to aluminium and
practice. Edited by A. Doucet and N. de Freitas. Statistics for Engineer- moderate acidification in freshwater. Estuar. Coast. Shelf Sci. 124:
ing and Information Science. pp. 197–223. 34–43.
Massiot-Granier, F., Prevost, E., Chaput, G., Potter, T., Smith, G., White, Tirronen, M., Perälä, T., and Kuparinen, A. 2021. Temporary Allee
J., et al. 2014. Embedding stock assessment within an integrated hi- effects among nonstationary recruitment dynamics in depleted
erarchical Bayesian life cycle modelling framework: an application gadid and flatfish populations. Fish Fish. 23(2):392–406. doi:10.1111/
to Atlantic salmon in the northeast Atlantic. ICES J. Mar. Sci. 71(7): faf.12623.
1653–1670. doi:10.1093/icesjms/fst240. Vähä, J.-P., Erkinaro, J., Falkegård, M., Orell, P., and Niemelä, E. 2016.
McGinnity, P., Prodöhl, P., Ferguson, A., Hynes, R., Maoiléidigh, N.O., Genetic stock identification of atlantic salmon and its evaluation in
Baker, N., et al. 2003. Fitness reduction and potential extinction of a large population complex. Can. J. Fish. Aquat. Sci. 74. doi:10.1139/
wild populations of Atlantic salmon, Salmo salar, as a result of inter- cjfas-2015-0606.
actions with escaped farm salmon. Proc. R. Soc. B, 270(1532): 2443– Vähä, J.-P., Erkinaro, J., Niemelä, E., and Primmer, C. 2007. Life-history
2450. doi:10.1098/rspb.2003.2520. and habitat features influence the with-river genetic structure of
Murphy, G.I. 1952. An analysis of silver salmon counts at Bendow Dam, Atlantic salmon. Mol. Ecol. 16: 2638–2654. doi:10.1111/j.1365-294X.
South Fork of Eel River, California. Calif. Fish Game, 38: 105–112. 2007.03329.x.
NASCO. 2017. Understanding the risks and benefits of hatchery and Walters, C.J. 2003. Folly and fantas[y in the analysis of spatial catch data.
stocking activities to wild Atlantic salmon populations. North Can. J. Fish. Aquat. Sci. 60(12): 1433–1436. doi:10.1139/f03-152.
Atlantic Salmon Conservation Organization Council Document WWF. 2001. The status of wild Atlantic salmon: a river by
CNL(17)61. Available from https://nasco.int/wp-content/uploads/2020/ river assessment. World Wildlife Fund. Available from
02/2017ThemeBasedSession.pdf. https://wwf.panda.org/wwf_news/?3729/The-Status-of-Wild-Atlantic-
Neuenhoff, R., Swain, D., Cox, S., McAllister, M., Trites, A., Walters, C., Salmon-A-River-by-River-Assessment.
and Hammill, M. 2019. Continued decline of a collapsed population
of Atlantic cod (Gadus morhua) due to predation-driven Allee
effects. Can. J. Fish Aquat. Sci. 76(1):168–184. doi:10.1139/
cjfas-2017-0190. Appendix A
Olmos, M., Massiot-Granier, F., Prévost, E., Chaput, G., Bradbury, I.R., Given an underlying predictive model and a change-point
Nevoux, M., and Rivot, E. 2019. ‘Evidence for spatial coherence in
time trends of marine life history traits of Atlantic salmon in the prior, the BOCPD method (Adams and MacKay 2007) infers
North Atlantic. Fish Fish. 20(2): 322–342. doi: 10.1111/faf.12345. the time since the last change point, the run length, at each
Olmos, M., Payne, M.R., Nevoux, M., Prévost, E., Chaput, G., Du Pon- time step. For the change-point model with input–output
tavice, H., et al. 2020. Spatial synchrony in the response of a long data, the run length posterior distribution can be formulated
range migratory species (Salmo salar) to climate change in the North
Atlantic Ocean. Glob. Change Biol. 26(3): 1319–1337. doi:10.1111/gcb. as (Perälä et al. 2017):
14913. (A1) p (rt | R1:t , S1:t )
Pardo, S.A., Bolstad, G.H., Dempson, J.B., April, J., Jones, R.A., Raab, ( )
D., and Hutchings, J.A. 2021. ‘Trends in marine survival of Atlantic ∑t−2 p (rt | r (r) (r)
t−1 ) p Rt | Rt−1, St−1, St p (rt−1 | R1:t−1, S1:t−1 )
salmon populations in eastern Canada. ICES J. Mar. Sci. 78: 2460– =
2473. doi:10.1093/icesjms/fsab118. = p (R | R , S , S )
rt−1 0 t 1:t−1 1:t−1 t
1710 Can. J. Fish. Aquat. Sci. 79: 1697–1711 (2022) | dx.doi.org/10.1139/cjfas-2021-0302
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Above, Rt:u = (Rt, . . . , Ru ) and R(r)
u = R(u−ru ):u, and similarly, St:u by maximizing the product of the smoothed run length prob-
= (St, …, Su) and S(r) = S − . abilities over all possible segmentations:
u (u ru ):u
With nonlinear models and arbitrary prior distributions ∏T
of the model parameters, the posterior distributions of the (A2) arg max p (ri = si | R1:T , S1:T )
s
model parameters are analytically intractable but can be i=1
inferred by a sequential Monte Carlo method using artifi- In this, the smoothed run length probabilities were com-
cial evolution of parameters (a particle filter; Perälä et al. puted recursively using the following equations (Särkkä
2017; Liu and West 2001). In this, the acceptable number 2013; Perälä et al. 2017):
of effective particles was set to half of the number of parti- (A3) p (rτ | R1:T , S1:T )
cles used in the filter. For the smoothing parameter in the ∑τ
particle filter we set the value 0.1, suggested by Liu and West = | p (r
p (r R S ) τ+1 | rτ ) p (rτ+1 | R1:T , S1:T )
τ 1:τ , 1:τ
(2001). ∑= p (rτ+1 | R1:τ , S )
r 1:τ
τ+1 0
A segmentation is a sequence s = (s1, …, sT) of run lengths τ−1
for time steps t = 1, …, T. The MLS of a time series was found (A4) p (rτ+1 | R1:τ , S1:τ ) = p (rτ+1 | rτ ) p (rτ | R1:τ , S1:τ )
rτ =0
Can. J. Fish. Aquat. Sci. 79: 1697–1711 (2022) | dx.doi.org/10.1139/cjfas-2021-0302 1711
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