Posterior densities

Figures 26 and 27 show the posterior densities for the estimated yearly amounts of brown trout smolts migrating downwards from both study rivers. The orange lines mark the credible intervals of the estimates (Gelman et al. 2014). The smolt run estimates in the beginning of the series (1999-2000) were extremely high in River Pirita and extremely low in River Ingarskila, due to the high uncertainty. The highest simulated value in the time series was 119092for in both rivers.

In River Pirita between the years 2001 and 2011 the estimates for the smolt run are somewhat leveled between 300 and 400 individuals per year. Between 2011 and 2014 the numbers of downward migrating smolts to drop between 200 and 100 individuals.

In River Ingarskila the trend seems to be reversed at first, with initial smolt numbers staying between 200 and just under 100 individuals. Between 2001 and 2003 there is very high uncertainty in the smolt run estimates. Between 2004 and 2010 the estimates stabilize between circa 400 and 300 individuals per year. In 2011 and 2012 there is a sharp drop, with 95 % intervals ranging

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between circa 150 and almost 0 individuals. In 2013 and 2014 the number smolts is estimated to be around 100 and 200 individuals.

Figure 26. 200 draws from the posterior density of yearly smolt run in River Pirita.

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Figure 27. 200 draws from the posterior density of yearly smolt run in River Ingarskila.

Figure 28 show the posterior distribution for the density 0+ trout parrs per 100 m² in both study rivers. The yearly mean values of 0+ parr density varied between 22.14and 48 individuals per 100 m² in River Pirita and between 22 and 48 in River Ingarskila.

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Figure 28. Posterior distribution of yearly 0+ trout parrs in the autumn period in River Pirita and Ingarskila.

Figure 29 shows the prior (red lines) and posterior (blue lines) densities of ρ, the variable describing trout’s affinity to migrate to sea at certain age in both study rivers, in the absence of mortality. In river Ingarskila the highest probability seems to be concentrated around age 3, and around age 4 in River Pirita. There is visibly more uncertainty remaining in the posterior distribution of River Ingarskila.

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Figure 29.Prior and posterior distributions for age-specific probability of smoltification (ρ) in the absence of mortality in study rivers.

Figure 30 shows the prior (red lines) and posterior (blue lines) densities of π, the variable used for estimating age-specific yearly survival probabilities. In river Pirita the probabilities are concentrated around 0.2 for newborn parrs, with relatively small uncertainty. Yearly survival probabilities rise as age increases and are increasingly more uncertain after age 3. In river Ingarskila the probability estimates are more uncertain for age 0 parrs and the slope of the logistic regression lines seem to be steeper than in River Pirita. For fish aged 6 and higher the probability estimates seem to approach 1.

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Figure 30.Prior and posterior distributions for age-specific yearly survival probability estimate (π) in the absence of smoltification in both study rivers.

Figures 31 and 32 show the resulting combinations of π and ρ parameters, used to calculate the actual estimates for survival and smoltification probabilities in formulas 5 and 7. In river Ingarskila the highest probability of smoltification seems to be concentrated around age 3, and around age 4 in River Pirita. There is visibly more uncertainty remaining in the posterior distribution of River Ingarskila. Both posteriors resemble the posterior distributions ρ.

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Figure 31. Posterior distributions for age-specific probability of smoltification (ρπ^1/4) in study rivers.

The age-specific survival probability P(survival) is the joint probability of survival and not-smoltifying. In other words it can be interpreted also as the probability of staying in the river another year. In River Pirita there is very little uncertainty for ages 1 to 3 and a very clear drop at age 3, after which probability increases. In River Ingarskila the posterior distribution of P(survival) is more leveled and contains more uncertainty at all ages. Posterior distributions in both rivers resemble an inverted version of P(smolt).

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Figure 32. Posterior distributions for age-specific probability of survival ((1-ρ)π^1/4) in study rivers.

Figures 33 – 35 represent the prior (red lines) and posterior (blue lines) densities of parameter µ, σ and τ in study rivers. Parameter µ, which determines the location of the probability peak in

parameter ρ, seems to have stabilized around age 3 and 3.5 in River Pirita and around age 4 and 4.5 in River Ingarskila. The posterior distribution is much narrower in River Pirita.

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Figure 33. Prior (red line) and posterior (blue line) distributions for parameter µ study rivers.

Parameter σ determines the range of ages, where individual trout can become migratory. In River Pirita the posterior distribution σ is quite narrow and centered approximately around 1.5. In River Ingarskila the distribution is significantly wider, indicating much higher uncertainty. The peak of the posterior distribution is located near 3.

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Figure 34. Prior (red line) and posterior (blue line) distributions for parameter σ study rivers.

Parameter τ controls maximum height of parameter ρ and on a population scale it can be interpreted as the proportion of population that migrates out to sea, in the absence of mortality. In River Pirita posterior distribution of τ is located close to 1 and centered around 0.95. In River Ingarskila the posterior distribution is much wider and contains more uncertainty. Posterior mean value is close to 0.45.

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Figure 35 Prior (red line) and posterior (blue line) distributions for parameter τ study rivers.

Figures 36 and 37 show posterior (blue lines) and prior (dashed red lines) of parameter απ and βπ in study rivers respectively. Parameter απ determines the intercept term for the logistic regression curve used to calculate the values for yearly probability estimate for survival (π). Parameter βπ determines the slope of the curve. The posterior distribution απ is centered approximately around -1 in River Pirita and around 0 in River Ingarskila. Posterior distribution of απ contains more

uncertainty in River Ingarskila, than in River Pirita. Posterior distributions of parameter βπ contain similar amounts uncertainty in both rivers. River Pirita’s posterior is slightly higher in density and its mean value is smaller than the posterior mean in River Ingarskila.

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Figure 36. Prior (red line) and posterior (blue line) distributions for parameter απ study rivers.

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Figure 37. Prior (red line) and posterior (blue line) distributions for parameter βπ study rivers

Figures 38 and 39 show the posterior densities of the catchability parameters in both observation models. Catchability in smolt trapping experiments (figure 38) seems to vary between 0 and 0.5 in both rivers throughout the time series.

Electrofishing catchability estimates vary between fish ages in both rivers (figure 39). In River Pirita there is a clear notch in catchability in age 6.This is also seen in River Ingarskila at age 2 and 8. Total range of catchability estimates in both rivers is between almost 1 and just under 0.1.

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Figure 38. Posterior distributions of yearly catchability estimates in smolt trapping experiments.

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Figure 39. Posterior distributions of age-specific catchability estimates in electrofishing experiments. Dashed red line indicates the posterior mean.