5. Discussion
5.5. Conclusions and suggestions for future work on the model
The model did not succeed in predicting the absolute amounts trout parrs and smolts. This was probably caused by some of the model assumptions and the relatively small dataset available. The effect of small the dataset is very evident when comparing the posterior distributions of model parameters used for River Ingarskila, with those of River Pirita.
A more realistic way to include electrofishing data might have increased the model’s fit to data. An alternative way for this could have been to model the data gathered from different sampling stations separately in a hierarchical model similar to the model proposed by Mäntyniemi et al. (2005b), with unequal catchability estimates.
Based on the good prediction of the age-distribution the River Pirita data were large enough for the model to learn the parameters controlling the smoltification model. This combined with the results of previously published observations’ analysis gives encouraging evidence that the novel idea presented here for modeling partial anadromy in Salmo trutta has potential for further uses. The model’s application to other species with partial anadromy, such as the rainbow trout
(Onchorynchus mykiss) and arctic char (Salvelinus alpinus) should also be studied in the future.
The observed 2014 River Pirita smolt catch was surprisingly low, given the high densities 0+ parrs in the two years before it. The phenomenon behind this could be a density-dependent mechanism that prevents migration especially in the youngest age groups, during high population densities.
High population densities limit trout growth and their ability to tolerate seawater (Jonsson &
Jonsson 2011). It is possible that this phenomenon could be modeled, for example using a variation of the Ricker function (Ricker 1954). It is possible that autumn migrations of 0+ smolts might have caused the small amount of smolts (Limburg et al. 2001; Jonsson et al. 2001; Taal et al. 2014).
Other ways of improving the model could include assigning the range of smolt ages (σ) to be a more specific interval, since the range of possible ages used in this study was unnecessarily wide (1+ - ≥ 9+), which was only needed to include the highest reported smolt age 9+ in literature (L’Abée-Lund 1989).
The τ parameter that can be interpreted as the stocks tendency to exhibit anadromy (HIndar et al.
1990; Charles et al. 2005) could be further studied in field experiments. These experiments could include tagging large numbers fish with fluorescent marker tags in autumn electrofishing surveys, and then calculating the proportion marked fish in the smolt catch the following spring. Other way
79
could be to capture pre-smolt trouts in the spring and measure their hormonal activity, which could indicate physiological preparation for migration (Jonsson & Jonsson 2011).
Possibly the best way of improving this model would be to include the sexually mature adult proportion of trout population into the model. This would “close the loop” between older fish and the newborn parrs, making the artificial modeling of 0+ parrs based on reproduction areas and expert elicitation unnecessary. This would increase the biological realism of the model significantly.
This way the sea phase could also be included, which would enable recommendations for catch quotas and possibly aid the protection of the extremely endangered species. The model presented in this thesis serves as a starting point for that work.
80 6. Acknowledgments
The making of this thesis was supported and funded by the Rapala charity foundation and I would like thank the foundation for their donation and their decision to support this type of work. Prof.
Samu Mäntyniemi has given technical, formal and methodological guidance. Thanks to long helpful discussions with him my personal learning curve has remained steep throughout the making of this thesis. I give special thanks to MSc Martin Kesler from the Estonian Marine Institute, University of Tartu, MSc Ari Saura from the National Resource Institute of Finland and BSc Aki Janatuinen for lending me their expert knowledge about the study rivers, and providing me with the River Pirita and River Ingarskila field survey data, without of which this thesis would have been impossible to make.
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88 Appendix A.
Graphical representation of the model.
89 Appendix B.
Table of brown trout smolt mean ages in different rivers on Europe, derived from litetature. * Combined average of two or more datasets.
Country River
90
91
Yearly_run[y,river]<-sum(Smolt_y[y,,river])+1 mean_age_y[y,river]<-inprod(weight[y,,river],age[]) for(a in 1:A){
Smolt_y[y,a,river]<-sum(Smolt[y,,a,river])
weight[y,a,river]<-Smolt_y[y,a,river]/Yearly_run[y,river]
} } }
##### LINK BETWEEN LOCAL PEAK AGE AND LATITUDE ######
for( river in 1:RIVERS){
obs_mean_age[river]~dnorm(mean_age[river],tau_obs_age[river])T(0,) # havaittu keski-ikä
tau_obs_age[river]<-1/pow(sd_obs_age[river],2) # havainnon mittausepävarmuus????
mean_age[river]<-mean(mean_age_y[,river]) #painotetun vuotuisen keski-iän keskiarvo }
for( river in 1:9){
sd_obs_age[river]~dunif(0,1) }
for( river in 10:RIVERS){
sd_obs_age[river]<-(age95[river]/1.96) }
for(river in 1:NA_RIVERS){
for(y in 1:years){
Parr_density[y,river]<-(TN[y,river]/sample_area[y,river])*100
92
Monitor_Parr[y,a,river]<-Parr[y,1,a,river]
for(t in 1:time){
parr[y,t,a,river]<-((x[y,t,a,river]/100)*tot_area[river]) # NEWBORN 0+ PARRS }
93
parr[y,1,a,river]~dpois(mu_parr[y,1,a,river])#~dbin(psurv[y,1,a,river],Parr[y-1,4,a-1,river]) # AGEING OF PARRS
mu_parr[y,1,a,river]<-psurv[y,1,a,river]*Parr[y-1,4,a-1,river]+0.01
Smolt[y,1,a,river]~dbin(psmolt[y,1,a,river],Parr[y,1,a,river]) #SMOLT PRODUCTION
x[y,1,a,river]<-parr[y-1,4,a-1,river]/tot_area[river]*100 for(t in 2:time){
94
Smolt[y,t,a,river]~dbin(psmolt[y,t,a,river],Parr[y,t,a,river]) }
95
Smolt[y,t,a,river]<-0#psmolt[y,t,a,river]*Parr[y,t,a,river]
}
x[y,t,a,river]<-parr[y,t,a,river]/tot_area[river]*100 # All parrs per 100 sqrmeters in other timesteps
apu_parr[y,t,a,river]<-round((parr[y,t,a,river]-Smolt[y,t,a,river])) Parr[y,t,a,river]<-round(parr[y,t,a,river])
96
x[y,1,1,river]<-prior_x[river]/psurv[y,1,1,river]/psurv[y,2,1,river] # 0+ parr per 100 sqrmeters in the begining of year
for(t in 2:time){
x[y,t,1,river]<-parr[y,t,1,river]/tot_area[river]*100 # 0+ parrs per 100 sqrmeters in other timesteps
} } }
for(river in 1:RIVERS){
prior_x[river]<-exp(ln_prior_x[river])
ln_prior_x[river]~dnorm(lmu_prior_x[river],ltau_prior_x[river]) lmu_prior_x[river]<-log(mu_prior_x[river])-0.5*lsd_prior_x[river]
ltau_prior_x[river]<-1/lsd_prior_x[river]
lsd_prior_x[river]<-log(pow(sd_prior_x[river],2)/pow(mu_prior_x[river],2)+1)
}
##### ARTIFICIAL EXPERT PRIORS FOR OTHER RIVERS #####
for(river in 3:RIVERS){
97 x[y,1,a,river]~dunif(1,100)
for(t in 2:time){
x[y,t,a,river]<-parr[y,t,a,river]/tot_area[river]*100 # Older parrs per 100 sqrmeters in other timesteps of year 1
} } } }
##### OWN PRIOR FOR OLDER AGE GROUPS IN PIRITA & INGARSKILA #####
for(river in 1:NA_RIVERS){
for(y in 1:1){
for(a in 2:A){
x[y,1,a,river]<-exp(ln_x[a])/psurv[y,1,1,river]/psurv[y,2,1,river]
for(t in 2:time){
x[y,t,a,river]<-parr[y,t,a,river]/tot_area[river]*100 # Older parrs per 100 sqrmeters in other timesteps of year 1
M_x[2]<-7.476602 # Ingarkilan datan >0+ kalojen keskimäär. tiheys samoilla koe-aloilla, joista datassa olevat kalat on peräisin
SD_x[2]<-25
98
M_x[3]<-0.399273 # Ingarkilan datan >1+ kalojen keskimäär. tiheys samoilla koe-aloilla, joista datassa olevat kalat on peräisin
M_x[4]<-4.385051 # > "ei määritetty" Saura arveli kalojen olevan pääasiassa 3+ ikäisiä M_x[5]<-0.5
alpha_pii[river]~dnorm(mu_alpha.pii,tau_alpha.pii) beta_pii[river]~dnorm(mu_beta.pii,tau_beta.pii) for(a in 1:A){
logit(pii[a,river])<-Pii[a,river]
Pii[a,river]~dnorm(mu_mu_pii[a,river],100)
mu_mu_pii[a,river]<-(alpha_pii[river]+(beta_pii[river]*age[a])) inst_pii[a,river]<-pow(pii[a,river],(1/4))
}
}##### INDIVIDUAL FISHES CHANCE OF SMOLTIFICATION #####
### P(smolt I age, river) ####
for( river in 1:RIVERS){
mu_p[river]<-ten_mu_p[river]*10 logit(ten_mu_p[river])<-MU_p[river]
MU_p[river]~dnorm(mu_mu_p[river],100)#tau_mu_p) peak_p[river]~dbeta(alpha_peak_p,beta_peak_p) mu_mu_p[river]<-alpha_p*latitude[river]+const_p s[river]~dunif(0.01,10)
99 p[1,river]<-0
for(a in 2:A){
p[a,river]<-peak_p[river]*exp((-pow(((age[a]-mu_p[river])/s[river]),2))) }
alpha_p~dnorm(mu_alpha_p,tau_alpha_p) const_p~dnorm(mu_const_p,tau_const_p) mu_peak_p<-0.5
#### STUDY RIVER VARIABLES FOR PLOTTING ####
mu_p_Pirita<-mu_p[1]
mu_p_Ingars<-mu_p[2]
100
tot_area[river]<-exp(ltot_area[river])
ltot_area[river]~dnorm(lmu_tot_area[river],ltau_tot_area[river]) lmu_tot_area[river]<-log(mu_tot_area[river])-0.5*lsd_tot_area[river]
lsd_tot_area[river]<-log(pow(sd_tot_area[river],2)/pow(mu_tot_area[river],2)+1) ltau_tot_area[river]<-1/lsd_tot_area[river]
for(y in 1:years){
#####COMBINED EXPERT PRIOR FOR RIVER INGARSKILANJOKI #####
mu_tot_area[2]<-mu_mu_prior_area[expert]
sd_tot_area[2]<-mu_sd_prior_area[expert]
mu_mu_prior_area[1]<-1220 # Ari Sauna (2015)
mu_mu_prior_area[2]<-1355.994 # Aki Janatuinen (2015)
101
catch[y,a,river]~dpois(mu_catch[y,a,river])
mu_catch[y,a,river]<-w[a,river]*n[y,3,a,river]+0.01
N[y,t,a,river]<-((parr[y,t,a,river]/tot_area[river])*sample_area[y,river]) }
} } }
for(a in 1:A){
mu_w[a,1]<-alpha_w1+beta_w1*age[a] #model1: catchability increases with age (length)
102
mu_w[a,2]<-alpha_w2+beta_w2*age[a] #model2: catchability decreases with age (length) for(river in 1:NA_RIVERS){
logit(w[a,river])<-W[a,river] # logistic regression for catchability at age (age assumed to correlate positively with lenght)
W[a,river]~dnorm(mu_w[a,w.model],100) # Bayesian model avereging for two types of catchability mechanisms
C[y,a,river]~dpois(mu_C[y,a,river]) # Amount of observed smolts in the trap mu_C[y,a,river]<-catchability[y,river]*Smolt[y,1,a,river]+0.01
for(t in 1:time){
smolt[y,t,a,river]<-round(Smolt[y,t,a,river]) }
103 alpha1[river]<-(mu_M[river]*eta.surv)
beta1[river]<-(1-mu_M[river])*eta.surv
alpha[river]<-(mu_catchability[river]*eta.trap.catch) beta[river]<-((1-mu_catchability[river])*eta.trap.catch)
mu_catchability[river]<-trapw[river]/riverw[river] # prior mean catchability is assumed to be the ratio between the river's width and the trap's width
for(y in 1:years){
catchability[y,river]~dbeta(alpha[river],beta[river]) # beta distribution for catchability Re_capture[y,river]~dbin(catchability[y,river],Tsurv[y,river] )
#(catchability[y,river],Tsurv[y,river]) # Higher mortality in tagging experiment with anesthesia and bulky tags, lower mortality in tagging experiment with tattoos and no anesthesia
Tsurv[y,river]<-round(tagged[y,river])
tagged[y,river]<-(Tagged[y,river]*p_tag_surv[river]) # Some proportion of tagged fish is assumed to die as a result of the tagging experiment
} }
##### MODEL TESTING VARIABLES #####
#####ADD NEW VARIABLES WHEN ADDING NEW RIVERS INTO THE DATASET#####
mm.p.value.C_PIRITA<-mean(mean.p.value.C[8:15,1])
mm.p.value.C_INGARSKILA<-mean(mean.p.value.C[12:14,2]) mm.p.value.catch_PIRITA<-mean(mean.p.value.catch[7:15,1])
mm.p.value.catch_INGARSKILA<-mean(mean.p.value.catch[11:15,2])
#### BAYESIAN P-VALUES FOR MODEL FIT #####
for(river in 1:NA_RIVERS){
for(y in 1:years){
mean.p.value.C[y,river]<-mean(p.value.C[y,,river])
mean.p.value.catch[y,river]<-mean(p.value.catch[y,,river]) for(a in 1:A){
p.value.C[y,a,river]<-step(C[y,a,river]-rep.C[y,a,river])
p.value.catch[y,a,river]<-step(catch[y,a,river]-rep.catch[y,a,river]) rep.C[y,a,river]~dpois(mu_rep.C[y,a,river])
104
mu_rep.C[y,a,river]<-(catchability[y,river]*smolt[y,1,a,river]) rep.catch[y,a,river]~dpois(mu_rep.catch[y,a,river])
mu_rep.catch[y,a,river]<-(w[a,river]*n[y,3,a,river]) }
} }
alpha_w1~dnorm(mu_alpha.w1,tau_alpha.w1) beta_w1~dnorm(mu_beta.w1,tau_beta.w1)
alpha_w2~dnorm(mu_alpha.w2,tau_alpha.w2) beta_w2~dnorm(mu_beta.w2,tau_beta.w2) }