Corresponding author: Abdul Rashid Jamnia (
Academic editor: M. Pinna
Smallscale fisheries substantially contribute to the reduction of poverty, local economies and food safety in many countries. However, limited and lowquality catches and effort data for smallscale fisheries complicate the stock assessment and management. Bayesian modelling has been advocated when assessing fisheries with limited data. Specifically, Bayesian models can incorporate information of the multiple sources, improve precision in the stock assessments and provide specific levels of uncertainty for estimating the relevant parameters. In this study, therefore, the statespace Bayesian generalised surplus production models will be used in order to estimate the stock status of fourteen Demersal fish species targeted by smallscale fisheries in Sistan and Baluchestan, Iran. The model was estimated using Markov chain Monte Carlo (
Jamnia AR, Keikha AA, Ahmadpour M, Cissé AA, Rokouei M (2018) Applying bayesian population assessment models to artisanal, multispecies fisheries in the Northern Mokran Sea, Iran. Nature Conservation 28: 61–89.
Human dependency on maritime and coastal resources is increasing (
Increased overexploitation of fishery and habitat destruction threaten the coastal and maritime resources. Smallscale fisheries often have limited and lowquality catch and effort data that complicates stock assessment and management. Globally, for example, only 10% to 50% of fish stocks in more developed countries and 5% to 20% of fish stocks in lessdeveloped countries have been scientifically assessed due to limited data (
Based on the various works (
Mostly, due to insufficient information about the time series of biological and management reference points of fish stocks, the scientific precise stock assessments have not been undertaken for the majority of fish species in Iran, especially in the southern coastal areas (the current study area). Therefore, due to the lack of information toward fisheries management reference points, most fisheries planning has not had any special effects on the sustainability of fish stocks reserves.
So far, there has been a lot of scientific motivation for assessing fish stocks in Iran, but it has not been implemented for two reasons; one the lack of sufficient information used in scientific stock assessment methods and second the complexity and timeconsuming of stock assessment methods in the limiteddata situations.
Bayesian modelling has been advocated to assess fisheries with limited data. Specifically, Bayesian models can incorporate information of the multiple sources such as academic literature, empirical research, biological theory and specialist judgement. This characteristic of the Bayesian models improves precision in the stock assessments and provides the specific levels of uncertainty for estimating the parameters (
Therefore, in the current study, because of the limited data, the statespace Bayesian generalised surplus production models used to estimate the stocks status of the fourteen demersal fish species targeted by smallscale fisheries in Sistan and Baluchestan (A coastal province southeast of Iran). This could provide scientific knowledge for the fisheries management and contribute to the researchers applying and improving the results of the current study in order to achieve the global environmental sustainability and marine ecology.
Hence, in the current study, based on the abovementioned stock assessment Bayesian approach, the management reference points provided for the fourteen fish species, including biomass, harvest rate and stock status, the implication of these for the sustainable management of the smallscale fisheries was discussed. Moreover, the estimates of biological parameters were compared to the previous findings of the fourteen species.
The fisheries examined in this study are located in the Sistan and Baluchestan Province (
Study area and the locations of fishing landing ports related to small scale fishing vessels.
Based on the local reportage of
Nine years (21 March 2006 to 18 March 2015) of fisheriesdependent commercial landings and effort data for the fourteen demersal fish species listed earlier were acquired from Iran’s National Fishery Data Collection and Reporting System Unit and also reports from the Provincial Fisheries Department. In addition, the used time series of catch and standardised CPUE values as relative abundance indices are considerable as the supplementary data. The nominal CPUE indices that derived from commercial fisheries’ logbooks are affected by some variables such as spatiotemporal and environmental factors. The considered standardised CPUE indices are reliable abundance indices which allow the implementation of the conservation and management measures and have been obtained by the most common and competent statistical approach in the domain of fisheries’ researches, such as generalised additive models (
Biomass dynamic models are popularly used for stock assessment when only catch and effort time series data are accessible (
The biomass dynamics model of the equation discrete time form is as follows (
In Equation 1,
Bayesian statespace models consist of three levels (
(I) a process equation which depicts the time dynamics of a stochastic process as a function of timeinvariant hyperparameters. (II) an observation equation based on populationspecific inspection data that are a function of the unobserved state process (
With regards to the Equation 1, the process equation describes the surplus production function in a generalised surplus production model (
where
Replacing Equation 2 in Equation 1 and multiplying the right hand side of the resultant equation with
Where
Equation 3 was reparameterised using relative biomass (
According to regular assumptions, CPUE values are relative abundance indices proportional to the biomass. The observation equation relates the unobserved states
where
An advantage of the Bayesian models is its ability to use the prior distributions based upon the existing knowledge to set plausible values for model parameters (
The reason for choosing the priors was based on the following rationale. First, based on the expert consultations of
Summary of the Prior distribution functions used for some parameters of all bayesian statespace







r ~ lognormal(1.1139,4.4814)  K ~ uniform(604,30200)  pi ~ uniform(0.01,0.135)pm = log(pi)P[1] ~ lognormal(pm, 1/σ^{2}) 

r ~ lognormal(0.2326,4.4814)  K ~ uniform(1089,54450)  pi ~ uniform(0.0132,0.125)pm = log(pi)P[1] ~ lognormal(pm, 1/σ^{2}) 

r ~ lognormal(1.4741,4.4814))  K ~ uniform(1180,59000)  pi ~ uniform(0.019,0.116)pm = log(pi)P[1] ~ lognormal(pm, 1/σ^{2}) 

r ~ lognormal(1.2447,4.4814)  K ~ uniform(704,35200)  pi ~ uniform(0.012,0.14)pm = log(pi)P[1] ~ lognormal(pm, 1/σ^{2}) 

r ~ lognormal(1.9888,4.4814)  K ~ uniform(4187,209350)  pi ~ uniform(0.01,0.135)pm = log(pi)P[1] ~ lognormal(pm, 1/σ^{2}) 

r ~ lognormal(0.5547,4.4814)  K ~ uniform(569,28450)  pi ~ uniform(0.014,0.132)pm = log(pi)P[1] ~ lognormal(pm, 1/σ^{2}) 

r ~ lognormal(1.8574,4.4814)  K ~ uniform(6456,322800)  pi~uniform(0.01,0.121)pm=log(pi)P[1]~lognormal(pm, 1/σ^{2}) 

r ~ lognormal(2.0425,4.4814)  K ~ uniform(1076,53800)  pi ~ uniform(0.0126,0.113)pm = log(pi)P[1] ~ lognormal(pm, 1/σ^{2}) 

r ~ lognormal(0.0615,4.4814)  K ~ uniform(2992,149600)  pi ~ uniform(0.01,0.114)pm = log(pi)P[1] ~ lognormal(pm, 1/σ^{2}) 

r ~ lognormal(1.0531,4.4814)  K ~ uniform(4429,221450)  pi ~ uniform(0.0171,0.1587)pm = log(pi)P[1] ~ lognormal(pm, 1/σ^{2}) 

r ~ lognormal(0.9886,4.4814)  K ~ uniform(2170,108500)  pi ~ uniform(0.0154,0.1286)pm = log(pi)P[1] ~ lognormal(pm, 1/σ^{2}) 

r ~ lognormal(1.5099,4.4814)  K ~ uniform(11001,55005)  pi ~ uniform(0.0194,0.105)pm = log(pi)P[1] ~ lognormal(pm, 1/σ^{2}) 

r ~ lognormal(1.0634,4.4814)  K ~ uniform(1746,87300)  pi ~ uniform(0.0164,0.1613)pm = log(pi)P[1] ~ lognormal(pm, 1/σ^{2}) 

r ~ lognormal(1.7514,4.4814)  K ~ uniform(712,35600)  pi ~ uniform(0.0163,0.12)pm = log(pi)P[1] ~ lognormal(pm, 1/σ^{2}) 
Based on
The major fisheries reference points for the
The stock biomass at which the maximum sustainable yield (
whilst,
The related value of
Finally, the relative fishing mortality rate
The Bayesian statespace combines the joint prior distributions of all parameters and unobservable conditions with the likelihood functions of the observations (
with square brackets indicating densities and N referring to the number of samples. Supplementary information on the abovementioned general factorisation of Bayesian model (Eq. 9) is available in
The Markov chain Monte Carlo (
In line with the aims of the current research, the results of Bayesian statespace
Phase diagram depiction of F/F_{MSY} and B/B_{MSY} for fourteen specified highcommercial demersal fish species, each panel is designate by the common name of the fish at the top. The numbers on purple circles represent the last two digits of the year related to abovementioned ratios.
Simulated biomass time series (solid line with squares) of fourteen specified highcommercial demersal fish species, with 95 % confidence intervals (grey dashed and dotted lines with triangle).
Table
Convergence and stationarity diagnostics of
Species  Geweke’s Zscore  GelmanRubin  HeidelbergerWelch’s pvalue  

Chain 1  Chain 2  Chain 3  Potential scale reduction factor (Ȓ)  Chain 1  Chain 2  Chain 3  
Min  Max  Mean  Min  Max  Mean  Min  Max  Mean  Chain 1  Chain 2  Chain 3  Min  Max  Mean  Min  Max  Mean  Min  Max  Mean  

1.73  1.48  0.228  1.86  1.62  0.065  1.72  1.452  0.135  1  1  1  0.006  0.9  0.383  0.05  0.9  0.546  0.027  0.97  0.4 

1.7  1.36  0.245  1.64  1.08  0.09  1.66  1.61  0.174  1  1  1  0.014  0.9  0.496  0.054  0.96  0.568  0.053  0.98  0.4 

1.36  1.13  0.227  1.14  1.48  0.129  1.7  1.36  0.22  1  1  1  0.004  0.95  0.447  0.058  0.91  0.513  0.052  0.99  0.68 

1.33  1.261  0.06  1.6  1.612  0.05  1.02  1.51  0.407  1  1  1  0.03  0.99  0.67  0.05  0.99  0.486  7E6  0.99  0.71 

1.79  1.365  0.068  1.55  1.52  0.252  1.77  1.4  0.264  1  1  1  0.007  0.99  0.619  0.007  0.99  0.568  0.07  0.98  0.477 

1.83  1.9  0.195  1.01  1.03  0.188  1.47  1.43  0.345  1  1  1  0.01  0.98  0.649  0.05  0.99  0.512  0.056  0.99  0.677 

1.06  1.98  0.181  1.47  1.37  0.11  1.45  1.84  0.02  1  1  1  0.05  0.98  0.391  0.05  0.98  0.44  0.01  0.99  0.412 

1.25  1.56  0.11  1.15  1.9  0.11  1.35  1.61  0.232  1  1  1  0.05  0.99  0.39  0.06  0.99  0.44  0.006  0.99  0.61 

1.11  1.91  0.018  1.63  1.3  0.251  1.88  1.06  0.268  1  1  1  0.01  0.99  0.7  0.07  0.95  0.49  0.002  0.99  0.62 

1.27  1.03  0.226  1.1  1.35  0.33  1.14  1.8  0.02  1  1  1  0.007  0.98  0.623  0.05  0.99  0.476  0.008  0.99  0.592 

1.18  1.11  0.035  1.18  1.78  0.007  1.08  1.24  0.176  1  1  1  0.05  0.99  0.49  0.07  0.97  0.34  0.06  0.98  0.57 

1.19  1.14  0.19  1.13  1.69  0.126  1.04  1.53  0.204  1  1  1  0.05  0.9  0.5  0.007  0.99  0.297  0.05  0.95  0.48 

1.25  1.51  0.13  1.23  1.21  0.12  1.04  1.07  0.048  1  1  1  0.05  0.9  0.5  0.05  0.9  0.5  0.02  0.98  0.61 

1.89  1.62  0.024  1.2  1.72  0.242  1.55  1.25  0.093  1  1  1  0.05  0.98  0.36  0.05  0.99  0.417  0.017  0.96  0.5 
In the first place, the Geweke diagnostic test was separately applied to verify convergence of the mean of each parameter obtained from the sampled values related to each single chain. In the following, the derived Zscore indicates convergence if its values be less than 2 at absolute value. Thus, as shown in Table
Summary of the posterior descriptive statistics is presented in Table
A summary of the posterior descriptive statistics for bayesian statespace
Parameter  Species  
















r  Mean  0.329  0.727  0.248  0.298  0.152  0.612  0.34  0.145  1.173  0.474  0.411  0.247  0.378  0.175 
S.D.  0.141  0.286  0.113  0.134  0.074  0.279  0.161  0.073  0.567  0.328  0.201  0.124  0.175  0.079  
MC error  0.001  0.004  0.001  0.001  9.8E4  0.002  0.001  8.3E4  0.004  0.009  0.002  0.001  0.002  7.6E4  
Perc. 2.5%  0.126  0.295  0.09  0.111  0.054  0.223  0.124  0.051  0.42  0.142  0.146  0.087  0.136  0.066  
Median  0.304  0.688  0.223  0.273  0.137  0.558  0.306  0.13  1.057  0.377  0.369  0.221  0.343  0.16  
Perc. 97.5%  0.668  1.393  0.529  0.627  0.336  1.295  0.748  0.332  2.598  1.314  0.92  0.561  0.806  0.367  
K  Mean  1058  1530  1995  1110  5175  1409  12080  1609  4015  6641  2580  11630  2146  1121 
S.D.  365.6  370  623.6  353  908.7  553.5  5477  445.7  902.6  1876  390.6  616.1  365.3  336  
MC error  2.726  3.717  6.953  2.64  18.11  5.416  51.99  4.183  6.027  28.51  4.339  6.865  4.086  2.851  
Perc. 2.5%  621.5  1104  1214  718.1  4215  634.5  6602  1095  3022  4504  2182  11020  1758  727.4  
Median  975.7  1438  1865  1017  4918  1318  10450  1498  3771  6149  2466  11450  2042  1041  
Perc. 97.5%  1975  2463  3526  2018  7565  2736  26630  2734  6334  11510  3607  13270  3109  1971  
q  Mean  0.001  0.001  0.001  0.001  0.001  0.001  5.5E4  0.001  0.001  0.001  9.5E4  4.3E4  0.001  0.001 
S.D.  5E4  3E4  4.4E4  4.2E4  1.5E4  7.2E4  1.9E4  3.4E4  2.5E4  3.2E4  1.3E4  3.2E5  1.6E4  4E4  
MC error  4E6  3E6  4.5E6  3E6  3E6  6.5E6  1.7E6  3E6  1.6E6  4.9E6  1.5E6  5E7  1.8E6  3.2E6  
Perc. 2.5%  8E4  8.8E4  8.4E4  8.3E4  6.9E4  8.5E4  2E4  8E4  7.7E4  6.8E4  6.6E4  3.6E4  6.9E4  8.4E4  
Median  0.001  0.001  0.001  0.001  0.001  0.001  5.5E4  0.001  0.001  0.001  9.5E4  4.3E4  0.001  0.001  
Perc. 97.5%  0.002  0.002  0.002  0.002  0.001  0.003  9.2E4  0.002  0.001  0.001  0.001  4.9E4  0.001  0.002  
z  Mean  0.953  0.89  0.995  0.96  0.993  0.987  0.983  1.001  0.996  1.047  1.006  0.982  0.993  0.965 
S.D.  0.708  0.661  0.709  0.688  0.695  0.712  0.698  0.704  0.699  0.72  0.73  0.691  0.701  0.711  
MC error  0.006  0.008  0.008  0.005  0.012  0.006  0.005  0.005  0.005  0.01  0.011  0.012  0.007  0.005  
Perc. 2.5%  0.112  0.108  0.119  0.117  0.122  0.118  0.121  0.12  0.118  0.131  0.118  0.12  0.117  0.109  
Median  0.779  0.723  0.829  0.795  0.84  0.821  0.82  0.842  0.838  0.89  0.836  0.824  0.832  0.792  
Perc. 97.5%  2.736  2.604  2.808  2.707  2.728  2.776  2.766  2.774  2.752  2.869  2.824  2.726  2.765  2.803  
σ^{2}  Mean  0.007  0.007  0.008  0.007  0.007  0.007  2.5E4  0.007  0.007  0.008  0.008  0.008  0.008  0.007 
S.D.  0.002  0.002  0.002  0.002  0.002  0.002  1.4E4  0.002  0.002  0.003  0.002  0.003  0.003  0.002  
MC error  1.2E5  1.5E5  1.6E5  1E5  1.3E5  1.4E5  8.7E7  1.6E5  1.4E5  2.3E5  1.5E5  1.8E5  1.8E5  1.2E5  
Perc. 2.5%  0.004  0.004  0.004  0.004  0.004  0.004  9.8E5  0.004  0.004  0.004  0.004  0.004  0.004  0.004  
Median  0.006  0.007  0.008  0.006  0.007  0.007  2E5  0.007  0.007  0.008  0.007  0.008  0.007  0.007  
Perc. 97.5%  0.012  0.014  0.015  0.012  0.012  0.139  6.3E4  0.014  0.013  0.017  0.014  0.016  0.015  0.012  
τ^{2}  Mean  0.358  0.071  0.021  0.459  0.012  0.079  0.121  0.068  0.082  0.027  0.056  0.028  0.046  0.145 
S.D.  0.105  0.023  0.007  0.134  0.004  0.025  0.045  0.022  0.026  0.01  0.019  0.011  0.016  0.044  
MC error  6E4  1.3E4  4.8E5  8E4  2.5E5  1.3E4  3.2E4  1.3E4  1.4E4  1E4  1E4  7.6E5  9.9E5  2.4E4  
Perc. 2.5%  0.206  0.037  0.009  0.266  0.006  0.042  0.06  0.035  0.044  0.01  0.028  0.012  0.022  0.08  
Median  0.341  0.068  0.02  0.437  0.012  0.075  0.112  0.064  0.078  0.026  0.053  0.026  0.044  0.138  
Perc. 97.5%  0.613  0.127  0.04  0.785  0.023  0.139  0.236  0.122  0.146  0.053  0.102  0.055  0.085  0.252 
Since the intrinsic growth rate
According to the results in Table
A summary of model selection information between Generalised Surplus Production Model (
Species  Models  




Total 
Total 


1.52  3.07 

10.48  12.38 

22.33  25.59 

2.352  3.87 

20.73  25.47 

7.267  9.49 

6.68  8.38 

11.24  13.14 

7.14  8.96 

2.65  6.16 

11.82  13.92 

8.68  10.98 

15.97  18.52 

8.02  9.68 
The results of Table
The marginal posterior means of the catchability coefficient (q) for
The marginal posterior means of the process noise variances, (σ^{2}) for
The marginal posterior means of the observation noise variances, (τ^{2}) for
A summary of the results of fisheries management reference points derived from Bayesian statespace
The Kobe plot characterises, relative biomass (
According to Figure
Simulated biomass time series of the fourteen specified highcommercial demersal fish species with 95% conﬁdence intervals are considerable as shown in Figure
According to the abovedescribed results of the Kobe diagrams, in which all stocks are in critical condition and are threatened with extinction, the trend plots of simulated biomass confirm the previous results, due to the Biomass not having a good increasing trend. As the charts in Figure
In summary, the Bayesian statespace
As mentioned in the introduction, the scientific precise stock assessments have not been undertaken in Iran, especially on the southern coastal areas (such as the current study area) because of insufficient and limited information. Accordingly, it is one of the important reasons for the inefficiency of the available fishery management and conservation strategies for sustaining the studied fish species population status in the current study area. This reason is due to lack of applicable information for fisheries management and conservation planning (such as fisheries management reference points, biomass, harvest rate and stock status) that can be obtained from scientific precise stock assessments. Thus, in the shortterm, the transferring of the obtained stock assessment outcomes of the current study to fisheries managers, planners and all other activists (such as fishermen) can improve the available fisheries strategies and harvesting treatments to rebuild and improve the current bad situation of studied fish species population status. Additionally, in the long run, the recommended use of the obtained stock assessment outcomes (e.g. management and biological reference points, biomass, harvest rate, stock status) for future research in line with appropriate ecosystembased fishery management will determine the best strategies for preventing overfishing, improving, sustaining and conserving the aboveoverfished stocks. Hence, the obtained stock assessment outcomes in a viability theory framework to investigate various fishing scenarios for the implementation of the sustainable fishery management in the smallscale fishery sector of the current study area were used providing the details of the recommended viability theory modelling as an appropriate ecosystembased fishery management approach in our further works.
The authors are grateful to Dr. Peter Sheldon Rankin from The University of Queensland, Australia, for his useful and constructive comments on estimating the abovementioned models. The authors thank the National Fishery Data Collection Unit of Iran Fisheries Organization, particularly Mr. Sabah Khorshidi Nergi, the head of National Fishery Data Collection Unit for providing the fishery data. The authors also acknowledge the Provincial Fisheries Department of Sistan and Baluchestan in Chabahar for providing complementary and description information about artisanal fishing vessels operating in the multispecies fishery of the study area and Offshore Fisheries Research Centre of Chabahar for its contribution in specifying fish species. Finally, the authors express their thanks to the anonymous reviewers for their comments that improved our manuscript.
Procedure of prior distributions functions used for parameters of all Bayesian statespace
Lognormal distribution procedure for intrinsic growth rate (r)
Standard Deviation = x
Average of Intrinsic Growth Rate (r) = y
Precision of Prior = 1/log(1 + x^2)
Average of Prior = log(y) – (0.5/ Precision of Prior)
r ~ dlnorm (Average of prior, Precision of prior)
Inverse Gamma Distribution Procedure for the Process and Observation Noise Variances
Shape Parameter = x
Scale Parameter=y
Gamma ~ dgamma (x, y)
InverseGamma = 1/Gamma
LogNormal Distribution Procedure for Initial Relative Biomass P[1]
B0=the Biomass in First Time
Kmin=minimum carrying capacity is considered equal to minimum Historical catches.
Kmax= maximum carrying capacity is considered equal to ten times the minimum Historical catches.
Pi ~ dunif(B0/Kmax, B0/Kmin)
isigma= Inverse Gamma Distribution for process noise variances
Pm[1] < log(Pi)
P[1] ~ dlnorm(Pm[1], isigma)
Trace plots for Bayesian statespace
Trace plots for Bayesian statespace
Trace plots for Bayesian statespace
Trace plots for Bayesian statespace
Trace plots for Bayesian statespace
Trace plots for Bayesian statespace
Trace plots for Bayesian statespace
Trace plots for Bayesian statespace
Trace plots for Bayesian statespace
Trace plots for Bayesian statespace
Trace plots for Bayesian statespace
Trace plots for Bayesian statespace
Trace plots for Bayesian statespace
Trace plots for Bayesian statespace
Trace plots for Bayesian statespace