In Chapter 1, I defined the research problem and methods to be used for com- pleting this project where I introduced the Deriso and Schnute model to lay down the foundation for modelling the growth of fish populations.
In Chapter 2, I reviewed basic probability theory, frequentist and Bayesian paradigms, dynamic Bayesian networks, non-parametric models and time series modelling for handling uncertainties in fish populations.
In Chapter 3, I developed and implemented methods for identifying the non- constant variance (heteroscedasticity) in the spawner-recruit relationship. I found
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heteroscedastic models tend to fit the S-R model inputs better than constant vari- ance models across the majority of stocks, and strong evidence for a negative co- efficient of heteroscedasticity in seven cases (Table A.1), including exploited cod,
herring and whiting stocks in addition to olive flounder and Peruvian anchoveta.
I advocate that the non-constant variance parameter in these cases deserves to be taken into account by managers. In contrast, only one stock was identified as having a positive coefficient of heteroscedasticity at the 95% confidence levels. To determine whether I can reliably estimate the sign of η1, I tested whether the
confidence interval lies in a region showing a consistent sign with the coefficient where I found that both frequentist and Bayesian methods led approximately to equivalent inference.
To reliably identify a negative coefficient of heteroscedasticity, managers or fish- eries scientists using the frequentist methods should check that their chosen con- fidence interval lies in the negative region; those using the Bayesian framework can consider the proposed priors (i.e. π1 or π2) as a non-informative benchmark
prior and check whether their Bayesian credible interval lies in the negative re- gion. I note that Bayesian approaches may be particularly useful where priors can be specified based on information about similar stocks in other locations. To protect this work against false positives or negatives, I recommend fisheries scientists to use both frequentist and Bayesian methods when assessing stocks for heteroscedasticity; if both methods agree then there would be strong support for our conclusion being correct; otherwise they should investigate the limitation of each method separately.
In Chapter 4, I extended the analysis of Chapter 3 by applying a Bayesian hier- archical model for assessing the sign of the coefficient of heteroscedasticity η1. I
found that the Bayesian hierarchical model applied to fish stocks living in a com- munity has reduced the uncertainty in parameter estimates of the S-R relationship compared to the case where the analysis is based on a single stock assessment. I proposed four different S-R relationships based on the Deriso-Schnute (Deriso, 1980; Schnute, 1985) model. These models (M1, M2, M3 and M4) are assessed
on five different geographical areas: Celtic sea, Faroe Plateau, Georges Bank, North-East Arctic and North sea; and three other macro scale marine column zones: pelagic, demersal and all populations. The macro scale marine analysis is aimed to assess the influence of grouping fish species, across different water depths, on the prediction accuracy of fish populations.
Results showed that the coefficient of heteroscedasticity deserves consideration in Faroe Plateau, North-East Arctic, pelagic and demersal communities because it had a better predictive accuracy on the test set; in contrast to the constant variance model (η1 = 0) that is found to have some significance for the Celtic
Sea, the North Sea and all populations as it provided a higher prediction accu- racy. The reliability of the sign of η1 is found to be approximately consistent in
two regions: Faroe Plateau and North-East Arctic with an approximate credible interval of 95% and 70% respectively.
Because the Deriso-Schnute model presents a singularity at γ = 0, I partitioned the search space into three disconnected zones (γ < 0, γ ≈ 0, γ > 0) so as to over- come this limitation. The models are analysed along with different constraints on γ; whereas the assessment on the test set helped us to identify the model with best prediction values. The modelM1 (with γ > 0 and γ≈ 0) is found to provide
the best recruitment prediction for the Faroe Plateau, North-East Arctic, pelagic and demersal water columns; M2 (with γ < 0) provided best accuracy for the
Georges Bank; M3 (with γ < 0) found to provide the best prediction for the
Celtic sea; and the model M4 (with γ > 0) found to provide the best prediction
for the North sea and all populations. I checked whether the prediction accuracy of fish recruitment is affected by pooling multiple populations across the water column zones; my results showed that estimating fish recruitment by restricting the analysis to species within their own community (i.e. pelagic or demersal) has a higher accuracy than pooling all fish populations together.
In this work, I provide to fishery managers (or policy makers) a new way of assess- ing the size of fish recruitment: I advocate the importance of collecting as many fish stock assessments within the same community as they can, then apply them to the four (or other) possible models so as to check the one that has the lowest RMSE value in recruitment prediction. A more compelling reason to conduct stock assessment selection based on water column is because I found an increase in accuracy compared to the case of pooling pelagic and demersal populations together.
On the ecosystem level I conclude that the sea surface is to some extent dis- connected from the sea bed in the sense that the water column mixing does not affect enormously nutrient supplies of these two habitats: I found that fish stock assessments are best analysed on their own community.
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In Chapter 5, I aimed to provide a statistical model capable of analysing ma- rine ecosystem response to environmental perturbations. The model consisted of analysing marine ecosystem data from several sources, with different temporal resolutions, bounded by the Northwest Coast of Scotland and Northern Ireland (Division VIa). This geographical area can have temperate oceanic plankton taxa as well as colder water plankton as the shelf-edge current can bring warmer water species around the top of Scotland and into the North Sea.
I collected 13 different random variables for both biotic and abiotic factors and five additional ICES fish populations from which I derived two data sets: the first is based on a listwise deletion for the fish populations, and the second is based on analysing the biotic and abiotic variables only. Since there is no general theory on how to combine processes and organisms that operate on different time and space scales together into a model, especially when one goes up the trophic levels, I applied a set of first order autoregressive models from which I built a revised ecological model (REMO) that outperformed the other models. I used REMO to simulate future responses with a set of different enquiries (E1-to-E8) to understand the impact of weather change on the marine ecosystem; the model showed serious risk values for fish larvae, fish eggs, krill and dinoflagellates when the sea surface temperature increases by 2◦C.
The analysis shows that the number of fish eggs appear to be increasing under the effect of temperatures, I explain this behaviour as the fecundity of female fish increases with water temperatures; the abundance of diatoms and large copepods are found to increase under warmer water temperatures; but the abundance of copepods are found to decrease with temperature. This is consistent with the the- ory that Calanus finmarchicus and Calanus helgolandicus copepods would occupy a niche (and grow) in cold and warm water temperatures respectively (Bonnet et al., 2008); these two species can co-occur in the same geographical region such that the former species becomes more abundant in cooler temperatures earlier in the year and the latter species becomes more abundant in warmer tempera- tures later in the year. The results showed that an increase of 20% in wind speed could destabilise the ecosystem by reducing the number of diatoms and copepods. However, the most serious risk remains that of the sea surface temperature where an increase by 2◦C could jeopardize the fish larvae in the short run; and hence deplete the fish stock size in the long run.