Table of Contents

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The aim of Approach 2 is to analyse impacts of different sources of uncertainty on the choice of alternative management approaches, in particular to identify those combinations of assessment and management actions that are robust to uncertainty.

Four different analyses that deal with Approach 2 have been undertaken, on of then during project months 1-18, and three during months 19-36. Levontin et al. (2004) and levontin et al. (2005) evaluated the impact of assuming semelparity when modelling an iteroparous species such as Atlantic salmon. In addition, two analyses, evaluating structural uncertainty at different stages of the assessment of the salmon stocks (Mäntyniemi et al. and Mäntyniemi, submitted), have been carried out.

*Levontin, P., McAllister, M. and Michielsens, C. (2004).* Evaluating the implications of assuming semelparity when modelling population dynamics of Atlantic salmon (Salmo salar L.). Imperial College, London. Research document.

**Abstract:** Population dynamics models for some iteroparous species, such as Atlantic salmon (Salmo salar L.), often assume for simplicity that all fish die after they spawn, i.e. semelparity. In this paper, we evaluate the magnitude and the direction of biases that are likely to be introduced by a semelparity assumption in assessments of iteroparous stocks. We do this by exploring alternative specifications of a population dynamics model specified for Baltic salmon that accounts for iteroparity. We found, in this model that the semelparity assumption can markedly affect estimates of fisheries management reference points, such as the maximum sustainable yield (MSY) and the fishing mortality rates at MSY. We found that iteroparity rates can strongly affect the values of the state of equilibrium of stock biomass, assumptions about productivity of the stock, and most significantly the parameters of the stock-recruit relationship.

*Levontin, P., McAllister, M. and Michielsens, C. (2005).* Evaluation of semelparity bias in parameter estimates for Baltic salmon (Salmo salar L.). Imperial College, London. Research document.

**Abstract:** In this paper, we explore how the estimates of the population dynamics model parameters can depend on semelparity/iteroparity assumption. For Baltic salmon, population model parameters are estimated using a state-space model fitted to mark-recapture (tagging) and effort data assuming semelparity. In case 40% of salmon however survive spawning, the current assessment underestimates the homing rates and catchability of the offshore fisheries, while coastal and river catchabilities are overestimated. Because some of the catchabilities are overestimated and others are underestimated the biases in the estimates of total exploitation rate are expected to be small. Using biased parameter estimates in the model that calculate fisheries manager's reference points leads to smaller biases on average.

*Mäntyniemi, S. Romakkaniemi, A. and Arjas,E.* Bayesian estimation of the number of individuals in a sample with a known weight. (Submitted).

**Abstract:** We introduce a Bayesian probability model for making inferences about the unknown number of individuals in a sample, based on known sample weight and on information provided by subsamples with known weights and corresponding counts. Inherent in the Bayesian approach, the model allows for an incorporation of prior information that is often available about the sample size and other uncertain parameter values. This approach can be applied to a wide range of similar problems. Here our main focus is stock assessment, where the task is the conversion of catch weight into the number of individuals in the catch. The model is easy to use due to availability of general purpose MCMC simulation software, and it can be used either in a stand alone fashion or embedded into more complex probability models.

*Mäntyniemi, S.* Bayesian population dynamics modelling: model specification, model checking and posterior computation. (Submitted).

**Abstract:** This paper illustrates certain theoretical and practical aspects of Bayesian population dynamics modelling in the context of juvenile salmon population. It is emphasised that when working under the Bayesian paradigm of statistical inference prior knowledge should be utilised in all levels of the model specification including the specification of the dynamic equations. This is in contrast to other recent papers which carry the message that subjective beliefs are incorporated only at the level of hyperparameters. To facilitate practical use of Bayesian state-space models, this paper demonstrates and proposes various ways to improve the computational efficiency and to assess model fit.

Levontin, P., McAllister, M. and Michielsens, C. (2004). Evaluating the implications of assuming semelparity when modelling population dynamics of Atlantic salmon (Salmo salar L.). Imperial College, London. Research document.

Levontin, P., McAllister, M. and Michielsens, C. (2005). Evaluation of semelparity bias in parameter estimates for Baltic salmon (Salmo salar L.). Imperial College, London. Research document.

Mäntyniemi, S. Romakkaniemi, A. and Arjas, Bayesian estimation of the number of individuals in a sample with a known weight. (Submitted).

Mäntyniemi, S. Bayesian population dynamics modelling: model specification, model checking and posterior computation(Submitted).

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