A Bayesian two-stage biomass model for stock assessment of data-limited species: An application to cuttlefish (Sepia officinalis) in the English Channel

Abstract

Cuttlefish is a key commercial species in the English Channel fishery in terms of landings and value. Age-based assessment methods are limited by time-consuming age determination with statoliths and the lack of stock assessment models tailored to this data-limited species. A two-stage biomass model is developed in the Bayesian state-space modelling framework that allows inferences to be made on the stock biomass at the start, middle and end of each fishing seasons between 1992 and 2014, while accounting for both process and measurement errors and to assimilate various sources of information. A method that uses ancillary length-frequency data is developed to provide an informative prior distribution for the biomass growth rate parameter g (E = 0.89) and its annual variability (CV = 0.1). The new model is a substantial improvement on the existing stock assessment method used by the International Council for the Exploration of the Seas. Taking into consideration a time-varying g parameter provides a more ecologically meaningful model with regard to the sensitivity of the cuttlefish population dynamics to environmental fluctuations and improves model fit. The model also provides predictions of the unexploited biomass in winter, which is based on survey data, and helps manage the stock in the event of strong depletion.

Introduction

Cephalopods stocks are difficult to assess and require specific models to be developed (Pierce and Guerra, 1994) because of the nature of their life cycle, including short life span and highly variable growth, and because of the difficulty of age determination (Bettencourt and Guerra, 2001, González et al., 2000, Lipinski et al., 1998). The lack of routine stock assessment methods for short-lived species restricts sharing of information and comparing status among stocks, and reinforces the need for a precautionary approach (Rodhouse et al., 2014).

The cuttlefish stock in the English Channel (Fig. 1) is data-limited. This stock is assumed to be a single unit because of high catch-per-unit-effort concentration in International Council for the Exploration of the Seas (ICES) divisions VIId and VIIe (Wang, 2003). It is a shared resource exploited by French and English fishermen (Engelhard et al., 2012). No European regulations apply to this stock despite its importance in terms of landings and value. The French inshore exploitation is managed by local rules such as minimum landing weight and mesh size. In England, no minimum landing size and no restrictions on the fishing season have been established for cuttlefish (Pierce et al., 2010).

The English Channel cuttlefish population is semelparous with a two-year lifespan. Migration outside the Channel is suspected to be very low (Boucaud-Camou and Boismery, 1991). Adults spawn inshore in shallow waters in spring and die. Hatching peaks in summer, and juveniles stay inshore until autumn. Recruitment into the fishery starts in October of the first year, and the annual cohort is fully recruited at the start of the second summer of life, i.e. one year after hatching. Tagging experiments have shown inshore-offshore seasonal migrations: cuttlefish concentrate offshore in the deeper central western part of the Channel during winter, and move inshore in spring for coastal feeding and spawning (Boucaud-Camou and Boismery, 1991). Seasonal migrations are mainly triggered by temperature, although day-length also influences pre-adult sexual maturation (Richard, 1971).

The stock has been assessed using a Thomson and Bell model based on monthly catch-at-age data (Royer et al., 2006), but the method, based on monthly length frequencies, was too data-demanding for a routine stock assessment. Furthermore, conversion of length frequencies into age is highly uncertain because growth and timing of migration might vary substantially according to seasons and years. A much less data demanding two-stage biomass model (Roel and Butterworth, 2000) was proposed for this stock (Gras et al., 2014). The model developed by Gras et al. (2014) represents the biomass of group 1+ individuals only, and assumes two stages among the exploited population: recruitment and full exploitation. Recruited biomass (B₁; evaluated on the first of July) is estimated using abundance indices from the Bottom Trawl survey (BTS) and the Channel Ground Fish Survey (CGFS). Spawning stock biomass (B₂) is then estimated using Landings Per Unit Effort (LPUE) from French and United Kingdom (UK) bottom trawl fisheries. The model is fitted to the time series of catches and abundance indices using a maximum likelihood framework that assumes observation errors only, and uncertainties about estimates are quantified using bootstrapping. The model suffers from several weaknesses. Firstly, it considers observation errors only and hence ignores process errors in the biomass dynamics. It also suffers from a lack of flexibility to change model assumptions and/or to assimilate other sources of available information or data. Secondly, the growth rate parameter g (between 12 and 23 months old cuttlefish) is assumed to be known and constant from year to year even though the growth rate of cephalopods is known to be highly sensitive to environmental fluctuations (Rodhouse et al., 2014). The parameter g includes natural mortality (set to 1.2 year⁻¹) and a mean growth rate in weight (based on historical data from Medhioub (1986) and set to 2.2 yr⁻¹), which are assumed to be constant in time and known without uncertainty. However, Gras et al. (2014) showed a high sensitivity of model outputs to the growth rate parameter, and advocated the use of more recent data that would provide a more accurate estimate of this parameter. Thirdly, the model only captures the dynamics of the 1+ component of the population. The time series of abundance indices from the CGFS survey is assumed to be based mainly on group 1+ individuals, although length frequencies suggest a mixture of 0+ and 1+. Indeed, the CGFS survey occurs in October, when cuttlefish migrate offshore. Some of the group 0 individuals are 3 months old at this time of the year and form the lower part of the survey length frequencies. Therefore, using the CGFS time series without processing the data to separate out the two cohorts might provide a biased estimate of group 1+ cuttlefish biomass.

In this work, we have perfected the two-stage biomass model adapted for cuttlefish, based on three substantive new contributions:

• The model is developed in a Bayesian state-space framework (Rivot et al., 2004, Buckland et al., 2007, Parent and Rivot, 2013), thus allowing for a comprehensive integration of the different sources of uncertainty by considering both process errors in the biomass dynamics and observation error in the data.

• We develop an informative prior (Hilborn and Liermann, 1998) on the biomass growth rate that takes advantage of various sources of available data to quantify the average growth rate and provide a credible range of variability over the years.

• We improve the quality of the data and the demographic realism of the model by explicitly considering that two separate age classes (0+ and 1 + ) can compose the abundance indices and the exploited biomass.

We first build a model considering the dynamics of 1+ only and a time-varying g parameter. We then evaluate the benefit of a time-varying g parameter instead and evaluate the sensitivity of the results to the amount of data used and the predictive capacity of the model. Finally, we explore the feasibility of considering the dynamics of the two cohorts (0+ and 1+) in the same model.