Table of Contents

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This page introduces the proposed operating model to be used for the assessment trials and full-feedback management simulations for the Nephrops case study. The model is based in FLR, with a sex-disaggregated, seasonal structure, along with varied stock-recruit possibilities. The underlying model itself is age-based, but tools are also included in the package to convert age-based population indices to length-based ones, for a given growth and error model.

Follow the link here to the code for the biological OM: nephOM.

The key parameters of the operating model are those of the selectivity ogive (which characterises exploitation rate-at-age), the stock-recruit parameters and the equilibrium exploitation pattern if required. We use the results of the ICES Workshop on Nephrops Selection (WKNEPHSEL, ICES, 2007b), and the stock numbers and fishing mortality estimates from an XSA assessment to condition the model (ICES, 2003a). In this case we are using the South Minch stock estimates.

Selectivity is a complex issue with respect to Nephrops, as there is differential selectivity-at-age (given differential growth curves) and issues of availability of females post-sexual maturation, as they largely remain in their burrows while incubating eggs. To deal with this we used a single estimate of the l50 for a logistic selection pattern from ICES WKNEPHSEL, which was then filtered through the inverse growth curves for both males and females, but with a cap (maximum selectivity) applied to the female selection pattern to account for the issues of availability to the fishery after sexual maturation. For the stock-recruit parameters, since there is no established stock-recruit relationship for this stock, a simple geometric mean total recruitment (males and females) is employed, assuming a 50-50 split between males and females. The log-residuals around this geometric mean recruitment are used to parameterise the recruitment deviations.

The equilibrium harvest rate was set by looking at the harvest rates in the first year (1981) of the WG estimates, and we assumed that the estimated selectivity pattern was that applied in the past.

The growth of Nephrops appears both sexually and stage dependent (Bell et al., 2007) with differing growth parameters for males and females and pre and post sexual maturation for the females – their growth rate slows down rapidly after the onset of sexual maturity. Also, the scale of lengths observed is very fine (catch data are typically detailed in 2mm bins) but they can grow to be 14 years old. These factors require some more intricate ideas (than previously implemented in FLR), than a simple filtration of the ages through the growth curve to be used when converting from age to length, via the growth function(s).

Given some growth relationship , where a is the age and the θ are the parameters of the growth model, then for a given age we have a single estimate of the animal’s length: l. However, for our case the key population variables (stock and catch numbers) are required at a very fine length scale and so the lengths associated with ages 1 through to 14 (as in our case) would miss a great many length bins at such a fine scale, as from one year to the next they would (especially at younger ages) grow through a number of length bins. A solution to this problem is not to consider an animal with age a, but to consider an animal whose age would in fact be in the interval a-0.5 to a+0.5. This gives us a corresponding interval of lengths that the animal could belong to. Individuals of a particular age are then assigned randomly to all length bins within the calculated interval.

Ageing error and process error with respect to length variability is applied via a simple log-normal error applied to the length as calculated via the growth curves. The associated CVs are different for the sexes, being much higher for the females than the males and this is accounted for in the conversion process.

Follow the link here to the code for the age to length conversion: nepha2l.

The key abundance index for Nephrops is the TV survey, which uses a swept area estimate of the number of Nephrops burrows, along with some assumptions about occupancy (across burrows, sexes and length classes). In order to obtain an estimate of total Nephrops biomass estimate for use in the assessment, numbers are multiplied by a mean individual weight.

To construct and condition the observation error model for this index we need to construct two main features:

1. The probability model for the observation error in the index. Assumed to be lognormal with no auto-correlation and CV derived from the actual annual confidence intervals of the survey estimates.

2. The potential ‘catchability’ structure (relative/absolute, and across years and length classes) for the index – in effect the potential ways in which the occupancy/detection assumptions are broken The issue of the potential breakage of the burrow occupancy/detection assumptions is a little more complex. The crux of the assumptions are that each burrow is occupied, and that the ratio of males to females in the sampled burrows mirrors that of the population as a whole, for each length class and that there are no changes year to year in these assumptions.

Assuming all the other assumptions (no sex and/or length occupation bias) hold true, the breaking of the assumption of 1 individual per burrow would essentially be variations in the total catchability/detection (Q) parameter from 1 – in the unlikely event of double occupancy of burrows, the true value of Q would be less than 1; if not all burrows are occupied then the value of Q would be greater than 1. For Q > 1, we are over-estimating the abundance; vice versa for values of Q < 1.

Assuming a burrow is always occupied by one animal only, but that there are differing chances overall of a burrow being occupied by a male/female or shorter/longer animal or of a burrow being detected differentially would manifest themselves not as changes in Q, but as sex/length specific decreases (for those less likely to occupy a burrow/have a less than detectable burrow) in the specific ‘catchability’ values – this would lead to potential under-estimation of these animals abundances’ and a subsequent bias would appear in the total numbers and, hence, the total biomass estimate.

The final potential issue is how the mean weight is calculated – it is this value that is then used to scale the total numbers estimate to a total biomass estimate. We look at the differences seen in the scaled abundance estimates when using a mean weight derived from a number of trawl surveys, the “true” mean stock weight and a mean weight calculated from the catch data, and how the scaled biomass estimates compare with the true total biomass.

A probability model is also required for the sampled catch. The sampling error in the catch data is simulated in a rudimentary way – a sampling CV-at-length is defined and then used to construct a variance-covariance matrix (assumed diagonal i.e. no correlation) for the catch-at-length (assuming a multivariate log-normal distribution). The true catch data are resampled using this variance-covariance matrix to give us a scaled-up sample of the catch data. For simplicity, and due to lacking any information to further condition this part of the observation error model, a simple 5% sampling CV was applied to all length classes. This may seem low but recall this is catch-at-length not catch-at-age data – the error here only represents the error incurred raising our sampled data to total removals, coming from both spatial/temporal heterogeneity and simple measuring error.

One main job of the OM is to produce simulated observations for use in assessing how the length-based stock assessment method performs, for a variety of observation error, bias, catchability-change and other regimes. To generate the observations, we will be using the FLR observation error package **FLOE**: FLR FLOE Wiki page.

Another intension is to explore how this, and other, assessment tools, tuning data sets and harvest control rules interact and perform as we develop some potential management procedures. The key element here is that we can simulate the assessment and management process together within the FLR framework, so we can perform a full management strategy evaluation on our proposed management procedures.

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