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The relatively simple stock assessment models we have described in our earlier articles can and frequently are attacked and criticized because they do not and cannot address some of the basic realities of natural fish populations. For example, surplus production models ignore the existence of different ages and/or size of fish in a population. VPA’s ignore the non-linear relationship between stock and recruitment that we described in previous articles, and yield-per-recruit analyses are often limited to addressing questions of gear selectivity or the optimal size or age at which to first start harvesting a cohort. The latter may then be used to set minimum size limits. When these simple methods are applied and presented in a situation where stock assessment results are being disputed, then they are frequently criticised because they do not describe one or another obvious population dynamics feature.
Often in these criticisms, data which were not and cannot be used in the simple assessment approach are referred to as providing evidence of a different productivity level or population size for the stock being examined. For example, CPUE data cannot be properly included in the traditional VPA analyses, mark and recapture data cannot be directly incorporated into any of the simple methods mentioned, and surplus production models cannot readily make use of catch or survey age structure data. Twenty years ago fisheries scientists tried to defend the use of simpler approaches on statistical grounds, and argued that as a rough rule of thumb no more than 2 or 3 important quantities can be estimated from typical catch statistics available for typical fisheries.
This approach has however changed over the years with the advent of a new generation of fisheries scientists. The general trend nowadays is to build models which are much more complex and which behave much more like our basic idea of how a real population behaves. There are a variety of terms that are used to refer to these models. Some of these terms are age-structured production models, size-based models, stock synthesis models. These models are able to make use of a much wider variety of data about fisheries and fish stocks than was previously possible. They also involve estimating a much larger number of important quantities than was previously considered advisable or even feasible. Ever more sophisticated computer hardware and software has made this new approach increasingly accessible to fisheries scientists.
A typical fishery stock assessment problem may involve the following data:
- Historic catch records for different components of the fishery (referring for example to different gear types, e.g. fixed gear and trawl gear).
- Historic CPUE indices for different gear types in the fishery.
- The age and/or size structure of the catch from different gear types.
- Scientific survey biomass indices, where there may be more than one survey in a year
- The age and/or size structure of fish sampled in the scientific surveys
- The sex ratio of fish in the commercial catch and in the surveys
- Results from mark-recapture studies.
For all of these data types, since the model is an attempt to reproduce on the computer the real situation as it has evolved since the fishery began, the model can be requested to output a ‘model quantity’ corresponding to any desired piece of data, be it CPUE, survey biomass, age or size structure information. For example, Fig. 1 shows a plot of the CPUE data for the South African rock lobster fishery. The diamonds show the data. The solid line shows the associated CPUE generated by the model.
Fig. 2 shows the survey biomass for the South African horse mackerel fishery where, triangles and squares denote actual survey data and the line gives a plot of the corresponding survey biomass values generated by the population model. Fig. 3 shows the age structure of the commercial catch for the abalone fishery in management zone B, as before the data are shown in comparison to the model generated values.
For these examples the models that are involved are the following:
- South African west coast rock lobster: a size-based population model
- South African horse mackerel: age-structured production model, spatially aggregated
- South African abalone: age-structured model, inshore-offshore spatial disaggregation.
Size-based models are appropriate for resources in which individual animals cannot be aged. In the case of fish, ageing is carried out by counting rings in the otoliths (ear bones). Since rock lobsters do not have any ear bones or hard parts which survive the annual moult, they cannot be aged. Consequently such population are best analyses using size-based methods. These methods are more complicated than age-based methods because with age the simple rule that fish are one year older a year later applies, whereas with size, fish are not necessarily all one cm or one mm longer one year later. Fish growth is a more complicated process than aging. Fish in a given size class at the beginning of one year either stay in that size class after a year or grow into larger size classes, or they may even shrink. A large number of factors therefore have to be tracked in size based models, far more than with age-based methods.
Spatial disaggregation is a term which implies that there are certain spatial features that are explicitly described in the model. In the case of abalone, the model makes a distinction between an inshore and an offshore component of the resource. In addition, the model mathematically describes the process of migration into deeper waters as individuals get older.
The credibility and reliability of a stock assessment model is gauged by its ability to reach good agreement between its various model quantities and the historical data trends. In order to obtain good agreement between model generated quantities and the data, the model is tuned. Figs. 1-3 actually show the best result possible when the model was tuned. Tuning, also called ‘model fitting’, is a numerical process which often requires considerable computing power and time. The model is governed by model parameters, and these parameters are items such as the level of natural mortality, recruitment levels for different amounts of spawning biomass, gear selectivity in relation to fish age or size, the pre-exploitation resource biomass, and fish migration rates if applicable to the model. Model fitting involves altering these model parameters in an intelligent manner so as to arrive at the best possible fit of the model.
The agreement between the data and the model, often referred to as the “goodness of fit”, will never be perfect, and the degree of imperfection or goodness of fit is a guide to the reliability of the predictions the model can make. In Figs 1-3 the goodness of fit is reflected in how close the data are to the corresponding model generated quantities. This is turn has a direct bearing on the reliability of forecasts and predictions from the model. The onus is on the fisheries scientist to quantify the reliability of the model’s predictions so as to put them into perspective for managers and decision makers.
Having tuned the model as best possible, the model is then ‘run into the future’ to see how the resource behaves under different future harvesting approaches. In this phase of the calculations the emphasis is not simply on what impact next year’s catch will make on the biomass at the end of that year, but rather on what will happen if one pursues a similar approach to the management of the resource over the next 10 or 20 years. Fig. 4 shows typical projections for the South African abalone resource in management Zone B, under a range of different levels of the future commercial and recreational catch, and different future levels of poaching.
In a real situation one seldom deals with a single best fitted model for exploring future scenarios. Rather there is normally some debate about the structure of the model, and so a number of different models, or model variants are developed, and all future scenarios are tested on all model variants to aid in formulating scientific management advice.
As we mentioned last time, these complex models are open to abuse. One problem is that the models produce results even when there are very few data available on the fishery, but scientists and others involved in the decision making process are seduced by the plausibility of the numbers that are being produced, or by seeing similar numbers produced over and over again, year after year. Some people refer to this phenomenon as hyper-rationality, one in which the numbers appear to be rational, but in reality they have no firm empirical foundation. The ease with which these models can be run on modern computers to produce what seem to be plausible results puts a burden on scientists to properly test the models to verify that their results are robust and useful.