# 2. CONCEPTS IN ESTIMATING CATCH

2.1 A GENERIC FORMULA FOR ESTIMATING CATCH
2.2 SECONDARY ESTIMATES

In this handbook there is no discussion of complete enumeration (=census) approaches for determining total catch, such as compulsory logbook data. In most small-scale fisheries the amount of information on total landings, species composition, prices, etc., is often large, highly distributed and difficult to collect so that the use of census approaches is impractical and sampling techniques are nearly always employed. Some exceptions occur in estimating total fishing effort and a detailed discussion on alternative approaches is given in Section 3.

This section describes a generic approach for estimating total catch from basic fishery sample data. Such estimation can be performed against any reference (= estimation context), most commonly a combination of a) a geographical stratum, b) a reference period and c) a specific boat/gear category. The estimation of secondary data such as catch by species, values and average fish size are also presented on the basis of the estimated total catch.

## 2.1 A GENERIC FORMULA FOR ESTIMATING CATCH

Total catch can be estimated from sample CPUE multiplied by estimated effort.

where:

• Catch (total)

refers to all species taken together and is usually computed within the logical context of a) a limited geographical area or stratum, b) a given reference period (i.e. a calendar month) and c) a specific boat/gear category.

• CPUE (sample, overall Catch-Per-Unit-Effort)

is an overall average deriving from sampling and expressing how much fish (all species) is caught by a unit effort. Sampling context is the same as that for the estimated catch.

• Effort (estimated from sample) is expressed uniformly in total number of boat-days within the same logical context used for total catch and overall CPUE. In this section total fishing effort is assumed to be known.

## 2.2 SECONDARY ESTIMATES

2.2.1 Catch by species

Once the total catch has been estimated, species composition is computed by means of the following simple formula:

where:

• Species catch

is the estimated catch for each species within the estimating context described earlier.

• SP

is a fraction of the total catch corresponding to a species and is formulated from the proportion of a species found in the samples.

• Catch

is the estimated total catch discussed earlier.

From catch by species and using the estimated effort, it is also possible to compute species-specific CPUEs.

2.2.2 Species value

Once the catch by species has been estimated, its value is computed by means of the following simple formula:

where:

• P is the sample first-sale price of a landed species.
• Species is the estimated species catch discussed earlier.

2.2.3 Estimated total value of landings

It is computed within the estimating context by simply adding up all estimated values by species.

2.2.4 Average weight per species

In addition to catch by species and prices, sample surveys usually provide also data relating to fish size (in weight units) on a sub-sampling basis. When this information is available, it is possible to produce estimates of average fish size for certain species.

2.2.5 Numerical example

The following theoretical example uses the formulae given above and illustrates a stepwise process for deriving primary and secondary estimates. For purposes of simplicity it involves only two species and the assumption that fishing effort is known.

A. Assumptions and sample data

Estimating context: Lake Volta, Area VII, February 2001, Gillnets
Estimated effort = 1,000 boat-days
Sample overall CPUE = 10 kg/boat-day

Species 1

Proportion of species 1 in samples = 60%
Sample price of Species 1 = 5,000 Cedis/kg
1,000 fish found in sub-samples of 500 kg
Species 2
Proportion of species 2 in samples = 40%
Sample price of species 2 = 6,000 Cedis/kg
1,000 fish found in sub-samples of 800 kg
B. Estimations
Estimated total catch = 10,000 kg (from formula 2.1)

Species 1

Catch of species 1 = 6,000 kg (from 2.2.1)
CPUE = 6 kg/boat-day
Value of species 1 = 30,000,000 Cedis (from 2.2.2)
Average weight of Species 1 = 0.5 kg
Species 2
Catch of species 2 = 4,000 kg (from 2.2.1)
CPUE = 4 kg/boat-day
Value of species 2 = 24,000,000 Cedis (from 2.2.2)
Average weight of Species 2 = 0.8 kg
Total value of landings = 54,000,000 Cedis
 SUMMARYAt this point readers are familiar with the parameters involved in the estimation of total catch and other secondary basic fishery statistics. The following points have been emphasized:(a) All estimations are performed within the context of a stratum, a reference period and a boat/gear category.(b) Within each context, estimates of total catch are derived from the sample overall CPUE and the estimated total effort.(c) Catch by species is estimated on the basis of sample species proportions and the estimated total catch. Species values are estimated on the basis of sample prices and the estimated catch by species.(d) Average weight per species is estimated on the basis of number of fish found in each species sample.(e) Total values for landings are computed on the basis of estimated species values.No mention has so far been made as to the mechanics for collecting the data required for formulating the above parameters. This is discussed in more detail in the coming sections that deal with the operational aspects of sample-based fishery surveys.