2.1 Presentation of the generic formula

ARTFISH is based on the concept of catch per unit effort (CPUE), using the following relationships:

\[ \mathrm{CPUE}=\frac{Catch}{Effort} \]

\[ \mathrm{Catch}=\mathrm{CPUE}\times\mathrm{Effort} \]

Where:

• Catch refers to the total catch (all species combined) and is usually estimated within a defined context:
  • a geographical area (stratum),
  • a reference period (e.g. one calendar month),
  • a specific fishing unit.
• CPUE (estimated from the sample) is the average catch per unit of effort. It represents the average quantity of fish (all species combined) caught per unit of effort within the same estimation context.
• Effort (estimated from the sample) is expressed as the total number of boat-days within the same estimation context.

CPUE and effort are estimated from sample data. The data sources may vary depending on the information available in each country and the survey design implemented.

Figure 1 illustrates the estimation process when sampling is performed in both time and space, that is, when only a subset of sampling days and landing sites is surveyed.

Figure 1. ARTFISH conceptual framework.

2.2 Stratification

As in most statistical methods, ARTFISH estimates are first computed for each stratum before being aggregated to produce estimates at higher levels (e.g. total national catch).

The first level of stratification generally corresponds to the reference period. In ARTFISH, data collection is usually organised on a monthly basis. However, fishing seasons may be more appropriate than calendar months in some contexts. The selected reference period therefore defines the first level of stratification.

Additional levels of stratification can be defined when required:

• Major strata, usually based on administrative, geographical, or temporal criteria.
• Minor strata, corresponding to subdivisions of a major stratum.
• Fishing units, representing the lowest level of stratification. Fishing units are defined to describe the structure of the fisheries sector within the country.

Major and minor strata are optional and should only be defined when justified by the local context or logistical constraints.

Important

Population parameters are always estimated at the lowest level of stratification. Estimates at higher levels are obtained by aggregating the corresponding lower-level estimates.

The sample size for each stratum can be determined using preliminary data. When no prior information is available, the following sampling effort is recommended:

• 8 to 12 sampling days per month;
• at least 30 landing surveys;
• at least 70 effort surveys.

4.1 Presentation

When sampling is performed in both time and space, the estimation of fishing effort requires three components.

Figure 3. Effort estimation principle.

Where:

• \(D\) is the raising factor expressing the total number of days with fishing activity during the reference period. It is estimated from an active days survey.
• \(F\) is the raising factor expressing the total number of fishing units potentially operating across all fishing sites within the stratum. It is estimated from a frame survey or a vessel registry.
• \(AC\) is the activity coefficient. Fishing unit activity can be estimated either through the boat activity coefficient (\(BAC\)), using vertical sampling (boat counts), or through the fishing activity coefficient (\(FAC\)), using horizontal sampling (fisher interviews).

The total fishing effort is therefore estimated as:

\[ \mathrm{Effort} = F \times D \times BAC \]

or

\[ \mathrm{Effort} = F \times D \times FAC \]

Both \(BAC\) and \(FAC\) express the probability that a fishing unit (boat) is active on any given day during the reference period. \(BAC\) is estimated from a boat activity survey, whereas \(FAC\) is estimated from fisher interviews.

4.2 Number of active vessels: Estimation of the raising factor expressing the total number of active fishing units (\(F\))

The raising factor \(F\) represents the number of boats that are active within the fishing fleet and are therefore potentially capable of fishing during the sampling period.

Depending on how the fleet is managed, \(F\) can be estimated from:

• a frame survey, when boats are not registered;
• a vessel registry, when registration with the fisheries or maritime administration is mandatory.

Other data sources may also be considered and are currently being explored, such as household surveys for small-scale fisheries.

For stratum \(i\) and fishing unit \(j\), \(F\) is calculated as the sum of the number of boats belonging to fishing unit \(j\) across all sites included in the stratum:

\[ F_{i,j} = \sum_{k=1}^{q} x_{i,j,k} \]

Where:

• \(x_{i,j,k}\) is the number of potentially active vessels of fishing unit \(j\) at site \(k\) within stratum \(i\).
• \(k\) is the site index, ranging from \(1\) to \(q\). (to complete if required)
• \(q\) is the total number of sites within stratum \(i\).
• \(F_{i,j}\) is the raising factor for stratum \(i\) and fishing unit \(j\).

4.3 Number of active days: Estimation of the time raising factor (\(D\))

The time raising factor \(D\) represents the total number of days during the reference period that are considered normal fishing days. It is obtained by starting from the total number of calendar days and subtracting days during which fishing is not expected to occur (e.g. weekends, public holidays, or bad weather).

The value of \(D\) is estimated for a given estimation context (reference period, geographical stratum, and fishing unit). The target population therefore corresponds to all calendar days within the reference period.

For stratum \(i\) and fishing unit \(j\), \(D\) can be calculated as:

\[ D_{i,j} = \text{Number of days in the month} - \text{Number of non-potentially fishing days} \]

Table 2. Example template for the active days survey.

For example, in Table 2, for Strata 1 and Fishing Unit 2:

\[ D = 31 - 9 = 22 \]

When several sites belong to the same stratum, \(D\) is calculated as the weighted mean of the site-specific values, using the number of boats as weights.

\[ D_{i,j} = \frac{\sum_{m=1}^{t} D_{i,j,m}\times x_{i,j,m}} {\sum_{m=1}^{t} x_{i,j,m}} \]

Where:

• \(m\) is the site index, ranging from \(1\) to \(t\).
• \(t\) is the total number of sampled sites.
• \(x_{i,j,m}\) is the number of active boats at site \(m\) in stratum \(i\) for fishing unit \(j\).
• \(D_{i,j,m}\) is the estimated number of active fishing days at site \(m\) in stratum \(i\) for fishing unit \(j\).

4.4 Activity coefficient: Estimation of the boat activity coefficient (\(BAC\)) or fishing activity coefficient (\(FAC\))

5.1 Catch per species per stratum

Once the total catch has been estimated, the catch of each species is obtained using the following relationship:

\[ SpeciesCatch = SP \times Catch \]

Where:

• \(SpeciesCatch\) is the estimated catch of a given species within the estimation context.
• \(SP\) is the proportion of the total catch represented by the species in the sampled landings.
• \(Catch\) is the estimated total catch within the estimation context.

Using the estimated fishing effort, species-specific CPUE values can also be calculated.

5.2 Total catch estimation

The total catch for a given reference period is obtained by summing the estimated catches across all strata (all fishing units and all major and minor strata, when applicable).

\[ TotalCatch = \sum_{i=1}^{S} Catch_i \]

Where:

• \(i\) is the stratum index, corresponding to a unique combination of reference period, geographical stratum, and fishing unit.
• \(S\) is the total number of strata. (to complete)

7 References

Stamatopoulos, C. (2002). Sample based fishery surveys: A technical handbook. FAO Fisheries Technical Paper No. 425. Rome: Food and Agriculture Organization of the United Nations. 132 pp. Available at: https://www.fao.org/3/y2790e/y2790e.pdf