# 3. THE SELECTION CURVE

All fishing gears are species and size selective. This implies that the species and size composition of an observed catch composition differ from that of the population fished. Selection can be expressed relative to the fish populations in the area fished and is then termed absolute selection. Absolute selection is difficult to estimate, as it requires full knowledge of the species and size composition on the populations fished. Most selection work relates to the catches of fish encountering the gear. This selection measure is termed relative selection.

The size selection of fishing gears is described by means of a selection curve. A selection curve may be defined as a curve, giving for each size of fish of a given species, the proportion of the population, which is caught and retained by a unit operation of the gear.

## 3.1 BARANOV'S PRINCIPLE OF GEOMETRIC SIMILARITY

A useful assumption for describing selection, especially relevant for gillnets, is the principle of geometric similarity (Baranov 1948). This axiom is by no means mandatory, but provides a convenient simplification of the selection process.

Baranov (1948) reasoned that the catch process of gillnets is a function of fish size and mesh size only. This led Baranov to formulate the principle of geometric similarity, which states that gillnet selectivity is only dependent on the size of the fish relative to that of the mesh. Writing the selectivity (s) as a function of mesh size (m) and fish size (z), the principle states that the selectivity is the same when fish size relative to mesh size (z/m) is the same, i.e.

s(z, m) = s(kz, km)

where k is any constant.

The principle of geometric similarity implies that when selection is expressed as a function of (z/m), so the fish size is normalised with mesh size, the selection curves from different mesh sizes will have exactly the same shape (Fig. 3.1).

Figure 3.1 The principle of geometric similarity. The upper panel shows the mesh selection for four different mesh-sizes. When the selection curves are congruent, i.e. magnifications of each other, they take the same form when plotted against the transformed length (i.e. fish-size/mesh-size). This curve, which may be called the master selection curve, is shown on the bottom panel.

The normalised selection curve (the selection curve plotted against normalised fish size) can be termed the master selection curve. The use of a master curve facilitates the interpretation of selection. For example, if the master selection curve is described by a normal distribution with parameters (μ, σ) the selection curve of any individual mesh-size (m) may be simply derived as (mμ, mσ).

## 3.2 RELATING SELECTION TO CATCH PROCESSES

The size selection of fishing gear is dependent on the gear characteristics and the morphology and behaviour of the fish. Information on how fish react towards the gear or how they are caught is therefore useful for modelling or interpreting selection.

### 3.2.1 Gillnets

The name gillnet indicates that the fish are meshed behind the gill cover. The term is somewhat misleading as fish are also caught by a number of other processes. The most prominent catch processes noticed in the literature are the following:

• Gilled The fish is meshed immediately behind the gill cover.

• Wedged The fish is meshed around the body somewhere behind the gill cover. Wedging is hardly distinguishable from gilling when the maximal girth is found at a position close to the gill cover.

• Snagged The fish is attached to the netting at the head region. This catch process is most common for species with protruding maxilla or preopercula.

• Entangled The fish is wrapped into the netting, held by pockets of netting or attached to the net by teeth, fins, spines or other projections. Fish that are already caught by other catch processes may subsequently be wrapped into the netting while struggling to free themselves. When recording catch processes, care should be given to classify such catches by the primary catch process.

Figure 3.2 The relation between fish size and catch process. For the smaller fish (top) the girth at the gills (indicated by the bar) matches the mesh-size and this fish is likely to be gilled. For the larger individual (bottom) the girth at the head region matches the mesh-size and this fish is therefore potentially snagged.

For a fish to be meshed the girth must match the mesh perimeter. For a given mesh size, different fish sizes are caught by the different catch processes (Fig. 3.2). The largest fish will be mainly snagged, whereas smaller fish are mainly gilled or wedged (Hickford and Schiel 1996, Methven and Schneider 1998). Entangling is less size dependent and may affect both large and smaller individuals (Hickford and Schiel 1996, Hovgård et al. 1999).

Figure 3.3 Length distribution of cod caught off Greenland by mesh size and catch process. From Hovgård, 1996a.

Figure 3.3 shows an example of how gilling and snagging can lead to a bi-modal size distribution of the catches. Girth measurements allow the modal length associated with the two catch processes to be linked together. If the mode corresponding to gilling is found at length L1 then the mode associated with snagging, L2, is found at:

where c1 and c2 are the proportionality between length and gill girth and maxilla girth, respectively.

The importance of various catch processes differs among species due to differences in morphology (see Marais 1985, for some examples).

### 3.2.2 Longlines

From a morphometric point of view, a fish must be able to engulf the baited hook. A few studies have related mouth width to hook size (Koike et al. 1968, Takeuchi and Koike 1969). If hook size is the sole factor determining selectivity, the selection curve should take some sigmoid shape (cf. Section 4.2 where this line of thinking is formalised for gillnets).

Prey size preferences may, however, also play a role resulting in large prey being avoided (e.g. Ralston 1990, Erzini et al. 1996). Including the effect of prey size preference implies that the selectivity curve should follow a bell shaped pattern with the ascending leg of the curve being caused by the morphometrics and the descending leg of the curve being due to an avoidance of larger bait sizes.

The importance of prey size preference may differ by species. It may be of little importance for voracious predators able to engulf a prey up to 30% of its own length (sigmoid curve), but it may be crucial for small invertebrate predators (bell curve).

## 3.3 SHAPE OF SELECTION CURVES

Selection curves can be classified as: 1) sigmoid, 2) bell-shaped and 3) two-peaked models.

• Trawl selection curves are described by sigmoid expressions that may be parameterised by various models (see for example, Wileman et al. 1996).

• Gillnet selection curves are either bell-shaped or two-peaked, where the latter formulation is useful when the catch are taken by two distinct catch processes. Two-peaked selection curves are typically represented by the sum of two bell-shaped distributions.

• Longline size selectivity has been presented by fundamentally different shapes of selection curves, either the bell-shaped or the sigmoid types (Ralston 1990, Kenchington 1993, Millar 1995).

The bell-shaped selectivity curves are often presented by functions derived from probability distributions known from statistics, such as normal, log-normal or gamma distribution functions. Using these expressions implies that the estimation of the selection of large fish is influenced by the catches of small individuals and vice versa.

Hamley (1975) notes that it is more appealing to model gillnet selectivity to the left and the right of the mode separately, as he finds no reason to expect that the selectivity above and below the mode is controlled by the same factors. This may be achieved by describing the selection to the right and left of the mode separately or by using a two-peaked selection curve explicitly accounting for different catch processes.

The parameterisation of a sample of selection curves is provided in Table 3.1 and Figure 3.4. All the selection expressions given in Table 3.1 follow the principle of geometric similarity. Millar (1995) presents a number of examples for selection curve expressions that do not comply with this assumption. Hovgård et al. (1999) supplies model formulation that includes terms for fish being randomly entangled.

The normal, log-normal and gamma selection curves are useful to describe bell shaped selection curves. The latter two formulations allow for a moderate amount of skewness, although in practice these expression often lead to very similar selection curves (Millar and Holst 1997, Hovgård et al. 1999). More skewed selection curves have often been obtained by using a skewed normal distribution derived by a truncated Gram-Charlier series (e.g. Regier and Robson 1966, Helser et al. 1991, Hansen et al. 1997). However, as Hamley (1975) notes, the terms omitted by the truncation becomes important when the shape deviates too much from the normal distribution, typically leading to negative estimated selections for some size groups. For this reason, this model formulation is not recommended.

The two sided model is useful for describing skewed selection curves as it allow any degree of skewness to the right or left of the mode. This model confirms Hamley's suggestion of expressing selection independently on the two sides of the mode.

Bi-modal models have been suggested to be particularly appropriate for situations where the fish are caught by two different processes, e.g. typically gilled or held by the mouth parts (Holt 1963, Hunter 1970, Hamley and Regier 1973, Hovgård 1996a). This model may potentially be used to describe skew-selection curves (Fig. 3.4), as two normal shaped selection curves fuse into a skew curve when the distance between the two modal values are small relative to the width of the selectivity curves (see Sparre and Venema 1992, p.108, for some useful rules of thumb). However, when different catch processes cannot be discerned, this model is not recommended, as the model is arguably over-parameterised (5 parameters) and the two modes can not be justified by physically processes.

A number of different sigmoid selection curves have been used mainly to describe trawl selection. Useful expressions may be found in Millar (1995) and Wileman et al. (1996).

Table 3.1 A sample of selection curve expressions. All models are formulated in accordance with the principle of geometric similarity (Baranov 1948) and are expressed using the transformed length (λ=length/mesh-size = l/m). Selectivity curves for actual mesh or hook size (ms) for fish measured in cm (l) are derived by using the parameters given on the right hand side.

 Transformed length formulation Direct length formulation NORMAL S(l | ms*k, ms*s) LOG-NORMAL S(l | 1n(ms)+k, s) GAMMA S(l |α, ms* β) BI-NORMAL S(l |m*k1, s*k2,ms*s1, ms*s2, b) TWO-SIDED S(l |ms*k,ms*s1, ms*s2) LOGISTIC S(l | α, β/ms)

The constant B used for scaling the bi-normal selection curve to a maximum selection
of 1 is:

Figure 3.4. Examples of the potential shapes of the selection curve expressions given in Table 3.1.