8 Consumption/biomass

Consumption (Q, t km^-2 year^-1) is the annual intake of food by a consumer group, and it is in EwE estimated as the product of the group’s biomass (B, t km^-2) and consumption/biomass ratio (Q/B, year^-1). To estimate consumption, we thus need to obtain estimates of B and Q/B for the consumer groups in models.

There are various approaches for estimating Q/B, and they can be split in (i) analytical methods and (ii) empirical methods:

(i) The analytical methods involve estimation of ration, pertaining to one or several size/age classes, and their subsequent extrapolation to a wide range of size/age classes, representing an age-structured population exposed to a constant or variable mortality. The required estimates of ration can be obtained from laboratory experiments, from studies of the dynamics of stomach contents in nature, or by combining laboratory and field data. There is an expanse of literature on this, to which we refer.

Characteristic for these methods is that they are resource- and time-consuming, and it is indeed not practical to set up laboratory or field experiment to estimate Q/B for all species or functional groups in an ecosystem model. Instead we rely on the second avenue, empirical combinations – along with estimates from analytical studies, where available.

(ii) There are a number of empirical regressions for prediction of Q/B from some easy-to-quantify characteristics of the animals for which the Q/B values are required.

Palomares and Pauly (1989^[1]; 1998^[2]) described based on a data set of relative food-consumption estimates (Q/B ) of marine and freshwater population (n=108 populations, 38 species) a predictive model for Q/B using asymptotic weight, habitat temperature, a morphological variable and food type as independent variables. Salinity was not found to affect Q/B in fish well adapted to fresh or saltwater (other things being equal). In contrast the total mortality (Z, per year) showed a strong, positive effect on Q/B and also on the gross food-conversion efficiency (defined by GE = Z/ (Q/B)), by affecting the ratio of small to large fish.

The authors presented three related models:

[latex]\log(Q/B)=7.964 - 0.204 \log W_{\infty}-1.965 \ T^{'}+0.083 \ A+0.532 \ h+0.398 \ d \tag{1}[/latex]

where, W_∞ is the asymptotic weight (g), T’ is an expression for the mean annual temperature of the water body, expressed using T’ = 1000/Kelvin (Kelvin = °C + 273.15), A is the aspect ratio (see Figure 2.1), h expresses food type (1 for herbivores, and 0 for detritivores and carnivores), and d is also expressing food type (1 for detritivores, and 0 for herbivores and carnivores)

The equation can be modified to investigate the effect on mortality on Q/B, and to derive predictive models of Q/B taking explicit account of different mortalities, values of Q/B were calculated using the equation above for mortalities corresponding to f · M, where f is a multiplicative factor with value of 0.5, 1, 2 or 4, and M is the natural mortality rate that is estimated from Pauly’s (1980) empirical relationship.

[latex]\log(Q/B)=8.056+0.300\log f - 0.201 \log W_{\infty}-1.989 \ T^{'}+0.081 \ A+0.532 \ h+0.393 \ d\tag{2}[/latex]

where f is the multiplicative factor introduced above, and the rest of the variables are as defined earlier.

For cases where estimated of total mortality, Z, (year^-1) are available, the following relation may be used:

[latex]\log(Q/B)=5.847+0.280\log Z - 0.152 \log W_{\infty}-1.360 \ T^{'}+0.062 \ A+0.510 \ h+0.390 \ d \tag{3}[/latex]

These relationships can be used only for fish groups that use their caudal fin as the (main) organ of propulsion.

Figure 1 Schematic representation of method to estimate the aspect ratio (A_r = h²/s) of the caudal fin of fish, given fin height (h) and surface area (s, in black).

Consumption/biomass ratios for fish are available in FishBase at the Life History tables for many species. Where analytical estimates are available those are included, while for species without such, there instead is an empirical relationship based on the equations above, see Figure 2.

Figure 2. FishBase Life History Tool for estimating Q/B from empirical relationship.