# 7 Production/biomass

Production refers to the elaboration of tissue (whether it survives or not) by a group over the period considered, expressed in whatever currency that has been selected. Total mortality, under the condition assumed for the construction of mass-balance models, equal to production over biomass (Allen, 1971^{[1]}). Therefore, one can use estimates of total mortality (Z) as input values for the production over biomass ratio (P/B) in Ecopath models. Some examples of how to obtain P/B values are given below.

For multi-stanza groups, the production term is actually the total mortality term, Z for each stanza. So, if as an example, you have a juvenile stanza group and use a bioenergetic model to calculate the production, you should subtract the amount that is recruited to the next (older) stanza from the production in order to get the actual mortality, which is what Ecosim needs to work with.

## Total mortality catch curves

Total mortalities can be estimated from catch curves, i.e., from catch composition data, either in terms of age-structured or of length-converted catch curves. The estimation can be carried out using appropriate software for analysis, but require careful consideration of how representative the samples are of the entire population, and the impact of related bias on the estimated mortality parameters.

## Total mortality from sum of components

The P/B rate can be estimated as the sum of natural mortality (*M = M0 + M2*, assuming that the *M1* term is included in *M0*) and fishing mortality (*F*), i.e., *Z = M + F* ignoring here potential migration and biomass accumulation. In the absence of catch-at-age data from an unexploited population, natural mortality for finfish can be estimated from an empirical relationship (Pauly, 1980^{[2]}) linking M, two parameters of the von Bertalanffy Growth Function (VBGF) and mean environmental temperature, i.e.,

[latex]M = K^{0.65} \cdot L_{\infty}^{-0.279} \cdot T_c^{0.462}\tag{1}[/latex]

where, *M* is the natural mortality (year^{-1}), *K* is the curvature parameter of the VBGF (year^{-1}), *L _{∞}* is the asymptotic length (total length, cm), and

*T*is the mean habitat (water) temperature, in °C .

_{c}In equilibrium situations, fishing mortality (*F*, year^{-1}) can be estimated directly from the catch (*C*, including discards, t km^{-2} year^{-1}) and biomass (*B*, t km^{-2})

[latex]F = C/B \tag{2}[/latex]

## Total mortality from average length

Beverton and Holt (1957^{[3]}) showed that total mortality (Z = P/B, year-1), in fish population whose individuals grow according to the von Bertalanffy Growth Function (VBGF), can be expressed as

[latex]Z=P/B=\frac{K \cdot (L_{\infty}-\bar L)}{\bar L-L^{'}}\tag{3}[/latex]

where *K* is the VBGF curvature parameter (year^{-1}, expressing the rate at which L_{∞} is approached), L_{∞} is the asymptotic length, i.e., the mean size the individuals in the population would reach if they were to live and grow indefinitely, *L̅* is the mean length in catches, and *L’* represents the mean length at entry into the fishery, assuming knife-edge selection. Note that the *L̅*–*L’* denominator must be positive.

## Total mortality and longevity

Mortality rates (*P/B = Z*) are not just nuisance parameters, they really mean something that one can relate to. How much does a population produce relative to its biomass? A lot for plankton and not very much for whales, right?

Mortality rates thus relates to size, e.g., for a small (1-2 mm) zooplankton like Acartia tonsa, the *P/B* is up around 45 year^{-1}. The much larger Calanus finmarchicus can live for several years and may have a P/B closer to 7 or 8 year^{-1}. Whales? *P/B* will be below 0.1 year^{-1}.

A good way to relate to such numbers is to turn them on their head. That is, think of the *B/P* ratio (year) to get a sense for the *P/B* (year^{-1}) ratio. So if a blue whale has a *P/B* of 0.025 year^{-1}, the inverse *B/P* is 40 years – that’s the average longevity of blue whales (if *P/B* indeed is 0.025 year^{-1}). Seals with *P/B* of 0.14 year-1 would have an average longevity of 7 years, cod with a *P/B* of 0.25 year^{-1} an average longevity of 4 years, and anchovy with *P/B* of 2.0 year^{-1} would on average live half a year.

It makes sense, and longevity provides a good handle for evaluating what reasonable estimates of P/B may be.

There is a Quick guide on how to calculate *P/B* and *Q/B* for EwE models by Daniel Vilas, Marta Coll, Chiara Piroddi, Jeroen Steenbeek, developed for the EC Safenet Project, available for download.

Attribution

This chapter is in part adapted from the unpublished EwE User Guide: Christensen V, C Walters, D Pauly, R Forrest. Ecopath with Ecosim. User Guide. November 2008.

- Allen, K. R. 1971. Relation between production and biomass. J. Fish. Res. Board Can., 28:1573-1581. doi 10.1139/f71-236 ↵
- Pauly, D. 1980. On the interrelationships between natural mortality, growth parameters, and mean environmental temperature in 175 fish stocks. J. Cons. int. Explor. Mer, 39:175-192. https://doi.org/10.1093/icesjms/39.2.175 ↵
- Beverton, R. J. H., and Holt, S. J., 1957. On the Dynamics of Exploited Fish Populations. Chapman and Hall, Facsimile reprint 1993, London. 533 pp. ↵