The invariance of production per unit of food consumed in fish populations

Abstract

The amount of biomass production per unit of food consumed (P/Q) represents an important quantity in ecosystem functioning, because it indicates how efficient a population transforms ingested food into biomass. Several investigations have noticed that P/Q remains relatively constant (or invariant) across fish population that feed at the same food-type level (carnivorous/herbivorous). Nevertheless, theoretical explanation for this invariant is still lacking. In this paper, we demonstrate that P/Q remains invariant across fish populations with stable-age distribution. Three key assumptions underpin the P/Q invariant: (1) the ratio between natural mortality M and von Bertalanffy growth parameter k (M/k ratio) should remain invariant across fish populations; (2) a parameter defining the fraction of ingested food available for growth needs to remain constant across fish that feed at the same trophic level; (3) third, the ratio between length at age 0 ($l_0$) and asymptotic length ($l_\infty$) should be constant across fish populations. The influence of these assumptions on the P/Q estimates were numerically assessed considering fish populations of different lifespan. Numerical evaluations show that the most critical condition highly relates to the first assumption, M/k. Results are discussed in the context of the reliability of the required assumption to consider the P/Q invariant in stable-age distributed fish populations.