The Gill-Oxygen Limitation Theory and size at maturity/maximum size relationships for salmonid populations occupying flowing waters

Abstract

The slowing of growth as fish age has long been believed to be related to energy expenditure for maturation, and this rationalization has been used to explain why, across nearly all fish species, the relationship between size at first maturity (L_m ) and maximum (L_max ) or asymptotic length (L_∞ ) is relatively constant. In contrast, the Gill-Oxygen Limitation Theory (GOLT) postulates that (a) fish growth slows because as they grow, their two-dimensional ability to extract oxygen from the water diminishes relative to their three-dimensional weight gain, and (b) they can only invest energy for maturation if oxygen supply at their size at first maturity (Q_m ) exceeds that needed for maintenance metabolism (Q_∞ ). It has been reported previously across dozens of marine fish species that the relationship between Q_m and Q_∞ is linear and, further, it can be mathematically converted to L_m vs. L_∞ by raising both terms to the power of D (the gill surface factor), resulting in a slope of 1.36. If the GOLT is universal, a similar slope should exist for L_m ^D vs. L_∞ ^D relationships for freshwater species across multiple individual populations that reside in disparate habitats, although to our knowledge this has never been evaluated. For analysis, we used existing data from previous studies conducted on 51 stream-dwelling populations of redband trout Oncorhynchus mykiss gairdneri, Yellowstone cutthroat trout O. clarkii bouvieri and mountain whitefish Prosopium williamsoni. The resulting L_m ^D vs. L_∞ ^D slopes combining all data points (1.35) or for all species considered separately (range = 1.29-1.40) were indeed equivalent to the slope originally produced for the marine species from which the GOLT-derived relationship was first reported. We briefly discuss select papers both supporting and resisting various aspects of the GOLT, note that it could potentially explain shrinking sizes of marine fish, and call for more concerted research efforts combining laboratory and field expertise in fish growth research.

Keywords: GOLT; Gill-Oxygen Limitation Theory; asymptotic length; size at maturity.