Avoiding fishy growth curves
Correspondence author. E-mail: firstname.lastname@example.org
- Somatic growth is a fundamental property of living organisms, and is of particular importance for species with indeterminate growth that can change in size continuously throughout their life. For example, fishes can increase in size by 2–6 orders of magnitude during their lifetime, resulting in changes in production, consumption and function at the ecosystem scale. Within species, growth rates are traded off against other life-history parameters, hence an accurate description of growth is essential to understand the comparative demography, productivity, fisheries yield and extinction risk of populations and species.
- The growth trajectory of indeterminate growing sharks and rays (elasmobranchs) and bony fishes (teleosts) is usually modelled using a three-parameter logarithmic function, the von Bertalanffy growth function (VBGF), to describe the total length of the average individual at any given age. Recently, however, a two-parameter form has gained popularity. Rather than being estimated in the model fitting process, the third y-intercept parameter (L0) of the VBGF has been interpreted as being biologically equivalent to, and thus fixed as, the empirically estimated size at birth.
- We tested the equivalence assumption that L0 is the same or similar to size at birth by comparing empirical estimates of size at birth available from the literature with estimates of L0 from published data from elasmobranchs, and found that even though there is an overlap of values, there is a high degree of variability between them.
- We calculate the bias in the growth coefficient (k) of the VBGF by comparison between the two- and three-parameter estimation methods. We show that slight deviations in fixed L0 can cause considerable bias in growth estimates in the two-parameter VBGF while providing no benefit even when L0 matches the true value. We show that the effect of this biased growth estimate has profound consequences for fisheries stock status.
- We strongly recommend the use of the three-parameter VBGF and discourage use of the two-parameter VBGF because it results in substantially biased growth estimates even with slight variations in the value of fixed L0.