Bailagh et a!.: Methods for determining length-at-age for two large scombrids 
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However, this method can be influenced by statistical 
dependency whereby estimated lengths at younger ages 
are dependent on lengths from older ages through the 
back-calculation process and are therefore suscepti- 
ble to bias in the presence of size-selective mortality 
(Vaughan and Burton, 1994; Pilling et al., 2002). Other 
drawbacks of back-calculation include the specialized 
equipment and software needed and the significant time 
required to obtain data. 
We demonstrated that although back-calculation 
was effective for estimating length-at-age for younger 
ages in the presence of selectivity within a fishery that 
selects for the faster growing younger fish, it appears 
to underestimate mean maximum length (LJ). This 
finding is shown by observed length-at-age data being 
consistently higher than the back-calculated VBGF for 
older age classes and is subject to the assumption that 
there is little or no selectivity acting on older fish. The 
underestimation of back-calculated mean maximum 
length is likely due to three effects: smaller length- 
at-age for younger fish; weighting of data in younger 
ages; and the negative correlation between the VBGF 
parameters of L... and K. Back-calculating to all annuli 
results in a disproportionate amount of data for young 
ages which, depending on the growth estimation method 
used, gives more weight to younger ages when fitting a 
VBGF. Because the VBGF parameters and K have 
been shown to be negatively correlated (Pilling et ah, 
2002), increasing the estimate of K through smaller 
length-at-age for younger ages, or a weighting of data 
in younger ages, will inevitably reduce the estimate of 
L x , and thus underestimate average maximum length. 
One option for overcoming this problem could be to 
constrain to the largest observed length, although 
some prior knowledge of the size-selectivity pattern 
of sampling gears is required to make an informed 
decision to constrain parameters (Gwinn et ah, 2010), 
Fishery-independent sampling can improve estimates 
of growth through the collection of small, slower 
growing young fish not fully represented in fishery- 
dependent samples. However, fishery-independent sam- 
pling is typically expensive and not always possible or 
practical. Methods have been developed to correct bias 
in length-at-age data; however, these require previous 
knowledge of selectivity patterns, mark-recapture 
data or intensive sampling over several consecutive 
