Tracey and Lyle: Age validation, growth modeling, and mortality estimates for Latris lineata 



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the primordial region (width approximately 300 ^m) 

 and mounted on a microscope slide. A stereo dissector 

 microscope at 25 x magnification was used to aid the 

 interpretation of increments in the mounted sections. 

 Increment measurements were made by using Leica IM " 

 image digitization and analysis software (Leica Micro- 

 systems, Wetzlar, Germany). All counts and increment 

 measurements were made without knowledge offish size, 

 sex, or date at capture to avoid reader bias. 



Position of the first annual increment was determined 

 by testing the close correspondence of otolith micro- 

 structure and body size between known-age individuals 

 reared from eggs in aquaria and wild-caught specimens. 

 To ensure that growth in cultured individuals also re- 

 flected growth in wild specimens, a hypothesis of com- 

 parable growth was tested by fitting traditional VBGFs 

 to the length-at-age data of 288 cultured individuals 

 (maximum known age: 4 years) and 268 wild specimens 

 (maximum otolith-derived age: 4 years). A likelihood 

 ratio test (Kimura, 1980) was then used to test for sig- 

 nificance. The VBGF model was in the form 



sampled from the strong 1993 cohort over the period 

 1995 through 1997, where the model was described as 



L, = LAI - <r« " V)+e. 



(2) 



where L, = length at age t; 



h v = average asymptotic length; 

 k = a constant describing how rapidly L„ is 



achieved; 

 t = the theoretical age where length equals 



zero; and 

 f = independent normally distributed (O, a 2 ) 

 error term. 



Modal progression of length frequencies from a strong 

 cohort of juvenile fish was sampled over a three-year pe- 

 riod (1995-97). This cohort provided an opportunity to 

 validate annual periodicity in increment deposition. By 

 applying an aging protocol based on position of the first 

 increment and assuming that each opaque+translucent 

 zonal pair represented one year of growth, this recruit- 

 ment pulse could be tracked over seven years in age- 

 frequency progression. 



A random subsample of 335 otoliths was read a sec- 

 ond time by the primary reader, and a second subsam- 

 ple of 46 otoliths by a second reader, both experienced 

 in otolith interpretation. Precision was assessed by 

 determining percentage agreement between repeated 

 readings, age bias plots (Campana et al., 1994), and 

 calculating the average percent error (APE) (Beamish 

 and Fournier, 1981). 



Growth modeling 



The length-frequency progression of a strong and dis- 

 crete cohort of fish indicated that striped trumpeter 

 may be subject to seasonal growth variability. This 

 variability was described by integrating a sinusoidal 

 function (Pitcher and MacDonald, 1973; Haddon, 2001) 

 into a standard VBGF and by applying this function 

 to the actual weekly length-at-age data of individuals 



L =L 1 



+ £, 



(3) 



where C = the magnitude of the oscillations above and 

 below the nonseasonal growth curve of the 

 sinusoidal cycle; 

 S = the starting point in weeks of the sinusoidal 



cycles; and 

 52 = the cycle period in weeks. 



The timing of seasonal growth was compared with 

 weekly average sea surface temperature (SST) on the 

 southeast coast of Tasmania over the sampling period, 

 calculated by using optimum interpolation (Reynolds 

 et al., 2002) of raw remotely sensed data from the ar- 

 ea (NOAA-CIRES 3 ). A sine function was fitted to the 

 weekly average SST by using least squares regression 

 to compare the timing and phase of growth and tem- 

 perature and test for a significant correlation. 



All individuals aged were assigned a "decimal" age, 

 where the decimal portion represented the proportion of 

 the year between a nominal average date of spawning 

 (1 st October) and the date of capture. We assumed a 

 nominal peak spawning date of 1 October based on an 

 assessment of monthly averaged gonadosomatic index 

 (Tracey, unpubl. data), which is consistent with that 

 observed for wild-caught broodstock held under ambient 

 conditions (Morehead 1 ). 



Growth of the sampled population was initially de- 

 scribed by using the standard von Bertalanffy growth 

 function (Eq. 2). However, a preliminary visual assess- 

 ment of the fit suggested it did not produce an adequate 

 representation of the entire data set. In an attempt to 

 find a model that better represented the data, the fit of 

 the standard von Bertalanffy growth function (VBGF S ) 

 was compared with an extension of the traditional von 

 Bertalanffy growth model fitted by minimization of the 

 sum of negative log-likelihood; normal distribution of 

 the error term. The model chosen was similar to that 

 used by Hearn and Polacheck (2003) and involved fit- 

 ting a VBGF function either side of an age at transfer- 

 ence, described as 



L ,= 



'L_ i (l- e -^«-«o.») +£ 



for t < t" 



(4) 



(L s + ( L, 2 - If )(1 - e*-"-'" ; ')+ e for t > t s 



3 Data sourced from the NOAA-CIRES Climate Diagnostics 

 Center, Boulder, CO 80305. http://www.cdc.noaa.gov/. 

 [Accessed 15 Sep. 2002) 



