Dennis et al.: Using otolith chronologies to identify extrinsic drivers of growth 
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Table 1 
A list of the variables used in mixed-effects modeling to 
investigate the sources of growth variation in common jack 
mackerel (Trachurus declivis) and redbait (Emmelichthys 
nitidus) collected off Kangaroo Island and New South 
Wales in Australia between 2014 and 2016. Environmen- 
tal data were collected for the period 2002-2016. 
Source 
Variable Description 
Age Fish age (in years) when growth 
increment was formed 
AgeCap Fish age (in years) when caught 
Year Year of growth increment formation 
YearClass Birth year of fish 
FishID Fish identification number 
SST Mean annual sea-surface 
temperature (°C) 
Chl-a Mean annual chlorophyll-a con- 
centration inferred from relative 
fluorescence per unit volume of 
the water body (in milligrams per 
cubic meter) 
IMOS’ 
IMos® 
through the OC3M algorithm (IMOS°), and Chl-a levels 
were also averaged to produce annual means. 
All fixed effects were mean centered to assist in inter- 
pretation of interaction terms and model convergence 
(Morrongiello and Thresher, 2015). All fish determined to 
have ages <2 years were excluded from analysis because, 
with the first increment being excluded for all fish, only 
a single increment measurement would be available for 
these individuals, and a single increment is insufficient 
to predict growth. The Akaike information criterion cor- 
rected for bias from small sample sizes (AIC,) was used to 
rank models, and AIC, weight was used to assess model 
likelihood: the smaller the weight, the lower the probabil- 
ity the model was “true” on the basis of the included can- 
didate models (Burnham and Anderson, 2004). Marginal 
and conditional coefficients of multiple determination (R?) 
were used as a measure of goodness of fit, and the con- 
tribution of the fixed effects (marginal R”) and the fixed 
and random effects (conditional R*) were used to explain 
variance of the response variable when added to the model 
(Nakagawa and Schielzeth, 2013). 
The optimal model explaining variation in fish growth 
(i.e., increment width) was determined by using a 2-step 
process whereby the best random-effect variables (Year 
and YearClass) were selected by sequentially adding 
them in increasing complexity to the models containing 
the full fixed-effect structure (i.e., the effects Age and 
AgeCap were included) through the use of the restricted 
maximum likelihood estimates of error (Zuur et al., 2009). 
The combination of models included Year and YearClass 
as random intercepts and used these same variables with 
Age included as a random slope on these variables. Ran- 
dom slopes of Age were included to allow greater flexibil- 
ity in growth estimations from the model and to remove 
age-dependent trends during the analysis. Inclusion of 
Year as a random intercept was intended to be equiva- 
lent to the use of traditional dendrochronology, enabling 
annual estimates of whether growth was high or low as a 
result of the environmental covariates in relation to the 
long-term mean (Morrongiello and Thresher, 2015). Sim- 
ilar to the use of Year, YearClass was used as a random 
intercept to estimate growth conditions for a group of fish 
(year cohorts) over their lifetime. FishID with a random 
Age slope was included in all models as a random intercept 
to allow the growth of each fish to vary beyond the model 
average by inducing a correlation among increment mea- 
surements within an individual. 
Estimates of the temporal similarity in growth (growth 
synchrony) were calculated with the interclass correlation 
coefficient. By using the full intrinsic effects model fit with 
Year intercept and YearClass intercept only, the correlation 
of growth increments among individuals was calculated. 
Growth chronologies were produced by extracting best 
linear unbiased predictors for each combination of species 
and region based on Year (variation in growth relative to 
the long-term mean) and YearClass (variation in growth 
conditions for a group of fish, i.e., year cohorts, over their 
lifetime relative to the long-term mean) (Morrongiello and 
Thresher, 2015). 
The best fixed effects (Age, AgeCap, or Age and AgeCap) 
were then identified by sequentially adding them in 
increasing complexity to the selected best random-effect 
variables. Random-effect variables were initially selected 
by using maximum likelihood estimates of error, and 
then they were refit with restricted maximum likeli- 
hood estimates of error to produce unbiased parameter 
estimates (Zuur et al., 2009). Once the optimal intrinsic 
model was identified, environmental variables were fit 
as fixed effects to relate the variability in growth to the 
extrinsic covariates. 
All analyses were performed in R, with the packages Ime4 
(Bates et al., 2015), effects (Fox, 2003), and AlCcmodagv 
(Mazerolle, 2015). 
Results 
A total of 247 common jack mackerel and 248 redbait from 
trawl tows conducted south of KI were aged, and 760 com- 
mon jack mackerel and 342 redbait from southeast NSW 
were aged. Age across both regions ranged from 1 year to 
15 years for common jack mackerel and from 0+ to 14 years 
for redbait. From these aged samples, a subset of ran- 
domly selected otoliths was measured for growth chronol- 
ogy analyses (Fig. 1). A combined total of 1674 increments 
on otoliths from 195 common jack mackerel (KI: 662 incre- 
ments, birth years 2003-2012; NSW: 425 increments, 
birth years 2007-2014) and on otoliths from 122 redbait 
(KI: 177 increments, birth years 2008-2012; NSW: 410 
increments, birth years 2001—2012) were measured, with 
the greatest number of individuals born between 2007 
and 2012 (Fig. 3). Years that corresponded to fish that 
had otoliths with <5 increments were removed from the 
