Karlou-Riga et al.: Sex change and oscillating growth pattern of Spicara smaris in the Saronikos Gulf (Greece) 
351 
Figure 2 
Concave side of the right otolith of a picarel (Spicara smaris) sampled in the 
Saronikos Gulf, Greece, in May 1999. D T =total otolith diameter; D^diameter 
of first annulus. 
tation criteria. The Bray and Curtis (1957) similarity 
index was used and data were square-root transformed. 
Growth parameters were estimated by the classic 
von Bertalanffy growth function (VBGF): 
L t = L«( 1 - e-« J -h>)), (1) 
where L, = TL at age t; 
= the mean asymptotic TL; 
K - the growth coefficient; and 
t 0 = the theoretical age at TL zero. 
A total of three different runs of the classic VBGF 
were tested: one including all individuals (sex deter¬ 
mined and sex undetermined), one run for the combi¬ 
nation (total) of males and females and one run for 
each sex to investigate possible differences in growth 
patterns between male and female picarel. Model pa¬ 
rameters were estimated by using the nonlinear least 
squares method fitted to the mean observed lengths- 
at-age (age in monthly units). In addition, the season¬ 
al (oscillating) VBGF (Pauly and Gaschutz 3 ) was also 
implemented in order to investigate a discontinuous 
growth pattern: 
L t = {l - exp - [K(t -t 0 )- ((^f-)sin(27iU - t s ))]}, (2) 
where C = the amplitude of the growth oscillation; and 
3 Pauly, D., and G. Gaschutz. 1979. A simple method for 
fitting oscillating length growth data, with a program for 
pocket calculators. ICES Council Meeting (C.M.) Docu¬ 
ments 1979/G:24, 26 p. 
ts - “summer point,” the beginning of the sinusoid 
growth oscillation with respect to t=0 and 
corresponds with the time of year when 
growth rate is highest and is related to the 
winter point ( tw ) by ts+0.5-tw. 
In all cases residual diagnostic plots and histograms 
showed that models fitted the data appropriately. It 
should be noted that for many species from the Medi¬ 
terranean Sea, the growth of young fish is very rapid 
(Caddy, 1989a, 1989b); therefore, the mean lengths-at- 
age have to be expressed over time intervals of less 
than 1 year, as was done in the present study. This ap¬ 
proach forces the growth curve close to the origin and 
provides a better data fit. Assuming 1 April as a con¬ 
ventional birthdate, we then expressed age in months. 
According to Allsop and West (2003a), length and 
age at sex change is the length or age at which 50% 
of the population are the second sex (male for protogy- 
nous fish, female for protandrous fish), and estimates 
of this value are based on the proportion of the num¬ 
ber of males in relation to the number of males and 
females either per length or per age. Dichotomous sex 
data (0:female; l:male) were modeled as a function of 
TL and age by using generalized linear models (GLM) 
with a binomial error distribution and a logit link. The 
analysis led to estimates of length and age at median 
(50%) female-to-male sex change (L 50 and A 50 , respec¬ 
tively). Standard errors for the L 50 and A 50 estimates 
were calculated by using the delta method. 
