Faunce et al.: Age, growth, and mortality of Cichlasoma urophthalmus 



45 



To increase the number of observations used for 

 fitting the prowtli model, we back-calculated past 

 size-al-age information for each sexed fish using 

 the Fraser-Lee melh(ul lollowing Devries and Frie 

 (1996); 



L, =[(L,, -a)/S,]S, +a, 



where L, = the back-calculated length of fish when 

 the /"' increment was formed; 

 L^ = the length of fish at capture; 

 S^ = the otolith radius at capture; and 

 S, = the otolith radius at the ;''' increment. 



The slope, {L^-a)IS^. was calculated for each fish as 

 the slope of a line connecting two points: (S^ , L, ) and 

 (0, a). The \'-intercept parameter a was determined 

 from the relationship between otolith radius and 

 standard length for all fish, and should approximate 

 the fish length at which otolith radius equals zero 

 (Devries and Frie, 1996). Because we could not accu- 

 rately determine the sex of each fish <70 mm. fish 

 whose sex could not be determined were included in 

 the fitting of both male and female growth cui-ves. 



Catch cui-\'es were analyzed with two methods to 

 determine annual mortality rates for Mayan cichlids. 

 Sun'ival rate (S) and its respective variance were es- 

 timated by using the empirical abundance data (Rob- 

 son and Chapman, 1961) and the regression of the 

 natural logarithm of year-class abundance (Ricker, 

 1975). The instantaneous rate of mortality (Z) was 

 derived from the relationship Z=-ln(e^). Total annual 

 mortality (A) was computed as A = 1-S. The age at 

 full recruitment to the hook-and-line gear based on 

 our catch cur\'e was determined to be four years. 



Results 



The fragile nature of Mayan cichlid otoliths caused 

 a high proportion (54'f ) to be lost during the cutting 

 process. However, only five of the 391 successfully 

 sectioned otoliths were discarded because a consen- 

 sus between readers could not be reached. A newly formed 

 opaque ring was generally obsei'V'ed in fish captured Jan- 

 uary-May, and the mean monthly marginal increment 

 reached a single yearly minimum in June for all age 

 classes examined (Fig. 3). These data indicate that the 

 opaque rings observed were annuli. 



The growth of young-of-year Mayan cichlids collected 

 with drop traps could be followed by the progression of 

 modal length from monthly length frequencies. Newly re- 

 cruited fish were present in August (mode=10 mm) and 

 grew to a size of 50 mm by June (Fig. 4). An early spawn- 

 ing event in 1993 (senior author, unpubl. data) produced 

 a smaller-size (20 mm) cohort that was obsen'ed in June. 

 Fish with one annulus were much larger (50-149 mm, 

 mean=97 mm) than the size of age-1 fish suggested from 

 our drop-trap data (June mode=50 mm). This information, 

 combined with the presence of marks in the inner region 



All individuals 



Figure 3 



Monthly mean marginal increment and range for all Mayan cich- 

 lids and pooled age classes 1-3 and 4-7. Note the consistent 

 annual minimum in June. Numbers indicate sample size. 



of the otolith, led us to conclude that the first annulus in 

 our age estimations was laid down between January and 

 May of the fish's second year of growth, and we added a 

 year to each individual's total age. 



Length-length and length-weight relationships are giv- 

 en in Table 1. As i-equired by the Fraser-Lee method 

 for back-calculation of size-at-age information, otolith ra- 

 dius and standard length were closely related (SL=131.2x 

 0R+A.Q2A1, n=37l, r^=0.80). Analysis of covariance did 

 not detect differences between the slopes of length-weight 

 relationships for males and females (F, y.j(,=0.15, P=0.696) 

 but did reveal significant differences between the re- 

 spective intercepts for males and females (F, g3g=4.10, 

 P=0.043). 



The length of Mayan cichlids at a given age was mod- 

 eled by the von Bertalanffy growth equation (Fig. 5). Pre- 

 dicted lengths fitted well with the final adjusted observed 



