DeMartini et al.: Validated morphological metric for lobster size at maturity 



29 



Discussion 



Properties of the EL-TW model 



In order to determine morphometric maturity, we first 

 attempted to use a method developed by Watters and 

 Hobday (1998). With this method splines were used to 

 model the relationship between the morphometric char- 

 acter and body size; then the morphometric size at which 

 the second derivative of the fitted curve is maximal is 

 computed. At first this technique is alluring in that it 

 makes no allometric or other assumption as to the shape 

 of the relationship between the morphometric character 

 and body size. It instead assumes that maturation cor- 

 responds to the maximum of the second derivative. This 

 assumption is likely invalid even if we assume that the 

 relationship between the morphometric character and 

 body size changes abruptly at maturation for each indi- 

 vidual (as at the pubertal molt in crustaceans) because 

 individuals in the population mature at different sizes. 

 When we applied the Watters and Hobday method, the 

 resulting body size estimate appeared to character- 

 ize the minimum, not the median, size at attainment 

 of sexual maturity in the population and was clearly 

 inappropriate for our needs. Our method generated 

 fitted splines that were comfortingly similar in shape 

 to the parametric logistic (sigmoidal function) models 

 that we used to estimate maturation with berried and 

 histological criteria. 



The magnitude of the difference between the sizes at 

 maturity estimated by our and the Watters and Hobday 

 (1998) model should vary in proportion to the magni- 

 tude of the difference between the minimum (0 O ) and 

 median ([0 o +0j]/2) body sizes at maturity and therefore 

 be case-dependent. In our slipper lobster case, the 8 

 and l estimates differed by about 6.6 mm; hence, the 

 two model estimates differed by about 6.6/2 = 3.3 mm 

 or approximately 7% of the [{6^+6-^)12} median. Because 

 other cases certainly include those in which immature 

 and adult sizes overlap even more greatly, we suggest 

 that our more general and accurate model be adopted. 



Functional versus physiological measures of maturity 



Morphological features can provide adequate if imperfect 

 measures of functional sexual maturity, as can physi- 

 ological evidence for gonadal maturity (Ennis, 1984). 

 Morphological features such as ovigerous condition can 

 underestimate the incidence of mature individuals, but 

 the degree to which they do so depends on numerous fac- 

 tors including species and population. Physiological met- 

 rics in some cases can provide more accurate estimators 

 of both body size and age at maturity because they reveal 

 the reproductive readiness of individuals at the time 

 of collection. Individual body size and age at maturity 

 can be decoupled from functional maturity metrics in 

 Crustacea, however. For example, some crustaceans like 

 majid crabs exhibit determinate growth following a ter- 

 minal, pubertal molt (Hartnoll, 1982). For such species, 

 size at attainment of sexual maturity is synonymous 



100 



50 

 Tail width (TW, mm) 



Figure 4 



Scatterplots and fitted curves of the relations between 

 body size (tail width, TW) and percent sexual maturity 

 based on functional maturity gauged by presence-absence 

 of berried condition (dotted curve), overlaid on gonadal 

 maturation gauged by microscopic examination of ovaries 

 (dark-line curve); the pleopod length-based morphometric 

 maturation point (MMP) estimate of size at functional 

 maturity is indicated by the large circle with cross-hairs 

 (©), for slipper lobster iScyllarides squammosus). A 

 3-parameter logistic equation was necessary to fit the 

 dotted curve; a 2-parameter logistic was sufficient to 

 fit the dark-line curve (see text). 



with the median body size of adults. These two attributes 

 are not synonymous for lobsters with indeterminate 

 growth. It is further obvious that the pleopods and other 

 allometric body parts of Crustacea like lobsters reflect 

 an array of gonadal maturities ranging from developing 

 immature to fully mature, which can be problematic 

 because some or many females might abort and resorb 

 developing gonadal eggs after the pubertal molt (Aiken 

 and Waddy, 1980) or may not become inseminated (Hey- 

 dorn, 1969). By attributing maturity to specimens that 

 either have not matured physiologically or that will not 

 reproduce although capable of doing so, appendage-to- 

 body proportions can underestimate the age at maturity 

 in Crustacea. The degree of underestimation should 

 be proportional to the incidence of gonadal resorption 

 during the intermolt period following the pubertal molt, 



