Modeling the growth of the Chilean loco, Concholepas concholepas (Bruguiere, 1789) using a modified Gompertz-type function

A modified Gompertz-type function was fitted by nonlinear numerical methods to the absolute growth rates(mm/day) of the marine gastropod Concholepas c oncholepas, known in Chile as "loco." The data for this study were obtained from laboratory and field experiments as well as from published and unpubl ished reports of loco growth. The fit of the modified Gompertz-type functio n was compared to the fit obtained with the commonly used von Bertalanffy f unction using the Akaike information criteria corrected by sample size bias (AIC(c)). The modified Gompertz function used in this study was dL/dt = (a (0)L(a1))*(exp(-a2L)) + a(3), where L is the peristomal length (mm), and a( 0), a(1), a(2) and a(3) are the parameters of the model. The biological mea ning of the constant a. of the function is equivalent to the asymptotic gro wth rate for the species. The von Bertalanffy growth rate equation can be e xpressed as dL/dt = - k (L-infinity - L). This equation represents a straig ht line with a negative slope equal to -k and with the y-axis intercept dL/ dt = 0, providing an estimate of L-infinity The fitted parameters obtained by fitting a modified Gompertz-type of model to the pooled growth rate data were a(0) = 2.9300e-05, a(1) = 4.2605, a(2) = 0.2011, and a(3) = 0.02852 w ith a degree of freedom corrected r(2) = 0.595. For the von Bertalanffy fun ction the fitted parameters were k = 5.943e-04 (day(-1)) and L, = 150.6 min with r(2) = 0.387. The AlCc of the Gompertz fit was -6,086; whereas, the A ICe of the von Bertalanffy fit was -5,611. The smaller AIC, value -6,086 in dicates that the modified Gompertz function provides a better fit to the lo co growth rate data. The form of the projected modified Gompertz-type growt h curve differs notably from the traditional von Bertalanffy curve for juve nile growth. The modified Gompertz model does not reach an asymptotic growt h level, predicting instead infinite growth, This latter property could eas ily explain reported historical findings of loco individuals measuring over 170 mm in peristomal length.