An indirect approach to estimate spawning fraction as applied to Sardinops sagax from northern Chile

The spawning fraction of fishes with multiple spawnings and indeterminate fecundity is normally estimated through biologically intensive and time-consuming histological procedures, such as the one based on the proportion of females with post-ovulatory follicles of 1 day of age. Alternative methods based on macroscopic observations of the gonads are desirable. We conceptualize the spawning fraction as an area under a normal distribution of females classified according to oocyte diameters in the more advanced batch. The area depends on the value of two parameters of the normal distribution (mean and standard deviation) and the diameter at which the oocytes start hydration, when they are ready to be spawned. This conceptualisation was applied to Sardinops sagax of northern Chile, for which additional knowledge allowed us to reduce the problem to specifying a single property of the normal distribution: the standard deviation. Calibration of the area under the normal curve against the spawning fraction derived from histological information yielded a calibrated standard deviation parameter in a monthly series spanning one year. This parameter in turn was statistically related to the gonadosomatic index, as a relative measure of gonadic development which is easy to obtain for any given fish population. Furthermore, the gonadosomatic index was shown to be a proper description of size-standardized gonadic development. The equation relating this index and the standard deviation was then used to predict the spawning fraction which was in close proximity to the histologically-derived spawning fraction. Through this approach the gonadosomatic index can be used for years in which no histological information is available, providing an indirect way to obtain the spawning fraction when a time series of the index is available.