Natural mortality and life history stage duration of Pacific sardine (Sardinops caeruleus) based on gnomonic time divisions

Natural mortality of three commercial penaeid shrimps (<em>Litopenaeus vannamei, L. stylirostris</em> and <em>Farfantepenaeus californiensis</em>) of the Gulf of California using gnomonic time divisions

“…In this study, the gnomonic interval model (Caddy 1996, Martínez-Aguilar et al 2005) was used to calculate the natural mortality values, M, for each life history stage in three penaeid shrimp species of the southern Gulf of California. The estimation of M for each gnomonic time interval requires the definition of the number of developmental stages during the life span of a species (Table 1); the duration of the first stage, which corresponds to the first gnomonic time interval, in this case the egg stage (Table 3); the mean lifetime fecundity (MLF) of each species (Table 2); and the individual durations of the life stages, which are used to calibrate the estimates (Table 4).…”

“…The typical lifespan of the penaeid shrimp is a year, so t n =∑ n i=1 ∆ i =365 days. Martínez-Aguilar et al (2005) also proposed the inclusion of the durations of the observed life stages as auxiliary information to fit estimates of M-at-age or M i to real data. This information is grouped to gradually obtain the best fit for the number and duration of the life stages estimated in the model, and the groupings are based on the biological characteristics of the life history stages, such as the respective habitats and predators.…”

“…Thus, the parameters α and G are calculated using Newton's algorithm (Martínez-Aguilar et al 2005), in which the values are selected when the sum of the life stage durations is equal (t n *G). Under the assumption of "stable population replacement", N i in the last gnomonic interval is equal to two (i.e.…”

“…The assumption of a constant M-value can be addressed by applying the gnomonic interval model proposed by Caddy (1991Caddy ( , 1996 and later expanded and improved by Martínez-Aguilar et al (2005). The gnomonic model has been applied to short-lived species such as squids, Loligo forbesi and L. vulgaris of the English Channel (Royer et al 2002) and Dosidicus gigas of the Gulf of California (Martínez-Aguilar et al 2010), and to penaeid shrimps, Farfantepenaeus duorarum and F. californiensis of the Gulf of Mexico and the Gulf of California, respectively (Ramírez-Rodríguez andArreguín-Sánchez 2003, García-Borbón 2009).…”

“…The gnomonic model has been applied to short-lived species such as squids, Loligo forbesi and L. vulgaris of the English Channel (Royer et al 2002) and Dosidicus gigas of the Gulf of California (Martínez-Aguilar et al 2010), and to penaeid shrimps, Farfantepenaeus duorarum and F. californiensis of the Gulf of Mexico and the Gulf of California, respectively (Ramírez-Rodríguez andArreguín-Sánchez 2003, García-Borbón 2009). Additionally, the model has been applied to some fish species, including the pacific sardine Sardinops caeruleus (Martínez-Aguilar et al 2005) and the red grouper Epinephelus morio, of the Gulf of Mexico (Giménez-Hurtado et al 2009). …”