ZEPEDA-BENITEZ ET AL.: AGE AND GROWTH MODELLING FOR EARLY STAGES OF THE JUMBO SQUID DOSIDICUS GIGAS CalCOFI Rep., Vol. 55, 2014 AGE AND GROWTH MODELLING FOR EARLY STAGES OF THE JUMBO SQUID DOSIDICUS GIGAS USING MULTI-MODEL INFERENCE VIRIDIANA Y. ZEPEDA-BENITEZ, CASIMIRO QUIÑONEZ-VELÁZQUEZ Centro de Investigaciones Biológicas del Noroeste (CIBNOR) Instituto Politécnico Nacional Instituto Politécnico Nacional 195 Centro Interdisciplinario de Ciencias Marinas (CICIMAR) Col. Playa Palo de Santa Rita Sur Av. Instituto Politécnico Nacional s/n La Paz, B.C.S. 23096, México Col. Playa Palo de Santa Rita Sur La Paz, B.C.S. 23096, México ENRIQUE MORALES-BOJÓRQUEZ Centro de Investigaciones Biológicas del Noroeste (CIBNOR) CÉSAR A. SALINAS-ZAVALA Instituto Politécnico Nacional 195 Centro de Investigaciones Biológicas del Noroeste (CIBNOR) Col. Playa Palo de Santa Rita Sur Instituto Politécnico Nacional 195 La Paz, B.C.S. 23096, México Col. Playa Palo de Santa Rita Sur ph: +52 (612) 123 8484; fax: + 52 (612) 125 3625 La Paz, B.C.S. 23096, México [email protected] ABSTRACT life stages of D. gigas can be used to assess important Age and growth were estimated for early growth factors regulating survival, as well as recruitment suc- stages of the jumbo squid Dosidicus gigas in the Gulf of cess (Boyle and Rodhouse 2005), it is defined as the California, based on daily growth increments in stato- number of individuals that reach a specified stage of liths. Three individual growth functions that showed the life cycle (e.g., metamorphosis, settlement, selected non-asymptotic patterns (two cases of the Schnute gen- by the fishery). The scarcity of information on age and eral model, and Tanaka model) were fitted to length- growth of early life stages of D. gigas is presently an at-age data. Using Akaike’s Information Criterion and impediment to describing spawning locations, hatch multi-model inference, we selected the best model to dates, and transport from offshore to recruitment areas describe the growth pattern. We found that the Schnute (advection), and availability for the fishing fleets in the general model was the best growth function describing Gulf of California. mantle length-at-age data for paralarvae and juveniles of Growth rates are critical to survival of paralarvae, as D. gigas, showing a power pattern. Absolute daily growth well as the dynamics of recruitment (Vidal et al. 2005). rate ranged from 0.03 to 1.66 mm day–1, with lower val- In general, if squid have several phases of early devel- ues for paralarvae and higher values for juveniles. opment or the number and duration of stages are large, then natural mortality increases. According to Nesis INTRODUCTION 1979, the limits of these phases or stages are defined by Dosidicus gigas is the most abundant commercial squid body size, and not the age at which the change hap- in the central Gulf of California. Although the fishing pens. For example, the cephalopod Spirula spirula has activity is well known in this area, life-history param- a single discontinuity in growth of its mantle, arms, eters of D. gigas have not been fully assessed and are tentacles, and fins. The discontinuity is characterized critical for understanding squid biology, as well as for by morphological changes expressed through relative proper management through stock assessment modelling growth (Nesis 1979). These changes correspond to the (Morales-Bojórquez et al. 2001; Morales-Bojórquez and transition from paralarval to juvenile phase (Clarke Nevárez-Martínez 2010). Thus, knowledge of D. gigas 1966). For the short fin squidIllex argentinus, the first has been limited to fishery-dependent data, and sev- discontinuity in growth coincides with the transition eral aspects of recruits and adult squid population. In from the paralarval to juvenile phase, which occurs contrast, little is known about the demography of the in a narrow range of 14–17 mm ML (Vidal 1994). paralarvae of D. gigas, and how their parameters vary spa- Between 25 and 35 days the larval growth rate of Sthe- tially and seasonally in the Gulf of California, although noteuthis pteropus shows a decreasing trend when the recent information about this issue has been reported by species changes from larvae to juvenile (Laptikhovsky Camarillo-Coop et al. 2010, 2013; and Rosa et al. 2013. et al. 1993). Vidal 1994 explained that, to be efficient Rapid growth appears to enhance survival of paralar- predators, rhynchoteuthions must be good swimmers. vae due to high predation during the early life stages Fast growth and slendering of the body is a result of (Boyle and Rodhouse 2005). Studies have suggested relatively slow growth of mantle weight, which causes that individuals that grow rapidly and achieve a larger the loss of the spherical shape and favors the develop- body size spend less time in the most vulnerable early ment of the cylindrical shape, which increases the effi- life stages (Cushing 1982). Understanding the factors ciency of jet propulsion. Paralarval growth in length responsible for differences in growth during the early of Ommastrephes bartramii is typically described by an 197 ZEPEDA-BENITEZ ET AL.: AGE AND GROWTH MODELLING FOR EARLY STAGES OF THE JUMBO SQUID DOSIDICUS GIGAS CalCOFI Rep., Vol. 55, 2014 Figure 1. Study area in the central Gulf of California, Mexico. Sampling sites Figure 2. Microstructure of a statolith of a juvenile (18.6 mm ML) of of two field surveys are shown. Dosidicus gigas. exponential equation (Bigelow and Landgraf 1993). mesh bongo net (Diekmann and Piatkowski 2002) and Arkhipkin 2004 analyzed the diversity in growth of juveniles with a dipnet. A total of 12 paralarvae and 93 squids (suborder Oegopsina), reporting that the tropi- juveniles were fixed in 95% ethanol. Measurements of cal species show non-asymptotic growth in comparison mantle length (ML) and body weight (BW) were taken to polar and deepwater species where the asymptotic to the near est 0.01 mm and 0.1 g, respectively. Statoliths growth is commonly observed. Fast growth has clear from each specimen were extracted and stored in 95% benefits in allowing paralarvae to pass more quickly ethanol for age determination. Sizes ranged from 2.8 to through its most vulnerable life history stages and to 67.8 mm ML; the most com mon size frequency interval develop faster physically and physiologically in order was identified as a mode at 24–26 mm ML. to improve its ability to detect and capture prey, as well as predator avoidance and resistance to environmental Statolith reading variability (Bigelow 1992). The statoliths were mounted on microscopic slides Fishery management and conservation of D. gigas in for reading growth increments on the dorsal dome based the Gulf of California is very important. Lack of basic on the Arkhipkin method (Dawe and Natsukari 1991). biological information of early stages of D. gigas reduces For juveniles, the statoliths were ground and polished, our understanding of the population dynamics of recruits since in this development stage the concave and convex and adult stock (Camarillo-Coop et al. 2010, 2013; regions of statolith are not well developed. Consequently, Zepeda-Benitez et al. in press). In this study an appro- any side can be used for grinding in juveniles. González priate growth model was identified to fit length-at-age et al. 2010 explained that for paralarvae (Loligo vulgaris) data for early stages of D. gigas in the Gulf of California the concave and convex surfaces must be ground. The based on multi-model inferences and generalized growth procedure is not clearly defined; however both tech- models. The implications of these growth models, as well niques allow the observation of growth lines. Paralarvae as the choice of models, are discussed in relation to the statoliths required only polishing. Increment counting new population biology of early stages of D. gigas. started at the nucleus and proceeded to the edge of the dorsal dome. Counts were carried out independently MATERIAL AND METHODS by two readers where they read the increments with transmitted light at 400× (fig. 2). Each increment was Squid sampling data collection assumed to be deposited daily, as has been determined Two research surveys on board the RV New Horizon to occur for other squid of the family Ommastrephidae were conducted in the central Gulf of California in June (Dawe et al. 1985; Nakamura and Sakurai 1991). The age 2006 and June 2007 (fig. 1). Samples of the early life of each individual was defined to be the average of the stages of D. gigas were collected in the Guaymas and del two independent counts. The index of average percent- Carmen Basins; paralarvae were captured with a 500 µm age error (IAPE) and coefficient of variation (CV) were 198 ZEPEDA-BENITEZ ET AL.: AGE AND GROWTH MODELLING FOR EARLY STAGES OF THE JUMBO SQUID DOSIDICUS GIGAS CalCOFI Rep., Vol. 55, 2014 The parameters were estimated by maximizing the nega- tive log-likelihood estimator (Hilborn and Mangel 1997) using the Newton algorithm (Neter et al. 1996). For the standard deviation (σ), the analytical solution is: n 1 ˆ 2 σ = n ∑ [ln L(t) – LnL(t)] √ t = 1 where n is the number of ages observed in the early stages of D. gigas. Confidence intervals were estimated using the bootstrap method described by Fournier and Archibald 1982. Model selection We compared the fits of the different candidate growth models using Akaike’s information criterion (AIC) (Burnham and Anderson 2002). The small-sample AICc was determined as follows: 2 × θi (θi + 1) , AICc = 2× – ln L(θi|data) + 2 × θi + n – θi – 1 where θi is the number of estimated parameters, n is the number of observations, and –ln L(θi|data) is the objective function for each candidate growth model.