Nota de investigación

 

Preliminary estimation of optimal sample size for assessing the recruitment of Mesodesma donacium (Lamarck, 1818) on beaches of central-north Chile: Application of the power analysis

 

Estimación preliminar del número óptimo de muestras para la evaluación del reclutamiento en Mesodesma donacium (Lamarck, 1818) en playas del centro-norte de Chile: Aplicación del análisis de poder

 

Marco A. Ortiz^1* and Wolfgang B. Stotz²

 

¹ Instituto de Investigaciones Oceanológicas, Facultad de Recursos del Mar. Universidad de Antofagasta, Casilla 170, Antofagasta, Chile. *E-mail: mortiz@uantof.cl

² Universidad Católica del Norte, Grupo de Ecología y Manejo de Recursos, Larrondo 1281, Casilla 117, Coquimbo, Chile.

 

Recibido en febrero de 2002;
aceptado en marzo de 2003.

 

Abstract

This work presents a preliminary study to estimate the optimal sample size for the assessment of recruitment of Mesodesma donacium, an important bivalve that supports an intensive fishery in the most important bays of northern Chile. The specific objective was to assess the influence of the cusps (bays and horns) on the abundance of early recruits (< 15 mm shell length) of M. donacium and to include this effect on the sampling program. The bays and horns produced a difference (noise) of ca 20% in the density estimation, which was supported by the low statistical power calculated (0.20, 0.25 and 0.30 for November, December and March, respectively). Based on these results, we suggest that the assessment of the recruitment of M. donacium requires a sampling which comprises both bays and horns in intermediate beaches of northern Chile. Based on the effect size estimated of ca 0.41 for the three study periods, 80 corers must be taken from bays as well as from horns as a preliminary sample size strategy. The a priori statistical power analysis is one of the most useful strategies for the estimation of optimum sample size when the goal is to assess any working hypothesis.

Key words: Mesodesma, recruitment, intermediate beaches, statistical power analysis, effect size.

 

Resumen

El presente trabajo es un estudio preliminar dirigido hacia la estimación del tamaño óptimo del número de muestras para la evaluación de la magnitud del reclutamiento del bivalvo Mesodesma donacium, un importante recurso pesquero en las más importantes bahías del norte de Chile. El objetivo específico fue evaluar el efecto que ejercen los valles y cúspides (típicos de playas tipo intermedias) en la abundancia de reclutas (< 15 mm de longitud anteroposterior de concha) de M. donacium y, consecuentemente, incluir este efecto en la definición de un programa óptimo de muestreo para estimar la abundancia del reclutamiento en esta especie. Los valles y cúspides produjeron una diferencia (ruido) de alrededor de 20% en la estimación de densidad, lo cual es apoyado por el bajo poder estadístico calculado (0.20, 0.25 y 0.30 para noviembre, diciembre y marzo, respectivamente). Basados en estos resultados, se sugiere que la evaluación de la abundancia en el reclutamiento de M. donacium requiere un programa de muestreo que incluya los valles y cúspides típicos de las playas intermedias del norte de Chile. Basados en el tamaño de efecto calculado (0.41 aproximadamente) para los tres periodos de estudio, en una estrategia preliminar de muestreo deberían ser consideradas 80 muestras, tomadas tanto en valles como en cúspides (160 en total). El análisis de poder estadístico a priori es una de las estrategias más útiles para la estimación del número óptimo de muestras cuando el objetivo es evaluar alguna hipótesis de trabajo con la mayor rebustez.

Palabras clave: Mesodesma, reclutamiento, playas intermedias, análisis de poder estadístico, tamaño del efecto.

 

Introduction

The variability and intensity of settlement and recruitment, both spatially and temporally, is important information for developing fishery strategies on exploited invertebrate species in intertidal and subtidal marine ecosystems (Hughes and Bourne, 1981; Underwood and Fairweather, 1989; Stotz et al., 1991). Moreover, recruitment is the most important factor for increasing adult abundance (Young et al., 1996). Thus, many studies have aimed to assess the impact of variation in both settlement and recruitment upon the population size and how the community structure is affected (e.g., Underwood and Denley, 1984; Connell, 1985; Menge and Sutherland, 1987; Raimondi, 1990; Robles, 1997; Comtet and Desbruyères, 1998; Smith and Witman, 1999).

The increase during the last decades in Chilean shellfish landings from intertidal and subtidal ecosystems has resulted in the overexploitation of many species (Bustamante and Castilla, 1987). The surf clam Mesodesma donacium (macha), which inhabits many sandy beaches of northern, central and southern Chile (Jaramillo, 1987), is an example of intense exploitation (Anonymous, 1980, 1997). This situation represents not only an ecological problem but also an important social one, because many artisanal fisheries of northern Chile are highly dependent on this species. In an intensive study of latitudinal and bathymetrical distribution of early settled juveniles of M. donacium (recruits < 15 mm maximum shell length) in the most important bays of the Region of Coquimbo (northern Chile), Ortiz and Stotz (1996) found that the density of recruits showed a periodic fluctuation along the beaches in Coquimbo, Guanaqueros and Tongoy Bay. Therefore, the objective of the present study is to estimate the optimal sample size (sampling program) for the assessment of recruitment in M. donacium, including the putative dependence of the periodic fluctuation of the juveniles on bays and horns along the beaches. These places may provide a continuous food supply for the recruits by the concentration of surf diatoms (Donn et al., 1986; Brown and McLachlan, 1990). In this work we define "recruits" as recently settled individuals that have survived to 15 mm length.

 

Materials and methods

The study was carried out in Tongoy Bay (30°150' S, 71°31' W), Region of Coquimbo (Chile). Tongoy Bay is protected from prevailing southwest winds by the Lengua de Vaca peninsula (Berrios et al., 1985). Ortiz and Stotz (1996) classified all beaches of the bay as intermediate morphody-namic types, characterized by fine to medium sands and surf zones with rip currents, bars, troughs and cusps (Brown and McLachlan, 1990). Cusps are undulations along the beach that break the beach face into a series of bays and horns (McLachlan and Hesp, 1984). Three samplings were carried out on 17 November and 18 December 1995, and 20 March 1996, to evaluate the effect of the beach topography (bays vs horns) upon the abundance of recently settled recruits (< 15 mm) of M. donacium. Nine, twelve and sixteen bays and horns sites were randomly chosen in November, December and March, respectively. One sample per site was taken at low tide from the mid-littoral zone between 0 and 1.0 m depth, using a 2.4-dm³ corer (buried ca 10 cm). That depth was reported to have the highest abundance of recruits (Ortiz and Stotz, 1996). The spawning period of M. donacium occurs between October and April (Peredo et al., 1987; Fuentes, 1988).

The Bartlett and Hartley tests were used to evaluate the normality of data. The F-ratio and Cochran tests were used to evaluate the heterogeneity of variances (Underwood, 1981, 1997). When non-normality and heterogeneity were significant (α < 0.005), the logarithmic transformation (log₁₀) was applied (Sokal and Rohlf, 1995; Underwood, 1981, 1997). The low type I error (α) was considered because the parametric tests are robust with non-normality of data and non-severe heterogeneity of variance (Box, 1953; Tiku et al., 1986; Underwood, 1997). Non-paired Student's t-tests (α < 0.05) were used to assess the significance between average recruit densities in bays and horns in each study period (Underwood, 1981, 1997). The statistical power analysis of the t-test was also estimated with α = 0.05 (Cohen, 1988). Through the power analysis and based on our results it was possible to estimate the optimal sample size to assess the recruitment of M. donacium in intermediate beaches.

 

Results and discussion

No significant differences were detected between the mean abundance of recruits in bays and horns during each study period (t-test, P = 0.41, P = 0.33 and P = 0.29); nevertheless, both produce a relevant difference (noise) of ca 20% in the estimations of recruit density (fig. 1). This noise is supported by the lower statistical power calculated of 0.20, 0.25 and 0.30 for November, December and March, respectively (fig. 1). Even though the t-tests applied were unable to reject H₀ (no difference in abundance of recruits in bays and horns), the higher level of type II error calculated for each period suggests that the bays and horns could have an effect on the abundance of recruitment of M. donacium. The similarity of the effect size values (~0.41) in the three study periods, despite the increase in the total number of samples from 9 to 16, suggests that in nature a real effect would exist (bays and horns affecting the density of recruits). Considering an effect size of ca 0.41 as realistic, an α = 0.05 and a power of 0.80, which is usually defined as minimally acceptable (Cohen, 1988; Peterman, 1990; Peterman and M'Gonigle, 1992; Underwood, 1981, 1997), the optimal sample size would be 80 corers taken from bays as well as from horns (160 in total). Even though the sample size for the period of time used in this work could be considered limited to assess any ecological hypothesis, it was sufficient for a preliminary study whose goal was to estimate the optimum sample size based on the power analysis. This strategy corresponds to the typical a priori case of power analysis (see Cohen, 1988; Peterman, 1990; Underwood, 1997; Ortiz, 2002). Eighty corers per bays and per horns (160 in total) undoubtedly would improve the accuracy, precision and variability of the estimates. Even though this number of samples is not excessively large, further field experiments must be conducted taking into account the aggregated distribution of recruits in the sampling design, before establishing a definite methodology to assess the recruitment of M. donacium. The estimation of optimum sample size through the statistical power analysis is one of the most robust strategies for that, because it relates the working hypothesis to the statistical test and reliability of the sampling design (Cohen, 1988; Peterman, 1990; Underwood, 1997; Ortiz, 2002).

 

Acknowledgements

This study was supported by funds from WWF (project director Wolfgang Stotz). We thank Eduardo Jaramillo, Carlos Jiménez and Sandra Jesse for their valuable comments and suggestions.

 

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