Sampling Larval Fish Populations: Choice of Sample Number and Size

Abstract

The number and size of larval fish samples are usually determined arbitrarily, despite the influence of these decisions on the precision of abundance estimates and the ability to detect differences among population estimates. Review of the literature suggests that most surveys of larval fish are based on few (median, 4), large (median, 300 m 3 ) samples. To evaluate current sampling designs, we developed a model, based on published data, to predict the variance in larval fish abundance among replicate samples. Inter-replicate variance (s 2 ) is strongly related to mean abundance (*) as: log,^ = 0.19 + 1.74• log IO *; r 2 = 0.93, P < 0.0001. This relationship was tested with an extensive data set collected in the Hudson River, New York (weekly samples over 14 years in 12 regions of the 250-km-long river), and was found to be general across environments, life history stages, and species. The model was not affected by sample volume. Our analysis shows that half of published studies estimated larval abundance with a coefficient of variation of the mean (SE/J?) of 0.5 or more and could only detect order-of-magnitude differences among sites or time periods. The s 2 /* equation provides guidelines to select the number and size of samples that should be taken to achieve a required level of precision and to detect a given difference among population means.

Using variance components to estimate power in a hierarchically nested sampling design

“…Estimates of power in surveys for larval DHP were high compared to surveys for other species of larval fish (Cyr et al 1992). The higher power for surveys of DHP larvae was likely attributed to a Values were attained from ln-transformed abundance estimates of DHP larvae from mid-March to mid-May.…”

“…For instance, Cyr et al (1992) estimated that about half of the surveys that focused sampling on the early life history stages of fish had less than 80% power to detect a one order of magnitude change in the abundance of larvae. Low power in surveys for larval fish is regrettable because mortality rate of larval fishes is often high in comparison to mortality at later life history stages, thus larval fish abundance may be an important indicator of year class strength (Diana 1995;Sammons and Bettoli 1998).…”

Detecting declines in catch rates of diverse trawl bycatch species, and implications for monitoring

“…The negative binomial distribution is also highly appropriate for data that is zero inflated (Warton, 2005), having the capacity to account for excess zeros (as well as large counts) through the over dispersion parameter, φ. There are numerous examples of Poisson and negative binomial models being used in practice to estimate catch rates of fish and other species (see Smith and Richardson, 1977;Jahn and Smith, 1987;Cyr et al, 1992;Power and Moser, 1999). Consequently, we considered that these models provided an adequate framework for determining the minimum sample size requirements for each bycatch group in this study.…”

A Monte Carlo Evaluation of the Stock Synthesis Assessment Program

“…An alternative method of specifying σ 2 has its roots in the work of Curtis (1943) and Bartlett (1947), who showed that transformations to homogenize variance can be determined from the relationship between σ 2 and µ. Inasmuch as the σ 2 to µ relationship is seldom known, it is frequently inferred from regressions of s 2 on x (Green 1979, Taylor 1980, Taylor et al 1983). This practice is quite common in fisheries work because s 2 and x are often found to be highly correlated (Taylor 1953, Small and Downham 1985, Porch and Fox 1990, Lester et al 1991, Cyr et al 1992, Warwick and Clarke 1993, Welch and Ishida 1993, Dong and Restrepo 1996. However, the relationship between s 2 and x is largely spurious.…”