Which are better, random or systematic acoustic surveys? A simulation using North Sea herring as an example

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This paper considers the design of acoustic surveys for estimating the mean abundance of spatially correlated populations. We examined how the choice of survey design affects the bias and precision of the sample mean as an estimator of mean abundance. Further, we investigated three different ways of estimating the error variance of the sample mean: the pooled within strata variance and two geostatistical variance estimators based on spherical and exponential models. First, we analysed four surveys to determine the spatial structure of the North Sea herring population. We developed forty different population models based on the observed amplitude and spatial distribution. We generated 1000 realizations of each model, each comprising 4000 potential transect means. Each realization was sub-sampled using eight different sampling strategies. From each realization and sampling strategy, we calculated the sample mean and three estimates of the variance of the sample mean. The simulations show that, for surfaces with local positive correlation, more precise estimates of the surface mean can be obtained using stratified random or systematic sampling than simple random sampling. The best strategy considered here was (a) a systematic survey with a geostatistical variance estimator, when the main objective is to obtain the most precise estimator of abundance, (b) a stratified random survey, with two transects per strata, and a pooled variance estimator, when an important objective of the survey is to obtain a good estimate of the variance of the abundance estimator.