A Simulation Study to Evaluate Biases in Population Characteristics Estimation Associated with Varying Bin Numbers in Size‐Based Age Subsampling

Abstract

In temperate waters, growth and mortality of bony fishes are frequently estimated from age information derived from the examination of annular rings on hard structures (e.g., otoliths). However, determining ages from hard structures can be time consuming, often requires sacrificing fish, and has associated costs for supplies and personnel time in processing or reading structures. Subsampling based on a target number of fish per length bin is commonly used to reduce time and costs but may introduce biases into the estimation of population characteristics. We wanted to understand how interactive effects of bin width, gear selectivity, and length‐at‐age variability influence the estimation of growth parameters, total instantaneous mortality (Z), and age frequency. We developed a simulation model to generate populations under the assumption that growth followed the von Bertalanffy growth model; we then sampled from those populations for age analysis based on no gear selectivity, dome‐shaped selectivity, and logistic selectivity. Furthermore, we wanted to determine whether observed biases could be corrected by using a weighting procedure during growth model fitting. Fifteen subsampling schemes were evaluated, with five different length bin widths and three target subsample sizes for each bin (subsampling levels). Gear selectivity, variability in length at age, and estimation procedures had a greater and more predictable influence on growth parameters than bin widths for size‐based subsampling. Dome‐shaped gear selectivity was associated with biases in growth parameter and Z estimation. Weighted regression based on weighting factors calculated from the original sample's length frequency generally improved the consistency of growth parameter estimates among subsampling schemes but did not always improve accuracy. No bin widths or subsample sizes were clearly superior across modeled scenarios. Consequently, alteration of bin widths seems less useful in reducing biases than using alternative estimation methods for population characteristics of interest and considering other external factors.

Climate Change May Cause Shifts in Growth and Instantaneous Natural Mortality of American Shad Throughout Their Native Range

“…For age‐classes in which the number of fish was fewer than 1,000 individuals, all data were used. Age‐based subsampling was recently demonstrated to be unbiased (Goodyear 2019), but neither that study nor the present study evaluated this assumption relative to gear selectivity, although this can be an important consideration (Hilling et al 2020). Therefore, we also ran models with subsamples of 10 and 100 fish per system per year to confirm that this choice did not arbitrarily influence model selection or statistical inference.…”

“…First, we assumed that the wide range of gears and methods used for fish collection were representative of these populations through time. Importantly, it has been demonstrated that gear selectivity can influence estimated VBGF parameters (Gwinn et al 2010) and in some instances can even override attempts to correct this through size-based subsampling within gears (Hilling et al 2020). Through inclusion of multiple gears and collection, our intention was to minimize the potential for bias from any given gear.…”

Evaluating the Performance of Methods Used to Estimate Growth Parameters from Subsampled Age Data

“…Importantly, the aged subsample is not a random sample of either the entire sample or the population, as these data are collected according to a fixed number of individuals per length‐group. Using a length‐stratified aged subsample without incorporating information from the entire sample has the potential to drastically bias growth estimates and should not be used to directly evaluate growth (Chang et al 2019; Goodyear 2019; Hilling et al 2020; Perreault et al 2020). Evaluating growth with length‐stratified subsampled age data should employ a method to “expand” those data to the entire sample such that estimation uses information from all fish collected (i.e., account for the length‐stratified sampling design).…”

“…The reweighting method of Chih (2009) estimates growth parameters by fitting the VBGM to length–age data in the aged subsample, where each observation is weighted by the ratio of the proportion of fish from the entire sample that belong to the fish’s length‐bin to the proportion of fish from the aged subsample that belong to the fish’s length‐bin. Hilling et al (2020) found that the reweighting method accurately estimated growth parameters for the population in some cases but performed poorly in other cases (e.g., with dome‐shaped selectivity when extracting the entire sample from the population). Perreault et al (2020), expanding on the work of Zhang and Cadigan (2019), described several methods for estimating growth that were based on the statistical theory of double sampling.…”

“…Goodyear (2019) evaluated five experimental sampling designs and showed that some designs, such as increasing effort to increase the number of individuals in larger length‐bins, could exacerbate biases. Hilling et al (2020) examined the effects of varying length‐bin width and subsample size when evaluating growth and found that no combination of bin width or sample size was superior in reducing bias. These papers focused on how growth estimates derived from the aged subsample estimated the true growth parameters of the population.…”