In fisheries management, the L50 is a commonly-monitored reproductive trait reflecting the sex-specific length (L) at which 50% of the fish are expected to exhibit developing gonads near the spawning period. Although different methods exist to estimate the L50, it is often obtained from a binomial generalized linear model (GLM) fitted with a logit link. To provide reliable parameter estimates for the production of the ogive from which the L50 is obtained, the logit link must be correctly specified, a prerequisite that is not always verified nor true. To identify the most-likely ogive, adequacy tests allowing to detect a lack-of-fit or any link misspecification should ideally be applied to competing binomial models that also consider alternative links, such as the probit and complementary log-log (cloglog). Because multiple estimates are often compared, their uncertainties should also be adequately quantified to detect any potential change, but no consensus exists about the method offering the best coverage probability. Here, we used a large-scale dataset of 23,681 walleye (Sander vitreus) females sampled in 90 harvested populations over two decades in Québec, Canada, to first estimate the L50 uncertainty under different simulation scenarios to identify the most accurate method regarding nominal coverage. Then, of 46 populations sampled in two different surveys, we assessed which link provided the best adequate estimation for each survey-specific L50 and used associated 84% CIs to determine if a change occurred based on whether they overlapped. The influence of gonad data characteristics on L50 uncertainty was also examined before assessing between-survey L50 variation with competing GLMs as an alternative approach. The analysis of the simulated data indicated that the Monte Carlo approach with bias-corrected and accelerated (BCa) interval offered the best coverage probability. The empirical analyses revealed that the probit was the most often adequate link to estimate the L50, followed by the cloglog, whereas the logit ranked last. When controlling for sample size, the level of L50 uncertainty increased with the percentage of overlap in length between walleye females with (1) and without (0) developing gonads, whereas it progressively decreased as the percentage of 1’s in the sample increased to then inversed, indicating that more balanced binary data yielded less L50 uncertainty. All analyses revealed that for a “true” or estimated effect size of ≤ 10%, the survey-specific 84% CIs often overlapped despite statistical support for a difference found in the best-supported GLM comparing both surveys. Overall, our study indicates that many analytical considerations, from gonad data structure characteristics, model adequacy assessment, up to how the L50 uncertainty is quantified and compared, need to be accounted for to achieve more reliable statistical inferences regarding the observed variation in this reproductive trait.
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