Nonparametric quantile regression captures regional variability and scaling deviations in Atlantic surfclam length-weight relationships

Abstract

The universality of the allometric model for describing the length-weight relationship in marine species has been questioned, particularly for some invertebrates such as sea urchins, clams, and barnacles. In such cases, nonparametric regression models may offer improved flexibility and capture specific patterns-such as inflection points in growth curves-not identified by standard parametric models. These features can support the identification of biologically meaningful thresholds relevant to fisheries, including size-dependent yield. Nonparametric quantile regression further enhances inference by characterizing variability across the entire distribution of body condition. Here, we assess the comparative performance of parametric and nonparametric regression models for the Atlantic surfclam, Spisula solidissima, using data collected from three regions along the U.S. Atlantic coast (Virginia, Delaware/Maryland, and New Jersey). First, we compare two mean regression approaches -a classic allometric model and a kernel-based nonparametric alternative- using a bootstrap-based procedure. Second, we apply quantile regression to both parametric and nonparametric frameworks to investigate size-dependent variation in growth patterns. Model selection for mean regressions was based on a hypothesis test contrasting the allometric model versus a general nonparametric alternative, while the quantile regressions were evaluated using a goodness-of-fit test derived from the cumulative sum of the gradient vector. Our results indicate that the allometric model provides a better fit in the mean regression context, while the nonparametric model proves more effective for quantile regression, particularly in detecting condition-dependent deviations and regional variability. Other long-lived marine bivalves, such as Arctica islandica and Mercenaria mercenaria, which show environmentally driven variation in growth and condition, may similarly benefit from modeling approaches that distinguish central from marginal populations.