Estimating continuous body size-based shifts in δ15N–δ13C space using multivariate hierarchical models

Abstract

address these issues, we suggest researchers utilize multivariate hierarchical models, which are a simple extension of univariate hierarchical methods. The models account for potential dependencies between δ 15 N and δ 13 C values, permit valid predictions of shifts in δ 15 N-δ 13 C space related to predictor variables, provide more accurate estimates of parameter uncertainty, and improved inferences on coefficients that correspond to groups with small to moderate quantities of data. We demonstrate advantages of multivariate hierarchical models by examining size-dependent shifts in δ 15 N-δ 13 C space in outmigrating post-smolt Chinook salmon sampled from an estuarine habitat. Given the prevalence of complex structure in ecological stable isotope data sets, multivariate hierarchical models should hold considerable value to food web and stable isotope ecologists.

Hierarchical Bayesian modeling of contrast sensitivity functions in a within-subject design

“…Although it has been used in many different disciplines, such as astronomy ( Thrane & Talbot, 2019 ), ecology ( Reum, Hovel, & Greene, 2015 ; Wikle, 2003 ), genetics ( Storz & Beaumont, 2002 ), machine learning ( Li & Perona, 2005 ), cognitive science ( Ahn, Krawitz, Kim, Busmeyer, & Brown, 2011 ; Lee, 2006 ; Lee & Mumford, 2003 ; Merkle, Smithson, & Verkuilen, 2011 ; Molloy, Bahg, Li, Steyvers, Lu, & Turner, 2018 ; Molloy, Bahg, Lu, & Turner, 2019 ; Rouder & Lu, 2005 ; Rouder et al, 2003 ; Wilson et al, 2020 ) and visual acuity ( Zhao, Lesmes, Dorr, & Lu, 2021 ), HBM has not been applied to analyze the CSF. Here, we develop a three-level HBM to model the entire CSF dataset in a single-factor (luminance), multi-condition (3 luminance conditions), and within-subject experiment design.…”

Hitting the moving target: modelling ontogenetic shifts with stable isotopes reveals the importance of isotopic turnover

“…Recent developments have also allowed bivariate modelling of continuous (i.e. gradual) ontogenetic shifts, for example by adding size as a covariate in Bayesian mixing models such as mixSIAR (Francis et al 2011;Stock & Semmens 2013), or by using multivariate hierarchical models (Reum, Hovel & Greene 2015). However, these previous applications of stable isotopes to gradual ontogenetic niche shifts ignored the often-significant time lag between diet and consumer tissue.…”

Quantifying Uncertainty of the Estimated Visual Acuity Behavioral Function With Hierarchical Bayesian Modeling

“…The HBM has been used in many different disciplines to model data with hierarchical structures, including astronomy, 56 ecology, 57 , 58 genetics, 59 and cognitive science. 50 , 51 , 53 , 60 – 65 By decomposing the variability of an entire dataset into distributions at multiple levels of the hierarchy, it can better quantify uncertainty at each level.…”