Bayesian spatiotemporal analysis of zero‐inflated biological population density data by a delta‐normal spatiotemporal additive model

Abstract

We evaluate the spatiotemporal changes in the density of a particular species of crustacean known as deep-water rose shrimp, Parapenaeus longirostris, based on biological sample data collected during trawl surveys carried out from 1995 to 2006 as part of the international project MEDITS (MEDiterranean International Trawl Surveys). As is the case for many biological variables, density data are continuous and characterized by unusually large amounts of zeros, accompanied by a skewed distribution of the remaining values. Here we analyze the normalized density data by a Bayesian delta-normal semiparametric additive model including the effects of covariates, using penalized regression with low-rank thin-plate splines for nonlinear spatial and temporal effects. Modeling the zero and nonzero values by two joint processes, as we propose in this work, allows to obtain great flexibility and easily handling of complex likelihood functions, avoiding inaccurate statistical inferences due to misclassification of the high proportion of exact zeros in the model. Bayesian model estimation is obtained by Markov chain Monte Carlo simulations, suitably specifying the complex likelihood function of the zero-inflated density data. The study highlights relevant nonlinear spatial and temporal effects and the influence of the annual Mediterranean oscillations index and of the sea surface temperature on the distribution of the deep-water rose shrimp density.

The increasing temperature as driving force for spatial distribution patterns of Parapenaeus longirostris (Lucas 1846) in the Strait of Sicily (Central Mediterranean Sea)

“…Although a significant effect of temperature is found, further highlighting its key role as ecological factor affecting the dynamics of the DPS population (e.g. Colloca et al, 2014;Ligas et al, 2011;Arcuti et al, 2016), only the 40% of the total deviance is explained by the model. This suggests that the depth range distribution, likewise to the patches dimension, is not influenced by the temperature alone.…”

“…Still, in other regions of the Mediterranean Sea, positive relationships between DPS abundance and increasing of sea temperature has been shown (i.e. Ionian Sea, central-northern Tyrrhenian Sea and Ligurian Sea; [Arcuti et al, 2016;D'Onghia et al, 2012;Ligas et al, 2011;Colloca et al, 2014]). Even in Moroccan Atlantic waters, the temperature positively influences the abundance levels of the species (Benchoucha et al, 2008).…”

Seasonal and spatial variability in rates of primary production and detritus release by intertidal stands of Laminaria digitata and Saccharina latissima on wave‐exposed shores in the northeast Atlantic

“…a generalized linear mixed model with a Tweedie distribution that also accounts for zero inflation (package Tweedie; Arcuti et al, 2013).…”

Modeling zero‐modified count and semicontinuous data in health services research Part 1: background and overview

“…Other recent developments include multivariate two‐part models , two‐part models for the joint analysis of longitudinal and survival outcomes , Tweedie regression models for semicontinuous data , skew‐normal ZIT models for left‐censored data , two‐part models for estimating expected cumulative cost of illness in the presence of censoring , four‐part models for jointly analyzing inpatient and outpatient costs , and Bayesian extensions of two‐part semicontinuous models . Several authors have proposed two‐part models for spatially referenced semicontinuous data . This ongoing work highlights a growing interest in semicontinuous data analysis and solidifies its current role as a vibrant area of statistical research.…”