A Single Index Approach to Integrated Species Distribution Modeling for Fisheries Abundance Data

Abstract

In fisheries ecology, species abundance data are often collected by multiple surveys, each with unique characteristics. This article is motivated by a dataset of Atlantic sea scallop abundance records along the northeast coast of the United States, collected from two bottom trawl surveys which cover a larger spatial domain but have low catch efficiency, and a dredge survey which is more efficient but more bounded in domain. Over the past decade, integrated species distribution models (ISDMs) that include common environmental effects along with correlated survey-specific spatial fields have been used to incorporate information from multiple surveys. While flexible, ISDMs can be susceptible to overfitting, which can complicate interpretability of the shared environmental effects, and potentially lead to poor predictive performance. To overcome these drawbacks, we introduce a novel single index ISDM, built from a single index (with spatial random effects) that represents a latent measure of the true species distribution, and survey-specific catch efficiency functions which map the single index to the survey-specific expected catch. In this article, these functions are constructed via logistic functions or semiparametric spline-based functions. Simulations and application to the motivating sea scallop abundance data demonstrate that the proposed single index ISDM offers more meaningful interpretations of the environmental effects and survey catch efficiency differences, while achieving similar to or better predictive performance than existing ISDMs.

Figures (11)

• Figure 1: Log of count of Atlantic sea scallops per area unit from the trawl and dredge surveys. Zero count is represented by dark blue in the figures.
• Figure 2: True (top) and estimated (bottom) CEFs for the simulation study. Each column represents one of the three CEF scenarios. The solid red/blue dashed lines correspond to functions $h_1(\cdot)$ and $h_2(\cdot)$ respectively. In the bottom row, the average estimated CEF across 100 simulated datasets is presented, while the shaded region corresponds to 95% pointwise intervals.
• Figure 3: Histograms of estimated covariate effects, obtained from fitting the siISDM to 100 simulated datasets in Scenarios 1 to 3 (top to bottom rows, respectively) of the simulation study. The three columns correspond to second, third and fourth coefficients in $\boldsymbol{\beta}$. The red vertical dashed line denote true parameter values.
• Figure 4: Top row: Estimated single index $\kappa(\cdot)$ for the four-parameter logistic siISDM, with the predicted mean (left) standard deviation of $\kappa(\cdot)$ (right) shown. Bottom row: Estimated CEFs in the four-parameter logistic function (left) and semiparametric spline-based (right) siISDM applied to the scallop abundance data. In both panels, the solid red line corresponds to $h_1(\cdot)$ for the pre-2009 bottom trawl survey, the dashed orange line corresponds to $h_2(\cdot)$ for the post-2009 bottom trawl survey, while the blue dotted line corresponds to the $h_3(\cdot)$ for the scallop dredge survey.
• Figure S1: Histograms of environmental covariates across the three surveys in the scallop abundance data.