A historical review of selectivity approaches and retrospective patterns in the Pacific halibut stock assessment

Highlights

• Retrospective bias in stock assessment results for Pacific halibut has been identified during three historical time-periods of analysis.

• In each case, amelioration of the bias was achieved through modification of the selectivity assumptions in the population dynamics model.

• Investigation of more flexible assumptions for the modeling of selectivity may be warranted for other species whenever evidence of poor model behavior is present.

Abstract

The Pacific halibut stock assessment has proven to be a particularly challenging application for the estimation of selectivity. Contributing factors include: extremely pronounced temporal changes in length-at-age, a steep vulnerability curve for commonly used hook sizes, a minimum length limit, relatively late (∼age 6–10) appearance of fish in survey and fishery data, and geographic heterogeneity in demographic parameters coupled with pronounced spatial trends in population abundance over time and significant ontogenetic migration over the stock range. Historical stock assessments have variously modeled selectivity as a function of length or age, employing nonparametric forms in attempting to account for these various factors. Despite these efforts, a strong retrospective bias in model results occurred during three separate time periods; each of which ultimately required modification of the selectivity parameterization to ameliorate that bias. This paper provides a summary of historical approaches, and the methods employed to address the most recent retrospective pattern.

Introduction

Integrated statistical fisheries stock assessments are now standard approaches in many parts of the world (Hilborn and Walters, 1992, Quinn and Deriso, 1999, Maunder and Punt, 2013, Fournier and Archibald, 1982, Megrey, 1989). These models fit to available fisheries-dependent and/or fisheries independent data and provide estimates of management-related quantities including reference points, stock size, and harvest rates. Time-series of catch and relative abundance estimates, together with biological information (lengths, ages, or both) from these time-series provide information on the population trend and the demographic components contributing to that trend.

A crucial aspect of these analyses lies in defining the observed number of fish at a particular length or age, relative to the number of fish estimated to exist at that length or age in the population dynamics model. This relationship is variously referred to as efficiency, effectiveness, or the combination of selectivity, and catchability. Because various definitions are used interchangeably in the fisheries literature, in this paper we identify and use four distinct terms:

• Availability: the relative probability a fish will be in the same area at the same time that the gear is being deployed.

• Vulnerability: the relative probability a fish that is present when and where survey (or fishing) gear is deployed will be captured (also commonly denoted as “gear selectivity” or “contact selectivity).

• Selectivity: the length- or age-based probabilities used to relate fish predicted to exist in a population to those that are observed in the data; this represents the combination of both vulnerability and availability.

• Catchability: the scaling coefficient between an index of abundance (or catch-per-effort) and the abundance at length or age that is most selected.

There are a number of biological and technical factors that can contribute to differences in vulnerability, availability, or both as a function of fish length, age, or both (Olsen and Laevastu, 1983, provide a detailed conceptual map of many factors influencing longline catch rates in general). Biological factors can include ontogenetic shifts among habitats, behavioral differences due to changes in diet, differences in growth rates among different habitats, morphology (jaw dimension, body length or shape, etc.), and many others. Technical factors may include physical aspects of sampling/fishing (mesh or hook size, set duration, towing speed, etc.), gear performance in different habitats, regulatory length-limits, and many others. These factors may be temporally variable or static; however in both cases interactions among them may result in highly variable selectivity or catchability over time.

The Pacific halibut stock assessment and management system has a long history of data collection and scientific analysis, serving as a testing ground for many of the fisheries modeling approaches that have been developed over the last several decades (Clark, 2003). Despite this history (or perhaps causing this history), Pacific halibut present a suite of difficult challenges to the modeling of selectivity. Such challenges are frequently present in other fisheries, but are infrequently observed en masse in a single stock assessment application. As such, Pacific halibut represent a unique and potentially illustrative case-study.

In this manuscript, we review the approaches taken over several decades of the Pacific halibut stock assessment, with a particular emphasis on the treatment of selectivity. We identify a recurrent theme of simplifying selectivity assumptions that, over three distinct time-periods, each became increasingly mismatched with the underlying population dynamics. We summarize the retrospective patterns in biomass estimates (and therefore management-related quantities) that appear to be a result of these mismatches. We then present the results of the most recent stock assessment as a more flexible long-term solution to these historical issues.