Model formulation, first column gives the equation number, the second column gives a description, and the final column gives the mathematical form of the dynamics.

<p>Model formulation, first column gives the equation number, the second column gives a description, and the final column gives the mathematical form of the dynamics.</p

Results from five retrospective “peels” compared to the posterior intervals (light gray = 95% interval, darker gray = 50% interval, black = 5% interval) of pre-fishery run biomass from the Bayesian model fit to the entire time series of data.

<p>Each “peel” is the posterior median of the model run with an additional year of data removed and is labeled numerically where a higher number denotes a peel of data further into the past.</p

Bayesian stock assessment of Pacific herring in Prince William Sound, Alaska - Fig 5

<p>Model estimates and the four time series of abundance estimates (1980–2012): (A) mile-days of milt, (B) egg deposition surveys, (C) ADF&G hydroacoustic estimates, and (D) PWSSC hydroacoustic estimates. The solid circles and lines represent the mean and 95% confidence intervals of the data (plus additional variance estimated by the model); the shaded polygons represent the respective posterior predictive intervals (light gray = 95% interval, darker gray = 50% interval, black = 5% interval).</p

Bayesian stock assessment of Pacific herring in Prince William Sound, Alaska

<div><p>The Pacific herring (<i>Clupea pallasii</i>) population in Prince William Sound, Alaska crashed in 1993 and has yet to recover, affecting food web dynamics in the Sound and impacting Alaskan communities. To help researchers design and implement the most effective monitoring, management, and recovery programs, a Bayesian assessment of Prince William Sound herring was developed by reformulating the current model used by the Alaska Department of Fish and Game. The Bayesian model estimated pre-fishery spawning biomass of herring age-3 and older in 2013 to be a median of 19,410 mt (95% credibility interval 12,150–31,740 mt), with a 54% probability that biomass in 2013 was below the management limit used to regulate fisheries in Prince William Sound. The main advantages of the Bayesian model are that it can more objectively weight different datasets and provide estimates of uncertainty for model parameters and outputs, unlike the weighted sum-of-squares used in the original model. In addition, the revised model could be used to manage herring stocks with a decision rule that considers both stock status and the uncertainty in stock status.</p></div

The four types of annual catch data, in thousands of metric tons, for Prince William Sound herring used in the Bayesian age-structured assessment model.

<p>Data for the three fisheries in the top panels are in the form of numbers of catch-at-age, so these were converted to annual total yield in mt using the weight-at-age (mt) data (1.7) for ease of display. Absent bars denote years that fishery did not run; all herring fisheries have been closed since 1999.</p

Recruitment (median and 95% credible intervals) in millions of age-3 fish, pre-fishery run biomass (median and 95% interval) in 10³ mt, the probability that pre-fishery run biomass has fallen below the lower regulatory threshold (Brd column), total instantaneous mortality for age 3–4 fish, and total instantaneous mortality for age 5–8 fish.

<p>Recruitment (median and 95% credible intervals) in millions of age-3 fish, pre-fishery run biomass (median and 95% interval) in 10³ mt, the probability that pre-fishery run biomass has fallen below the lower regulatory threshold (Brd column), total instantaneous mortality for age 3–4 fish, and total instantaneous mortality for age 5–8 fish.</p

A schematic of the seasonal timing of fishing and sampling events included in the assessment model along with a schematic of a single cohort over seven years.

<p>Starting in the center of the spiral, the width of each separately colored curl represents the relative size of the cohort at a certain age and lighter colors denote younger ages of the cohort in earlier years. The cohort is reduced by fishery and non-fishery mortality effects (in that order) after the first 6 months (event A) and the last 6 months (event B) of every year before becoming a year older. The plus group is represented as a complete circle with two inputs: herring of age 8 and herring already in the plus group.</p

Results from the sensitivity analysis using the fixed value of 0.35 yr-1 for background natural mortality.

<p>See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0172153#pone.0172153.g007" target="_blank">Fig 7</a> caption for explanation of panels, colors, and symbols.</p

Bayesian stock assessment of Pacific herring in Prince William Sound, Alaska - Fig 7

<p>(A) Estimated recruitment at age-3 (posterior intervals; light gray = 95% interval, darker gray = 50% interval, black = 5% interval), (B) estimated pre-fishery biomass (posterior intervals; light gray = 95% interval, darker gray = 50% interval, black = 5% interval) and the probability that pre-fishery biomass is below the lower regulatory threshold (LRT) of 22,000 short tons (19,958 mt) (connected black points) with the upper regulatory threshold (URT: 42,500 short tons, 38,555 mt) shown for reference, (C) posterior distribution of estimated pre-fishery biomass for 2013 with the 95% credible interval (light grey) and the median (black) shown, and (D) posterior median exploitation rates (black points) with 95% posterior intervals (segments)—“X” characters represent years the fishery was closed.</p

Commercial harvests of Pacific herring reported for Prince William Sound, 1914 through 2012 [5].

<p>Commercial harvests of Pacific herring reported for Prince William Sound, 1914 through 2012 [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0172153#pone.0172153.ref005" target="_blank">5</a>].</p