Stock Health Tracker: concepts & considerations

Froese’s indicators

The Stock Health Tracker (SHT) was designed to address a need for visualizing and tracking simple metrics of fishery health. Currently, the SHT includes three metrics of fishery health based on length frequency data and life history information, proposed by Rainier Froese (2004): 1) percent mature fish in the catch, 2) percent optimal sized fish in the catch, and 3) percent megaspawners in the catch. The interactive interface allows users to explore their length frequency data and visualize the 3 indicators.

Mature fish in the catch is proposed by Froese (2004) as a simple metric that can be described as “Let them spawn!”. This metric is calculated relative to the length at which 50% of fish are mature, which serves as a threshold to determine maturity. The goal for mature fish in the catch is 100%, as it is generally recommended to allow fish to reproduce at least once before becoming vulnerable to fishing. Mature fish in the catch is calculated as the percentage of the length composition that is equal to or greater than L50. This metric requires fishery catch (fishery-dependent data set) and a life history with specified length at 50% maturity (L50). The Stock Health Tracker will provide a warning when these criteria are not met. For data sets of raw lengths, this metric is calculated prior to any binning of length. For data sets of frequencies, this metric is calculated by separating bins according to bin mid points.

Optimal sizes in the catch is proposed by Froese (2004) as a simple metric that can be described as “Let them grow!”. Optimal size refers to the length at which a fish cohort achieves its maximum biomass, and thus, fishing sizes close to or within this optimal size should ensure high yields by weight. This metric is presented as the percentage of the length composition of the catch within within the defined range (i.e., Lopt +/-10%). This metric requires fishery catch (fishery-dependent data set) and a life history with specified M, K, and Linf. For data sets of raw lengths, this metric is calculated prior to any binning of length. For data sets of frequencies, this metric is calculated by separating bins according to bin mid-points.

Fish above the size limit is a metric of compliance for fisheries where a minimum size limit has been established.This metric is calculated as the percentage of the length composition that is equal to or greater than the size limit. This metric requires setting a value in the size limit field in the control panel. For data sets of raw lengths, this metric is calculated prior to any binning of length. For data sets of frequencies, this metric is calculated by separating bins according to bin mid points.

Mega-spawners in the catch is proposed by Froese (2004) as a simple metric that can be described as “Let the mega-spawners live!”. Mega-spawners are those larger than the optimal size range, thus they should comprise a low percentage of the catch. This metric is calculated as as the percentage of the length composition equal to or greater than Lmega, where Lmega = Lopt×1.1. This metric requires fishery catch (fishery-dependent data set) and a life history with specified M, K, and Linf. For data sets of raw lengths, this metric is calculated prior to any binning of length. For data sets of frequencies, this metric is calculated by separating bins according to bin mid points. Interpretation of mega-spawners metric is nuanced because while it may be desirable to leave mega-spawners in the water, if mega-spawners are not present in the catch but are not being intentionally avoided by fishers, a lack of mega-spawners could be an indication of overfishing. Therefore, if mega-spawners are part of the catch, we expect to see some mega-spawners, as evidence of these individuals persisting in the catch; however, the catch should not comprise solely mega-spawners. For these reasons, Froese (2004) suggests a target of 30% to 40% of mega-spawners in the catch. In the case where mega-spawners are being avoided by fishers due to market preferences, gear selectivity or through other intentional interventions, such as slot limits, we would not expect to see these fish in the catch, but this would not be cause for alarm.

The indicators contained in Stock Health Tracker should not be conflated with stock assessment. Stock assessment is typically focused on the current status of a stock, including estimation of fishing mortality (or proxy F/M) and size selectivity, two elements of fishing mortality exerted on a fish stock. While some indicators are similarly focused on stock status, it is crucial to understand the specific aspects of a fishery that an indicator is intended to address. For example, the Froese indicators address size selectivity as it relates to recruitment overfishing and growth overfishing (Froese 2004) but do not address fishing mortality directly. Thus, it might be possible to have a high proportion of mature fish in the catch and high fishing mortality, estimated by an indicator and a stock assessment, respectively. Despite the nuances of interpreting different indicators and quantities produced by stock assessment, there is reason to expect that adherence to good practices related to size selectivity provides a rational basis for sustainable fisheries (e.g., see Prince and Hordyk 2019).

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Indicators by grouping variable

Where a length data set includes a grouping variable (e.g., year or fleet), the above described metrics can be presented by group, for example, as a time series where year is used as a grouping variable. Additionally, two other metrics are available, typically presented according to grouping variable. Average length in the catch: this metric provides a summary of average length according to a grouping variable like year or fleet, based on user-defined inputs. Changes in average length can be an indicator of fishery sustainability, with downward trends typically indicative of an increase in fishing mortality. Sample size in the catch: this metric can be a useful summary of sufficiency of monitoring programs or participation in length-sampling programs by fishers. It is intended to capture a simple but fundamental metric of length sampling sufficiency.

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Length-based spawning potential ratio (LBSPR)

Spawning potential ratio (SPR) is an indicator of fishery health commonly used in fisheries science. SPR is a comparison of the reproductive capacity of a fish population when fished to when it is theoretically unfished.

LBSPR is a data-limited stock assessment method that is used to estimate spawning potential ratio (SPR) from length composition data from the catch of an exploited population or stock (Hordyk et al. 2015b, 2016). The basis for the LBSPR method is that life history parameters, fishing mortality, and fishery selectivity determine the length frequency distribution of a stock, and also, the reproductive output as measured using SPR. Accordingly, if fishery-dependent length frequency distributions can be observed (data set input) along with life history parameters (parameter inputs), then statistical estimates can be obtained for F/M and selectivity-at-length parameters that would have given rise to the observed length frequency distribution. Taken a step further, parameter inputs and estimated quantities can be used to calculate corresponding SPR. To use the LBSPR assessment method within the Stock Health Tracker, the following inputs are required:

  • Fishery-dependent length data object (i.e., length observations from fishery catch) created using the FishKit Data Repository.
  • Life history object created using the FishKit Data Repository that contains M and K or the ratio of M/K, asymptotic length, a logistic maturity curve (both L50 and ΔL95), and optionally length-weight alpha and beta parameters.

Following specification of these inputs, FishKit addresses three additional parameter requirements of LBSPR: coefficient of variation of asymptotic length, beta parameter of length-fecundity relationship, and bin size for length-frequency data. Coefficient of variation of asymptotic length is specified at a value of 0.1, which is also the default value used in the R package LBSPR. The beta parameter of length-fecundity relationship fecundity is set equal to the beta parameter of the length-weight relationship of the specified life history, if available, otherwise a value of 3.0 is specified. Finally, the R package LBSPR requires binned length data. When a length data set contains raw lengths, the wrapper function applies a bin width of 1 cm is used to create necessary binning. When a length data set contains frequencies, the bin width of the length data set is used. Each of these three parameters cannot be modified by the user, thus, if alternatives are sought, running the analysis directly in R package LBSPR may be a viable alternative.

Having aligned necessary inputs with required formatting of the R package LBSPR, a maximum likelihood fitting routine can be applied to estimate key quantities and calculate SPR. Before running the estimation routine, the user must choose between two mathematical models used in the fitting process, known as ‘absel’ and ‘GTG’. The model ‘absel’ is an age-structured approximation of population dynamics giving rise to length frequency distribution, while ‘GTG’ is a length-based approximation. The ‘GTG’ model provides an improved representation of the process of size-based fishery selectivity (Hordyk et al. 2016). The ‘GTG’ model is the default option in the R package LBSPR and in the Stock Health Tracker. Readers interested in a deeper understanding of length vs. age selectivity and the adjacent topic of reaction norms for sexual maturation should see Lee (1912) and Stearns and Koella (1986).

The results of LBSPR are visualized in the Stock Health Tracker according to the plots and tables produced by the R package LBSPR (https://adrianhordyk.github.io/LBSPR/index.html). The user should refer to GitHub documentation and peer-reviewed literature for interpretation of modeling results (Hordyk et al. 2015d, 2016). To help ensure reliability of results of LBSPR, the following issues and assumptions must be considered:

  • Fish experience constant natural mortality and growth rates, growth must be adequately described by the von Bertalanffy equation, and both sexes must have the same growth curve and the sex ratio of the catch is parity, or the model uses the biological parameters and length composition of female fish only (Hordyk et al. 2015c).
  • The fishing gear used to collect the length data must have asymptotic selectivity. Do not use LBSPR if this requirement cannot be met. Length data from fisheries with gear that domed or right-hand selectivity cannot be used.
  • Estimates of SPR can be sensitive to coefficient of variation of asymptotic length (Hordyk et al. 2015d). Currently, this parameter cannot be changed in the Stock Health Tracker, consider running the analysis directly in R package LBSPR as a viable alternative.
  • Estimates of SPR can be sensitive to bin size. Users with access to raw lengths may choose to create multiple length frequency data sets using a variety of bin sizes to better understand the degree of uncertainty in SPR estimates that arise from binning assumptions.
  • LBSPR is an equilibrium metric (e.g., population or stock is relatively steady-state with constant recruit) (Hordyk et al. 2015d). In application, the effects of inter-annual variability in fishing mortality on SPR estimation are a complex topic. In brief, observed length frequency distributions reflect the recent history of fishing mortality over the stock’s component cohorts. Readers should review Hordyk et al. (2015c) for discussion of this topic. Additionally, particularly strong or weak recruitment events may produce biased estimates of SPR (Hordyk et al. 2015d, 2015a).
  • Life history parameters must be reliable. See Hordyk et al. (2015d) for examples of degree of bias introduced from unreliable parameters. When uncertainty persists, repeating the analysis using different life history versions can assist in determining the degree of uncertainty in SPR (see section Confronting life history uncertainty).
  • Pooling length data from multiple fleets, especially those with different selectivity patterns, can produce biased estimates of SPR. Data weighting methods can help address this problem and should be addressed by an experienced analyst.

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