Size Limit Builder: concepts & considerations
The Size Limit Builder is used to explore the effects of minimum size limits and harvestable slot limits on fishing yields and protection of spawners. Prince and Hordyk (2019) provide a timely reminder that size limits are one of the most accessible management measures, requiring only rule-of-thumb approaches based on a size at maturity to conserve reproductive output and sustain “pretty good yields.” Likewise, size limits are an accessible form of ‘data-less’ management for fisheries with limited data availability or limited capacity for alternative forms of fisheries management (Prince and Hordyk 2019). The Size Limit Builder provides a platform for highlighting trade-offs between fishery yield and conservation of reproductive output that is consistent with the well-established practice of managing fisheries using size selectivity (Hilborn 2010; Prince and Hordyk 2019).
Size limits and slot limits
The Size Limit Builder can be used to evaluate Minimum size limits or Harvestable slot limits. Size limits are a fishery management option that places a minimum and/or maximum length at capture allowed for a given species. Minimum size limits set at or above length at maturity allow individuals to spawn before becoming susceptible to fishing. Maximum size limits can protect the largest individuals of a given species. A protected slot limit specifies a size range (both minimum and maximum) that prohibits capture within the interval. Alternatively, harvestable slot limits define an interval within which capture may occur.
F/M
Within the Size Limit Builder, adjacent to the sustainability score and catch score dials that are centrally located at the top of screen, a slider labeled fishing mortality rate presents this quantity as the ratio of fishing mortality to natural mortality, F/M. This ratio is used simply to present fishing mortality on a consistent scale across all life histories. The default value of F/M is 2.0, although this field can be modified. This slider can be hidden by the user but doing so always resets F/M to its default quantity of 2.0.The default value of 2.0 (an assumed high value of F/M) is specified in relation to an assumption that F/M of 1.0 should reasonably produce long-term harvest rates close to those maximum YPR, especially when fishing does not occur before the age of maturity (Walters and Martell 2004). In the absence of other information, F/M > 1.0 takes a pessimistic view of resource state. The default assumption F/M = 2.0 is intended to guide users towards size limit options that produce sustainability scores that sufficiently guard against high or uncontrollable fishing mortality.
Relevant Modules:
Selectivity and retention
In the Size Limit Builder, users will encounter two scenarios involving selectivity: (i) a selectivity function has been optionally activated that describes selectivity or vulnerability to the fishing gear or (ii) no selectivity function is activated. Importantly, minimum size limits or slot limits are always specified as patterns of retention. As the user specifies minimum size limits or slot limits, selectivity is not modified. This means that the Size Limit Builder does not evaluate changes to gear selectivity, only to retention. Discard mortality is not included in the Size Limit Builder, in other words, discard mortality is always assumed to be zero. In the situation where no selectivity function is activated (probably the most common use-case), a default selectivity of ‘full’ selection by 1.0 cm is specified. This default selectivity is a necessary place-holder for computations, but is inconsequential to SPR or YPR calculations because discard mortality is always assumed to be zero. In situations where selectivity is activated, the corresponding selectivity pattern is accounted for in calculations of SPR and YPR (e.g., removals).
The shape of selectivity or vulnerability to the fishing gear, Vul, is restricted to logistic selectivity or exponential logistic; always with maximum selectivity equal to one. Logistic selectivity is specified with parameters SL50 and ΔSL95, reflecting the length at which 50% of the population is vulnerable to the gear and the length increment to which 95% of the population is vulnerable to the gear, respectively. Exponential logistic at length is:
〖Vul〗_L=exp(p3×p1(p2-L))/((1-exp(p1(p2-L))) ),
where p1 is ascending rate, p2 length at peak selectivity, and p3 is descending rate. See Technical documentation for correctly formatted equations and additional information.
Relevant Modules:
Sustainability score and catch score
Relevant Modules:
Equilibrium & transitional dynamics
The Size Limit Builder was initially constructed to present sustainability score and catch score as equilibrium metrics (i.e., metrics shown in dials centrally located at the top of screen on ‘Step 2 Build size limits’). Equilibrium refers to the state of a fish population where recruitment, growth, and mortality (both natural mortality and fishing mortality), and size selectivity and retention (e.g., size limits), are constant over time and have produced a balance between births and deaths, such that stock size, age-structure, and catches are relatively stable. Equilibrium metrics represent the stable or equilibrium state that is anticipated to be reached, in the longer-term, following implementation of a size limit. Calculations of equilibrium per-recruit quantities are performed on a monthly time step; thus, this analysis is suitable for both short-lived species (e.g., those with lifespans of 5 years or less or natural mortality of 0.6 or greater) and long-lived species.
Moving beyond presentation of equilibrium metrics, transitional dynamics introduces a temporal component of per-recruit analysis. Where equilibrium sustainability score and equilibrium catch score calculate the end-state effect of a size limit or slot limit, transitional dynamics addresses the changes over time that occur when management measures are modified. Transitional dynamics introduces a temporal component to per-recruit analysis, allowing visualization of the shifts experienced by a fish population after implementation of a size limit, from its current state and towards a new equilibrium. In producing forward-looking projections, transitional dynamics follows the same assumption of constant recruitment that is made in per-recruit analysis. Constant recruitment is approximated using a steepness of 0.99 of the Beverton-Holt stock recruitment relationship. Additionally, there is no inter-annual recruitment variability. See Technical documentation section for further details. Unlike equilibrium per-recruit analysis, transitional dynamics are calculated on an annual time step, thus this analysis is not suitable for short-lived species (e.g., those with lifespans of 5 years or less or natural mortality of 0.6 or greater).
As an example of transitional dynamics, consider changes that are likely to occur to the catch score and sustainability score following enacting an increase to the minimum size limit. When a size limit is increased, an immediate reduction in total landings often occurs because the smallest size classes, which were traditionally found in the landings, are now unavailable. However, through time, allowing for growth prior to becoming vulnerable to fishing may lead to an overall improvement to the total weight of the landings, as measured by YPR. Additionally, increased reproductive output prior to becoming vulnerable to fishing will likely lead to an increase in SPR. The time horizons over which these changes occur are projected using numerical simulations in a process that is known as transitional dynamics (Ault et al. 2009).
Uncertainty in resource state
Implementing a size limit, where one previously did not exist or where an existing size limit is modified, promotes a change to the fishery. In this section, we discuss how to contextualize and interpret changes created by size limits using the metrics sustainability score and catch score.
Change is relative, but relative to what? In answering this question, it is useful to consider how the resource (via the sustainability score) and fishery catch (via the catch score) will change relative to current conditions. In doing so, users of the Size Limit Builder will likely be faced with two situations related to their intended application:
- The current state of the resource and its fishery is unknown or poorly known, nevertheless, size limits are viewed as useful options to conserve reproductive output and produce “pretty good yields.”
- The current state of the resource is known, some knowledge exists, or there is willingness to construct plausible scenarios; and accordingly, changes created by size limits can be compared to current conditions.
The Size Limit Builder is useful in both situations, as discussed below.
Unknown state of the resource
The first situation involves high uncertainty about the current state of the fishery resource. The centrally located dials “Sustainability score” and “Catch score” (i.e., those centrally located at the top of screen on “Step 2 Build size limits”) are calculated as equilibrium metrics. Importantly, calculation of equilibrium metrics requires limited consideration (but see next paragraphs) of the current state of the resource, and thus, provides a feasible set of metrics for decision-making in the situation of unknown stock status. Thus, the anticipated consequences of specifying a size limit or slot limit are presented as longer-term effects on the sustainability score and catch score that arise once the fish population becomes stabilized under a new management measure.
Equilibrium metrics are not focused on ‘where we are now’ but are focused on ‘where we are headed’ under a proposed size limit. However, there is a key assumption about fishing mortality rate in equilibrium calculations that users must be aware of. The Size Limit Builder characterizes a fishery according to its selectivity & retention (e.g., a size limit) and its fishing mortality rate. Given the assumption in this section that the current state of the resource is unknown, it is also unlikely that fishing mortality rate would be known. Nevertheless, fishing mortality rate is a required quantity needed to calculate the equilibrium sustainability score and catch score. To address this problem, users are provided with two strategies.
In the first strategy to address uncertain fishing mortality, a default level of fishing mortality experienced by the fish stock is set to a high value. This approach is aimed at identifying size limit options that produce sustainability score(s) and catch score(s) that are resilient to, or are deemed satisfactory in the face of, the presence of high fishing mortality. In the second strategy to address uncertain fishing mortality, users can examine whether a given size limit provides a satisfactory sustainability score and catch score across a plausible range of F/M. Examining scores across a plausible range of F/M can be carried out by modifying fishing mortality slider (by adjusting Relative Fishing Mortality F/M at the top of screen on ‘Step 2 Build size limits’) or by exploring the sustainability score contour plot and catch score contour plot shown in the “Advanced analysis” tab. Both options enable identification of size limit options that produce satisfactory outcomes across a wide range of F/M, which is useful for selecting a size limit that will likely be successful regardless of future changes in F/M.
Known or assumed resource state
The second situation involves fisheries where there is some knowledge, or willingness to construct plausible scenarios, about the current state of the fishery resource. Within the tab labeled “Transitional dynamics,” a richer set of tools is provided for examining the effects of size limits (or harvestable slot limits) on the sustainability score and catch score. This richer toolset allows the user to be explicit about the current state of the resource, thus allowing changes created by a size limit to be examined in relation to the current state. The challenge in using this toolset is that additional inputs are required, namely assumptions about current equilibrium sustainability score and current retention pattern of the fishery. Calculations are then made to produce the expected distribution of F/M that would have been necessary for the current equilibrium conditions.
The benefit of this approach is that upon setting a size limit option, updating of the equilibrium sustainability score and catch score are calculated based on the expected F/M from the current fishery. Additionally, in between current and longer-term equilibriums, transitional dynamics are calculated and presented as changes in the sustainability score and catch score over various time horizons. The “Transitional dynamics” tab also allows assumptions about current sustainability score and current retention pattern of the fishery to be specified as uncertainty ranges. These uncertainty ranges are propagated into calculations of current F/M and all subsequent equilibrium and transitional dynamics metrics, which are reported as quantity ranges. Thus, the “Transitional dynamics” tab works cohesively to calculate equilibriums and transitional patterns, while also propagating uncertainty about current resource state into calculations of sustainability score and catch score.
Uncertainty in life history
Life history parameters are central to calculation of the sustainability score and catch score. Users should anticipate that the sustainability score and catch score could be sensitive to selected life history parameter estimates. The Size Limit Builder provides tools to address the question of degree of sensitivity to life history parameter estimates to estimates of both equilibrium metrics and transitional dynamics.
Within the tab labeled “Uncertainty test,” the calculations presented in the centrally located dials labeled “Sustainability score” and “Catch score” (i.e., these dials are centrally located at the top of screen on ‘Step 2 Build size limits’) can be extended to address life history uncertainty. Uncertainty tests are carried out in three steps. First, select one or more retained options to include in the test. If you subsequently create additional retained options, you can always update your uncertainty tests. Second, select one life history parameter to modify and specify an upper and lower bound. Upper and lower bounds are not used to define a statistical sampling distribution; rather, two discrete uncertainty tests are run, one at the lower bound and a second at the upper bound. Three, run the uncertainty test. Running the uncertainty test will re-calculate the sustainability and catch scores at the lower and upper parameter bounds, producing an expected set of outcomes (lower, original quantity, upper). In this way, uncertainty testing is structured as a process for discrete examinations of the effects of modifying one parameter, while maintaining all other parameters at the original values, on the calculation of sustainability score and catch score.
Within the tab labelled “Transitional dynamics,” life history uncertainty can be explored while calculating transitional dynamics. In setting up inputs to transitional dynamics, the original life history parameters can be optionally modified. The user has the flexibility to modify one or more life history parameters concurrently, enabling different configurations of life history parameters to be examined. A simple approach could involve modifying one parameter, while maintaining all other parameters at the original values, to create a clear picture of the effects of a given life history parameter on patterns in resulting transitional dynamics. Where exploration of multiple management options is evaluated against alternative scenarios about life history parameters, a factorial all-combinations approach is recommended to produce a thorough set of comparisons of modeling results.
As a technical note, when one or more life history parameters are modified in an uncertainty test (either uncertainty test or transitional dynamics), the sustainability score and catch score are recalculated. This includes recalculations of the SPR and YPR arrays according to combinations of size limit and fishing mortality rate (see the section Sustainability score and catch score). The catch score is scaled relative to the maximum YPR, where maximum YPR is the highest value of YPR found across this array. Thus, when a life history parameter is modified in an uncertainty test, maximum YPR is re-calculated and used in the updated calculation of the catch score.