Ecological Archives A020-057-A1

J. Wilson White, Louis W. Botsford, Elizabeth A. Moffitt, and Douglas T. Fischer. 2010. Decision analysis for designing marine protected areas for multiple species with uncertain fishery status. Ecological Applications 20:1523–1541.

Appendix A. Summary of fishery stock information used to obtain values of the fraction of lifetime egg production (FLEP) and critical replacement threshold (CRT)..


Invertebrate Fisheries

West Coast Groundfish Stocks

Literature Cited


In this appendix, we summarize the information available regarding fishery stock status for each California species.  We focus on estimates of the fraction of lifetime egg production (FLEP, the lifetime reproductive effort realized on average by a successful recruit, relative to the unfished value) and the critical replacement threshold (CRT, the slope at the origin of the stock-recruit curve), which is the value of FLEP below which a population does not persist.  The amount of data varies by species, and for some only rough estimates of current FLEP and the CRT are possible.  For some species there has  not been a stock assessment to determine the status, and even for species that have been assessed, the status is not known with certainty. For some assessed species, assessment conclusions rest upon speculative assumptions about the CRT.  For all of the species, there are several plausible estimates for both FLEP and CRT.  Here we explain the values chosen for analysis in our model and the weighting scheme applied to the various combinations of FLEP and CRT in order to represent the optimistic and pessimistic future fishery management scenarios.  The distribution of probabilities associated with each scenario for each species is summarized in Table 2 in the main text.  Since the actual values of FLEP and CRT are poorly known, the process of assigning weights is subjective and the values chosen here are for illustrative purposes only.  For the optimistic scenario, we generally assigned high weights to low values of CRT and high values of FLEP.  For the pessimistic scenario, we based probabilities on the contemporary management success for each species; we made this scenario more precautionary by assuming higher values for CRT and lower values for FLEP, especially when less empirical information on those values was available (Smith et al. 2007).

The information available for each species varies in part because each is managed by one or both of two different management authorities.  Red abalone and red sea urchin are managed by the State of California, and black rockfish, cabezon, canary rockfish and lingcod are also managed under the U.S. federal regional council process through the Pacific Fisheries Management Council. Because the definition of overfished (and "overfishing", which typically refers to the condition of continuing to harvest an overfished stock) differs between regulatory agencies, we do not use that term to classify fisheries in our analysis.  Rather we focus on whether FLEP of new recruits is below the CRT, a state that leads to population collapse at equilibrium.

Invertebrate fisheries

Red abalone (Haliotis rufescens)

The history of management of abalone fisheries in California is an example of serial depletion (Karpov et al. 2000), and one species, white abalone Haliotis sorenseni, is listed under the Endangered Species Act.  Red abalone harvest is permitted only in northern California (north of San Francisco Bay), where they are taken in a recreational free-diving fishery only (SCUBA is prohibited).  Because of that the northern California stock was believed to be protected from overfishing by the presence of a spatial refuge consisting of the area occupied by abalone that is deeper than the limits of free diving.  In recent years that has not been viewed as reliable protection, but red abalone densities have been nonetheless stable over the past decade (CDFG 2005).

There have been some analyses of population dynamics of red abalone (Tegner et al. 1989), but there has been no stock assessment.  There is some concern over the understanding of population parameters since recently estimated natural mortality rates (Leaf et al. 2007). are so high that very few individuals would survive to fishable age (see Appendix B).

Because no stock assessment has been conducted and there is no estimate of the CRT or FLEP for this species, we chose a value of CRT = 0.35 and used FLEP = 0.4, 0.3, and 0.2 in the model, spanning a range of potential fishery conditions.  For the optimistic scenario, we assigned 100% probability to FLEP = 0.4, indicating a sustainably fished stock.  For the pessimistic scenario, we assumed there was a 50:50 chance of FLEP exceeding the CRT, and chose weights of 0.5, 0.25, and 0.25 for FLEP = 0.4, 0.3, and 0.2, respectively.  This weighting reflects the data suggesting that population densities have been stable for several years, indicating that the stock is sustainably fished, discounted by the observation of long term recruitment failure in other California abalones (CDFG 2005) and the fact that the management plan presumes MPAs will be present.

Red sea urchin (Strongylocentrotus franciscanus)

There has also been no official stock assessment of the red sea urchin.  Nonetheless, growth and mortality rates estimated from size distribution data in the 1990s provide the necessary information (Morgan, et al. 2000).  Those estimates were used to calculate both YPR (yield per recruit) and EPR (eggs per recruit) (Morgan, et al. 1999, Botsford, et al. 2004).  Those calculations indicated FLEP (EPR) was less than 20 percent of the unfished value.  Since that time, catches have remained steady but currently most individuals are harvested immediately after reaching legal size (CDFG 2003), so it is possible that FLEP is actually lower.  Nonetheless, we used a value of FLEP = 0.2 in the model.  Lacking an estimate of the CRT, we used values of 0.35 (conservative) and 0.15 (non-conservative). 

For the optimistic scenario, we placed the full weight on CRT = 0.15, so that FLEP > CRT.  For the pessimistic scenario, we assumed a 50:50 chance that FLEP < CRT, so we assigned a weight of 0.5 to each value of the CRT, holding FLEP = 0.2.

West Coast Groundfish Stocks   

The groundfish species included here all have stock assessments based on single interbreeding populations over a spatial scale of hundreds of kilometers.  In addition to that simplifying assumption, they also do not account for ontogenetic movement of younger rockfish from nearshore to offshore waters.  Nonetheless, these assessments represent the best available information on the status of these species in most cases.

Black rockfish (Sebastes melanops)

The most recent stock assessment of black rockfish (Sampson 2007) assumed a threshold steepness value of 0.6, which corresponds to CRT = 16% (steepness, h, is alternative parameter used to describe the slope of the stock recruit curve; CRT = (1-h)/4h, Martell et al. 2008).  Alternatively, Dorn (2002) analyzed the stock-recruit curves for several west coast rockfish species using a hierarchical Bayesian approach.  There were insufficient data to estimate steepness for black rockfish alone, but the overall estimate for all species was h = 0.7, corresponding to CRT = 0.11.  A third estimate of CRT derives from the observation that managing rockfish stocks with a target SPR (= FLEP) of 0.35 in the 1990s produced undesirably low population abundances (Ralston 1998), so CRT may be in the vicinity of 0.35 for those species (Clark 2002, Ralston 2002). 

As for estimates of FLEP, the stock assessment's model projections of biomass ages 2 and greater shows a decline to low values in the 1990s followed by an increase in the late 1990s to a peak near 2005 (third figure in Executive Summary of Sampson 2007).  The coastwide value of  biomass depletion dipped below 40% in the 1990s before returning to a value of 70% in the mid 2000s (Fig. 31 in Sampson 2007).  These values would roughly correspond to FLEP = 0.4 and FLEP = 0.7.  Strictly speaking, biomass depletion does not necessarily predict FLEP, but if the biomass depletion has not yet led to decreased recruitment then the two valeus should be similar.  There is one trend in the data in the opposite direction from these projections:  the CPUE in the recreational fishery in California shows a declining trend since 2000 (Fig. 14 in Sampson 2007).

Another assessment of the status of black rockfish is more closely focused on local California populations and is based on size distributions from the California recreational fishery.  Comparison of size distributions in the early 1980s with those in more recent years indicates the current value of FLEP = 0.13 (O'Farrell and Botsford 2006).  This estimate assumes the size distribution in 1980 is near the unfished state.  To the extent that it is not (i.e., that the size structure had already been substantially altered by fishing by 1980), this estimate of FLEP is optimistic (i.e., biased high).

Based on these results, we considered three different estimates of the CRT for black rockfish (0.11, 0.16, and 0.35) and two estimates of FLEP: 0.7, based on the depletion estimate from the latest stock assessment, and 0.13, drawn from O'Farrell and Botsford's (2006) results.  For the optimistic future fishery scenario, we used FLEP = 0.7 and assigned equal probabilities to the three values of CRT.  For the pessimistic scenario we used FLEP = 0.13 with equal weighting among the CRT values.

Cabezon (Scorpaenichthys marmorata)

The most recent stock assessment of cabezon divides the stock into northern and southern California substocks (Cope and Punt 2005). The stock assessment  focuses on the depletion reference point, i.e., the fraction to which spawning stock biomass (SSB) has been depleted, rather than the replacement reference point (i.e., SPR or FLEP and CRT).

The current spawning biomass in northern California is 40% of the unfished value, which places it in the precautionary zone under both federal and state regulations.  The previous stock assessment made projections of the probability distribution of depletion 12 years in the future, over a range of assumptions involving natural mortality, steepness and possible management.  The mode of this distribution was just below 40 percent, still in the precautionary zone.  Their base model used a steepness value of 0.7, which correspond to CRT values of 11%, although the likelihood profile for steepness actually suggests the biologically implausible value of unity, which tends to indicate the available data were not informative regarding steepness.

Several declining trends in cabezon data are cause for concern.  The three estimates of CPUE for California all exhibit long term declines (Figs. 6 and 8 in Cope et al. 2004), albeit with a slight increase in the most recent data year (Fig. 34 in Cope and Punt 2005).  The estimated spawning output is declining both in the long term, as well as in the short-term (i.e., since the late 1990s) decline (Cope et al. 2004; Fig. 49 in Cope and Punt 2005). 

Based on these results we used the value FLEP = 0.4, corresponding to the recent estimates of depletion, as well as the lower value FLEP = 0.3 as a conservative alternative.  Once again, we are assuming that recruitment has been relatively constant so that depletion and FLEP are similar.  For the CRT, we used values of CRT = 0.11 (based on the value used in the stock assessment) as well as the more conservative estimate of CRT = 0.35 based on the poor quality of the data.  For the optimistic fishery scenario, we used CRT = 0.11 and assigned equal weight to the two FLEP values; for the pessimistic scnenario we used CRT = 0.35 and assigned weights 0.75 and 0.25 to FLEP = 0.3 and FLEP = 0.4, respectively.  This choice reflects the unknown nature of the CRT and the evidence for declining CPUE under the current management regime.

Canary rockfish (Sebastes pinniger)

The canary rockfish was declared overfished in the year 2000, and the most recent stock assessment contains a summary of information from the rebuilding plan, as well as an estimate of the current status (Stewart 2007).  SPR (i.e., FLEP) declined approximately linearly from a value near 60 percent in 1970 to less than 10 percent in the 1990s.  However, in response to reductions in trip limits and spatial closures, it is projected to have increased to > 90% recently.  The values of the CRT used in models in the stock assessment were 51% (i.e., steepness = 0.329) and 31% (i.e., steepness = 0.449).  The former value was derived from Dorn's (2002) analysis, and is well-supported because data are actually available at low stock abundances.  Abundance reached its lowest level in the mid 1990s, and has increased since then to between 1 and 7 percent of the estimated unfished spawning biomass.

Based on these results we used CRT = 0.51, a well-supported value, and FLEP = 0.9 (representing the current estimate of SPR) and FLEP = 0.1 (representing the current estimate of total spawning biomass).  For the optimistic scenario we assigned 100% of the weight to the FLEP = 0.9 case; for the pessimistic scenario we assigned weights of 0.75 and 0.25 to FLEP = 0.9 and FLEP = 0.1, respectively.  These weights reflect the strong evidence that the stock is well managed and rebuilding but the non-negligible possibility that future management will again be unsuccessful.  For example, one cause of concern is that the nature of the fishery is changing, with the fraction of catch in the recreational fishery increasing from an average of 6 percent of the catch to 60 percent.

Lingcod (Ophiodon elongatus)

The most recent stock assessment for lingcod divides the population into two separate populations, with the southern one (Eureka, California to Monterey, California) being the one of interest here (Jagielo and Wallace 2005).  The depletion level of the southern stock is a spawning biomass that is 24% of the unfished state, which is a level considered overfished under both state and federal guidelines (i.e., less than 30% and 25%, respectively).  The stock assessment indicates abundance reached a low in the mid-1990s, and has increased slightly since then (Fig. ES-1 in Jaglielo and Wallace 2005).  The stock assessment assumed a CRT of 3% (i.e., steepness = 0.9).  Sensitivity analyses explored the range from CRT = 0% (steepness = 1.0) to CRT = 6% (steepness = 0.8). 

The trawl logbook CPUE for the years used in the assessment showed a decline from 1978 to 1997, with a possible leveling off in the mid-1990s (Fig. 9 in Jaglielo and Wallace 2005).  The most recent value of CPUE from the National Marine Fisheries Service trawl survey has the highest value observed since the survey began in the late 1970s (Fig. 2, App II in Jaglielo and Wallace 2005).  The estimated exploitation rate has declined from values near 0.2 in the early 1990s to values near 0.1 since 2000.

Based on these results we used values of CRT = 0.03 (the value assumed by the stock assessment) and CRT = 0.35 (a more conservative value, given the lack of empirical data), along with the value FLEP = 0.24, based on the current level of depletion for the California stock.  In the optimistic scenario we assigned the full weight to CRT = 0.03; in the pessimistic scenario we assigned 75% weight to CRT = 0.35 and 25% to CRT = 0.03, reflecting the lack of empirical support for the lower CRT value and the recent steep declines in CPUE in this species. 


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