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Retrospective patterns are systematic changes in estimates of population size, or other assessment model-derived quantities, that occur as additional years of data are added to, or removed from, a stock assessment. These patterns are an insidious problem, and can lead to severe errors when providing management advice. Here, we use a simulation framework to show that temporal changes in selectivity, natural mortality, and growth can induce retrospective patterns in integrated, age-structured models. We explore the potential effects on retrospective patterns of catch history patterns, as well as model misspecification due to not accounting for time-varying biological parameters and selectivity. We show that non-zero values for Mohn’s ρ (a common measure for retrospective patterns) can be generated even where there is no model misspecification, but the magnitude of Mohn’s ρ tends to be lower when the model is not misspecified. The magnitude and sign of Mohn’s ρ differed among life histories, with different life histories reacting differently from each type of temporal change. The value of Mohn’s ρ is not related to either the sign or magnitude of bias in the estimate of terminal year biomass. We propose a rule of thumb for values of Mohn’s ρ which can be used to determine whether a stock assessment shows a retrospective pattern.

Assumptions about the future productivity of a stock are necessary to calculate sustainable catches in fisheries management. Fisheries scientists often assume the number of young fish entering a population (recruitment) is related to the biomass of spawning adults and that recruitment dynamics do not change over time. Thus, managers often use a target biomass based on spawning biomass as the basis for calculating sustainable catches. However, we show recruitment and spawning biomass are not positively related over the observed range of stock sizes for 61% of 224 stocks in the RAM Legacy Stock Assessment Database. Furthermore, 85% of stocks for which spawning biomass may not drive recruitment dynamics over the observed ranges exhibit shifts in average recruitment, which is often used in proxies for target biomasses. Our results suggest that the environment more strongly influences recruitment than spawning biomass over the observed stock sizes for many stocks. Management often endeavours to maintain stock sizes within the observed ranges, so methods for setting management targets that include changes within an ecosystem may better define the status of some stocks, particularly as climate changes.

Center for the Advancement of Population Assessment Methodology, 8901 La Jolla ShoresDrive,La Jolla, CA 92037, USA*Corresponding author: tel: +1 206 543 4270; fax: +1 206 685 7471; e-mail: kfjohns@uw.eduJohnson,K.F.,Monnahan,C.C.,McGilliard,C.R.,Vert-pre,K.A.,Anderson,S.C.,Cunningham,C.J.,Hurtado-Ferro,F.,Licandeo,R.R.,Muradian,M.L.,Ono,K.,Szuwalski,C.S.,Valero,J.L.,Whitten,A.R.,andPunt,A.E.Time-varyingnaturalmortalityinfisheriesstockassessmentmodels:identifyingadefaultapproach. – ICESJournalofMarineScience,doi:10.1093/icesjms/fsu055.Received4 September 2013; revised 1 March 2014; accepted 3 March 2014.A typical assumption used in most fishery stock assessments is that natural mortality (M) is constant across time and age. However, M is rarelyconstant in reality as a result of the combined impacts of exploitation history, predation, environmental factors, and physiological trade-offs.Misspecification or poor estimation of M can lead to bias in quantities estimated using stock assessment methods, potentially resulting inbiasedestimatesoffisheryreferencepointsandcatchlimits,withthemagnitudeofbiasbeinginfluencedbylifehistoryandtrendsinfishingmor-tality. Monte Carlo simulations were used to evaluate the ability of statistical age-structured population models to estimate spawning-stockbiomass,fishingmortality,andtotalallowablecatchwhenthetrueMwasage-invariant,buttime-varying.Configurationsofthestockassessmentmethod,implementedinStockSynthesis,includedasingleage-andtime-invariantMparameter,specifiedatoneofthethreelevels(high,medium,andlow)oranestimatedM.Themin–max(i.e.mostrobust)approachtospecifyingMwhenitisthoughttovaryacrosstimewastoestimateM.The least robust approach for most scenarios examined was to fix M at a high value, suggesting that the consequences of misspecifying M areasymmetric.Keywords: model misspecification, natural mortality,population models, reference points, simulation, Stock Synthesis, time-varying.

Management of marine resources depends on the assessment of stock status in relation to established reference points. However, many factors contribute to uncertainty in stock assessment outcomes, including data type and availability, life history, and exploitation history. A simulation–estimation framework was used to examine the level of bias and accuracy in assessment model estimates related to the quality and quantity of length and age composition data across three life-history types (cod-, flatfish-, and sardine-like species) and three fishing scenarios. All models were implemented in Stock Synthesis, a statistical age-structured stock assessment framework. In general, the value of age composition data in informing estimates of virgin recruitment (R0), relative spawning-stock biomass (SSB100/SSB0), and terminal year fishing mortality rate (F100), decreased as the coefficient of variation of the relationship between length and age became greater. For this reason, length data were more informative than age data for the cod and sardine life histories in this study, whereas both sources of information were important for the flatfish life history. Historical composition data were more important for short-lived, fast-growing species such as sardine. Infrequent survey sampling covering a longer period was more informative than frequent surveys covering a shorter period.

Szuwalski (1) has greatly misinterpreted the principal message of our report (2). We did not claim you could reliably estimate regime shifts for individual stocks. Table 2 in our report (2) clearly shows that the chance of improper assignment of the hypothesis is very high, even when you have a long time-series of data in hand. At any point in time, managers will rarely know if observed changes in productivity are a result of regime changes, changes in biomass, or random.

Fish stocks fluctuate both in abundance and productivity (net population increase), and there are many examples demonstrating that productivity increased or decreased due to changes in abundance caused by fishing and, alternatively, where productivity shifted between low and high regimes, entirely unrelated to abundance. Although shifts in productivity regimes have been described, their frequency and intensity have not previously been assessed. We use a database of trends in harvest and abundance of 230 fish stocks to evaluate the proportion of fish stocks in which productivity is primarily related to abundance vs. those that appear to manifest regimes of high or low productivity. We evaluated the statistical support for four hypotheses: ( i ) the abundance hypothesis, where production is always related to population abundance; ( ii ) the regimes hypothesis, where production shifts irregularly between regimes that are unrelated to abundance; ( iii ) the mixed hypothesis, where even though production is related to population abundance, there are irregular changes in this relationship; and ( iv ) the random hypothesis, where production is random from year to year. We found that the abundance hypothesis best explains 18.3% of stocks, the regimes hypothesis 38.6%, the mixed hypothesis 30.5%, and the random hypothesis 12.6%. Fisheries management agencies need to recognize that irregular changes in productivity are common and that harvest regulation and management targets may need to be adjusted whenever productivity changes.

Assumptions about the future productivity of a stock are necessary to calculate sustainable catches in fisheries management. Fisheries scientists often assume the number of young fish entering a population (recruitment) is related to the biomass of spawning adults and that recruitment dynamics do not change over time. Thus, managers often use a target biomass based on spawning biomass as the basis for calculating sustainable catches. However, we show recruitment and spawning biomass are not positively related over the observed range of stock sizes for 61% of 224 stocks in the RAM Legacy Stock Assessment Database. Furthermore, 85% of stocks for which spawning biomass may not drive recruitment dynamics over the observed ranges exhibit shifts in average recruitment, which is often used in proxies for target biomasses. Our results suggest that the environment more strongly influences recruitment than spawning biomass over the observed stock sizes for many stocks. Management often endeavours to maintain stock sizes within the observed ranges, so methods for setting management targets that include changes within an ecosystem may better define the status of some stocks, particularly as climate changes.