Comment on temperature-dependent stock–recruit modeling for Pacific sardine (Sardinops sagax) in Jacobson and MacCall (1995), McClatchie et al. (2010), and Lindegren and Checkley (2013)

Abstract

Jacobson and MacCall (1995, JM) estimated spawner–recruit models for the northern stock of Pacific sardine (Sardinops sagax) along the western coast of North America with log recruitment and log recruitment success as the dependent variables. Log recruitment models are the topic of this comment and most important for Pacific sardine. JM used data (N = 34) for 1935–1963 and 1985–1990 (Fig. 1). Their preferred log recruitmentmodel included a statistically significant nonlinear relationship with spawning biomass and a statistically significant linear relationship with three season average sea surface temperature data collected at Scripps Pier (SPSST) in San Diego, California. McClatchie et al. (2010, MEA) reevaluated the spawner–recruit relationship for Pacific sardine using additional data for 1991– 2008 (Fig. 1). They found a statistically significant relationship between spawning biomass and log recruitment. However, the relationship with SPSST “broke down” when additional data were included. Loss of statistical significance as data accumulate is a common and important problem in modeling recruitment using environmental variables (Myers 1998). Lindegren and Checkley (2013, LC) revisited the question of temperature effects on Pacific sardine recruitment using a shorter but more recent set of spawning biomass and recruitment data (1981– 2010) and annual (rather than three-season average) environmental indices. LC’s environmental data included SPSST, mean sea surface temperatures at 5–15 m measured in the Southern California Bight spawning habitat during California Cooperative Oceanic Fisheries Investigations (CalCOFI) cruises, and several other candidate data sets. LC did not use data for 1935–1965 because spawning biomass and recruitment estimates used as data for 1981–2010 could be obtained from a single assessment model source (JM andMEA used data from several sources). LC found that annual SPSST data were statistically significant although SST at 5–15m fromCalCOFI cruises was a better predictor for log recruitment and log recruitment success. CalCOFI SST data were used in their best models. Apart from using different data sets, LC did not explain differences in results from the three studies beyond pointing out the different modeling approaches in MEA and LC. The explanation is a main goal our comment. Uncertainty about on-and-off-again temperature effects on Pacific sardine recruitment is important. Myers (1998) identified Pacific sardine as one of only two cases in which environment– recruitment relationships had held up with the passage of time and were used in stock assessment work. JM’s results were used to help predict recruitments in stock assessment modeling during 1996 to 2003 when analysts switched to stock assessment programs that did not accommodate environmental effects on recruitment. The Pacific Fishery Management Council adopted an SPSST-dependent environmental control rule for Pacific sardine with maximum harvest rates varying from 5% under cool conditions to 15% under warm conditions based on JM’s findings. The control rule was used until MEA published their results (Pacific Fishery Management Council 1998). Based on a stock assessment finalized in 2011 (Hill et al. 2011) and MEA’s results, SPSSTdependent control rule was abandoned and the Pacific Fishery Management Council’s Science and Statistical Committee concluded that “... temperature, or another correlated environmental variable, may be important in sardine recruitment, but that the SIO [SPSST] index is not reflective of the temperature in the area of greatest sardine spawning activity and is no longer correlated with sardine productivity.” (Pacific Fishery Management Council 2011). MEA’s results and lack of an explanation for different conclusions among JM, MEA, and LC caused considerable uncertainty and controversy about environmental effects on recruitment of Pacific sardine. After reconsidering methods and reanalyzing MEA’s data, we determined that their models suffered from statistical shortcomings that caused misleading results. In particular, MEA fit log recruitment and other models by linear regression in two steps. In the first step, log recruitment was regressed on spawning biomass, and the p value for spawning biomass was calculated from the results of the first regression. In the second step, residuals from step one were regressed on SPSST, and the p value for SPSST was calculated from the results of the second regression. The intent of MEA’s modeling approach was to remove densitydependent effects before estimating environmental effects. However, sequential regression on residuals gives incorrect parameter estimates, p values, and other results when the predictor variables are correlated (the correlation between spawning biomass and SPSST data used by MEAwas = −0.23). Weisberg (1980, pp. 35–40) gives a clear demonstration of this problem inmultiple regression analysis, and it is straightforward to show by simulation that a correlation of = −0.23 is sufficient to undermine statistical results. This problem occurs because the relative importance of spawning biomass and SPSST in predicting recruitment is obscured to the extent that the predictor variables S and T are cor-