A comment on ‘ ‘ What catch data can tell us about the status of global fisheries ’ ’ ( Froese et al . 2012 )

There is considerable interest in the state of the world’s natural fishery resources. The paper by Froese et al. (2012) is a recent example of applying a set of ad hoc decision rules to a time series of catch data in order to assign the world’s fisheries to categories of exploitation and hence make generalisations about their current status. They conclude that the percentage of stocks that are over-exploited is worse than previously reported in FAO (2010). The approach used by Froese et al. is based on an algorithm proposed by Froese and Kesner-Reyes (2002) which has been heavily criticised both on theoretical grounds and from simulation studies (Branch et al. 2011; Daan et al. 2011; Wilberg and Miller 2007). In their recent paper, Froese et al. (2012) produce additional analyses to support their method which assumes that maximum sustainable yield (MSY) lies in the interval (0.5Cmax, Cmax), where Cmax is the maximum observed catch in the time series. Unfortunately, these analyses do not support their contention that MSY for a particular stock is related to maximum catch in a predictable way and renders their conclusions unsafe. Froese et al. suggest that Cmax is highly correlated with MSY for a set of fully assessed fish stocks in the northeast Atlantic. Whilst the coefficient of determination, R, appears impressively high (Fig. 1a), it hides the fact that the relationship, which is plotted on a log scale, is simply a feature of the fact that the stocks examined differ by several orders of magnitude. The variation in catch within a stock is far less than the variation in catch between stocks, so choosing two values from each stock (Cmax, MSY) results in taking two values of very similar magnitude. Hence, plotting these pairs where each stock has a vastly different scale is little different from plotting x on x. It is obvious that small stocks will have a low MSY and large stocks will have a high MSY. It does not mean Cmax can predict MSY, or vice versa, with any useful precision. It can be shown through a simple simulation that the correlation is largely unrelated to a relationship between MSY and Cmax. In the simulation, a catch is selected at random from each stock and the R calculated for each realisation of the relationship between log catch and log MSY. The result of a series of 10,000 simulations is shown in Fig. 1. Figure 1a shows the original relationship reported by Froese et al. Also shown is the relationship that had the highest R based on selecting a catch at random. As can be seen, it is possible to obtain a better R using just a random catch. While obtaining an R value larger than the Cmax relationship is fairly rare in the simulations, it is not fortuitous. Figure 1b shows the frequency distribution of the R values from the simulations. Nearly all the R values are larger than 0.9 with the mode at 0.95. In effect, any random catch from the time series is highly correlated with MSY when examined across stocks of widely differing magnitude. Hence, the statement by Froese et al. that MSY explains 98 % of the variance in Cmax hides the fact that almost all of the variation explained is due to the difference in scale between stocks since MSY will explain most of the variation in any randomly chosen catch. The high correlation between Cmax and MSY fails when the effect of stock size is accounted for. Froese et al. give the regression equation for the relationship in Fig. 1a as: Communicated by M. Coll.