Current knowledge of population size

The need for a more precautionary approach stems from the lack of knowledge of the current and recent population sizes of Antarctic toothfish and of the mechanisms regulating future population growth. The population size estimates used in Appendices R and N are based upon a very limited time series of returns from an exploratory fishery, supplemented by limited tagging and recapture studies carried out on fishing vessels. The population biology of the first 10 years of life is almost completely unknown. Current population size and the likely response of the population to the on-going harvest are therefore highly uncertain.

Present estimates of population size are based on tagging that began in 2001–02, but relatively few fish were tagged during the first 3 years of the programme. Systematic tagging began in the 2005–06 season. Appendix R restricted the analysis to a subset of vessels and trips that met certain data quality standards. Based on these data, recovered tags first exceeded ten individuals in 2005, and the analysis was based on the total of 474 recoveries (of 13 308 tags), almost all of the recoveries taking place in the period from 2005 until the end of the season in 2009 (Appendix R table 10). Large numbers of recoveries in 2010 and 2011 combined with reclassification of earlier data in the 2012 report (Appendix N table 10a) raised these totals to 859 and 19 514 respectively. In comparison, the programme undertaken to estimate cod (Gadus morhua L.) exploitation rates off the north-east coast of Newfoundland (in 1997–2002) involved tagging over 26 000 fish, with nearly 4000 recoveries by 2003 (www.dfo-mpo.gc.ca/csas-sccs/publications/resdocs-docrech/2003/2003_032-eng.htm). This much larger programme, independent of fisheries vessels, has still not provided a basis for agreement on current densities or harvesting regulations (Hutchings & Rangeley Reference Hutchings and Rangeley2011).

Mark-recapture based estimates of population size require assumptions about lack of variation in survival, random spatial mixing, behavioural homogeneity, lack of behavioural changes caused by capture/tagging events, and matching spatial distributions of sampling and the sampled population. The average individual properties may differ between sexes and age/size classes, and, if potentially significant in magnitude, these differences should be known. There are many gaps in the Ross Sea data, which cause problems for the population size estimates. Both fish mortality rates and the movements of fish relative to vessels have significant uncertainties. Mortality rates appear to be based on observed size structure of captured fish (Dunn et al. Reference Dunn, Horn and Hanchet2006), which also creates a number of uncertainties. All tagging was done on fishing vessels, which are limited by CCAMLR regulations to longlines at depths > 550 m, and which concentrate their effort where catch rates have proved to be the highest (Ross Sea slope, depths 800–1200 m; Hanchet et al. Reference Hanchet, Mormede and Dunn2010). This means that the spatial distribution of tagging and recovery effort was unlikely to match that of the population. The nature and consequences of these mortality and movement uncertainties are discussed below.

The description of population size estimation in Appendices R and N are essentially the same as those in Dunn & Hanchet (Reference Dunn and Hanchet2010). This involves using a computer program to fit a simple size-structured population model to the catch and tagging/recovery data, by minimizing an objective function reflecting differences between observed data and model predictions. Their method generates surprisingly narrow confidence intervals for the estimates of population sizes. For example, Appendix R (p. 23) gives an estimate of 2009 biomass as 49 580 tonnes with 95% confidence intervals of 12.2% below that figure (43 530) to 16.3% above that figure (57 670). More surprisingly, Appendix R asserts that this biomass in 2009 was 79.9% of the pre-fishing biomass, with 95% confidence intervals of 77.7–82.2%. The 2012 update (Appendix N) claims, with two more years of data, that the ‘current’ (unclear if it is 2011 or 2012) proportion of biomass remaining is larger, 80.0%, with still narrower 95% confidence intervals of 78.6–81.3%. The projected 1.5% annual decline due to harvesting (Appendix N) should have changed the 79.9% estimated reduction in 2009 to 76.9% in 2011, but the latter figure is significantly below the lower confidence bounds for ‘current’. The estimate of current Ross Sea biomass in 2012 (Appendix N), 59 110 tonnes, is 1440 tonnes greater than the upper 95% confidence interval for the 2009 population given in the 2011 SC-CAMLR report. The estimated original (‘Ross Sea base case’) biomass from 2012 (73 870) exceeds the upper 95% confidence interval for that original biomass estimated in 2011 (70 090). Perhaps the 2012 figures are more accurate, but the contrast certainly casts great doubt on the 95% confidence intervals in both reports, which are based on essentially the same methods. In fact, outright assumptions of several key relationships and parameters make all of these estimates and their confidence intervals questionable.

The survival rate of tagged individuals is important for estimating biomass. Appendix R (SC-CAMLR 2011) sets the mortality rate during tagging as 10%. If 20% of tagged individuals die due to tagging within a year of being marked, the number of tags present in future years will be overestimated by approximately 10% and the population size estimate will be too high by approximately the same amount. However, the basis provided for the 10% figure in Dunn & Hanchet (Reference Dunn and Hanchet2010) is that 10% is double the estimate in a study (Agnew et al. Reference Agnew, Moir-Clark, McCarthy, Unwin, Ward, Jones, Breedt, du Plessis, van Heerdon and Moreno2005) of a related species (D. eleginoides Smitt). The latter study measured survival over 12 hours in holding tanks on fishing vessels following capture and tagging. This fails to account for mortality due to post-release predation or infections, both potential causes of mortality in recently released tagged individuals. The method also ignores slow starvation (or increased predation risk over a longer time period) due to jaw or neurological damage (injuries to the jaw were noted frequently in Agnew et al. Reference Agnew, Moir-Clark, McCarthy, Unwin, Ward, Jones, Breedt, du Plessis, van Heerdon and Moreno2005). Differences in the species, the size distribution, the tagging technique, the conditions on the vessel and other factors could also mean differences in survival of tagged D. mawsoni. The finding of a recently tagged D. mawsoni in the stomach of a larger individual (Petrov & Tatarnikov Reference Petrov and Tatarnikov2010) shows that predation is indeed a possibility. (See also the comment about small hooked fish being wounded by large fish in Ainley et al. Reference Ainley, Nur, Eastman, Ballard, Parkinson, Evans and DeVries2012.) A tagging-related mortality of 20% is just as likely as the 10% assumed, and this alone would put biomass estimates well outside of the 95% confidence intervals, assuming all other parameters were accurately and precisely estimated.

The estimate of natural mortality also affects the population size estimate by determining number of surviving tagged individuals. The figure for natural mortality used in Appendices R and N projections was proposed as a possible value of natural mortality for D. eleginoides in 2006 (Hillary et al. Reference Hillary, Kirkwood and Agnew2006) based on the idea of life-history invariants (Charnov Reference Charnov1993). These ‘invariants’, however, are only rough correlations between pairs of life-history traits evident in very large sets of species, so they provide a very weak basis for estimating those trait values in any particular species. A later estimate of natural mortality based on size/age structure (Dunn et al. Reference Dunn, Horn and Hanchet2006) curiously came up with exactly the same figure for D. mawsoni, and that figure was adopted in the Appendices N and R analyses. Dunn et al. (Reference Dunn, Horn and Hanchet2006) estimated a single natural mortality for all individuals using both Chapman-Robson (Reference Chapman and Robson1960) and Hoenig (Reference Hoenig1983) methods (as well as an unpublished modification of the Hoenig method by Andre Punt). All of these depend on accurate assessment of age structure and the assumption of a stable age distribution with equal mortality across age classes. The Chapman-Robson method, as applied by Dunn et al. (Reference Dunn, Horn and Hanchet2006), is based on average age above the age at which all fish are vulnerable to sampling. Hoenig's method and its variants are based on the minimum age of the oldest 1% of the sample. The observed age distributions are confounded in unknown ways by potential differences in size- and age-specific probabilities of capture. Extreme value statistics, such as the maximum age figure in Hoenig's method are extremely sensitive to sample size, and could easily be too high if there are significant increases in mortality associated with senescence. Furthermore, mortality is usually a function of age and size, and often sex. An attempt to measure natural mortality in the Heard/McDonald Island populations of D. eleginoides by Candy et al. (Reference Candy, Welsford, Lamb, Verdouw and Hutchins2011) resulted in an estimate of 0.155 with wide 95% confidence intervals (0.055–0.250). While it is uncertain how confidence intervals can be determined for figures based on so many unverified assumptions, it is likely that the uncertainties in D. mawsoni natural mortality are comparable to those reported by Candy et al. (Reference Candy, Welsford, Lamb, Verdouw and Hutchins2011). Such uncertainties would be sufficient to alter population size estimates by more than a few percent.

Assumptions regarding behaviour and movement could result in much larger errors in population size estimates than assumptions about mortality rates. Increased avoidance of longlines following capture, tagging and release would inflate the population size estimate but nothing is known about this possibility. Movement of individuals out of the area where fishing vessels operate would reduce recapture probability, and would again increase population size estimates. This seems likely for larger individuals, which must travel long distances to the putative spawning grounds (Petrov & Tatarnikov Reference Petrov and Tatarnikov2010, Ashford et al. Reference Ashford, Dinniman, Brooks, Andrews, Hofmann, Cailliet, Jones and Ramanna2012). Smaller individuals are negatively buoyant and appear to move relatively little. However, lack of fish movement can also result in overly large population estimates if the fishing vessels move moderate distances from year-to-year to avoid locations that have been depleted by fishing of sedentary individuals in the previous year(s). This again reduces tag recovery rates (and inflates population size estimates) relative to the ideal assumptions of random sampling across the entire range by humans and rapid random movement by fish.

Movement, as well as nearly everything else about young fish is unknown, as they are virtually absent from the catch (SC-CAMLR 2011, 2012). The analysis by Ashford et al. (Reference Ashford, Dinniman, Brooks, Andrews, Hofmann, Cailliet, Jones and Ramanna2012) of otolith chemistry supports a common spawning area for the entire population. The exact location is as yet unknown, eggs and larvae have not been observed, and subsequent movements of individuals to/from supposed spawning grounds (seamounts north of the Ross Sea; Hanchet et al. Reference Hanchet, Rickard, Fenaughty, Dunn and Williams2008) have not been documented directly.

Uncertainty about fish movement also affects the interpretation of likely future temporal changes in tag returns. If fish occur in spatially heterogeneous environments that differ in resource productivity, correlated movements of fish (towards the most productive areas) and vessels (to areas with more fish) obscure population declines. It appears that a lack of awareness of this type of correlated movement was a major factor in the lack of warning of the decline of Atlantic cod (Gadus morhua) during the decade preceding the collapse (Hutchings Reference Hutchings1996). Such correlations can lead to abrupt collapses of the population (Abrams et al. Reference Abrams, Ruokolainen, Shuter and McCann2012)

Estimates of pre-harvesting biomass are also particularly problematic, as there was no survey programme that preceded fishing. The Dunn & Hanchet (Reference Dunn and Hanchet2010) approach used by SC-CAMLR (2011, 2012) is based on fitting population sizes to a population dynamics model that assumes a constant environment, with the only change in recent years being the addition of fishing. The recent population estimates fix the pre-harvest population at a level slightly higher than that estimated for the first few years of harvesting. A meaningful estimate of baseline population size would also have to consider population variability, as we have no idea whether the toothfish population at the year immediately before the start of the fishery (1997) was anywhere near the average for the twentieth century, or even for the last few decades of that century.

In summary, the claims that the current population size of D. mawsoni is known to within 10–15%, and the extent of current fractional reduction from baseline to within 1–2% are insupportable given that: i) the effective number of years of tag recoveries is less than the time required for a female to reach maturity (Parker & Grimes Reference Parker and Grimes2010), ii) both tagging and recovery have been carried out only on fishing vessels and only in a small part of the habitat used by the species, iii) movement patterns of fish and boats relative to fish are very poorly known, iv) the natural variation in the size and composition of the unharvested population is completely unknown, and v) the estimated post-tagging mortality rate is based on a figure for another species which, even for that species, lacks any consideration of increased predation and disease risk of tagged individuals. All of these limitations introduce potential errors whose size could be extremely large, but cannot meaningfully be estimated, given the data described in those articles. The narrow confidence intervals in published work reflect an unrealistic approach to estimating uncertainties.

Lack of knowledge of population dynamics

Projecting future population sizes over a significant time interval requires some knowledge of the direct and indirect effects of population size on the per individual birth minus death rate, as well as what those rates are currently. There is presently no evidence with which to estimate the effects of density dependence on vital rates in Antarctic toothfish. The dogma in fisheries is that density dependence primarily affects reproduction and/or juvenile survival, leading to a stock-recruitment relationship. Unfortunately there are no data that can be used to determine such a relationship for D. mawsoni, given that most individuals caught in the Ross Sea regional fishery after 2003 are 10–15 years of age (Ashford et al. Reference Ashford, Dinniman, Brooks, Andrews, Hofmann, Cailliet, Jones and Ramanna2012 fig. 5) and, thus are late-stage pre-recruits. The estimated modal age of maturity is 12.8 for males and 16.6 years for females (Parker & Grimes Reference Parker and Grimes2010, Appendix R). The lack of data on small individuals means that we have very little direct information on the reproductive rate or the stock-recruitment relationship, let alone the effect of fishing on recruitment. Male D. mawsoni that hatched when the reported catch approached its current target level (2002–03) are just now beginning to attain reproductive maturity, the average female will not do so for another 6 years according to the modal life-history parameters cited above. Even then, the first few recruits will only have experienced significantly reduced density in the latter part of their juvenile period. There has been an initial attempt to census smaller pre-recruit size classes using a chartered commercial fishing vessel (www.niwa.co.nz/news/survey-reveals-plenty-of-fish-in-the-ross-sea). This document indicates that a regular survey would be proposed at the next FSA working group meeting. Few details about the survey that was undertaken are given, although fish in the 70–100 cm length class are described as abundant. This is consistent with previous catches on the southern shelf (cf. Ashford et al. Reference Ashford, Dinniman, Brooks, Andrews, Hofmann, Cailliet, Jones and Ramanna2012). The size distribution in this new survey is similar to that sampled in 1999–2003 (SC-CAMLR 2012). The nearly linear length vs age relationship that is likely to be found in the juveniles of most long-lived fish (Quince et al. Reference Quince, Shuter, Abrams and Lester2008) combined with the Appendix R estimates of age at maturity indicates that the 2012 NIWA survey sample consists of fish that are at least 8–10 years old (cf. Brooks et al. Reference Brooks, Andrews, Ashford, Ramanna, Jones, Lundstrom and Cailliet2011). Thus, they still do not provide a basis for detecting any effect of fishing-caused changes in spawning stock biomass on recruitment.

The population projections described in Appendices R and N were made using a Beverton-Holt stock-recruitment relationship with a steepness parameter of 0.75 and log-normally distributed variability in recruitment having a standard deviation of 0.6. All aspects of this projection scheme are based on assumptions rather than data for D. mawsoni, and the reasoning underlying those assumptions is not laid out in the two reports. These two parameter values are similar to the mean values in a collection of stock-recruitment data by Myers et al. (Reference Myers, Bowen and Barrowman1999), and this similarity was used to justify these figures in Dunn et al. (Reference Dunn, Horn and Hanchet2006), which appears to be the original source of these assumptions for Appendices R and N. However, this does not mean that these average values will be anywhere close to the best-fit values for D. mawsoni, should data become available to determine them at some future time. Nor is there any evidence to judge the applicability of the Beverton-Holt form of the relationship.

Unintended overexploitation of many other fish stocks has occurred in spite of a much longer history of exploitation, more extensive and fisheries-independent efforts to monitor population size, and more complete knowledge of population dynamics, including recruitment rates of small individuals (Longhurst Reference Longhurst2010). Hutchings & Reynolds (Reference Hutchings and Reynolds2004) provide a general review of the many previous cases of overexploitation. Hutchings & Myers (Reference Hutchings and Myers1994) analyse the role of exploitation in the collapse of the comparatively well-studied northern Atlantic cod, a population that had been heavily exploited since 1860 and studied intensively for several decades before the collapse. A great deal of data existed on stock size and recruitment but uncertainties about this relationship permitted harvesting levels that collapsed the stock. The durations of both harvesting and programmes to estimate population sizes of Antarctic toothfish are brief in comparison.

As a result of the limited time-span of population data, there is also no evidentiary basis for estimating a low-density growth rate for Antarctic toothfish, as low spawning stock biomass relative to the un-fished state has not occurred during the period which has been studied. Some knowledge of the stock-recruitment relationship and low-density rate of increase (or more generally, density dependence) are essential aspects of any single-species approach to modelling population dynamics. Such knowledge is obviously essential for estimating the biomass that produces maximum sustainable yield (MSY). Understanding density dependence is thus required to design regulations that ensure sustainable harvesting, and to estimate the risk of population collapse and the probability of recovery following such an event. Hutchings (Reference Hutchings2001), Hutchings & Rangeley (Reference Hutchings and Rangeley2011), and Keith & Hutchings (Reference Keith and Hutchings2012) have argued that lack of data from significant periods of low-stock abundance is a more general problem with the use of current stock-recruitment data to estimate parameters in hypothetical stock-recruitment relationships. There are strong reasons for believing that recruitment processes may change qualitatively after a significant period of greatly reduced stock biomass (see also Neubauer et al. Reference Neubauer, Jensen, Hutchings and Baum2013).

Possible ecosystem responses

A basic problem with the traditional single-species approach used in the SC-CAMLR analyses is that the population dynamics of almost all fish species are determined by its food resources, predators and environment (i.e. by the rest of the ecosystem) than by its current population density. A multi-species or ‘ecosystem’ approach to fisheries management has now been widely endorsed (Link Reference Link2010), even by previous critics (cf. Walters & Martell 2004 to Hilborn & Walters Reference Hilborn and Walters1992). It is mandated by the Article II objectives of the CCAMLR, and has been endorsed for analyses of the Antarctic system generally, although not for toothfish (Constable et al. Reference Constable, de la Mare, Agnew, Everson and Miller2000). The lack of both basic theory and empirical studies has delayed effective implementation of such an approach for toothfish. Moreover, even the attempted use of multi-species approaches in the Antarctic toothfish system has largely been restricted to estimating the impact of the D. mawsoni fishery on other species in its food-web. However, the ecosystem also determines the form of density dependence experienced by a high trophic level predator like adult D. mawsoni, and simple food-web models show that traditional stock-recruitment models cannot reflect a large fraction of the range of possible relationships (Abrams Reference Abrams2009a, Reference Abrams2009b, Tschirhart Reference Tschirhart2012). Hill et al. (Reference Hill, Watters, Punt, McAllister, Le Quere and Turner2008) argue that the uncertainties of ecosystem model structure call for analyses of a variety of models, a theme re-emphasized for the Southern Ocean by Murphy et al. (Reference Murphy, Cavanagh and Hofman2012). Analysis of multiple models is a good approach in theory, but its value depends on the range of models being a good reflection of the potential range of biological reality. There is no evidence that enough is known about the role of toothfish in the Antarctic marine ecosystem to narrow the range of potential models to a manageable number that includes all plausible ones. A frequently used alternative to the ‘many models’ approach under ecosystem-model-based management is to employ computer packages designed for marine fish communities, such as Ecopath with Ecosim (Christensen & Walters Reference Christensen and Walters2004); this usually involves accepting an order of magnitude more assumptions about unknown quantities than do the single-species models.

Even in the absence of a full ecosystem model, accounting for the strongest interacting members of the biological community should improve population projections for a species of interest. Such ‘strong interactors’ must form the backbone of a full ecosystem model. If this more limited multi-species approach is not possible, then a predictive ecosystem model is out of the question. Predators and food species are the main factors involved in producing density dependence in fish. If all density dependence in D. mawsoni arose from predation and cannibalism of eggs and larvae, something would have to be known about these processes to deduce a stock-recruitment relationship. Unfortunately, nothing is known about the early life-history stages of D. mawsoni. Moreover, it is evolutionarily unlikely that density dependence should be restricted to a single life stage. As a large predator, it seems likely that density dependence in adult D. mawsoni arises at least partially from either depletion of prey or shifts in the composition of the prey to less nutritious and less catchable types as the toothfish becomes more abundant. The general range of impacts of these food-web processes on the regulation and dynamics of a predator population have been discussed (Abrams Reference Abrams2009a, Reference Abrams2009b). These studies suggest that a wide variety of relationships between standing biomass and yield are possible, and that many plausible assumptions lead to dramatic decreases in equilibrium yields over a small range of harvest rates that are only slightly above the MSY rate (Abrams Reference Abrams2009a, Reference Abrams2009b). The general consumer-resource models analysed in these studies indicate that equilibrium stock sizes close to 20% of the unexploited size frequently entail exploitation rates only marginally below rates which, if sustained over time, would cause extinction.

If food is the main source of density dependence in a predatory species, then knowledge of the predator's functional and numerical response shapes, plus the resource populations’ dynamics (density dependence and interactions) and nutritional qualities are required to determine what level of exploitation maximizes yield and how abundance shifts with greater or lesser exploitation (Abrams Reference Abrams2009a, Reference Abrams2009b). Furthermore, translating such information into relationships between harvest and equilibrium abundance would also require a breakdown of many of the species into size or age classes. In addition, the seasonal and spatial changes in diet need to be understood. Although there have been studies of D. mawsoni diet (Eastman Reference Eastman1985a, Reference Eastman1985b, Fenaughty et al. Reference Fenaughty, Stevens and Hanchet2003, Hanchet et al. Reference Hanchet, Stevenson, Horn and Blackwell2003, Stevens Reference Stevens2004, Roberts et al. Reference Roberts, Xavier and Agnew2011, Stevens et al. Reference Stevens, Dunn, Pinkerton and Forman2012), all of these are restricted in terms of location, size classes, or time-of-year, and all except Eastman (Reference Eastman1985a, Reference Eastman1985b) involve only fish from the continental slope or seamounts. Diet in the shelf study was dramatically different from that over the slope. Only Stevens et al. (Reference Stevens, Dunn, Pinkerton and Forman2012) combine diet determinations with measurements of prey abundance to quantify predator functional responses to different prey species. However, even in this study, the fact that only catch per unit effort (CPUE) data were used to estimate prey abundance lends a high degree of uncertainty to the resulting functional response estimates. While grenadiers (Macrourus spp.) have been identified as the most abundant prey in more than one deep water (seamount or slope) study, cephalopods are frequently reported in toothfish stomachs from those areas, as well as a variety of other fish species and invertebrates. Stevens et al. (Reference Stevens, Dunn, Pinkerton and Forman2012) found higher selectivity for fish species that were less represented in the diet. Moreover, the diet of D. mawsoni caught in the water column over the shelf, which includes mostly sub-adult individuals, appears to be dominated by the mid-water prey species, Pleuragramma antarcticum Boulenger (Eastman Reference Eastman1985a, Reference Eastman1985b, Fenaughty et al. Reference Fenaughty, Eastman and Sidell2008). Euphausids (Euphausia superba Dana or E. crystallorophias Holt & Tattersall), are a potentially important component of the diets of both small and large D. mawsoni (LaMesa & Eastman 2012, Fenaughty et al. Reference Fenaughty, Eastman and Sidell2008). The diet is sufficiently diverse that it would be difficult to deduce how changes in D. mawsoni would affect its food supply. The migratory life history of this species (Hanchet et al. Reference Hanchet, Rickard, Fenaughty, Dunn and Williams2008, Ashford et al. Reference Ashford, Dinniman, Brooks, Andrews, Hofmann, Cailliet, Jones and Ramanna2012) with different food sources in different places is likely to increase the possibility of alternative equilibrium states and abrupt changes in population size in response to continuous environmental change (Schreiber & Rudolf Reference Schreiber and Rudolf2008).

Other aspects of the relationship of D. mawsoni to its food-web are also poorly known. It is not known whether post-spawning fish recover their fat-depleted condition in the food-sparse ocean waters where they are thought to spawn. Switching the ecological role of toothfish, the effect of mammalian predators (toothed whales and seals), both in producing mortality and in limiting foraging times and locations, has yet to be studied. Given that D. mawsoni is likely to be one of the two most important fish prey species of large predatory mammals in the Ross Sea region (Testa et al. Reference Testa, Siniff, Ross and Winter1985, Ainley & Siniff Reference Ainley and Siniff2009), it is probable that higher-level predatory influences on toothfish dynamics are substantial. Predator avoidance behaviour and predator-driven dispersal can greatly change population dynamics in theoretical and experimental systems (Werner & Peacor Reference Werner and Peacor2003, Abrams Reference Abrams2010). The importance of such behaviourally mediated effects has been recognized (Ahrens et al. Reference Ahrens, Walters and Christensen2012). Everson (Reference Everson1970) provides one of the first descriptions of shifting habitat use driven by seal predation in an Antarctic fish (Notothenia neglecta Nybelin), and Alonzo et al. (Reference Alonzo, Switzer and Mangel2003) argue that predator avoidance by the diel vertical migration of krill has a major effect on their dynamics in the Antarctic ecosystem. A complete lack of knowledge of similar potential non-consumptive effects of predators on or prey of D. mawsoni makes it difficult to justify any particular family of food web models to guide harvesting. All of this implies that we are far from being able to construct a predictive model of the dynamics of Antarctic toothfish that incorporates realistic descriptions of its most important and direct food web interactions.

The above considerations have not prevented attempts to model the food-web (or ecosystem) of the Ross Sea (Pinkerton et al. Reference Pinkerton, Bradford-Grieve and Hanchet2010) using Ecopath with Ecosim (Christensen & Walters Reference Christensen and Walters2004). Applications of this package in the fisheries literature have increased rapidly since its introduction, but this has not been accompanied by either general acceptance of Ecosim in the broader ecological community or critical examination within the fisheries community. The constantly changing nature of the program makes critical analysis of the models difficult. However, analyses of explicit food-web models have shown that such unknown functions as size-specific growth rates, consumer functional responses, and the presence and nature of adaptive changes in foraging can all have dramatic effects (e.g. de Roos & Persson Reference De Roos and Persson2002, Abrams Reference Abrams2010). Ecosim assumes a functional response formula with strong negative effects of consumers on their own responses (Christensen & Walters Reference Christensen and Walters2004). This greatly reduces the possibility of consumer extinctions and reduces the magnitudes of trophic cascades and other indirect effects. There are qualitative uncertainties about toothfish diet, and essentially no direct information bearing on functional responses. The functional form of population dynamics models for one of the most important Antarctic populations (krill) still involves major unknowns (Atkinson et al. Reference Atkinson, Nicol, Kawaguchi, Pakhomov, Quetin, Ross, Hill, Reiss, Siegel and Tarling2012). As a result, the conclusions of the analyses of the 35-component computer models described by Pinkerton et al. (Reference Pinkerton, Bradford-Grieve and Hanchet2010) should be viewed with caution.

Does reduced harvesting following a one-half reduction in stock size provide reasonable insurance against a collapse?

Because the conclusions reached here are at odds with various international assurances of sustainability, it is worthwhile addressing the reasons for this difference. The positive assessments seem to be based on the assumptions that the target level of exploitation is relatively low and that population size assessments will allow adjustment of quotas in time to halt unanticipated declines in the population. If the procedures for estimating toothfish population size were improved it might be possible to place more confidence intervals on the estimates. If this occurs, and if harvesting is reduced or temporarily stopped when biomass drops below one-half of the estimated pre-exploitation biomass, will this ensure the continued existence of a healthy population? In the recent literature (e.g. Hilborn Reference Hilborn2010, Hilborn & Stokes Reference Hilborn and Stokes2010), it is commonly assumed that maximum sustained yields are usually attained at biomass levels that are significantly less than one-half of the unexploited level. For example, Hilborn (Reference Hilborn2010) shows that yields close to the optimum most often require that populations be below 60% of their unharvested abundance, and are usually attained when the population is in the range of 20–25% of unharvested abundance. This might be seen to imply rapid regeneration from even one-quarter of pre-exploitation biomass and makes a reduction of 50% seem like a relatively conservative target. However, the Beverton-Holt relationship itself is an assumption for almost all fisheries, with existing data being consistent with a wide variety of other relationships (e.g. Ludwig Reference Ludwig1998), and the parameter values of the best-fit Beverton-Holt relationship are highly uncertain. Analyses of such existing stock-recruitment data have shown that data from low stock abundance are frequently sparse (see below) and, when available, generally exhibit much greater variability than at higher stock sizes (Myers Reference Myers2001). This variability is what would be expected if community responses to low stock densities of the focal species were important determinants of its rate of increase from those densities. Maximizing temporal average yields in fluctuating environments (i.e. all real environments), generally requires harvesting at rates considerably below the MSY-point of the corresponding deterministic model (Ludwig Reference Ludwig1998). Fluctuations in many Ross Sea environmental variables have been particularly large in recent years (Stammerjohn et al. Reference Stammerjohn, Massom, Rind and Martinson2012). Maximizing yields in models where the food supply of the harvested species determines reproductive rate often entails MSY at populations much greater than 50% of unexploited biomass, even in constant environments (Abrams Reference Abrams2009a, Reference Abrams2009b).

There are reasons for suspecting that single-species models are likely to underestimate the risk of collapse posed by high levels of harvesting of large predatory species in a food-web. Food-web models of predators at high trophic levels whose young have different diets often exhibit two or more equilibria or attractors and the presence of abrupt changes that are irreversible on a short timescale. Such outcomes have been described in different models by Walters & Kitchell (Reference Walters and Kitchell2001), de Roos & Persson (Reference De Roos and Persson2002) and Abrams (Reference Abrams2011). A common mechanism producing an alternative state with few or no predators is that depression of predator populations allows increases in the size and/or numbers of prey, which then have adverse effects on juvenile predators (either via competition with or predation on the juveniles). This is not a purely theoretical result. It is one of the main explanations proposed for the non-recovery of cod stocks in the north-west Atlantic (e.g. Swain & Sinclair Reference Swain and Sinclair2000, Swain Reference Swain2011), and it could easily apply to D. mawsoni. Hutchings (Reference Hutchings2000, Reference Hutchings2001) catalogues a variety of stocks that have failed to recover following population reductions due to fishing despite drastic declines in harvesting (Longhurst Reference Longhurst2010). This is inconsistent with the single-species Beverton-Holt relationship, but is expected when shifts in food-web structure brought on by heavy exploitation of adults of a large predatory species produce decreased per capita growth rates, due either to changes in population structure or food-web interactions. Keith & Hutchings (Reference Keith and Hutchings2012) found evidence of such low population traps for heavily exploited Canadian cod and Alaskan Walleye Pollock (Theragra chalcogramma (Pallas)). They also suggest that one-third of the species in the Myers database exhibit no evidence of density compensation (higher per capita growth at lower densities) when the analysis is restricted to species that have experienced low standing stock biomasses. Hutchings & Rangeley (Reference Hutchings and Rangeley2011) conclude that ‘Emergent and demographic Allee effects, coupled with altered interspecific interactions, render questionable the presumption that the recovery of heavily depleted populations can be reliably forecasted by population dynamical behaviour during the decline.’ While higher target abundances reduce the possibility of collapse due to food-web shifts, the nearly complete lack of quantitative knowledge of predator-prey relationships in the D. mawsoni food-web makes it impossible to estimate the density at which such regime shifts might become possible.

The possibility of regime shifts also places limits on the use of adaptive management and knowledge of population size to ensure against collapse of a target population, even if population size were known accurately. Regime shifts can in theory be triggered by either harvesting or environmental change. Because we do not know the range of historical densities of D. mawsoni, or the point at which a major food-web shift might occur, even accurate knowledge of current densities is unlikely to provide warning of a collapse due to a harvest-driven regime shift. Environmentally driven regime shifts on a decadal scale have been described for the Southern Ocean (Dayton Reference Dayton1989, Jenouvrier et al. Reference Jenouvrier, Weimerskirch, Barbraud, Park and Cazelles2005). The possibility of decadal changes in food availability was proposed as one possibility to explain long-term changes in the condition of toothfish caught in McMurdo Sound (Ainley et al. Reference Ainley, Nur, Eastman, Ballard, Parkinson, Evans and DeVries2012). La Mesa & Eastman (2012) suggest that climate change could easily collapse the population of Pleuragramma antarcticum, which is a key food source for D. mawsoni, at least over the shelf.

Other complications for population projection

Spatial structure in the environment combined with movement of individuals can greatly alter population dynamics, and it is well known that D. mawsoni can travel thousands of kilometres (Eastman & DeVries Reference Eastman and DeVries2000, Hanchet et al. Reference Hanchet, Rickard, Fenaughty, Dunn and Williams2008, Petrov & Tatarnikov Reference Petrov and Tatarnikov2010). Recent work (Ashford et al. Reference Ashford, Dinniman, Brooks, Andrews, Hofmann, Cailliet, Jones and Ramanna2012, Hanchet et al. Reference Hanchet, Rickard, Fenaughty, Dunn and Williams2008) argues that D. mawsoni in the south-east Pacific Basin and Ross Sea is likely to constitute a single population with spawning most likely among the seamounts north of the Ross Sea slope, and subsequent dispersal to other areas driven by currents. Nevertheless, details of the movements are largely unknown. This complicates the use of mark-recapture techniques to monitor population size. It also means that exploitation of fish across part of the range may provide a misleading estimate of total population size and/or productivity, as a significant input to the fishery in early years may well come from immigration rather than reproduction. Theoretical models (Abrams et al. Reference Abrams, Ruokolainen, Shuter and McCann2012) have shown the potential for abrupt population collapse with increased harvesting in a system having spatially heterogeneous harvest combined with food-based habitat choice by the harvested species. If an abrupt collapse in adult densities occurs, the lengthy juvenile period for D. mawsoni and the fact that spawning is not likely to be annual (Parker & Grimes Reference Parker and Grimes2010, Ashford et al. Reference Ashford, Dinniman, Brooks, Andrews, Hofmann, Cailliet, Jones and Ramanna2012) will prevent rapid recovery.

Other mechanisms can delay the recovery of overexploited stocks. Adaptive evolutionary shifts in life-history traits of the exploited species are possible (e.g. Heino & Godø Reference Heino and Godø2002, Walsh et al. Reference Walsh, Munch, Chiba and Conover2006, Longhurst Reference Longhurst2010). There is also evidence from some species that shifts to a smaller and younger average female size can affect egg quality as well as reproductive output (Berkeley et al. Reference Berkeley, Hixon, Larson and Love2004). Neither of these mechanisms appears to be included in the models used to estimate the maximum sustainable harvest of D. mawsoni (Appendices R and N). Either could produce a lower than desired stock abundance that could persist for many generations despite reduced harvesting (Shust & Kozlov Reference Shust and Kozlov2006).

In many systems illegal fishing is a problem, and Appendix R lists some IUU (illegal, unreported and unregulated) catches of D. mawsoni. It is difficult to judge the extent of illegal fishing in the Antarctic, although the extreme environment provides some protection, and the presence of observers on all licensed boats presumably ensures compliance. On the other hand, by its nature IUU fishing is extremely difficult to quantify. Its level is thought to be low in the Ross Sea region but high in neighbouring waters (Österblom et al. Reference Österblom, Sumaila, Bodin, Sundberg and Press2010, Ainley & Pauly Reference Ainley and Pauly2013). The fact that the currently established quota can be caught legally, both in the Ross Sea and waters to the west, within one month (as has been the case in recent years) indicates that significant biomass could be caught illegally over a very short time period. Indeed, an illegal 130 km long gillnet with 29 tons of D. mawsoni was recovered off East Antarctica in 2009 (www.traffic.org/home/2009/11/6/australia-confiscates-130-km-long-deepwater-gillnet.html). The ability to rapidly capture large quantities of fish makes detection of illegal activities more difficult (and adds to the general problems of monitoring such activities in remote areas likely frequented by the Ross Sea stock). In several other important fisheries, IUU catch has been estimated to exceed 30% of total catch (Doulman Reference Doulman2001). Mortality due to unreported catch and discarding of small individuals likely contributed to the Atlantic cod collapse (Myers et al. Reference Myers, Hutchings and Barrowman1997). Mortality of discarded individuals and individuals that sustain injuries freeing themselves from longlines could have a large effect on a species like D. mawsoni.

While the above analysis is based on analyses of populations in the greater Ross Sea area, much of it is likely to apply to other D. mawsoni populations, some of which have had or may in the future have exploratory fisheries (Ainley & Pauly Reference Ainley and Pauly2013). A number of the above criticisms of D. mawsoni fishery practices apply to many other currently exploited fish species that lack a long history of either harvesting or research. This certainly includes many populations of the Patagonian toothfish (D. eleginoides) in the Antarctic and elsewhere. The possibility of over-exploitation of Ross Sea Antarctic toothfish is particularly high for several reasons. There is far less of a historical record of exploitation and its effects, as there was no commercial fishing prior to 1997. The long juvenile period combined with the short history of the fishery means that there is no knowledge of the effects of density on recruitment. This long juvenile period combined with the current inability to census fish during their first decade of life means that a collapse of recruitment would be likely to remain hidden for a decade. Efforts to reverse such an event would then require another decade before increases in newborns translated into an increase in the spawning stock, even if reduced fishing was immediately successful in raising the birth rate. Because of its lack of anti-freeze and the fact that it is also subject to the same forces promoting exploitation, Patagonian toothfish (D. eleginoides) populations are unlikely to increase and substitute for the Antarctic species in the functioning of the Ross Sea ecosystem.

The Antarctic environment, and especially that of the Ross Sea region, is undergoing extreme and rapid alteration in the ice environment (Stammerjohn et al. Reference Stammerjohn, Massom, Rind and Martinson2012). It would be surprising if this did not have major effects on the food web in which D. mawsoni is embedded, which would then affect maximum harvest rates as well as the entire production-harvest relationship. For example, the eventual predicted loss of ice cover over increasing areas and time periods could greatly increase predation rates by mammals (whales and seals); habitat selection by D. mawsoni to reduce predation risk in turn could diminish their food intake and growth rates. Increases in ice cover over the shorter term could have the opposite effects in some areas, including the Ross Sea, where such increases have occurred in recent decades (Stammerjohn et al. Reference Stammerjohn, Massom, Rind and Martinson2012). However, the time course and ultimate extent of such changes cannot be predicted with any accuracy at present. The fact that very significant environmental changes are likely within a time span equal to two generations of the harvested species means that population growth parameters estimated using data from one decade may well be inaccurate in the next.