Changes in abundance of the northern Benguela sardine stock during the decade 1990 &#150 2000, with comments on the relative importance of fishing and the environment

The northern Benguela stock of sardine Sardinops sagax used to be considered one of the major clupeoid stocks of the world; it supported an average annual catch of >700 000 tons throughout the 1960s. The stock has been in a depressed state for more than two decades, as demonstrated by annual catches that averaged around 50 000 tons between 1978 and 1989 and only slightly more in the 1990s. It has experienced fluctuations in abundance of several orders of magnitude during the most recent decade. Population size increased until 1992, when the acoustic estimate of biomass was about 750 000 tons. Catches increased accordingly, averaging 100 000 tons between 1992 and 1995, but from 1992 to 1996 the stock was in decline and the lowest annual catch in the history of the fishery was taken in 1996. Although there was a small increase during the last three years of the decade, the stock remains seriously depleted. Survey-based recruitment indices suggest that the changes in the 1990s were initiated by fluctuations in recruitment, but the decline was almost certainly exacerbated by continued fishing. Poor recruitment and decreasing catch rates between 1993 and 1996 in a number of other key resources suggest that system-wide environmental changes were an important factor in the decline of the sardine stock at that time. Anomalous oceanographic conditions, such as extensive hypoxic shelf waters in 1993/94 and a Benguela Niño in 1995, support this conclusion.Keywords: environmental effects, fishing effects, northern Benguela, recruitment, sardineAfrican Journal of Marine Science 2001, 23: 67–8

An overview of the living marine resources of Namibia

This paper gives an overview of the main living marine resources of Namibia. It focuses on the scientific research conducted during the past decade as input to the management of these resources. The distribution and habitats of the most important harvested species and the main seabird populations are briefly described and discussed. The life histories of the major exploited species are summarized, with emphasis on spatial and temporal spawning patterns, dispersal of early life stages, migration patterns of recruits and adults, and diet, the latter particularly as it relates to potential competition between species. A number of commercially important species, such as the hake Merluccius capensis and M. paradoxus, deep-sea red crab Chaceon maritae, West Coast rock lobster Jasus lalandii, skipjack tuna Katsuwonus pelamis, southern albacore Thunnus alalunga and to a lesser extent Cape horse mackerel Trachurus capensis, southern African sardine Sardinops sagax and Cape anchovy Engraulis capensis, are distributed across national boundaries, requiring regional cooperation in research and management. The history and current status of the major fisheries is discussed. Over the past 30–40 years total annual catches have declined from a peak of around 2 million tons in the late 1960s to less than a million tons in the 1990s. This decline has been due, mainly, to a collapse in the sardine stock in the late 1960s and 1970s, and a reduction in the catches of hake and horse mackerel under a conservative management strategy in the past decade. Changes in the abundance and distribution of commercially important species, as determined by acoustic and trawl surveys and catch-based analytical methods, are presented. The effect of major environmental anomalies on the distribution and abundance of the resources in recent years is discussed. The most dramatic anomaly in recent years was the wide-scale advection of low-oxygen water into the northern Benguela from the Angola Dome in 1994, and the subsequent Benguela Niño of 1995, which appear to have severely impacted the Namibian sardine population and many other resources. The present socio-economic value of the Namibian fishing industry is given together with the broad policy, legislation and formal structures for managing the living marine resources.Keywords: Benguela, exploitation, fisheries, management, marine resources, NamibiaAfrican Journal of Marine Science 2001, 23: 5–3

Development of acoustic techniques for assessment of orange roughy Hoplostethus atlanticus biomass off Namibia, and of methods for correcting for bias

Orange roughy form dense spawning aggregations in specific small areas in deep water on the Namibian shelf between late June and early August each year. The biomass in three such areas, where most commercial fishing occurs (the Johnies, Frankies and Rix Quota Management Areas, or QMAs) has been assessed acoustically each year since 1997. Acoustic estimates of the aggregated portion of the biomass (the only component that can be assessed reliably using acoustics) were obtained for all three QMAs in 1997 and 1998, but only for Frankies in 1999 owing to increased problems with target identification as the biomass declined. The methodology developed for these surveys, including the equipment used, survey design, target identification, data processing and error analysis are described. Some important biases that should be corrected for when estimating absolute abundance of orange roughy acoustically are addressed. Individual sources of error were quantified as well as possible, and input to an error model that simulated the error process and produced probability density functions of absolute biomass, from which the mean absolute biomass and its standard error could be computed for each survey, effectively correcting for identified sources of bias and quantifying the overall uncertainty. The correction factors ranged from 1.58 to 1.71 and the CVs increased by factors of 1.2–2.1. Target strength uncertainty and negative bias attributable to the dead zone close to the bottom were considered to be the most serious errors. The acoustic estimates indicate a substantial decline in orange roughy biomass in all three QMAs since 1997, in accord with indices from contemporaneous swept-area surveys and the catch rate of the commercial fleet. Acoustic estimates have already been used extensively to manage the resource and are likely to remain important in the future. Keywords: acoustics, deep-water fisheries, orange roughy, surveyAfrican Journal of Marine Science 2001, 23: 223–24

On the new approach to variable separation in the time-dependent Schr\"odinger equation with two space dimensions

We suggest an effective approach to separation of variables in the Schr\"odinger equation with two space variables. Using it we classify inequivalent potentials $V(x_1,x_2)$ such that the corresponding Schr\" odinger equations admit separation of variables. Besides that, we carry out separation of variables in the Schr\" odinger equation with the anisotropic harmonic oscillator potential $V=k_1x_1^2+k_2x_2^2$ and obtain a complete list of coordinate systems providing its separability. Most of these coordinate systems depend essentially on the form of the potential and do not provide separation of variables in the free Schr\" odinger equation ($V=0$).Comment: 21 pages, latex, to appear in the "Journal of Mathematical Physics" (1995

Hydrodynamic reductions of the heavenly equation

We demonstrate that Pleba\'nski's first heavenly equation decouples in infinitely many ways into a triple of commuting (1+1)-dimensional systems of hydrodynamic type which satisfy the Egorov property. Solving these systems by the generalized hodograph method, one can construct exact solutions of the heavenly equation parametrized by arbitrary functions of a single variable. We discuss explicit examples of hydrodynamic reductions associated with the equations of one-dimensional nonlinear elasticity, linearly degenerate systems and the equations of associativity.Comment: 14 page

A thick shell Casimir effect

We consider the Casimir energy of a thick dielectric-diamagnetic shell under a uniform velocity light condition, as a function of the radii and the permeabilities. We show that there is a range of parameters in which the stress on the outer shell is inward, and a range where the stress on the outer shell is outward. We examine the possibility of obtaining an energetically stable configuration of a thick shell made of a material with a fixed volume

Changes in some key biological parameters of the northern Benguela sardine stock

During the past 50 years, more than 15 million tons of sardine have been harvested from the northern Benguela ecosystem. The sardine population has undergone changes in abundance estimated to range over more than two orders of magnitude, but for the past two decades it is estimated to have remained at less than 10% of former levels of abundance. Some key changes in biological parameters, notably age composition and rates of natural mortality, are discussed in relation to the changes in abundance. Literature values for the period before the 1990s are compared to values calculated from acoustic survey population estimates thereafter. Although these recent data are potentially biased, and often lack estimates of precision, it is argued that they are sufficient to demonstrate general trends. The likelihood of the sardine stock recovering is seemingly reduced owing to the recent high rate of adult natural mortality.Keywords: biological parameters, exploitation, mortality, northern Benguela, sardine, Sardinops sagaxAfrican Journal of Marine Science 2001, 23: 111–12

On the nature of the most obscured C-rich AGB stars in the Magellanic Clouds

The stars in the Magellanic Clouds with the largest degree of obscuration are used to probe the highly uncertain physics of stars in the asymptotic giant branch (AGB) phase of evolution. Carbon stars in particular, provide key information on the amount of third dredge-up (TDU) and mass loss. We use two independent stellar evolution codes to test how a different treatment of the physics affects the evolution on the AGB. The output from the two codes are used to determine the rates of dust formation in the circumstellar envelope, where the method used to determine the dust is the same for each case. The stars with the largest degree of obscuration in the LMC and SMC are identified as the progeny of objects of initial mass $2.5-3~M_{\odot}$ and $\sim 1.5~M_{\odot}$, respectively. This difference in mass is motivated by the difference in the star formation histories of the two galaxies, and offers a simple explanation of the redder infrared colours of C-stars in the LMC compared to their counterparts in the SMC. The comparison with the Spitzer colours of C-rich AGB stars in the SMC shows that a minimum surface carbon mass fraction $X(C) \sim 5\times 10^{-3}$ must have been reached by stars of initial mass around $1.5~M_{\odot}$. Our results confirm the necessity of adopting low-temperature opacities in stellar evolutionary models of AGB stars. These opacities allow the stars to obtain mass-loss rates high enough ($\gtrsim 10^{-4}M_{\odot}/yr$) to produce the amount of dust needed to reproduce the Spitzer coloursComment: 14 pages, 5 figures, 1 table; accepted for publication in MNRAS Main Journa