An elementary model of animal aggregation is presented. The group-size distributions resulting from this model are truncated power laws. The predictions of the model are found to be consistent with data that describe the groupsize distributions of tuna fish, sardinellas, and African buffaloes.

The fear of a rapid depletion of world fish stocks because of over-exploitation is increasing. Analysis of 1519 main series of the FAO world fisheries catch database over the last 50 years reveals that 366 fisheries' collapses occurred, that is nearly one fishery of four. The robustness of this result is tested by performing several complementary analyses using different conservative options. The number of collapses has been stable through time since 1950s indicating no improvement in the overall fisheries management. Three typical patterns emerge from the analysis of catch series during the period preceding the collapses: smooth collapse (33%), i.e. a long regular decline, erratic collapse (45%), i.e. a fall after several ups and downs, and a plateau-shaped collapse (21%), i.e. a sudden fall after a relatively long and stable persistence of high level of catches. Using a simple mathematical model, we relate the plateau-shaped collapses (which are, by nature, the most difficult to predict) to surreptitiously increasing exploitation and a depensatory mechanism at low population levels. Thus, a stable level of catch over several years is shown to conceal the risk of a sudden collapse. This jeopardizes the common assumption that considers the stability of catch as a goal for fisheries sustainability.

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Recruitment success of anchovy Engraulis encrasicolus in the southern Benguela is thought to depend largely on the passive transport of eggs and larvae from their warm-water spawning area, located in the southern part of their distribution range (Agulhas Bank), to their cold-water nursery grounds located 500 km away on the west coast of South Africa. In order to test this hypothesis, the output of a 3D hydrodynamic model was coupled to a particle-tracking model, allowing the quantification of different factors such as the timing and precise location of spawning activity, the frequency of spawning activity within a month, the level of aggregation of the spawning stock, and the interannual variability of transport due to mesoscale processes. Results from the model indicate that spawning season and area have a major effect on transport success. The most favourable period for spawning was September to March, peaking in November, and the western Agulhas Bank was the most favourable spawning area. A low success rate of passive transport to the core inshore nursery area in the model suggests that additional processes such as swimming or advection are required for larvae to reach this area. In general, there was good agreement between observed spawning patterns and the optimal temporal and spatial strata where particle transport was most successful, suggesting that the spawning strategy of anchovy is mainly the result of an adaptation to the circulation patterns in the region. Nonetheless, some discrepancies were observed between the success of transport and actual spawning patterns, and temperature may also be an important factor to take into consideration to fully explain how this originally temperate species is able to survive in an area of highly contrasting temperatures.KEY WORDS: Individual-based model · Transport success · Anchovy · Ichthyoplankton · Recruitment · Reproductive strategy · Southern Benguela · Engraulis encrasicolus Resale or republication not permitted without written consent of the publisherMar Ecol Prog Ser 250: [247][248][249][250][251][252][253][254][255][256][257][258][259][260][261][262] 2003 total purse-seine fishery catch (Barange et al. 1999). Catches during the 1950s and early 1960s were dominated by adult sardine, peaking at ~400 000 t in 1961-62, but declined to <100 000 t by 1967 ). This collapse was followed by a rapid increase in catches of anchovy, which replaced sardine as the dominant species during the 1970s and 1980s (Crawford et al. 1987). In addition to these decadalscale fluctuations in abundance, direct acoustic estimates of pelagic fish abundance since 1984 (Hampton 1987, Barange et al. 1999) have indicated considerable annual variability in recruitment of both sardine and anchovy, particularly the latter (Fig. 1). Estimated variations in anchovy recruitment were 5-fold during the period 1984 to 1999 and increased to nearly 20-fold after 2 yr of exceptional recruitment in 2000 and 2001. Recruitment of pelagic fish is the net result of a continuous series of l...