Gaughan et al.: Distribution of Sard/nops sagax off southwestern Australia 



621 



counted. Estimation of egg production was undertaken 

 by fitting a negative exponential model (Picquelle and 

 Stauffer, 1985) and was derived from the y-axis inter- 

 cept of the regression model, representing time 0. The 

 number of stages used to fit the model depended on the 

 egg abundance for each stage; the best fitting model 

 was chosen visually from an iterative sequence of fits. 

 The best fit was not necessarily that with the smallest 

 CV but rather that which intuitively did not violate our 

 understanding of natural mortality rates as determined 

 from the literature. For example, the slope of the regres- 

 sion model must be negative and egg mortality rates 

 should fall within the broad range of 0.9-3.9/d (e.g., 

 Smith et al., 1989). 



Estimation of spawning area 



According to water temperatures during each survey and 

 the stage of egg development, Sardinops eggs were deter- 

 mined to have been spawned either the previous night 

 ("day-1") or two nights previous ("day-2") as described 

 by Fletcher et al. (1996). The total survey area was esti- 

 mated by constructing a polygon around all stations. The 

 spawning area was defined as the area in which day-1 

 Sardinops eggs were found (Fletcher et al., 1996a). The 

 areas of the polygons around stations that had day-1 

 eggs, referred to as positive stations, were summed to 

 estimate the spawning area for each zone. When positive 



stations occurred on the margin of the sampling area, 

 polygons for these positive stations were drawn as for the 

 embedded positive stations, but the areas of these poly- 

 gons were extended by a standardized amount beyond 

 the sampling areas (Wolf and Smith, 1986). 



The proportion of positive stations (PPS) was calcu- 

 lated for each survey. The proportion of the survey area 

 (PSA) that consisted of spawning area was also evalu- 

 ated in each case. PPS and PSA were positively corre- 

 lated at each region (Table 2); this result was expected 

 and indicated that PPS provides a realistic representa- 

 tion of changes in spawning area. The relationships 

 between PPS and the areal estimates of spawning area 

 were not as strong, but these latter estimates suffered 

 as potential predictors of biomass in our study because 

 of the large differences in numbers of plankton samples 

 collected between surveys (Table 1). PPS is thus not 

 only an objective measure but can also be considered 

 as an index of spawning area. 



Modeling of spawning biomass 



The collapse in distribution of Sardinops at each of four 

 locations in southern Western Australia in 1999 is shown 

 by the decline in spawning area (Fig. 2). The importance 

 of this collapse in providing contrast for model fitting 

 in otherwise poor data sets (few points with either flat 

 or clumped distributions) is evident from linear fits of 



