John E. Feenstra

Estimating length-transition probabilities as polynomial functions of premoult length

In length-based lobster stock-assessment models where the population is subdivided into discrete length classes, growth is represented as a matrix of length-transition probabilities. At specific times during the model year, the length-transition probabilities specify the proportions growing into larger length classes. These probabilities are calculated by integration of gamma or normal distributions over the length intervals of each larger length class. The mean growth from any given length category is commonly modelled by a von Bertalanffy or other continuous growth curve. The coefficients of variation, describing variance among individuals, are modelled by functions constant or linear with length. These approaches have yielded good descriptions of growth for males and juveniles, but the von Bertalanffy curve does not capture the rapid decrease in mean growth rate after maturity for females. We generalized this length-transition model by writing the parameters of the growth distributions as polynomial functions of carapace length. This generalization procedure increases the number of parameters depending on the degree of polynomial employed. In fits to South Australian rock lobster (Jasus edwardsii) tagrecovery data, each increase in polynomial degree yielded a significantly better fit for females and successfully represented the decrease in growth at maturity. For males, the von Bertalanffy description was little improved by higher polynomials.

FIELD TRIALS AND SIMULATIONS OF POINT-NEAREST-NEIGHBOR DISTANCE METHODS FOR ESTIMATING ABALONE DENSITY

Abstract We investigated evidence for bias in estimates of abalone density from the point-nearest-neighbor (PNN) diver survey method wherein divers measure distances between abalone and from random points to nearest abalone. Field and simulation tests of the PNN survey method were undertaken. In two plots of a lightly exploited abalone population in South Australia, all the greenlip abalone (Haliotis laevigata Donovan) were enumerated by divers, providing the true density in both study regions. Clustering of abalone was visually evident and quantified by a Hopkins test. The study areas were gridded into 1-m2 quadrats. Divers measured distances from randomly selected grid points to the nearest abalone, and from that nearest abalone to its nearest neighbor. A second set of inter-abalone distances from every fifth tagged abalone were also measured. Two PNN estimator formulas, of Byth (1982) and Diggle (1975), were used to estimate abalone density. The resulting estimates from both PNN estimators were biased, underestimating true (enumerated) density by 18% to 29% and 18% to 55% in the two sites respectively. The Byth estimator showed less underestimation. Clustering of abalone is a likely cause of density underestimation in the two study areas. Simulated PNN surveys in simulated clustered populations quantified both overestimation and underestimation bias. Randomly interspersed individuals (“loners”) reduced density underestimation, and centrally (rather than uniformly) distributed clusters worsened it. Because the spatial distributions of abalone and other invertebrates are often clustered, this strong bias is problematic for the use of PNN as a survey method for estimating density in these populations.

A diver survey method to quantify the clustering of sedentary invertebrates by the scale of spatial autocorrelation

Sedentary benthic invertebrates exhibit clustering at a range of spatial scales. Animal clustering reduces the precision of diver surveys and can accelerate overexploitation in dive fisheries. Dive harvesters target the densest aggregations of males and females that produce the highest rates of egg fertilisation during mass spawning events. By quantifying these effects of harvesting on fertilisation success, measuring animal clustering can inform stock management for reproductive sustainability. We present a method to measure the spatial extent of density aggregations down to 1 m, extending a previously described leaded-line survey design. Applying this method to abalone, research divers counted individuals in successive 1 × 2 m2 quadrats lying along adjoining pairs of 1 × 100 m2 transects. Clusters were observed as neighbouring quadrats of high animal density. Spatial autocorrelations at inter-quadrat distances of 1 to 100 m were calculated for four surveys, with eight pairs of transects swum in each survey. For all four surveys, inside two survey regions, spatial autocorrelation declined to non-significant levels at a distance of ~20 m. Quantified by the distance within which density counts are correlated, this quadrat-within-transect method provides a diver survey measure of the scale of spatial aggregation for sedentary invertebrates such as abalone, sea cucumbers and urchins.