Multiple stable reference points in oyster populations: biological relationships for the eastern oyster (Crassostrea virginica) in Delaware Bay

Abstract—In the first of two companion papers, a 54-yr time series for the oyster population in the New Jersey waters of Delaware Bay was analyzed to develop biological relationships necessary to evaluate maximum sustainable yield (MSY) reference points and to consider how multiple stable points affect reference point-based management. The time series encompassed two regime shifts, one circa 1970 that ushered in a 15-yr period of high abundance, and a second in 1985 that ushered in a 20-yr period of low abundance. The intervening and succeeding periods have the attributes of alternate stable states. The biological relationships between abundance, recruitment, and mortality were unusual in four ways. First, the broodstock–recruitment relationship at low abundance may have been driven more by the provision of settlement sites for larvae by the adults than by fecundity. Second, the natural mortality rate was temporally unstable and bore a nonlinear relationship to abundance. Third, combined high abundance and low mortality, though likely requiring favorable environmental conditions, seemed also to be a self-reinforcing phenomenon. As a consequence, the abundance –mortality relationship exhibited both compensatory and depensatory components. Fourth, the geographic distribution of the stock was intertwined with abundance and mortality, such that interrelationships were functions both of spatial organization and inherent populatio

Multiple stable reference points in oyster populations: implications for reference point-based management

In the second of two companion articles, a 54-year time series for the oyster population in the New Jersey waters of Delaware Bay is analyzed to examine how the presence of multiple stable states affects reference-point–based management. Multiple stable states are described by four types of reference points. Type I is the carrying capacity for the stable state: each has associated with it a type-II reference point wherein surplus production reaches a local maximum. Type-II reference points are separated by an intermediate surplus production low (type III). Two stable states establish a type-IV reference point, a point-of-no-return that impedes recovery to the higher stable state. The type-II to type-III differential in surplus production is a measure of the difficulty of rebuilding the population and the sensitivity of the population to collapse at high abundance. Surplus production projections show that the abundances defining the four types of reference points are relatively stable over a wide range of uncertainties in recruitment and mortality rates. The surplus production values associated with type-II and type-III reference points are much more uncertain. Thus, biomass goals are more easily established than fishing mortality rates for oyster population

Validation of a method for estimating realized annual fecundity in a multiple spawner, the long-snouted seahorse (Hippocampus guttulatus), using underwater visual census

The long-snouted seahorse (Hippocampus guttulatus) (Cuvier, 1829), was used to validate the pre-dictive accuracy of three progressively realistic models for estimating the realized annual fecundity of asyn-chronous, indeterminate, multiple spawners. Underwater surveys and catch data were used to estimate the duration of the reproductive season, female spawning frequency, male brooding frequency, and batch fecun-dity. The most realistic model, a generalization of the spawning fraction method, produced unbiased estimates of male brooding frequency (mean ±standard deviation [SD]=4.2 ±1.6 broods/year). Mean batch fecundity and realized annual fecundity were 213.9 (±110.9) and 903.6 (±522.4), respectively. However, females prepared significantly more clutches than the number of broods produced by males. Thus, methods that infer spawning frequency from patterns in female egg production may lead to significant overestimates of realized annual fecundity. The spawning fraction method is broadly applicable to many taxa that exhibit parental care and can be applied nondestructively to species for which conservation is a concern.

Estimates of commercial longline selectivity for Pacific halibut (Hippoglossus stenolepis) from multiple marking experiments

The term “selectivity” refers to the relationship between the size (or age) of a fish and its vulnerability to a given kind of fishing gear. A selectivity schedule, along with other parameters, is normally estimated in the course of fitting a stock assessment model, and the estimated schedule can have a large effect on both the estimate of present stock abundance and the choice of an appropriate harvest rate. The form of the relationship is usually not known and not well determined by the data, and equally good model fits can often be obtained with different plausible specifications of selectivity. Choosing among the model fits and associated abundance estimates in this situation is problematic (Sigler, 1999; Sullivan et al., 19

Multiple environmental states affecting penaeid shrimp production in Peru

A modification of the Schaefer surplus-production model was used to account for environmental induced variations of shrimp (Penaeus vannamei) catch in northern Peru. Based on time series of catch, effort, river discharge and sea surface temperature, fluctuations in catch of shrimps are explained and discussed with respect to multiple level of carrying capacity and hence different maximum sustainable yields.

Maximum likelihood estimation of mortality and growth with individual variability from multiple length-frequency data

We consider estimation of mortality rates and growth parameters from length-frequency data of a fish stock and derive the underlying length distribution of the population and the catch when there is individual variability in the von Bertalanffy growth parameter L∞. The model is flexible enough to accommodate 1) any recruitment pattern as a function of both time and length, 2) length-specific selectivity, and 3) varying fishing effort over time. The maximum likelihood method gives consistent estimates, provided the underlying distribution for individual variation in growth is correctly specified. Simulation results indicate that our method is reasonably robust to violations in the assumptions. The method is applied to tiger prawn data (Penaeus semisulcatus) to obtain estimates of natural and fishing mortality.