Long-range interactions in turbulence and the energy decay problem.

We discuss the long-range interactions that arise in homogeneous turbulence as a consequence of the Biot-Savart law. We note that, somewhat surprisingly, these long-range correlations are very weak in decaying, isotropic turbulence, and we argue that this should also be true for magnetohydrodynamic, rotating and stratified turbulence. If this is indeed the case, it is possible to make explicit predictions for the rate of decay of energy in these anisotropic systems, and it turns out that these predictions are consistent with the available numerical and experimental evidence.

The effects of size-selective fisheries on the stock dynamics of and sperm limitation in sex-changing fish

Fisheries models have traditionally focused on patterns of growth, fecundity, and survival of fish. However, reproductive rates are the outcome of a variety of interconnected factors such as life-history strategies, mating patterns, population sex ratio, social interactions, and individual fecundity and fertility. Behaviorally appropriate models are necessary to understand stock dynamics and predict the success of management strategies. Protogynous sex-changing fish present a challenge for management because size-selective fisheries can drastically reduce reproductive rates. We present a general framework using an individual-based simulation model to determine the effect of life-history pattern, sperm production, mating system, and management strategy on stock dynamics. We apply this general approach to the specific question of how size-selective fisheries that remove mainly males will impact the stock dynamics of a protogynous population with fixed sex change compared to an otherwise identical dioecious population. In this dioecious population, we kept all aspects of the stock constant except for the pattern of sex determination (i.e. whether the species changes sex or is dioecious). Protogynous stocks with fixed sex change are predicted to be very sensitive to the size-selective fishing pattern. If all male size classes are fished, protogynous populations are predicted to crash even at relatively low fishing mortality. When some male size classes escape fishing, we predict that the mean population size of sex-changing stocks will decrease proportionally less than the mean population size of dioecious species experiencing the same fishing mortality. For protogynous species, spawning-per-recruit measures that ignore fertilization rates are not good indicators of the impact of fishing on the population. Decreased mating aggregation size is predicted to lead to an increased effect of sperm limitation at constant fishing mortality and effort. Marine protected areas have the potential to mitigate some effects of fishing on sperm limitation in sex-changing populations.

Recruitment and spawning-stock biomass distribution of bay anchovy (Anchoa mitchilli) in Chesapeake Bay

Recruitment of bay anchovy (Anchoa mitchilli) in Chesapeake is related to variability in hydrological conditions and to abundance and spatial distribution of spawning stock biomass (SSB). Midwater-trawl surveys conducted for six years, over the entire 320-km length of the bay, provided information on anchovy SSB, annual spatial patterns of recruitment, and their relationships to variability in the estuarine environment. SSB of anchovy varied sixfold in 1995–2000; it alone explained little variability in young-of-the-year (YOY) recruitment level in October, which varied ninefold. Recruitments were low in 1995 and 1996 (47 and 31 Z 109) but higher in 1997–2000 (100 to 265 Z 109). During the recruitment process the YOY population migrated upbay before a subsequent fall-winter downbay migration. The extent of the downbay migration by maturing recruits was greatest in years of high freshwater input to the bay. Mean dissolved oxygen (DO) was more important than freshwater input in controlling distribution of SSB and shifts in SSB location between April– May (prespawning) and June–August (spawning) periods. Recruitments of bay anchovy were higher when mean DO was lowest in the downbay region during the spawning season. It is hypothesized that anchovy recruitment level is inversely related to mean DO concentration because low DO is associated with high plankton productivity in Chesapeake Bay. Additionally, low DO conditions may confine most bay anchovy spawners to the downbay region, where production of larvae and juveniles is enhanced. A modified Ricker stock-recruitment model indicated density-compensatory recruitment with respect to SSB and demonstrated the importance of spring-summer DO levels and spatial distribution of SSB as controllers of bay anchovy recruitment.

Coupling ecology and economy: modeling optimal release scenarios for summer flounder (Paralichthys dentatus) stock enhancement

Increasing interest in the use of stock enhancement as a management tool necessitates a better understanding of the relative costs and benefits of alternative release strategies. We present a relatively simple model coupling ecology and economic costs to make inferences about optimal release scenarios for summer flounder (Paralichthys dentatus), a subject of stock enhancement interest in North Carolina. The model, parameterized from mark-recapture experiments, predicts optimal release scenarios from both survival and economic standpoints for varyious dates-of-release, sizes-at-release, and numbers of fish released. Although most stock enhancement efforts involve the release of relatively small fish, the model suggests that optimal results (maximum survival and minimum costs) will be obtained when relatively large fish (75–80 mm total length) are released early in the nursery season (April). We investigated the sensitivity of model predictions to violations of the assumption of density-independent mortality by including density-mortality relationships based on weak and strong type-2 and type-3 predator functional responses (resulting in depensatory mortality at elevated densities). Depending on postrelease density, density-mortality relationships included in the model considerably affect predicted postrelease survival and economic costs associated with enhancement efforts, but do not alter the release scenario (i.e. combination of release variables) that produces optimal results. Predicted (from model output) declines in flounder over time most closely match declines observed in replicate field sites when mortality in the model is density-independent or governed by a weak type-3 functional response. The model provides an example of a relatively easy-to-develop predictive tool with which to make inferences about the ecological and economic potential of stock enhancement of summer flounder and provides a template for model creation for additional species that are subjects of stock enhancement interest, but for which limited empirical data exist.

Sizes of walleye pollock (Theragra chalcogramma) and Atka mackerel (Pleurogrammus monopterygius) consumed by the western stock of Steller sea lions (Eumetopias jubatus) in Alaska from 1999 to 2000

Prey-size selectivity by Steller sea lions (Eumetopias jubatus) is relevant for understanding the foraging behavior of this declining predator, but studies have been problematic because of the absence and erosion of otoliths usually used to estimate fish length. Therefore, we developed regression formulae to estimate fish length from seven diagnostic cranial structures of walleye pollock (Theragra chalcogramma) and Atka mackerel (Pleurogrammus monopterygius). For both species, all structure measurements were related with fork length of prey (r2 range: 0.78−0.99). Fork length (FL) of walleye pollock and Atka mackerel consumed by Steller sea lions was estimated by applying these regression models to cranial structures recovered from scats (feces) collected between 1998 and 2000 across the range of the Alaskan western stock of Steller sea lions. Experimentally derived digestion correction factors were applied to take into account loss of size due to digestion. Fork lengths of walleye pollock consumed by Steller sea lions ranged from 3.7 to 70.8 cm (mean=39.3 cm, SD=14.3 cm, n=666) and Atka mackerel ranged from 15.3 to 49.6 cm (mean=32.3 cm, SD=5.9 cm, n=1685). Although sample sizes were limited, a greater proportion of juvenile (≤20 cm) walleye pollock were found in samples collected during the summer (June−September) on haul-out sites (64% juveniles, n=11 scats) than on summer rookeries (9% juveniles, n=132 scats) or winter (February−March) haul-out sites (3% juveniles, n=69 scats). Annual changes in the size of Atka mackerel consumed by Steller sea lions corresponded to changes in the length distribution of Atka mackerel resulting from exceptionally strong year classes. Considerable overlap (>51%) in the size of walleye pollock and Atka mackerel taken by Steller sea lions and the sizes of these species caught by the commercial trawl fishery were demonstrated.

Sizes of walleye pollock (Theragra chalcogramma) consumed by the eastern stock of Steller sea lions (Eumetopias jubatus) in Southeast Alaska from 1994 to 1999

Lengths of walleye pollock (Theragra chalcogramma) consumed by Steller sea lions (Eumetopias jubatus) were estimated by using allometric regressions applied to seven diagnostic cranial structures recovered from 531 scats collected in Southeast Alaska between 1994 and 1999. Only elements in good and fair condition were selected. Selected structural measurements were corrected for loss of size due to erosion by using experimentally derived condition-specific digestion correction factors. Correcting for digestion increased the estimated length of fish consumed by 23%, and the average mass of fish consumed by 88%. Mean corrected fork length (FL) of pollock consumed was 42.4 ±11.6 cm (range=10.0−78.1 cm, n=909). Adult pollock (FL>45.0 cm) occurred more frequently in scats collected from rookeries along the open ocean coastline of Southeast Alaska during June and July (74% adults, mean FL=48.4 cm) than they did in scats from haul-outs located in inside waters between October and May (51% adults, mean FL=38.4 cm). Overall, the contribution of juvenile pollock (≤20 cm) to the sea lion diet was insignificant; whereas adults contributed 44% to the diet by number and 74% by mass. On average, larger pollock were eaten in summer at rookeries throughout Southeast Alaska than at rookeries in the Gulf of Alaska and the Bering Sea. Overall it appears that Steller sea lions are capable of consuming a wide size range of pollock, and the bulk of fish fall between 20 and 60 cm. The use of cranial hard parts other than otoliths and the application of digestion correction factors are fundamental to correctly estimating the sizes of prey consumed by sea lions and determining the extent that these sizes overlap with the sizes of pollock caught by commercial fisheries.

A general framework for integrating environmental time series into stock assessment models: model description, simulation testing, and example

We present a method to integrate environmental time series into stock assessment models and to test the significance of correlations between population processes and the environmental time series. Parameters that relate the environmental time series to population processes are included in the stock assessment model, and likelihood ratio tests are used to determine if the parameters improve the fit to the data significantly. Two approaches are considered to integrate the environmental relationship. In the environmental model, the population dynamics process (e.g. recruitment) is proportional to the environmental variable, whereas in the environmental model with process error it is proportional to the environmental variable, but the model allows an additional temporal variation (process error) constrained by a log-normal distribution. The methods are tested by using simulation analysis and compared to the traditional method of correlating model estimates with environmental variables outside the estimation procedure. In the traditional method, the estimates of recruitment were provided by a model that allowed the recruitment only to have a temporal variation constrained by a log-normal distribution. We illustrate the methods by applying them to test the statistical significance of the correlation between sea-surface temperature (SST) and recruitment to the snapper (Pagrus auratus) stock in the Hauraki Gulf–Bay of Plenty, New Zealand. Simulation analyses indicated that the integrated approach with additional process error is superior to the traditional method of correlating model estimates with environmental variables outside the estimation procedure. The results suggest that, for the snapper stock, recruitment is positively correlated with SST at the time of spawning.

Developing a growth-transition matrix for the stock assessment of the green sea urchin (Strongylocentrotus droebachiensis) off Maine

The green sea urchin (Strongylocentrotus droebachiensis) is important to the economy of Maine. It is the state’s fourth largest fishery by value. The fishery has experienced a continuous decline in landings since 1992 because of decreasing stock abundance. Because determining the age of sea urchins is often difficult, a formal stock assessment demands the development of a size-structured population dynamic model. One of the most important components in a size-structured model is a growth-transition matrix. We developed an approach for estimating the growth-transition matrix using von Bertalanffy growth parameters estimated in previous studies of the green sea urchin off Maine. This approach explicitly considers size-specific variations associated with yearly growth increments for these urchins. The proposed growth-transition matrix can be updated readily with new information on growth, which is important because changes in stock abundance and the ecosystem will likely result in changes in sea urchin key life history parameters including growth. This growth-transition matrix can be readily incorporated into the size-structured stock assessment model that has been developed for assessing the green sea urchin stock off Maine.

Stock-rebuilding time isopleths and constant-F stock-rebuilding plans for overfished stocks

Stock-rebuilding time isopleths relate constant levels of fishing mortality (F), stock biomass, and management goals to rebuilding times for overfished stocks. We used simulation models with uncertainty about FMSY and variability in annual intrinsic growth rates (ry) to calculate rebuilding time isopleths for Georges Bank yellowtail flounder, Limanda ferruginea, and cowcod rockfish, Sebastes levis, in the Southern California Bight. Stock-rebuilding time distributions from stochastic models were variable and right-skewed, indicating that rebuilding may take less or substantially more time than expected. The probability of long rebuilding times increased with lower biomass, higher F, uncertainty about FMSY, and autocorrelation in ry values. Uncertainty about FMSY had the greatest effect on rebuilding times. Median recovery times from simulations were insensitive to model assumptions about uncertainty and variability, suggesting that median recovery times should be considered in rebuilding plans. Isopleths calculated in previous studies by deterministic models approximate median, rather than mean, rebuilding times. Stochastic models allow managers to specify and evaluate the risk (measured as a probability) of not achieving a rebuilding goal according to schedule. Rebuilding time isopleths can be used for stocks with a range of life histories and can be based on any type of population dynamics model. They are directly applicable with constant F rebuilding plans but are also useful in other cases. We used new algorithms for simulating autocorrelated process errors from a gamma distribution and evaluated sensitivity to statistical distributions assumed for ry. Uncertainty about current biomass and fishing mortality rates can be considered with rebuilding time isopleths in evaluating and designing constant-F rebuilding plans.