A Bayesian method for identification of stock mixtures from molecular marker data

Molecular markers have been demonstrated to be useful for the estimation of stock mixture proportions where the origin of individuals is determined from baseline samples. Bayesian statistical methods are widely recognized as providing a preferable strategy for such analyses. In general, Bayesian estimation is based on standard latent class models using data augmentation through Markov chain Monte Carlo techniques. In this study, we introduce a novel approach based on recent developments in the estimation of genetic population structure. Our strategy combines analytical integration with stochastic optimization to identify stock mixtures. An important enhancement over previous methods is the possibility of appropriately handling data where only partial baseline sample information is available. We address the potential use of nonmolecular, auxiliary biological information in our Bayesian model.

A prior for steepness in stock-recruitment relationships, based on an evolutionary persistence principle

Priors are existing information or beliefs that are needed in Bayesian analysis. Informative priors are important in obtaining the Bayesian posterior distributions for estimated parameters in stock assessment. In the case of the steepness parameter (h), the need for an informative prior is particularly important because it determines the stock-recruitment relationships in the model. However, specifications of the priors for the h parameter are often subjective. We used a simple population model to derive h priors based on life history considerations. The model was based on the evolutionary principle that persistence of any species, given its life history (i.e., natural mortality rate) and its exposure to recruitment variability, requires a minimum recruitment compensation that enables the species to rebound consistently from low critical abundances (Nc). Using the model, we derived the prior probability distributions of the h parameter for fish species that have a range of natural mortality, recruitment variabilities, and Nt values.

A simulation model of the dynamics of Peruvian anchoveta (Engraulis ringens)

The article describes the key elements of a model simulating the dynamics of the anchoveta (Engraulis ringens) in the Peruvian upwelling system (4 degrees to 14 degrees South). This model, based on coupled differential equations, is parametrized mainly using empirical data and functional relationships presented in two volumes issued by ICLARM in 1987 and 1989, and may thus be viewed as test of the hypotheses presented therein. Results to date suggest that present knowledge of mechanisms controlling the anchoveta stock is essentially consistent, and sufficient to build a model reflecting essential features of the stock biomass and recruitment dynamics.

Sex-change rules, stock dynamics, and the performance of spawning-per-recruit measures in protogynous stocks

Predicting and under-standing the dynamics of a population requires knowledge of vital rates such as survival, growth, and reproduction. However, these variables are influenced by individual behavior, and when managing exploited populations, it is now generally realized that knowledge of a species’ behavior and life history strategies is required. However, predicting and understanding a response to novel conditions—such as increased fishing-induced mortality, changes in environmental conditions, or specific management strategies—also require knowing the endogenous or exogenous cues that induce phenotypic changes and knowing whether these behaviors and life history patterns are plastic. Although a wide variety of patterns of sex change have been observed in the wild, it is not known how the specific sex-change rule and cues that induce sex change affect stock dynamics. Using an individual based model, we examined the effect of the sex-change rule on the predicted stock dynamics, the effect of mating group size, and the performance of traditional spawning-per-recruit (SPR) measures in a protogynous stock. We considered four different patterns of sex change in which the probability of sex change is determined by 1) the absolute size of the individual, 2) the relative length of individuals at the mating site, 3) the frequency of smaller individuals at the mating site, and 4) expected reproductive success. All four pat-terns of sex change have distinct stock dynamics. Although each sex-change rule leads to the prediction that the stock will be sensitive to the size-selective fishing pattern and may crash if too many reproductive size classes are fished, the performance of traditional spawning-per-recruit measures, the fishing pattern that leads to the greatest yield, and the effect of mating group size all differ distinctly for the four sex-change rules. These results indicate that the management of individual species requires knowledge of whether sex change occurs, as well as an understanding of the endogenous or exogenous cues that induce sex change.

Review of size- and age-dependence in batch spawning: implications for stock assessment of fish species exhibiting indeterminate fecundity

Most assessments of fish stocks use some measure of the reproductive potential of a population, such as spawning biomass. However, the correlation between spawning biomass and reproductive potential is not always strong, and it likely is weakest in the tropics and subtropics, where species tend to exhibit indeterminate fecundity and release eggs in batches over a protracted spawning season. In such cases, computing annual reproductive output requires estimates of batch fecundity and the annual number of batches—the latter subject to spawning frequency and duration of spawning season. Batch fecundity is commonly measured by age (or size), but these other variables are not. Without the relevant data, the annual number of batches is assumed to be invariant across age. We reviewed the literature and found that this default assumption lacks empirical support because both spawning duration and spawning frequency generally increase with age or size. We demonstrate effects of this assumption on measures of reproductive value and spawning potential ratio, a metric commonly used to gauge stock status. Model applications showed substantial sensitivity to age dependence in the annual number of batches. If the annual number of batches increases with age but is incorrectly assumed to be constant, stock assessment models would tend to overestimate the biological reference points used for setting harvest rates. This study underscores the need to better understand the age- or size-dependent contrast in the annual number of batches, and we conclude that, for species without evidence to support invariance, the default assumption should be replaced with one that accounts for age- or size-dependence.

In search of climate effects on Atlantic Croaker (Micropogonias undulatus) stock off the U.S. Atlantic coast with Bayesian state-space biomass dynamic models

Atlantic Croaker (Micropogonias undulatus) production dynamics along the U.S. Atlantic coast are regulated by fishing and winter water temperature. Stakeholders for this resource have recommended investigating the effects of climate covariates in assessment models. This study used state-space biomass dynamic models without (model 1) and with (model 2) the minimum winter estuarine temperature (MWET) to examine MWET effects on Atlantic Croaker population dynamics during 1972–2008. In model 2, MWET was introduced into the intrinsic rate of population increase (r). For both models, a prior probability distribution (prior) was constructed for r or a scaling parameter (r0); imputs were the fishery removals, and fall biomass indices developed by using data from the Multispecies Bottom Trawl Survey of the Northeast Fisheries Science Center, National Marine Fisheries Service, and the Coastal Trawl Survey of the Southeast Area Monitoring and Assessment Program. Model sensitivity runs incorporated a uniform (0.01,1.5) prior for r or r0 and bycatch data from the shrimp-trawl fishery. All model variants produced similar results and therefore supported the conclusion of low risk of overfishing for the Atlantic Croaker stock in the 2000s. However, the data statistically supported only model 1 and its configuration that included the shrimp-trawl fishery bycatch. The process errors of these models showed slightly positive and significant correlations with MWET, indicating that warmer winters would enhance Atlantic Croaker biomass production. Inconclusive, somewhat conflicting results indicate that biomass dynamic models should not integrate MWET, pending, perhaps, accumulation of longer time series of the variables controlling the production dynamics of Atlantic Croaker, preferably including winter-induced estimates of Atlantic Croaker kills.

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.

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.

A probabilistic energy model for non-domestic building sectors applied to analysis of school buildings in greater London

The diversity of non-domestic buildings at urban scale poses a number of difficulties to develop models for large scale analysis of the stock. This research proposes a probabilistic, engineering-based, bottom-up model to address these issues. In a recent study we classified London's non-domestic buildings based on the service they provide, such as offices, retail premise, and schools, and proposed the creation of one probabilistic representational model per building type. This paper investigates techniques for the development of such models. The representational model is a statistical surrogate of a dynamic energy simulation (ES) model. We first identify the main parameters affecting energy consumption in a particular building sector/type by using sampling-based global sensitivity analysis methods, and then generate statistical surrogate models of the dynamic ES model within the dominant model parameters. Given a sample of actual energy consumption for that sector, we use the surrogate model to infer the distribution of model parameters by inverse analysis. The inferred distributions of input parameters are able to quantify the relative benefits of alternative energy saving measures on an entire building sector with requisite quantification of uncertainties. Secondary school buildings are used for illustrating the application of this probabilistic method. © 2012 Elsevier B.V. All rights reserved.

Numerical study of soil heterogeneity effects on contaminant transport in unsaturated soil (model development and validation)

The movement of chemicals through soil to groundwater is a major cause of degradation of water resources. In many cases, serious human and stock health implications are associated with this form of pollution. The study of the effects of different factors involved in transport phenomena can provide valuable information to find the best remediation approaches. Numerical models are increasingly being used for predicting or analyzing solute transport processes in soils and groundwater. This article presents the development of a stochastic finite element model for the simulation of contaminant transport through soils with the main focus being on the incorporation of the effects of soil heterogeneity in the model. The governing equations of contaminant transport are presented. The mathematical framework and the numerical implementation of the model are described. The comparison of the results obtained from the developed stochastic model with those obtained from a deterministic method and some experimental results shows that the stochastic model is capable of predicting the transport of solutes in unsaturated soil with higher accuracy than deterministic one. The importance of the consideration of the effects of soil heterogeneity on contaminant fate is highlighted through a sensitivity analysis regarding the variance of saturated hydraulic conductivity as an index of soil heterogeneity. © 2011 John Wiley & Sons, Ltd.

The role of payout ratio in the relationship between stock returns and dividend yield

ap Gwilym, Owain, McManus, Ian, and Thomas, Stephen, 'The role of payout ratio in the relationship between stock returns and dividend yield', Journal of Business Finance & Accounting (2004) 31(9-10) pp.1355-1387 RAE2008

A study of the Hobson and Rogers volatility model

We firstly examine the model of Hobson and Rogers for the volatility of a financial asset such as a stock or share. The main feature of this model is the specification of volatility in terms of past price returns. The volatility process and the underlying price process share the same source of randomness and so the model is said to be complete. Complete models are advantageous as they allow a unique, preference independent price for options on the underlying price process. One of the main objectives of the model is to reproduce the `smiles' and `skews' seen in the market implied volatilities and this model produces the desired effect. In the first main piece of work we numerically calibrate the model of Hobson and Rogers for comparison with existing literature. We also develop parameter estimation methods based on the calibration of a GARCH model. We examine alternative specifications of the volatility and show an improvement of model fit to market data based on these specifications. We also show how to process market data in order to take account of inter-day movements in the volatility surface. In the second piece of work, we extend the Hobson and Rogers model in a way that better reflects market structure. We extend the model to take into account both first and second order effects. We derive and numerically solve the pde which describes the price of options under this extended model. We show that this extension allows for a better fit to the market data. Finally, we analyse the parameters of this extended model in order to understand intuitively the role of these parameters in the volatility surface.