The complex variation of hydraulic conductivity in natural aquifer materials is represented in a continuum sense as a spatial stochastic process which is characterized by a covariance function. Assuming statistical homogeneity, the theory of spectral analysis is used to solve perturbed forms of the stochastic differential equation describing flow through porous media with randomly varying hydraulic conductivity. From analyses of unidirectional mean flows which are perturbed by one-and three-dimensional variations of the logarithm of the hydraulic conductivity, local relationships between the head variance and the log conductivity variance are obtained. The results show that the head variance produced by three-dimensional statistical isotropic conductivity perturbations is only 5% of that in the corresponding one-dimensional case. The head variance is also strongly dependent on the correlation distance of the log conductivity covariance function. These results emphasize the importance of including spatial correlation structure and multidimensional effects in stochastic simulation of groundwater flow. HYDRAULIC CONDUCTIVITY AS A STOCHASTIC PROCESSCasual observation of roadcuts, gravel pits, and other outcrops of sedimentary deposits which are potential water-transmitting units demonstrates that properties which affect hydraulic conductivity, such as grain size, are highly variable even within a given geologic deposit. One would also notice that the variation of the properties is not completely disordered in space; rather, one may observe a structured arrangement of bodies of different sediment types which may exhibit typical dimensions but are not completely regular. These two characteristics would also be seen in quantitative observations of flow properties such as geophysical well logs or laboratory tests of core samples. The properties are highly variable; hydraulic conductivity may vary by 3 orders of magnitude and porosity by tens of percent within a single sedimentary deposit. Such data also show some spatial structure which might be described as layers of clay, sand, or gravel with recognizable but variable thickness.Aware of this complex structure and extreme variability of flow properties, groundwater hydrologists and others have undertaken the formidable task of trying to observe and predict the quantity and quality of waters moving through these materials. This has been accomplished to some degree by ignoring the complexity or more appropriately by some implicit averaging of the flow equation to introduce an average flow property. Transmissivity is an example of such an averaged property which results from integration of the flow equation over depth. Major advances in computer-based methods during the last decade have made it possible to solve very complicated flow equations with complex boundary conditions and parameter configurations. However, most hydrologists now recognize that the predictive capabilities of such models are limited because the parameters of the models are difficult to determine. Much...

The stochastic differential equation describing one-dimensional flow in a statistically homogeneous porous medium is solved exactly, and the results are compared with an approximate solution considering small perturbations in the logarithm of the hydraulic conductivity. The results show that the logarithmic approximation is valid when the standard deviation of the natural logarithm of the hydraulic conductivity ar is less than.1; the errors increase rapidly for ar > 1. The effective hydraulic conductivity of statistically homogeneous media with one-, two-, and three-dimensional perturbations is determined to the first order in a?. The effective conductivity is found to be the harmonic mean for one-dimensional flow, the geometric mean for two-dimensional flow, and (1 + a?/6) times the geometric mean for three-dimensional flow. The application of stochastic analysis is illustrated through two elementary network design problems that demonstrate the importance of the correlation length of the hydraulic conductivity and the role of measurement error.

The lack of an immediate‐release sedative (i.e., one for which no postsedation holding or withdrawal period is required) jeopardizes fish and fisheries research and poses considerable risk to those involved in aquatic resource management and the operation of public hatcheries and commercial fish farms. Carbon dioxide may be used as an immediate‐release sedative, but it is slow‐acting and difficult to apply uniformly and effectively. Tricaine methanesulfonate (MS‐222) is easier to apply but requires a 21‐d withdrawal period. The lack of an immediate‐release sedative approved by the U.S. Food and Drug Administration (FDA) is a consequence of numerous factors, including the complexities of the approval process, the substantial human and monetary resources involved, and the specialized nature of the work. Efforts are currently underway to demonstrate the safety and effectiveness of benzocaine‐ and eugenol‐based products as immediate‐release sedatives. However, pursuing approvals within the current framework will consume an exorbitant amount of public and private resources and will take years to complete, even though both compounds are “generally recognized as safe” for certain applications by the FDA. We recommend using risk management–based approaches to increase the efficiency of the drug approval process and the availability of safe and effective drugs, including immediate‐release sedatives, for use in the fisheries and aquaculture disciplines.

Background Infectious hematopoietic necrosis (IHN) is a disease of salmonid fish that is caused by the IHN virus (IHNV). Under intensive aquaculture conditions, IHNV can cause significant mortality and economic losses. Currently, there is no proven and cost-effective method for IHNV control. Clear Springs Foods, Inc. has been applying selective breeding to improve genetic resistance to IHNV in their rainbow trout breeding program. The goals of this study were to elucidate the genetic architecture of IHNV resistance in this commercial population by performing genome-wide association studies (GWAS) with multiple regression single-step methods and to assess if genomic selection can improve the accuracy of genetic merit predictions over conventional pedigree-based best linear unbiased prediction (PBLUP) using cross-validation analysis. Results Ten moderate-effect quantitative trait loci (QTL) associated with resistance to IHNV that jointly explained up to 42% of the additive genetic variance were detected in our GWAS. Only three of the 10 QTL were detected by both single-step Bayesian multiple regression (ssBMR) and weighted single-step GBLUP (wssGBLUP) methods. The accuracy of breeding value predictions with wssGBLUP (0.33–0.39) was substantially better than with PBLUP (0.13–0.24). Conclusions Our comprehensive genome-wide scan for QTL revealed that genetic resistance to IHNV is controlled by the oligogenic inheritance of up to 10 moderate-effect QTL and many small-effect loci in this commercial rainbow trout breeding population. Taken together, our results suggest that whole genome-enabled selection models will be more effective than the conventional pedigree-based method for breeding value estimation or the marker-assisted selection approach for improving the genetic resistance of rainbow trout to IHNV in this population.

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