Size of flatfish larvae at transformation, functional demands and historical constraints

At hatching the larvae of flatfish closely resemble the bilateral symmetric larvae of other teleosts, especially perciforms. Literature data show that transformation to asymmetric benthic juveniles normally occurs at body lengths between 10 and 25 mm. Unexpectedly, minimal size at its completion (including eye migration) can be 4.1 mm SL and maximal size is over 72 mm. In this paper we consider the functional requirements for a successful switch from a symmetric pelagic larva to a typical asymmetric juvenile benthic flatfish partly based on evidence from other teleosts. The unfavourable period of eye migration and transition to a benthic habitat requires some food reserves and rewiring and/or recalibration of vision and gravity-associated structures utilised previously by the still symmetric larvae for e.g. food detection. Binocular fixation of the prey probably occurs in that stage. Critical or sensitive periods occurring during development of fish larvae suggest that a completely functional symmetric stage of development must precede transformation. The normal size range in flatfish larvae at transformation seems to confirm our considerations. Recent data on temperature effects during development provide an explanation for metamorphosis at the minimal size. Some evidence for paedomorphic heterochrony in flatfish larvae is presented.     

Resource Model Updating For Compositional Geometallurgical Variables

In the field of mineral resources extraction, one main challenge is to meet production targets in terms of geometallurgical properties. These properties influence the processing of the ore and are often represented in resource modeling by coregionalized variables with a complex relationship between them. Valuable data are available about geometalurgical properties and their interaction with the beneficiation process given sensor technologies during production monitoring. The aim of this research is to update resource models as new observations become available. A popular method for updating is the ensemble Kalman filter. This method relies on Gaussian assumptions and uses a set of realizations of the simulated models to derive sample covariances that can propagate the uncertainty between real observations and simulated ones. Hence, the relationship among variables has a compositional nature, such that updating these models while keeping the compositional constraints is a practical requirement in order to improve the accuracy of the updated models. This paper presents an updating framework for compositional data based on ensemble Kalman filter which allows us to work with compositions that are transformed into a multivariate Gaussian space by log-ratio transformation and flow anamorphosis. This flow anamorphosis, transforms the distribution of the variables to joint normality while reasonably keeping the dependencies between components. Furthermore, the positiveness of those variables, after updating the simulated models, is satisfied. The method is implemented in a bauxite deposit, demonstrating the performance of the proposed approach.

     

Modeling and Fitting of Three-Dimensional Mineral Microstructures by Multinary Random Fields

Mathematical Geosciences - Modeling a mineral microstructure accurately in three dimensions can render realistic mineralogical patterns which can be used for three-dimensional processing...     

Discriminant Analysis for Compositional Data Incorporating Cell-Wise Uncertainties

Mathematical Geosciences - In the geosciences it is still uncommon to include measurement uncertainties into statistical methods such as discriminant analysis, but, especially for trace elements,...     

Geostatistics for Compositional Data: An Overview

Mathematical Geosciences - This paper presents an overview of results for the geostatistical analysis of collocated multivariate data sets, whose variables form a composition, where the components...     

Joint Consistent Mapping of High-Dimensional Geochemical Surveys

Geochemical surveys often contain several tens of components, obtained from different horizons and with different analytical techniques. These are used either to obtain elemental concentration maps or to explore links between the variables. The first task involves interpolation, the second task principal component analysis (PCA) or a related technique. Interpolation of all geochemical variables (in wt% or ppm) should guarantee consistent results: At any location, all variables must be positive and sum up to 100 %. This is not ensured by any conventional geostatistical technique. Moreover, the maps should ideally preserve any link present in the data. PCA also presents some problems, derived from the spatial dependence between the observations, and the compositional nature of the data. Log-ratio geostatistical techniques offer a consistent solution to all these problems. Variation-variograms are introduced to capture the spatial dependence structure: These are direct variograms of all possible log ratios of two components. They can be modeled with a function analogous to the linear model of coregionalization (LMC), where for each spatial structure there is an associated variation matrix describing the links between the components. Eigenvalue decompositions of these matrices provide a PCA of that particular spatial scale. The whole data set can then be interpolated by cokriging. Factorial cokriging can also be used to map a certain spatial structure, eventually projected onto those principal components (PCs) of that structure with relevant contribution to the spatial variability. If only one PC is used for a certain structure, the maps obtained represent the spatial variability of a geochemical link between the variables. These procedures and their advantages are illustrated with the horizon C Kola data set, with 25 components and 605 samples covering most of the Kola peninsula (Finland, Norway, Russia).     

Efficient Representation of Laguerre Mosaics with an Application to Microstructure Simulation of Complex Ore

Mathematical Geosciences - Laguerre mosaics have been an important modeling approach in astronomy, physics, crystallography, geology and mathematics for several decades. In materials science, they...     

Kriging of Regionalized Directions, Axes, and Orientations I. Directions and Axes

The problem to predict a direction, axis, or orientation (rotation) from corresponding geocoded data is discussed and a general solution by virtue of embedding a sphere/hemisphere in a real vector space is presented. Its explicit justification in terms of mathematical assumptions concerning stationarity/homogeneity and isotropy is included. The data are modelled by a stationary random field, and the spatial correlation is represented by modified multivariate variograms and covariance functions. Various types of isotropy assumptions concerning invariance under translation/rotation of the data locations, the measurements, or a combination of both, can be distinguished and lead to different simplifications of the general cross-covariance function. Beyond spatial prediction a measure of confidence in the estimates is provided.     

Stochastic Modelling of Mineral Exploration Targets

Mathematical Geosciences - Mineral deposits are metal enrichment anomalies, occurring as local manifestations of the interplay between various geological processes that operate at a wide range of...     

Local Ranking of Geological Conceptual Models in Non-stationary Settings Using Multi-point Geostatistics

Mathematical Geosciences - In geomodeling, it is commonly accepted that the distribution of physical properties is controlled by the architecture of geological objects. However, insufficient data...