High Vein Density Research Articles

Minor millets as model system to study C<sub>4</sub> photosynthesis -A review

C<sub>4</sub> photosynthesis is the primary mode of carbon capture and drives productivity in several major food crops and bioenergy grasses. Gains in productivity associated with C<sub>4</sub> photosynthesis include improved water and nitrogen use efficiencies. Within grasses rice and brachypodium are used as model species. Since these two crops are using C<sub>3</sub> photosynthesis for their growth and development, it cannot be used as model for to study C<sub>4</sub> photosynthesis. In order to characterize the evolutionary innovations and to provide genomic insight into crop improvement for the many important crop species, a new genomic and genetic model species is required. Minor millets have small diploid genomes, shorter life cycles, self pollination and prolific seed production. Due to these characteristics it gains importance over major C<sub>4</sub> species which lack all of these traits. Within Minor millets, <italic>Setaria italica</italic> and <italic>Setaria viridis</italic> are used as model systems since these crops fulfils all the traits responsible to be a model species. Importantly, <italic>Setaria</italic> species uses NADP-Malic enzyme subtype C<sub>4</sub> photosynthetic system to fix carbon and therefore is a potential powerful model system for dissecting C<sub>4</sub> photosynthesis. C<sub>4</sub> grasses have a shorter distance between longitudinal veins in the leaves than C<sub>3</sub> grasses. The C<sub>4</sub> grasses have denser transverse and small longitudinal veins than the C<sub>3</sub> grasses. It indicates that C<sub>4</sub> grasses have a structurally superior photosynthate translocation and water distribution system by developing denser networks of small longitudinal and transverse veins. <italic>Setaria</italic> has high vein density and kranz anatomy that helps to concentrate CO<sub>2</sub> in the bundle sheath cells. This minimizes photorespiration thereby prevents the loss of energy.

Structural Channelling of Metamorphic Fluids on Islay, Scotland: Implications for Paleoclimatic Reconstruction

Analysis of the delta O-18 and delta C-13 values of carbonate rocks from Islay, Scotland reveals structural channelling of metamorphic fluids through the axial region of a major en echelon anticlinal fold system. Metamorphic fluid flow produced axial planar veins with higher vein density in the axial region of the fold. Fluid: rock ratios were more than 30: 1 within this axial region, at least four times greater than the regional mean ratio of 7.6 +/- 1.5:1 for carbonate rocks on Islay. This supports the interpretation that metamorphic fluids were channelled through the axial region of the Islay Anticline. Fluid: rock ratios were calculated using a model for coupled delta O-18 and delta C-13 exchange with a metamorphic fluid. The metamorphic fluid was calculated to have delta O-18 and delta C-13 values of 15.3 parts per thousand and -6.1 parts per thousand, respectively and X-CO2 of 0.2. This is in isotopic and chemical equilibrium with chlorite- and graphite-bearing metamudstones that are structurally below the folded metacarbonate rocks on Islay. Devolatilization of these metamudstones is therefore a likely source mechanism for this metamorphic fluid. Removal of the effects of metamorphic fluid flow on delta C-13 values recorded by metacarbonate rocks on Islay allows us to re-evaluate evidence used to reconstruct Neoproterozoic climate. This evidence includes a large negative delta C-13 excursion reported from the Lossit Limestone Formation. This unit underlies the Port Askaig Formation, which is dominated by diamictites that have been interpreted as glacial tillites. This 'Islay anomaly' has been correlated with other such anomalies worldwide and together with overlying tillites has been cited as evidence of major (worldwide) glaciation events. In this study, we show that the magnitude of this negative delta C-13 anomaly can partly be explained by exchange with metamorphic fluids. However, we also show that extremely negative delta C-13 values in the Bonahaven Dolomite Formation, which overlies the Port Askaig Formation and has been interpreted as a 'cap carbonate', cannot be attributed to metamorphic fluid flow.

Two forward genetic screens for vein density mutants in sorghum converge on a cytochrome P450 gene in the brassinosteroid pathway

The specification of vascular patterning in plants has interested plant biologists for many years. In the last decade a new context has emerged for this interest. Specifically, recent proposals to engineer C(4) traits into C(3) plants such as rice require an understanding of how the distinctive venation pattern in the leaves of C(4) plants is determined. High vein density with Kranz anatomy, whereby photosynthetic cells are arranged in encircling layers around vascular bundles, is one of the major traits that differentiate C(4) species from C(3) species. To identify genetic factors that specify C(4) leaf anatomy, we generated ethyl methanesulfonate- and γ-ray-mutagenized populations of the C(4) species sorghum (Sorghum bicolor), and screened for lines with reduced vein density. Two mutations were identified that conferred low vein density. Both mutations segregated in backcrossed F(2) populations as homozygous recessive alleles. Bulk segregant analysis using next-generation sequencing revealed that, in both cases, the mutant phenotype was associated with mutations in the CYP90D2 gene, which encodes an enzyme in the brassinosteroid biosynthesis pathway. Lack of complementation in allelism tests confirmed this result. These data indicate that the brassinosteroid pathway promotes high vein density in the sorghum leaf, and suggest that differences between C(4) and C(3) leaf anatomy may arise in part through differential activity of this pathway in the two leaf types.

Morphological and physiological divergences within Quercus ilex support the existence of different ecotypes depending on climatic dryness.

Several studies show apparently contradictory findings about the functional convergence within the Mediterranean woody flora. In this context, this study evaluates the variability of functional traits within holm oak (Quercus ilex) to elucidate whether provenances corresponding to different morphotypes represent different ecotypes locally adapted to the prevaling stress levels. Several morphological and physiological traits were measured at leaf and shoot levels in 9-year-old seedlings of seven Q. ilex provenances including all recognized morphotypes. Plants were grown in a common garden for 9 years under the same environmental conditions to avoid possible biases due to site-specific characteristics. Leaf morphometry clearly separates holm oak provenances into 'ilex' (more elongated leaves with low vein density) and 'rotundifolia' (short and rounded leaves with high vein density) morphotypes. Moreover, these morphotypes represent two consistent and very contrasting functional types in response to dry climates, mainly in terms of leaf area, major vein density, leaf specific conductivity, resistance to drought-induced cavitation and turgor loss point. The 'ilex' and 'rotundifolia' morphotypes correspond to different ecotypes as inferred from their contrasting functional traits. To the best of our knowledge, this is the first time that the combined use of morphological and physiological traits has provided support for the concept of these two holm oak morphotypes being regarded as two different species.

From proto-Kranz to C4 Kranz: building the bridge to C4 photosynthesis.

In this review, we examine how the specialized "Kranz" anatomy of C4 photosynthesis evolved from C3 ancestors. Kranz anatomy refers to the wreath-like structural traits that compartmentalize the biochemistry of C4 photosynthesis and enables the concentration of CO2 around Rubisco. A simplified version of Kranz anatomy is also present in the species that utilize C2 photosynthesis, where a photorespiratory glycine shuttle concentrates CO2 into an inner bundle-sheath-like compartment surrounding the vascular tissue. C2 Kranz is considered to be an intermediate stage in the evolutionary development of C4 Kranz, based on the intermediate branching position of C2 species in 14 evolutionary lineages of C4 photosynthesis. In the best-supported model of C4 evolution, Kranz anatomy in C2 species evolved from C3 ancestors with enlarged bundle sheath cells and high vein density. Four independent lineages have been identified where C3 sister species of C2 plants exhibit an increase in organelle numbers in the bundle sheath and enlarged bundle sheath cells. Notably, in all of these species, there is a pronounced shift of mitochondria to the inner bundle sheath wall, forming an incipient version of the C2 type of Kranz anatomy. This incipient version of C2 Kranz anatomy is termed proto-Kranz, and is proposed to scavenge photorespiratory CO2. By doing so, it may provide fitness benefits in hot environments, and thus represent a critical first stage of the evolution of both the C2 and C4 forms of Kranz anatomy.

Increasing leaf vein density by mutagenesis: laying the foundations for C4 rice.

A high leaf vein density is both an essential feature of C4 photosynthesis and a foundation trait to C4 evolution, ensuring the optimal proportion and proximity of mesophyll and bundle sheath cells for permitting the rapid exchange of photosynthates. Two rice mutant populations, a deletion mutant library with a cv. IR64 background (12,470 lines) and a T-DNA insertion mutant library with a cv. Tainung 67 background (10,830 lines), were screened for increases in vein density. A high throughput method with handheld microscopes was developed and its accuracy was supported by more rigorous microscopy analysis. Eight lines with significantly increased leaf vein densities were identified to be used as genetic stock for the global C4 Rice Consortium. The candidate population was shown to include both shared and independent mutations and so more than one gene controlled the high vein density phenotype. The high vein density trait was found to be linked to a narrow leaf width trait but the linkage was incomplete. The more genetically robust narrow leaf width trait was proposed to be used as a reliable phenotypic marker for finding high vein density variants in rice in future screens.

Evolution of a unique anatomical precision in angiosperm leaf venation lifts constraints on vascular plant ecology

The main role of leaf venation is to supply water across the photosynthetic surface to keep stomata open and allow access to atmospheric CO2 despite evaporative demand. The optimal uniform delivery of water occurs when the distance between veins equals the depth of vein placement within the leaf away from the evaporative surface. As presented here, only angiosperms maintain this anatomical optimum across all leaf thicknesses and different habitats, including sheltered environments where this optimization need not be required. Intriguingly, basal angiosperm lineages tend to be underinvested hydraulically; uniformly high optimization is derived independently in the magnoliids, monocots and core eudicots. Gymnosperms and ferns, including available fossils, are limited by their inability to produce high vein densities. The common association of ferns with shaded humid environments may, in part, be a direct evolutionary consequence of their inability to produce hydraulically optimized leaves. Some gymnosperms do approach optimal vein placement, but only by virtue of their ability to produce thick leaves most appropriate in environments requiring water conservation. Thus, this simple anatomical metric presents an important perspective on the evolution and phylogenetic distribution of plant ecologies and further evidence that the vegetative biology of flowering plants-not just their reproductive biology-is unique.

Leaf photosynthetic rate of tropical ferns is evolutionarily linked to water transport capacity.

Ferns usually have relatively lower photosynthetic potential than angiosperms. However, it is unclear whether low photosynthetic potential of ferns is linked to leaf water supply. We hypothesized that there is an evolutionary association of leaf water transport capacity with photosynthesis and stomatal density in ferns. In the present study, a series of functional traits relating to leaf anatomy, hydraulics and physiology were assessed in 19 terrestrial and 11 epiphytic ferns in a common garden, and analyzed by a comparative phylogenetics method. Compared with epiphytic ferns, terrestrial ferns had higher vein density (Dvein), stomatal density (SD), stomatal conductance (gs), and photosynthetic capacity (Amax), but lower values for lower epidermal thickness (LET) and leaf thickness (LT). Across species, all traits varied significantly, but only stomatal length (SL) showed strong phylogenetic conservatism. Amax was positively correlated with Dvein and gs with and without phylogenetic corrections. SD correlated positively with Amax, Dvein and gs, with the correlation between SD and Dvein being significant after phylogenetic correction. Leaf water content showed significant correlations with LET, LT, and mesophyll thickness. Our results provide evidence that Amax of the studied ferns is linked to leaf water transport capacity, and there was an evolutionary association between water supply and demand in ferns. These findings add new insights into the evolutionary correlations among traits involving carbon and water economy in ferns.

Characterisation and 3D modelling of a nuggety, vein-hosted gold ore body, Sunrise Dam, Western Australia

In high-nugget gold ore bodies, samples taken from drill core for gold assay are typically too small to allow for the extreme spatial variability in grade and are a poor representation of the underlying distribution of mineralisation. The GQ North lode at the Sunrise Dam Gold Mine in Western Australia is a good example of an orebody which has a very strong nugget effect (coefficient of variation >20) and that has proved very problematic to model. Gold is hosted in vein stockworks and shear zones and although there is a clear spatial relationship between mineralisation and alteration, high vein density and well-developed foliations, the relationship is best defined statistically because the association between high gold grades and various combinations of these features is non-trivial. We present a method for automating the inclusion of geological data (proxies for gold mineralisation) into the prediction of mineralised rocks, using conditional probability. The method uses the gold assays and the logged geological data to calculate the probability that rocks with particular geological features will be mineralised. The ore body can then be modelled automatically using interpolation software with isosurfaces indicating the regions with highest probability of gold mineralisation. A good understanding of the geological features associated with mineralisation and consistent geological logging are important prerequisites for successful conditional probability modelling of drill hole data.

Hydraulic engineering of the angiosperm leaf: do the Baileyan trends in perforation plate evolution account for the origin of high vein density?

Hydraulic engineering of the angiosperm leaf: do the Baileyan trends in perforation plate evolution account for the origin of high vein density?

Hydraulic tuning of vein cell microstructure in the evolution of angiosperm venation networks

High vein density (D(V)) evolution in angiosperms represented a key functional transition. Yet, a mechanistic account on how this hydraulic transformation evolved remains lacking. We demonstrate that a consequence of producing high D(V is that veins must become very small to fit inside the leaf, and that angiosperms are the only clade that evolved the specific type of vessel required to yield sufficiently conductive miniature leaf veins. From 111 species spanning key divergences in vascular plant evolution, we show, using analyses of vein conduit evolution in relation to vein packing, that a key xylem innovation associated with high D(V) evolution is a strong reduction in vein thickness and simplification of the perforation plates of primary xylem vessels. Simple perforation plates in the leaf xylem occurred only in derived angiosperm clades exhibiting high D(V) (> 12 mm mm(-2)). Perforation plates in the vessels of other species, including extant basal angiosperms, consisted of resistive scalariform types that were associated with thicker veins and much lower D(V). We conclude that a reduction in within-vein conduit resistance allowed vein size to decrease. We suggest that this adaptation may have been a critical evolutionary step that enabled dramatic D(V) elaboration in angiosperms.

Leaf fossil record suggests limited influence of atmospheric CO2 on terrestrial productivity prior to angiosperm evolution.

Declining CO(2) over the Cretaceous has been suggested as an evolutionary driver of the high leaf vein densities (7-28 mm mm(-2)) that are unique to the angiosperms throughout all of Earth history. Photosynthetic modeling indicated the link between high vein density and productivity documented in the modern low-CO(2) regime would be lost as CO(2) concentrations increased but also implied that plants with very low vein densities (less than 3 mm mm(-2)) should experience substantial disadvantages with high CO(2). Thus, the hypothesized relationship between CO(2) and plant evolution can be tested through analysis of the concurrent histories of alternative lineages, because an extrinsic driver like atmospheric CO(2) should affect all plants and not just the flowering plants. No such relationship is seen. Regardless of CO(2) concentrations, low vein densities are equally common among nonangiosperms throughout history and common enough to include forest canopies and not just obligate shade species that will always be of limited productivity. Modeling results can be reconciled with the fossil record if maximum assimilation rates of nonflowering plants are capped well below those of flowering plants, capturing biochemical and physiological differences that would be consistent with extant plants but previously unrecognized in the fossil record. Although previous photosynthetic modeling suggested that productivity would double or triple with each Phanerozoic transition from low to high CO(2), productivity changes are likely to have been limited before a substantial increase accompanying the evolution of flowering plants.

Angiosperms Helped Put the Rain in the Rainforests: The Impact of Plant Physiological Evolution on Tropical Biodiversity1

The recycling of transpired water is well known to be an important source of rainfall, particularly in the tropics, and angiosperms have transpiration capacities higher than any other plants throughout evolutionary history. Thus, the evolution and rise to ecological dominance of flowering plants are proposed to have strongly altered climate. Transpiration capacity is closely correlated with leaf vein density, and the average vein density of angiosperm leaves is four times greater than that of all other plants, living or extinct. A rapid transition to high vein densities occurred separately in three or more flowering plant lineages about 100 million years ago. Climate modeling of the impact of this physiological revolution indicates that the tropics would be hotter, drier, and more seasonal in the absence of the angiosperms, and the overall area of tropical rainforest would decline substantially. Because angiosperm diversity is influenced by rainforest area and by precipitation abundance and evenness, the high diversity of angiosperms is partially a product of a positive feedback loop with the climate modifications initiated by the angiosperms themselves. Lineage diversifications among vertebrate and invertebrate animals and nonangiospermous plants in the wake of the angiosperm radiation may be tied to the unprecedented impact of angiosperms on climate.

Structural and hydraulic correlates of heterophylly in Ginkgo biloba

This study investigates the functional significance of heterophylly in Ginkgo biloba, where leaves borne on short shoots are ontogenetically distinct from those on long shoots. Short shoots are compact, with minimal internodal elongation; their leaves are supplied with water through mature branches. Long shoots extend the canopy and have significant internodal elongation; their expanding leaves receive water from a shoot that is itself maturing. Morphology, stomatal traits, hydraulic architecture, Huber values, water transport efficiency, in situ gas exchange and laboratory-based steady-state hydraulic conductance were examined for each leaf type. Both structure and physiology differed markedly between the two leaf types. Short-shoot leaves were thinner and had higher vein density, lower stomatal pore index, smaller bundle sheath extensions and lower hydraulic conductance than long-shoot leaves. Long shoots had lower xylem area:leaf area ratios than short shoots during leaf expansion, but this ratio was reversed at shoot maturity. Long-shoot leaves had higher rates of photosynthesis, stomatal conductance and transpiration than short-shoot leaves. We propose that structural differences between the two G. biloba leaf types reflect greater hydraulic limitation of long-shoot leaves during expansion. In turn, differences in physiological performance of short- and long-shoot leaves correspond to their distinct ontogeny and architecture.

Isotopic constraints of vein carbonates on fluid sources and processes associated with the ongoing brittle deformation within the accretionary wedge of Taiwan

Terra Nova, 22, 251–256, 2010 Abstract The continuously distributed, well-preserved fracture-filling carbonates were collected from the cores retrieved from the Taiwan Chelungpu-fault Drilling Program between 400 and 2000 m depth for carbon and oxygen isotope analyses to constrain the fluid compositions and processes associated with brittle deformation within the accretionary wedge. The isotope analyses of fracture-filling carbonates yielded δ18O values steadily increasing with depth. The δ13C values exhibited a pattern similar to that of δ18O values at shallower depths, but an opposite trend at greater depths. Such variations in the isotopic compositions could be best explained by a mixing of shallow, meteoric water and deeply rooted fluid carrying isotopic signatures of various microbial processes. The notable excursion of δ18O values might infer a conduit for the lateral fluid transport along the high vein density zone. Overall, the isotopic patterns preclude the substantial influence of early diagenesis and suggest pervasive fluid percolation through the fracture network.

Shifts in leaf vein density through accelerated vein formation in C4 Flaveria (Asteraceae).

Leaf venation in many C(4) species is characterized by high vein density, essential in facilitating rapid intercellular diffusion of C(4) photosynthetic metabolites between different tissues (mesophyll, bundle sheath). Greater vein density has been hypothesized to be an early step in C(4) photosynthesis evolution. Development of C(4) vein patterning is thought to occur from either accelerated or prolonged procambium formation, relative to ground tissue development. Cleared and sectioned tissues of phylogenetically basal C(3) Flaveria robusta and more derived C(4) Flaveria bidentis were compared for vein pattern in mature leaves and vein pattern formation in developing leaves. In mature leaves, major vein density did not differ between C(3) and C(4) Flaveria species, whereas minor veins were denser in C(4) species than in C(3) species. The developmental study showed that both major and minor vein patterning in leaves of C(3) and C(4) species were initiated at comparable stages (based on leaf length). An additional vein order in the C(4) species was observed during initiation of the higher order minor veins compared with the C(3) species. In the two species, expansion of bundle sheath and mesophyll cells occurred after vein pattern was complete and xylem differentiation was continuous in minor veins. In addition, mesophyll cells ceased dividing sooner and enlarged less in C(4) species than in C(3) species. Leaf vein pattern characteristic to C(4) Flaveria was achieved primarily through accelerated and earlier offset of higher order vein formation, rather than other modifications in the timing of vein pattern formation, as compared with C(3) species. Earlier cessation of mesophyll cell division and reduced expansion also contributed to greater vein density in the C(4) species. The relatively late expansion of bundle sheath and mesophyll cells shows that vein patterning precedes ground tissue development in C(4) species.

Geochemical and Geochronological Constraints on Mineralization within the Hilltop, Lewis, and Bullion Mining Districts, Battle Mountain-Eureka Trend, Nevada

The Hilltop, Lewis, and Bullion mining districts, located within the northern Shoshone Range, Lander County, Nevada, are part of the greater Battle Mountain-Eureka trend. Historic production of mostly Ag with Au, Cu, Pb, and Zn from all three districts exploited ≤ 3-m-wide quartz veins hosted mainly within upper plate Ordovician-Devonian siliceous and siliciclastic rocks of the Roberts Mountains allochthon. Eocene felsic intrusive rocks, located both proximal and distal to the vein deposits, were emplaced throughout the northern Shoshone Range along a west-northwest trend; molybdenite mineralization is associated with some intrusive rocks, and some intrusive rocks host vein-type mineralization. New and previously published radiometric ages for primary igneous minerals from unaltered rocks within and/or proximal to mineralized areas are nearly coincident with published Re-Os ages for several northern Shoshone Range molybdenite occurrences (40.1 ± 0.6 Ma, avg), supporting a relationship between pluton emplacement and molybdenite mineralization. Age differences between quartz vein-hosted gold ± base metal mineralization (e.g., 38.3 ± 0.1 Ma: Gray Eagle mine, Bullion district) and nearby intrusive rocks (e.g., 39.0 ± 0.1 Ma: Granite Mountain) imply that vein mineralization probably formed during prolonged hydrothermal activity, synchronous with or subsequent to igneous rock emplacement, or from heat associated with a second, slightly younger phase of intrusive igneous activity. Primary fluid inclusion salinity (0–6.4 wt % NaCl equiv) and Th (115°–425°C) data from ore-bearing vein quartz, in conjunction with measured δ18OVSMOW data (−0.97 to +17.3‰), indicate that vein-forming fluids contained variable mixtures of magmatic and meteoric components (calculated δ18OVSMOW values of −16.0 to +13.3‰) and spanned the epithermal-porphyry temperature continuum. New and previously published stable isotope (C, O, and S) data from vein-hosted ore and gangue minerals, unaltered and altered siliceous (upper plate) host rocks, and unaltered carbonate (lower plate and upper plate) rocks indicate mixed and variable sources of vein-hosted ore and gangue components and variable interaction between some vein-forming fluids and nonsiliceous rock types (carbonates, bedded barite) that underlie the northern Shoshone Range. Large vein widths, high vein densities, and lack of evidence supporting fluid boiling in primary fluid inclusions suggest that vein deposits of the northern Shoshone Range probably formed at shallow depths (≤1 km) under lithostatic conditions. Geochronology and stable isotope data support a temporal and genetic link between Eocene magmatism, quartz vein-hosted precious and base metal mineralization, and molybdenite (porphyry) mineralization within the Hilltop, Lewis, and Bullion mining districts.

The Fossil Record of Plant Physiology and Development—What Leaves Can Tell Us

Plants provide unmatched opportunities to evaluate long debated evolutionary patterns in terms of the detailed biology of the fossil organisms. Leaves serve here as an example of how those advantages can be exploited. Over the history of vascular plants, three important transitions in leaf evolution—the origin of laminate leaves, the progressive loss of seed plant morphological diversity, and the evolution of more angiosperm-like leaves—also represent major shifts in leaf development and physiology. These transitions often occurred in parallel in different lineages, such as the evolution of marginal growth in each of at least four independent origins of laminate leaves during the Devonian and Carboniferous. Each also entailed dramatic reorganizations of leaf hydraulics. For example, the length of the finest distributary vein order varies from up to tens of centimeters down to hundreds of microns in successive groups of dominant seed plants. Angiosperms impose an additional trend upon these patterns with the evolution of their uniquely high vein densities. Vein density strongly influences and can provide a proxy for other physiological characteristics, such as assimilation and transpiration rates. The large increase in transpiration capacity accompanying the evolution of angiosperm leaf traits may even play an important role in feeding precipitation and thereby altering local climate.

Fractal analysis of a mineralised vein deposit: Curraghinalt gold deposit, County Tyrone

Quantitative description and prediction of vein hosted deposits using fractal statistics have been tested using data collected from the Curraghinalt gold deposit, Sperrin Mountains, County Tyrone, N. Ireland. Goldbearing quartz veins are hosted by Neo-Proterozoic Dalradian (Southern Highland Group) age psammites, pelitic schists and graphitic schists. Veins trend E to ESE and cross-cut regional structures. Vein thickness (z) distributions closely approximate a power-law distribution of the form N(⩾ z) = cz -D ,with an exponent (D) of 0.76 over three orders of magnitude. Vein spacing data approximate a log normal distribution with a mean of 2.92m. Numerical analysis indicates that the veins are more clustered than expected from a random distribution. Regions of high percentage extension and high vein density define vein clusters. The vein clustering relationship may be combined with the power-law thickness distribution and used in a predictive manner. The data may be used to constrain the probability of intersecting veins of potentially mineable dimension.