# evolution: Th-U evolution diagram In IsoplotR: Statistical Toolbox for Radiometric Geochronology

## Description

Plots Th-U data on a ^{234}U/^{238}U-^{230}Th/^{238}U evolution diagram, a ^{234}U/^{238}U-age diagram, or (if ^{234}U/^{238}U is assumed to be in secular equilibrium), a ^{230}Th/^{232}Th-^{238}U/^{232}Th diagram, calculates isochron ages.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23``` ```evolution( x, xlim = NULL, ylim = NULL, alpha = 0.05, transform = FALSE, detritus = 0, show.numbers = FALSE, levels = NA, clabel = "", ellipse.fill = c("#00FF0080", "#FF000080"), ellipse.stroke = "black", line.col = "darksalmon", isochron = FALSE, model = 1, exterr = TRUE, sigdig = 2, hide = NULL, omit = NULL, omit.fill = NA, omit.stroke = "grey", ... ) ```

## Arguments

 `x` an object of class `ThU` `xlim` x-axis limits `ylim` y-axis limits `alpha` probability cutoff for the error ellipses and confidence intervals `transform` if `TRUE`, plots ^{234}U/^{238}U vs. Th-U age. `detritus` detrital ^{230}Th correction (only applicable when `x\$format` is `2` or `3`. `0`: no correction `1`: project the data along an isochron fit `2`: correct the data using an assumed initial ^{230}Th/^{232}Th-ratio for the detritus. `3`: correct the data using the measured present day ^{230}Th/^{238}U, ^{232}Th/^{238}U and ^{234}U/^{238}U-ratios in the detritus. `show.numbers` label the error ellipses with the grain numbers? `levels` a vector with additional values to be displayed as different background colours within the error ellipses. `clabel` label of the colour legend. `ellipse.fill` Fill colour for the error ellipses. This can either be a single colour or multiple colours to form a colour ramp. Examples: a single colour: `rgb(0,1,0,0.5)`, `'#FF000080'`, `'white'`, etc.; multiple colours: `c(rbg(1,0,0,0.5)`, `rgb(0,1,0,0.5))`, `c('#FF000080','#00FF0080')`, `c('blue','red')`, `c('blue','yellow','red')`, etc.; a colour palette: `rainbow(n=100)`, `topo.colors(n=100,alpha=0.5)`, etc.; or a reversed palette: `rev(topo.colors(n=100,alpha=0.5))`, etc. For empty ellipses, set `ellipse.fill=NA` `ellipse.stroke` the stroke colour for the error ellipses. Follows the same formatting guidelines as `ellipse.fill` `line.col` colour of the age grid `isochron` fit a 3D isochron to the data? `model` if `isochron=TRUE`, choose one of three regression models: `1`: maximum likelihood regression, using either the modified error weighted least squares algorithm of York et al. (2004) for 2-dimensional data, or the Maximum Likelihood formulation of Ludwig and Titterington (1994) for 3-dimensional data. These algorithms take into account the analytical uncertainties and error correlations, under the assumption that the scatter between the data points is solely caused by the analytical uncertainty. If this assumption is correct, then the MSWD value should be approximately equal to one. There are three strategies to deal with the case where MSWD>1. The first of these is to assume that the analytical uncertainties have been underestipmated by a factor √{MSWD}. `2`: ordinary least squares regression: a second way to deal with over- or underdispersed datasets is to simply ignore the analytical uncertainties. `3`: maximum likelihood regression with overdispersion: instead of attributing any overdispersion (MSWD > 1) to underestimated analytical uncertainties (model 1), one can also attribute it to the presence of geological uncertainty, which manifests itself as an added (co)variance term. `exterr` propagate the decay constant uncertainty in the isochron age? `sigdig` number of significant digits for the isochron age `hide` vector with indices of aliquots that should be removed from the plot. `omit` vector with indices of aliquots that should be plotted but omitted from the isochron age calculation. `omit.fill` fill colour that should be used for the omitted aliquots. `omit.stroke` stroke colour that should be used for the omitted aliquots. `...` optional arguments to the generic `plot` function

## Details

Similar to the `concordia` diagram (for U-Pb data) and the `helioplot` diagram (for U-Th-He data), the evolution diagram simultaneously displays the isotopic composition and age of U-series data. For carbonate data (Th-U formats 1 and 2), the Th-U evolution diagram consists of a scatter plot that sets out the ^{234}U/^{238}U-activity ratios against the ^{230}Th/^{238}U-activity ratios as error ellipses, and displays the initial ^{234}U/^{238}U-activity ratios and ages as a set of intersecting lines. Alternatively, the ^{234}U/^{238}U-ratios can also be set out against the ^{230}Th-^{234}U-^{238}U-ages. In both types of evolution diagrams, `IsoplotR` provides the option to project the raw measurements along the best fitting isochron line and thereby remove the detrital ^{230}Th-component. This procedure allows a visual assessment of the degree of homogeneity within a dataset, as is quantified by the MSWD.

Neither the U-series evolution diagram, nor the ^{234}U/^{238}U vs. age plot is applicable to igneous datasets (Th-U formats 3 and 4), in which ^{234}U and ^{238}U are in secular equilibrium. For such datasets, `IsoplotR` produces an Osmond-style regression plot that is decorated with a fanning set of `isochron` lines.

## References

Ludwig, K.R. and Titterington, D.M., 1994. Calculation of ^{230}Th/U isochrons, ages, and errors. Geochimica et Cosmochimica Acta, 58(22), pp.5031-5042.

Ludwig, K.R., 2003. Mathematical-statistical treatment of data and errors for ^{230}Th/U geochronology. Reviews in Mineralogy and Geochemistry, 52(1), pp.631-656.

`isochron`
 ```1 2 3 4 5 6``` ```attach(examples) evolution(ThU) dev.new() evolution(ThU,transform=TRUE, isochron=TRUE,model=1) ```