Author: Niklas Hohmann

# admtools: Getting Started

#### Niklas Hohmann

# Introduction

This vignette is an introduction to the admtools package.

## Installation

### From GitHub

### From CRAN

To install the package from CRAN, run

    install.packages("admtools")

To install the package from GitHub, first install the remotes package:

    install.packages("remotes")

Then run

    remotes::install_github(repo = "MindTheGap-ERC/admtools",
                            build_vignettes = TRUE,
                            ref = "HEAD",
                            dependencies = TRUE)

to install the latest stable version.

## Loading the package

Load the package using

    library(admtools)

This makes all functions in the package available.

## Getting help

Use

    help(package = "admtools")

to get an overview of the available help pages of the package, and

    ?admtools

to view a simple help page for the package.

Vignettes are a long form of package documentation that provide more detailed examples. To list the available vignettes, use

    browseVignettes(package = "admtools") # opens in Browser
    #or
    vignette(package = "admtools")

## The adm and multiadm classes

The admtools package defines three main classes: `adm,` `sac` and `multiadm`. The class `adm` represent a single age-depth model, from which information can be extracted (e.g. completeness, number of hiatuses, etc.) and that can be used to transform data between the stratigraphic domain and time domain. The `multiamd` class is a list of `adm` objects. `multiadm` objects are used to represent uncertainties of age-depth models. Objects of type `sac` are sediment accumulation curves that can contain information on erosion, and can be turned into age-depth models.

## Conventions

In contrast to its name, the admtools package currently deals with time and height instead of age and depth. In this sense, the age-depth models are time-height models. Both time and height can be negative values. To handle ages, use time before the present. To handle depths, use height below a point of reference (e.g., the sediment surface).

## Example

This example explains the construction and application of `adm` objects. As example data we use outputs from CarboCAT Lite, a model of carbonate platform growth (Burgess 2013, 2023). This data is automatically loaded in the background by the package. To get some info of the data use

    ?CarboCATLite_data

This data is identical to scenario A from Hohmann et al. (2024) as published in Hohmann et al. (2023). See therein for details on the simulation, reproducibility, and a chronostratigraphic chart and a figure showing a transect through the carbonate platform.

### Defining age-depth models

The standard constructor for age-depth models is `tp_to_adm` (“tie point to age-depth model”). It returns an objecto of class `adm`. This object combines information of stratigraphic heights and times and erosive interval. It allows to transform data between the stratigraphic and the time domain, and identify which data is destroyed due to hiatuses.

As example, I use the timing and stratigraphic positions of tie points taken from CarboCAT Lite to construct an age-depth model, and use the option to directly associate length and time units with it.

    # see ?tp_to_adm for detailed documentation
    my_adm = tp_to_adm(t = CarboCATLite_data$time_myr,
                      h = CarboCATLite_data$height_2_km_offshore_m,
                      L_unit = "m",
                      T_unit = "Myr")

This age-depth model represents the relationship between elapsed model time and accumulated sediment 2 km offshore in a synthetic carbonate platform.

## Representation

Typing the name `my_adm` in the console will only tell that the generated variable is an age-depth model

    my_adm
    #> age-depth model

To get a quick overview of the properties of `my_adm`, use `summary`:

    summary(my_adm)
    #> age-depth model
    #> Total duration: 2 Myr
    #> Total thickness: 146.0621 m
    #> Stratigraphic completeness: 32.65 %
    #> 10 hiatus(es)

If you want to inspect the insides of the object, use `str`:

    str(my_adm)
    #> List of 5
    #>  $ t     : num [1:2001] 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 ...
    #>  $ h     : num [1:2001] 0 0 0.609 1.095 1.722 ...
    #>  $ destr : logi [1:2000] TRUE FALSE FALSE FALSE FALSE FALSE ...
    #>  $ T_unit: chr "Myr"
    #>  $ L_unit: chr "m"
    #>  - attr(*, "class")= chr "adm"

You can manually manipulate the fields of the `adm` object by treating it like a list. I do not recommend doing so, as it might result in unexpected downstream behavior. If you want to extract tie points use `get_L_tp` and `get_T_tp`.

You can plot `adm` objects via the standard `plot` function. Here, I use the option to highlight hiatuses in red, and increase the linw width of the conservative ( = non-destructive) intervals.

    # see ?plot.adm for plotting options for adm objects
    plot(my_adm,
         col_destr = "red",
         lwd_acc = 2)
    T_axis_lab() # plot time axis label, see ?T_axis_lab for details
    L_axis_lab() # plot height axis label, see ?L_axis_lab for details

You can also plot sedimentation rates in the time domain using `plot_sed_rate_t`“:

    plot_sed_rate_t(my_adm)

For more information on the extraction of sedimentation rates in the time domain see the functions `sed_rate_t` and `sed_rate_t_fun`. Sedimentation rates in the length domain can be extracted using `sed_rate_l` and `sed_rate_l_fun` and plotted via `plot_sed_rate_l`. In addition, condensation (time preserved per stratigraphic increment) can be examined using the functions `condensation`, `condensation_fun` and `plot_condensation`.

## Extracting data from age-depth models

Use the functions `get_total_duration`, `get_total_thickness`, `get_completeness`, and `get_hiat_no` to extract information:

    get_total_duration(my_adm) #total time covered by the age-depth model
    #> [1] 2
    get_total_thickness(my_adm) # total thickness of section represented by the adm
    #> [1] 146.0621
    get_completeness(my_adm) # stratigraphic completeness as proportion
    #> [1] 0.3265
    get_incompleteness(my_adm) # stratigraphic incompleteness (= 1- strat. incompleteness)
    #> [1] 0.6735
    get_hiat_no(my_adm) # number of hiatuses
    #> [1] 10

For more detailed information, you can use

- `get_hiat_duration` to get a vector of hiatus durations
- `get_hiat_list` to get a list of hiatus positions and duration.

For example, to plot a histogram of hiatus durations, use

    hist(x = get_hiat_duration(my_adm),
         freq = TRUE,
         xlab = "Hiatus duration [Myr]",
         main = "Hiatus duration 2 km offshore")

The function `is_destructive` can be used to examine whether points in time coincide with hiatuses:

    is_destructive(my_adm,
                   t = c(0.1,0.5))
    #> [1] FALSE  TRUE

### Transforming data between time and stratigraphic domain

#### Heights and times

The functions `get_height` and `get_time` are the workhorses to transform data using age-depth models.

- `get_time` takes and `adm` object and vector of heights `h` (stratigraphic positions), and returns a vector of times
- `get_height` takes an `adm` object and vector of times `t` and returns a vector of associated stratigraphic positions

As example, say we want to know the time of deposition of the following stratigraphic positions:

    h = c(30,120) # stratigraphic positions
    get_time(my_adm,
             h = h)
    #> [1] 0.1380552 1.2704696

Conversely, to determine what parts of the section are deposited as a specific time, use

    t = c(0.2,1.4)
    get_height(my_adm,
               t = t)
    #> [1] 39.13951       NA

Here, the `NA` indicates that the time 1.4 coincides with erosion. If you want to know the stratigraphic position of the hiatus that coincides with that time, use the option `destructive = FALSE`:

    t = c(0.2,1.4)
    get_height(my_adm,
               t = t,
               destructive = FALSE)
    #> [1]  39.13951 126.27764

Alternatively, you can also use the wrappers `strat_to_time` and `time_to_strat` for the transformation. For expanded modeling features please use the `StratPal` package (Github | Webpage | CRAN). It provides more biological context and utility functions to build modeling pipelines that include ecological, taphonomic, stratigraphic, and evolutionary effects.

#### Phylogenetic trees

The `admtools` package can transform complex objects between the time and stratigraphic domain. This is done using the functions `strat_to_time` and `time_to_strat`.

As an example, we transform a chronogram (a phylogenetic tree where branch length represents time). An example tree following the birth-death model is stored with the package as the variable `timetree`. See `?timetree` for details on how this tree was generated.

    #install.packages("ape") Package for analyses of phylogenetics and evolution
    # see ?ape::rlineage for help
    #set.seed(1)

    ape::plot.phylo(timetree) # see also ?ape::plot.phylo
    axis(1)
    mtext("Time [Myr]", side = 1, line = 2.5)

You can transform the tree using `time_to_strat`:

    tree_in_strat_domain = time_to_strat(obj = timetree,
                                         x = my_adm)

Plotting the resulting tree along the stratigraphic column shows how the evolutionary relationships would be preserved 2 km offshore in the simulated carbonate platform:

    ape::plot.phylo(tree_in_strat_domain, direction = "upwards")
    axis(side = 2)
    mtext("Stratigraphic Height [m]",
          side = 2,
          line = 2)

#### Lists and time/stratigraphic series

admtools can transform lists from the time to the height domain and vice versa given they have elements with names `h` or `t`. These lists can be interpreted as time/stratigraphic series, where times and stratigraphic positions are associated with measured values. Note that these are not `ts` objects as used by the `stats` package, as they will be generally heterodistant due to the irregular nature of the age-depth transformation.

As example, we simulate trait evolution over 2 Myr using a Brownian motion, and transform the simulation into the stratigraphic domain.

    t = seq(0, 2, by = 0.001) # times
    BM = function(t){
      #" Simulate Brownian motion at times t
      li = list("t" = t,
                "y" = cumsum(c(0, rnorm(n = length(t) - 1, mean = 0, sd = sqrt(diff(t))))))
      class(li) = c("timelist", "list") # assign class `timelist` for easy plotting, see ?plot.timelist
      return(li)
    }
    evo_list = BM(t)
    plot(x = evo_list,
         xlab = "Time [Myr]",
         ylab = "Trait Value",
         type = "l")

    strat_list = time_to_strat(obj = evo_list,
                                x = my_adm)
    plot(x = strat_list,
         orientation = "lr",
         type = "l",
         xlab = "Stratigraphic Height [m]",
         ylab = "Trait Value",
         main = "Trait Evolution 2 km Offshore")

Note the jump in traits generated by the erosional interval in `my_adm`. Both `time_to_strat` and `strat_to_time` return `stratlist` and `timelist` objects when applied to lists. These are like ordinary lists, but come with simplified plotting optionality, see `?plot.stratlist` and `?plot.timelist` for details.

For expanded modeling features with biological context, please use the `StratPal` package (Github | Webpage | CRAN). It provides light wrappers around `admtools` and out of the box modeling of trait evolution.

#### Numeric vectors

Numeric vectors can be transformed using `time_to_strat` and `strat_to_time` too. These are essentially high level wrappers around `get_height` and `get_time`. See functions `time_to_strat.numeric` and `strat_to_time.numeric` for details.

## Further information

For an overview of the structure of the `admtools` package and the classes used therein see

    vignette("admtools_doc")

For details on plotting ADMs see

    vignette("adm_plotting)

For information on estimating age-depth models from sedimentation rates, see

    vignette("adm_from_sedrate")

For information on estimating age-depth models from tracer contents of rocks and sediments, see

    vignette("adm_from_trace_cont")

For information on depth-depth curves and correlation see

    vignette("correlation")

## References

- Burgess, Peter. “CarboCAT: A cellular automata model of heterogeneous carbonate strata.” Computers & geosciences 53 (2013): 129-140. DOI: 10.1016/j.cageo.2011.08.026

- Burgess, Peter. “CarboCAT Lite v1.0.1”. Zenodo 2023. DOI: 10.5281/zenodo.8402578

- Hohmann, Niklas; Koelewijn, Joël R.; Burgess, Peter; Jarochowska, Emilia. 2024. “Identification of the mode of evolution in incomplete carbonate successions.” BMC Ecology and Evolution 24, 113. https://doi.org/10.1186/s12862-024-02287-2.

- Hohmann, Niklas, Koelewijn, Joël R.; Burgess, Peter; Jarochowska, Emilia. 2023. “Identification of the Mode of Evolution in Incomplete Carbonate Successions - Supporting Data.” Open Science Framework. https://doi.org/10.17605/OSF.IO/ZBPWA, published under the CC-BY 4.0 license.