patterntodepositionmodel: Use sedimentary dilution/condensation of known patterns to create age model

Description

Takes a pair of a stratigraphic and a temporal pattern to determine the deposition model that transforms them into each other. The deposition model is returned as an age model.

Usage

patterntodepositionmodel(xheight, yheight, 
    xage = NULL, yage = NULL,
    heightmode = 'piecewise linear', agemode = 'piecewise linear',
    atheight=NULL,atage=NULL,rescalefor=1,timetype='time')

Arguments

xheight

A vector of strictly increasing numbers

yheight

A vector of strictly positive numbers. xheight and yheight define the stratigraphic pattern. By default, it is assumed to be piecewise linear and is accordingly given by approxfun(xheight,yheight). This can be changed to a binned representation using the option heightmode (see below)

xage

OPTIONAL, default is NULL

yage

OPTIONAL, default is NULL. xage and yage can be used to define the temporal pattern used for the reconstruction of the deposition model. If no input is handed over (default setting), it is assumed that the temporal pattern is constant over a time interval of duration 1. Using the option agemode allows to define both piecewise linear and binned temporal patterns (see below)

heightmode

OPTIONAL, default is 'piecewise linear'. Either 'piecewise linear' or 'binned'. Determines whether xheight and yheight are taken as a piecewise linear or a binned description of the stratigraphic pattern. In the first case, length(xheight) needs to match length(yheight), and the stratigraphic pattern is given by approxfun(xheight,yheight). In the second case, length(xheight) needs to match length(yheight)+1, and the value of the stratigraphic pattern between the stratigraphic heights xheight[i] and xheight[i+1] is given by yheight[i]

agemode

OPTIONAL, default is 'piecewise linear'. Either 'piecewise linear' or 'binned'. Determines whether xage and yage are taken as a piecewise linear or a binned description of the temporal pattern. In the first case, length(xage) needs to match length(yage), and the temporal pattern is given by approxfun(xage,yage). In the second case, length(xage) needs to match length(yage)+1, and the value of the temporal pattern between the ages xage[i] and xage[i+1] is given by yage[i]

atheight

OPTIONAL, default is NULL. Stratigraphic heights that should be included in the age model. By default, the function chooses those heights automatically

atage

OPTIONAL, default is NULL. Ages that should be included in the age model. By default, the function chooses those ages automatically

rescalefor

OPTIONAL, default is 1. Either a strictly positive number, 'temporal pattern', or 'stratigraphic pattern'. Determines what the total input into the sediment is.

timetype

OPTIONAL, default is "time". Either "time" or "age", determines whether input/output will be interpreted/given as time or age

Value

If timetype='time', a list containing the following entries:

time

Vector of times

height

Vector of stratigraphic heights

report

A short summary of the task performed

If timetype='age', a list containing the following entries:

age

Vector of ages

height

Vector of stratigraphic heights

report

A short summary of the task performed

age/time and height form the age model in the sense that the age/time at which height[i] was deposited is given by age[i]/time[i]. Conversely at the age/time age[i]/time[i], height[i] was deposited

References

Hohmann, Niklas. 2018. Quantifying the Effects of Changing Deposition Rates and Hiatii on the Stratigraphic Distribution of Fossils. <doi:10.13140/RG.2.2.23372.51841>

Examples

Run this code

# NOT RUN {
### Reconstruct deposition model based on condensation/dilution of a constant input
#assume a constant input of pollen (this is an arbitrary choice) into the sediment through time
#this is the observed stratigraphic pattern
my.xheight=seq(0,10,by=1)
my.yheight=seq(0,3,length.out=11)+rexp(11)
plot(my.xheight,my.yheight,xlab='Stratigraphic Height',ylab='Pollen Abundance',type='l',
  ylim=c(0,max(my.yheight)),main='Stratigraphic Pattern')
#reconstruct deposition model based on the assumption of constant pollen input in time
my.agemodel=patterntodepositionmodel(xheight=my.xheight,yheight=my.yheight)
my.agemodel$report
agemodelage=my.agemodel$time
agemodelheight=my.agemodel$height
plot(agemodelage,agemodelheight,type='l',
  lwd=6,main='Reconstructed Deposition Models as Age Model')
legend('topleft',legend='Age Model',lwd=6,col='black')
#approximate deposition rate (=derivative of the age model)
grad=diff(agemodelheight)/diff(agemodelage)
xbase=agemodelage[-1]
plot(xbase,grad,xlab='Time',ylab='Deposition Rate',
  main='Reconstructed Deposition Model as Deposition Rate',type='l',lwd=6,ylim=c(0,max(grad)))

#now assume pollen input into the sediment is decreasing and lasts for 2 time units
my.xage=c(0,2)
my.yage=c(5,1)
plot(my.xage,my.yage,type='l',xlab='Time',ylab='Pollen Input',ylim=c(0,max(my.yage)),
  lwd=6,main='Temporal Pattern')
#reconstruct age model based on these updated assumptions
my.agemodel2=patterntodepositionmodel(xheight=my.xheight,yheight=my.yheight,
    xage=my.xage,yage=my.yage)
my.agemodel2$report
agemodelage2=my.agemodel2$time
agemodelheight2=my.agemodel2$height
plot(agemodelage2,agemodelheight2,type='l',lwd=6, 
  main='Reconstructed Deposition Model as Age Model')
legend('topleft',legend='Age Model',lwd=6,col='black')

#if a pattern is given as bins, use the option 'heightmode' or 'agemode'
#define stratigraphic pattern as binned function
my.xheight3=seq(0,10,length.out=11) #borders of the bins used to define the stratigraphic pattern
my.yheight3=seq(0,3,length.out=10)+rexp(10) #note that xheight has one element more than yheight
barplot(my.yheight3,width=diff(my.xheight3),ylab='Pollen Abundance',xlab='Stratigraphic Height',
  space=0,main='Stratigraphic Pattern')
#reconstruct age model as in the first example, but with the binned pollen observation 
#  in stratigraphic height
#Note that pollen input in time is again assumed to be constant 
#(default setting if no xage and yage given)
my.agemodel3=patterntodepositionmodel(xheight=my.xheight3,yheight=my.yheight3,heightmode='binned')
my.agemodel3$report
agemodelage3=my.agemodel3$time
agemodelheight3=my.agemodel3$height
plot(agemodelage3,agemodelheight3,type='l',lwd=6,
  main='Reconstructed Deposition Model as Age Model')
legend('topleft',legend='Age Model',lwd=6,col='black')
#The same option is also available for the temporal pattern (no example given)

# }