knitr::opts_chunk$set( collapse = TRUE, comment = "#>", fig.width = 5, fig.height = 5 )
library(FossilSim)
This vignette provides information about how the package stores and outputs information about fossil sampling times via the fossils
object and available options for simulating fossil recovery.
The fossils
object contains information about fossil sampling times and their relationship to the corresponding phylo
and taxonomy
objects.
In some simulation conditions we may know the age of fossils precisely.
Alternatively, there may be some uncertainty associated with specimen ages, i.e. we only know the age to within some stratigraphic interval, which can be incorporated into the fossils
object.
The object contains a dataframe with species and age information for each fossil with the following 4 fields:
sp
the label of the corresponding species. This label matches the edge labels in the corresponding phylo
object or the species labels in the corresponding taxonomy
object if taxonomic information was provided
edge
the label of the sampled node or tip in the phylogeny, i.e the node at the end of the edge along which the fossil was sampled
hmin
the age of the fossil or the youngest bound of the time interval in which the fossil was sampled
hmax
the oldest bound of the time interval in which the fossil was sampled. This is equal to hmin
if exact sampling times are known
The object also contains a logical variable from.taxonomy
indicating whether the fossil record was simulated using a taxonomy
object, in which case from.taxonomy = TRUE
, or from a phylo
object in which case from.taxonomy = FALSE
(the default).
The simplest model of fossil recovery is a Poisson sampling process, where fossils are sampled along lineages with constant rate $\psi$ (function argument rate
).
Fossils can be simulated using a phylo
object or an existing taxonomy
object generated using the function sim.taxonomy
.
If a phylo
rather than a taxonomy
object is passed to the function, it will assume that all speciation has occurred via symmetric (i.e. bifurcating, $\beta = 1$) speciation, i.e. every edge in the tree represents a unique species.
This applies to all functions used to simulate fossils.
# set the random number generator seed to generate the same results using the same code set.seed(1234) # simulate a tree using TreeSim conditioned on tip number lambda = 1 mu = 0.2 tips = 8 t = TreeSim::sim.bd.taxa(n = tips, numbsim = 1, lambda = lambda, mu = mu)[[1]] # t is an object of class phylo t # use t$edge, t$edge.length, t$root.edge to see the tree attributes # Simulate fossils rate = 3 # poisson sampling rate f = sim.fossils.poisson(rate = rate, tree = t) f
Each entry in the fossils
dataframe corresponds to a fossil sampling time.
sp
and edge
are the species and edge labels, respectively, which will be the same here since we assume symmetric speciation.
hmin
and hmax
are the youngest and oldest sampling ages associated with each fossil, respectively.
Since this function returns exact fossil sampling times hmin
and hmax
are equal.
# plot fossil occurrences plot(f, tree = t)
# plot stratigraphic ranges plot(f, tree = t, show.ranges = TRUE)
# plot stratigraphic ranges only plot(f, tree = t, show.ranges = TRUE, show.fossils = FALSE, show.tree = FALSE) # add stratigraphic intervals plot(f, tree = t, show.strata = TRUE, strata = 4) # more tips on plotting strata # http://simpson-carl.github.io/articles/15/timescales.to.base
# simulate taxonomy under mixed speciation beta = 0.5 # probability of symmetric speciation lambda.a = 1.2 # rate of anagenetic speciation s = sim.taxonomy(tree = t, beta = beta, lambda.a = lambda.a) # simulate fossils f = sim.fossils.poisson(rate = rate, taxonomy = s) f # plot the output and color fossils by taxonomy plot(f, tree = t, taxonomy = s, show.taxonomy = TRUE)
Note that sp
and edge
are not all equal, since some species are assigned to multiple edges, and some edges are associated with multiple species.
Under the interval-dependent model, fossil recovery changes in a piece-wise manner across a set of user defined intervals.
Interval ages can be specified using a fixed set of uniform length intervals, by passing the function the maximum interval age (max.age
) and the number of intervals (strata
), or a vector of non-uniform intervals (interval.ages
).
The function tree.max
can be used to assign a maximum age based on tree age. If the tree has a root.edge
the function will return the origin time, otherwise the function returns the root age.
# define max interval age based on tree age max.age = tree.max(t) # define the number of intervals strata = 4 # define a vector of sampling rates, where the first entry corresponds the youngest interval rates = c(1, 0.1, 1, 0.1) # simulate fossils f = sim.fossils.intervals(tree = t, rates = rates, max.age = max.age, strata = strata) # plot the output plot(f, tree = t, show.strata = TRUE, strata = strata)
If no maximum is provided to the plotting function and strata
> 1, the function tree.max
is used to define max.age
.
# the following will sample a random set of interval ages between 0 and max.age times = c(0, sort(runif(3, min = 0, max = max.age)), max.age) # define a vector of sampling rates from youngest to oldest rates = c(1, 0.1, 1, 0.1) # simulate fossils f = sim.fossils.intervals(tree = t, rates = rates, interval.ages = times) # plot the output and show sampling or proxy data plot(f, tree = t, show.strata = TRUE, interval.ages = times, show.proxy = TRUE, proxy = rates)
Fossil recovery can also be specified using a set of per-interval probabilities. At most one fossil per species will be sampled per interval using this approach.
# define max interval age based on tree age max.age = tree.max(t) # define the number of intervals strata = 4 # define a vector of sampling probabilities from youngest to oldest probabilities = c(1.0, 0.5, 0.2, 0.1) # simulate fossils f = sim.fossils.intervals(tree = t, probabilities = probabilities, max.age = max.age, strata = strata) # plot the output plot(f, tree = t, show.strata = TRUE, strata = strata)
To incorporate age uncertainty into the output using the function sim.fossils.intervals
set use.exact.times = FALSE
.
In this case hmin
and hmax
will represent the youngest and oldest age associated with the fossil, respectively.
When we plot the output the function will place the fossils at the mid-point of the corresponding interval.
This means in some cases fossils will not appear along their corresponding edge.
# simulate fossils f = sim.fossils.intervals(tree = t, probabilities = probabilities, max.age = max.age, strata = strata, use.exact.times = FALSE) f # plot the output plot(f, tree = t, show.strata = TRUE, strata = strata)
Alternatively, if you simulate fossils using a function that only returns exact fossil sampling times, e.g. using the sim.fossils.poisson
function, you can later assign fossils to different intervals using the sim.interval.ages
function.
You can also generate output using this function that respect the species duration times by setting use.species.ages = TRUE
, i.e. the function will not return a value for hmin
or hmax
that are younger or older than the true species age.
To use this option you also need to pass a phylo
or taxonomy
object to the function.
# simulate fossils f = sim.fossils.poisson(tree = t, rate = 3) # reassign fossils to intervals f = sim.interval.ages(fossils = f, tree = t, max.age = max.age, strata = strata, use.species.ages = TRUE) # plot the output plot(f, tree = t, show.strata = TRUE, strata = strata)
The function sim.fossils.environment
can be used to simulate fossil recovery that reflects species environmental preferences.
The variables that control the distribution and abundance of species also control depositional environment, meaning changes in ecological or environmental gradient across a given area will be reflected in the patterns of deposition.
A species response curve, which describes the abundance of a species relative to an environmental gradient, can therefore be used to model distributions of fossil occurrences. See the plot below for examples.
@Holland1995 described a three parameter Gaussian model for simulating environment-dependent fossil recovery.
In this model each species has three parameters, species preferred depth ($PD$), depth tolerance ($DT$) and peak abundance ($PA$) (function arguments PD
, DT
and PA
).
The probability of fossil recovery during a given interval of time is a function of water depth, given by,
$Pr_{collection_i}(d) = PA * exp(-(d - PD)^2/ (2*DT^2))$,
where $d$ is current water depth, $PD$ and $DT$ are the mean and the standard deviation of the distribution, respectively, and $PA$ describes the amplitude of the distribution.
Here the model is described in the context of marine taxa, however the model and the function sim.fossils.environment
can be applied to any environmental or depositional context, in which some measure of environmental gradient can be generated.
The following code snippet illustrate how to explore the role of the model parameters $PD$, $DT$ and $PA$ in determining species response curves.
# define a set of colors for 4 species # color palette chosen using RColorBrewer cols = c("#E41A1C", "#377EB8", "#984EA3", "#4DAF4A") # red, blue, purple, green # species response curve function response.curve = function(x, pd, dt, pa) pa * exp(-(x - pd)^2/ (2*dt^2)) # define species variables # species 1 PA = 1 # peak abundance PD = 2 # preferred depth DT = 1 # depth tolerance # plot species resonse curve curve(response.curve(x, PD, DT, PA), -2, 6, bty = "n", xlab = "relative depth", ylab = "Pr(collection)", xlim = c(-6,6), lwd = 1.5, col = cols[1]) # redefine depth tolerance and compare the output # species 2 DT = 0.5 curve(response.curve(x, PD, DT, PA), -1, 5, add = TRUE, lwd = 1.5, col = cols[2]) # redefine preferred depth and compare the output # species 3 PD = -2 curve(response.curve(x, PD, DT, PA), -5, 1, add = TRUE, lwd = 1.5, col = cols[3]) # redefine prferred depth and peak abundance # species 4 PD = -4 PA = 0.5 curve(response.curve(x, PD, DT, PA), -6, -2.2, add = TRUE, lwd = 1.5, col = cols[4])
The user is free to use a vector containing any gradient values to simulate fossil occurrences.
In the following example we will use a vector of gradient values generated using the function sim.gradient
, which return values for the following simple sine wave function,
$y = dsin(cyclespi*(x-1/4))$, where $x$ is the number of intervals or strata.
The function output can be used to represent changes in relative water depth, where the number of cycles may be equivalent to the number of transgression/regression events.
Interval ages can be specified in the same way as the function sim.fossils.intervals
via max.age
and strata
or the intervals
vector.
# define the interval parameters strata = 20 times = seq(0, tree.max(t), length.out = strata+1) # simulate gradient values wd = sim.gradient(strata, depth = 6) # wd is a vector representing relative water depth wd # define species trait values # species 1 PD = 1 DT = 2 PA = 1 # simulate fossils f = sim.fossils.environment(tree = t, interval.ages = times, proxy.data = wd, PD = PD, DT = DT, PA = PA) # plot output and include proxy data & preferred depth plot(f, tree = t, interval.ages = times, show.strata = TRUE, show.proxy = TRUE, proxy.data = wd, show.preferred.environ = TRUE, preferred.environ = PD, fossil.col = cols[1]) # redefine species trait values # species 2 DT = 0.5 # simulate fossils f = sim.fossils.environment(tree = t, interval.ages = times, proxy.data = wd, PD = PD, DT = DT, PA = PA) # plot output plot(f, tree = t, interval.ages = times, show.strata = TRUE, show.proxy = TRUE, proxy.data = wd, show.preferred.environ = TRUE, preferred.environ = PD, fossil.col = cols[2]) # redefine species trait values # species 3 PD = -2 # simulate fossils f = sim.fossils.environment(tree = t, interval.ages = times, proxy.data = wd, PD = PD, DT = DT, PA = PA) # plot output plot(f, tree = t, interval.ages = times, show.strata = TRUE, show.proxy = TRUE, proxy.data = wd, show.preferred.environ = TRUE, preferred.environ = PD, fossil.col = cols[3]) # define species trait values # species 4 PD = -4 PA = 0.5 # simulate fossils f = sim.fossils.environment(tree = t, interval.ages = times, proxy.data = wd, PD = PD, DT = DT, PA = PA) # plot output plot(f, tree = t, interval.ages = times, show.strata = TRUE, show.proxy = TRUE, proxy.data = wd, show.preferred.environ = TRUE, preferred.environ = PD, fossil.col = cols[4])
Variation in fossil recovery parameters across different lineages or species can be generated using the function sim.trait.values
.
The function output is a vector of simulated trait values that can be used to specify the rate
parameter in sim.fossils.poisson
or the PD
, DT
and PA
parameters in sim.fossils.environment
.
Trait values can be simulated for a given phylo
or taxonomy
object.
If the function is provided with a phylo
object, trait values are simulated assuming bifurcating speciation and simulated trait values are output for each edge in the order in which they appear in the phylo
object dataframe.
If the tree also has a root edge (tree$root.edge
), the first entry in the vector will correspond to the first entry in the vector.
If the function is provided with a taxonomy
object, simulated trait values are output for each species in the order in which they appear in the taxonomy
object dataframe.
Under the autocorrelated
model, traits evolve along lineages according to a Brownian motion process, where the strength of the relationship between ancestor and descendant values is determined by the parameter $\nu$ (function argument v
).
New trait values are drawn from a lognormal distribution, where the mean is equal to the value of the ancestor and the variance is a function of $\nu$ and the species or edge duration.
If $\nu$ is small values will be more similar between ancestor and descendants, and if $\nu$ is zero all trait values will be equal.
This is model is described in @Heath2014 and is equivalent to the autocorrelated relaxed clock model described in @Kishino2001.
# define the initial rate at the root or origin rate = 1 # simulate rates under the autocorrelated trait values model (the default option) rates = sim.trait.values(init = rate, tree = t, v = 0.01) # simulated rates rates # simulate fossils f = sim.fossils.poisson(tree = t, rate = rates) # plot the output plot(f, tree = t)
Under the independent
model a new trait value is drawn for each species from any valid user-specified distribution dist
.
To be valid the function just has to return a single value.
# define the initial rate at the root or origin rate = 1 # define the distribution used to sample new rates # in this case an exponential with mean = 1 dist = function() { rexp(1) } # simulate trait values under the independent trait values model rates = sim.trait.values(init = rate, tree = t, model = "independent", dist = dist) # simulate fossils f = sim.fossils.poisson(tree = t, rate = rates) # plot the output plot(f, tree = t)
The parameter change.pr
is the probability that changes in trait values are coincident with speciation events.
At each speciation event change occurs with probability change.pr
and new values are drawn from any valid user-specified distribution dist
.
If change.pr = 1
a change will occur at every speciation event and the model will be the same as above.
# define the initial value at the root or origin rate = 1 # define the distribution used to sample new rates # in this case an exponential with a mean ~ 3 dist = function() { rexp(1, 1/4) } # define the probability of the trait value changing at each speciation event change.pr = 0.5 # simulate trait values under the independent trait values model rates = sim.trait.values(init = rate, tree = t, model = "independent", dist = dist, change.pr = change.pr) # simulate fossils f = sim.fossils.poisson(tree = t, rate = rates) # plot the output plot(f, tree = t)
Lineage specific values generated using sim.trait.values
can also be passed to the the function sim.fossils.environment
to define the PD
, DT
, and PA
parameters.
# define constant values for preferred depth and depth tolerance PD = 2 DT = 0.5 # simulate lineage variable peak abundance values # define the distribution used to sample new PA values # in this case a uniform in the interval 0, 1 dist = function() { runif(1) } # simulate trait values under the independent model PA = sim.trait.values(init = 0.1, tree = t, model = "independent", dist = dist) # simulate fossils f = sim.fossils.environment(tree = t, interval.ages = times, proxy.data = wd, PD = PD, DT = DT, PA = PA) # plot the output plot(f, tree = t, show.strata = TRUE, interval.ages = times)
The functions sim.extant.samples
and sim.tip.samples
can be used to simulate incomplete extant species and tip sampling, respectively. The parameter rho
is the probability that an extant species or a tip will be sampled.
# simulate fossils f = sim.fossils.poisson(tree = t, rate = rates) # simulate extant species sampling f2 = sim.extant.samples(fossils = f, tree = t, rho = 0.5) # plot the output plot(f2, tree = t, extant.col = "red") # for tip sampling only, create a fossil object with no fossils f = fossils() # simulate tip sampling f2 = sim.tip.samples(fossils = f, tree = t, rho = 0.75) # plot the output plot(f2, tree = t)
See the paleotree
vignette to see how FossilSim
objects can be converted into paleotree
objects.
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