Learning objectives

1. Exploring fossil occurrences
2. Diversity patterns in deep time
3. The spatial distribution of the record
4. Drawing conclusions from the fossil record
5. Technical note: Dating fossils in absolute time

Introduction

Thus far, we’ve been typically dealing with evolutionary processes that occur over short timescales – mostly not more than a few hundred generations. But this generational scale of evolutionary change pales in comparison to the vastness of geological time. In this lab, we will explore the evolutionary history of clades through tens (sometimes hundreds) of millions of years, via the major source of direct evidence on deep time: the fossil record.

For this tutorial, you must install the palebioDB R package.

install.packages("paleobioDB")

Then, load all packages required into your workspace:

library(evolved)
library(paleobioDB)

Exploring fossil occurrences

We’ve downloaded a fossil dataset for you to work with today (dinos_fossil). All occurrence data were originally obtained from the Paleobiology database, a free-to-use resource that is the standard repository for such data and which has been used by hundreds or thousands of researchers to study the history and dynamics of biodiversity in deep time.

We kept as many occurrences as possible from the original datasets, but removed some extraneous data (e.g. notes on preservation, notes on the paleoenvironment, the original reference for the data, etc.) to make them easier to use. We also removed occurrences with poor time resolution (i.e., the timespan between the maximum and minimum ages of the strata associated with that fossil), and we removed all fossil occurrences not identified to the species level.

To illustrate what these data look like, let’s read and view part of the dinosaur occurrence data. First, we’ll read the file:

data("dinos_fossil")

Then, we’ll check the basic properties of the dinos dataframe:

dim(dinos_fossil)

## [1] 15527    13

You can see that there are 15527 rows (each row is an occurrence) and 13 columns (each column is an attribute of each occurrence).

So what are these columns?

colnames(dinos_fossil) 

##  [1] "phylum"         "class"          "order"          "family"        
##  [5] "genus"          "species"        "early_interval" "late_interval" 
##  [9] "max_ma"         "min_ma"         "midpoint"       "lng"           
## [13] "lat"

It is always good to check the rows and columns (as we just did) to verify that data were correctly loaded.

In our data, we see columns for:

phylum, class, order, family, genus, species = The taxon associated with that occurrence for that hierarchical level.

early_interval, late_interval = The name of the early (furthest from present) and the name of the late (closest to present) intervals associated with that occurrence. Some of those intervals appear in the GSA geologic timescale (link here).

min_ma, max_ma = The maximum (oldest; farthest in time from the present) and minimum (youngest; closest to present) ages associated with that occurrence. Note that these ages are in units of millions of years ago (abbreviated to “mya”), in absolute time.

midpoint = The date (in millions of years ago) of the exact halfway point of the interval the fossil was found in. We will explain this variable a bit further in this tutorial.

lng, lat = The longitude and latitude of the location the fossil was found in. These coordinates are for the fossil’s location in the present. The “paleo” latitude and longitude (which we removed prior to loading the data in the package) of each fossil occurrence would be an estimate of the location where that organism actually lived, given what we know about plate tectonics and the age of the fossil.

More on how fossil dating works (i.e., how we can determine min_ma and max_ma) and its limitations are in the technical note “Dating fossils in absolute time” at the end of this tutorial.

Now, using the function head(), we can view the first n rows of the dataset:

head(dinos_fossil, n = 5)

##     phylum        class              order              family
## 1 Chordata Ornithischia NO_ORDER_SPECIFIED    Chaoyangsauridae
## 2 Chordata   Saurischia       Avetheropoda NO_FAMILY_SPECIFIED
## 3 Chordata   Saurischia       Avetheropoda NO_FAMILY_SPECIFIED
## 4 Chordata   Saurischia       Avetheropoda     Tyrannosauridae
## 5 Chordata   Saurischia       Avetheropoda     Tyrannosauridae
##               genus                   species early_interval late_interval
## 1    Chaoyangsaurus     Chaoyangsaurus youngi Late Tithonian   Valanginian
## 2 Protarchaeopteryx Protarchaeopteryx robusta Late Barremian  Early Aptian
## 3       Caudipteryx          Caudipteryx zoui Late Barremian  Early Aptian
## 4       Gorgosaurus      Gorgosaurus libratus Late Campanian              
## 5       Gorgosaurus      Gorgosaurus libratus Late Campanian              
##   max_ma min_ma midpoint       lng      lat
## 1  150.8 132.90   141.85  123.9667 42.93330
## 2  130.0 122.46   126.23  120.7333 41.80000
## 3  130.0 122.46   126.23  120.7333 41.80000
## 4   83.5  70.60    77.05 -111.5287 50.74073
## 5   83.5  70.60    77.05 -111.5493 50.73701

You will notice that the head() output wraps around your console output screen because it is too wide to be displayed in one viewing frame. The functions dim(), colnames(), and head() are useful for inspecting the datasets that you’ve loaded.

The exercises below use the dinosaur data for illustrative purposes, but the functions we’ve provided (and associated exercises) will work for any of the other datasets (trilobites, ammonites, mammals).

As a warm-up, let’s count how many occurrences there are for a famous dinosaur genus, like Majungasaurus. An interesting quick note here is that there is a Majungasaurus full skeleton reconstruction in the University of Michigan Museum of Natural History that anyone can visit.

sum(dinos_fossil$genus == "Majungasaurus")

## [1] 25

Now let’s try its more famous relative, the T-rex. How many occurrences of T-rex are there in our dataset?

sum(dinos_fossil$species == "Tyrannosaurus rex")

## [1] 70

Important to consider: most of what we know about the T-rex comes from these 70 fossil specimens!

Trex <- dinos_fossil[dinos_fossil$species == "Tyrannosaurus rex",]

#this still has the same columns as the dinosaur dataset:
colnames(Trex)

##  [1] "phylum"         "class"          "order"          "family"        
##  [5] "genus"          "species"        "early_interval" "late_interval" 
##  [9] "max_ma"         "min_ma"         "midpoint"       "lng"           
## [13] "lat"

plotRawFossilOccs(Trex, use.midpoint =  F, knitr = T)

plotRawFossilOccs(Trex, use.midpoint = F, knitr = T)
segments(x0 = min(Trex$midpoint),
         x1 = max(Trex$midpoint),
         y0 = 35, y1 = 35, lwd=3, col="red"
          )

plotRawFossilOccs(dinos_fossil, tax.lvl = "species", knitr = T)

plotRawFossilOccs(dinos_fossil, tax.lvl  = "family", knitr = T)

plotRawFossilOccs(dinos_fossil, tax.lvl  = "order", knitr = T)

hist(dinos_fossil$midpoint,
     breaks=100, #increasing breaks to see data in a better precision
     xlab="Absolute time (Mya)", main = "Fossil Occurrence midpoints",
     
     #reversing axis to represent past -> present
     xlim=c(rev(range(dinos_fossil$midpoint))) 
     )

# first we load the species list:
data("birds_spp")

# then we count the number of extant dinosaurs within our fossil dataset:
n_fossilized_dinos <- sum(birds_spp %in% dinos_fossil$species)

#then we calculate the proportion:
n_fossilized_dinos/length(birds_spp)

## [1] 0.1139798

Diversity patterns in deep time

We can use two simple methods to calculate diversity curves in the fossil record (see fig 1-III):

The standard method, which simply sums up taxa that occur in the same interval, and thus calculates the diversity within each interval.

The range-through method, which only sums up species that are observed before and after a given stratigraphic interval, and thus calculates the diversity at interval boundaries. This method guarantees we are measuring diversity that co-occurs in time.

Both methods interpolate (“fill in”) gaps in a species’ fossil record between occurrences, by counting a species as being present in any interval that is between the first and last fossil occurrences (FAD and LAD, respectively). Meaning: an interval that does not have an occurrence, but that is between the first and last intervals containing occurrences, is counted as containing that species; see taxon D in Figure 1 for a visual example.

The function calcFossilDivTT do these calculations for you, and you can use the argument method to decide which method will be employed.

# This line calculates diversity through the standard method:
SM <- calcFossilDivTT(dinos_fossil, method = "stdmethod")

# and this one calculates diversity using the range-through method:
RG <- calcFossilDivTT(dinos_fossil, method = "rangethrough")


# Now we can create an empty plot to store our estimates:
plot(NA, 
     xlim=rev(range(c(RG$age, SM$age))),
     ylim=range(c(RG$div, SM$div)),
     xlab="Absolute time (Mya)",
     ylab="Diversity"
     )  

# and then add the standard method diversity:
lines(x=SM$age, y = SM$div, type = "l", lwd=2)  

# and finally add the range-through diversity:
lines(x=RG$age, y = RG$div, type = "l", col="blue", lwd=2)  

As you can see, even when we calculate diversity through corrected methods, the pull of the recent still distorts our perception of diversity trends: the number of bird fossils increases our diversity line so much that it limits our ability to visualize changes deeper in the past. We can account for this in two ways.

The first and simpler way is to manually restrict our y-axis. We will also add a mark representing the time of the K-Pg mass extinction with a red vertical line in the following plot.

#Creating a plot:
plot(NA, 
     xlim=rev(range(c(RG$age, SM$age))),
     
     ylim=c(0,700), # here is the part of the code I changed, in
                    # comparison with the former chunk of code
     
     xlab="Absolute time (Mya)",
     ylab="Diversity"
     )  

# adding the standard method diversity:
lines(x=SM$age, y = SM$div, type = "l", lwd=2)  

# adding the range-through diversity:
lines(x=RG$age, y = RG$div, type = "l", col="blue", lwd=2) 

# Here, red line marks the K-Pg mass extinction:
abline(v=66, col="red")

Instead of restricting our y-axis, we could use the log scale to highlight proportional changes in diversity. In the below plot, we will plot species richness in log base 2. This means every increment of 1 unit on the log scale equals doubling the number of species, and each unit decrease on this scale equals halving the number of species.

# Plotting again our diversity curves (note
# this is exactly what we did in the previous section), but in log scale
plot(NA, 
     xlim=rev(range(c(RG$age, SM$age))),
     ylim=range(c(0, max(log(c(RG$div, SM$div), base = 2)))), # note the base 2
     xlab="Absolute time (Mya)",
     ylab="Diversity")  

# adding the standard method diversity:
lines(x=SM$age, 
      y = log(SM$div, base=2),
      type = "l", lwd=2)  
# adding the range-through diversity:
lines(x=RG$age, 
      y = log(RG$div, base = 2),
      type = "l", col="blue", lwd=2)

# Here, red line marks the K-Pg mass extinction:
abline(v=66, col="red")

The spatial distribution of the record

The density of fossil occurrences also varies in space. We can plot this unevenness using the function pbdb_map_occur from the paleobioDB R package.

# Plotting number of occurrences in space:

# you can change the size of the cells using the  argument "res"
pbdb_map_occur(dinos_fossil, res = 1, cex = 0.3)

## class       : SpatRaster 
## dimensions  : 169, 370, 1  (nrow, ncol, nlyr)
## resolution  : 1, 1  (x, y)
## extent      : -180, 190, -85.19218, 83.80782  (xmin, xmax, ymin, ymax)
## coord. ref. : lon/lat WGS 84 (CRS84) (OGC:CRS84) 
## source(s)   : memory
## name        : sum 
## min value   :   1 
## max value   : 459

Just as a curiosity, we can also plot the spatial distribution of the T-rex using the dataset we created earlier in this tutorial.

pbdb_map_occur(Trex, res = 1, cex=0.7)

## class       : SpatRaster 
## dimensions  : 169, 370, 1  (nrow, ncol, nlyr)
## resolution  : 1, 1  (x, y)
## extent      : -180, 190, -85.19218, 83.80782  (xmin, xmax, ymin, ymax)
## coord. ref. : lon/lat WGS 84 (CRS84) (OGC:CRS84) 
## source(s)   : memory
## name        : sum 
## min value   :   1 
## max value   :  22

Drawing conclusions from the fossil record

In this tutorial, we briefly explored the fossil record of dinosaurs only, but we gave you 3 other datasets: Trilobites, Mammals, and Ammonites.

Explore them using the same set of functions and techniques that we used above, and then answer:

Apart from the incompleteness of the record, you may have realized that another layer of complexity in the fossil record is the lack of temporal resolution most fossil occurrences have. Sometimes the imprecision is larger than 20 million years, which is a large amount of time – but why do we have so much imprecision in those estimates? We will explore this in the last section of this tutorial.

Technical note: Dating fossils in absolute time

As you may know, we can use the U²³⁸ − Pb²⁰⁶ decay series to estimate the absolute ages of igneous rocks (e.g., granite, basalt, volcanic ash, “frozen lava”, etc). Zircon is a silicate mineral that is widely-used for radiometric dating, because it forms crystals (e.g., when magma cools into rock) that selectively include U²³⁸ and exclude all the decay products. This happens because U²³⁸ is trapped in the zircon crystal after it forms. Then, the crystal begins to accumulate all of the decay products, but in this case, these products are kept trapped within the crystal structure. Physicists have determined that after 4.5 billion years (4,500,000,000 years; 4 × 10⁹ years), roughly 50% of a sample of pure U²³⁸ will have decayed into Pb²⁰⁶. Thus, by looking at the ratio of U²³⁸ and Pb²⁰⁶ in a sample, we can estimate the ages of an igneous rock and thus gain insights into the age of fossil-bearing sedimentary layers.

To apply this method, we first have to estimate the decay rate of U²³⁸. An exponential decay process can be modeled as

where U_t is the amount of U²³⁸ at time t, U₀ is the starting amount, t is the elapsed time (since the formation of the zircon crystal), and k is the radioactive decay constant for U²³⁸. Consequently, we need to estimate k for any dating we may wish to do. We can estimate k because we know the half-life ( = $t_{\frac{1}{2}}$) of U²³⁸: this is the value of t where an initial quantity of U₀ = 1 will have decayed by half, or U_t = 0.5. Rearranging the equation gives:

$k = \frac{log 2}{t_{\frac{1}{2}}}$

Note we have to use the natural log (i.e. base = e) in the equation above. More on the method of half-lives can be found here.

Now, using the decay constant k obtained above, we can apply equation (1) to date the rock layers given an estimate of the ratio of U²³⁸ to Pb²⁰⁶. These estimates are typically made using ionizing mass spectrometry; note also that we need the ratio of the number of atoms of U and Pb, not the ratio of masses. Suppose, for a zircon crystal, that we have estimated the ratios of uranium to lead as W_U : W_Pb. This lets us directly estimate U_t and U₀ in the decay equation above. If you think of W_U as the amount of uranium currently in the sample, then the total amount that you started with had to have been W_U plus W_Pb, because every Pb²⁰⁶ atom is the result of decay from exactly one U²³⁸ atom. Thus, W_U = U_t and U₀ = W_U + W_Pb.

Know, we can come back to equation (1), solve for t, and get to the equation that allow you to estimate the age of a rock layer, given you measured certain amounts of W_U and W_Pb.

Example on how fossil layers can be dated using zircon crystals. Note that percentages represent atomic fractions, not percentages by mass.

As an extra reading, you can find an interesting outreach article about zircon dating here.

A last important point is that not all fossiliferous sites have the conditions that allow us to do zircon dating, which means that paleontologists have to use other techniques to date those fossils. This involves a lot of work and usually adds uncertainty on the dating process. If you have 14 minutes of your free time, and want to see how important and yet difficult it is to date a fossil, you could watch this short video from the youtube channel PBS Eons.

References:

Jetz, W., Thomas, G. H., Joy, J. B., Hartmann, K., & Mooers, A. O. (2012). The global diversity of birds in space and time. Nature, 491(7424), 444-448.

Upham, N. S., Esselstyn, J. A., & Jetz, W. (2019). Inferring the mammal tree: species-level sets of phylogenies for questions in ecology, evolution, and conservation. PLoS biology, 17(12), e3000494.