The course in which this exercise is used is an upper-division, elective course for undergraduates majoring in Environmental Studies, Marine Science, and Biology (FGCU does not have a Geology Major) that is taught once every two years (titled: Geobiology). The course focuses on the applications of paleontological data to problems in those disciplines. The exercise is applicable for any college-level audience enrolled in a course in paleontology, paleobiology, zoology, or botany.

The exercise is completed over a series of class meetings to allow students to work individually at first and then re-engage to compile results and discuss their interpretations.

Students should have background on the following topics: (1) Sepkoski diversity curve and the Three Great Faunas; (2) adaptive radiations and their causes; (3) descriptive statistics (including histogram generation, mean, mode, median, skewness). In addition, though not essential, a familiarity with the types of clades that compose the Cambrian Fauna is helpful. This provides some "real fossil" context to the use of genus-level range data. Our fossil collection is limited, though I do provide a display of some of the Cambrian taxa and then supplement this with photographs.

The activity is introduced as an in-class teaching activity. Students are provided with laptops and access to the Sepkoski database. (Alternatively and to save time, students can be provided with the genus-level range data already collected for each clade.) Data are collected, plotted as histograms, and descriptive statistics are generated in class. Students are asked to email the results to me; I compile them; and then redistribute them to everyone in the class. Additional time is reserved in class for students, in small groups, to interpret the results. Finally students are asked to complete a writing assignment (see exercise description).

1. Understanding of processes associated with macroevolution: speciation, cladogenesis, and transpecific evolution.
2. Familiarity with the Sepkoski curve, the Three Great Faunas, patterns of diversification, and the underlying causes.
3. Testing stochastic versus deterministic causal hypotheses for patterns in evolution. Employing methods and philosophy of probabilistic paleontology.

- Hypothesis testing. Testing of alternative hypotheses.

- Experience using on-line databases and in use of Excel.
- Generating and interpreting histograms and descriptive statistics.
- Collaborative experience.
- Expository writing skills enhanced.

Purpose & Overview:

Many evolutionary biologists and paleontologists have debated whether patterns of diversification through geologic time, like those seen in the Sepkoski Phanerozoic diversity curve, are deterministic or a result of stochastic (i.e., random) processes. Said another way, have patterns in evolutionary diversification been caused by intrinsic or extrinsic factors (e.g., newly evolved morphologic innovations or new ecologic opportunities leading to adaptive radiations) or can they be explained simply by random processes? One way to test these two alternative hypotheses is to generate diversity patterns mathematically in random computer simulations and then compare these stochastically generated patterns to real data-based patterns from the fossil record. If the two are sufficiently different (i.e., their means are shown to be unequal statistically), then the random, null hypothesis can be rejected and the alternative, deterministic hypothesis corroborated. This approach, whereby real patterns are compared to randomly simulated ones, is known as "probabilistic paleontology". Accepting a random, null hypothesis has serious implications for the history of life. If the patterns seen through time could be due to random processes exclusively, then our ideas about natural selection and species selection need to be seriously reconsidered. Perhaps these processes do exist, but they would be of little consequence when it came to long term trends in earth's biota. Some paleontologists have suggested that not only are deterministic factors important, but during types of innovation and ecological opportunity radiating clades should be bottom heavy – much more species-rich early in their history. Through subsequent history selection eliminates those species less able to compete while those better-adapted species persist. In such situations the tree of life more resembles a pruned bush with many low branches and few persisting higher up (Gould et al. 1987; Gould 1990).

This exercise applies a probabilistic approach to testing causal hypotheses for the pattern of within-clade diversity through the Paleozoic. Metazoans (animals) radiated rapidly in the Cambrian and quickly populated the marine world. Paleontologists have long debated the cause of this radiation. Each person in the class looks at the diversification of 1 or more families of fossils within the Cambrian Fauna. Each student graphically represents within-family diversity data by compiling the ranges of genera through stages of the Paleozoic. Data for ranges of fossil genera are obtained from Sepkoski's compendium (2002) which is accessible through a couple of web sites (see reference list below). The class assumes a priori that randomly generated clade diversity diagrams, when the rates of speciation and extinction are equal, are symmetrical about the mean (Gould et al. 1987).

Materials:

1. Laptop computers running Excel. One per student or fewer if students work in small groups.
2. Access to the Sepkoski database (see URLs below).
3. Sample fossils or images of members of the clade for which each student is compiling range data.
4. Geological time scale showing absolute ages by geologic stage.

Procedure:

1. Each student or small student group is assigned one of the Cambrian Fauna clades from the list of 24.
2. Using the online Sepkoski database, the genera belonging to that clade and their stratigraphic ranges are obtained. The stage of earliest occurrence of a genus in that clade defines the clade's time of origin; the last occurrence of genus defines the clade's extinction. The time between the clade's origination through its extinction defines the temporal units on the histogram's x-axis.
3. In table form, the number of genera extant in each stage is recorded. This defines the number of occurrences along the histogram's y-axis.
4. The temporal mid-point of each stage defines the bin's central value. The file "Sample Clade Statistics" demonstrates how the descriptive statistics are obtained from these ages.

The following files are uploaded as supportive teaching materials:

1. PowerPoint file introducing the exercise and providing the necessary background. Titled: Bottom Heavy Clade Presentation.
2. Handout given to students describing the exercise. Word file titled: Exercise 4 Clade Diversity Exercise.
3. Summary statistics for a collection of Cambrian Fauna clades generated by students. This is intended as sample results and shouldn't be shared with students. Excel file titled: Cambrian Clade Statistics.
4. Handout with a list of 24 Cambrian clades to be included in the analysis using the Sepkoski genus-level compendium. Word file titled: Cambrian Fauna Clades.
5. Excel file showing how descriptive statistics are calculated from the range data. Title: Sample Clade Statistics.
6. File containing genus-level range data for each of the clades included in the above handout. This could be provided to students at the onset or students could acquire these data on their own. Excel file titled: Cambrian Clades in Sepkoski Genus-level Compendium.

- This exercise was attempted only once since this activity was posted. A number of difficulties were identified and repaired for this publication. First, because histograms are plotted with values increasing to the right along the x-axis while diversity diagrams are plotted from past to recent (high to low dates) along the x-axis, much confusion ensued when labeling a distribution top- vs. bottom-heavy or left or right skewed. Second, histograms are not readily produced with Excel, at least without the added-on statistics pack, which generated trouble when calculating mean, mode, and median. The next permutation of the exercise will presumably run more smoothly.
- Other instructors may judge this as too time-consuming to emphasize what may be perceived as a straight forward concept. If for no other reason, I found it useful as a means for getting students to work with data and the Sepkoski compendium.

A collection of helpful references is included within the exercise description handout.

In addition, the following URLs provide access to Sepkoski's data:

1. Sepkoski's online genus-level database at UW Madison: http://strata.geology.wisc.edu/jack/.
2. The Paleobiology Database: http://paleodb.org/cgi-bin/bridge.pl.
3. To purchase Sepkoski, 2002: http://www.priweb.org/bookstore/info_BAP.html#BAP363.