This exercise is designed for an upper level (junior to senior) undergraduate paleontology course taken by geoscience majors (Geology and Earth & Space Science Education majors) and individuals in related majors such as Anthropology or Biology (and Biology Education).

The skills and concepts that students need coming into the course include basic familiarity with Earth History and the Geologic Time Scale (i.e, knowledge of the time units in the Phanerozoic and an understanding of how they are defined by chronostratigraphic ("time-rock") units); a bit of paleogeographic background so that they are familiar with such now-defunct continents and seaways as Laurentia, Iapetus, the Tethys, etc.; a rudimentary knowledge of Plate Tectonics, sedimentary facies and depositional environments, and the hierarchy of Linnaean grades; and fundamental mathematical skills to understand the simple equations used to calculate the indices.

This exercise is part of a sequence of activities and can be used either as a stand-alone lab (expanded somewhat, if that is the case) or an in-class activity to reinforce and augment coverage of the same basic concepts in other labs and lectures on faunal provincialism, paleobiogeography, and quantitative comparison of different faunas. It is best used in the middle or later part of the course, after previous activities have ensured that all students have the necessary background on the spatial and temporal distribution, ecology, and biostratigraphic utility of trilobites and ammonites in the Paleozoic and Mesozoic, respectively.

That the students develop

- a familiarity with the ecology, paleogeographic distribution, and utility of trilobites and ammonites for correlation and biogeographic/paleoenvironmental reconstruction

- both the ability to calculate diversity indices and an awareness of what it is we use them to quantify

- some knowledge of the paleogeography of the Early Paleozoic and early Mesozoic Eras

That students develop

- the ability to give proper consideration to, and accurately discriminate the relative influence of the method (e.g. which diversity index was used), aspects of the data (taxonomic grade selected for comparison, imperfections due to taxonomic and/or stratigraphic imprecision or inaccuracy), and real paleobiological/geological factors on the similarity indices.

-the ability to construct multiple hypotheses that cover a broad spectrum of geologically reasonable possibilities, and devise ways of testing them with new data.

-an awareness of the peril of simplistic and/or deductive interpretation of paleobiogeographic data (e.g., the terranes have very different faunas, therefore they were far apart) -- or any other kind of data, for that matter.

- an appreciation that the numbers that emerge from a quantitative analysis do not by themselves answer the question; they merely form the foundation for a critical analysis of the information

How essential it is, when the goal is to arrive at a correct conclusion regarding events or conditions in earth's past, that paleontological data given due consideration as one of the most valuable types of information available for that purpose; conversely, that use of paleontological data alone for that purpose is no better than not considering them at all.

After being introduced to some widely used similarity indices through a brief introductory lecture and reading assignment, students receive a handout that includes the genus-level presence/absence data for Jurassic ammonite faunas from the Boreal Craton and four accreted terranes that make up much of what is now western North America. The handout also includes several tables that present values calculated from those data for four different indices, and a map showing the current distribution of the terranes (all extracted from Hammer and Harper, 2006). The students then work collaboratively, in pairs or small groups, to answer a few rudimentary questions that require first-order interpretation of the data to get them comfortable with how the data are presented, and to demonstrate how different indices produce different rankings of relative similarity for the five faunas. For many of the students, it is their first encounter with quantitatively derived, but clearly ambiguous results – and the struggle begins ("but which one is right?") The exercise then tests them with more complex questions that require (without specific announcement) that they devise multiple explanations for low indices (dissimilar faunas) between Sonomia and the Boreal Craton, and critically evaluate those possible explanations. When they are led to the correct conclusion, that a simplistic interpretation of the dissimilarity as a product of geographic separation conflicts with the well established timing of Sonomia's arrival in the Triassic (based on other geologic evidence), it impresses upon them the importance of considering all the data available. In this case, the data falsify the hypothesis that Sonomia was still far away from North America, and require a different explanation for the faunal contrast, such as a latitudinal separation and/or physical separation by some barrier (perhaps highlands created by the Sonoman Orogeny). The second phase of the exercise involves analysis of a pronounced contrast reported by Loch (2007) in the taxonomic composition of Lower Ordovician trilobite faunas in what is now eastern and western North America, quantified by the Jaccard Index. With the geologic context leaving no doubt that both faunas inhabited the same paleocontinent, the stage is set for discussion of a strong (again, perhaps paleolatitudinal) contrast in environment/lithofacies that produced the contrast. The questions posed in this part of the exercise challenge the students to recognize the strong influence of relative sample sizes (a pitfall of that index), a different taxonomic level (trilobite species, as compared to ammonite genera), and perhaps other factors such as stratigraphic imprecision and inaccuracy in taxonomic assignment in producing values very different from those in the first case study.

Evaluation of the students's success in meeting the goals of the exercise are assessed in real time during the exercise through individual and group responses to the questions. The class typically is fairly small, allowing me to require every student to be the spokesperson for the group at some point in the exercise. The success is more rigorously evaluated through performance on lecture exams later in the term.