Biochronology as a Traveling Salesman Problem Introduction to the Conop9 Seriation Programs PETER M. SADLER Department of Earth Sciences, University of California, Riverside CA 92507 PETER M. SADLER Department of Earth Sciences, University of California, Riverside CA 92507 Biochronology As A Traveling Salesman Problem: Introduction To The Conop9 Seriation Programs CONTENTS 0. What is it? I. Biostratigraphy and Biozones II. Chronostratigraphy and Time Lines III. Graphic Correlation IV. Constrained Optimization V. The Traveling Salesman’s Solution VI. Inside Composite Time Lines VII. Late Cretaceous of Antarctica VIII. Silurian of Baltica IX. Classic Riley Formation Data X. Mohawkian Facies Problems XI. Liassic Ammonites of England XII. Carboniferous of the Harz Mountains XIII. References XIV. Acknowledgements XV. Worksheets to Print iii ORGANIZATION Sections I through VI briefly review the history and theory of various aspects of biochronology. The sections enjoy some overlap and may be read separately. Sections VII through XII introduce case histories to illustrate the use of the seriation program, CONOP9, and the custom data manager CONMAN9. The CONOP software is compiled for Windows and delivered with three additional PDF documents: a “Reference Manual” and “Users’ Guide” to CONOP9 and an introduction to CONMAN9 titled “Starting.” PROGRAM DOWNLOADS: The CONOP and CONMAN programs, together with manuals, data sets, and classroom exercises, can be downloaded from the Spring 2009 GEO 206B website at UC Riverside [http://.ilearn.ucr.edu] by clicking the following buttons and tabs: Guest Login > Courses > Course Catalog > Geosciences(GEO) > Spring 2009(1) > GEO 206B 001 09S 2nd PDF Edition, October 2010 University of California, Riverside California 92521, USA The second edition corrects figures IV4, IV5, and IV6 Prepared for a course sponsored by The Chinese Academy of Science 39 East Beijing Road, Nanjing 210008 iv 0. What is it? What is it? as new information is discovered at other localities. What is it like? If this considered to be forward progress, brute In Save the Cat, Blake Synder (2005) asks these force can be said to invert the process; it starts with questions of every screen-play. Here are answers in a crude guess at a possible time-line of all events his terms: and modifies the sequence by random mutation until the fit with all the field data cannot be improved any more. : Brute-Force Biochronology Title The number of mutations far exceeds the number of events in the time-line. There is an Log-Line: Search-algorithms meet field-data obvious analogy with genetic mutation and survival and together sequence the history of life. of the fittest.. Recourse to this type of computer-assisted trial- Genre: Buddy Movie and-error approach becomes worthwhile in Species: Town Mouse and Country Mouse biochronology after a critical volume of data has been compiled. It becomes necessary when that Story Arc: Cautious distrust turns to mutual volume overwhelms the human “neck-top” respect as algorithms and data join forces to computer. perform quality control and interpretation, changing the practice of biochronology. How is this a Traveling Salesman Problem? Not because the brute-force method needs to be What is biochronology? pitched, door-to-door, like a screenplay! The Biochronology pieces together time-lines of events Traveling Salesman Problem has become one of the in Earth history, mostly the originations and favorite challenges for computer scientists. They extinctions of ancient species, but also volcanic ash fondly call it the TSP; it is deceptively easy to state falls, geomagnetic field reversals and excursions in and tedious to solve. Many practical problems are ocean composition. Time lines help fictional so closely analogous to the TSP that they can be detectives solve murders and help paleobiologists solved by adapting the same methods. The discover the scope and circumstances of extinctions, paleobiological time-line task has been shown to be chart the course of evolution, compile the impacts one of the analogous problems. of environmental change, refine the geologic time scale, and more. Maybe it belongs in the “superhero” genre? Is the Book as Good as the Movie? No! The colloquial question-and-answer style of this page works well from the podium in a short What is Brute Force? course setting, especially with software that In this context, brute force means imagining provides run-time animations. Regrettably, the rest millions of working hypotheses and testing them all of this accompanying book is much denser reading. against the data to see which is fittest – a job for a It works with still images. It must frequently tell fast computing machine that slavishly follows rather than show. And it needs to fill-in rigorous simple rules through tedious repetitions. definitional details and provide answers to questions The human expert might use one rich that not all readers would care to ask. stratigraphic section as the first approximation of a paleobiologic time-line and modify it progressively v I. Biostratigraphy and Biozones Summarizes the origins, evolution, and methods of biostratigraphy. Figure I.1 Range of a taxon in life (gray), the observed range of the fossil taxon (black) in stratigraphic sections (rectangles), and the time lines defined by the origination and extinction of the taxon. I.1 A Brief History identification of strata in different places that were deposited during the same time interval. Biostratigraphers study the distribution of fossils William Smith (1799) simply traced strata across in sedimentary strata. They have two motives – England using fossil content to augment similarities of reconstructing the history of life and developing a rock type and topographic expression (Lauden, 1976). relative time scale for other geologic studies. Throughout the Paris Basin, Cuvier and Brongniart More than two hundred years ago, before (1808) mapped a suite of coarse units on the basis of formulation of the theory of evolution (Darwin 1859), different faunal assemblages which they believed to be it became apparent that the same general succession separated by catastrophic events. Phillips (1829) of faunas could be recognized in different rocks at established that some fossils could be used to correlate widely separated locations. Trilobites appeared between different rock types and Murchison (in before ammonites, for example, and dinosaurs Sedgwick and Murchison, 1939) ventured to insert became abundant before mammals. Such newly found faunas from southwest England into a gap observations led to the major divisions of the in the faunal succession established elsewhere. Phanerozoic time scale – the Paleozoic, Mesozoic, Adopting bold reasoning from Lonsdale, they used the and Cenozoic eras – and to attempts to resolve much intermediate nature of the new faunas between those finer subdivisions using fossil species. These previously known, rather than direct observation of an subdivisions enable time correlation – the occurrence in intervening strata. 6 D’Orbigny (1851) and Oppel (1858) began the record to correlate between exploration wells, adding practice of correlating strata using units of shorter rapidly to the volume of biostratigraphic information, duration (stages and zones) defined by the ranges of and turning to computers to store and analyze it all fossil assemblages and individual taxa. These and other (Carney and Pierce, 1995; McGowran, 2005). The pioneers established practices of qualitative Deep Sea Drilling Project led to internationally biochronology that were followed for a hundred years standardized, high-resolution subdivisions based on without recourse to numerical methods. microfossils extracted from cores of the ocean floors. The resolving power of correlation improved At the same time, computer scientists found in significantly when petroleum companies began to natural selection a trial-and-error process that could apply sequences of microfossil species to the task. A be mimicked by algorithms to solve difficult century after Spencer (1864) had embraced natural optimization problems. By the 1980’s paleontologists selection as a means to understand both biological and had experimented with a wide range of numerical economic change, petroleum geologist Alan Shaw approaches to biochronology (Tipper, 1988) and (1964) formulated “economy-of-fit” as a graphical evolutionary heuristics were flourishing as a means to means to reconcile differences in detail between the compute very good answers to complex scheduling successions of species found in separate outcrops of and engineering problems. Personal computers made the same age. it practical for individual paleontologists to exploit all At Shell Oil Company, recognition of these these developments and build detailed paleobiological differences was fueling concerns about the validity of time-lines of faunal assemblages (Guex, 1991) and fossils for correlation (Shaw, 1995); some preferred to species first and last appearances (Alroy, 1992). proceed as if rock units were of uniform age and only The basic practices of correlation also adapted to the timing of appearance and disappearance of fossil the increasing availability of radioisotopic dates and species varied from place to place (diachronism). Of the calibration of global events such as geomagnetic course, the boundaries of rock units and species reversals and excursions in the isotopic composition ranges can both be diachronous. Shaw’s correlation of oceanic water events. Particularly