Recurrent hierarchical patterns and the fractal distribution of fossil localities

Roy E Plotnick

doi:10.1130/g38828.1

Abstract

Abstract Understanding the spatial structure of fossil localities is critical for interpreting Earth system processes based on their geographic distribution. Coordinates of marine and terrestrial sites in the conterminous United States for 17 time bins were analyzed using point pattern statistics. Lacunarity analysis shows that the spatial distributions of sites are fractal for almost every studied interval, indicating that clumping of localities occurs at multiple scales. Random hierarchical multiplicative processes provide a theoretical null model for the distribution of collecting sites, consistent with their occurrence being a complex product of numerous biological, geological, and anthropogenic processes acting at many spatial and temporal scales. Mechanistic models for the formation, preservation, and exposure of fossil localities and other geologic entities can be tested using point pattern and related spatial statistics.

Highlights

Due to their importance in forming the framework for the interpretation of Earth system history, numerous attempts have been made to quantify and model temporal patterns of fossil and sedimentary deposit occurrence (Sadler, 2004; Peters, 2006; Smith and McGowan, 2011; Kemp, 2012; Miall, 2015; Holland, 2016)
Latitudes and longitudes in degrees of fossil collections of all taxa from the conterminous United States in 17 chronostratigraphic bins were downloaded from the Paleobiology Database and were parsed into terrestrial or marine depositional environments (Fig. DR1 in the GSA Data Repository1)
DR2 and DR3 in the Data Repository). This is consistent with self-similar patterns of spatial distribution (Plotnick et al, 1993, 1996); that is, the distribution of the points forms random clumps at multiple scales

Summary

Introduction

Due to their importance in forming the framework for the interpretation of Earth system history, numerous attempts have been made to quantify and model temporal patterns of fossil and sedimentary deposit occurrence (Sadler, 2004; Peters, 2006; Smith and McGowan, 2011; Kemp, 2012; Miall, 2015; Holland, 2016). Many of these studies indicate that much of the stratigraphic record is self-similar (fractal) in time (Bailey and Smith, 2005; Schlager, 2010; Kemp, 2012). There are no statistical models for the distribution of localities that can be used for

Methods

Results

Discussion

Conclusion