Biophysical basis for the geometry of conical stromatolites

Abstract

Stromatolites may be Earth's oldest macroscopic fossils; however, it remains controversial what, if any, biological processes are recorded in their morphology. Although the biological interpretation of many stromatolite morphologies is confounded by the influence of sedimentation, conical stromatolites form in the absence of sedimentation and are, therefore, considered to be the most robust records of biophysical processes. A qualitative similarity between conical stromatolites and some modern microbial mats suggests a photosynthetic origin for ancient stromatolites. To better understand and interpret ancient fossils, we seek a quantitative relationship between the geometry of conical stromatolites and the biophysical processes that control their growth. We note that all modern conical stromatolites and many that formed in the last 2.8 billion years display a characteristic centimeter-scale spacing between neighboring structures. To understand this prominent-but hitherto uninterpreted-organization, we consider the role of diffusion in mediating competition between stromatolites. Having confirmed this model through laboratory experiments and field observation, we find that organization of a field of stromatolites is set by a diffusive time scale over which individual structures compete for nutrients, thus linking form to physiology. The centimeter-scale spacing between modern and ancient stromatolites corresponds to a rhythmically fluctuating metabolism with a period of approximately 20 hr. The correspondence between the observed spacing and the day length provides quantitative support for the photosynthetic origin of conical stromatolites throughout geologic time.

Fig. 1.

Small conical stromatolites often grow into fields with a regular spacing between neighboring structures. Such fields can be found in laboratory cultures (A), hot springs in YNP (B), 2.8 billion years old Archean stromatolites [reproduced from Grey (14)] (C), and 1.7 billion years old Proterozoic stromatolites from the Aphebian Mistassini Group (19) (D). Each scale bar is 1 cm. Image in (B) courtesy of the Geological Survey of Western Australia, Department of Mines and Petroleum. © State of Western Australia 2009.

Fig. 2.

(A) Regularly spaced conical structures grow in in still side pools of hot springs in Yellowstone National Park. (B) In fast moving sections of the stream, the mat is often flat. The purple knife in is 8.1 cm long.

Fig. 3.

Periodically spaced stromatolites record periodic forcing. (A) Initially the mat (green) only takes in nutrients from its immediate surroundings (blue arrows). As time progresses, nutrients become locally depleted and the mat takes up nutrients from a larger volume (red lines). Because the radial extent of the harvest grows with the square root of time, the maximal extent of these gradients ℓ is set by the span of time that the mat is active (black). To avoid direct competition for nutrients, vertical structures must be spaced as to prevent overlapping harvests; i.e., of order ℓ. Thus, the spacing between cones records the span of time they are active. Centimeter spacing corresponds to a rhythmically fluctuating metabolism with a period of approximately 20 hr. (B) Cultures grown in the lab display the predicted square-root dependence of spacing on day length.

Fig. 4.

When cone-forming bacteria grow in still water, they grow into a roughly hexagonal arrangement. Laboratory cultures grow into such an organization on both the smooth surface of a glass beaker (A) or on the surface of a growing mat (B); both scale bars are 1 mm. When stromatolites grow in moving water, competition is mediated by advection as well as diffusion. (C) In a unidirectional flow, long ridges grow with a centimeter-scale spacing between ridges. The blue arrow indicates the direction of flow. On either side of the channel the mat is too thick to permit flow. The scale bar is 30 cm. (D) The regular spacing and roughly hexagonal arrangement of 1.4 Gya conical stromatolites from the Bakal formation (31, 32) may be due to competition for nutrients mediated by eddy diffusivity. The hammer is 27.9 cm long.