A case for biotic morphogenesis of coniform stromatolites

Abstract

Mathematical models have recently been used to cast doubt on the biotic origin of stromatolites. Here by contrast we propose a biotic model for stromatolite morphogenesis which considers the relationship between upward growth of a phototropic or phototactic biofilm (v) and mineral accretion normal to the surface (λ). These processes are sufficient to account for the growth and form of many ancient stromatolities. Domical stromatolites form when v is less than or comparable to λ. Coniform structures with thickened apical zones, typical of Conophyton, form when v >> λ. More angular coniform structures, similar to the stromatolites claimed as the oldest macroscopic evidence of life, form when v >>> λ.

Pattern formation in stromatolites: insights from mathematical modelling

“…A central point in our analysis consists of ascertaining whether the band interfaces observed in the previous figure can be somehow associated with the sequential profiles of a function h(x,t) which solves equation (1.1) for a suitable choice of the parameters n, l and D therein. This is the basic assumption made [32,33]. For instance, in an earlier study [32] authors assert that, under suitable assumptions on the equation parameters 'numerical solutions of equation (1.1) (our notation) yield interfaces that evolve to a statistical steady state with fractal dimension D f (our notation) ffi 2.6 independent of the initial conditions.…”

“…Figure 8 provides information on the behaviour in time of the corresponding solutions. It is interesting to compare figure 8 with figure 1 in the study of Batchelor et al [33]. In both cases, one makes use of explicit formulae to represent the solutions.…”

“…In both cases, one makes use of explicit formulae to represent the solutions. However, the authors in [33] are able to derive their plots through formulae (2.1) and (2.2) therein because they consider initial values with a single maximum. In our case, the initial value has several maxima, so that characteristics originating from them may intersect in time, which eventually results in loss of regularity and cusp formation.…”

“…Moreover, analyses and simulation of the corresponding models should shed light into the manner in which stromatolites are formed. To the best of our knowledge, mathematical models of stromatolite formation have been proposed and discussed only recently [32][33][34]. The choice of equations selected to model their formation basically reduces to the so-called Kardar-Parisi-Zhang (KPZ) stochastic equation [35] …”

The evolution of inorganic carbon concentrating mechanisms in photosynthesis

“…Giordano et al (2005) and Raven & Larkum (2007) show that cyanobacteria in stromatolites could have low intracellular CO 2 concentrations and high O 2 concentrations, despite high external CO 2 and negligible O 2 (see Anbar et al 2007;Kaufman et al 2007) in the medium some 2.3-2.5 Gyr ago. The reasoning here is that the cyanobacteria in a stromatolite are separated from the medium by a millimetre or centimetre of unstirred interstitial water in a mineral and organic polymer, which adds tortuosity to the aqueous diffusion path (although the possibility of photomotion by the cyanobacteria, altering their distribution on the illuminated relative to the shaded side, must be acknowledged; Batchellor et al 2004). Here we explore the implications of UV screening as a factor favouring the occurrence of cyanobacteria in stromatolites and other dense benthic populations.…”