Mathematical studies of morphology in early life palaeobiology - Hoekzema, R (2015)
The overarching topic of this thesis is the mathematical study of morphology, applied to palaeobiology, more specifically the palaeobiology of early life. The first part of this thesis concerns the study of growth in the enigmatic late Ediacaran macrobiota (579-541 Ma). A new framework is presented for quantitative comparison of the ontogeny of dickinsoniomorphs and rangeomorphs, and this setup is applied to the iconic Ediacaran taxa Dickinsonia costata and Charnia masoni. The methodology, based on measurements of branch/segment lengths at different stages of ontogeny, reveals an intricate, complex system of growth in both taxa. The segments of Dickinsonia grow in two stages of growth, a first phase of rapid growth and a second phase of slower inflation. After around 50 segments are present on each side of the axis, the rate of insertion starts to decrease while the growth of the organism continues. I speculate that this switch might reflect a change from somatic to reproductive growth. Interestingly, a very similar mode of growth is found in the first order branches of Charnia masoni, which also grow in two distinct phases, and potentially can be seen to halt their insertion after around 18-20 branches are present on each side of the organism, while the organism continues to grow. In contrast, the second order branches do not follow this pattern but continue to be added. These modes of growth are reconstructed in a computer model. This model can be extended to other Ediacaran life forms, effectively generating a "morphospace" of rangeomorphs and dickinsoniomorphs. The second part of this thesis focuses on the biological or abiological origin of the iconic trace fossil Paleodictyon, shaped like a hexagonal mesh. This ichnogenus occasionally displays incredible regularity, as well as a very high connectivity, a very broad environmental tolerance and a temporal range from the Cambrian until the present day. Despite extensive research on modern patterns, no organism has yet been identified as creator. These facts cast doubt on the biogenic interpretation of Paleodictyon. I propose the hypothesis that some of these patterns are created abiotically by regular hexagonal standing Faraday waves resulting from events such as earthquakes. This hypothesis is put to the test by means of experiments and computer modelling of the wave. In particular, a hexagonal pattern very similar to the most regular specimens of Paleodictyon could be formed in experiments and preserved on the surface of a calcium carbonate paste.