Fractal analysis of the egg shell ornamentation in anostracans cysts: a quantitative approach to the morphological variations in Chirocephalus ruffoi

Abstract

The external ornamentations of the cysts in anostracans are often characterized by crests and ridges. However, their variation cannot be properly quantified by traditional morphometrics. We propose a fractal-based analysis through box-counting to evaluate and compare differences between groups. Box-counting provides a value (fractal dimension, FD) which is proportional to the coverage and space-filling property of a geometrical pattern. Therefore, it is useful to quantify features associated with the spatial organization of the crests. Crests height is moderately correlated with cyst body diameter at individual (R = 0.27; P < 0.0001) and population (R = 0.58; P = 0.05) level. The geometric pattern of the crests is not related to the cyst body size, suggesting that allometric components influencing the spatial distribution of the crests are absent or negligible. There is a faint correlation between crests geometry and height (R = 0.20; P = 0.003). Interestingly, the distribution of the FDs is bimodal, revealing two distinct morphotypes that may be associated with structural constraints, genetics, or environmental components. Taking into account the limited information on the factors shaping the external crests of the cysts, this approach can be useful in evaluating phylogenetic and ecological influences on the final phenotype of the cysts.