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Tran et al. 2023: Vertical Exaggeration When Using Unconverted LLS Data in Ontogenetic Sequences of Ammonite Sutures

ABSTRACT: Size-independent modifications to the fractal method have been employed by ammonite researchers since the 1990s as a way to exercise consistency when measuring ammonite sutures, and make use of those published without a scale index. In 2021, a new method to extrapolate the full hemisuture’s fractal dimension using just the lateral lobe (L) and second saddle (S2) (the LLS method) further adapted these methods The fractal dimension of the portion defined by the lateral lobe and second saddle (LLS) of an ammonoid suture can be measured by the Richardson method and adjusted to reflect the fractal dimension of the full hemisuture by dividing by a factor consistent at the genus level. Our paper explores the amount of vertical exaggeration exhibited by unconverted LLS data across the ontogeny of individual genera by examining suture ontogeny of 7 genera representing 3 highly disparate families on 8 ontogenetic sequences of very immature ammonites. We tested 4 variables from the spreadsheet, including fractal dimensions in the Richardson and unconverted LLS methods; S(Lmax), the proportion of (L) to the hemisuture; and the calculated conversion value for each suture. We found that conversion values are only necessary for sutures at or nearing the point of maturity, which we define in this study as the first suture that shows 3 levels of infolding. We found that vertical exaggeration increased over ontogeny, although conversion values are only needed after the onset of maturity. Overall, immature sutures, regardless of taxonomic affinity, conversion value (V) is approximately equal to 1. Prior to the onset of maturity, variance around V=1 were not statistically significant. After maturity, conversion values become necessary.