The growth of snail shells can be described by simple mathematical rules. Variation in a few parameters can explain much of the diversity of shell shapes seen in nature. However, empirical studies of gastropod shell shape variation typically use geometric morphometric approaches, which do not capture this growth pattern. We have developed a way to infer a set of developmentally descriptive shape parameters based on three-dimensional logarithmic helicospiral growth and using landmarks from two-dimensional shell images as input. We demonstrate the utility of this approach, and compare it to the geometric morphometric approach, using a large set of Littorina saxatilis shells in which locally adapted populations differ in shape. Our method can be modified easily to make it applicable to a wide range of shell forms, which would allow for investigations of the similarities and differences between and within many different species of gastropods.

This study examines the relative importance of different factors influencing students' performance in first year university mathematics. Characteristics (motivation, actions and beliefs) of students at three universities in Sweden (n=1007) were measured twice; when entering the university and at the end of the first year. Principal Component Analysis (PCA) and Orthogonal Projection to Least Squares (OPLS) analysis were used for the identification of constructs and analysis of the predictive power of the constructs, respectively. Four important constructs were found which we label Self-efficacy, Motivation type, Study habits and Views of mathematics.When entering university, these four constructs predicted 14% of the variation in students' level of success at university math, as measured by their grades in university mathematics, while 37% could be predicted at the end of their first year at the university. When comparing the four constructs, self-efficacy is the best predictor, yet, by it self, only explaining 5% of the variation when measured in the beginning of the university studies, but 21% at the end of the first year. Upper secondary grades alone predicted 17% of the variation in first year university grades. Together, students' upper secondary grades and the four constructs predicted 21% and 43% of students' university mathematics grades, when constructs pertained to upper secondary school and university, respectively.Study habits were found to be more important for predicting university achievement for the third of the students' with the lowest upper secondary grades. Relying on the textbook and frequent interaction with peers during the university studies, at the expense of using internet-based resources for learning, contributed positively to university achievement for this same group. The association between students' view of mathematics and their university performance was low for students with intermediate and high upper secondary grades, and non-existing for students with lower grades.

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