Principal elements of the fish scale pattern. Because the widths of layers are proportional to growth rate, widths of incremental bands are also a measure of growth rate. In the present work we will call this graphical element the incremental band. Graphical elements of the growth cycle are the forming front and the circuli, or band ( Figure 1). The cycle of growth is described by three variables: (i) a moment at time T when the cycle begins (this temporal instant may be designated arbitrarily as the forming front), (ii) the growth rate at the time T, and (iii) the direction of growth. Each layer is developed during one cycle of growth. Such patterns are defined as possessing sequentially formed structural layers over time. Method Principal elementsįish scale patterns are defined by structural elements representing single cycles of development. Images were transferred to a Leica Quantimet 550 High Resolution Image Analysis System (Cambridge, UK) by an Adimec MX12P 10 bit 1K × 1K grayscale resolution camera (Stoneham, MA) to enhance detail, to improve the visual contrast, and to perform gray level processing protocols resulting in a binary image. Specimens were imaged with a Leica MZ-APO Stereo Zoom Microscope (Bannockburn, IL) configured with 0.6× planapochromatic lens and substage oblique illumination. Specimens of fish scales were mounted in water on glass microscope slides and cover slipped. Thus, this species was chosen as the exemplar for the present work. For the purpose of demonstrating the efficacy of the proposed model for understanding life history, it is also acknowledged that the Atlantic salmon scale pattern has a complicated anisotropic structure. The Atlantic salmon ( Salmo salar) is an important commercial fish species ( Holm et al., 1996), and many works are devoted to the study of its life history via fish scale pattern analyses ( MacPhail, 1974). Our goal is to develop such a method, and to achieve this goal we propose to model the fish scale incremental pattern in order to provide a quantitative description of growth rate variability. Presently, there is no method for the quantification of rhythmical structures, which takes anisotropy into account. Thus, circuli structure is an important element of the parameterization procedure for studies of fish life history. the size and number of circuli is a function of the direction of measurement ( Smolyar et al., 1988 Smolyar et al., 1994). The difficulties inherent in formalization procedures and parameterization of fish scales are due to incremental pattern anisotropy, i.e. The analytical processing of fish scales has often depended upon qualified and skilled personnel and, in even this case, the results may depend upon an investigator's perceptions and preconceptions ( Cook and Guthrie, 1987). Fish scale research is hampered, however, because not all steps in their analysis have been formalized ( Casselman, 1983). This is so because such patterns, rhythmically constructed from rings called bands, circuli, or growth increments, record events in fish life history and thus, also, the state of the habitat ( Matlock et al., 1993 Fabré and Saint-Paul, 1998 Friedland et al., 2000). The capability of the model for analysing objects with similar structural attributes as found in fish scale incremental patterns, such as those found in coral, otoliths, shells, and bones, is demonstrated.įish scale incremental patterns serve as sources of information, which may help to address broader issues in the marine sciences ( Beamish and McFarlane, 1987 Garlander, 1987 Lund and Hansen, 1991). The model is used to formalize procedures necessary for the quantification of fish scale growth rate. This model is based on a representation of the fish scale pattern as a relay network, taking anisotropy in the form of discontinuities and convergences of incremental structural elements into account, and the widths of growth increments in different directions. A discrete model of fish scale incremental pattern is proposed, which takes into account the incremental structure in 2D. The index of structural anisotropy is introduced, which serves as a measure of the fuzziness of growth-rate quantification. We show, however, that because of anisotropy, fish scale growth rate variability can be described in fuzzy terms. The structure of growth patterns on fish scales is characteristically anisotropic: the number of circuli and their widths significantly vary with the direction of measurement.
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