View source for MOVING REFERENCE MODELS

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== Limitations of the [[FIXED REFERENCE MODELS|fixed-reference models]] ==

The [[FIXED REFERENCE MODELS|fixed-reference models]] rely on an abstract coordinate, which is arbitrarily defined and unfortunately has no morphogenetic or physiological meaning. Chambers (circles or spheres) are rotated and translated along these artificial axes, which are fixed and serve as a reference line for the growth process. Therefore, while these models can simulate simple planispiral, trochospiral or uniserial chamber arrangement, they cannot simulate more complex patterns found in foraminifera. For instance, they cannot model gradual or abrupt changes of growth modes that cause different chamber arrangements during ontogeny, such as planispiral and switching to biserial or [[Strepto-uniserial|streptospiral to uniserial]] (CITED AFTER [[Tyszka & Topa 2005]]).

== Moving-reference models ==

[[Image:Reference1mov.jpg|thumb|right|222px| <font size="2">'''The moving-reference model reffers to a coordinate frame, which moves in every step of the model.''']]
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These constraints can be overcome by abandoning a fixed-reference frame in favor of a moving-reference system. In general, the moving reference model is based on simple principles of motion and stepwise growth. At each growth step, the aperture migrates to a new position, according to locally defined rules (Ackerly 1989). Such models have been employed in simulating ammonite growth. Okamoto (1988) proposed a tube model for all types of shell coiling, including heteromorph forms with abrupt changes of coiling patterns. His approach integrates accretional growth of the aperture (opening of the shell) without defining any fixed coordinate system. A similar moving-reference frame has been used in simulating radiate accretive growth of marine sessile organisms, such as corals and sponges, where the growth axis is associated with the local maximum of growth (e.g., Kaandorp 1994; Hammer, 1998; Kaandorp and Kuebler 2001). A comparable approach was used in simulating plant growth (Lindenmayer 1968; Prusinkiewicz and Lindenmayer 1990). CITED AFTER [[Tyszka & Topa 2005]].

== Model [[parameters]] ==

[[Image:Model_parameters.jpg|thumb|left|222px|<font size="2">Moving-reference model parameters <font size="1">(''after [[Tyszka 2006]]'', modified)</font>]]

The model includes 6 parameters, representing [[MORPHOSPACE|'''morphospace''']] dimensions (after [[Tyszka 2006]], modified): 
* Chamber scaling ratios defined in 3-dimensional space by 3 parameters: 
** '''kx''' - chamber width ratio, 
** '''ky''' - chamber height ratio, 
** '''kz''' - chamber depth ratio. 
If all chamber scaling ratios equal each other, i.e., kx = ky = kz, a new chamber is isometric to the previous one. Any differences in chamber scaling ratios cause allometric growth of successive chambers.
* '''TF''' (translation factor) controls an overlap of successive chambers (see Fig.); the “0” TF value places the centre of a new chamber directly at the aperture of the last chamber. This parameter ranges from “-1” to “+1” values. Higher values detach a new chamber from the existing shell that represents a “forbidden zone” sensu Berger (1969)
* '''&phi;'''  as a deviation angle (deflection angle) - an angle between the local reference line and the line defining the centre of a new chamber; it ranges from -180° to 180°. Higher or lower out of range values can be recalculated to the values from the given range
* '''&beta;''' as a rotation angle; this parameter is necessary in 3-dimensional space. It ranges from -180° to 180°; higher or lower values can also be recalculated.





== see: [[Simulation steps]] in the moving reference model ==



[[Category:Models|*]]