Difference between revisions of "1D-morphospace"

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[[Image:1DmorphoModel1.jpg|thumb|right|200px|<font size="2"> The one-dimensional morphospace as a section through the 3D-morphospace. The figure below presents such a morphospace of two-dimensional foraminiferal shells along the changing deflection angle parameter (DeltaFi) </div>]]</font size>
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| [[Foraminifera]] | [[VirtuaLab]]  | [[MORPHOSPACE]]  |   '''[[2D-morphospace]]''' |  '''[[3D-morphospace]]''' | '''[[Morphotree|nD-morphospace]]''' | [[REFERENCES]] |
  
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<font size="3">One-dimensional morphospace can be treated as a traverse through the three-dimensional morphospace of all possible morphologies.
 
  
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In order to understand general behavior in morphospace, it is best to focus on a deterministic model based on non-random parameters. It seems clear that simulated shell morphology is very sensitive to changes of the deviation angle (DeltaFi, deflection angle) parameter. Therefore, discrete steps of ( )i from  to  have been chosen to test the response of morphotypes to different values of this parameter. Two other two parameters are set constant (i.e.  ; ) for all simulated forms and for all time steps. The resulting variability of shell patterns reveals four areas (phases) of characteristic morphologies (see Fig. below after [[REFERENCES|Topa & Tyszka, 2005]] - fig. 12):
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[[Image:1DmorphoModel1.jpg|thumb|left|200px|<font size="2"> The one-dimensional morphospace as a section through the [[3D-morphospace]]. The figure below presents such a morphospace of two-dimensional foraminiferal shells along the changing deflection angle parameter (&Delta;&phi;)  </div>]]</font size>
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: - biserial forms (DeltaFi varies from 0 to 38.7),
 
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: - mixed forms (DeltaFi from  to  ),
 
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: - trochospiral forms (DeltaFi from  to ),
 
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: - uniserial forms (DeltaFi from ... to ...).
 
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These four areas are separated by three phase transitions (the term introduced in the context of morphospaces by M. Paszkowski, 2003, personal communication): (a) from biserial to mixed forms; (b) from mixed to trochospiral forms; and (c) from trochospiral to uniserial forms. The first two (a & b) transitions are abrupt because the morphology rapidly changes its patterns. The last transition (c) is gradual from strictly trochospiral, through to coiled uniserial forms, to uniserial forms. It is important to note that shells with  for all i reveal a tendency towards development of an areal aperture, in contrast to the basal aperture generated at smaller  values (after [[REFERENCES|Topa & Tyszka, 2005]])
 
  
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<math>\Alpha\ \Beta\ \Gamma\ \Delta\ \Epsilon\ \Zeta\ \Eta\ \Theta\ \Iota\ \Kappa\ \Lambda\ \Mu\ \Nu\ \Xi\ \Pi\ \Rho\ \Sigma\ \Tau\ \Upsilon\ \Phi\ \Chi\ \Psi\ \Omega</math><br/><br/>
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{| width="75%" bgcolor="#fff4f4" id="toc"
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<math>\alpha\ \beta\ \gamma\ \delta\ \epsilon\ \zeta\ \eta\ \theta\ \iota\ \kappa\ \lambda\ \mu\ \nu\ \xi\ \pi\ \rho\ \sigma\ \tau\ \upsilon\ \phi\ \chi\ \psi\ \omega</math><br/><br/>
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!align="left" colspan="2"|One-dimensional morphospace can be treated as a traverse through the three-dimensional morphospace of all possible morphologies.
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<math>\varepsilon\ \digamma\ \vartheta\ \varkappa\ \varpi\ \varrho\ \varsigma\ \varphi</math>
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|}
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</td>
 
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</tr>
 
  
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[[Image:1Dmorphospace1b.jpg|thumb|left|900px| <font size="2">1D-morphospace with constant parameters: GF=1.1; TF=0.4; and changing DeltaFi-parameter (after [[REFERENCES|Tyszka & Topa, 2005]], modified)]]</font size>
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In order to understand general behavior in [[MORPHOSPACE|morphospace]], it is best to focus on a deterministic model based on non-random parameters. It seems clear that simulated shell morphology is very sensitive to changes of the deviation angle (&Delta;&phi;, deflection angle) parameter. Therefore, discrete steps of ( )i from  to  have been chosen to test the response of morphotypes to different values of this parameter. Two other two parameters are set constant (i.e.  ;  ) for all simulated forms and for all time steps. The resulting variability of shell patterns reveals four areas (phases) of characteristic morphologies (see Fig. below after [[Tyszka & Topa 2005|Topa & Tyszka, 2005]] - fig. 12):
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: - biserial forms (&Delta;&phi; varies from 0&deg; to 38.844&deg;),
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: - mixed forms (&Delta;&phi; from 38.862&deg; to 54.324&deg;),
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: - trochospiral forms (&Delta;&phi; from 54.342&deg; to 158.814&deg;),
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: - uniserial forms (&Delta;&phi; from 158.815&deg; to 180&deg;).
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These four areas are separated by three phase transitions (the term introduced in the context of [[MORPHOSPACE|morphospaces]] by M. Paszkowski, 2003, personal communication): (a) from biserial to mixed forms; (b) from mixed to trochospiral forms; and (c) from trochospiral to uniserial forms. The first two (a & b) transitions are abrupt because the morphology rapidly changes its patterns. The last transition (c) is gradual from strictly trochospiral, through to coiled uniserial forms, to uniserial forms. It is important to note that shells with &Delta;&phi;>117&deg; for all ''i'' reveal a tendency towards development of an areal aperture, in contrast to the basal aperture generated at smaller  values (after [[Tyszka & Topa 2005|Topa & Tyszka, 2005]])
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[[Image:1Dmorphospace1b.jpg|thumb|left|900px| <font size="2">1D-morphospace with constant parameters: GF=1.1; TF=0.4; and changing &Delta;&phi;-parameter (after [[REFERENCES|Tyszka & Topa, 2005]], modified)]]</font size>

Latest revision as of 11:20, 3 July 2006