Transition Studies in  Flowering Plants 
by Rolf Baumberger

Dynamics 0

A new Kind of Analyses 

If one examines a biological system in an evolutive way, one usually uses conventional selection-theoretical tools. The statement is, therefore, always related to this theory and physically not objective. One must, therefore, start from the object and describe it as physically as possible. It that one has to build a tool from the ground up that makes physical statements possible in the first place. A phase space is proposed. In phase space, one can integrate all data of a living-being provided the data density is sufficiently compelling. The statement one makes with such a phase space is always instantaneous probability states. 


A) A large number of color locations of the corollas (in the area of Fig1) of Diplacus puniceus, Diplacus australis, and the mixed forms are determined. However, the values per individual are measured only once, and no mean values are used.

B) With the help of the statistics program R a phase plot is made.

C) In this phase space, a point cloud (yellow points) is visible, which is more or less dense.  The density per cuboid thus varies depending on the origin of the rennet measured values. Outside the point cloud, the density is almost zero. In the area around Y and R, the density is maximally high. Such places with maximum point density are now called attractors. The density of the point cloud decreases exponentially with the distance to the attractors.

Thus the relative maxima have already been found empirically. These points are extraordinary. By the way, the model can be extended by further levels with the condition that the data density for each level is sufficiently high. (later)

The Color Phase Space

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Fig. Stepwise Floral Color Shift along the Transect B1 ... B6

The figure shows the frequency distribution of color tones (Lab) in a Lab color space. The point A contains forms of the Diplacus australis with yellow flowers, the point B is occupied by the types of the red-flowering species Diplacus puniceus. Along an east-west section, 216 plant data from 6 populations were recorded. Striking is the frequency distribution, which decreases sharply with the distance to the respective maximum. Also, paths what we name trajectories are to be identified. We call points A and B as attractors. 

Figure 1A under Diplacus 1 shows a transect (B1 ... B6). - If one clicks on the right arrow in the graphic above, one will see the color distribution (light green) beginning with B1 yellow and ending with B6 red spatially distributed. A temporal change of a transitive population at one site looks, by the way, very similar. However, this takes 15 to 20 years to complete.

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Stepwise Floral Character shift along the Transect B1 ... B6

Combining the lab phase space with the space of three further variable flower characteristics results in an informative distribution.  The flower characteristics change gradually from the yellow to the red form (swipe or enlarge).


The present form of representation in a phase space of extensive data packets now in connection with transect plants clearly brings a leap in quality. The data are presented more precisely and objectively, the results can be readily displayed graphically, and you can also standardize (for example, point frequency). Besides, the phase space can be extended (e.g., for molecular genetic or genotypic data).

Modern colorimeters are very accurate, they are more reliable than the color perception of the human eye. - It becomes immediately apparent that the color deviation from the mean value is minimal in an adapted population of red-flowered Diplacus puniceus
The phase space can not only give information about the total variance, but it also helps in the evaluation of intermediate forms and gives information about the dynamic change of populations.
In the present case, the phase space does not support the hybridization hypothesis.  It seems much more probable that one form (yellow) is abandoned in favor of a red shape, and the new structure is gradually approached. It is evident that not only populations go through this process, but also every individual participates. 
At the unique point (attractor point), the form seems to be dynamically stable, what seems not to be true outside of this point.