Transition Studies in Flowering Plants  

by Rolf Baumberger

A new Kind of Analyses

The Color Phase Space

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. 

Now, in 12 km increments from population to population, we see the following differences in distribution:

C6: all types are yellow, they are pure Diplacus australis forms.

C5: Most forms are dark yellow, some even have reds. However, there are no shapes here with the typical yellowing as under C6.

C4: Even more pronounced than under C5. It lacks typical red as well as typical yellow forms.

C3: Most orange and red tones, yellow forms are absent.

C2: All reds, they are close to the attractor point B.

C1: Virtually all are in attractor B, and they are pure Diplacus puniceus morphs.


Now we test whether the frequency distribution within the transect has changed after only five years or not.

 A change can be made visible. On the one hand, there are fewer points in the point cloud, but there is an accumulation of points around the red attractor.

 With this determination, a course direction is determined at the same time. The direction goes from yellow to red (see arrowhead).

Sometimes one didn't see what one saw.

The following time series is very informative: The color representations of the two populations are compared over a significant time interval of > 15 years. In the flip-book, all the color locations seem to move to a point in the room, the attractor point. The spatial distance between the mean values ​​and the attractor point is massively reduced. The attractor point cannot be calculated; it has to be determined empirically. 

Finally, two plants are monitored in transition over 14 years. At the beginning and the end of the study, the two plants are each self-pollinated and the color values ​​of four times 36 individuals are plotted. Here, too, shows an analogous picture. In the flip-book, the points aim at the two attractor points. - Another three individuals show in monitoring a course on the trajectories; they also aim for the red attractor. 


◊ Course from A to B on trajectories, A and B are attractor points or are dynamically stable points. Attractor points have to be determined empirically. They are not predictable a priori. The course is spontaneous but non-stochastic in phase space.

 ◊ Individuals in a transition zone all show a very similar dynamic shape. They all change from A (yellow insect pollinated individual) to B (red bird-pollinated individual).

◊ This conversion takes time (> 10 years) and is as a rule irreversible.

 ◊ Although this conversion is non-generative, the result is hereditary.

 ◊ These findings are consistent with physical laws (trajectories, attractor points = dynamic equilibrium). They conflict with the theory of natural selection. Besides, one would have to extend the Mendelian Law to be in line again.