The Amazingly Conserved Relationship Between Meiosis Timing and Floral Development
For more information, see Li, P., and M.O. Johnston. 1999. Evolution of meiosis timing during floral development. Proceedings of the Royal Society B: Biological Sciences 266: 185-190. [Abstract] [Article in PDF]
Inflorescence as developmental clock
Here is a rather typical inflorescence - a structure that produces flowers. At one end - the older - formerly open flowers have withered and are becoming fruits. In the direction just younger to these, there are flowers opening and becoming available for pollen transfer. The very youngest parts of the inflorescence occur at the tip, which requires a microscope to see, and in this photo would be near the center of the coiled inflorescence. Immediately next to the growing inflorescence tip is the floral primordium, which is a bump of cells representing the very youngest stage of a flower.
In the example above, the floral positions along the inflorescence represent a time series, a developmental clock. This is very convenient for developmental studies. The only requirements for an inflorescence to act as a developmental clock are that it continues to grow (adding new primordia) during the observation period and that the rate of adding new floral primordia does not change over time. If desired, the time separating floral positions can be determined simply by counting the number of flowers that open in a given period. Below is such an inflorescence shown diagramatically. Position 0 is the primordium and position 19 is the youngest open flower.
The total developmental time of a flower, from primordium to corolla opening, varies among individuals within a population and among species.
RAFT
At some point during the development of each flower, meiosis occurs in the anther and in the ovules. Here we are concerned only with anther meiosis, the end of which is marked by the formation of pollen tetrads
No matter how long a flower takes to develop, we can consider it on a unit scale, where 0 represents its initiation as a floral primordium and 1 represents corolla opening. In species where the inflorescence acts as a developmental clock, explained above, one can determine the timing of any event, such as tetrad formation, relative to the 0 and 1 endpoints. We can define RAFT as the Relative Age of a Flower at Tetrad Formation. RAFT is thus a fraction representing the proportion of development time preceding tetrad formation.
For example, say that tetrads are formed at bud position 9 and the youngest open flower is at position 19, as in the schematic inflorescence above. Here RAFT = 9/19 = 0.47.
The Puzzle
The surprise finding
What values of RAFT would you expect to find? I think most of us would guess that RAFT could occur almost anywhere between 0 and 1, possibly being more or less constant within a species, but varying greatly among species. To calculate RAFT, we (Ping Li, that is) dissected inflorescences of 32 species. In addition, we were able to calculate RAFT from published data for four more species, for a total of 36 species representing 13 families. The amazing fact is that RAFT appears to occur at only a few values, namely
0.45, 0.62 and 0.73.
We have named each of these three values a "RAFT class." The puzzle is: Why is the timing of tetrad formation so evolutionarily constrained?
Developmental meaning
For each RAFT class, the ratio of the time before meiosis termination to the total developmental time is constant by definition. Developmentally, this means either that the time interval preceding meiosis determines the time following (left diagram below), or that an external agent maintains the two times in constant proportion (right diagram below). In the diagram below, P = primordium, T = tetrad formation and A = anthesis (corolla opening).
Mathematical sequences: numerology
We have found that there are mathematical sequences into which the three RAFT classes seem to fit. Here we mention three such sequences. One of these sequences might represent the true developmental process responsible for the RAFT classes being so discrete. There is an extensive literature in the mathematical modeling of development. Many of the aspects of such models are also found in the three sequences we present here. These aspects include tau (the golden ratio, ubiquitous in plant development), logarithms and pi.
Notice that 0.45 = 0.62 X 0.73. Therefore, one of the RAFT classes might simply be a combination of the other two.
Below are two of the sequences. The third involves the relation RAFT = 1 - RAFT k, where k is a simple whole number or fraction.
One last puzzle piece
For many of the species studied, in addition to relative times, we were able to determine the absolute times preceding and following tetrad formation. On average, total floral developmental time is shortest in species of class 0.45, longer in species of class 0.62 and longest in species of class 0.73. It appears that the timing differences are mostly accounted for by changes in the time before tetrads formation, while the time between tetrads and flower opening increases little from class 0.45 to 0.62 to 0.73. This is shown in the figure. [Abstract] [Article in PDF]
Above diagrams and photos by Ping Li